Subgroups — C₂₃×#60955 #19208581

Order 5888.

1804 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3460	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3262	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3259	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3257	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3243	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3241	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3224	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3220	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3203	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3199	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3198	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3171	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3106	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3105	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3102	C₂	1	2	yes	maximal, complemented
18	C₂₃×#3100	C₂	1	2	yes	maximal, complemented
19	C₂₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#544	C₂²	1	2	yes	complemented
21	C₂₃×#542	—	2	2	no	—
22	C₂₃×#542	C₂²	1	2	yes	—
23	C₂₃×#542	C₂²	1	2	yes	complemented
24	C₂₃×#540	—	2	2	no	—
25	C₂₃×#540	C₂²	1	2	yes	—
26	C₂₃×#540	C₂²	1	2	yes	complemented
27	C₂₃×#538	—	2	2	no	—
28	C₂₃×#538	—	2	2	no	—
29	C₂₃×#537	C₂²	1	2	yes	—
30	C₂₃×#535	C₂²	1	2	yes	—
31	C₂₃×#535	C₂²	1	2	yes	complemented
32	C₂₃×#532	—	2	2	no	—
33	C₂₃×#532	C₂²	1	2	yes	—
34	C₂₃×#532	C₂²	1	2	yes	complemented
35	C₂₃×#529	—	2	2	no	—
36	C₂₃×#529	C₂²	1	2	yes	—
37	C₂₃×#529	C₂²	1	2	yes	complemented
38	C₂₃×#525	—	2	2	no	—
39	C₂₃×#525	—	2	2	no	—
40	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
41	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
42	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
43	C₂₃×#501	C₂²	1	2	yes	complemented
44	C₂₃×#500	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#499	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#496	C₂²	1	2	yes	—
47	C₂₃×#495	C₂²	1	1	yes	characteristic
48	C₂₃×#493	C₂²	1	1	yes	characteristic
49	C₂₃×#490	C₂²	1	2	yes	complemented
50	C₂₃×#489	C₂²	1	2	yes	complemented
51	C₂₃×#488	C₂²	1	2	yes	complemented
52	C₂₃×#486	C₂²	1	2	yes	complemented
53	C₂₃×#485	C₂²	1	2	yes	complemented
54	C₂₃×#484	C₂²	1	2	yes	complemented
55	C₂₃×#482	C₂²	1	2	yes	—
56	C₂₃×#482	C₂²	1	2	yes	—
57	C₂₃×#482	C₂²	1	2	yes	complemented
58	C₂₃×#481	C₂²	1	2	yes	—
59	C₂₃×#480	C₂²	1	2	yes	—
60	C₂₃×#480	C₂²	1	2	yes	complemented
61	C₂₃×#479	C₂²	1	2	yes	complemented
62	C₂₃×#478	C₂²	1	2	yes	complemented
63	C₂₃×#478	C₂²	1	2	yes	complemented
64	C₂₃×#478	C₂²	1	2	yes	complemented
65	C₂₃×#477	C₂²	1	2	yes	complemented
66	C₂₃×#476	C₂²	1	2	yes	complemented
67	C₂₃×#474	C₂²	1	2	yes	complemented
68	C₂₃×#474	C₂²	1	2	yes	complemented
69	C₂₃×#469	C₂²	1	2	yes	—
70	C₂₃×#469	C₂²	1	2	yes	complemented
71	C₂₃×#468	C₂²	1	2	yes	complemented
72	C₂₃×#468	C₂²	1	2	yes	complemented
73	C₂₃×#467	C₂²	1	1	yes	characteristic, complemented
74	C₂₃×#466	C₂²	1	1	yes	characteristic
75	C₂₃×#466	C₂²	1	1	yes	characteristic
76	C₂₃×#466	C₂²	1	2	yes	complemented
77	C₂₃×#466	C₂²	1	1	yes	characteristic, complemented
78	C₂₃×#465	C₂²	1	2	yes	complemented
79	C₂₃×#464	C₂²	1	2	yes	complemented
80	C₂₃×#463	C₂²	1	2	yes	—
81	C₂₃×#463	C₂²	1	2	yes	—
82	C₂₃×#463	C₂²	1	2	yes	complemented
83	C₂₃×#460	C₂²	1	2	yes	complemented
84	C₂₃×#459	C₂²	1	2	yes	—
85	C₂₃×#459	C₂²	1	2	yes	—
86	C₂₃×#459	C₂²	1	2	yes	complemented
87	C₂₃×#452	C₂²	1	2	yes	complemented
88	C₂₃×#450	C₂²	1	2	yes	complemented
89	C₂₃×#449	C₂²	1	2	yes	—
90	C₂₃×#449	C₂²	1	2	yes	—
91	C₂₃×#449	C₂²	1	2	yes	complemented
92	C₂₃×#447	C₂²	1	2	yes	—
93	C₂₃×#447	C₂²	1	2	yes	—
94	C₂₃×#447	C₂²	1	2	yes	complemented
95	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
96	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
97	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
98	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
99	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
100	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
101	C₄×D₈×C₂₃	C₂²	1	2	yes	—
102	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
103	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
104	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
105	C₂₃×#433	C₂²	1	2	yes	complemented
106	C₂₃×#433	C₂²	1	2	yes	complemented
107	C₂₃×#431	C₂²	1	2	yes	complemented
108	C₂₃×#431	C₂²	1	2	yes	complemented
109	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
