Subgroups — C₂₃×#60324 #19207950

Order 5888.

1894 conjugacy classes of subgroups.

The subgroup lattice has 1180 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3481	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2995	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2994	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2993	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2978	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2976	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2975	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2973	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2971	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2969	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2967	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
19	D₄×M₁₆×C₂₃	C₂	1	2	yes	maximal, complemented
20	D₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂₃×#2933	C₂	1	2	yes	maximal, complemented
22	C₂₃×#2930	C₂	1	2	yes	maximal, complemented
23	C₂×C₂₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₂₃×#131	C₂²	1	2	yes	complemented
25	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	complemented
26	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	complemented
27	C₂₃×#559	C₄	1	1	yes	characteristic
28	C₂₃×#554	C₄	1	1	yes	characteristic
29	C₂₃×#554	C₄	1	1	yes	characteristic
30	C₂₃×#553	C₄	1	1	yes	characteristic
31	C₂₃×#553	C₄	1	1	yes	characteristic
32	C₂₃×#553	C₄	1	2	yes	—
33	C₂₃×#551	C₄	1	2	yes	—
34	C₂₃×#551	C₄	1	2	yes	—
35	C₂₃×#546	C₄	1	2	yes	—
36	C₂₃×#546	C₄	1	1	yes	characteristic
37	C₂₃×#546	C₄	1	1	yes	characteristic
38	D₄²×C₂₃	C₄	1	1	yes	characteristic
39	C₂₃×#532	C₂²	1	1	yes	characteristic
40	C₂₃×#529	C₂²	1	1	yes	characteristic
41	C₂₃×#529	C₂²	1	2	yes	—
42	C₂₃×#529	C₂²	1	1	yes	characteristic
43	C₂₃×#525	C₂²	1	2	yes	—
44	C₂₃×#525	C₂²	1	2	yes	—
45	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
46	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
49	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
50	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#446	C₂²	1	2	yes	complemented
54	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
55	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
56	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#436	C₂²	1	1	yes	characteristic
58	C₂₃×#436	C₂²	1	1	yes	characteristic
59	C₂₃×#436	C₂²	1	1	yes	characteristic
60	C₂₃×#436	C₂²	1	1	yes	characteristic
61	C₂₃×#436	C₂²	1	2	yes	complemented
62	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#436	C₂²	1	2	yes	complemented
64	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#436	C₂²	1	2	yes	complemented
67	C₂₃×#436	C₂²	1	2	yes	complemented
68	C₂₃×#436	C₂²	1	2	yes	complemented
69	C₂₃×#436	C₂²	1	2	yes	complemented
70	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
71	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
72	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
73	C₂₃×#436	C₂²	1	2	yes	complemented
74	C₂₃×#436	C₂²	1	2	yes	complemented
75	C₂₃×#435	C₂²	1	1	yes	characteristic
76	C₂₃×#435	C₂²	1	2	yes	—
77	C₂₃×#435	C₂²	1	1	yes	characteristic
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	1	yes	characteristic, complemented
83	C₂₃×#435	C₂²	1	2	yes	complemented
84	C₂₃×#435	C₂²	1	2	yes	complemented
85	C₂₃×#435	C₂²	1	2	yes	complemented
86	C₂₃×#435	C₂²	1	2	yes	complemented
87	C₂₃×#435	C₂²	1	2	yes	complemented
88	C₂₃×#435	C₂²	1	2	yes	complemented
89	C₂₃×#435	C₂²	1	2	yes	complemented
90	C₂₃×#435	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#435	C₂²	1	2	yes	complemented
92	C₂₃×#435	C₂²	1	2	yes	complemented
93	C₂₃×#435	C₂²	1	2	yes	complemented
94	C₂₃×#435	C₂²	1	2	yes	complemented
95	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
96	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
97	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
98	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
99	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
100	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
101	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#433	C₂²	1	2	yes	complemented
103	C₂₃×#433	C₂²	1	2	yes	complemented
104	C₂₃×#433	C₂²	1	2	yes	complemented
105	C₂₃×#433	C₂²	1	2	yes	complemented
106	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
107	C₂₃×#432	C₂²	1	2	yes	complemented
108	C₂₃×#432	C₂²	1	2	yes	complemented
109	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
110	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
112	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
113	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
114	C₂₃×#424	C₂²	1	2	yes	complemented
115	C₂₃×#424	C₂²	1	2	yes	complemented
116	C₂₃×#423	C₂²	1	2	yes	complemented
117	C₂₃×#423	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
120	C₂₃×#408	C₂²	1	2	yes	complemented
121	C₂₃×#408	C₂²	1	2	yes	complemented
122	C₂₃×#408	C₂²	1	2	yes	complemented
123	C₂₃×#407	C₂²	1	2	yes	complemented
124	C₂₃×#407	C₂²	1	2	yes	complemented
125	C₂₃×#407	C₂²	1	2	yes	complemented
126	C₂₃×#407	C₂²	1	2	yes	complemented
127	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
128	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
129	C₂₃×#405	C₂²	1	2	yes	complemented
130	C₂₃×#405	C₂²	1	2	yes	complemented
131	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
132	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
133	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
136	C₂×#41×C₂₃	C₂×C₄	1	1	yes	characteristic
137	C₂×#41×C₂₃	C₂³	1	2	yes	—
138	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
139	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
140	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
141	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
142	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
143	C₂₃×#131	—	4	4	no	—
144	C₂×M₁₆×C₂₃	—	4	4	no	—
145	C₂×M₁₆×C₂₃	—	4	4	no	—
146	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
147	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
148	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
149	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
150	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
152	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
153	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
154	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
155	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
156	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
157	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
158	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
159	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
160	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
161	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
162	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
163	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
164	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
165	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
167	C₂₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
168	C₂₃×#127	C₂×C₄	1	1	yes	characteristic
169	C₂₃×#126	C₂×C₄	1	2	yes	—
