Subgroups — C₂₃×#61740 #19209366

Order 5888.

1880 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3357	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3347	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3341	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3325	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3319	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3305	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3238	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3226	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3194	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3186	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3094	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3091	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#555	—	2	1	no	—
19	C₂₃×#555	—	2	1	no	—
20	C₂₃×#555	—	2	2	no	—
21	C₂₃×#555	C₂²	1	2	yes	—
22	C₂₃×#555	C₂²	1	2	yes	complemented
23	C₂₃×#555	C₂²	1	4	yes	complemented
24	C₂₃×#555	C₂²	1	1	yes	characteristic, complemented
25	C₂₃×#554	C₂²	1	1	yes	characteristic, complemented
26	C₂₃×#553	—	2	1	no	—
27	C₂₃×#553	C₂²	1	2	yes	complemented
28	C₂₃×#550	C₂²	1	1	yes	characteristic, complemented
29	C₂₃×#546	—	2	2	no	—
30	C₂₃×#546	C₂²	1	2	yes	complemented
31	D₄²×C₂₃	—	2	1	no	—
32	D₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#540	—	2	1	no	—
34	C₂₃×#538	—	2	2	no	—
35	C₂₃×#532	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₂₃×#529	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#124	—	2	2	no	—
39	C₂₃×#525	C₂²	1	2	yes	—
40	C₂×C₂₃×#121	—	2	1	no	—
41	C₂×C₂₃×#121	C₂²	1	2	yes	—
42	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
43	C₂₃×#518	—	2	1	no	—
44	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₂₃×#117	—	2	1	no	—
47	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
48	C₂₃×#501	C₂²	1	2	yes	complemented
49	C₂₃×#500	C₂²	1	2	yes	complemented
50	C₂₃×#489	C₂²	1	2	yes	complemented
51	C₂₃×#486	C₂²	1	2	yes	complemented
52	C₂₃×#485	C₂²	1	4	yes	complemented
53	C₂₃×#484	C₂²	1	1	yes	characteristic, complemented
54	C₂₃×#483	C₂²	1	2	yes	complemented
55	C₂₃×#482	C₂²	1	4	yes	complemented
56	C₂₃×#482	C₂²	1	4	yes	complemented
57	C₂₃×#482	C₂²	1	4	yes	complemented
58	C₂₃×#482	C₂²	1	4	yes	complemented
59	C₂₃×#481	C₂²	1	1	yes	characteristic
60	C₂₃×#481	C₂²	1	2	yes	complemented
61	C₂₃×#480	C₂²	1	2	yes	—
62	C₂₃×#480	C₂²	1	2	yes	complemented
63	C₂₃×#480	C₂²	1	4	yes	complemented
64	C₂₃×#480	C₂²	1	2	yes	complemented
65	C₂₃×#478	C₂²	1	2	yes	complemented
66	C₂₃×#477	C₂²	1	2	yes	complemented
67	C₂₃×#476	C₂²	1	2	yes	complemented
68	C₂₃×#476	C₂²	1	2	yes	complemented
69	C₂₃×#474	C₂²	1	4	yes	complemented
70	C₂₃×#469	C₂²	1	4	yes	complemented
71	C₂₃×#468	C₂²	1	4	yes	complemented
72	C₂₃×#466	C₂²	1	4	yes	complemented
73	C₂₃×#466	C₂²	1	4	yes	complemented
74	C₂₃×#463	C₂²	1	2	yes	complemented
75	C₂₃×#459	C₂²	1	2	yes	complemented
76	C₂₃×#450	C₂²	1	1	yes	characteristic, complemented
77	C₂₃×#449	C₂²	1	4	yes	complemented
78	C₂₃×#447	C₂²	1	1	yes	characteristic
79	C₂₃×#447	C₂²	1	2	yes	complemented
80	C₂₃×#447	C₂²	1	4	yes	complemented
81	C₂₃×#442	C₂²	1	4	yes	complemented
82	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
83	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
84	C₂₃×#436	C₂²	1	2	yes	complemented
85	C₂₃×#435	C₂²	1	4	yes	complemented
86	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
87	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
88	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
89	C₂₃×#428	C₂²	1	4	yes	complemented
90	C₂₃×#427	C₂²	1	4	yes	complemented
91	C₂₃×#418	C₂²	1	4	yes	complemented
92	C₂₃×#416	C₂²	1	4	yes	complemented
93	C₂₃×#407	C₂²	1	2	yes	complemented
94	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
95	C₂×#41×C₂₃	—	2	1	no	—
96	C₂×#41×C₂₃	C₂³	1	2	yes	—
97	C₂²×Q₈×C₂₃	—	2	1	no	—
98	C₂²×D₄×C₂₃	—	2	2	no	—
99	C₂²×D₄×C₂₃	—	2	2	no	—
100	C₂²×D₄×C₂₃	—	2	1	no	—
101	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
102	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
103	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₂₃	—	2	1	no	—
105	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
