Subgroups — C₂₃×#60322 #19207948

Order 5888.

1858 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3459	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2995	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2993	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2992	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2992	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2978	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2977	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2976	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2974	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2973	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2969	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2967	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
15	D₄×M₁₆×C₂₃	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2933	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2933	C₂	1	2	yes	maximal, complemented
18	C₂₃×#2930	C₂	1	2	yes	maximal, complemented
19	C₂×C₂₃×#436	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₂₃×#131	C₂²	1	2	yes	complemented
21	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
23	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	complemented
24	C₂₃×#543	C₄	1	1	yes	characteristic
25	C₂₃×#539	C₄	1	2	yes	—
26	C₂₃×#539	C₄	1	2	yes	—
27	C₂₃×#539	C₄	1	2	yes	—
28	C₂₃×#538	C₄	1	1	yes	characteristic
29	C₂₃×#538	C₄	1	1	yes	characteristic
30	C₂₃×#538	C₄	1	2	yes	—
31	C₂₃×#538	C₄	1	2	yes	—
32	C₂₃×#534	C₄	1	1	yes	characteristic
33	C₂₃×#534	C₄	1	2	yes	—
34	C₂₃×#529	C₂²	1	1	yes	characteristic
35	C₂₃×#529	C₂²	1	1	yes	characteristic
36	C₂₃×#529	C₂²	1	2	yes	—
37	C₂₃×#529	C₂²	1	2	yes	—
38	C₂₃×#525	C₂²	1	2	yes	—
39	C₂₃×#525	C₂²	1	2	yes	—
40	C₂₃×#525	C₂²	1	2	yes	—
41	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
43	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
44	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#446	C₂²	1	2	yes	complemented
46	C₂₃×#446	C₂²	1	2	yes	complemented
47	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
48	C₈×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#436	C₂²	1	2	yes	complemented
50	C₂₃×#436	C₂²	1	2	yes	complemented
51	C₂₃×#436	C₂²	1	2	yes	complemented
52	C₂₃×#436	C₂²	1	2	yes	complemented
53	C₂₃×#436	C₂²	1	1	yes	characteristic, complemented
54	C₂₃×#436	C₂²	1	2	yes	complemented
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	1	yes	characteristic, complemented
60	C₂₃×#436	C₂²	1	2	yes	complemented
61	C₂₃×#435	C₂²	1	2	yes	complemented
62	C₂₃×#435	C₂²	1	2	yes	complemented
63	C₂₃×#435	C₂²	1	2	yes	complemented
64	C₂₃×#435	C₂²	1	2	yes	complemented
65	C₂₃×#435	C₂²	1	2	yes	complemented
66	C₂₃×#435	C₂²	1	2	yes	complemented
67	C₂₃×#435	C₂²	1	2	yes	complemented
68	C₂₃×#435	C₂²	1	2	yes	complemented
69	C₂₃×#435	C₂²	1	2	yes	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	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
80	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
81	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
82	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
83	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
84	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
85	C₈×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
86	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
87	C₂₃×#433	C₂²	1	2	yes	complemented
88	C₂₃×#433	C₂²	1	2	yes	complemented
89	C₂₃×#433	C₂²	1	2	yes	complemented
90	C₂₃×#433	C₂²	1	2	yes	complemented
91	C₂₃×#433	C₂²	1	2	yes	complemented
92	C₂₃×#433	C₂²	1	2	yes	complemented
93	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
94	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
95	C₂₃×#432	C₂²	1	2	yes	complemented
96	C₂₃×#431	C₂²	1	2	yes	complemented
97	C₂₃×#424	C₂²	1	2	yes	complemented
98	C₂₃×#424	C₂²	1	2	yes	complemented
99	C₂₃×#424	C₂²	1	2	yes	complemented
100	C₂₃×#423	C₂²	1	2	yes	complemented
101	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
102	C₂₃×#408	C₂²	1	2	yes	complemented
103	C₂₃×#408	C₂²	1	2	yes	complemented
104	C₂₃×#408	C₂²	1	2	yes	complemented
105	C₂₃×#407	C₂²	1	2	yes	—
106	C₂₃×#407	C₂²	1	2	yes	complemented
107	C₂₃×#407	C₂²	1	2	yes	complemented
108	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
109	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
111	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
112	C₂₃×#405	C₂²	1	2	yes	complemented
113	C₂₃×#405	C₂²	1	2	yes	complemented
114	C₂₃×#405	C₂²	1	2	yes	complemented
115	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
116	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
117	C₂×#41×C₂₃	C₂³	1	2	yes	—
118	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
119	C₂²×D₄×C₂₃	C₂×C₄	1	2	yes	—
120	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
123	C₂₃×#131	—	4	4	no	—
124	C₂×M₁₆×C₂₃	—	4	2	no	—
125	C₂×M₁₆×C₂₃	—	4	2	no	—
126	C₂×M₁₆×C₂₃	—	4	4	no	—
127	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
128	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
129	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
130	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
131	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
132	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
133	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
134	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
135	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
136	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
137	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
138	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
139	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
142	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
143	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
144	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
145	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
146	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
147	C₂₃×#126	C₂×C₄	1	2	yes	—
148	C₂₃×#126	C₂×C₄	1	2	yes	—