170	C₂₃×#126	C₂×C₄	1	2	yes	—
171	C₂₃×#126	C₂×C₄	1	2	yes	—
172	C₂₃×#126	C₂×C₄	1	2	yes	—
173	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
174	C₂₃×#125	C₂×C₄	1	2	yes	—
175	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
176	C₂₃×#124	C₂×C₄	1	2	yes	—
177	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
178	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
179	C₂₃×#124	C₂×C₄	1	2	yes	—
180	C₂₃×#123	C₂×C₄	1	2	yes	—
181	C₂₃×#123	C₂×C₄	1	2	yes	—
182	C₂₃×#123	C₂×C₄	1	2	yes	—
183	C₂₃×#123	C₂×C₄	1	2	yes	—
184	C₂₃×#123	C₂×C₄	1	2	yes	—
185	C₂₃×#123	C₂×C₄	1	2	yes	—
186	C₂₃×#123	C₂×C₄	1	2	yes	—
187	C₂₃×#123	C₂×C₄	1	2	yes	—
188	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
189	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
190	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
191	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
192	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
193	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
194	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
195	C₂₃×#121	C₂×C₄	1	2	yes	—
196	C₂₃×#121	C₂×C₄	1	2	yes	—
197	C₂₃×#121	C₂×C₄	1	2	yes	—
198	C₂₃×#121	C₂×C₄	1	2	yes	—
199	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
200	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
201	C₂₃×#121	C₂×C₄	1	2	yes	—
202	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
203	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
204	C₂₃×#121	C₂×C₄	1	2	yes	—
205	C₂₃×#120	C₂×C₄	1	2	yes	—
206	C₂₃×#120	C₂×C₄	1	2	yes	—
207	C₂₃×#120	C₂×C₄	1	2	yes	—
208	C₂₃×#120	C₂×C₄	1	2	yes	—
209	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
210	C₄×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
211	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
212	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
213	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
214	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
215	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
216	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
217	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
218	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
219	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
220	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
221	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
222	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
223	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
224	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
225	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
226	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
227	C₄×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
228	C₄×D₄×C₂₃	C₂³	1	2	yes	—
229	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
230	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
231	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
232	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
233	C₄×D₄×C₂₃	C₂³	1	2	yes	—
234	C₄×D₄×C₂₃	C₂³	1	2	yes	—
235	C₄×D₄×C₂₃	C₂³	1	2	yes	—
236	C₄×D₄×C₂₃	C₂³	1	2	yes	—
237	C₄×D₄×C₂₃	C₂³	1	2	yes	—
238	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
239	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
240	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
241	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
242	C₂₃×#117	C₂×C₄	1	2	yes	—
243	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
244	C₂₃×#117	C₂×C₄	1	1	yes	characteristic
245	C₂₃×#117	C₂³	1	2	yes	—
246	C₂₃×#117	C₂³	1	2	yes	—
247	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
250	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
251	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
252	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
253	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
254	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
255	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
256	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
257	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
258	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
259	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
260	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
262	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
263	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
264	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
265	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
266	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
267	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
268	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
269	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
270	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
271	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
272	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
273	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
274	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
275	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
276	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
278	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
279	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
282	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
283	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
284	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
285	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
286	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
287	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
288	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
289	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
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	1	yes	characteristic
294	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
295	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
296	C₂₃×#97	C₂³	1	1	yes	characteristic
297	C₂₃×#97	C₂³	1	1	yes	characteristic
298	C₂₃×#97	C₂³	1	2	yes	—
299	C₂₃×#97	C₂³	1	1	yes	characteristic
300	C₂₃×#97	C₂³	1	1	yes	characteristic
301	C₂₃×#97	C₂³	1	2	yes	—
302	C₂₃×#97	C₂³	1	2	yes	—
303	C₂₃×#97	C₂³	1	2	yes	—
304	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
305	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
306	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
307	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₂₃	C₂³	1	2	yes	—
309	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₂₃	C₂³	1	2	yes	—
312	C₄×C₈×C₂₃	C₂³	1	2	yes	—
313	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
314	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
315	#41×C₂₃	—	4	2	no	—
316	#41×C₂₃	—	4	2	no	—
317	#41×C₂₃	—	4	2	no	—
318	#41×C₂₃	—	4	2	no	—
319	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
320	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
321	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
322	C₂×D₄×C₂₃	—	4	2	no	—
323	C₂×D₄×C₂₃	—	4	2	no	—
324	C₂×D₄×C₂₃	—	4	4	no	—
325	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
326	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
