Subgroups — C₂₃×#60240 #19207866

Order 5888.

2136 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#41×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2981	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2980	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2978	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2977	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2976	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2976	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2974	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2973	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2933	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2932	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2930	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2929	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₂₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2880	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2879	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₂₃×#408	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
25	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₂₃×#131	C₂²	1	1	yes	characteristic, complemented
30	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
31	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
32	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
33	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
34	C₂₃×#550	C₄	1	1	yes	characteristic
35	D₄×Q₈×C₂₃	C₄	1	1	yes	characteristic
36	C₂₃×#548	C₄	1	1	yes	characteristic
37	C₂₃×#548	C₄	1	1	yes	characteristic
38	C₂₃×#547	C₄	1	2	yes	—
39	C₂₃×#547	C₄	1	1	yes	characteristic
40	C₂₃×#546	C₄	1	2	yes	—
41	C₂₃×#546	C₄	1	2	yes	—
42	C₂₃×#546	C₄	1	1	yes	characteristic
43	C₂₃×#546	C₄	1	1	yes	characteristic
44	D₄²×C₂₃	C₄	1	1	yes	characteristic
45	D₄²×C₂₃	C₄	1	2	yes	—
46	C₂₃×#532	C₂²	1	1	yes	characteristic
47	C₂₃×#532	C₂²	1	2	yes	—
48	C₂₃×#525	C₂²	1	1	yes	characteristic
49	C₂₃×#525	C₂²	1	1	yes	characteristic
50	C₂₃×#525	C₂²	1	2	yes	—
51	C₂₃×#525	C₂²	1	2	yes	—
52	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
55	C₂₃×#436	C₂²	1	2	yes	complemented
56	C₂₃×#436	C₂²	1	2	yes	complemented
57	C₂₃×#436	C₂²	1	2	yes	complemented
58	C₂₃×#436	C₂²	1	2	yes	complemented
59	C₂₃×#436	C₂²	1	2	yes	complemented
60	C₂₃×#436	C₂²	1	2	yes	complemented
61	C₂₃×#435	C₂²	1	1	yes	characteristic
62	C₂₃×#435	C₂²	1	1	yes	characteristic
63	C₂₃×#435	C₂²	1	2	yes	—
64	C₂₃×#435	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×#435	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#435	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#435	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×#435	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×#435	C₂²	1	1	yes	characteristic, complemented
70	C₂₃×#435	C₂²	1	2	yes	complemented
71	C₂₃×#435	C₂²	1	2	yes	complemented
72	C₂₃×#435	C₂²	1	2	yes	complemented
73	C₂₃×#435	C₂²	1	2	yes	complemented
74	C₂₃×#435	C₂²	1	2	yes	complemented
75	C₂₃×#435	C₂²	1	2	yes	complemented
76	C₂₃×#435	C₂²	1	2	yes	complemented
77	C₂₃×#435	C₂²	1	2	yes	complemented
78	C₂₃×#435	C₂²	1	2	yes	complemented
79	C₂₃×#435	C₂²	1	2	yes	complemented
80	C₂₃×#435	C₂²	1	2	yes	complemented
81	C₂₃×#435	C₂²	1	2	yes	complemented
82	C₂₃×#435	C₂²	1	2	yes	complemented
83	C₂₃×#435	C₂²	1	2	yes	complemented
84	C₂₃×#435	C₂²	1	2	yes	complemented
85	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
86	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
87	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
88	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
89	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
90	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
91	C₂₃×#433	C₂²	1	2	yes	complemented
92	C₂₃×#433	C₂²	1	2	yes	complemented
93	C₂₃×#433	C₂²	1	2	yes	complemented
94	C₂₃×#433	C₂²	1	2	yes	complemented
95	C₂₃×#432	C₂²	1	2	yes	complemented
96	C₂₃×#432	C₂²	1	2	yes	complemented
97	C₂₃×#432	C₂²	1	2	yes	complemented
98	C₂₃×#431	C₂²	1	2	yes	complemented
99	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
100	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
101	C₂₃×#423	C₂²	1	1	yes	characteristic, complemented
102	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
103	C₂₃×#408	C₂²	1	1	yes	characteristic
104	C₂₃×#408	C₂²	1	1	yes	characteristic
105	C₂₃×#408	C₂²	1	1	yes	characteristic
106	C₂₃×#408	C₂²	1	1	yes	characteristic
107	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
108	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
109	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
110	C₂₃×#408	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#408	C₂²	1	2	yes	complemented
112	C₂₃×#408	C₂²	1	2	yes	complemented
113	C₂₃×#408	C₂²	1	2	yes	complemented
114	C₂₃×#408	C₂²	1	2	yes	complemented
115	C₂₃×#408	C₂²	1	2	yes	complemented
116	C₂₃×#408	C₂²	1	2	yes	complemented
117	C₂₃×#408	C₂²	1	2	yes	complemented
118	C₂₃×#408	C₂²	1	2	yes	complemented
119	C₂₃×#407	C₂²	1	1	yes	characteristic, complemented
120	C₂₃×#407	C₂²	1	1	yes	characteristic, complemented
121	C₂₃×#407	C₂²	1	2	yes	complemented
122	C₂₃×#407	C₂²	1	2	yes	complemented
123	C₂₃×#407	C₂²	1	2	yes	complemented
124	C₂₃×#407	C₂²	1	2	yes	complemented
125	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
126	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
128	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
129	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
130	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
131	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
132	C₂₃×#405	C₂²	1	1	yes	characteristic, complemented
133	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₂₃	—	4	2	no	—
136	C₂×#41×C₂₃	—	4	2	no	—
137	C₂×#41×C₂₃	—	4	2	no	—
138	C₂×#41×C₂₃	—	4	2	no	—
139	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
140	C₂×#41×C₂₃	C₂×C₄	1	2	yes	—
141	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
142	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
143	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
144	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
145	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
146	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
148	C₂×#41×C₂₃	C₂³	1	2	yes	—
149	C₂×#41×C₂₃	C₂³	1	2	yes	—
150	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
151	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
152	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
153	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
154	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
155	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
156	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
157	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
158	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
159	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
160	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
161	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
162	C₂₃×#131	—	4	2	no	—
163	C₂₃×#131	—	4	2	no	—
164	C₂₃×#131	—	4	2	no	—
165	C₂₃×#131	—	4	2	no	—
166	C₂×M₁₆×C₂₃	—	4	2	no	—
167	C₂×M₁₆×C₂₃	—	4	2	no	—
168	C₂×M₁₆×C₂₃	—	4	2	no	—
169	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
170	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
171	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
172	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
173	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
174	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
175	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
176	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
177	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