149	C₂₃×#126	C₂×C₄	1	2	yes	—
150	C₂₃×#126	C₂×C₄	1	2	yes	—
151	C₂₃×#126	C₂×C₄	1	2	yes	—
152	C₂₃×#126	C₂×C₄	1	2	yes	—
153	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
154	C₂₃×#125	C₂×C₄	1	1	yes	characteristic
155	C₂₃×#125	C₂×C₄	1	2	yes	—
156	C₂₃×#125	C₂×C₄	1	2	yes	—
157	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
158	C₂₃×#124	C₂×C₄	1	1	yes	characteristic
159	C₂₃×#124	C₂×C₄	1	2	yes	—
160	C₂₃×#124	C₂×C₄	1	2	yes	—
161	C₂₃×#123	C₂×C₄	1	2	yes	—
162	C₂₃×#123	C₂×C₄	1	2	yes	—
163	C₂₃×#123	C₂×C₄	1	2	yes	—
164	C₂₃×#123	C₂×C₄	1	2	yes	—
165	C₂₃×#123	C₂×C₄	1	2	yes	—
166	C₂₃×#123	C₂×C₄	1	2	yes	—
167	C₂₃×#123	C₂×C₄	1	2	yes	—
168	C₂₃×#123	C₂×C₄	1	2	yes	—
169	C₂₃×#123	C₂×C₄	1	2	yes	—
170	C₂₃×#123	C₂×C₄	1	2	yes	—
171	C₂₃×#123	C₂×C₄	1	2	yes	—
172	C₂₃×#123	C₂×C₄	1	2	yes	—
173	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
174	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
175	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
176	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
177	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
178	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
179	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
180	C₂₃×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
181	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
182	C₂₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
183	C₂₃×#121	C₂×C₄	1	2	yes	—
184	C₂₃×#121	C₂×C₄	1	2	yes	—
185	C₂₃×#121	C₂×C₄	1	2	yes	—
186	C₂₃×#121	C₂×C₄	1	2	yes	—
187	C₂₃×#121	C₂×C₄	1	2	yes	—
188	C₂₃×#121	C₂×C₄	1	2	yes	—
189	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
190	C₂₃×#121	C₂×C₄	1	1	yes	characteristic
191	C₂₃×#121	C₂×C₄	1	2	yes	—
192	C₂₃×#121	C₂×C₄	1	2	yes	—
193	C₂₃×#120	C₂×C₄	1	2	yes	—
194	C₂₃×#120	C₂×C₄	1	2	yes	—
195	C₂₃×#120	C₂×C₄	1	2	yes	—
196	C₂₃×#120	C₂×C₄	1	2	yes	—
197	C₂₃×#120	C₂×C₄	1	2	yes	—
198	C₂₃×#120	C₂×C₄	1	2	yes	—
199	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
200	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
201	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
202	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
203	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
204	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
205	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
206	C₄×D₄×C₂₃	C₂×C₄	1	2	yes	—
207	C₄×D₄×C₂₃	C₂³	1	2	yes	—
208	C₄×D₄×C₂₃	C₂³	1	2	yes	—
209	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
210	C₄×D₄×C₂₃	C₂³	1	2	yes	—
211	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
212	C₄×D₄×C₂₃	C₂³	1	2	yes	—
213	C₄×D₄×C₂₃	C₂³	1	2	yes	—
214	C₄×D₄×C₂₃	C₂³	1	2	yes	—
215	C₄×D₄×C₂₃	C₂³	1	2	yes	—
216	C₄×D₄×C₂₃	C₂³	1	2	yes	—
217	C₂₃×#117	C₂³	1	2	yes	—
218	C₂₃×#117	C₂³	1	2	yes	—
219	C₂₃×#117	C₂³	1	2	yes	—
220	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
221	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
222	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
223	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
224	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
225	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	2	yes	—
226	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
228	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
229	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
230	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
231	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
232	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
233	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
234	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
235	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
236	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
237	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
238	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
239	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
240	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
241	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
242	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
243	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
244	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
245	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
246	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
247	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
248	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
249	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
250	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
251	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
252	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
253	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
254	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
255	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
256	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
260	C₂₃×#97	C₂³	1	2	yes	—
261	C₂₃×#97	C₂³	1	2	yes	—
262	C₂₃×#97	C₂³	1	2	yes	—
263	C₂₃×#97	C₂³	1	2	yes	—
264	C₂₃×#97	C₂³	1	2	yes	—
265	C₂₃×#97	C₂³	1	2	yes	—
266	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
267	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
268	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
269	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
270	C₄×C₈×C₂₃	C₂³	1	2	yes	—
271	C₄×C₈×C₂₃	C₂³	1	2	yes	—
272	C₄×C₈×C₂₃	C₂³	1	2	yes	—
273	C₄×C₈×C₂₃	C₂³	1	2	yes	—
274	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
275	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
276	C₂⁴×C₂₃	C₂²×C₄	1	2	yes	—
277	#41×C₂₃	—	4	2	no	—
278	#41×C₂₃	—	4	2	no	—
279	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
280	C₂×Q₈×C₂₃	C₂²×C₄	1	1	yes	characteristic
281	C₂×Q₈×C₂₃	C₂²×C₄	1	2	yes	—
282	C₂×D₄×C₂₃	—	4	2	no	—
283	C₂×D₄×C₂₃	—	4	4	no	—
284	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
285	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
286	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
287	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