327	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
328	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
329	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
330	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
331	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
332	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
333	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
334	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
335	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
336	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
337	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
338	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
339	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
340	C₂²×C₄×C₂₃	—	4	2	no	—
341	C₂²×C₄×C₂₃	—	4	2	no	—
342	C₂²×C₄×C₂₃	—	4	2	no	—
343	C₂²×C₄×C₂₃	—	4	2	no	—
344	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
345	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
346	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
347	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
348	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
349	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
350	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
351	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
352	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
353	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
354	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
355	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
356	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
357	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
358	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
362	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
363	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
364	M₁₆×C₂₃	—	2	2	no	—
365	M₁₆×C₂₃	—	2	4	no	—
366	M₁₆×C₂₃	—	2	4	no	—
367	M₁₆×C₂₃	—	2	2	no	—
368	M₁₆×C₂₃	—	4	2	no	—
369	M₁₆×C₂₃	—	4	2	no	—
370	M₁₆×C₂₃	—	4	2	no	—
371	M₁₆×C₂₃	—	4	2	no	—
372	M₁₆×C₂₃	—	4	1	no	—
373	M₁₆×C₂₃	—	4	2	no	—
374	M₁₆×C₂₃	—	4	2	no	—
375	M₁₆×C₂₃	—	4	1	no	—
376	M₁₆×C₂₃	—	4	2	no	—
377	C₂×C₈×C₂₃	—	2	2	no	—
378	C₂×C₈×C₂₃	—	2	4	no	—
379	C₂×C₈×C₂₃	—	4	2	no	—
380	C₂×C₈×C₂₃	—	4	1	no	—
381	C₂×C₈×C₂₃	—	4	2	no	—
382	C₂×C₈×C₂₃	—	4	2	no	—
383	C₂×C₈×C₂₃	—	4	2	no	—
384	C₂×C₈×C₂₃	—	4	2	no	—
385	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
386	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
387	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
388	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
391	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
392	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
393	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
397	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
398	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
399	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
400	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
401	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
402	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
403	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
404	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
405	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
406	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
407	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
408	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
409	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
410	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
411	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
412	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
413	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
414	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
415	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
416	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
417	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
418	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
419	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
420	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
421	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
422	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
423	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
424	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
425	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
426	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
427	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
428	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
429	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
430	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
431	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
432	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
433	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
434	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
435	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
436	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
437	C₂²⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
438	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
439	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
440	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
441	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
442	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
443	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
444	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
445	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
446	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
447	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
448	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
449	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
450	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
451	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
452	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
453	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
454	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
455	C₄²×C₂₃	C₂⁴	1	2	yes	—
456	#60324	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
457	C₂³×C₂₃	—	2	4	no	—
458	C₂³×C₂₃	—	4	2	no	—
459	C₂³×C₂₃	—	4	2	no	—
460	C₂³×C₂₃	—	4	2	no	—
461	C₂³×C₂₃	—	4	2	no	—
462	C₂³×C₂₃	—	4	2	no	—
463	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
464	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
465	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
466	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
467	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
468	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
469	Q₈×C₂₃	—	2	2	no	—
470	Q₈×C₂₃	—	4	2	no	—
471	Q₈×C₂₃	—	4	1	no	—
472	D₄×C₂₃	—	2	2	no	—
473	D₄×C₂₃	—	2	4	no	—
474	D₄×C₂₃	—	2	2	no	—
475	D₄×C₂₃	—	2	2	no	—
476	D₄×C₂₃	—	2	2	no	—
477	D₄×C₂₃	—	2	2	no	—
478	D₄×C₂₃	—	4	2	no	—
479	D₄×C₂₃	—	4	2	no	—
480	D₄×C₂₃	—	4	2	no	—
481	D₄×C₂₃	—	4	2	no	—
482	D₄×C₂₃	—	4	2	no	—
483	D₄×C₂₃	—	4	2	no	—
484	D₄×C₂₃	—	4	2	no	—
