Subgroups — C₂₃×#61728 #19209354

Order 5888.

2076 conjugacy classes of subgroups.

The subgroup lattice has 922 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×#547	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3354	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3345	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3335	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3332	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3306	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3294	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3239	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3227	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3192	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3188	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×#3092	C₂	1	2	yes	maximal, complemented
16	C₂×C₂₃×#481	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₂₃	—	2	1	no	—
19	C₂₃×#555	C₂²	1	1	yes	characteristic, complemented
20	C₂₃×#554	C₂²	1	1	yes	characteristic, complemented
21	C₂₃×#553	—	2	1	no	—
22	C₂₃×#553	C₂²	1	2	yes	complemented
23	C₂₃×#550	C₂²	1	1	yes	characteristic, complemented
24	C₂₃×#547	—	2	1	no	—
25	C₂₃×#547	—	2	2	no	—
26	C₂₃×#547	—	2	1	no	—
27	C₂₃×#547	C₂²	1	2	yes	—
28	C₂₃×#547	C₂²	1	4	yes	complemented
29	C₂₃×#547	C₂²	1	2	yes	complemented
30	C₂₃×#546	—	2	2	no	—
31	C₂₃×#546	C₂²	1	2	yes	complemented
32	D₄²×C₂₃	—	2	1	no	—
33	D₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
34	C₂₃×#540	—	2	1	no	—
35	C₂₃×#538	—	2	2	no	—
36	C₂₃×#532	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#529	C₂²	1	1	yes	characteristic
39	C₂₃×#525	C₂²	1	2	yes	—
40	C₂×C₂₃×#123	—	2	2	no	—
41	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
42	C₂×C₂₃×#121	C₂²	1	2	yes	—
43	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
44	C₂₃×#518	—	2	1	no	—
45	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
48	C₂₃×#501	C₂²	1	2	yes	complemented
49	C₂₃×#498	C₂²	1	2	yes	complemented
50	C₂₃×#489	C₂²	1	2	yes	complemented
51	C₂₃×#486	C₂²	1	2	yes	complemented
52	C₂₃×#484	C₂²	1	2	yes	complemented
53	C₂₃×#484	C₂²	1	1	yes	characteristic, complemented
54	C₂₃×#483	C₂²	1	4	yes	complemented
55	C₂₃×#482	C₂²	1	4	yes	complemented
56	C₂₃×#481	C₂²	1	2	yes	—
57	C₂₃×#481	C₂²	1	1	yes	characteristic
58	C₂₃×#481	C₂²	1	2	yes	complemented
59	C₂₃×#481	C₂²	1	2	yes	complemented
60	C₂₃×#481	C₂²	1	4	yes	complemented
61	C₂₃×#481	C₂²	1	4	yes	complemented
62	C₂₃×#481	C₂²	1	4	yes	complemented
63	C₂₃×#481	C₂²	1	2	yes	complemented
64	C₂₃×#480	C₂²	1	4	yes	complemented
65	C₂₃×#478	C₂²	1	2	yes	complemented
66	C₂₃×#476	C₂²	1	4	yes	complemented
67	C₂₃×#476	C₂²	1	2	yes	complemented
68	C₂₃×#475	C₂²	1	2	yes	complemented
69	C₂₃×#474	C₂²	1	2	yes	complemented
70	C₂₃×#469	C₂²	1	4	yes	complemented
71	C₂₃×#469	C₂²	1	4	yes	complemented
72	C₂₃×#466	C₂²	1	4	yes	complemented
73	C₂₃×#465	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	C₂×C₂₃×#106	C₂²	1	4	yes	complemented
91	C₂₃×#417	C₂²	1	4	yes	complemented
92	C₂×C₂₃×#102	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	2	no	—
96	C₂×#41×C₂₃	—	2	4	no	—
97	C₂×#41×C₂₃	—	2	2	no	—
98	C₂×#41×C₂₃	—	2	1	no	—
99	C₂×#41×C₂₃	—	4	8	no	—
100	C₂×#41×C₂₃	C₂³	1	2	yes	—
101	C₂²×Q₈×C₂₃	—	2	1	no	—
102	C₂²×D₄×C₂₃	—	2	2	no	—
103	C₂²×D₄×C₂₃	—	2	2	no	—