288	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
289	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
290	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
291	C₂×D₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
292	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
293	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
294	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
295	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
296	C₂×D₄×C₂₃	C₂²×C₄	1	2	yes	—
297	C₂²×C₄×C₂₃	—	4	1	no	—
298	C₂²×C₄×C₂₃	—	4	1	no	—
299	C₂²×C₄×C₂₃	—	4	2	no	—
300	C₂²×C₄×C₂₃	—	4	1	no	—
301	C₂²×C₄×C₂₃	—	4	1	no	—
302	C₂²×C₄×C₂₃	—	4	2	no	—
303	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
304	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
305	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
306	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
307	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
308	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
309	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
310	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
311	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
312	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
313	C₂²×C₄×C₂₃	C₂²×C₄	1	2	yes	—
314	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
318	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
319	M₁₆×C₂₃	—	2	4	no	—
320	M₁₆×C₂₃	—	2	4	no	—
321	M₁₆×C₂₃	—	2	4	no	—
322	M₁₆×C₂₃	—	4	2	no	—
323	M₁₆×C₂₃	—	4	2	no	—
324	M₁₆×C₂₃	—	4	2	no	—
325	M₁₆×C₂₃	—	4	2	no	—
326	M₁₆×C₂₃	—	4	2	no	—
327	M₁₆×C₂₃	—	4	2	no	—
328	M₁₆×C₂₃	—	4	2	no	—
329	C₂×C₈×C₂₃	—	2	2	no	—
330	C₂×C₈×C₂₃	—	2	4	no	—
331	C₂×C₈×C₂₃	—	4	2	no	—
332	C₂×C₈×C₂₃	—	4	1	no	—
333	C₂×C₈×C₂₃	—	4	2	no	—
334	C₂×C₈×C₂₃	—	4	1	no	—
335	C₂×C₈×C₂₃	—	4	1	no	—
336	C₂×C₈×C₂₃	—	4	2	no	—
337	C₂×C₈×C₂₃	—	4	2	no	—
338	C₂×C₈×C₂₃	—	4	2	no	—
339	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
340	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
341	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
342	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
343	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
344	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
345	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
346	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
347	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
348	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
349	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
350	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
351	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
352	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
353	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
354	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
355	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
356	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
357	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
358	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
359	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
360	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
361	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
362	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
363	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
364	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
365	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
366	C₄⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
367	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
368	C₄⋊C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
369	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
370	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
371	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
372	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
373	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
374	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
375	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
376	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
377	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
378	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
379	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
380	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
381	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
382	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
383	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
384	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
385	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
386	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
387	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
388	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
389	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
390	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
391	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
392	C₂²⋊C₄×C₂₃	C₂²×C₄	1	2	yes	—
393	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
394	C₄²×C₂₃	C₂²×C₄	1	1	yes	characteristic
395	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
396	C₄²×C₂₃	C₂²×C₄	1	2	yes	—
397	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
398	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
399	C₄²×C₂₃	C₂⁴	1	2	yes	—
400	C₄²×C₂₃	C₂⁴	1	2	yes	—
401	#60322	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
402	C₂³×C₂₃	—	2	2	no	—
403	C₂³×C₂₃	—	2	2	no	—
404	C₂³×C₂₃	—	4	1	no	—
405	C₂³×C₂₃	—	4	1	no	—
406	C₂³×C₂₃	—	4	2	no	—
407	C₂³×C₂₃	—	4	2	no	—
408	C₂³×C₂₃	—	4	1	no	—
409	C₂³×C₂₃	—	4	1	no	—
410	C₂³×C₂₃	—	4	2	no	—
411	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
412	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
413	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
414	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
415	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
416	Q₈×C₂₃	—	4	1	no	—