106	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
107	C₂×D₈×C₂₃	C₂³	1	2	yes	—
108	C₂×D₈×C₂₃	C₂³	1	4	yes	—
109	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
110	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
111	C₂₃×C₄⋊Q₈	—	2	1	no	—
112	C₂₃×C₄⋊Q₈	—	2	1	no	—
113	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
116	C₂₃×#127	—	2	1	no	—
117	C₂₃×#127	C₂³	1	1	yes	characteristic
118	C₂₃×#126	—	2	2	no	—
119	C₂₃×#126	—	2	1	no	—
120	C₂₃×#125	—	2	1	no	—
121	C₂₃×#125	C₂³	1	1	yes	characteristic
122	C₂₃×#124	—	2	4	no	—
123	C₂₃×#124	—	2	4	no	—
124	C₂₃×#124	—	2	4	no	—
125	C₂₃×#124	—	2	4	no	—
126	C₂₃×#124	—	2	2	no	—
127	C₂₃×#124	—	2	1	no	—
128	C₂₃×#124	C₂³	1	1	yes	characteristic
129	C₂₃×#123	—	2	2	no	—
130	C₂₃×#123	—	2	1	no	—
131	C₂₃×#123	—	2	2	no	—
132	C₂₃×#123	—	2	2	no	—
133	C₂₃×C₂²⋊Q₈	—	2	2	no	—
134	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
136	C₂₃×#121	—	2	2	no	—
137	C₂₃×#121	—	2	2	no	—
138	C₂₃×#121	—	2	2	no	—
139	C₂₃×#121	—	2	4	no	—
140	C₂₃×#121	—	2	1	no	—
141	C₂₃×#121	—	2	2	no	—
142	C₂₃×#121	—	2	1	no	—
143	C₂₃×#121	—	2	2	no	—
144	C₂₃×#121	—	2	2	no	—
145	C₂₃×#121	—	2	2	no	—
146	C₂₃×#121	—	2	1	no	—
147	C₂₃×#121	—	2	2	no	—
148	C₂₃×#121	—	2	2	no	—
149	C₂₃×#121	C₂³	1	2	yes	—
150	C₂₃×#121	C₂³	1	2	yes	—
151	C₂₃×#121	C₂³	1	4	yes	—
152	C₂₃×#121	C₂³	1	4	yes	—
153	C₂₃×#121	C₂³	1	2	yes	—
154	C₂₃×#121	C₂³	1	1	yes	characteristic
155	C₂₃×#121	C₂³	1	2	yes	—
156	C₂₃×#120	—	2	2	no	—
157	C₂₃×#120	—	2	2	no	—
158	C₂₃×#120	—	2	2	no	—
159	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
160	C₄×D₄×C₂₃	—	2	1	no	—
161	C₄×D₄×C₂₃	—	2	2	no	—
162	C₄×D₄×C₂₃	—	2	1	no	—
163	C₄×D₄×C₂₃	—	2	2	no	—
164	C₄×D₄×C₂₃	—	2	1	no	—
165	C₄×D₄×C₂₃	—	2	2	no	—
166	C₄×D₄×C₂₃	—	2	1	no	—
167	C₄×D₄×C₂₃	—	2	1	no	—
168	C₄×D₄×C₂₃	—	2	1	no	—
169	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
170	C₄×D₄×C₂₃	D₄	1	2	yes	—
171	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
172	C₄×D₄×C₂₃	C₂³	1	2	yes	—
173	C₄×D₄×C₂₃	C₂³	1	2	yes	—
174	C₄×D₄×C₂₃	C₂³	1	2	yes	—
175	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₂₃	C₂³	1	2	yes	—
178	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
179	C₂₃×#117	—	2	2	no	—
180	C₂₃×#117	—	2	2	no	—
181	C₂₃×#117	—	2	1	no	—
182	C₂₃×#117	—	2	2	no	—
183	C₂₃×#117	—	2	2	no	—
184	C₂₃×#117	—	2	4	no	—
185	C₂₃×#117	—	2	1	no	—
186	C₂₃×#117	C₂³	1	2	yes	—
187	C₂₃×#117	C₂³	1	4	yes	—
188	C₂₃×#117	C₂³	1	4	yes	—
189	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
190	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
191	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
192	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
195	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
196	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
197	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
200	C₂×C₄²×C₂₃	—	2	2	no	—
201	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
202	C₂₃×#107	C₂³	1	2	yes	—
203	C₂₃×#107	C₂³	1	4	yes	—
204	C₂₃×#107	C₂³	1	4	yes	—
205	C₂₃×#107	C₂³	1	4	yes	—
206	C₂₃×#106	C₂³	1	4	yes	—
207	C₂₃×#106	C₂³	1	4	yes	—
208	C₂₃×#106	C₂³	1	2	yes	—
209	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
210	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₂₃×#103	C₂³	1	2	yes	—
212	C₂₃×#103	C₂³	1	4	yes	—
213	C₂₃×#102	C₂³	1	4	yes	—
214	C₂₃×#102	C₂³	1	4	yes	—
215	C₂₃×#102	C₂³	1	2	yes	—
216	C₂₃×#102	C₂³	1	4	yes	—
217	C₂₃×#102	C₂³	1	4	yes	—
218	C₂₃×#102	C₂³	1	2	yes	—
219	C₂₃×#102	C₂³	1	2	yes	—
220	C₂₃×#102	C₂³	1	4	yes	—
221	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
222	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
223	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
224	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
225	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₂₃×#97	C₂³	1	2	yes	—
227	C₄×C₈×C₂₃	C₂³	1	2	yes	—
228	C₂⁴×C₂₃	—	2	1	no	—
229	C₂⁴×C₂₃	—	2	2	no	—
230	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
231	#41×C₂₃	—	4	4	no	—
232	#41×C₂₃	—	8	2	no	—
233	C₂×Q₈×C₂₃	—	2	1	no	—
234	C₂×Q₈×C₂₃	—	2	2	no	—
235	C₂×Q₈×C₂₃	—	2	2	no	—
236	C₂×Q₈×C₂₃	—	8	2	no	—
237	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
238	C₂×D₄×C₂₃	—	2	2	no	—
239	C₂×D₄×C₂₃	—	2	2	no	—