485	D₄×C₂₃	—	4	1	no	—
486	D₄×C₂₃	—	4	2	no	—
487	C₂×C₄×C₂₃	—	2	2	no	—
488	C₂×C₄×C₂₃	—	2	2	no	—
489	C₂×C₄×C₂₃	—	2	2	no	—
490	C₂×C₄×C₂₃	—	2	2	no	—
491	C₂×C₄×C₂₃	—	2	1	no	—
492	C₂×C₄×C₂₃	—	2	2	no	—
493	C₂×C₄×C₂₃	—	2	1	no	—
494	C₂×C₄×C₂₃	—	2	2	no	—
495	C₂×C₄×C₂₃	—	2	1	no	—
496	C₂×C₄×C₂₃	—	2	2	no	—
497	C₂×C₄×C₂₃	—	2	1	no	—
498	C₂×C₄×C₂₃	—	2	2	no	—
499	C₂×C₄×C₂₃	—	2	1	no	—
500	C₂×C₄×C₂₃	—	2	2	no	—
501	C₂×C₄×C₂₃	—	2	2	no	—
502	C₂×C₄×C₂₃	—	2	1	no	—
503	C₂×C₄×C₂₃	—	4	2	no	—
504	C₂×C₄×C₂₃	—	4	2	no	—
505	C₂×C₄×C₂₃	—	4	2	no	—
506	C₂×C₄×C₂₃	—	4	2	no	—
507	C₂×C₄×C₂₃	—	4	2	no	—
508	C₂×C₄×C₂₃	—	4	2	no	—
509	C₂×C₄×C₂₃	—	4	2	no	—
510	C₂×C₄×C₂₃	—	4	1	no	—
511	C₂×C₄×C₂₃	—	4	1	no	—
512	C₂×C₄×C₂₃	—	4	2	no	—
513	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
514	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
515	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
516	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
517	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
518	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
519	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
520	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
521	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
522	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
523	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
524	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
525	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
526	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
527	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
528	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
529	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
530	C₈×C₂₃	—	2	2	no	—
531	C₈×C₂₃	—	2	1	no	—
532	C₈×C₂₃	—	2	2	no	—
533	C₈×C₂₃	—	2	1	no	—
534	C₈×C₂₃	—	2	2	no	—
535	C₈×C₂₃	—	2	1	no	—
536	C₈×C₂₃	—	2	1	no	—
537	C₈×C₂₃	—	2	2	no	—
538	C₈×C₂₃	—	2	1	no	—
539	C₈×C₂₃	—	2	1	no	—
540	C₈×C₂₃	—	2	1	no	—
541	C₈×C₂₃	H(5,𝔽₂)	1	2	yes	—
542	#3481	C₂×C₂₃	1	1	yes	characteristic
543	#2995	C₂×C₂₃	1	2	yes	complemented
544	#2994	C₂×C₂₃	1	1	yes	characteristic, complemented
545	#2993	C₂×C₂₃	1	1	yes	characteristic, complemented
546	#2990	C₂×C₂₃	1	1	yes	characteristic, complemented
547	#2989	C₂×C₂₃	1	1	yes	characteristic, complemented
548	#2981	C₂×C₂₃	1	1	yes	characteristic, complemented
549	#2978	C₂×C₂₃	1	2	yes	complemented
550	#2976	C₂×C₂₃	1	2	yes	complemented
551	#2975	C₂×C₂₃	1	1	yes	characteristic, complemented
552	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
553	#2973	C₂×C₂₃	1	2	yes	complemented
554	#2971	C₂×C₂₃	1	1	yes	characteristic, complemented
555	#2969	C₂×C₂₃	1	1	yes	characteristic, complemented
556	#2967	C₂×C₂₃	1	2	yes	complemented
557	#2966	C₂×C₂₃	1	1	yes	characteristic, complemented
558	#2965	C₂×C₂₃	1	1	yes	characteristic, complemented
559	#2935	C₂×C₂₃	1	1	yes	characteristic, complemented
560	D₄×M₁₆	C₂×C₂₃	1	2	yes	complemented
561	D₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
562	#2933	C₂×C₂₃	1	2	yes	complemented
563	#2930	C₂×C₂₃	1	2	yes	complemented
564	C₂×#436	C₂×C₂₃	1	1	yes	characteristic, complemented
565	C₂²×C₂₃	—	2	1	no	—
566	C₂²×C₂₃	—	2	1	no	—
567	C₂²×C₂₃	—	2	1	no	—
568	C₂²×C₂₃	—	2	2	no	—
569	C₂²×C₂₃	—	2	2	no	—
570	C₂²×C₂₃	—	2	2	no	—
571	C₂²×C₂₃	—	2	1	no	—
572	C₂²×C₂₃	—	2	1	no	—
573	C₂²×C₂₃	—	2	1	no	—
574	C₂²×C₂₃	—	2	1	no	—
575	C₂²×C₂₃	—	2	2	no	—
576	C₂²×C₂₃	—	2	1	no	—
577	C₂²×C₂₃	—	2	2	no	—
578	C₂²×C₂₃	—	2	2	no	—
579	C₂²×C₂₃	—	2	2	no	—
580	C₂²×C₂₃	—	2	2	no	—
581	C₂²×C₂₃	—	2	2	no	—
582	C₂²×C₂₃	—	8	4	no	—
583	C₂²×C₂₃	—	8	4	no	—
584	C₂²×C₂₃	#568	1	2	yes	—
585	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
586	C₄×C₂₃	—	2	1	no	—
587	C₄×C₂₃	—	2	2	no	—
588	C₄×C₂₃	—	2	1	no	—
589	C₄×C₂₃	—	2	2	no	—
590	C₄×C₂₃	—	2	2	no	—
591	C₄×C₂₃	—	2	1	no	—
592	C₄×C₂₃	—	2	1	no	—
593	C₄×C₂₃	—	2	1	no	—
594	C₄×C₂₃	—	2	1	no	—
595	C₄×C₂₃	—	2	1	no	—
596	C₄×C₂₃	—	2	1	no	—
597	C₄×C₂₃	—	2	1	no	—
598	C₄×C₂₃	—	2	2	no	—
599	C₄×C₂₃	—	2	1	no	—
600	C₄×C₂₃	—	2	2	no	—
601	C₄×C₂₃	#568	1	2	yes	—
602	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
603	C₄×C₂₃	#585	1	1	yes	characteristic
604	C₂×#131	C₂²×C₂₃	1	2	yes	complemented
605	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	complemented
606	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	complemented
607	#559	C₄×C₂₃	1	1	yes	characteristic
608	#554	C₄×C₂₃	1	1	yes	characteristic
609	#554	C₄×C₂₃	1	1	yes	characteristic
610	#553	C₄×C₂₃	1	1	yes	characteristic
611	#553	C₄×C₂₃	1	1	yes	characteristic
612	#553	C₄×C₂₃	1	2	yes	—
613	#551	C₄×C₂₃	1	2	yes	—
614	#551	C₄×C₂₃	1	2	yes	—
615	#546	C₄×C₂₃	1	2	yes	—
616	#546	C₄×C₂₃	1	1	yes	characteristic
617	#546	C₄×C₂₃	1	1	yes	characteristic
618	D₄²	C₄×C₂₃	1	1	yes	characteristic
619	#532	C₂²×C₂₃	1	1	yes	characteristic
620	#529	C₂²×C₂₃	1	1	yes	characteristic
621	#529	C₂²×C₂₃	1	2	yes	—
622	#529	C₂²×C₂₃	1	1	yes	characteristic
623	#525	C₂²×C₂₃	1	2	yes	—
624	#525	C₂²×C₂₃	1	2	yes	—
625	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
626	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
627	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
628	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
629	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
630	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
631	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
632	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
633	#446	C₂²×C₂₃	1	2	yes	complemented
634	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
635	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
636	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
637	#436	C₂²×C₂₃	1	1	yes	characteristic
638	#436	C₂²×C₂₃	1	1	yes	characteristic
639	#436	C₂²×C₂₃	1	1	yes	characteristic
640	#436	C₂²×C₂₃	1	1	yes	characteristic
641	#436	C₂²×C₂₃	1	2	yes	complemented
642	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
643	#436	C₂²×C₂₃	1	2	yes	complemented
644	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
645	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
646	#436	C₂²×C₂₃	1	2	yes	complemented
647	#436	C₂²×C₂₃	1	2	yes	complemented
648	#436	C₂²×C₂₃	1	2	yes	complemented
649	#436	C₂²×C₂₃	1	2	yes	complemented
650	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
651	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
652	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
653	#436	C₂²×C₂₃	1	2	yes	complemented
654	#436	C₂²×C₂₃	1	2	yes	complemented
655	#435	C₂²×C₂₃	1	1	yes	characteristic
656	#435	C₂²×C₂₃	1	2	yes	—
657	#435	C₂²×C₂₃	1	1	yes	characteristic
658	#435	C₂²×C₂₃	1	2	yes	complemented
659	#435	C₂²×C₂₃	1	2	yes	complemented
660	#435	C₂²×C₂₃	1	2	yes	complemented
661	#435	C₂²×C₂₃	1	2	yes	complemented
662	#435	C₂²×C₂₃	1	1	yes	characteristic, complemented
663	#435	C₂²×C₂₃	1	2	yes	complemented
664	#435	C₂²×C₂₃	1	2	yes	complemented
665	#435	C₂²×C₂₃	1	2	yes	complemented
666	#435	C₂²×C₂₃	1	2	yes	complemented
667	#435	C₂²×C₂₃	1	2	yes	complemented
668	#435	C₂²×C₂₃	1	2	yes	complemented
669	#435	C₂²×C₂₃	1	2	yes	complemented
670	#435	C₂²×C₂₃	1	1	yes	characteristic, complemented
671	#435	C₂²×C₂₃	1	2	yes	complemented
672	#435	C₂²×C₂₃	1	2	yes	complemented