417	Q₈×C₂₃	—	4	1	no	—
418	Q₈×C₂₃	—	4	2	no	—
419	D₄×C₂₃	—	2	4	no	—
420	D₄×C₂₃	—	2	4	no	—
421	D₄×C₂₃	—	4	2	no	—
422	D₄×C₂₃	—	4	2	no	—
423	D₄×C₂₃	—	4	2	no	—
424	D₄×C₂₃	—	4	2	no	—
425	D₄×C₂₃	—	4	1	no	—
426	D₄×C₂₃	—	4	1	no	—
427	D₄×C₂₃	—	4	2	no	—
428	D₄×C₂₃	—	4	2	no	—
429	D₄×C₂₃	—	4	2	no	—
430	D₄×C₂₃	—	4	2	no	—
431	D₄×C₂₃	—	4	2	no	—
432	C₂×C₄×C₂₃	—	2	2	no	—
433	C₂×C₄×C₂₃	—	2	1	no	—
434	C₂×C₄×C₂₃	—	2	2	no	—
435	C₂×C₄×C₂₃	—	2	2	no	—
436	C₂×C₄×C₂₃	—	2	2	no	—
437	C₂×C₄×C₂₃	—	2	2	no	—
438	C₂×C₄×C₂₃	—	2	1	no	—
439	C₂×C₄×C₂₃	—	2	2	no	—
440	C₂×C₄×C₂₃	—	2	2	no	—
441	C₂×C₄×C₂₃	—	2	2	no	—
442	C₂×C₄×C₂₃	—	2	2	no	—
443	C₂×C₄×C₂₃	—	4	1	no	—
444	C₂×C₄×C₂₃	—	4	2	no	—
445	C₂×C₄×C₂₃	—	4	2	no	—
446	C₂×C₄×C₂₃	—	4	2	no	—
447	C₂×C₄×C₂₃	—	4	2	no	—
448	C₂×C₄×C₂₃	—	4	1	no	—
449	C₂×C₄×C₂₃	—	4	2	no	—
450	C₂×C₄×C₂₃	—	4	1	no	—
451	C₂×C₄×C₂₃	—	4	2	no	—
452	C₂×C₄×C₂₃	—	4	2	no	—
453	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
454	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
455	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
456	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
457	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
458	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
459	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
460	C₂×C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
461	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
462	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
463	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
464	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
465	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
466	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
467	C₈×C₂₃	—	2	2	no	—
468	C₈×C₂₃	—	2	1	no	—
469	C₈×C₂₃	—	2	2	no	—
470	C₈×C₂₃	—	2	2	no	—
471	C₈×C₂₃	—	2	2	no	—
472	C₈×C₂₃	—	2	1	no	—
473	C₈×C₂₃	—	2	2	no	—
474	C₈×C₂₃	—	2	1	no	—
475	C₈×C₂₃	—	2	2	no	—
476	C₈×C₂₃	H(5,𝔽₂)	1	2	yes	—
477	#3459	C₂×C₂₃	1	1	yes	characteristic
478	#2995	C₂×C₂₃	1	2	yes	complemented
479	#2993	C₂×C₂₃	1	2	yes	complemented
480	#2992	C₂×C₂₃	1	1	yes	characteristic, complemented
481	#2992	C₂×C₂₃	1	1	yes	characteristic, complemented
482	#2978	C₂×C₂₃	1	2	yes	complemented
483	#2977	C₂×C₂₃	1	2	yes	complemented
484	#2976	C₂×C₂₃	1	2	yes	complemented
485	#2974	C₂×C₂₃	1	2	yes	complemented
486	#2973	C₂×C₂₃	1	1	yes	characteristic, complemented
487	#2969	C₂×C₂₃	1	2	yes	complemented
488	#2967	C₂×C₂₃	1	2	yes	complemented
489	#2966	C₂×C₂₃	1	1	yes	characteristic, complemented
490	#2966	C₂×C₂₃	1	1	yes	characteristic, complemented
491	D₄×M₁₆	C₂×C₂₃	1	2	yes	complemented
492	#2933	C₂×C₂₃	1	2	yes	complemented
493	#2933	C₂×C₂₃	1	2	yes	complemented
494	#2930	C₂×C₂₃	1	2	yes	complemented
495	C₂×#436	C₂×C₂₃	1	1	yes	characteristic, complemented
496	C₂²×C₂₃	—	2	1	no	—
497	C₂²×C₂₃	—	2	1	no	—
498	C₂²×C₂₃	—	2	2	no	—
499	C₂²×C₂₃	—	2	2	no	—
500	C₂²×C₂₃	—	2	2	no	—
501	C₂²×C₂₃	—	2	2	no	—
502	C₂²×C₂₃	—	2	2	no	—
503	C₂²×C₂₃	—	2	2	no	—
504	C₂²×C₂₃	—	2	2	no	—
505	C₂²×C₂₃	—	2	2	no	—
506	C₂²×C₂₃	—	2	2	no	—
507	C₂²×C₂₃	—	2	2	no	—
508	C₂²×C₂₃	—	2	2	no	—
509	C₂²×C₂₃	—	2	2	no	—
510	C₂²×C₂₃	—	8	2	no	—
511	C₂²×C₂₃	—	8	2	no	—
512	C₂²×C₂₃	—	8	4	no	—
513	C₂²×C₂₃	#568	1	2	yes	—
514	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
515	C₄×C₂₃	—	2	1	no	—
516	C₄×C₂₃	—	2	2	no	—
517	C₄×C₂₃	—	2	2	no	—
518	C₄×C₂₃	—	2	2	no	—
519	C₄×C₂₃	—	2	2	no	—
520	C₄×C₂₃	—	2	1	no	—
521	C₄×C₂₃	—	2	1	no	—
522	C₄×C₂₃	—	2	2	no	—
523	C₄×C₂₃	—	2	2	no	—
524	C₄×C₂₃	—	2	1	no	—
525	C₄×C₂₃	—	2	1	no	—
526	C₄×C₂₃	—	2	2	no	—
527	C₄×C₂₃	—	2	2	no	—
528	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
529	C₄×C₂₃	#585	1	1	yes	characteristic
530	C₂×#131	C₂²×C₂₃	1	2	yes	complemented
531	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
532	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
533	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	complemented
534	#543	C₄×C₂₃	1	1	yes	characteristic
535	#539	C₄×C₂₃	1	2	yes	—
536	#539	C₄×C₂₃	1	2	yes	—
537	#539	C₄×C₂₃	1	2	yes	—
538	#538	C₄×C₂₃	1	1	yes	characteristic
539	#538	C₄×C₂₃	1	1	yes	characteristic
540	#538	C₄×C₂₃	1	2	yes	—
541	#538	C₄×C₂₃	1	2	yes	—
542	#534	C₄×C₂₃	1	1	yes	characteristic
543	#534	C₄×C₂₃	1	2	yes	—
544	#529	C₂²×C₂₃	1	1	yes	characteristic
545	#529	C₂²×C₂₃	1	1	yes	characteristic
546	#529	C₂²×C₂₃	1	2	yes	—
547	#529	C₂²×C₂₃	1	2	yes	—
548	#525	C₂²×C₂₃	1	2	yes	—
549	#525	C₂²×C₂₃	1	2	yes	—
550	#525	C₂²×C₂₃	1	2	yes	—
551	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
552	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
553	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
554	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
555	#446	C₂²×C₂₃	1	2	yes	complemented
556	#446	C₂²×C₂₃	1	2	yes	complemented
557	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
558	C₈×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
559	#436	C₂²×C₂₃	1	2	yes	complemented
560	#436	C₂²×C₂₃	1	2	yes	complemented
561	#436	C₂²×C₂₃	1	2	yes	complemented
562	#436	C₂²×C₂₃	1	2	yes	complemented
563	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
564	#436	C₂²×C₂₃	1	2	yes	complemented
565	#436	C₂²×C₂₃	1	2	yes	complemented
566	#436	C₂²×C₂₃	1	2	yes	complemented
567	#436	C₂²×C₂₃	1	2	yes	complemented
568	#436	C₂²×C₂₃	1	2	yes	complemented
569	#436	C₂²×C₂₃	1	1	yes	characteristic, complemented
570	#436	C₂²×C₂₃	1	2	yes	complemented
571	#435	C₂²×C₂₃	1	2	yes	complemented
572	#435	C₂²×C₂₃	1	2	yes	complemented
573	#435	C₂²×C₂₃	1	2	yes	complemented
574	#435	C₂²×C₂₃	1	2	yes	complemented
575	#435	C₂²×C₂₃	1	2	yes	complemented
576	#435	C₂²×C₂₃	1	2	yes	complemented
577	#435	C₂²×C₂₃	1	2	yes	complemented
578	#435	C₂²×C₂₃	1	2	yes	complemented
579	#435	C₂²×C₂₃	1	2	yes	complemented
580	#435	C₂²×C₂₃	1	2	yes	complemented
581	#435	C₂²×C₂₃	1	2	yes	complemented
582	#435	C₂²×C₂₃	1	2	yes	complemented
583	#435	C₂²×C₂₃	1	2	yes	complemented
584	#435	C₂²×C₂₃	1	2	yes	complemented
585	#435	C₂²×C₂₃	1	2	yes	complemented
586	#435	C₂²×C₂₃	1	2	yes	complemented
587	#435	C₂²×C₂₃	1	2	yes	complemented