240	C₂×D₄×C₂₃	—	2	1	no	—
241	C₂×D₄×C₂₃	—	2	2	no	—
242	C₂×D₄×C₂₃	—	2	2	no	—
243	C₂×D₄×C₂₃	—	2	2	no	—
244	C₂×D₄×C₂₃	—	2	4	no	—
245	C₂×D₄×C₂₃	—	2	4	no	—
246	C₂×D₄×C₂₃	—	2	1	no	—
247	C₂×D₄×C₂₃	—	2	1	no	—
248	C₂×D₄×C₂₃	—	2	1	no	—
249	C₂×D₄×C₂₃	—	2	2	no	—
250	C₂×D₄×C₂₃	—	4	2	no	—
251	C₂×D₄×C₂₃	—	4	2	no	—
252	C₂×D₄×C₂₃	—	4	4	no	—
253	C₂×D₄×C₂₃	—	4	4	no	—
254	C₂×D₄×C₂₃	—	8	4	no	—
255	C₂×D₄×C₂₃	—	8	4	no	—
256	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
257	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
258	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
260	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
261	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₂₃	—	2	1	no	—
263	C₂²×C₄×C₂₃	—	2	2	no	—
264	C₂²×C₄×C₂₃	—	2	2	no	—
265	C₂²×C₄×C₂₃	—	2	2	no	—
266	C₂²×C₄×C₂₃	—	2	2	no	—
267	C₂²×C₄×C₂₃	—	2	1	no	—
268	C₂²×C₄×C₂₃	—	2	2	no	—
269	C₂²×C₄×C₂₃	—	2	2	no	—
270	C₂²×C₄×C₂₃	—	4	4	no	—
271	C₂²×C₄×C₂₃	—	4	4	no	—
272	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
276	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
277	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
279	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
280	SD₁₆×C₂₃	—	4	2	no	—
281	D₈×C₂₃	—	4	2	no	—
282	D₈×C₂₃	—	4	4	no	—
283	M₁₆×C₂₃	—	4	4	no	—
284	C₂×C₈×C₂₃	—	4	4	no	—
285	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
286	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
287	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
288	C₄⋊C₄×C₂₃	—	2	2	no	—
289	C₄⋊C₄×C₂₃	—	2	2	no	—
290	C₄⋊C₄×C₂₃	—	2	1	no	—
291	C₄⋊C₄×C₂₃	—	2	2	no	—
292	C₄⋊C₄×C₂₃	—	2	2	no	—
293	C₄⋊C₄×C₂₃	—	2	1	no	—
294	C₄⋊C₄×C₂₃	—	2	1	no	—
295	C₄⋊C₄×C₂₃	—	2	1	no	—
296	C₄⋊C₄×C₂₃	—	2	1	no	—
297	C₄⋊C₄×C₂₃	—	2	2	no	—
298	C₄⋊C₄×C₂₃	—	2	1	no	—
299	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
300	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
301	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
303	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
304	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
307	C₂²⋊C₄×C₂₃	—	2	4	no	—
308	C₂²⋊C₄×C₂₃	—	2	4	no	—
309	C₂²⋊C₄×C₂₃	—	2	2	no	—
310	C₂²⋊C₄×C₂₃	—	2	2	no	—
311	C₂²⋊C₄×C₂₃	—	2	1	no	—
312	C₂²⋊C₄×C₂₃	—	2	1	no	—
313	C₂²⋊C₄×C₂₃	—	2	1	no	—
314	C₂²⋊C₄×C₂₃	—	2	2	no	—
315	C₂²⋊C₄×C₂₃	—	2	4	no	—
316	C₂²⋊C₄×C₂₃	—	2	4	no	—
317	C₂²⋊C₄×C₂₃	—	2	2	no	—
318	C₂²⋊C₄×C₂₃	—	2	2	no	—
319	C₂²⋊C₄×C₂₃	—	2	2	no	—
320	C₂²⋊C₄×C₂₃	—	2	2	no	—
321	C₂²⋊C₄×C₂₃	—	2	1	no	—
322	C₂²⋊C₄×C₂₃	—	2	2	no	—
323	C₂²⋊C₄×C₂₃	—	2	1	no	—
324	C₂²⋊C₄×C₂₃	—	2	2	no	—
325	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
326	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
327	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
328	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
329	C₄²×C₂₃	—	2	4	no	—
330	C₄²×C₂₃	—	2	4	no	—
331	C₄²×C₂₃	—	2	2	no	—
332	C₄²×C₂₃	—	2	1	no	—
333	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
336	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
337	#61740	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
338	C₂³×C₂₃	—	2	4	no	—
339	C₂³×C₂₃	—	2	2	no	—
340	C₂³×C₂₃	—	2	1	no	—
341	C₂³×C₂₃	—	2	2	no	—
342	C₂³×C₂₃	—	4	2	no	—
343	C₂³×C₂₃	—	4	2	no	—
344	C₂³×C₂₃	—	4	2	no	—
345	C₂³×C₂₃	—	4	2	no	—
346	C₂³×C₂₃	—	4	4	no	—
347	C₂³×C₂₃	—	4	2	no	—
348	C₂³×C₂₃	—	8	2	no	—
349	C₂³×C₂₃	—	8	2	no	—
350	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
351	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
352	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
353	Q₈×C₂₃	—	2	2	no	—
354	Q₈×C₂₃	—	8	2	no	—
355	Q₈×C₂₃	—	8	2	no	—
356	Q₈×C₂₃	—	8	1	no	—
357	D₄×C₂₃	—	2	2	no	—
358	D₄×C₂₃	—	2	2	no	—
359	D₄×C₂₃	—	2	2	no	—
360	D₄×C₂₃	—	2	2	no	—
361	D₄×C₂₃	—	2	2	no	—
362	D₄×C₂₃	—	2	4	no	—
363	D₄×C₂₃	—	4	2	no	—
364	D₄×C₂₃	—	4	2	no	—
365	D₄×C₂₃	—	4	4	no	—
366	D₄×C₂₃	—	4	2	no	—
367	D₄×C₂₃	—	4	4	no	—
368	D₄×C₂₃	—	4	2	no	—
369	D₄×C₂₃	—	8	2	no	—
370	D₄×C₂₃	—	8	1	no	—
371	D₄×C₂₃	—	8	4	no	—
372	D₄×C₂₃	—	8	4	no	—
373	D₄×C₂₃	—	8	2	no	—
374	D₄×C₂₃	—	8	2	no	—
375	D₄×C₂₃	—	8	2	no	—
376	C₂×C₄×C₂₃	—	2	2	no	—
377	C₂×C₄×C₂₃	—	2	2	no	—
378	C₂×C₄×C₂₃	—	2	4	no	—
379	C₂×C₄×C₂₃	—	2	4	no	—
380	C₂×C₄×C₂₃	—	2	2	no	—