110	C₂₃×#424	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#408	C₂²	1	1	yes	characteristic
112	C₂₃×#408	C₂²	1	1	yes	characteristic
113	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₂₃	—	2	2	no	—
116	C₂×#41×C₂₃	—	2	2	no	—
117	C₂×#41×C₂₃	C₂³	1	2	yes	—
118	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
119	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
120	C₂³×C₄×C₂₃	—	2	2	no	—
121	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
122	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
125	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
126	C₂×D₈×C₂₃	C₂³	1	2	yes	—
127	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
128	C₂×D₈×C₂₃	C₂³	1	2	yes	—
129	C₂×D₈×C₂₃	C₂³	1	2	yes	—
130	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
131	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
132	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
134	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
135	C₂₃×C₄⋊Q₈	—	2	2	no	—
136	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₂₃×#127	—	2	2	no	—
139	C₂₃×#127	C₂³	1	2	yes	—
140	C₂₃×#127	C₂³	1	2	yes	—
141	C₂₃×#126	—	2	2	no	—
142	C₂₃×#126	—	2	2	no	—
143	C₂₃×#126	—	2	2	no	—
144	C₂₃×#126	—	2	2	no	—
145	C₂₃×#125	—	2	2	no	—
146	C₂₃×#125	C₂³	1	2	yes	—
147	C₂₃×#125	C₂³	1	2	yes	—
148	C₂₃×#124	—	2	2	no	—
149	C₂₃×#124	—	2	2	no	—
150	C₂₃×#124	—	2	2	no	—
151	C₂₃×#124	—	2	2	no	—
152	C₂₃×#124	—	2	2	no	—
153	C₂₃×#124	C₂³	1	2	yes	—
154	C₂₃×#124	C₂³	1	2	yes	—
155	C₂₃×#123	—	2	2	no	—
156	C₂₃×#123	—	2	2	no	—
157	C₂₃×#123	—	2	2	no	—
158	C₂₃×#123	—	2	2	no	—
159	C₂₃×#123	—	2	2	no	—
160	C₂₃×#123	—	2	2	no	—
161	C₂₃×#123	—	2	2	no	—
162	C₂₃×#123	—	2	2	no	—
163	C₂₃×C₂²⋊Q₈	—	2	2	no	—
164	C₂₃×C₂²⋊Q₈	—	2	2	no	—
165	C₂₃×C₂²⋊Q₈	—	2	2	no	—
166	C₂₃×C₂²⋊Q₈	—	2	2	no	—
167	C₂₃×C₂²⋊Q₈	—	2	2	no	—
168	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
169	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
170	C₂₃×#121	—	2	2	no	—
171	C₂₃×#121	—	2	2	no	—
172	C₂₃×#121	—	2	2	no	—
173	C₂₃×#121	—	2	2	no	—
174	C₂₃×#121	—	2	2	no	—
175	C₂₃×#121	—	2	2	no	—
176	C₂₃×#121	—	2	2	no	—
177	C₂₃×#121	—	2	2	no	—
178	C₂₃×#121	—	2	2	no	—
179	C₂₃×#121	—	2	2	no	—
180	C₂₃×#121	—	2	2	no	—
181	C₂₃×#121	C₂³	1	2	yes	—
182	C₂₃×#121	C₂³	1	2	yes	—
183	C₂₃×#121	C₂³	1	2	yes	—
184	C₂₃×#121	C₂³	1	2	yes	—
185	C₂₃×#121	C₂³	1	2	yes	—
186	C₂₃×#121	C₂³	1	2	yes	—
187	C₂₃×#120	—	2	2	no	—
188	C₂₃×#120	—	2	2	no	—
189	C₂₃×#120	—	2	2	no	—
190	C₂₃×#120	—	2	2	no	—
191	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
192	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
193	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
194	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
195	C₄×D₄×C₂₃	—	2	2	no	—
196	C₄×D₄×C₂₃	—	2	2	no	—
197	C₄×D₄×C₂₃	—	2	2	no	—
198	C₄×D₄×C₂₃	—	2	2	no	—
199	C₄×D₄×C₂₃	—	2	2	no	—
200	C₄×D₄×C₂₃	—	2	2	no	—
201	C₄×D₄×C₂₃	—	2	2	no	—
202	C₄×D₄×C₂₃	—	2	2	no	—
203	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
204	C₄×D₄×C₂₃	D₄	1	2	yes	—
205	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
206	C₄×D₄×C₂₃	D₄	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	2	yes	—
210	C₄×D₄×C₂₃	C₂³	1	2	yes	—
211	C₄×D₄×C₂₃	C₂³	1	2	yes	—
212	C₄×D₄×C₂₃	C₂³	1	2	yes	—
213	C₂₃×#117	—	2	2	no	—
214	C₂₃×#117	—	2	2	no	—
215	C₂₃×#117	—	2	2	no	—
216	C₂₃×#117	C₂³	1	2	yes	—
217	C₂₃×#117	C₂³	1	1	yes	characteristic
218	C₂₃×#117	C₂³	1	2	yes	—
219	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
221	C₂×C₄²×C₂₃	—	2	2	no	—
222	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
224	C₂₃×#107	C₂³	1	1	yes	characteristic
225	C₂₃×#107	C₂³	1	1	yes	characteristic
226	C₂₃×#107	C₂³	1	2	yes	—
227	C₂₃×#107	C₂³	1	1	yes	characteristic
228	C₂₃×#107	C₂³	1	2	yes	—
229	C₂₃×#107	C₂³	1	2	yes	—
230	C₂₃×#107	C₂³	1	1	yes	characteristic
231	C₂₃×#106	C₂³	1	2	yes	—
232	C₂₃×#106	C₂³	1	2	yes	—
233	C₂₃×#106	C₂³	1	2	yes	—
234	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
235	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
236	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
237	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
238	C₂₃×#103	C₂³	1	2	yes	—
239	C₂₃×#103	C₂³	1	2	yes	—
240	C₂₃×#103	C₂³	1	2	yes	—
241	C₂₃×#103	C₂³	1	2	yes	—
242	C₂₃×#102	C₂³	1	2	yes	—
243	C₂₃×#102	C₂³	1	2	yes	—
244	C₂₃×#102	C₂³	1	2	yes	—
245	C₂₃×#102	C₂³	1	2	yes	—
246	C₂₃×#102	C₂³	1	2	yes	—
247	C₂₃×#102	C₂³	1	2	yes	—
248	C₂₃×#102	C₂³	1	2	yes	—
249	C₂₃×#102	C₂³	1	2	yes	—
250	C₂₃×#102	C₂³	1	2	yes	—
251	C₂₃×#102	C₂³	1	2	yes	—
252	C₂₃×#102	C₂³	1	2	yes	—