178	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
179	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
180	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
181	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
182	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
183	C₂²×C₈×C₂₃	—	4	2	no	—
184	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
185	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
186	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
187	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
188	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
189	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
190	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
191	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
192	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
193	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
194	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
195	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
196	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
197	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
198	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
199	C₂₃×C₄⋊Q₈	C₂×C₄	1	2	yes	—
200	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
201	C₂₃×#127	C₂×C₄	1	2	yes	—
202	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
203	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
204	C₂₃×#124	C₂×C₄	1	2	yes	—
205	C₂₃×#124	C₂×C₄	1	2	yes	—
206	C₂₃×#123	C₂×C₄	1	2	yes	—
207	C₂₃×#123	C₂×C₄	1	2	yes	—
208	C₂₃×#123	C₂×C₄	1	2	yes	—
209	C₂₃×#123	C₂×C₄	1	2	yes	—
210	C₂₃×#123	C₂×C₄	1	2	yes	—
211	C₂₃×#123	C₂×C₄	1	2	yes	—
212	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
213	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
214	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
215	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
216	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
217	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
218	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
219	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
220	C₂₃×#121	C₂×C₄	1	2	yes	—
221	C₂₃×#121	C₂×C₄	1	2	yes	—
222	C₂₃×#121	C₂×C₄	1	2	yes	—
223	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
224	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
225	C₂₃×#121	C₂×C₄	1	2	yes	—
226	C₂₃×#121	C₂×C₄	1	2	yes	—
227	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
228	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
229	C₂₃×#121	C₂×C₄	1	2	yes	—
230	C₂₃×#121	C₂×C₄	1	2	yes	—
231	C₂₃×#121	C₂×C₄	1	2	yes	—
232	C₂₃×#121	C₂×C₄	1	2	yes	—
233	C₂₃×#121	C₂×C₄	1	2	yes	—
234	C₂₃×#120	C₂×C₄	1	2	yes	—
235	C₂₃×#120	C₂×C₄	1	2	yes	—
236	C₂₃×#120	C₂×C₄	1	2	yes	—
237	C₂₃×#120	C₂×C₄	1	2	yes	—
238	C₂₃×#120	C₂×C₄	1	2	yes	—
239	C₂₃×#120	C₂×C₄	1	2	yes	—
240	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
241	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
242	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
243	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
244	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
245	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
246	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
247	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
248	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
249	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
250	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
251	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
252	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
253	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
254	C₄×D₄×C₂₃	C₂³	1	2	yes	—
255	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₂₃	C₂³	1	2	yes	—
257	C₄×D₄×C₂₃	C₂³	1	2	yes	—
258	C₄×D₄×C₂₃	C₂³	1	2	yes	—
259	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₂₃	C₂³	1	2	yes	—
262	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
263	C₄×D₄×C₂₃	C₂³	1	2	yes	—
264	C₂₃×#117	C₂³	1	1	yes	characteristic
265	C₂₃×#117	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
268	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
271	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
272	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
274	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
279	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
280	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
281	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
282	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
283	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
284	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
286	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
287	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
288	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
289	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
290	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
291	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
292	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
293	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
294	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
295	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
296	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
297	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
298	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
299	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
300	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
301	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
302	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
303	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
304	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
305	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
310	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₂₃×#97	C₂³	1	1	yes	characteristic
313	C₂₃×#97	C₂³	1	1	yes	characteristic
314	C₂₃×#97	C₂³	1	1	yes	characteristic
315	C₂₃×#97	C₂³	1	1	yes	characteristic
316	C₂₃×#97	C₂³	1	2	yes	—
317	C₂₃×#97	C₂³	1	2	yes	—
318	C₂₃×#97	C₂³	1	2	yes	—
319	C₄×C₈×C₂₃	C₂³	1	2	yes	—
320	C₄×C₈×C₂₃	C₂³	1	2	yes	—
321	C₄×C₈×C₂₃	C₂³	1	2	yes	—
322	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
323	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
324	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
325	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
326	#41×C₂₃	—	2	2	no	—
327	#41×C₂₃	—	2	2	no	—
328	#41×C₂₃	—	2	2	no	—
329	#41×C₂₃	—	2	2	no	—
330	#41×C₂₃	—	2	2	no	—
331	#41×C₂₃	—	2	2	no	—
332	#41×C₂₃	—	4	2	no	—
333	#41×C₂₃	—	4	2	no	—
334	#41×C₂₃	—	4	2	no	—
335	#41×C₂₃	—	4	2	no	—
336	#41×C₂₃	—	4	4	no	—
337	#41×C₂₃	—	4	4	no	—
338	#41×C₂₃	—	4	2	no	—
339	#41×C₂₃	—	4	2	no	—
340	#41×C₂₃	—	4	2	no	—
341	#41×C₂₃	—	4	2	no	—
342	C₂×Q₈×C₂₃	—	4	2	no	—
343	C₂×Q₈×C₂₃	—	4	2	no	—
344	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
345	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
346	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
347	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
348	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
349	C₂×D₄×C₂₃	—	4	2	no	—
350	C₂×D₄×C₂₃	—	4	2	no	—
351	C₂×D₄×C₂₃	—	4	2	no	—
352	C₂×D₄×C₂₃	—	4	4	no	—
353	C₂×D₄×C₂₃	—	4	4	no	—
354	C₂×D₄×C₂₃	—	4	4	no	—
355	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
356	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
357	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
358	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
359	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