673	#435	C₂²×C₂₃	1	2	yes	complemented
674	#435	C₂²×C₂₃	1	2	yes	complemented
675	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
676	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
677	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
678	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
679	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
680	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
681	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
682	#433	C₂²×C₂₃	1	2	yes	complemented
683	#433	C₂²×C₂₃	1	2	yes	complemented
684	#433	C₂²×C₂₃	1	2	yes	complemented
685	#433	C₂²×C₂₃	1	2	yes	complemented
686	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
687	#432	C₂²×C₂₃	1	2	yes	complemented
688	#432	C₂²×C₂₃	1	2	yes	complemented
689	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
690	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
691	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
692	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
693	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
694	#424	C₂²×C₂₃	1	2	yes	complemented
695	#424	C₂²×C₂₃	1	2	yes	complemented
696	#423	C₂²×C₂₃	1	2	yes	complemented
697	#423	C₂²×C₂₃	1	1	yes	characteristic, complemented
698	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
699	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
700	#408	C₂²×C₂₃	1	2	yes	complemented
701	#408	C₂²×C₂₃	1	2	yes	complemented
702	#408	C₂²×C₂₃	1	2	yes	complemented
703	#407	C₂²×C₂₃	1	2	yes	complemented
704	#407	C₂²×C₂₃	1	2	yes	complemented
705	#407	C₂²×C₂₃	1	2	yes	complemented
706	#407	C₂²×C₂₃	1	2	yes	complemented
707	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
708	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
709	#405	C₂²×C₂₃	1	2	yes	complemented
710	#405	C₂²×C₂₃	1	2	yes	complemented
711	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
712	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
713	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
714	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
715	C₂×C₂₃	—	2	2	no	—
716	C₂×C₂₃	—	4	1	no	—
717	C₂×C₂₃	—	4	2	no	—
718	C₂×C₂₃	—	4	2	no	—
719	C₂×C₂₃	—	4	1	no	—
720	C₂×C₂₃	—	4	2	no	—
721	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
722	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
723	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
724	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
725	C₂×#41	C₂×C₄×C₂₃	1	1	yes	characteristic
726	C₂×#41	C₂³×C₂₃	1	2	yes	—
727	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
728	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
729	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
730	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
731	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
732	#131	—	4	4	no	—
733	C₂×M₁₆	—	4	4	no	—
734	C₂×M₁₆	—	4	4	no	—
735	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
736	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
737	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
738	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
739	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
740	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
741	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
742	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
743	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
744	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
745	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
746	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
747	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
748	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
749	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
750	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
751	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
752	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
753	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
754	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
755	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
756	C₄⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
757	#127	C₂×C₄×C₂₃	1	1	yes	characteristic
758	#126	C₂×C₄×C₂₃	1	2	yes	—
759	#126	C₂×C₄×C₂₃	1	2	yes	—
760	#126	C₂×C₄×C₂₃	1	2	yes	—
761	#126	C₂×C₄×C₂₃	1	2	yes	—
762	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
763	#125	C₂×C₄×C₂₃	1	2	yes	—
764	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
765	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
766	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
767	#124	C₂×C₄×C₂₃	1	2	yes	—
768	#124	C₂×C₄×C₂₃	1	2	yes	—
769	#123	C₂×C₄×C₂₃	1	2	yes	—
770	#123	C₂×C₄×C₂₃	1	2	yes	—
771	#123	C₂×C₄×C₂₃	1	2	yes	—
772	#123	C₂×C₄×C₂₃	1	2	yes	—
773	#123	C₂×C₄×C₂₃	1	2	yes	—
774	#123	C₂×C₄×C₂₃	1	2	yes	—
775	#123	C₂×C₄×C₂₃	1	2	yes	—
776	#123	C₂×C₄×C₂₃	1	2	yes	—
777	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
778	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
779	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
780	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
781	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
782	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
783	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
784	#121	C₂×C₄×C₂₃	1	2	yes	—
785	#121	C₂×C₄×C₂₃	1	2	yes	—
786	#121	C₂×C₄×C₂₃	1	2	yes	—
787	#121	C₂×C₄×C₂₃	1	2	yes	—
788	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
789	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
790	#121	C₂×C₄×C₂₃	1	2	yes	—
791	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
792	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
793	#121	C₂×C₄×C₂₃	1	2	yes	—
794	#120	C₂×C₄×C₂₃	1	2	yes	—
795	#120	C₂×C₄×C₂₃	1	2	yes	—
796	#120	C₂×C₄×C₂₃	1	2	yes	—
797	#120	C₂×C₄×C₂₃	1	2	yes	—
798	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
799	C₄×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
800	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
802	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
803	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
804	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
805	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
806	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
807	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
808	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
809	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
810	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
811	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
812	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
813	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
814	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
815	C₄×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
816	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
817	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
818	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
819	C₄×D₄	C₂³×C₂₃	1	2	yes	—
820	C₄×D₄	C₂³×C₂₃	1	2	yes	—
821	C₄×D₄	C₂³×C₂₃	1	2	yes	—
822	C₄×D₄	C₂³×C₂₃	1	2	yes	—