253	C₂₃×#102	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×#97	C₂³	1	2	yes	—
259	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
260	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
261	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₂₃	C₂³	1	2	yes	—
264	C₂⁴×C₂₃	—	2	2	no	—
265	#41×C₂₃	—	4	1	no	—
266	#41×C₂₃	—	4	1	no	—
267	#41×C₂₃	—	4	2	no	—
268	#41×C₂₃	—	4	2	no	—
269	#41×C₂₃	—	8	4	no	—
270	#41×C₂₃	—	8	4	no	—
271	C₂×Q₈×C₂₃	—	2	2	no	—
272	C₂×Q₈×C₂₃	—	2	2	no	—
273	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
274	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
275	C₂×D₄×C₂₃	—	2	2	no	—
276	C₂×D₄×C₂₃	—	2	2	no	—
277	C₂×D₄×C₂₃	—	2	2	no	—
278	C₂×D₄×C₂₃	—	2	2	no	—
279	C₂×D₄×C₂₃	—	2	2	no	—
280	C₂×D₄×C₂₃	—	2	2	no	—
281	C₂×D₄×C₂₃	—	2	2	no	—
282	C₂×D₄×C₂₃	—	2	2	no	—
283	C₂×D₄×C₂₃	—	2	2	no	—
284	C₂×D₄×C₂₃	—	2	2	no	—
285	C₂×D₄×C₂₃	—	2	2	no	—
286	C₂×D₄×C₂₃	—	2	2	no	—
287	C₂×D₄×C₂₃	—	4	2	no	—
288	C₂×D₄×C₂₃	—	4	2	no	—
289	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
290	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
291	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
292	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
293	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
294	C₂²×C₄×C₂₃	—	2	2	no	—
295	C₂²×C₄×C₂₃	—	2	2	no	—
296	C₂²×C₄×C₂₃	—	2	2	no	—
297	C₂²×C₄×C₂₃	—	2	2	no	—
298	C₂²×C₄×C₂₃	—	2	2	no	—
299	C₂²×C₄×C₂₃	—	2	2	no	—
300	C₂²×C₄×C₂₃	—	2	2	no	—
301	C₂²×C₄×C₂₃	—	2	2	no	—
302	C₂²×C₄×C₂₃	—	8	4	no	—
303	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
304	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
306	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
309	Q₁₆×C₂₃	—	4	1	no	—
310	SD₁₆×C₂₃	—	4	2	no	—
311	SD₁₆×C₂₃	—	4	2	no	—
312	SD₁₆×C₂₃	—	4	2	no	—
313	D₈×C₂₃	—	4	2	no	—
314	D₈×C₂₃	—	4	1	no	—
315	D₈×C₂₃	—	4	1	no	—
316	D₈×C₂₃	—	4	1	no	—
317	D₈×C₂₃	—	4	2	no	—
318	D₈×C₂₃	—	4	2	no	—
319	M₁₆×C₂₃	—	4	1	no	—
320	M₁₆×C₂₃	—	4	1	no	—
321	C₂×C₈×C₂₃	—	4	1	no	—
322	C₂×C₈×C₂₃	—	4	1	no	—
323	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
324	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
325	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
326	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
327	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
328	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
329	C₄⋊C₄×C₂₃	—	2	2	no	—
330	C₄⋊C₄×C₂₃	—	2	2	no	—
331	C₄⋊C₄×C₂₃	—	2	2	no	—
332	C₄⋊C₄×C₂₃	—	2	2	no	—
333	C₄⋊C₄×C₂₃	—	2	2	no	—
334	C₄⋊C₄×C₂₃	—	2	2	no	—
335	C₄⋊C₄×C₂₃	—	2	2	no	—
336	C₄⋊C₄×C₂₃	—	2	2	no	—
337	C₄⋊C₄×C₂₃	—	2	2	no	—
338	C₄⋊C₄×C₂₃	—	2	2	no	—
339	C₄⋊C₄×C₂₃	—	2	2	no	—
340	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
341	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
342	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
343	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
344	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
346	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
347	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
348	C₂²⋊C₄×C₂₃	—	2	2	no	—
349	C₂²⋊C₄×C₂₃	—	2	2	no	—
350	C₂²⋊C₄×C₂₃	—	2	2	no	—
351	C₂²⋊C₄×C₂₃	—	2	2	no	—
352	C₂²⋊C₄×C₂₃	—	2	2	no	—
353	C₂²⋊C₄×C₂₃	—	2	2	no	—
354	C₂²⋊C₄×C₂₃	—	2	2	no	—
355	C₂²⋊C₄×C₂₃	—	2	2	no	—
356	C₂²⋊C₄×C₂₃	—	2	2	no	—
357	C₂²⋊C₄×C₂₃	—	2	2	no	—
358	C₂²⋊C₄×C₂₃	—	2	2	no	—
359	C₂²⋊C₄×C₂₃	—	2	2	no	—
360	C₂²⋊C₄×C₂₃	—	2	2	no	—
361	C₂²⋊C₄×C₂₃	—	2	2	no	—
362	C₂²⋊C₄×C₂₃	—	2	2	no	—
363	C₂²⋊C₄×C₂₃	—	2	2	no	—
364	C₂²⋊C₄×C₂₃	—	2	2	no	—
365	C₂²⋊C₄×C₂₃	—	2	2	no	—
366	C₂²⋊C₄×C₂₃	—	2	2	no	—
367	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
368	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
369	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
370	C₄²×C₂₃	—	2	2	no	—
371	C₄²×C₂₃	—	2	2	no	—
372	C₄²×C₂₃	—	2	2	no	—
373	C₄²×C₂₃	C₂×D₄	1	2	yes	—
374	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
375	C₄²×C₂₃	C₂×D₄	1	2	yes	—
376	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
377	C₄²×C₂₃	C₂⁴	1	2	yes	—
378	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
379	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
380	#60955	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
381	C₂³×C₂₃	—	2	2	no	—
382	C₂³×C₂₃	—	2	2	no	—
383	C₂³×C₂₃	—	2	2	no	—
384	C₂³×C₂₃	—	4	4	no	—
385	C₂³×C₂₃	—	8	2	no	—
386	C₂³×C₂₃	—	8	2	no	—
387	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
388	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
389	Q₈×C₂₃	—	2	2	no	—
390	Q₈×C₂₃	—	2	2	no	—
391	Q₈×C₂₃	—	4	1	no	—
392	Q₈×C₂₃	—	8	2	no	—