360	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
361	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
362	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
363	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
364	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
365	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
366	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
367	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
368	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
369	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
370	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
371	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
372	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
373	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
374	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
375	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
376	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
377	C₂²×C₄×C₂₃	—	2	2	no	—
378	C₂²×C₄×C₂₃	—	2	2	no	—
379	C₂²×C₄×C₂₃	—	2	2	no	—
380	C₂²×C₄×C₂₃	—	2	2	no	—
381	C₂²×C₄×C₂₃	—	4	2	no	—
382	C₂²×C₄×C₂₃	—	4	2	no	—
383	C₂²×C₄×C₂₃	—	4	2	no	—
384	C₂²×C₄×C₂₃	—	4	2	no	—
385	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
386	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
387	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
388	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
389	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
390	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
391	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
392	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
393	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
394	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
395	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
396	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
397	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
398	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
399	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
400	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
401	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
402	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
406	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
407	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
409	M₁₆×C₂₃	—	2	2	no	—
410	M₁₆×C₂₃	—	2	2	no	—
411	M₁₆×C₂₃	—	2	2	no	—
412	M₁₆×C₂₃	—	2	2	no	—
413	M₁₆×C₂₃	—	4	1	no	—
414	M₁₆×C₂₃	—	4	1	no	—
415	M₁₆×C₂₃	—	4	1	no	—
416	M₁₆×C₂₃	—	4	1	no	—
417	M₁₆×C₂₃	—	4	2	no	—
418	M₁₆×C₂₃	—	4	2	no	—
419	M₁₆×C₂₃	—	4	2	no	—
420	M₁₆×C₂₃	—	4	2	no	—
421	M₁₆×C₂₃	—	4	2	no	—
422	M₁₆×C₂₃	—	4	2	no	—
423	C₂×C₈×C₂₃	—	2	2	no	—
424	C₂×C₈×C₂₃	—	2	2	no	—
425	C₂×C₈×C₂₃	—	2	2	no	—
426	C₂×C₈×C₂₃	—	2	2	no	—
427	C₂×C₈×C₂₃	—	4	1	no	—
428	C₂×C₈×C₂₃	—	4	1	no	—
429	C₂×C₈×C₂₃	—	4	1	no	—
430	C₂×C₈×C₂₃	—	4	1	no	—
431	C₂×C₈×C₂₃	—	4	2	no	—
432	C₂×C₈×C₂₃	—	4	2	no	—
433	C₂×C₈×C₂₃	—	4	2	no	—
434	C₂×C₈×C₂₃	—	4	2	no	—
435	C₂×C₈×C₂₃	—	4	2	no	—
436	C₂×C₈×C₂₃	—	4	2	no	—
437	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
438	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
439	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
440	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
441	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
442	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
443	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
444	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
445	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
446	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
447	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
448	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
450	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
451	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
452	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
453	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
454	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
455	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
456	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
457	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
458	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
459	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
460	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
461	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
462	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
463	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
464	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
465	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
466	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
467	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
468	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
469	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
470	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
471	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
472	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
473	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
474	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
475	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
476	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
477	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
478	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
479	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
480	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
481	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
482	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
483	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
484	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
485	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
486	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
487	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
488	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
489	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
490	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
491	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
492	C₄²×C₂₃	C₂⁴	1	2	yes	—
493	#60240	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
494	C₂³×C₂₃	—	2	2	no	—
495	C₂³×C₂₃	—	2	2	no	—
496	C₂³×C₂₃	—	2	2	no	—
497	C₂³×C₂₃	—	2	4	no	—
498	C₂³×C₂₃	—	4	1	no	—
499	C₂³×C₂₃	—	4	2	no	—
500	C₂³×C₂₃	—	4	2	no	—
501	C₂³×C₂₃	—	4	1	no	—
502	C₂³×C₂₃	—	4	2	no	—
503	C₂³×C₂₃	—	4	1	no	—
504	C₂³×C₂₃	—	4	2	no	—
505	C₂³×C₂₃	—	4	2	no	—
506	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
507	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
508	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
509	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
510	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
511	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
512	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
513	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
514	Q₈×C₂₃	—	2	2	no	—
515	Q₈×C₂₃	—	2	2	no	—
516	Q₈×C₂₃	—	2	2	no	—
517	Q₈×C₂₃	—	4	2	no	—
518	Q₈×C₂₃	—	4	2	no	—
519	D₄×C₂₃	—	2	4	no	—
520	D₄×C₂₃	—	2	4	no	—
521	D₄×C₂₃	—	2	4	no	—
522	D₄×C₂₃	—	2	2	no	—
523	D₄×C₂₃	—	2	2	no	—
524	D₄×C₂₃	—	2	4	no	—
525	D₄×C₂₃	—	2	2	no	—
526	D₄×C₂₃	—	2	2	no	—
527	D₄×C₂₃	—	2	2	no	—
528	D₄×C₂₃	—	4	1	no	—
529	D₄×C₂₃	—	4	2	no	—
530	D₄×C₂₃	—	4	1	no	—
531	D₄×C₂₃	—	4	2	no	—
532	D₄×C₂₃	—	4	2	no	—
533	D₄×C₂₃	—	4	2	no	—
534	D₄×C₂₃	—	4	2	no	—
535	D₄×C₂₃	—	4	2	no	—
536	D₄×C₂₃	—	4	2	no	—
537	D₄×C₂₃	—	4	2	no	—
538	D₄×C₂₃	—	4	2	no	—