381	C₂×C₄×C₂₃	—	2	2	no	—
382	C₂×C₄×C₂₃	—	2	1	no	—
383	C₂×C₄×C₂₃	—	2	4	no	—
384	C₂×C₄×C₂₃	—	2	1	no	—
385	C₂×C₄×C₂₃	—	2	2	no	—
386	C₂×C₄×C₂₃	—	2	1	no	—
387	C₂×C₄×C₂₃	—	4	2	no	—
388	C₂×C₄×C₂₃	—	4	2	no	—
389	C₂×C₄×C₂₃	—	4	2	no	—
390	C₂×C₄×C₂₃	—	4	4	no	—
391	C₂×C₄×C₂₃	—	4	2	no	—
392	C₂×C₄×C₂₃	—	4	4	no	—
393	C₂×C₄×C₂₃	—	4	4	no	—
394	C₂×C₄×C₂₃	—	4	2	no	—
395	C₂×C₄×C₂₃	—	8	2	no	—
396	C₂×C₄×C₂₃	—	8	2	no	—
397	C₂×C₄×C₂₃	—	8	2	no	—
398	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
401	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
402	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
403	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
406	C₈×C₂₃	—	2	2	no	—
407	C₈×C₂₃	—	2	4	no	—
408	C₈×C₂₃	—	2	2	no	—
409	#3519	C₂×C₂₃	1	1	yes	characteristic, complemented
410	C₂×#555	C₂×C₂₃	1	1	yes	characteristic, complemented
411	#3357	C₂×C₂₃	1	2	yes	complemented
412	#3347	C₂×C₂₃	1	4	yes	complemented
413	#3341	C₂×C₂₃	1	2	yes	complemented
414	#3325	C₂×C₂₃	1	2	yes	complemented
415	#3319	C₂×C₂₃	1	4	yes	complemented
416	#3305	C₂×C₂₃	1	2	yes	complemented
417	#3238	C₂×C₂₃	1	1	yes	characteristic, complemented
418	#3226	C₂×C₂₃	1	1	yes	characteristic, complemented
419	#3194	C₂×C₂₃	1	2	yes	complemented
420	#3186	C₂×C₂₃	1	2	yes	complemented
421	#3109	C₂×C₂₃	1	1	yes	characteristic, complemented
422	#3105	C₂×C₂₃	1	1	yes	characteristic, complemented
423	#3094	C₂×C₂₃	1	2	yes	complemented
424	#3091	C₂×C₂₃	1	2	yes	complemented
425	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
426	C₂²×C₂₃	—	2	1	no	—
427	C₂²×C₂₃	—	2	1	no	—
428	C₂²×C₂₃	—	2	2	no	—
429	C₂²×C₂₃	—	2	2	no	—
430	C₂²×C₂₃	—	2	2	no	—
431	C₂²×C₂₃	—	2	2	no	—
432	C₂²×C₂₃	—	2	2	no	—
433	C₂²×C₂₃	—	2	2	no	—
434	C₂²×C₂₃	—	4	2	no	—
435	C₂²×C₂₃	—	4	2	no	—
436	C₂²×C₂₃	—	4	1	no	—
437	C₂²×C₂₃	—	4	2	no	—
438	C₂²×C₂₃	—	4	1	no	—
439	C₂²×C₂₃	—	4	2	no	—
440	C₂²×C₂₃	—	4	2	no	—
441	C₂²×C₂₃	—	4	1	no	—
442	C₂²×C₂₃	—	4	2	no	—
443	C₂²×C₂₃	—	8	4	no	—
444	C₂²×C₂₃	—	8	4	no	—
445	C₂²×C₂₃	—	16	4	no	—
446	C₂²×C₂₃	#576	1	2	yes	—
447	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
448	C₄×C₂₃	—	2	1	no	—
449	C₄×C₂₃	—	2	2	no	—
450	C₄×C₂₃	—	2	2	no	—
451	C₄×C₂₃	—	2	1	no	—
452	C₄×C₂₃	—	2	1	no	—
453	C₄×C₂₃	—	2	1	no	—
454	C₄×C₂₃	—	4	1	no	—
455	C₄×C₂₃	—	4	2	no	—
456	C₄×C₂₃	—	4	1	no	—
457	C₄×C₂₃	—	4	4	no	—
458	C₄×C₂₃	—	4	1	no	—
459	C₄×C₂₃	—	4	2	no	—
460	C₄×C₂₃	#575	1	2	yes	—
461	C₄×C₂₃	#585	1	2	yes	—
462	#555	—	2	1	no	—
463	#555	—	2	1	no	—
464	#555	—	2	2	no	—
465	#555	C₂²×C₂₃	1	2	yes	—
466	#555	C₂²×C₂₃	1	1	yes	characteristic, complemented
467	#555	C₂²×C₂₃	1	2	yes	complemented
468	#555	C₂²×C₂₃	1	4	yes	complemented
469	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
470	#553	—	2	1	no	—
471	#553	C₂²×C₂₃	1	2	yes	complemented
472	#550	C₂²×C₂₃	1	1	yes	characteristic, complemented
473	#546	—	2	2	no	—
474	#546	C₂²×C₂₃	1	2	yes	complemented
475	D₄²	—	2	1	no	—
476	D₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
477	#540	—	2	1	no	—
478	#538	—	2	2	no	—
479	#532	C₂²×C₂₃	1	1	yes	characteristic
480	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
481	#529	C₂²×C₂₃	1	1	yes	characteristic
482	C₂×#124	—	2	2	no	—
483	#525	C₂²×C₂₃	1	2	yes	—
484	C₂×#121	—	2	1	no	—
485	C₂×#121	C₂²×C₂₃	1	2	yes	—
486	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
487	#518	—	2	1	no	—
488	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
489	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
490	C₂×#117	—	2	1	no	—
491	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
492	#501	C₂²×C₂₃	1	2	yes	complemented
493	#500	C₂²×C₂₃	1	2	yes	complemented
494	#489	C₂²×C₂₃	1	2	yes	complemented
495	#486	C₂²×C₂₃	1	2	yes	complemented
496	#485	C₂²×C₂₃	1	4	yes	complemented
497	#484	C₂²×C₂₃	1	1	yes	characteristic, complemented
498	#483	C₂²×C₂₃	1	2	yes	complemented
499	#482	C₂²×C₂₃	1	4	yes	complemented
500	#482	C₂²×C₂₃	1	4	yes	complemented
501	#482	C₂²×C₂₃	1	4	yes	complemented
502	#482	C₂²×C₂₃	1	4	yes	complemented
503	#481	C₂²×C₂₃	1	1	yes	characteristic
504	#481	C₂²×C₂₃	1	2	yes	complemented
505	#480	C₂²×C₂₃	1	2	yes	—
506	#480	C₂²×C₂₃	1	2	yes	complemented
507	#480	C₂²×C₂₃	1	4	yes	complemented
508	#480	C₂²×C₂₃	1	2	yes	complemented