393	Q₈×C₂₃	—	8	2	no	—
394	D₄×C₂₃	—	2	2	no	—
395	D₄×C₂₃	—	2	2	no	—
396	D₄×C₂₃	—	2	2	no	—
397	D₄×C₂₃	—	2	2	no	—
398	D₄×C₂₃	—	2	2	no	—
399	D₄×C₂₃	—	2	2	no	—
400	D₄×C₂₃	—	4	2	no	—
401	D₄×C₂₃	—	4	1	no	—
402	D₄×C₂₃	—	4	4	no	—
403	D₄×C₂₃	—	4	4	no	—
404	D₄×C₂₃	—	8	2	no	—
405	D₄×C₂₃	—	8	2	no	—
406	D₄×C₂₃	—	8	2	no	—
407	D₄×C₂₃	—	8	2	no	—
408	D₄×C₂₃	—	8	2	no	—
409	D₄×C₂₃	—	8	2	no	—
410	D₄×C₂₃	—	8	2	no	—
411	D₄×C₂₃	—	8	2	no	—
412	D₄×C₂₃	—	8	2	no	—
413	D₄×C₂₃	—	8	2	no	—
414	C₂×C₄×C₂₃	—	2	4	no	—
415	C₂×C₄×C₂₃	—	2	2	no	—
416	C₂×C₄×C₂₃	—	2	1	no	—
417	C₂×C₄×C₂₃	—	2	1	no	—
418	C₂×C₄×C₂₃	—	2	2	no	—
419	C₂×C₄×C₂₃	—	2	2	no	—
420	C₂×C₄×C₂₃	—	2	2	no	—
421	C₂×C₄×C₂₃	—	2	2	no	—
422	C₂×C₄×C₂₃	—	2	2	no	—
423	C₂×C₄×C₂₃	—	2	2	no	—
424	C₂×C₄×C₂₃	—	2	2	no	—
425	C₂×C₄×C₂₃	—	4	2	no	—
426	C₂×C₄×C₂₃	—	4	1	no	—
427	C₂×C₄×C₂₃	—	4	4	no	—
428	C₂×C₄×C₂₃	—	4	4	no	—
429	C₂×C₄×C₂₃	—	4	4	no	—
430	C₂×C₄×C₂₃	—	4	4	no	—
431	C₂×C₄×C₂₃	—	8	2	no	—
432	C₂×C₄×C₂₃	—	8	2	no	—
433	C₂×C₄×C₂₃	—	8	2	no	—
434	C₂×C₄×C₂₃	—	8	2	no	—
435	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
437	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
441	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
444	C₈×C₂₃	—	2	1	no	—
445	C₈×C₂₃	—	2	1	no	—
446	C₈×C₂₃	—	2	1	no	—
447	C₈×C₂₃	—	2	1	no	—
448	C₈×C₂₃	—	2	2	no	—
449	C₈×C₂₃	—	2	2	no	—
450	#3460	C₂×C₂₃	1	2	yes	complemented
451	#3262	C₂×C₂₃	1	1	yes	characteristic, complemented
452	#3259	C₂×C₂₃	1	1	yes	characteristic, complemented
453	#3257	C₂×C₂₃	1	2	yes	complemented
454	#3243	C₂×C₂₃	1	2	yes	complemented
455	#3241	C₂×C₂₃	1	2	yes	complemented
456	#3224	C₂×C₂₃	1	2	yes	complemented
457	#3220	C₂×C₂₃	1	2	yes	complemented
458	#3203	C₂×C₂₃	1	1	yes	characteristic, complemented
459	#3199	C₂×C₂₃	1	1	yes	characteristic, complemented
460	#3198	C₂×C₂₃	1	2	yes	complemented
461	#3171	C₂×C₂₃	1	2	yes	complemented
462	#3169	C₂×C₂₃	1	1	yes	characteristic, complemented
463	#3168	C₂×C₂₃	1	1	yes	characteristic, complemented
464	#3106	C₂×C₂₃	1	2	yes	complemented
465	#3105	C₂×C₂₃	1	2	yes	complemented
466	#3102	C₂×C₂₃	1	2	yes	complemented
467	#3100	C₂×C₂₃	1	2	yes	complemented
468	#2922	C₂×C₂₃	1	1	yes	characteristic, complemented
469	C₂²×C₂₃	—	2	1	no	—
470	C₂²×C₂₃	—	2	2	no	—
471	C₂²×C₂₃	—	2	2	no	—
472	C₂²×C₂₃	—	2	1	no	—
473	C₂²×C₂₃	—	2	2	no	—
474	C₂²×C₂₃	—	2	1	no	—
475	C₂²×C₂₃	—	4	2	no	—
476	C₂²×C₂₃	—	4	2	no	—
477	C₂²×C₂₃	—	4	2	no	—
478	C₂²×C₂₃	—	4	2	no	—
479	C₂²×C₂₃	—	4	2	no	—
480	C₂²×C₂₃	—	4	2	no	—
481	C₂²×C₂₃	—	4	2	no	—
482	C₂²×C₂₃	—	4	2	no	—
483	C₂²×C₂₃	—	4	2	no	—
484	C₂²×C₂₃	—	8	8	no	—
485	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
486	C₄×C₂₃	—	2	1	no	—
487	C₄×C₂₃	—	2	2	no	—
488	C₄×C₂₃	—	2	1	no	—
489	C₄×C₂₃	—	2	2	no	—
490	C₄×C₂₃	—	2	1	no	—
491	C₄×C₂₃	—	2	2	no	—
492	C₄×C₂₃	—	2	1	no	—
493	C₄×C₂₃	—	4	2	no	—
494	C₄×C₂₃	—	4	2	no	—
495	C₄×C₂₃	—	4	2	no	—
496	C₄×C₂₃	—	4	2	no	—
497	C₄×C₂₃	—	4	2	no	—
498	C₄×C₂₃	#576	1	2	yes	—
499	C₄×C₂₃	#585	1	1	yes	characteristic
500	C₄×C₂₃	#585	1	1	yes	characteristic
501	#544	C₂²×C₂₃	1	2	yes	complemented
502	#542	—	2	2	no	—
503	#542	C₂²×C₂₃	1	2	yes	—
504	#542	C₂²×C₂₃	1	2	yes	complemented
505	#540	—	2	2	no	—
506	#540	C₂²×C₂₃	1	2	yes	—
507	#540	C₂²×C₂₃	1	2	yes	complemented
508	#538	—	2	2	no	—
509	#538	—	2	2	no	—
510	#537	C₂²×C₂₃	1	2	yes	—
511	#535	C₂²×C₂₃	1	2	yes	—
512	#535	C₂²×C₂₃	1	2	yes	complemented
513	#532	—	2	2	no	—
514	#532	C₂²×C₂₃	1	2	yes	—
515	#532	C₂²×C₂₃	1	2	yes	complemented
516	#529	—	2	2	no	—
517	#529	C₂²×C₂₃	1	2	yes	—
518	#529	C₂²×C₂₃	1	2	yes	complemented
519	#525	—	2	2	no	—
520	#525	—	2	2	no	—
521	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
522	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
523	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
524	#501	C₂²×C₂₃	1	2	yes	complemented
525	#500	C₂²×C₂₃	1	1	yes	characteristic, complemented
526	#499	C₂²×C₂₃	1	1	yes	characteristic, complemented
527	#496	C₂²×C₂₃	1	2	yes	—
528	#495	C₂²×C₂₃	1	1	yes	characteristic
529	#493	C₂²×C₂₃	1	1	yes	characteristic
530	#490	C₂²×C₂₃	1	2	yes	complemented
531	#489	C₂²×C₂₃	1	2	yes	complemented
532	#488	C₂²×C₂₃	1	2	yes	complemented
533	#486	C₂²×C₂₃	1	2	yes	complemented
534	#485	C₂²×C₂₃	1	2	yes	complemented
535	#484	C₂²×C₂₃	1	2	yes	complemented
536	#482	C₂²×C₂₃	1	2	yes	—
537	#482	C₂²×C₂₃	1	2	yes	—
538	#482	C₂²×C₂₃	1	2	yes	complemented
539	#481	C₂²×C₂₃	1	2	yes	—
540	#480	C₂²×C₂₃	1	2	yes	—
541	#480	C₂²×C₂₃	1	2	yes	complemented
542	#479	C₂²×C₂₃	1	2	yes	complemented
543	#478	C₂²×C₂₃	1	2	yes	complemented
544	#478	C₂²×C₂₃	1	2	yes	complemented