539	D₄×C₂₃	—	4	2	no	—
540	D₄×C₂₃	—	4	2	no	—
541	C₂×C₄×C₂₃	—	2	2	no	—
542	C₂×C₄×C₂₃	—	2	2	no	—
543	C₂×C₄×C₂₃	—	2	2	no	—
544	C₂×C₄×C₂₃	—	2	2	no	—
545	C₂×C₄×C₂₃	—	2	2	no	—
546	C₂×C₄×C₂₃	—	2	2	no	—
547	C₂×C₄×C₂₃	—	2	1	no	—
548	C₂×C₄×C₂₃	—	2	1	no	—
549	C₂×C₄×C₂₃	—	2	1	no	—
550	C₂×C₄×C₂₃	—	2	1	no	—
551	C₂×C₄×C₂₃	—	2	2	no	—
552	C₂×C₄×C₂₃	—	2	2	no	—
553	C₂×C₄×C₂₃	—	2	2	no	—
554	C₂×C₄×C₂₃	—	2	2	no	—
555	C₂×C₄×C₂₃	—	2	1	no	—
556	C₂×C₄×C₂₃	—	2	1	no	—
557	C₂×C₄×C₂₃	—	2	1	no	—
558	C₂×C₄×C₂₃	—	2	1	no	—
559	C₂×C₄×C₂₃	—	2	2	no	—
560	C₂×C₄×C₂₃	—	2	2	no	—
561	C₂×C₄×C₂₃	—	4	2	no	—
562	C₂×C₄×C₂₃	—	4	2	no	—
563	C₂×C₄×C₂₃	—	4	2	no	—
564	C₂×C₄×C₂₃	—	4	2	no	—
565	C₂×C₄×C₂₃	—	4	2	no	—
566	C₂×C₄×C₂₃	—	4	2	no	—
567	C₂×C₄×C₂₃	—	4	1	no	—
568	C₂×C₄×C₂₃	—	4	2	no	—
569	C₂×C₄×C₂₃	—	4	1	no	—
570	C₂×C₄×C₂₃	—	4	2	no	—
571	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
572	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
573	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
574	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
575	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
576	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
577	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
578	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
579	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
580	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
581	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
582	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
583	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
584	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
585	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
586	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
587	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
588	C₈×C₂₃	—	2	1	no	—
589	C₈×C₂₃	—	2	1	no	—
590	C₈×C₂₃	—	2	1	no	—
591	C₈×C₂₃	—	2	1	no	—
592	C₈×C₂₃	—	2	1	no	—
593	C₈×C₂₃	—	2	1	no	—
594	C₈×C₂₃	—	2	1	no	—
595	C₈×C₂₃	—	2	1	no	—
596	C₈×C₂₃	—	2	2	no	—
597	C₈×C₂₃	—	2	2	no	—
598	C₈×C₂₃	—	2	2	no	—
599	C₈×C₂₃	—	2	2	no	—
600	D₄×#41	C₂×C₂₃	1	1	yes	characteristic
601	#2981	C₂×C₂₃	1	2	yes	complemented
602	#2980	C₂×C₂₃	1	2	yes	complemented
603	#2978	C₂×C₂₃	1	2	yes	complemented
604	#2977	C₂×C₂₃	1	2	yes	complemented
605	#2976	C₂×C₂₃	1	2	yes	complemented
606	#2976	C₂×C₂₃	1	2	yes	complemented
607	#2974	C₂×C₂₃	1	2	yes	complemented
608	#2973	C₂×C₂₃	1	2	yes	complemented
609	#2935	C₂×C₂₃	1	1	yes	characteristic, complemented
610	D₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
611	#2933	C₂×C₂₃	1	1	yes	characteristic, complemented
612	#2933	C₂×C₂₃	1	1	yes	characteristic, complemented
613	#2932	C₂×C₂₃	1	1	yes	characteristic, complemented
614	#2930	C₂×C₂₃	1	1	yes	characteristic, complemented
615	#2929	C₂×C₂₃	1	1	yes	characteristic, complemented
616	C₂×#435	C₂×C₂₃	1	1	yes	characteristic, complemented
617	#2925	C₂×C₂₃	1	1	yes	characteristic, complemented
618	#2923	C₂×C₂₃	1	1	yes	characteristic, complemented
619	#2880	C₂×C₂₃	1	1	yes	characteristic, complemented
620	#2880	C₂×C₂₃	1	1	yes	characteristic, complemented
621	#2879	C₂×C₂₃	1	1	yes	characteristic, complemented
622	C₂×#408	C₂×C₂₃	1	1	yes	characteristic, complemented
623	C₂²×C₂₃	—	2	1	no	—
624	C₂²×C₂₃	—	2	1	no	—
625	C₂²×C₂₃	—	2	1	no	—
626	C₂²×C₂₃	—	2	1	no	—
627	C₂²×C₂₃	—	2	1	no	—
628	C₂²×C₂₃	—	2	1	no	—
629	C₂²×C₂₃	—	2	1	no	—
630	C₂²×C₂₃	—	2	2	no	—
631	C₂²×C₂₃	—	2	2	no	—
632	C₂²×C₂₃	—	2	2	no	—
633	C₂²×C₂₃	—	2	2	no	—
634	C₂²×C₂₃	—	2	1	no	—
635	C₂²×C₂₃	—	2	1	no	—
636	C₂²×C₂₃	—	2	2	no	—
637	C₂²×C₂₃	—	2	1	no	—
638	C₂²×C₂₃	—	2	2	no	—
639	C₂²×C₂₃	—	2	2	no	—
640	C₂²×C₂₃	—	2	1	no	—
641	C₂²×C₂₃	—	2	1	no	—
642	C₂²×C₂₃	—	2	2	no	—
643	C₂²×C₂₃	—	2	2	no	—
644	C₂²×C₂₃	—	2	1	no	—
645	C₂²×C₂₃	—	4	4	no	—
646	C₂²×C₂₃	—	8	4	no	—
647	C₂²×C₂₃	—	8	2	no	—
648	C₂²×C₂₃	—	8	4	no	—
649	C₂²×C₂₃	#518	1	2	yes	—
650	C₂²×C₂₃	#568	1	2	yes	—
651	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
652	C₄×C₂₃	—	2	1	no	—
653	C₄×C₂₃	—	2	1	no	—
654	C₄×C₂₃	—	2	1	no	—
655	C₄×C₂₃	—	2	1	no	—
656	C₄×C₂₃	—	2	2	no	—
657	C₄×C₂₃	—	2	2	no	—
658	C₄×C₂₃	—	2	2	no	—
659	C₄×C₂₃	—	2	1	no	—
660	C₄×C₂₃	—	2	1	no	—
661	C₄×C₂₃	—	2	2	no	—
662	C₄×C₂₃	—	2	1	no	—
663	C₄×C₂₃	—	2	1	no	—
664	C₄×C₂₃	—	2	2	no	—
665	C₄×C₂₃	#518	1	2	yes	—
666	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
667	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
668	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
669	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
670	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
671	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
672	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
673	C₂×#131	C₂²×C₂₃	1	1	yes	characteristic, complemented
674	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
675	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
676	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
677	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
678	#550	C₄×C₂₃	1	1	yes	characteristic
679	D₄×Q₈	C₄×C₂₃	1	1	yes	characteristic
680	#548	C₄×C₂₃	1	1	yes	characteristic
681	#548	C₄×C₂₃	1	1	yes	characteristic
682	#547	C₄×C₂₃	1	2	yes	—
683	#547	C₄×C₂₃	1	1	yes	characteristic
684	#546	C₄×C₂₃	1	2	yes	—
685	#546	C₄×C₂₃	1	2	yes	—
686	#546	C₄×C₂₃	1	1	yes	characteristic
687	#546	C₄×C₂₃	1	1	yes	characteristic
688	D₄²	C₄×C₂₃	1	1	yes	characteristic
689	D₄²	C₄×C₂₃	1	2	yes	—
690	#532	C₂²×C₂₃	1	1	yes	characteristic
691	#532	C₂²×C₂₃	1	2	yes	—
692	#525	C₂²×C₂₃	1	1	yes	characteristic
693	#525	C₂²×C₂₃	1	1	yes	characteristic
694	#525	C₂²×C₂₃	1	2	yes	—
695	#525	C₂²×C₂₃	1	2	yes	—
696	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
697	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
698	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
699	#436	C₂²×C₂₃	1	2	yes	complemented
700	#436	C₂²×C₂₃	1	2	yes	complemented
701	#436	C₂²×C₂₃	1	2	yes	complemented
702	#436	C₂²×C₂₃	1	2	yes	complemented
703	#436	C₂²×C₂₃	1	2	yes	complemented
704	#436	C₂²×C₂₃	1	2	yes	complemented
705	#435	C₂²×C₂₃	1	1	yes	characteristic
706	#435	C₂²×C₂₃	1	1	yes	characteristic
707	#435	C₂²×C₂₃	1	2	yes	—
708	#435	C₂²×C₂₃	1	1	yes	characteristic, complemented
709	#435	C₂²×C₂₃	1	1	yes	characteristic, complemented
710	#435	C₂²×C₂₃	1	1	yes	characteristic, complemented
711	#435	C₂²×C₂₃	1	1	yes	characteristic, complemented
712	#435	C₂²×C₂₃	1	1	yes	characteristic, complemented
713	#435	C₂²×C₂₃	1	1	yes	characteristic, complemented
714	#435	C₂²×C₂₃	1	2	yes	complemented
715	#435	C₂²×C₂₃	1	2	yes	complemented
716	#435	C₂²×C₂₃	1	2	yes	complemented
717	#435	C₂²×C₂₃	1	2	yes	complemented
718	#435	C₂²×C₂₃	1	2	yes	complemented
719	#435	C₂²×C₂₃	1	2	yes	complemented
720	#435	C₂²×C₂₃	1	2	yes	complemented
721	#435	C₂²×C₂₃	1	2	yes	complemented
722	#435	C₂²×C₂₃	1	2	yes	complemented
723	#435	C₂²×C₂₃	1	2	yes	complemented
724	#435	C₂²×C₂₃	1	2	yes	complemented
725	#435	C₂²×C₂₃	1	2	yes	complemented
726	#435	C₂²×C₂₃	1	2	yes	complemented
727	#435	C₂²×C₂₃	1	2	yes	complemented
728	#435	C₂²×C₂₃	1	2	yes	complemented
729	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
730	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
731	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
732	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
733	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
734	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
735	#433	C₂²×C₂₃	1	2	yes	complemented
736	#433	C₂²×C₂₃	1	2	yes	complemented
737	#433	C₂²×C₂₃	1	2	yes	complemented
738	#433	C₂²×C₂₃	1	2	yes	complemented
739	#432	C₂²×C₂₃	1	2	yes	complemented
740	#432	C₂²×C₂₃	1	2	yes	complemented
741	#432	C₂²×C₂₃	1	2	yes	complemented
742	#431	C₂²×C₂₃	1	2	yes	complemented