509	#478	C₂²×C₂₃	1	2	yes	complemented
510	#477	C₂²×C₂₃	1	2	yes	complemented
511	#476	C₂²×C₂₃	1	2	yes	complemented
512	#476	C₂²×C₂₃	1	2	yes	complemented
513	#474	C₂²×C₂₃	1	4	yes	complemented
514	#469	C₂²×C₂₃	1	4	yes	complemented
515	#468	C₂²×C₂₃	1	4	yes	complemented
516	#466	C₂²×C₂₃	1	4	yes	complemented
517	#466	C₂²×C₂₃	1	4	yes	complemented
518	#463	C₂²×C₂₃	1	2	yes	complemented
519	#459	C₂²×C₂₃	1	2	yes	complemented
520	#450	C₂²×C₂₃	1	1	yes	characteristic, complemented
521	#449	C₂²×C₂₃	1	4	yes	complemented
522	#447	C₂²×C₂₃	1	1	yes	characteristic
523	#447	C₂²×C₂₃	1	2	yes	complemented
524	#447	C₂²×C₂₃	1	4	yes	complemented
525	#442	C₂²×C₂₃	1	4	yes	complemented
526	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
527	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
528	#436	C₂²×C₂₃	1	2	yes	complemented
529	#435	C₂²×C₂₃	1	4	yes	complemented
530	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
531	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
532	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
533	#428	C₂²×C₂₃	1	4	yes	complemented
534	#427	C₂²×C₂₃	1	4	yes	complemented
535	#418	C₂²×C₂₃	1	4	yes	complemented
536	#416	C₂²×C₂₃	1	4	yes	complemented
537	#407	C₂²×C₂₃	1	2	yes	complemented
538	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
539	C₂×C₂₃	—	2	2	no	—
540	C₂×C₂₃	—	4	2	no	—
541	C₂×C₂₃	—	4	2	no	—
542	C₂×C₂₃	—	8	2	no	—
543	C₂×C₂₃	—	8	2	no	—
544	C₂×C₂₃	—	8	1	no	—
545	C₂×C₂₃	#3485	1	1	yes	characteristic
546	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
547	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
548	C₂×#41	—	2	1	no	—
549	C₂×#41	C₂³×C₂₃	1	2	yes	—
550	C₂²×Q₈	—	2	1	no	—
551	C₂²×D₄	—	2	2	no	—
552	C₂²×D₄	—	2	2	no	—
553	C₂²×D₄	—	2	1	no	—
554	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
555	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
556	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
557	C₂³×C₄	—	2	1	no	—
558	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
559	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
560	C₂×D₈	C₂³×C₂₃	1	2	yes	—
561	C₂×D₈	C₂³×C₂₃	1	4	yes	—
562	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
563	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
564	C₄⋊Q₈	—	2	1	no	—
565	C₄⋊Q₈	—	2	1	no	—
566	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
567	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
568	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
569	#127	—	2	1	no	—
570	#127	C₂³×C₂₃	1	1	yes	characteristic
571	#126	—	2	2	no	—
572	#126	—	2	1	no	—
573	#125	—	2	1	no	—
574	#125	C₂³×C₂₃	1	1	yes	characteristic
575	#124	—	2	4	no	—
576	#124	—	2	4	no	—
577	#124	—	2	4	no	—
578	#124	—	2	4	no	—
579	#124	—	2	2	no	—
580	#124	—	2	1	no	—
581	#124	C₂³×C₂₃	1	1	yes	characteristic
582	#123	—	2	2	no	—
583	#123	—	2	1	no	—
584	#123	—	2	2	no	—
585	#123	—	2	2	no	—
586	C₂²⋊Q₈	—	2	2	no	—
587	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
588	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
589	#121	—	2	2	no	—
590	#121	—	2	2	no	—
591	#121	—	2	4	no	—
592	#121	—	2	2	no	—
593	#121	—	2	1	no	—
594	#121	—	2	2	no	—
595	#121	—	2	2	no	—
596	#121	—	2	2	no	—
597	#121	—	2	2	no	—
598	#121	—	2	1	no	—
599	#121	—	2	1	no	—
600	#121	—	2	2	no	—
601	#121	—	2	2	no	—
602	#121	C₂³×C₂₃	1	1	yes	characteristic
603	#121	C₂³×C₂₃	1	2	yes	—
604	#121	C₂³×C₂₃	1	2	yes	—
605	#121	C₂³×C₂₃	1	2	yes	—
606	#121	C₂³×C₂₃	1	4	yes	—
607	#121	C₂³×C₂₃	1	4	yes	—
608	#121	C₂³×C₂₃	1	2	yes	—
609	#120	—	2	2	no	—
610	#120	—	2	2	no	—
611	#120	—	2	2	no	—
612	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
613	C₄×D₄	—	2	1	no	—
614	C₄×D₄	—	2	2	no	—
615	C₄×D₄	—	2	2	no	—
616	C₄×D₄	—	2	1	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	1	no	—
620	C₄×D₄	—	2	1	no	—
621	C₄×D₄	—	2	1	no	—
622	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
623	C₄×D₄	D₄×C₂₃	1	2	yes	—
624	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
625	C₄×D₄	C₂³×C₂₃	1	2	yes	—
626	C₄×D₄	C₂³×C₂₃	1	2	yes	—
627	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
628	C₄×D₄	C₂³×C₂₃	1	2	yes	—
629	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
630	C₄×D₄	C₂³×C₂₃	1	2	yes	—