545	#478	C₂²×C₂₃	1	2	yes	complemented
546	#477	C₂²×C₂₃	1	2	yes	complemented
547	#476	C₂²×C₂₃	1	2	yes	complemented
548	#474	C₂²×C₂₃	1	2	yes	complemented
549	#474	C₂²×C₂₃	1	2	yes	complemented
550	#469	C₂²×C₂₃	1	2	yes	—
551	#469	C₂²×C₂₃	1	2	yes	complemented
552	#468	C₂²×C₂₃	1	2	yes	complemented
553	#468	C₂²×C₂₃	1	2	yes	complemented
554	#467	C₂²×C₂₃	1	1	yes	characteristic, complemented
555	#466	C₂²×C₂₃	1	1	yes	characteristic
556	#466	C₂²×C₂₃	1	1	yes	characteristic
557	#466	C₂²×C₂₃	1	2	yes	complemented
558	#466	C₂²×C₂₃	1	1	yes	characteristic, complemented
559	#465	C₂²×C₂₃	1	2	yes	complemented
560	#464	C₂²×C₂₃	1	2	yes	complemented
561	#463	C₂²×C₂₃	1	2	yes	—
562	#463	C₂²×C₂₃	1	2	yes	—
563	#463	C₂²×C₂₃	1	2	yes	complemented
564	#460	C₂²×C₂₃	1	2	yes	complemented
565	#459	C₂²×C₂₃	1	2	yes	—
566	#459	C₂²×C₂₃	1	2	yes	—
567	#459	C₂²×C₂₃	1	2	yes	complemented
568	#452	C₂²×C₂₃	1	2	yes	complemented
569	#450	C₂²×C₂₃	1	2	yes	complemented
570	#449	C₂²×C₂₃	1	2	yes	—
571	#449	C₂²×C₂₃	1	2	yes	—
572	#449	C₂²×C₂₃	1	2	yes	complemented
573	#447	C₂²×C₂₃	1	2	yes	—
574	#447	C₂²×C₂₃	1	2	yes	—
575	#447	C₂²×C₂₃	1	2	yes	complemented
576	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
577	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
578	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
579	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
580	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
581	C₄×D₈	C₂²×C₂₃	1	2	yes	—
582	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
583	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
584	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
585	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
586	#433	C₂²×C₂₃	1	2	yes	complemented
587	#433	C₂²×C₂₃	1	2	yes	complemented
588	#431	C₂²×C₂₃	1	2	yes	complemented
589	#431	C₂²×C₂₃	1	2	yes	complemented
590	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
591	#424	C₂²×C₂₃	1	1	yes	characteristic, complemented
592	#408	C₂²×C₂₃	1	1	yes	characteristic
593	#408	C₂²×C₂₃	1	1	yes	characteristic
594	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
595	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
596	C₂×C₂₃	—	4	1	no	—
597	C₂×C₂₃	—	4	2	no	—
598	C₂×C₂₃	—	8	2	no	—
599	C₂×C₂₃	—	8	2	no	—
600	C₂×C₂₃	—	8	2	no	—
601	C₂×C₂₃	#3449	1	1	yes	characteristic
602	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
603	C₂×C₂₃	#3584	1	1	yes	characteristic
604	C₂×#41	—	2	2	no	—
605	C₂×#41	—	2	2	no	—
606	C₂×#41	C₂³×C₂₃	1	2	yes	—
607	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
608	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
609	C₂³×C₄	—	2	2	no	—
610	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
611	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
612	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
613	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
614	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
615	C₂×D₈	C₂³×C₂₃	1	2	yes	—
616	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
617	C₂×D₈	C₂³×C₂₃	1	2	yes	—
618	C₂×D₈	C₂³×C₂₃	1	2	yes	—
619	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
620	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
621	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
622	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
623	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
624	C₄⋊Q₈	—	2	2	no	—
625	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
626	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
627	#127	—	2	2	no	—
628	#127	C₂³×C₂₃	1	2	yes	—
629	#127	C₂³×C₂₃	1	2	yes	—
630	#126	—	2	2	no	—
631	#126	—	2	2	no	—
632	#126	—	2	2	no	—
633	#126	—	2	2	no	—
634	#125	—	2	2	no	—
635	#125	C₂³×C₂₃	1	2	yes	—
636	#125	C₂³×C₂₃	1	2	yes	—
637	#124	—	2	2	no	—
638	#124	—	2	2	no	—
639	#124	—	2	2	no	—
640	#124	—	2	2	no	—
641	#124	—	2	2	no	—
642	#124	C₂³×C₂₃	1	2	yes	—
643	#124	C₂³×C₂₃	1	2	yes	—
644	#123	—	2	2	no	—
645	#123	—	2	2	no	—
646	#123	—	2	2	no	—
647	#123	—	2	2	no	—
648	#123	—	2	2	no	—
649	#123	—	2	2	no	—
650	#123	—	2	2	no	—
651	#123	—	2	2	no	—
652	C₂²⋊Q₈	—	2	2	no	—
653	C₂²⋊Q₈	—	2	2	no	—
654	C₂²⋊Q₈	—	2	2	no	—
655	C₂²⋊Q₈	—	2	2	no	—
656	C₂²⋊Q₈	—	2	2	no	—
657	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
658	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
659	#121	—	2	2	no	—
660	#121	—	2	2	no	—
661	#121	—	2	2	no	—
662	#121	—	2	2	no	—
663	#121	—	2	2	no	—
664	#121	—	2	2	no	—
665	#121	—	2	2	no	—
666	#121	—	2	2	no	—
667	#121	—	2	2	no	—
668	#121	—	2	2	no	—