743	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
744	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
745	#423	C₂²×C₂₃	1	1	yes	characteristic, complemented
746	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
747	#408	C₂²×C₂₃	1	1	yes	characteristic
748	#408	C₂²×C₂₃	1	1	yes	characteristic
749	#408	C₂²×C₂₃	1	1	yes	characteristic
750	#408	C₂²×C₂₃	1	1	yes	characteristic
751	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
752	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
753	#408	C₂²×C₂₃	1	2	yes	complemented
754	#408	C₂²×C₂₃	1	2	yes	complemented
755	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
756	#408	C₂²×C₂₃	1	1	yes	characteristic, complemented
757	#408	C₂²×C₂₃	1	2	yes	complemented
758	#408	C₂²×C₂₃	1	2	yes	complemented
759	#408	C₂²×C₂₃	1	2	yes	complemented
760	#408	C₂²×C₂₃	1	2	yes	complemented
761	#408	C₂²×C₂₃	1	2	yes	complemented
762	#408	C₂²×C₂₃	1	2	yes	complemented
763	#407	C₂²×C₂₃	1	2	yes	complemented
764	#407	C₂²×C₂₃	1	2	yes	complemented
765	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
766	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
767	#407	C₂²×C₂₃	1	2	yes	complemented
768	#407	C₂²×C₂₃	1	2	yes	complemented
769	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
770	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
771	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
772	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
773	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
774	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
775	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
776	#405	C₂²×C₂₃	1	1	yes	characteristic, complemented
777	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
778	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic, complemented
779	C₂×C₂₃	—	2	2	no	—
780	C₂×C₂₃	—	2	2	no	—
781	C₂×C₂₃	—	4	1	no	—
782	C₂×C₂₃	—	4	1	no	—
783	C₂×C₂₃	—	4	2	no	—
784	C₂×C₂₃	—	4	2	no	—
785	C₂×C₂₃	—	4	2	no	—
786	C₂×C₂₃	—	4	1	no	—
787	C₂×C₂₃	C₂×#518	1	1	yes	characteristic
788	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
789	C₂×C₂₃	#3573	1	1	yes	characteristic
790	C₂×#41	—	4	2	no	—
791	C₂×#41	—	4	2	no	—
792	C₂×#41	—	4	2	no	—
793	C₂×#41	—	4	2	no	—
794	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
795	C₂×#41	C₂×C₄×C₂₃	1	2	yes	—
796	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
797	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
798	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
799	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
800	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
801	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
802	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
803	C₂×#41	C₂³×C₂₃	1	2	yes	—
804	C₂×#41	C₂³×C₂₃	1	2	yes	—
805	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
806	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
807	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
808	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
809	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
810	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
811	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
812	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
813	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
814	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
815	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
816	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
817	#131	—	4	2	no	—
818	#131	—	4	2	no	—
819	#131	—	4	2	no	—
820	#131	—	4	2	no	—
821	C₂×M₁₆	—	4	2	no	—
822	C₂×M₁₆	—	4	2	no	—
823	C₂×M₁₆	—	4	2	no	—
824	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
825	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
826	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
827	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
828	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
829	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
830	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
831	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
832	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
833	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
834	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
835	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
836	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
837	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
838	C₂²×C₈	—	4	2	no	—
839	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
840	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
841	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
842	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
843	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
844	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
845	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
846	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
847	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
848	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
849	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
850	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
851	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
852	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
853	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
854	C₄⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
855	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
856	#127	C₂×C₄×C₂₃	1	2	yes	—
857	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
858	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
859	#124	C₂×C₄×C₂₃	1	2	yes	—
860	#124	C₂×C₄×C₂₃	1	2	yes	—
861	#123	C₂×C₄×C₂₃	1	2	yes	—
862	#123	C₂×C₄×C₂₃	1	2	yes	—
863	#123	C₂×C₄×C₂₃	1	2	yes	—
864	#123	C₂×C₄×C₂₃	1	2	yes	—
865	#123	C₂×C₄×C₂₃	1	2	yes	—
866	#123	C₂×C₄×C₂₃	1	2	yes	—
867	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
868	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
869	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
870	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
871	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
872	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
873	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
874	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
875	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
876	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
877	#121	C₂×C₄×C₂₃	1	2	yes	—
878	#121	C₂×C₄×C₂₃	1	2	yes	—
879	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
880	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
881	#121	C₂×C₄×C₂₃	1	2	yes	—
882	#121	C₂×C₄×C₂₃	1	2	yes	—
883	#121	C₂×C₄×C₂₃	1	2	yes	—
884	#121	C₂×C₄×C₂₃	1	2	yes	—
885	#121	C₂×C₄×C₂₃	1	2	yes	—
886	#121	C₂×C₄×C₂₃	1	2	yes	—
887	#121	C₂×C₄×C₂₃	1	2	yes	—
888	#121	C₂×C₄×C₂₃	1	2	yes	—
889	#120	C₂×C₄×C₂₃	1	2	yes	—
890	#120	C₂×C₄×C₂₃	1	2	yes	—
891	#120	C₂×C₄×C₂₃	1	2	yes	—
892	#120	C₂×C₄×C₂₃	1	2	yes	—
893	#120	C₂×C₄×C₂₃	1	2	yes	—
894	#120	C₂×C₄×C₂₃	1	2	yes	—
895	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
896	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
897	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
898	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
899	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
900	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
901	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
902	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
903	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
904	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