631	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
632	#117	—	2	2	no	—
633	#117	—	2	2	no	—
634	#117	—	2	2	no	—
635	#117	—	2	2	no	—
636	#117	—	2	4	no	—
637	#117	—	2	1	no	—
638	#117	—	2	1	no	—
639	#117	C₂³×C₂₃	1	4	yes	—
640	#117	C₂³×C₂₃	1	4	yes	—
641	#117	C₂³×C₂₃	1	2	yes	—
642	C₂×C₄⋊C₄	—	2	1	no	—
643	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
644	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
645	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
646	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
647	C₂×C₂²⋊C₄	—	2	2	no	—
648	C₂×C₂²⋊C₄	—	2	2	no	—
649	C₂×C₂²⋊C₄	—	2	1	no	—
650	C₂×C₂²⋊C₄	—	2	2	no	—
651	C₂×C₂²⋊C₄	—	2	2	no	—
652	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
653	C₂×C₄²	—	2	2	no	—
654	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
655	#107	C₂³×C₂₃	1	2	yes	—
656	#107	C₂³×C₂₃	1	4	yes	—
657	#107	C₂³×C₂₃	1	4	yes	—
658	#107	C₂³×C₂₃	1	4	yes	—
659	#106	C₂³×C₂₃	1	4	yes	—
660	#106	C₂³×C₂₃	1	4	yes	—
661	#106	C₂³×C₂₃	1	2	yes	—
662	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
663	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
664	#103	C₂³×C₂₃	1	2	yes	—
665	#103	C₂³×C₂₃	1	4	yes	—
666	#102	C₂³×C₂₃	1	4	yes	—
667	#102	C₂³×C₂₃	1	4	yes	—
668	#102	C₂³×C₂₃	1	2	yes	—
669	#102	C₂³×C₂₃	1	4	yes	—
670	#102	C₂³×C₂₃	1	4	yes	—
671	#102	C₂³×C₂₃	1	2	yes	—
672	#102	C₂³×C₂₃	1	2	yes	—
673	#102	C₂³×C₂₃	1	4	yes	—
674	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
675	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
676	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
677	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
678	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
679	#97	C₂³×C₂₃	1	2	yes	—
680	C₄×C₈	C₂³×C₂₃	1	2	yes	—
681	C₂₃	#61740	1	1	yes	characteristic, direct product factor, Sylow
682	C₂⁴	—	2	1	no	—
683	C₂⁴	—	2	2	no	—
684	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
685	#41	—	4	4	no	—
686	#41	—	8	2	no	—
687	C₂×Q₈	—	2	1	no	—
688	C₂×Q₈	—	2	2	no	—
689	C₂×Q₈	—	2	2	no	—
690	C₂×Q₈	—	8	2	no	—
691	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	2	no	—
694	C₂×D₄	—	2	1	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	2	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	—	2	1	no	—
702	C₂×D₄	—	2	1	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	4	2	no	—
706	C₂×D₄	—	4	4	no	—
707	C₂×D₄	—	4	4	no	—
708	C₂×D₄	—	8	4	no	—
709	C₂×D₄	—	8	4	no	—
710	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
711	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
712	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
713	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
714	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
715	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
716	C₂²×C₄	—	2	1	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	2	no	—
720	C₂²×C₄	—	2	2	no	—
721	C₂²×C₄	—	2	1	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	4	4	no	—
725	C₂²×C₄	—	4	4	no	—
726	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
727	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
728	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
729	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
730	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
732	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
734	SD₁₆	—	4	2	no	—
735	D₈	—	4	2	no	—
736	D₈	—	4	4	no	—
737	M₁₆	—	4	4	no	—
738	C₂×C₈	—	4	4	no	—
739	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
740	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
741	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	1	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	1	no	—
748	C₄⋊C₄	—	2	1	no	—
749	C₄⋊C₄	—	2	1	no	—
750	C₄⋊C₄	—	2	1	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
754	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
755	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
756	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
757	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
758	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
759	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
760	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