588	#435	C₂²×C₂₃	1	2	yes	complemented
589	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
590	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
591	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
592	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
593	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
594	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
595	C₈×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
596	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
597	#433	C₂²×C₂₃	1	2	yes	complemented
598	#433	C₂²×C₂₃	1	2	yes	complemented
599	#433	C₂²×C₂₃	1	2	yes	complemented
600	#433	C₂²×C₂₃	1	2	yes	complemented
601	#433	C₂²×C₂₃	1	2	yes	complemented
602	#433	C₂²×C₂₃	1	2	yes	complemented
603	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
604	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
605	#432	C₂²×C₂₃	1	2	yes	complemented
606	#431	C₂²×C₂₃	1	2	yes	complemented
607	#424	C₂²×C₂₃	1	2	yes	complemented
608	#424	C₂²×C₂₃	1	2	yes	complemented
609	#424	C₂²×C₂₃	1	2	yes	complemented
610	#423	C₂²×C₂₃	1	2	yes	complemented
611	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
612	#408	C₂²×C₂₃	1	2	yes	complemented
613	#408	C₂²×C₂₃	1	2	yes	complemented
614	#408	C₂²×C₂₃	1	2	yes	complemented
615	#407	C₂²×C₂₃	1	2	yes	—
616	#407	C₂²×C₂₃	1	2	yes	complemented
617	#407	C₂²×C₂₃	1	2	yes	complemented
618	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
619	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
620	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
621	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
622	#405	C₂²×C₂₃	1	2	yes	complemented
623	#405	C₂²×C₂₃	1	2	yes	complemented
624	#405	C₂²×C₂₃	1	2	yes	complemented
625	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
626	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
627	C₂×C₂₃	—	2	2	no	—
628	C₂×C₂₃	—	4	2	no	—
629	C₂×C₂₃	—	4	2	no	—
630	C₂×C₂₃	—	4	2	no	—
631	C₂×C₂₃	—	4	2	no	—
632	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
633	C₂×C₂₃	C₂×#568	1	1	yes	characteristic
634	C₂×C₂₃	#3573	1	1	yes	characteristic
635	C₂×#41	C₂³×C₂₃	1	2	yes	—
636	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
637	C₂²×D₄	C₂×C₄×C₂₃	1	2	yes	—
638	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
639	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
640	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
641	#131	—	4	4	no	—
642	C₂×M₁₆	—	4	2	no	—
643	C₂×M₁₆	—	4	2	no	—
644	C₂×M₁₆	—	4	4	no	—
645	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
646	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
647	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
648	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
649	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
650	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
651	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
652	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
653	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
654	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
655	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
656	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
657	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
658	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
659	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
660	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
661	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
662	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
663	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
664	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
665	#126	C₂×C₄×C₂₃	1	2	yes	—
666	#126	C₂×C₄×C₂₃	1	2	yes	—
667	#126	C₂×C₄×C₂₃	1	2	yes	—
668	#126	C₂×C₄×C₂₃	1	2	yes	—
669	#126	C₂×C₄×C₂₃	1	2	yes	—
670	#126	C₂×C₄×C₂₃	1	2	yes	—
671	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
672	#125	C₂×C₄×C₂₃	1	1	yes	characteristic
673	#125	C₂×C₄×C₂₃	1	2	yes	—
674	#125	C₂×C₄×C₂₃	1	2	yes	—
675	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
676	#124	C₂×C₄×C₂₃	1	1	yes	characteristic
677	#124	C₂×C₄×C₂₃	1	2	yes	—
678	#124	C₂×C₄×C₂₃	1	2	yes	—
679	#123	C₂×C₄×C₂₃	1	2	yes	—
680	#123	C₂×C₄×C₂₃	1	2	yes	—
681	#123	C₂×C₄×C₂₃	1	2	yes	—
682	#123	C₂×C₄×C₂₃	1	2	yes	—
683	#123	C₂×C₄×C₂₃	1	2	yes	—
684	#123	C₂×C₄×C₂₃	1	2	yes	—
685	#123	C₂×C₄×C₂₃	1	2	yes	—
686	#123	C₂×C₄×C₂₃	1	2	yes	—
687	#123	C₂×C₄×C₂₃	1	2	yes	—
688	#123	C₂×C₄×C₂₃	1	2	yes	—
689	#123	C₂×C₄×C₂₃	1	2	yes	—
690	#123	C₂×C₄×C₂₃	1	2	yes	—
691	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
692	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
693	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
694	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
695	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
696	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
697	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
698	C₂²⋊Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
699	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
700	C₂²⋊Q₈	C₂×C₄×C₂₃	1	2	yes	—
701	#121	C₂×C₄×C₂₃	1	2	yes	—
702	#121	C₂×C₄×C₂₃	1	2	yes	—
703	#121	C₂×C₄×C₂₃	1	2	yes	—
704	#121	C₂×C₄×C₂₃	1	2	yes	—
705	#121	C₂×C₄×C₂₃	1	2	yes	—
706	#121	C₂×C₄×C₂₃	1	2	yes	—
707	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
708	#121	C₂×C₄×C₂₃	1	1	yes	characteristic
709	#121	C₂×C₄×C₂₃	1	2	yes	—
710	#121	C₂×C₄×C₂₃	1	2	yes	—
711	#120	C₂×C₄×C₂₃	1	2	yes	—
712	#120	C₂×C₄×C₂₃	1	2	yes	—
713	#120	C₂×C₄×C₂₃	1	2	yes	—
714	#120	C₂×C₄×C₂₃	1	2	yes	—
715	#120	C₂×C₄×C₂₃	1	2	yes	—
716	#120	C₂×C₄×C₂₃	1	2	yes	—
717	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
718	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
719	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
720	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
721	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
722	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
723	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