905	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
906	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
907	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
908	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
909	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
910	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
911	C₄×D₄	C₂³×C₂₃	1	2	yes	—
912	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
913	C₄×D₄	C₂³×C₂₃	1	2	yes	—
914	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
915	C₄×D₄	C₂³×C₂₃	1	2	yes	—
916	C₄×D₄	C₂³×C₂₃	1	2	yes	—
917	C₄×D₄	C₂³×C₂₃	1	2	yes	—
918	C₄×D₄	C₂³×C₂₃	1	2	yes	—
919	#117	C₂³×C₂₃	1	1	yes	characteristic
920	#117	C₂³×C₂₃	1	2	yes	—
921	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
922	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
923	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
924	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
925	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
926	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
927	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
928	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
929	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
930	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
931	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
932	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
933	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
934	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
935	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
936	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
937	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
938	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
939	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
940	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
941	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
942	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
943	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
944	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
945	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
946	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
947	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
948	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
949	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
950	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
951	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
952	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
953	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
954	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
955	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
956	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
957	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
958	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
959	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
960	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
961	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
962	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
963	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
964	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
965	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
966	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
967	#97	C₂³×C₂₃	1	1	yes	characteristic
968	#97	C₂³×C₂₃	1	1	yes	characteristic
969	#97	C₂³×C₂₃	1	1	yes	characteristic
970	#97	C₂³×C₂₃	1	1	yes	characteristic
971	#97	C₂³×C₂₃	1	2	yes	—
972	#97	C₂³×C₂₃	1	2	yes	—
973	#97	C₂³×C₂₃	1	2	yes	—
974	C₄×C₈	C₂³×C₂₃	1	2	yes	—
975	C₄×C₈	C₂³×C₂₃	1	2	yes	—
976	C₄×C₈	C₂³×C₂₃	1	2	yes	—
977	C₂₃	#60240	1	1	yes	characteristic, direct product factor, Sylow
978	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
979	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
980	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
981	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
982	#41	—	2	2	no	—
983	#41	—	2	2	no	—
984	#41	—	2	2	no	—
985	#41	—	2	2	no	—
986	#41	—	2	2	no	—
987	#41	—	2	2	no	—
988	#41	—	4	2	no	—
989	#41	—	4	2	no	—
990	#41	—	4	2	no	—
991	#41	—	4	2	no	—
992	#41	—	4	4	no	—
993	#41	—	4	4	no	—
994	#41	—	4	2	no	—
995	#41	—	4	2	no	—
996	#41	—	4	2	no	—
997	#41	—	4	2	no	—
998	C₂×Q₈	—	4	2	no	—
999	C₂×Q₈	—	4	2	no	—
1000	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
1001	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
1002	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
1003	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
1004	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
1005	C₂×D₄	—	4	2	no	—
1006	C₂×D₄	—	4	2	no	—
1007	C₂×D₄	—	4	4	no	—
1008	C₂×D₄	—	4	4	no	—
1009	C₂×D₄	—	4	2	no	—
1010	C₂×D₄	—	4	4	no	—
1011	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1012	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
1013	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1014	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1015	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
1016	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
1017	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
1018	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1019	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1020	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1021	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
1022	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1023	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
1024	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
1025	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
1026	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
1027	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
1028	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
1029	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
1030	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
1031	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
1032	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
1033	C₂²×C₄	—	2	2	no	—
1034	C₂²×C₄	—	2	2	no	—
1035	C₂²×C₄	—	2	2	no	—
1036	C₂²×C₄	—	2	2	no	—
1037	C₂²×C₄	—	4	2	no	—
1038	C₂²×C₄	—	4	2	no	—
1039	C₂²×C₄	—	4	2	no	—
1040	C₂²×C₄	—	4	2	no	—
1041	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1042	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1043	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1044	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1045	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1046	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1047	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
1048	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1049	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
1050	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1051	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
1052	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
1053	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
1054	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
1055	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
1056	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
1057	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1058	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1059	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1060	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1061	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1062	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