669	#121	—	2	2	no	—
670	#121	C₂³×C₂₃	1	2	yes	—
671	#121	C₂³×C₂₃	1	2	yes	—
672	#121	C₂³×C₂₃	1	2	yes	—
673	#121	C₂³×C₂₃	1	2	yes	—
674	#121	C₂³×C₂₃	1	2	yes	—
675	#121	C₂³×C₂₃	1	2	yes	—
676	#120	—	2	2	no	—
677	#120	—	2	2	no	—
678	#120	—	2	2	no	—
679	#120	—	2	2	no	—
680	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
681	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
682	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
683	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
684	C₄×D₄	—	2	2	no	—
685	C₄×D₄	—	2	2	no	—
686	C₄×D₄	—	2	2	no	—
687	C₄×D₄	—	2	2	no	—
688	C₄×D₄	—	2	2	no	—
689	C₄×D₄	—	2	2	no	—
690	C₄×D₄	—	2	2	no	—
691	C₄×D₄	—	2	2	no	—
692	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
693	C₄×D₄	D₄×C₂₃	1	2	yes	—
694	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
695	C₄×D₄	D₄×C₂₃	1	2	yes	—
696	C₄×D₄	C₂³×C₂₃	1	2	yes	—
697	C₄×D₄	C₂³×C₂₃	1	2	yes	—
698	C₄×D₄	C₂³×C₂₃	1	2	yes	—
699	C₄×D₄	C₂³×C₂₃	1	2	yes	—
700	C₄×D₄	C₂³×C₂₃	1	2	yes	—
701	C₄×D₄	C₂³×C₂₃	1	2	yes	—
702	#117	—	2	2	no	—
703	#117	—	2	2	no	—
704	#117	—	2	2	no	—
705	#117	C₂³×C₂₃	1	2	yes	—
706	#117	C₂³×C₂₃	1	2	yes	—
707	#117	C₂³×C₂₃	1	1	yes	characteristic
708	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
709	C₂×C₂²⋊C₄	—	2	2	no	—
710	C₂×C₄²	—	2	2	no	—
711	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
712	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
713	#107	C₂³×C₂₃	1	1	yes	characteristic
714	#107	C₂³×C₂₃	1	1	yes	characteristic
715	#107	C₂³×C₂₃	1	2	yes	—
716	#107	C₂³×C₂₃	1	1	yes	characteristic
717	#107	C₂³×C₂₃	1	2	yes	—
718	#107	C₂³×C₂₃	1	2	yes	—
719	#107	C₂³×C₂₃	1	1	yes	characteristic
720	#106	C₂³×C₂₃	1	2	yes	—
721	#106	C₂³×C₂₃	1	2	yes	—
722	#106	C₂³×C₂₃	1	2	yes	—
723	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
724	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
725	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
726	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
727	#103	C₂³×C₂₃	1	2	yes	—
728	#103	C₂³×C₂₃	1	2	yes	—
729	#103	C₂³×C₂₃	1	2	yes	—
730	#103	C₂³×C₂₃	1	2	yes	—
731	#102	C₂³×C₂₃	1	2	yes	—
732	#102	C₂³×C₂₃	1	2	yes	—
733	#102	C₂³×C₂₃	1	2	yes	—
734	#102	C₂³×C₂₃	1	2	yes	—
735	#102	C₂³×C₂₃	1	2	yes	—
736	#102	C₂³×C₂₃	1	2	yes	—
737	#102	C₂³×C₂₃	1	2	yes	—
738	#102	C₂³×C₂₃	1	2	yes	—
739	#102	C₂³×C₂₃	1	2	yes	—
740	#102	C₂³×C₂₃	1	2	yes	—
741	#102	C₂³×C₂₃	1	2	yes	—
742	#102	C₂³×C₂₃	1	2	yes	—
743	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
744	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
745	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
746	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
747	#97	C₂³×C₂₃	1	2	yes	—
748	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
749	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
750	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
751	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
752	C₄×C₈	C₂³×C₂₃	1	2	yes	—
753	C₂₃	#60955	1	1	yes	characteristic, direct product factor, Sylow
754	C₂⁴	—	2	2	no	—
755	#41	—	4	1	no	—
756	#41	—	4	1	no	—
757	#41	—	4	2	no	—
758	#41	—	4	2	no	—
759	#41	—	8	4	no	—
760	#41	—	8	4	no	—
761	C₂×Q₈	—	2	2	no	—
762	C₂×Q₈	—	2	2	no	—
763	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
764	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	2	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	2	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	—	2	2	no	—
773	C₂×D₄	—	2	2	no	—
774	C₂×D₄	—	2	2	no	—
775	C₂×D₄	—	2	2	no	—
776	C₂×D₄	—	2	2	no	—
777	C₂×D₄	—	4	2	no	—
778	C₂×D₄	—	4	2	no	—
779	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
780	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
781	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
782	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
783	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	—	2	2	no	—
788	C₂²×C₄	—	2	2	no	—
789	C₂²×C₄	—	2	2	no	—
790	C₂²×C₄	—	2	2	no	—
791	C₂²×C₄	—	2	2	no	—
792	C₂²×C₄	—	8	4	no	—
793	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
794	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
795	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
796	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
798	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
799	Q₁₆	—	4	1	no	—
800	SD₁₆	—	4	2	no	—
801	SD₁₆	—	4	2	no	—
802	SD₁₆	—	4	2	no	—
803	D₈	—	4	2	no	—
804	D₈	—	4	1	no	—
805	D₈	—	4	1	no	—
806	D₈	—	4	1	no	—
807	D₈	—	4	2	no	—
808	D₈	—	4	2	no	—
809	M₁₆	—	4	1	no	—
810	M₁₆	—	4	1	no	—
811	C₂×C₈	—	4	1	no	—