761	C₂²⋊C₄	—	2	4	no	—
762	C₂²⋊C₄	—	2	4	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	2	no	—
765	C₂²⋊C₄	—	2	1	no	—
766	C₂²⋊C₄	—	2	1	no	—
767	C₂²⋊C₄	—	2	1	no	—
768	C₂²⋊C₄	—	2	2	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	2	1	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
780	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
781	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
782	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
783	C₄²	—	2	4	no	—
784	C₄²	—	2	4	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	1	no	—
787	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
788	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
789	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
790	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
791	C₂³	—	2	4	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	1	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	4	2	no	—
796	C₂³	—	4	2	no	—
797	C₂³	—	4	2	no	—
798	C₂³	—	4	2	no	—
799	C₂³	—	4	4	no	—
800	C₂³	—	4	2	no	—
801	C₂³	—	8	2	no	—
802	C₂³	—	8	2	no	—
803	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
804	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
805	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
806	Q₈	—	2	2	no	—
807	Q₈	—	8	2	no	—
808	Q₈	—	8	2	no	—
809	Q₈	—	8	1	no	—
810	D₄	—	2	2	no	—
811	D₄	—	2	2	no	—
812	D₄	—	2	2	no	—
813	D₄	—	2	2	no	—
814	D₄	—	2	2	no	—
815	D₄	—	2	4	no	—
816	D₄	—	4	2	no	—
817	D₄	—	4	2	no	—
818	D₄	—	4	4	no	—
819	D₄	—	4	2	no	—
820	D₄	—	4	4	no	—
821	D₄	—	4	2	no	—
822	D₄	—	8	2	no	—
823	D₄	—	8	1	no	—
824	D₄	—	8	4	no	—
825	D₄	—	8	4	no	—
826	D₄	—	8	2	no	—
827	D₄	—	8	2	no	—
828	D₄	—	8	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	4	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	4	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	4	2	no	—
842	C₂×C₄	—	4	2	no	—
843	C₂×C₄	—	4	4	no	—
844	C₂×C₄	—	4	2	no	—
845	C₂×C₄	—	4	4	no	—
846	C₂×C₄	—	4	4	no	—
847	C₂×C₄	—	4	2	no	—
848	C₂×C₄	—	8	2	no	—
849	C₂×C₄	—	8	2	no	—
850	C₂×C₄	—	8	2	no	—
851	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
852	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
853	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
854	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
855	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
856	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
857	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
858	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
859	C₈	—	2	2	no	—
860	C₈	—	2	4	no	—
861	C₈	—	2	2	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	2	1	no	—
864	C₂²	—	2	2	no	—
865	C₂²	—	2	2	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	2	2	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	4	2	no	—
872	C₂²	—	4	1	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	8	4	no	—
880	C₂²	—	8	4	no	—
881	C₂²	—	16	4	no	—
882	C₂²	C₂₃×#576	1	2	yes	—
883	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
884	C₄	—	2	1	no	—
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	1	no	—
890	C₄	—	4	1	no	—
891	C₄	—	4	2	no	—
892	C₄	—	4	1	no	—
893	C₄	—	4	4	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	2	no	—
896	C₄	C₂₃×#575	1	2	yes	—
897	C₄	C₂₃×#585	1	2	yes	—
898	C₂	—	2	2	no	—
899	C₂	—	4	2	no	—
900	C₂	—	4	2	no	—
901	C₂	—	8	2	no	—
902	C₂	—	8	1	no	—
903	C₂	—	8	2	no	—
904	C₂	C₂₃×#3485	1	1	yes	characteristic
905	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
906	C₂	C₂×C₂₃×#576	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3519	C₂	semidirect
2. C₂×C₂₃×#555	C₂	semidirect
3. C₂₃×#3357	C₂	semidirect
4. C₂₃×#3347	C₂	semidirect
5. C₂₃×#3341	C₂	semidirect
6. C₂₃×#3325	C₂	semidirect
7. C₂₃×#3319	C₂	semidirect
8. C₂₃×#3305	C₂	semidirect
9. C₂₃×#3238	C₂	semidirect
10. C₂₃×#3226	C₂	semidirect
11. C₂₃×#3194	C₂	semidirect
12. C₂₃×#3186	C₂	semidirect
13. C₂₃×#3109	C₂	semidirect
14. C₂₃×#3105	C₂	semidirect
15. C₂₃×#3094	C₂	semidirect
16. C₂₃×#3091	C₂	semidirect
17. C₂₃×#2974	C₂	semidirect
22. C₂₃×#555	C₂²	semidirect
23. C₂₃×#555	C₂²	semidirect
24. C₂₃×#555	C₂²	semidirect
25. C₂₃×#554	C₂²	semidirect
27. C₂₃×#553	C₂²	semidirect
28. C₂₃×#550	C₂²	semidirect