823	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
824	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
825	C₄×D₄	C₂³×C₂₃	1	2	yes	—
826	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
827	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
828	C₄×D₄	C₂³×C₂₃	1	2	yes	—
829	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
830	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
831	#117	C₂×C₄×C₂₃	1	2	yes	—
832	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
833	#117	C₂×C₄×C₂₃	1	1	yes	characteristic
834	#117	C₂³×C₂₃	1	2	yes	—
835	#117	C₂³×C₂₃	1	2	yes	—
836	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
837	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
838	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
839	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
840	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
841	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
842	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
843	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
844	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
845	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
846	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
847	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
848	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
849	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
850	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
851	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
852	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
853	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
854	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
855	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
856	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
857	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
858	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
859	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
861	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
863	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
864	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
865	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
866	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
867	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
868	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
869	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
870	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
871	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
872	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
873	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
874	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
875	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
876	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
877	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
878	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
879	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
880	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
881	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
882	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
883	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
884	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
885	#97	C₂³×C₂₃	1	1	yes	characteristic
886	#97	C₂³×C₂₃	1	1	yes	characteristic
887	#97	C₂³×C₂₃	1	2	yes	—
888	#97	C₂³×C₂₃	1	1	yes	characteristic
889	#97	C₂³×C₂₃	1	1	yes	characteristic
890	#97	C₂³×C₂₃	1	2	yes	—
891	#97	C₂³×C₂₃	1	2	yes	—
892	#97	C₂³×C₂₃	1	2	yes	—
893	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
894	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
895	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
896	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
897	C₄×C₈	C₂³×C₂₃	1	2	yes	—
898	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
899	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
900	C₄×C₈	C₂³×C₂₃	1	2	yes	—
901	C₄×C₈	C₂³×C₂₃	1	2	yes	—
902	C₂₃	#60324	1	1	yes	characteristic, direct product factor, Sylow
903	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
904	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
905	#41	—	4	2	no	—
906	#41	—	4	2	no	—
907	#41	—	4	2	no	—
908	#41	—	4	2	no	—
909	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
910	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
911	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
912	C₂×D₄	—	4	2	no	—
913	C₂×D₄	—	4	2	no	—
914	C₂×D₄	—	4	4	no	—
915	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
916	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
917	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
918	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
919	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
920	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
921	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
922	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
923	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
924	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
925	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
926	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
927	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
928	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
929	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
930	C₂²×C₄	—	4	2	no	—
931	C₂²×C₄	—	4	2	no	—
932	C₂²×C₄	—	4	2	no	—
933	C₂²×C₄	—	4	2	no	—
934	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
935	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
936	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
937	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
938	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
939	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
940	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
941	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
942	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
943	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
944	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
945	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
946	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
947	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
948	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
949	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
950	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
951	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
952	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
953	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
954	M₁₆	—	2	2	no	—
955	M₁₆	—	2	4	no	—
956	M₁₆	—	2	4	no	—
957	M₁₆	—	2	2	no	—
958	M₁₆	—	4	2	no	—
959	M₁₆	—	4	2	no	—
960	M₁₆	—	4	2	no	—
961	M₁₆	—	4	2	no	—
962	M₁₆	—	4	2	no	—
963	M₁₆	—	4	1	no	—
964	M₁₆	—	4	2	no	—
965	M₁₆	—	4	2	no	—
966	M₁₆	—	4	1	no	—
967	C₂×C₈	—	2	2	no	—
968	C₂×C₈	—	2	4	no	—
969	C₂×C₈	—	4	2	no	—
970	C₂×C₈	—	4	2	no	—
971	C₂×C₈	—	4	2	no	—
972	C₂×C₈	—	4	2	no	—
973	C₂×C₈	—	4	2	no	—