812	C₂×C₈	—	4	1	no	—
813	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
814	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
815	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
816	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
817	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
818	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
831	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
832	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
833	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
834	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
835	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
836	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
837	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	2	2	no	—
850	C₂²⋊C₄	—	2	2	no	—
851	C₂²⋊C₄	—	2	2	no	—
852	C₂²⋊C₄	—	2	2	no	—
853	C₂²⋊C₄	—	2	2	no	—
854	C₂²⋊C₄	—	2	2	no	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
858	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
859	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
860	C₄²	—	2	2	no	—
861	C₄²	—	2	2	no	—
862	C₄²	—	2	2	no	—
863	C₄²	C₂×D₄×C₂₃	1	2	yes	—
864	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
865	C₄²	C₂×D₄×C₂₃	1	2	yes	—
866	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
867	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
868	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
869	C₄²	C₂⁴×C₂₃	1	2	yes	—
870	C₂³	—	2	2	no	—
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	4	4	no	—
874	C₂³	—	8	2	no	—
875	C₂³	—	8	2	no	—
876	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
877	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
878	Q₈	—	2	2	no	—
879	Q₈	—	2	2	no	—
880	Q₈	—	4	1	no	—
881	Q₈	—	8	2	no	—
882	Q₈	—	8	2	no	—
883	D₄	—	2	2	no	—
884	D₄	—	2	2	no	—
885	D₄	—	2	2	no	—
886	D₄	—	2	2	no	—
887	D₄	—	2	2	no	—
888	D₄	—	2	2	no	—
889	D₄	—	4	2	no	—
890	D₄	—	4	1	no	—
891	D₄	—	4	4	no	—
892	D₄	—	4	4	no	—
893	D₄	—	8	2	no	—
894	D₄	—	8	2	no	—
895	D₄	—	8	2	no	—
896	D₄	—	8	2	no	—
897	D₄	—	8	2	no	—
898	D₄	—	8	2	no	—
899	D₄	—	8	2	no	—
900	D₄	—	8	2	no	—
901	D₄	—	8	2	no	—
902	D₄	—	8	2	no	—
903	C₂×C₄	—	2	4	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	1	no	—
906	C₂×C₄	—	2	1	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	4	2	no	—
915	C₂×C₄	—	4	1	no	—
916	C₂×C₄	—	4	4	no	—
917	C₂×C₄	—	4	4	no	—
918	C₂×C₄	—	4	4	no	—
919	C₂×C₄	—	4	4	no	—
920	C₂×C₄	—	8	2	no	—
921	C₂×C₄	—	8	2	no	—
922	C₂×C₄	—	8	2	no	—
923	C₂×C₄	—	8	2	no	—
924	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
925	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
926	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
927	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
928	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
929	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
930	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
931	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
932	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
933	C₈	—	2	1	no	—
934	C₈	—	2	1	no	—
935	C₈	—	2	1	no	—
936	C₈	—	2	1	no	—
937	C₈	—	2	2	no	—
938	C₈	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	1	no	—
943	C₂²	—	2	1	no	—
944	C₂²	—	2	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	4	2	no	—
949	C₂²	—	4	2	no	—
950	C₂²	—	4	2	no	—
951	C₂²	—	4	2	no	—
952	C₂²	—	4	2	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	8	8	no	—
955	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
956	C₄	—	2	2	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	2	no	—
959	C₄	—	2	1	no	—
960	C₄	—	2	1	no	—
961	C₄	—	2	2	no	—
962	C₄	—	2	1	no	—
963	C₄	—	4	2	no	—
964	C₄	—	4	2	no	—
965	C₄	—	4	2	no	—
966	C₄	—	4	2	no	—
967	C₄	—	4	2	no	—
968	C₄	C₂₃×#576	1	2	yes	—
969	C₄	C₂₃×#585	1	1	yes	characteristic
970	C₄	C₂₃×#585	1	1	yes	characteristic
971	C₂	—	4	2	no	—
972	C₂	—	4	1	no	—
973	C₂	—	8	2	no	—
974	C₂	—	8	2	no	—
975	C₂	—	8	2	no	—
976	C₂	C₂₃×#3449	1	1	yes	characteristic
977	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
978	C₂	C₂₃×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3460	C₂	semidirect
2. C₂₃×#3262	C₂	semidirect
3. C₂₃×#3259	C₂	semidirect
4. C₂₃×#3257	C₂	semidirect
5. C₂₃×#3243	C₂	semidirect
6. C₂₃×#3241	C₂	semidirect
7. C₂₃×#3224	C₂	semidirect
8. C₂₃×#3220	C₂	semidirect
9. C₂₃×#3203	C₂	semidirect
10. C₂₃×#3199	C₂	semidirect
11. C₂₃×#3198	C₂	semidirect
12. C₂₃×#3171	C₂	semidirect
13. C₂₃×#3169	C₂	semidirect
14. C₂₃×#3168	C₂	semidirect
15. C₂₃×#3106	C₂	semidirect