724	C₄×D₄	C₂×C₄×C₂₃	1	2	yes	—
725	C₄×D₄	C₂³×C₂₃	1	2	yes	—
726	C₄×D₄	C₂³×C₂₃	1	2	yes	—
727	C₄×D₄	C₂³×C₂₃	1	2	yes	—
728	C₄×D₄	C₂³×C₂₃	1	2	yes	—
729	C₄×D₄	C₂³×C₂₃	1	2	yes	—
730	C₄×D₄	C₂³×C₂₃	1	2	yes	—
731	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
732	C₄×D₄	C₂³×C₂₃	1	2	yes	—
733	C₄×D₄	C₂³×C₂₃	1	2	yes	—
734	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
735	#117	C₂³×C₂₃	1	2	yes	—
736	#117	C₂³×C₂₃	1	2	yes	—
737	#117	C₂³×C₂₃	1	2	yes	—
738	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
739	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
741	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
742	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
743	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	2	yes	—
744	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
745	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
746	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
747	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
748	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
749	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
750	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
751	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
752	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
753	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
754	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
755	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
756	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
757	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
758	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
759	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
760	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
761	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
762	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
763	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
764	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
765	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
766	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
767	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
768	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
769	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
770	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
771	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
772	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
773	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
774	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
775	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
776	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
777	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
778	#97	C₂³×C₂₃	1	2	yes	—
779	#97	C₂³×C₂₃	1	2	yes	—
780	#97	C₂³×C₂₃	1	2	yes	—
781	#97	C₂³×C₂₃	1	2	yes	—
782	#97	C₂³×C₂₃	1	2	yes	—
783	#97	C₂³×C₂₃	1	2	yes	—
784	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
785	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
786	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
787	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
788	C₄×C₈	C₂³×C₂₃	1	2	yes	—
789	C₄×C₈	C₂³×C₂₃	1	2	yes	—
790	C₄×C₈	C₂³×C₂₃	1	2	yes	—
791	C₄×C₈	C₂³×C₂₃	1	2	yes	—
792	C₂₃	#60322	1	1	yes	characteristic, direct product factor, Sylow
793	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
794	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
795	C₂⁴	C₂²×C₄×C₂₃	1	2	yes	—
796	#41	—	4	2	no	—
797	#41	—	4	2	no	—
798	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
799	C₂×Q₈	C₂²×C₄×C₂₃	1	1	yes	characteristic
800	C₂×Q₈	C₂²×C₄×C₂₃	1	2	yes	—
801	C₂×D₄	—	4	2	no	—
802	C₂×D₄	—	4	4	no	—
803	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
804	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
805	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
806	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
807	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
808	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
809	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
810	C₂×D₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
811	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
812	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
813	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
814	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
815	C₂×D₄	C₂²×C₄×C₂₃	1	2	yes	—
816	C₂²×C₄	—	4	1	no	—
817	C₂²×C₄	—	4	1	no	—
818	C₂²×C₄	—	4	2	no	—
819	C₂²×C₄	—	4	1	no	—
820	C₂²×C₄	—	4	1	no	—
821	C₂²×C₄	—	4	2	no	—
822	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
823	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
824	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
825	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
826	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
827	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
828	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
829	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
830	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
831	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
832	C₂²×C₄	C₂²×C₄×C₂₃	1	2	yes	—
833	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
834	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
836	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
838	M₁₆	—	2	4	no	—
839	M₁₆	—	2	4	no	—
840	M₁₆	—	2	4	no	—
841	M₁₆	—	4	2	no	—
842	M₁₆	—	4	2	no	—
843	M₁₆	—	4	2	no	—
844	M₁₆	—	4	2	no	—
845	M₁₆	—	4	2	no	—
846	M₁₆	—	4	2	no	—
847	M₁₆	—	4	2	no	—
848	C₂×C₈	—	2	2	no	—
849	C₂×C₈	—	2	4	no	—
850	C₂×C₈	—	4	1	no	—
851	C₂×C₈	—	4	1	no	—
852	C₂×C₈	—	4	2	no	—
853	C₂×C₈	—	4	2	no	—
854	C₂×C₈	—	4	2	no	—
855	C₂×C₈	—	4	2	no	—
856	C₂×C₈	—	4	1	no	—
857	C₂×C₈	—	4	2	no	—
858	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
859	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
860	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
861	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