1063	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1064	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
1065	M₁₆	—	2	2	no	—
1066	M₁₆	—	2	2	no	—
1067	M₁₆	—	2	2	no	—
1068	M₁₆	—	2	2	no	—
1069	M₁₆	—	4	1	no	—
1070	M₁₆	—	4	1	no	—
1071	M₁₆	—	4	1	no	—
1072	M₁₆	—	4	1	no	—
1073	M₁₆	—	4	2	no	—
1074	M₁₆	—	4	2	no	—
1075	M₁₆	—	4	2	no	—
1076	M₁₆	—	4	2	no	—
1077	M₁₆	—	4	2	no	—
1078	M₁₆	—	4	2	no	—
1079	C₂×C₈	—	2	2	no	—
1080	C₂×C₈	—	2	2	no	—
1081	C₂×C₈	—	2	2	no	—
1082	C₂×C₈	—	2	2	no	—
1083	C₂×C₈	—	4	1	no	—
1084	C₂×C₈	—	4	1	no	—
1085	C₂×C₈	—	4	1	no	—
1086	C₂×C₈	—	4	1	no	—
1087	C₂×C₈	—	4	2	no	—
1088	C₂×C₈	—	4	2	no	—
1089	C₂×C₈	—	4	2	no	—
1090	C₂×C₈	—	4	2	no	—
1091	C₂×C₈	—	4	2	no	—
1092	C₂×C₈	—	4	2	no	—
1093	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1094	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1095	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1096	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1097	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1098	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
1099	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1100	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1101	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1102	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1103	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1104	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
1105	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1106	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1107	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1108	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1109	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1110	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1111	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1112	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1113	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1114	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1115	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1116	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1117	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1118	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1119	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1120	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1121	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1122	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1123	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1124	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1125	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1126	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1127	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1128	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1129	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1130	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1131	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1132	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1133	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1134	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1135	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1136	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1137	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1138	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1139	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1140	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1141	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1142	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
1143	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
1144	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
1145	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
1146	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1147	C₄²	C₂⁴×C₂₃	1	2	yes	—
1148	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1149	C₂³	—	2	2	no	—
1150	C₂³	—	2	2	no	—
1151	C₂³	—	2	4	no	—
1152	C₂³	—	2	2	no	—
1153	C₂³	—	4	1	no	—
1154	C₂³	—	4	2	no	—
1155	C₂³	—	4	2	no	—
1156	C₂³	—	4	1	no	—
1157	C₂³	—	4	2	no	—
1158	C₂³	—	4	1	no	—
1159	C₂³	—	4	2	no	—
1160	C₂³	—	4	2	no	—
1161	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
1162	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
1163	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
1164	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1165	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1166	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1167	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
1168	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
1169	Q₈	—	2	2	no	—
1170	Q₈	—	2	2	no	—
1171	Q₈	—	2	2	no	—
1172	Q₈	—	4	2	no	—
1173	Q₈	—	4	2	no	—
1174	D₄	—	2	2	no	—
1175	D₄	—	2	2	no	—
1176	D₄	—	2	4	no	—
1177	D₄	—	2	4	no	—
1178	D₄	—	2	4	no	—
1179	D₄	—	2	4	no	—
1180	D₄	—	2	2	no	—
1181	D₄	—	2	2	no	—
1182	D₄	—	2	2	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	4	2	no	—
1186	D₄	—	4	2	no	—
1187	D₄	—	4	2	no	—
1188	D₄	—	4	2	no	—
1189	D₄	—	4	1	no	—
1190	D₄	—	4	2	no	—
1191	D₄	—	4	1	no	—
1192	D₄	—	4	2	no	—
1193	D₄	—	4	2	no	—
1194	D₄	—	4	2	no	—
1195	D₄	—	4	2	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	2	no	—
1203	C₂×C₄	—	2	2	no	—
1204	C₂×C₄	—	2	2	no	—
1205	C₂×C₄	—	2	2	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	2	1	no	—
1210	C₂×C₄	—	2	2	no	—
1211	C₂×C₄	—	2	2	no	—
1212	C₂×C₄	—	2	2	no	—
1213	C₂×C₄	—	2	2	no	—
1214	C₂×C₄	—	2	2	no	—
1215	C₂×C₄	—	2	2	no	—
1216	C₂×C₄	—	4	2	no	—
1217	C₂×C₄	—	4	2	no	—
1218	C₂×C₄	—	4	2	no	—
1219	C₂×C₄	—	4	2	no	—
1220	C₂×C₄	—	4	2	no	—
1221	C₂×C₄	—	4	2	no	—
1222	C₂×C₄	—	4	1	no	—
1223	C₂×C₄	—	4	2	no	—
1224	C₂×C₄	—	4	1	no	—
1225	C₂×C₄	—	4	2	no	—
1226	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1227	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1228	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1229	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1230	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1231	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1232	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1233	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1234	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1235	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1236	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1237	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1238	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1239	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1240	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1241	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1242	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1243	C₈	—	2	1	no	—
1244	C₈	—	2	1	no	—
1245	C₈	—	2	1	no	—
1246	C₈	—	2	1	no	—
1247	C₈	—	2	1	no	—
1248	C₈	—	2	1	no	—
1249	C₈	—	2	1	no	—
1250	C₈	—	2	1	no	—
1251	C₈	—	2	2	no	—
1252	C₈	—	2	2	no	—
1253	C₈	—	2	2	no	—
1254	C₈	—	2	2	no	—
1255	C₂²	—	2	1	no	—
1256	C₂²	—	2	1	no	—
1257	C₂²	—	2	1	no	—
1258	C₂²	—	2	1	no	—
1259	C₂²	—	2	1	no	—
1260	C₂²	—	2	1	no	—
1261	C₂²	—	2	1	no	—
1262	C₂²	—	2	2	no	—
1263	C₂²	—	2	2	no	—
1264	C₂²	—	2	2	no	—
1265	C₂²	—	2	2	no	—
1266	C₂²	—	2	1	no	—
1267	C₂²	—	2	1	no	—
1268	C₂²	—	2	2	no	—
1269	C₂²	—	2	1	no	—
1270	C₂²	—	2	2	no	—
1271	C₂²	—	2	2	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	2	2	no	—
1275	C₂²	—	2	2	no	—
1276	C₂²	—	2	1	no	—
1277	C₂²	—	4	4	no	—
1278	C₂²	—	8	4	no	—
1279	C₂²	—	8	2	no	—
1280	C₂²	—	8	4	no	—
1281	C₂²	C₂₃×#518	1	2	yes	—
1282	C₂²	C₂₃×#568	1	2	yes	—
1283	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
1284	C₄	—	2	1	no	—
1285	C₄	—	2	1	no	—
1286	C₄	—	2	1	no	—