104	C₂²×D₄×C₂₃	—	2	1	no	—
105	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
106	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
107	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₂₃	—	2	2	no	—
109	C₂³×C₄×C₂₃	—	2	1	no	—
110	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
111	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
112	C₂×D₈×C₂₃	C₂³	1	2	yes	—
113	C₂×D₈×C₂₃	C₂³	1	4	yes	—
114	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
115	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
116	C₂₃×C₄⋊Q₈	—	2	1	no	—
117	C₂₃×C₄⋊Q₈	—	2	1	no	—
118	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
120	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₂₃×#127	—	2	1	no	—
122	C₂₃×#127	C₂³	1	1	yes	characteristic
123	C₂₃×#126	—	2	2	no	—
124	C₂₃×#126	—	2	1	no	—
125	C₂₃×#125	—	2	1	no	—
126	C₂₃×#125	C₂³	1	1	yes	characteristic
127	C₂₃×#124	—	2	2	no	—
128	C₂₃×#124	—	2	1	no	—
129	C₂₃×#124	C₂³	1	1	yes	characteristic
130	C₂₃×#123	—	2	2	no	—
131	C₂₃×#123	—	2	1	no	—
132	C₂₃×#123	—	2	2	no	—
133	C₂₃×#123	—	2	4	no	—
134	C₂₃×#123	—	2	4	no	—
135	C₂₃×#123	—	2	4	no	—
136	C₂₃×#123	—	2	4	no	—
137	C₂₃×#123	—	2	2	no	—
138	C₂₃×C₂²⋊Q₈	—	2	2	no	—
139	C₂₃×C₂²⋊Q₈	—	2	2	no	—
140	C₂₃×C₂²⋊Q₈	—	2	4	no	—
141	C₂₃×C₂²⋊Q₈	—	2	2	no	—
142	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
143	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
144	C₂₃×#121	—	2	2	no	—
145	C₂₃×#121	—	2	1	no	—
146	C₂₃×#121	—	2	2	no	—
147	C₂₃×#121	—	2	2	no	—
148	C₂₃×#121	—	2	2	no	—
149	C₂₃×#121	—	2	1	no	—
150	C₂₃×#121	—	2	2	no	—
151	C₂₃×#121	—	2	1	no	—
152	C₂₃×#121	—	2	2	no	—
153	C₂₃×#121	—	2	2	no	—
154	C₂₃×#121	C₂³	1	4	yes	—
155	C₂₃×#121	C₂³	1	4	yes	—
156	C₂₃×#121	C₂³	1	2	yes	—
157	C₂₃×#121	C₂³	1	2	yes	—
158	C₂₃×#121	C₂³	1	2	yes	—
159	C₂₃×#121	C₂³	1	1	yes	characteristic
160	C₂₃×#121	C₂³	1	2	yes	—
161	C₂₃×#120	—	2	2	no	—
162	C₂₃×#120	—	2	2	no	—
163	C₂₃×#120	—	2	2	no	—
164	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
165	C₄×D₄×C₂₃	—	2	1	no	—
166	C₄×D₄×C₂₃	—	2	2	no	—
167	C₄×D₄×C₂₃	—	2	1	no	—
168	C₄×D₄×C₂₃	—	2	2	no	—
169	C₄×D₄×C₂₃	—	2	1	no	—
170	C₄×D₄×C₂₃	—	2	2	no	—
171	C₄×D₄×C₂₃	—	2	1	no	—
172	C₄×D₄×C₂₃	—	2	1	no	—
173	C₄×D₄×C₂₃	—	2	1	no	—
174	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
175	C₄×D₄×C₂₃	D₄	1	2	yes	—
176	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
177	C₄×D₄×C₂₃	C₂³	1	2	yes	—
178	C₄×D₄×C₂₃	C₂³	1	2	yes	—
179	C₄×D₄×C₂₃	C₂³	1	2	yes	—
180	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
181	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
182	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
183	C₄×D₄×C₂₃	C₂³	1	2	yes	—
184	C₂₃×#117	—	2	1	no	—
185	C₂₃×#117	—	2	1	no	—
186	C₂₃×#117	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
188	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
189	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
190	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
191	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
193	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
194	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
195	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
198	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
200	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