862	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
863	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
864	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
865	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
866	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
867	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
868	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
869	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
870	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
871	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
872	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
873	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
874	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
875	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
876	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
877	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
878	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
879	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
880	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
881	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
882	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
883	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
884	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
885	C₄⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
886	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
887	C₄⋊C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
888	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
889	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
890	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
891	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
892	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
893	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
894	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
895	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
896	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
897	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
898	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
899	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
900	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
901	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
902	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
903	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
904	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
905	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
906	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
907	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
908	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
909	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
910	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
911	C₂²⋊C₄	C₂²×C₄×C₂₃	1	2	yes	—
912	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
913	C₄²	C₂²×C₄×C₂₃	1	1	yes	characteristic
914	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
915	C₄²	C₂²×C₄×C₂₃	1	2	yes	—
916	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
917	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
918	C₄²	C₂⁴×C₂₃	1	2	yes	—
919	C₄²	C₂⁴×C₂₃	1	2	yes	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	2	no	—
922	C₂³	—	4	1	no	—
923	C₂³	—	4	1	no	—
924	C₂³	—	4	2	no	—
925	C₂³	—	4	2	no	—
926	C₂³	—	4	1	no	—
927	C₂³	—	4	1	no	—
928	C₂³	—	4	2	no	—
929	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
930	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
931	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
932	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
933	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
934	Q₈	—	4	2	no	—
935	Q₈	—	4	1	no	—
936	Q₈	—	4	1	no	—
937	D₄	—	2	4	no	—
938	D₄	—	2	4	no	—
939	D₄	—	4	2	no	—
940	D₄	—	4	2	no	—
941	D₄	—	4	2	no	—
942	D₄	—	4	2	no	—
943	D₄	—	4	2	no	—
944	D₄	—	4	2	no	—
945	D₄	—	4	2	no	—
946	D₄	—	4	1	no	—
947	D₄	—	4	1	no	—
948	D₄	—	4	2	no	—
949	D₄	—	4	2	no	—
950	C₂×C₄	—	2	2	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	2	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	4	1	no	—
962	C₂×C₄	—	4	2	no	—
963	C₂×C₄	—	4	2	no	—
964	C₂×C₄	—	4	2	no	—
965	C₂×C₄	—	4	2	no	—
966	C₂×C₄	—	4	1	no	—
967	C₂×C₄	—	4	2	no	—
968	C₂×C₄	—	4	2	no	—
969	C₂×C₄	—	4	1	no	—
970	C₂×C₄	—	4	2	no	—
971	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
972	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
973	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
974	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
975	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
976	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
977	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
978	C₂×C₄	C₂³×C₄×C₂₃	1	1	yes	characteristic
979	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
980	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
981	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
982	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
983	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
984	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
985	C₈	—	2	2	no	—
986	C₈	—	2	1	no	—
987	C₈	—	2	2	no	—
988	C₈	—	2	2	no	—
989	C₈	—	2	2	no	—
990	C₈	—	2	1	no	—
991	C₈	—	2	2	no	—
992	C₈	—	2	1	no	—
993	C₈	—	2	2	no	—
994	C₈	C₂₃×H(5,𝔽₂)	1	2	yes	—
995	C₂²	—	2	1	no	—
996	C₂²	—	2	1	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	2	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	2	2	no	—
1006	C₂²	—	2	2	no	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	2	no	—
1009	C₂²	—	8	2	no	—
1010	C₂²	—	8	2	no	—
1011	C₂²	—	8	4	no	—
1012	C₂²	C₂₃×#568	1	2	yes	—
1013	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
1014	C₄	—	2	1	no	—
1015	C₄	—	2	2	no	—
1016	C₄	—	2	2	no	—
1017	C₄	—	2	2	no	—
1018	C₄	—	2	2	no	—
1019	C₄	—	2	1	no	—
1020	C₄	—	2	1	no	—
1021	C₄	—	2	2	no	—
1022	C₄	—	2	2	no	—
1023	C₄	—	2	1	no	—