974	C₂×C₈	—	4	1	no	—
975	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
976	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
977	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
978	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
979	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
980	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
981	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
982	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
983	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
984	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
985	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
986	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
987	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
988	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
989	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
990	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
991	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
992	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
993	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
994	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
995	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
996	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
997	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
998	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
999	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1000	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1001	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1002	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1003	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1004	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1005	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1006	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1007	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1008	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1009	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1010	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1011	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1012	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1013	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1014	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1015	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1016	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1017	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1018	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1019	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1020	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1021	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1022	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1023	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1024	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1025	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1026	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1027	C₂²⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
1028	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1029	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1030	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1031	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1032	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
1033	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
1034	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
1035	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
1036	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
1037	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
1038	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
1039	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
1040	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
1041	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1042	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1043	C₄²	C₂⁴×C₂₃	1	2	yes	—
1044	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1045	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
1046	C₂³	—	2	4	no	—
1047	C₂³	—	4	2	no	—
1048	C₂³	—	4	2	no	—
1049	C₂³	—	4	2	no	—
1050	C₂³	—	4	2	no	—
1051	C₂³	—	4	2	no	—
1052	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1053	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1054	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
1055	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
1056	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
1057	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
1058	Q₈	—	2	2	no	—
1059	Q₈	—	4	2	no	—
1060	Q₈	—	4	1	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	4	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	2	no	—
1065	D₄	—	2	2	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	4	2	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	4	1	no	—
1075	D₄	—	4	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	2	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	4	2	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	1	no	—
1100	C₂×C₄	—	4	1	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1103	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1104	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1105	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1106	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1107	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1108	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1109	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1110	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1111	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1112	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1113	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1114	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1115	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1116	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
1117	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
1118	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1119	C₈	—	2	2	no	—
1120	C₈	—	2	1	no	—
1121	C₈	—	2	2	no	—
1122	C₈	—	2	1	no	—
1123	C₈	—	2	2	no	—
1124	C₈	—	2	1	no	—
1125	C₈	—	2	1	no	—
1126	C₈	—	2	2	no	—
1127	C₈	—	2	1	no	—
1128	C₈	—	2	1	no	—
1129	C₈	—	2	1	no	—
1130	C₈	C₂₃×H(5,𝔽₂)	1	2	yes	—
1131	C₂²	—	2	1	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	1	no	—
1134	C₂²	—	2	2	no	—
1135	C₂²	—	2	2	no	—
1136	C₂²	—	2	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	1	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	1	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	2	2	no	—
1146	C₂²	—	2	2	no	—
1147	C₂²	—	2	2	no	—
1148	C₂²	—	8	4	no	—
1149	C₂²	—	8	4	no	—
1150	C₂²	C₂₃×#568	1	2	yes	—
1151	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
1152	C₄	—	2	1	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	2	2	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	1	no	—
1161	C₄	—	2	1	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	2	1	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	2	1	no	—