16. C₂₃×#3105	C₂	semidirect
17. C₂₃×#3102	C₂	semidirect
18. C₂₃×#3100	C₂	semidirect
19. C₂₃×#2922	C₂	semidirect
20. C₂₃×#544	C₂²	semidirect
23. C₂₃×#542	C₂²	semidirect
26. C₂₃×#540	C₂²	semidirect
31. C₂₃×#535	C₂²	semidirect
34. C₂₃×#532	C₂²	semidirect
37. C₂₃×#529	C₂²	semidirect
41. C₄×#41×C₂₃	C₂²	semidirect
42. C₂×C₄×D₄×C₂₃	C₂²	semidirect
43. C₂₃×#501	C₂²	semidirect
44. C₂₃×#500	C₂²	semidirect
45. C₂₃×#499	C₂²	semidirect
49. C₂₃×#490	C₂²	semidirect
50. C₂₃×#489	C₂²	semidirect
51. C₂₃×#488	C₂²	semidirect
52. C₂₃×#486	C₂²	semidirect
53. C₂₃×#485	C₂²	semidirect
54. C₂₃×#484	C₂²	semidirect
57. C₂₃×#482	C₂²	semidirect
60. C₂₃×#480	C₂²	semidirect
61. C₂₃×#479	C₂²	semidirect
62. C₂₃×#478	C₂²	semidirect
63. C₂₃×#478	C₂²	semidirect
64. C₂₃×#478	C₂²	semidirect
65. C₂₃×#477	C₂²	semidirect
66. C₂₃×#476	C₂²	semidirect
67. C₂₃×#474	C₂²	semidirect
68. C₂₃×#474	C₂²	semidirect
70. C₂₃×#469	C₂²	semidirect
71. C₂₃×#468	C₂²	semidirect
72. C₂₃×#468	C₂²	semidirect
73. C₂₃×#467	C₂²	semidirect
76. C₂₃×#466	C₂²	semidirect
77. C₂₃×#466	C₂²	semidirect
78. C₂₃×#465	C₂²	semidirect
79. C₂₃×#464	C₂²	semidirect
82. C₂₃×#463	C₂²	semidirect
83. C₂₃×#460	C₂²	semidirect
86. C₂₃×#459	C₂²	semidirect
87. C₂₃×#452	C₂²	semidirect
88. C₂₃×#450	C₂²	semidirect
91. C₂₃×#449	C₂²	semidirect
94. C₂₃×#447	C₂²	semidirect
95. C₄×Q₁₆×C₂₃	C₂²	semidirect
96. C₄×SD₁₆×C₂₃	C₂²	semidirect
97. C₄×SD₁₆×C₂₃	C₂²	semidirect
98. C₄×SD₁₆×C₂₃	C₂²	semidirect
102. C₄×D₈×C₂₃	C₂²	semidirect
103. C₄×D₈×C₂₃	C₂²	semidirect
104. C₄×D₈×C₂₃	C₂²	semidirect
105. C₂₃×#433	C₂²	semidirect
106. C₂₃×#433	C₂²	semidirect
107. C₂₃×#431	C₂²	semidirect
108. C₂₃×#431	C₂²	semidirect
109. C₂₃×#424	C₂²	semidirect
110. C₂₃×#424	C₂²	semidirect
113. C₄×M₁₆×C₂₃	C₂²	semidirect
114. C₂×C₄×C₈×C₂₃	C₂²	semidirect
380. #60955	C₂₃	direct (N × H)
450. #3460	C₂×C₂₃	semidirect
451. #3262	C₂×C₂₃	semidirect
452. #3259	C₂×C₂₃	semidirect
453. #3257	C₂×C₂₃	semidirect
454. #3243	C₂×C₂₃	semidirect
455. #3241	C₂×C₂₃	semidirect
456. #3224	C₂×C₂₃	semidirect
457. #3220	C₂×C₂₃	semidirect
458. #3203	C₂×C₂₃	semidirect
459. #3199	C₂×C₂₃	semidirect
460. #3198	C₂×C₂₃	semidirect
461. #3171	C₂×C₂₃	semidirect
462. #3169	C₂×C₂₃	semidirect
463. #3168	C₂×C₂₃	semidirect
464. #3106	C₂×C₂₃	semidirect
465. #3105	C₂×C₂₃	semidirect
466. #3102	C₂×C₂₃	semidirect
467. #3100	C₂×C₂₃	semidirect
468. #2922	C₂×C₂₃	semidirect
501. #544	C₂²×C₂₃	semidirect
504. #542	C₂²×C₂₃	semidirect
507. #540	C₂²×C₂₃	semidirect
512. #535	C₂²×C₂₃	semidirect
515. #532	C₂²×C₂₃	semidirect
518. #529	C₂²×C₂₃	semidirect
522. C₄×#41	C₂²×C₂₃	semidirect
523. C₂×C₄×D₄	C₂²×C₂₃	semidirect
524. #501	C₂²×C₂₃	semidirect
525. #500	C₂²×C₂₃	semidirect
526. #499	C₂²×C₂₃	semidirect
530. #490	C₂²×C₂₃	semidirect
531. #489	C₂²×C₂₃	semidirect
532. #488	C₂²×C₂₃	semidirect
533. #486	C₂²×C₂₃	semidirect
534. #485	C₂²×C₂₃	semidirect
535. #484	C₂²×C₂₃	semidirect
538. #482	C₂²×C₂₃	semidirect
541. #480	C₂²×C₂₃	semidirect
542. #479	C₂²×C₂₃	semidirect
543. #478	C₂²×C₂₃	semidirect
544. #478	C₂²×C₂₃	semidirect
545. #478	C₂²×C₂₃	semidirect
546. #477	C₂²×C₂₃	semidirect
547. #476	C₂²×C₂₃	semidirect
548. #474	C₂²×C₂₃	semidirect
549. #474	C₂²×C₂₃	semidirect
551. #469	C₂²×C₂₃	semidirect
552. #468	C₂²×C₂₃	semidirect
553. #468	C₂²×C₂₃	semidirect
554. #467	C₂²×C₂₃	semidirect
557. #466	C₂²×C₂₃	semidirect
558. #466	C₂²×C₂₃	semidirect
559. #465	C₂²×C₂₃	semidirect
560. #464	C₂²×C₂₃	semidirect
563. #463	C₂²×C₂₃	semidirect
564. #460	C₂²×C₂₃	semidirect
567. #459	C₂²×C₂₃	semidirect
568. #452	C₂²×C₂₃	semidirect
569. #450	C₂²×C₂₃	semidirect
572. #449	C₂²×C₂₃	semidirect
575. #447	C₂²×C₂₃	semidirect
576. C₄×Q₁₆	C₂²×C₂₃	semidirect
577. C₄×SD₁₆	C₂²×C₂₃	semidirect
578. C₄×SD₁₆	C₂²×C₂₃	semidirect
579. C₄×SD₁₆	C₂²×C₂₃	semidirect
583. C₄×D₈	C₂²×C₂₃	semidirect
584. C₄×D₈	C₂²×C₂₃	semidirect
585. C₄×D₈	C₂²×C₂₃	semidirect
586. #433	C₂²×C₂₃	semidirect
587. #433	C₂²×C₂₃	semidirect
588. #431	C₂²×C₂₃	semidirect
589. #431	C₂²×C₂₃	semidirect
590. #424	C₂²×C₂₃	semidirect
591. #424	C₂²×C₂₃	semidirect
594. C₄×M₁₆	C₂²×C₂₃	semidirect
595. C₂×C₄×C₈	C₂²×C₂₃	semidirect
753. C₂₃	#60955	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×#3460	2
C₂₃×#3262	2
C₂₃×#3259	2
C₂₃×#3257	2
C₂₃×#3243	2
C₂₃×#3241	2
C₂₃×#3224	2
C₂₃×#3220	2
C₂₃×#3203	2
C₂₃×#3199	2
C₂₃×#3198	2
C₂₃×#3171	2
C₂₃×#3169	2
C₂₃×#3168	2
C₂₃×#3106	2
C₂₃×#3105	2
C₂₃×#3102	2
C₂₃×#3100	2
C₂₃×#2922	2
#60955	23

Subgroups — C23×#60955 #19208581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60955 #19208581