1287	C₄	—	2	1	no	—
1288	C₄	—	2	2	no	—
1289	C₄	—	2	2	no	—
1290	C₄	—	2	2	no	—
1291	C₄	—	2	1	no	—
1292	C₄	—	2	1	no	—
1293	C₄	—	2	2	no	—
1294	C₄	—	2	1	no	—
1295	C₄	—	2	1	no	—
1296	C₄	—	2	2	no	—
1297	C₄	C₂₃×#518	1	2	yes	—
1298	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1299	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1300	C₂	—	2	2	no	—
1301	C₂	—	2	2	no	—
1302	C₂	—	4	1	no	—
1303	C₂	—	4	1	no	—
1304	C₂	—	4	2	no	—
1305	C₂	—	4	1	no	—
1306	C₂	—	4	2	no	—
1307	C₂	—	4	2	no	—
1308	C₂	C₂×C₂₃×#518	1	1	yes	characteristic
1309	C₂	C₂×C₂₃×#568	1	1	yes	characteristic
1310	C₂	C₂₃×#3573	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂⁴×C₄
prime radical	D₄×#41×C₂₃	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂₃×#2981	C₂	semidirect
3. C₂₃×#2980	C₂	semidirect
4. C₂₃×#2978	C₂	semidirect
5. C₂₃×#2977	C₂	semidirect
6. C₂₃×#2976	C₂	semidirect
7. C₂₃×#2976	C₂	semidirect
8. C₂₃×#2974	C₂	semidirect
9. C₂₃×#2973	C₂	semidirect
10. C₂₃×#2935	C₂	semidirect
11. D₄×M₁₆×C₂₃	C₂	semidirect
12. C₂₃×#2933	C₂	semidirect
13. C₂₃×#2933	C₂	semidirect
14. C₂₃×#2932	C₂	semidirect
15. C₂₃×#2930	C₂	semidirect
16. C₂₃×#2929	C₂	semidirect
17. C₂×C₂₃×#435	C₂	semidirect
18. C₂₃×#2925	C₂	semidirect
19. C₂₃×#2923	C₂	semidirect
20. C₂₃×#2880	C₂	semidirect
21. C₂₃×#2880	C₂	semidirect
22. C₂₃×#2879	C₂	semidirect
23. C₂×C₂₃×#408	C₂	semidirect
26. C₂×C₂₃×#131	C₂²	semidirect
27. C₂×C₂₃×#131	C₂²	semidirect
28. C₂×C₂₃×#131	C₂²	semidirect
29. C₂×C₂₃×#131	C₂²	semidirect
30. C₂²×M₁₆×C₂₃	C₂²	semidirect
31. C₂²×M₁₆×C₂₃	C₂²	semidirect
32. C₂²×M₁₆×C₂₃	C₂²	semidirect
33. C₂³×C₈×C₂₃	C₂²	semidirect
55. C₂₃×#436	C₂²	semidirect
56. C₂₃×#436	C₂²	semidirect
57. C₂₃×#436	C₂²	semidirect
58. C₂₃×#436	C₂²	semidirect
59. C₂₃×#436	C₂²	semidirect
60. C₂₃×#436	C₂²	semidirect
64. C₂₃×#435	C₂²	semidirect
65. C₂₃×#435	C₂²	semidirect
66. C₂₃×#435	C₂²	semidirect
67. C₂₃×#435	C₂²	semidirect
68. C₂₃×#435	C₂²	semidirect
69. C₂₃×#435	C₂²	semidirect
70. C₂₃×#435	C₂²	semidirect
71. C₂₃×#435	C₂²	semidirect
72. C₂₃×#435	C₂²	semidirect
73. C₂₃×#435	C₂²	semidirect
74. C₂₃×#435	C₂²	semidirect
75. C₂₃×#435	C₂²	semidirect
76. C₂₃×#435	C₂²	semidirect
77. C₂₃×#435	C₂²	semidirect
78. C₂₃×#435	C₂²	semidirect
79. C₂₃×#435	C₂²	semidirect
80. C₂₃×#435	C₂²	semidirect
81. C₂₃×#435	C₂²	semidirect
82. C₂₃×#435	C₂²	semidirect
83. C₂₃×#435	C₂²	semidirect
84. C₂₃×#435	C₂²	semidirect
85. C₈×D₄×C₂₃	C₂²	semidirect
86. C₈×D₄×C₂₃	C₂²	semidirect
87. C₈×D₄×C₂₃	C₂²	semidirect
88. C₈×D₄×C₂₃	C₂²	semidirect
89. C₈×D₄×C₂₃	C₂²	semidirect
90. C₈×D₄×C₂₃	C₂²	semidirect
91. C₂₃×#433	C₂²	semidirect
92. C₂₃×#433	C₂²	semidirect
93. C₂₃×#433	C₂²	semidirect
94. C₂₃×#433	C₂²	semidirect
95. C₂₃×#432	C₂²	semidirect
96. C₂₃×#432	C₂²	semidirect
97. C₂₃×#432	C₂²	semidirect
98. C₂₃×#431	C₂²	semidirect
99. C₂₃×#424	C₂²	semidirect
100. C₂₃×#424	C₂²	semidirect
101. C₂₃×#423	C₂²	semidirect
102. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
107. C₂₃×#408	C₂²	semidirect
108. C₂₃×#408	C₂²	semidirect
109. C₂₃×#408	C₂²	semidirect
110. C₂₃×#408	C₂²	semidirect
111. C₂₃×#408	C₂²	semidirect
112. C₂₃×#408	C₂²	semidirect
113. C₂₃×#408	C₂²	semidirect
114. C₂₃×#408	C₂²	semidirect
115. C₂₃×#408	C₂²	semidirect
116. C₂₃×#408	C₂²	semidirect
117. C₂₃×#408	C₂²	semidirect
118. C₂₃×#408	C₂²	semidirect
119. C₂₃×#407	C₂²	semidirect
120. C₂₃×#407	C₂²	semidirect
121. C₂₃×#407	C₂²	semidirect
122. C₂₃×#407	C₂²	semidirect
123. C₂₃×#407	C₂²	semidirect
124. C₂₃×#407	C₂²	semidirect
125. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
126. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
127. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
128. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
129. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
130. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
131. C₂₃×#405	C₂²	semidirect
132. C₂₃×#405	C₂²	semidirect
133. C₄×M₁₆×C₂₃	C₂²	semidirect
134. C₂×C₂₃×#97	C₂²	semidirect
493. #60240	C₂₃	direct (N × H)
601. #2981	C₂×C₂₃	semidirect
602. #2980	C₂×C₂₃	semidirect
603. #2978	C₂×C₂₃	semidirect
604. #2977	C₂×C₂₃	semidirect
605. #2976	C₂×C₂₃	semidirect
606. #2976	C₂×C₂₃	semidirect
607. #2974	C₂×C₂₃	semidirect
608. #2973	C₂×C₂₃	semidirect
609. #2935	C₂×C₂₃	semidirect
610. D₄×M₁₆	C₂×C₂₃	semidirect
611. #2933	C₂×C₂₃	semidirect
612. #2933	C₂×C₂₃	semidirect
613. #2932	C₂×C₂₃	semidirect
614. #2930	C₂×C₂₃	semidirect
615. #2929	C₂×C₂₃	semidirect
616. C₂×#435	C₂×C₂₃	semidirect
617. #2925	C₂×C₂₃	semidirect
618. #2923	C₂×C₂₃	semidirect
619. #2880	C₂×C₂₃	semidirect
620. #2880	C₂×C₂₃	semidirect
621. #2879	C₂×C₂₃	semidirect
622. C₂×#408	C₂×C₂₃	semidirect
670. C₂×#131	C₂²×C₂₃	semidirect
671. C₂×#131	C₂²×C₂₃	semidirect
672. C₂×#131	C₂²×C₂₃	semidirect
673. C₂×#131	C₂²×C₂₃	semidirect
674. C₂²×M₁₆	C₂²×C₂₃	semidirect
675. C₂²×M₁₆	C₂²×C₂₃	semidirect
676. C₂²×M₁₆	C₂²×C₂₃	semidirect
677. C₂³×C₈	C₂²×C₂₃	semidirect
699. #436	C₂²×C₂₃	semidirect
700. #436	C₂²×C₂₃	semidirect
701. #436	C₂²×C₂₃	semidirect
702. #436	C₂²×C₂₃	semidirect
703. #436	C₂²×C₂₃	semidirect
704. #436	C₂²×C₂₃	semidirect
708. #435	C₂²×C₂₃	semidirect
709. #435	C₂²×C₂₃	semidirect
710. #435	C₂²×C₂₃	semidirect
711. #435	C₂²×C₂₃	semidirect
712. #435	C₂²×C₂₃	semidirect
713. #435	C₂²×C₂₃	semidirect
714. #435	C₂²×C₂₃	semidirect
715. #435	C₂²×C₂₃	semidirect
716. #435	C₂²×C₂₃	semidirect
717. #435	C₂²×C₂₃	semidirect
718. #435	C₂²×C₂₃	semidirect
719. #435	C₂²×C₂₃	semidirect
720. #435	C₂²×C₂₃	semidirect
721. #435	C₂²×C₂₃	semidirect
722. #435	C₂²×C₂₃	semidirect
723. #435	C₂²×C₂₃	semidirect
724. #435	C₂²×C₂₃	semidirect
725. #435	C₂²×C₂₃	semidirect
726. #435	C₂²×C₂₃	semidirect
727. #435	C₂²×C₂₃	semidirect
728. #435	C₂²×C₂₃	semidirect
729. C₈×D₄	C₂²×C₂₃	semidirect
730. C₈×D₄	C₂²×C₂₃	semidirect
731. C₈×D₄	C₂²×C₂₃	semidirect
732. C₈×D₄	C₂²×C₂₃	semidirect
733. C₈×D₄	C₂²×C₂₃	semidirect
734. C₈×D₄	C₂²×C₂₃	semidirect
735. #433	C₂²×C₂₃	semidirect
736. #433	C₂²×C₂₃	semidirect
737. #433	C₂²×C₂₃	semidirect
738. #433	C₂²×C₂₃	semidirect
739. #432	C₂²×C₂₃	semidirect
740. #432	C₂²×C₂₃	semidirect
741. #432	C₂²×C₂₃	semidirect
742. #431	C₂²×C₂₃	semidirect
743. #424	C₂²×C₂₃	semidirect
744. #424	C₂²×C₂₃	semidirect
745. #423	C₂²×C₂₃	semidirect
746. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
751. #408	C₂²×C₂₃	semidirect
752. #408	C₂²×C₂₃	semidirect
753. #408	C₂²×C₂₃	semidirect
754. #408	C₂²×C₂₃	semidirect
755. #408	C₂²×C₂₃	semidirect
756. #408	C₂²×C₂₃	semidirect
757. #408	C₂²×C₂₃	semidirect
758. #408	C₂²×C₂₃	semidirect
759. #408	C₂²×C₂₃	semidirect
760. #408	C₂²×C₂₃	semidirect
761. #408	C₂²×C₂₃	semidirect
762. #408	C₂²×C₂₃	semidirect
763. #407	C₂²×C₂₃	semidirect
764. #407	C₂²×C₂₃	semidirect
765. #407	C₂²×C₂₃	semidirect
766. #407	C₂²×C₂₃	semidirect
767. #407	C₂²×C₂₃	semidirect
768. #407	C₂²×C₂₃	semidirect
769. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
770. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
771. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
772. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
773. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
774. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
775. #405	C₂²×C₂₃	semidirect
776. #405	C₂²×C₂₃	semidirect
777. C₄×M₁₆	C₂²×C₂₃	semidirect
778. C₂×#97	C₂²×C₂₃	semidirect
977. C₂₃	#60240	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₄×#41×C₂₃	2
C₂₃×#2981	2
C₂₃×#2980	2
C₂₃×#2978	2
C₂₃×#2977	2
C₂₃×#2976	2
C₂₃×#2974	2
C₂₃×#2973	2
C₂₃×#2935	2
D₄×M₁₆×C₂₃	2
C₂₃×#2933	2
C₂₃×#2932	2
C₂₃×#2930	2
C₂₃×#2929	2
C₂×C₂₃×#435	2
C₂₃×#2925	2
C₂₃×#2923	2
C₂₃×#2880	2
C₂₃×#2879	2
C₂×C₂₃×#408	2
#60240	23

Subgroups — C23×#60240 #19207866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60240 #19207866