1166	C₄	—	2	2	no	—
1167	C₄	C₂₃×#568	1	2	yes	—
1168	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1169	C₄	C₂₃×#585	1	1	yes	characteristic
1170	C₂	—	2	2	no	—
1171	C₂	—	4	1	no	—
1172	C₂	—	4	2	no	—
1173	C₂	—	4	2	no	—
1174	C₂	—	4	2	no	—
1175	C₂	—	4	1	no	—
1176	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1177	C₂	C₂×C₂₃×#568	1	1	yes	characteristic
1178	C₂	C₂×C₂₃×#568	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	C₂₃×#3481	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×#2995	C₂	semidirect
3. C₂₃×#2994	C₂	semidirect
4. C₂₃×#2993	C₂	semidirect
5. C₂₃×#2990	C₂	semidirect
6. C₂₃×#2989	C₂	semidirect
7. C₂₃×#2981	C₂	semidirect
8. C₂₃×#2978	C₂	semidirect
9. C₂₃×#2976	C₂	semidirect
10. C₂₃×#2975	C₂	semidirect
11. C₂₃×#2974	C₂	semidirect
12. C₂₃×#2973	C₂	semidirect
13. C₂₃×#2971	C₂	semidirect
14. C₂₃×#2969	C₂	semidirect
15. C₂₃×#2967	C₂	semidirect
16. C₂₃×#2966	C₂	semidirect
17. C₂₃×#2965	C₂	semidirect
18. C₂₃×#2935	C₂	semidirect
19. D₄×M₁₆×C₂₃	C₂	semidirect
20. D₄×M₁₆×C₂₃	C₂	semidirect
21. C₂₃×#2933	C₂	semidirect
22. C₂₃×#2930	C₂	semidirect
23. C₂×C₂₃×#436	C₂	semidirect
24. C₂×C₂₃×#131	C₂²	semidirect
25. C₂²×M₁₆×C₂₃	C₂²	semidirect
26. C₂²×M₁₆×C₂₃	C₂²	semidirect
50. C₂₃×#446	C₂²	semidirect
51. C₂₃×#446	C₂²	semidirect
52. C₂₃×#446	C₂²	semidirect
53. C₂₃×#446	C₂²	semidirect
54. C₂₃×#446	C₂²	semidirect
55. C₈×Q₈×C₂₃	C₂²	semidirect
56. C₈×Q₈×C₂₃	C₂²	semidirect
61. C₂₃×#436	C₂²	semidirect
62. C₂₃×#436	C₂²	semidirect
63. C₂₃×#436	C₂²	semidirect
64. C₂₃×#436	C₂²	semidirect
65. C₂₃×#436	C₂²	semidirect
66. C₂₃×#436	C₂²	semidirect
67. C₂₃×#436	C₂²	semidirect
68. C₂₃×#436	C₂²	semidirect
69. C₂₃×#436	C₂²	semidirect
70. C₂₃×#436	C₂²	semidirect
71. C₂₃×#436	C₂²	semidirect
72. C₂₃×#436	C₂²	semidirect
73. C₂₃×#436	C₂²	semidirect
74. C₂₃×#436	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. C₂₃×#435	C₂²	semidirect
86. C₂₃×#435	C₂²	semidirect
87. C₂₃×#435	C₂²	semidirect
88. C₂₃×#435	C₂²	semidirect
89. C₂₃×#435	C₂²	semidirect
90. C₂₃×#435	C₂²	semidirect
91. C₂₃×#435	C₂²	semidirect
92. C₂₃×#435	C₂²	semidirect
93. C₂₃×#435	C₂²	semidirect
94. C₂₃×#435	C₂²	semidirect
95. C₈×D₄×C₂₃	C₂²	semidirect
96. C₈×D₄×C₂₃	C₂²	semidirect
97. C₈×D₄×C₂₃	C₂²	semidirect
98. C₈×D₄×C₂₃	C₂²	semidirect
99. C₈×D₄×C₂₃	C₂²	semidirect
100. C₈×D₄×C₂₃	C₂²	semidirect
101. C₈×D₄×C₂₃	C₂²	semidirect
102. C₂₃×#433	C₂²	semidirect
103. C₂₃×#433	C₂²	semidirect
104. C₂₃×#433	C₂²	semidirect
105. C₂₃×#433	C₂²	semidirect
106. C₂₃×#432	C₂²	semidirect
107. C₂₃×#432	C₂²	semidirect
108. C₂₃×#432	C₂²	semidirect
109. C₂₃×#432	C₂²	semidirect
110. C₂₃×#431	C₂²	semidirect
111. C₂₃×#431	C₂²	semidirect
112. C₂₃×#431	C₂²	semidirect
113. C₂₃×#431	C₂²	semidirect
114. C₂₃×#424	C₂²	semidirect
115. C₂₃×#424	C₂²	semidirect
116. C₂₃×#423	C₂²	semidirect
117. C₂₃×#423	C₂²	semidirect
118. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
119. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
120. C₂₃×#408	C₂²	semidirect
121. C₂₃×#408	C₂²	semidirect
122. C₂₃×#408	C₂²	semidirect
123. C₂₃×#407	C₂²	semidirect
124. C₂₃×#407	C₂²	semidirect
125. C₂₃×#407	C₂²	semidirect
126. C₂₃×#407	C₂²	semidirect
127. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
128. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
129. C₂₃×#405	C₂²	semidirect
130. C₂₃×#405	C₂²	semidirect
131. C₄×M₁₆×C₂₃	C₂²	semidirect
132. C₄×M₁₆×C₂₃	C₂²	semidirect
133. C₄×M₁₆×C₂₃	C₂²	semidirect
134. C₂×C₄×C₈×C₂₃	C₂²	semidirect
456. #60324	C₂₃	direct (N × H)
543. #2995	C₂×C₂₃	semidirect
544. #2994	C₂×C₂₃	semidirect
545. #2993	C₂×C₂₃	semidirect
546. #2990	C₂×C₂₃	semidirect
547. #2989	C₂×C₂₃	semidirect
548. #2981	C₂×C₂₃	semidirect
549. #2978	C₂×C₂₃	semidirect
550. #2976	C₂×C₂₃	semidirect
551. #2975	C₂×C₂₃	semidirect
552. #2974	C₂×C₂₃	semidirect
553. #2973	C₂×C₂₃	semidirect
554. #2971	C₂×C₂₃	semidirect
555. #2969	C₂×C₂₃	semidirect
556. #2967	C₂×C₂₃	semidirect
557. #2966	C₂×C₂₃	semidirect
558. #2965	C₂×C₂₃	semidirect
559. #2935	C₂×C₂₃	semidirect
560. D₄×M₁₆	C₂×C₂₃	semidirect
561. D₄×M₁₆	C₂×C₂₃	semidirect
562. #2933	C₂×C₂₃	semidirect
563. #2930	C₂×C₂₃	semidirect
564. C₂×#436	C₂×C₂₃	semidirect
604. C₂×#131	C₂²×C₂₃	semidirect
605. C₂²×M₁₆	C₂²×C₂₃	semidirect
606. C₂²×M₁₆	C₂²×C₂₃	semidirect
630. #446	C₂²×C₂₃	semidirect
631. #446	C₂²×C₂₃	semidirect
632. #446	C₂²×C₂₃	semidirect
633. #446	C₂²×C₂₃	semidirect
634. #446	C₂²×C₂₃	semidirect
635. C₈×Q₈	C₂²×C₂₃	semidirect
636. C₈×Q₈	C₂²×C₂₃	semidirect
641. #436	C₂²×C₂₃	semidirect
642. #436	C₂²×C₂₃	semidirect
643. #436	C₂²×C₂₃	semidirect
644. #436	C₂²×C₂₃	semidirect
645. #436	C₂²×C₂₃	semidirect
646. #436	C₂²×C₂₃	semidirect
647. #436	C₂²×C₂₃	semidirect
648. #436	C₂²×C₂₃	semidirect
649. #436	C₂²×C₂₃	semidirect
650. #436	C₂²×C₂₃	semidirect
651. #436	C₂²×C₂₃	semidirect
652. #436	C₂²×C₂₃	semidirect
653. #436	C₂²×C₂₃	semidirect
654. #436	C₂²×C₂₃	semidirect
658. #435	C₂²×C₂₃	semidirect
659. #435	C₂²×C₂₃	semidirect
660. #435	C₂²×C₂₃	semidirect
661. #435	C₂²×C₂₃	semidirect
662. #435	C₂²×C₂₃	semidirect
663. #435	C₂²×C₂₃	semidirect
664. #435	C₂²×C₂₃	semidirect
665. #435	C₂²×C₂₃	semidirect
666. #435	C₂²×C₂₃	semidirect
667. #435	C₂²×C₂₃	semidirect
668. #435	C₂²×C₂₃	semidirect
669. #435	C₂²×C₂₃	semidirect
670. #435	C₂²×C₂₃	semidirect
671. #435	C₂²×C₂₃	semidirect
672. #435	C₂²×C₂₃	semidirect
673. #435	C₂²×C₂₃	semidirect
674. #435	C₂²×C₂₃	semidirect
675. C₈×D₄	C₂²×C₂₃	semidirect
676. C₈×D₄	C₂²×C₂₃	semidirect
677. C₈×D₄	C₂²×C₂₃	semidirect
678. C₈×D₄	C₂²×C₂₃	semidirect
679. C₈×D₄	C₂²×C₂₃	semidirect
680. C₈×D₄	C₂²×C₂₃	semidirect
681. C₈×D₄	C₂²×C₂₃	semidirect
682. #433	C₂²×C₂₃	semidirect
683. #433	C₂²×C₂₃	semidirect
684. #433	C₂²×C₂₃	semidirect
685. #433	C₂²×C₂₃	semidirect
686. #432	C₂²×C₂₃	semidirect
687. #432	C₂²×C₂₃	semidirect
688. #432	C₂²×C₂₃	semidirect
689. #432	C₂²×C₂₃	semidirect
690. #431	C₂²×C₂₃	semidirect
691. #431	C₂²×C₂₃	semidirect
692. #431	C₂²×C₂₃	semidirect
693. #431	C₂²×C₂₃	semidirect
694. #424	C₂²×C₂₃	semidirect
695. #424	C₂²×C₂₃	semidirect
696. #423	C₂²×C₂₃	semidirect
697. #423	C₂²×C₂₃	semidirect
698. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
699. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
700. #408	C₂²×C₂₃	semidirect
701. #408	C₂²×C₂₃	semidirect
702. #408	C₂²×C₂₃	semidirect
703. #407	C₂²×C₂₃	semidirect
704. #407	C₂²×C₂₃	semidirect
705. #407	C₂²×C₂₃	semidirect
706. #407	C₂²×C₂₃	semidirect
707. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
708. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
709. #405	C₂²×C₂₃	semidirect
710. #405	C₂²×C₂₃	semidirect
711. C₄×M₁₆	C₂²×C₂₃	semidirect
712. C₄×M₁₆	C₂²×C₂₃	semidirect
713. C₄×M₁₆	C₂²×C₂₃	semidirect
714. C₂×C₄×C₈	C₂²×C₂₃	semidirect
902. C₂₃	#60324	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3481	2
C₂₃×#2995	2
C₂₃×#2994	2
C₂₃×#2993	2
C₂₃×#2990	2
C₂₃×#2989	2
C₂₃×#2981	2
C₂₃×#2978	2
C₂₃×#2976	2
C₂₃×#2975	2
C₂₃×#2974	2
C₂₃×#2973	2
C₂₃×#2971	2
C₂₃×#2969	2
C₂₃×#2967	2
C₂₃×#2966	2
C₂₃×#2965	2
C₂₃×#2935	2
D₄×M₁₆×C₂₃	2
C₂₃×#2933	2
C₂₃×#2930	2
C₂×C₂₃×#436	2
#60324	23

Subgroups — C23×#60324 #19207950

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60324 #19207950