1024	C₄	—	2	1	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	2	no	—
1027	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1028	C₄	C₂₃×#585	1	1	yes	characteristic
1029	C₂	—	2	2	no	—
1030	C₂	—	4	2	no	—
1031	C₂	—	4	2	no	—
1032	C₂	—	4	2	no	—
1033	C₂	—	4	2	no	—
1034	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1035	C₂	C₂×C₂₃×#568	1	1	yes	characteristic
1036	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	C₂₃×#3459	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×#2993	C₂	semidirect
4. C₂₃×#2992	C₂	semidirect
5. C₂₃×#2992	C₂	semidirect
6. C₂₃×#2978	C₂	semidirect
7. C₂₃×#2977	C₂	semidirect
8. C₂₃×#2976	C₂	semidirect
9. C₂₃×#2974	C₂	semidirect
10. C₂₃×#2973	C₂	semidirect
11. C₂₃×#2969	C₂	semidirect
12. C₂₃×#2967	C₂	semidirect
13. C₂₃×#2966	C₂	semidirect
14. C₂₃×#2966	C₂	semidirect
15. D₄×M₁₆×C₂₃	C₂	semidirect
16. C₂₃×#2933	C₂	semidirect
17. C₂₃×#2933	C₂	semidirect
18. C₂₃×#2930	C₂	semidirect
19. C₂×C₂₃×#436	C₂	semidirect
20. C₂×C₂₃×#131	C₂²	semidirect
22. C₂²×M₁₆×C₂₃	C₂²	semidirect
23. C₂²×M₁₆×C₂₃	C₂²	semidirect
43. C₂₃×#446	C₂²	semidirect
44. C₂₃×#446	C₂²	semidirect
45. C₂₃×#446	C₂²	semidirect
46. C₂₃×#446	C₂²	semidirect
47. C₈×Q₈×C₂₃	C₂²	semidirect
48. C₈×Q₈×C₂₃	C₂²	semidirect
49. C₂₃×#436	C₂²	semidirect
50. C₂₃×#436	C₂²	semidirect
51. C₂₃×#436	C₂²	semidirect
52. C₂₃×#436	C₂²	semidirect
53. C₂₃×#436	C₂²	semidirect
54. C₂₃×#436	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
61. C₂₃×#435	C₂²	semidirect
62. C₂₃×#435	C₂²	semidirect
63. C₂₃×#435	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. C₈×D₄×C₂₃	C₂²	semidirect
80. C₈×D₄×C₂₃	C₂²	semidirect
81. C₈×D₄×C₂₃	C₂²	semidirect
82. C₈×D₄×C₂₃	C₂²	semidirect
83. C₈×D₄×C₂₃	C₂²	semidirect
84. C₈×D₄×C₂₃	C₂²	semidirect
85. C₈×D₄×C₂₃	C₂²	semidirect
86. C₈×D₄×C₂₃	C₂²	semidirect
87. C₂₃×#433	C₂²	semidirect
88. C₂₃×#433	C₂²	semidirect
89. C₂₃×#433	C₂²	semidirect
90. C₂₃×#433	C₂²	semidirect
91. C₂₃×#433	C₂²	semidirect
92. C₂₃×#433	C₂²	semidirect
93. C₂₃×#432	C₂²	semidirect
94. C₂₃×#432	C₂²	semidirect
95. C₂₃×#432	C₂²	semidirect
96. C₂₃×#431	C₂²	semidirect
97. C₂₃×#424	C₂²	semidirect
98. C₂₃×#424	C₂²	semidirect
99. C₂₃×#424	C₂²	semidirect
100. C₂₃×#423	C₂²	semidirect
101. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
102. C₂₃×#408	C₂²	semidirect
103. C₂₃×#408	C₂²	semidirect
104. C₂₃×#408	C₂²	semidirect
106. C₂₃×#407	C₂²	semidirect
107. C₂₃×#407	C₂²	semidirect
109. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
110. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
111. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
112. C₂₃×#405	C₂²	semidirect
113. C₂₃×#405	C₂²	semidirect
114. C₂₃×#405	C₂²	semidirect
115. C₄×M₁₆×C₂₃	C₂²	semidirect
116. C₂×C₄×C₈×C₂₃	C₂²	semidirect
401. #60322	C₂₃	direct (N × H)
478. #2995	C₂×C₂₃	semidirect
479. #2993	C₂×C₂₃	semidirect
480. #2992	C₂×C₂₃	semidirect
481. #2992	C₂×C₂₃	semidirect
482. #2978	C₂×C₂₃	semidirect
483. #2977	C₂×C₂₃	semidirect
484. #2976	C₂×C₂₃	semidirect
485. #2974	C₂×C₂₃	semidirect
486. #2973	C₂×C₂₃	semidirect
487. #2969	C₂×C₂₃	semidirect
488. #2967	C₂×C₂₃	semidirect
489. #2966	C₂×C₂₃	semidirect
490. #2966	C₂×C₂₃	semidirect
491. D₄×M₁₆	C₂×C₂₃	semidirect
492. #2933	C₂×C₂₃	semidirect
493. #2933	C₂×C₂₃	semidirect
494. #2930	C₂×C₂₃	semidirect
495. C₂×#436	C₂×C₂₃	semidirect
530. C₂×#131	C₂²×C₂₃	semidirect
532. C₂²×M₁₆	C₂²×C₂₃	semidirect
533. C₂²×M₁₆	C₂²×C₂₃	semidirect
553. #446	C₂²×C₂₃	semidirect
554. #446	C₂²×C₂₃	semidirect
555. #446	C₂²×C₂₃	semidirect
556. #446	C₂²×C₂₃	semidirect
557. C₈×Q₈	C₂²×C₂₃	semidirect
558. C₈×Q₈	C₂²×C₂₃	semidirect
559. #436	C₂²×C₂₃	semidirect
560. #436	C₂²×C₂₃	semidirect
561. #436	C₂²×C₂₃	semidirect
562. #436	C₂²×C₂₃	semidirect
563. #436	C₂²×C₂₃	semidirect
564. #436	C₂²×C₂₃	semidirect
565. #436	C₂²×C₂₃	semidirect
566. #436	C₂²×C₂₃	semidirect
567. #436	C₂²×C₂₃	semidirect
568. #436	C₂²×C₂₃	semidirect
569. #436	C₂²×C₂₃	semidirect
570. #436	C₂²×C₂₃	semidirect
571. #435	C₂²×C₂₃	semidirect
572. #435	C₂²×C₂₃	semidirect
573. #435	C₂²×C₂₃	semidirect
574. #435	C₂²×C₂₃	semidirect
575. #435	C₂²×C₂₃	semidirect
576. #435	C₂²×C₂₃	semidirect
577. #435	C₂²×C₂₃	semidirect
578. #435	C₂²×C₂₃	semidirect
579. #435	C₂²×C₂₃	semidirect
580. #435	C₂²×C₂₃	semidirect
581. #435	C₂²×C₂₃	semidirect
582. #435	C₂²×C₂₃	semidirect
583. #435	C₂²×C₂₃	semidirect
584. #435	C₂²×C₂₃	semidirect
585. #435	C₂²×C₂₃	semidirect
586. #435	C₂²×C₂₃	semidirect
587. #435	C₂²×C₂₃	semidirect
588. #435	C₂²×C₂₃	semidirect
589. C₈×D₄	C₂²×C₂₃	semidirect
590. C₈×D₄	C₂²×C₂₃	semidirect
591. C₈×D₄	C₂²×C₂₃	semidirect
592. C₈×D₄	C₂²×C₂₃	semidirect
593. C₈×D₄	C₂²×C₂₃	semidirect
594. C₈×D₄	C₂²×C₂₃	semidirect
595. C₈×D₄	C₂²×C₂₃	semidirect
596. C₈×D₄	C₂²×C₂₃	semidirect
597. #433	C₂²×C₂₃	semidirect
598. #433	C₂²×C₂₃	semidirect
599. #433	C₂²×C₂₃	semidirect
600. #433	C₂²×C₂₃	semidirect
601. #433	C₂²×C₂₃	semidirect
602. #433	C₂²×C₂₃	semidirect
603. #432	C₂²×C₂₃	semidirect
604. #432	C₂²×C₂₃	semidirect
605. #432	C₂²×C₂₃	semidirect
606. #431	C₂²×C₂₃	semidirect
607. #424	C₂²×C₂₃	semidirect
608. #424	C₂²×C₂₃	semidirect
609. #424	C₂²×C₂₃	semidirect
610. #423	C₂²×C₂₃	semidirect
611. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
612. #408	C₂²×C₂₃	semidirect
613. #408	C₂²×C₂₃	semidirect
614. #408	C₂²×C₂₃	semidirect
616. #407	C₂²×C₂₃	semidirect
617. #407	C₂²×C₂₃	semidirect
619. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
620. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
621. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
622. #405	C₂²×C₂₃	semidirect
623. #405	C₂²×C₂₃	semidirect
624. #405	C₂²×C₂₃	semidirect
625. C₄×M₁₆	C₂²×C₂₃	semidirect
626. C₂×C₄×C₈	C₂²×C₂₃	semidirect
792. C₂₃	#60322	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×#3459	2
C₂₃×#2995	2
C₂₃×#2993	2
C₂₃×#2992	2
C₂₃×#2978	2
C₂₃×#2977	2
C₂₃×#2976	2
C₂₃×#2974	2
C₂₃×#2973	2
C₂₃×#2969	2
C₂₃×#2967	2
C₂₃×#2966	2
D₄×M₁₆×C₂₃	2
C₂₃×#2933	2
C₂₃×#2930	2
C₂×C₂₃×#436	2
#60322	23

Subgroups — C23×#60322 #19207948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60322 #19207948