30. C₂₃×#546	C₂²	semidirect
32. D₄²×C₂₃	C₂²	semidirect
36. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
42. C₂×C₂₃×#121	C₂²	semidirect
45. C₂×C₄×D₄×C₂₃	C₂²	semidirect
47. C₂×C₂₃×#117	C₂²	semidirect
48. C₂₃×#501	C₂²	semidirect
49. C₂₃×#500	C₂²	semidirect
50. C₂₃×#489	C₂²	semidirect
51. C₂₃×#486	C₂²	semidirect
52. C₂₃×#485	C₂²	semidirect
53. C₂₃×#484	C₂²	semidirect
54. C₂₃×#483	C₂²	semidirect
55. C₂₃×#482	C₂²	semidirect
56. C₂₃×#482	C₂²	semidirect
57. C₂₃×#482	C₂²	semidirect
58. C₂₃×#482	C₂²	semidirect
60. C₂₃×#481	C₂²	semidirect
62. C₂₃×#480	C₂²	semidirect
63. C₂₃×#480	C₂²	semidirect
64. C₂₃×#480	C₂²	semidirect
65. C₂₃×#478	C₂²	semidirect
66. C₂₃×#477	C₂²	semidirect
67. C₂₃×#476	C₂²	semidirect
68. C₂₃×#476	C₂²	semidirect
69. C₂₃×#474	C₂²	semidirect
70. C₂₃×#469	C₂²	semidirect
71. C₂₃×#468	C₂²	semidirect
72. C₂₃×#466	C₂²	semidirect
73. C₂₃×#466	C₂²	semidirect
74. C₂₃×#463	C₂²	semidirect
75. C₂₃×#459	C₂²	semidirect
76. C₂₃×#450	C₂²	semidirect
77. C₂₃×#449	C₂²	semidirect
79. C₂₃×#447	C₂²	semidirect
80. C₂₃×#447	C₂²	semidirect
81. C₂₃×#442	C₂²	semidirect
82. C₄×SD₁₆×C₂₃	C₂²	semidirect
83. C₄×D₈×C₂₃	C₂²	semidirect
84. C₂₃×#436	C₂²	semidirect
85. C₂₃×#435	C₂²	semidirect
86. C₈×D₄×C₂₃	C₂²	semidirect
87. C₂₃×#432	C₂²	semidirect
88. C₂₃×#431	C₂²	semidirect
89. C₂₃×#428	C₂²	semidirect
90. C₂₃×#427	C₂²	semidirect
91. C₂₃×#418	C₂²	semidirect
92. C₂₃×#416	C₂²	semidirect
93. C₂₃×#407	C₂²	semidirect
94. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
337. #61740	C₂₃	direct (N × H)
409. #3519	C₂×C₂₃	semidirect
410. C₂×#555	C₂×C₂₃	semidirect
411. #3357	C₂×C₂₃	semidirect
412. #3347	C₂×C₂₃	semidirect
413. #3341	C₂×C₂₃	semidirect
414. #3325	C₂×C₂₃	semidirect
415. #3319	C₂×C₂₃	semidirect
416. #3305	C₂×C₂₃	semidirect
417. #3238	C₂×C₂₃	semidirect
418. #3226	C₂×C₂₃	semidirect
419. #3194	C₂×C₂₃	semidirect
420. #3186	C₂×C₂₃	semidirect
421. #3109	C₂×C₂₃	semidirect
422. #3105	C₂×C₂₃	semidirect
423. #3094	C₂×C₂₃	semidirect
424. #3091	C₂×C₂₃	semidirect
425. #2974	C₂×C₂₃	semidirect
466. #555	C₂²×C₂₃	semidirect
467. #555	C₂²×C₂₃	semidirect
468. #555	C₂²×C₂₃	semidirect
469. #554	C₂²×C₂₃	semidirect
471. #553	C₂²×C₂₃	semidirect
472. #550	C₂²×C₂₃	semidirect
474. #546	C₂²×C₂₃	semidirect
476. D₄²	C₂²×C₂₃	semidirect
480. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
486. C₂×#121	C₂²×C₂₃	semidirect
489. C₂×C₄×D₄	C₂²×C₂₃	semidirect
491. C₂×#117	C₂²×C₂₃	semidirect
492. #501	C₂²×C₂₃	semidirect
493. #500	C₂²×C₂₃	semidirect
494. #489	C₂²×C₂₃	semidirect
495. #486	C₂²×C₂₃	semidirect
496. #485	C₂²×C₂₃	semidirect
497. #484	C₂²×C₂₃	semidirect
498. #483	C₂²×C₂₃	semidirect
499. #482	C₂²×C₂₃	semidirect
500. #482	C₂²×C₂₃	semidirect
501. #482	C₂²×C₂₃	semidirect
502. #482	C₂²×C₂₃	semidirect
504. #481	C₂²×C₂₃	semidirect
506. #480	C₂²×C₂₃	semidirect
507. #480	C₂²×C₂₃	semidirect
508. #480	C₂²×C₂₃	semidirect
509. #478	C₂²×C₂₃	semidirect
510. #477	C₂²×C₂₃	semidirect
511. #476	C₂²×C₂₃	semidirect
512. #476	C₂²×C₂₃	semidirect
513. #474	C₂²×C₂₃	semidirect
514. #469	C₂²×C₂₃	semidirect
515. #468	C₂²×C₂₃	semidirect
516. #466	C₂²×C₂₃	semidirect
517. #466	C₂²×C₂₃	semidirect
518. #463	C₂²×C₂₃	semidirect
519. #459	C₂²×C₂₃	semidirect
520. #450	C₂²×C₂₃	semidirect
521. #449	C₂²×C₂₃	semidirect
523. #447	C₂²×C₂₃	semidirect
524. #447	C₂²×C₂₃	semidirect
525. #442	C₂²×C₂₃	semidirect
526. C₄×SD₁₆	C₂²×C₂₃	semidirect
527. C₄×D₈	C₂²×C₂₃	semidirect
528. #436	C₂²×C₂₃	semidirect
529. #435	C₂²×C₂₃	semidirect
530. C₈×D₄	C₂²×C₂₃	semidirect
531. #432	C₂²×C₂₃	semidirect
532. #431	C₂²×C₂₃	semidirect
533. #428	C₂²×C₂₃	semidirect
534. #427	C₂²×C₂₃	semidirect
535. #418	C₂²×C₂₃	semidirect
536. #416	C₂²×C₂₃	semidirect
537. #407	C₂²×C₂₃	semidirect
538. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
681. C₂₃	#61740	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×#3519	2
C₂×C₂₃×#555	2
C₂₃×#3357	2
C₂₃×#3347	2
C₂₃×#3341	2
C₂₃×#3325	2
C₂₃×#3319	2
C₂₃×#3305	2
C₂₃×#3238	2
C₂₃×#3226	2
C₂₃×#3194	2
C₂₃×#3186	2
C₂₃×#3109	2
C₂₃×#3105	2
C₂₃×#3094	2
C₂₃×#3091	2
C₂₃×#2974	2
#61740	23

Subgroups — C23×#61740 #19209366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61740 #19209366