201	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
202	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
203	C₂₃×#107	C₂³	1	2	yes	—
204	C₂₃×#107	C₂³	1	4	yes	—
205	C₂₃×#106	C₂³	1	2	yes	—
206	C₂₃×#106	C₂³	1	4	yes	—
207	C₂₃×#106	C₂³	1	4	yes	—
208	C₂₃×#106	C₂³	1	4	yes	—
209	C₂₃×#106	C₂³	1	4	yes	—
210	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
212	C₂₃×#103	C₂³	1	2	yes	—
213	C₂₃×#103	C₂³	1	4	yes	—
214	C₂₃×#102	C₂³	1	2	yes	—
215	C₂₃×#102	C₂³	1	4	yes	—
216	C₂₃×#102	C₂³	1	4	yes	—
217	C₂₃×#102	C₂³	1	4	yes	—
218	C₂₃×#102	C₂³	1	4	yes	—
219	C₂₃×#102	C₂³	1	2	yes	—
220	C₂₃×#102	C₂³	1	2	yes	—
221	C₂₃×#102	C₂³	1	4	yes	—
222	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
223	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
224	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
225	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
226	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
227	C₂₃×#97	C₂³	1	2	yes	—
228	C₄×C₈×C₂₃	C₂³	1	2	yes	—
229	C₂⁴×C₂₃	—	2	1	no	—
230	C₂⁴×C₂₃	—	2	2	no	—
231	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
232	#41×C₂₃	—	4	4	no	—
233	#41×C₂₃	—	4	16	no	—
234	#41×C₂₃	—	4	8	no	—
235	#41×C₂₃	—	4	8	no	—
236	#41×C₂₃	—	8	2	no	—
237	C₂×Q₈×C₂₃	—	2	2	no	—
238	C₂×Q₈×C₂₃	—	2	2	no	—
239	C₂×Q₈×C₂₃	—	2	1	no	—
240	C₂×Q₈×C₂₃	—	4	4	no	—
241	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
242	C₂×D₄×C₂₃	—	2	4	no	—
243	C₂×D₄×C₂₃	—	2	2	no	—
244	C₂×D₄×C₂₃	—	2	2	no	—
245	C₂×D₄×C₂₃	—	2	1	no	—
246	C₂×D₄×C₂₃	—	2	4	no	—
247	C₂×D₄×C₂₃	—	2	4	no	—
248	C₂×D₄×C₂₃	—	2	2	no	—
249	C₂×D₄×C₂₃	—	2	2	no	—
250	C₂×D₄×C₂₃	—	2	2	no	—
251	C₂×D₄×C₂₃	—	2	1	no	—
252	C₂×D₄×C₂₃	—	2	1	no	—
253	C₂×D₄×C₂₃	—	2	1	no	—
254	C₂×D₄×C₂₃	—	2	2	no	—
255	C₂×D₄×C₂₃	—	4	2	no	—
256	C₂×D₄×C₂₃	—	4	4	no	—
257	C₂×D₄×C₂₃	—	4	8	no	—
258	C₂×D₄×C₂₃	—	4	4	no	—
259	C₂×D₄×C₂₃	—	8	4	no	—
260	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
261	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
262	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
263	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
264	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
265	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₂₃	—	2	1	no	—
267	C₂²×C₄×C₂₃	—	2	2	no	—
268	C₂²×C₄×C₂₃	—	2	4	no	—
269	C₂²×C₄×C₂₃	—	2	4	no	—
270	C₂²×C₄×C₂₃	—	2	2	no	—
271	C₂²×C₄×C₂₃	—	2	1	no	—
272	C₂²×C₄×C₂₃	—	2	2	no	—
273	C₂²×C₄×C₂₃	—	2	2	no	—
274	C₂²×C₄×C₂₃	—	2	2	no	—
275	C₂²×C₄×C₂₃	—	2	2	no	—
276	C₂²×C₄×C₂₃	—	4	4	no	—
277	C₂²×C₄×C₂₃	—	4	4	no	—
278	C₂²×C₄×C₂₃	—	4	8	no	—
279	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
282	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
284	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
286	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
287	SD₁₆×C₂₃	—	4	2	no	—
288	D₈×C₂₃	—	4	4	no	—
289	D₈×C₂₃	—	4	2	no	—
290	M₁₆×C₂₃	—	4	4	no	—
291	C₂×C₈×C₂₃	—	4	4	no	—
292	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
293	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
294	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
295	C₄⋊C₄×C₂₃	—	2	1	no	—
296	C₄⋊C₄×C₂₃	—	2	2	no	—
297	C₄⋊C₄×C₂₃	—	2	4	no	—
298	C₄⋊C₄×C₂₃	—	2	4	no	—
299	C₄⋊C₄×C₂₃	—	2	2	no	—
300	C₄⋊C₄×C₂₃	—	2	2	no	—
301	C₄⋊C₄×C₂₃	—	2	2	no	—
302	C₄⋊C₄×C₂₃	—	2	1	no	—
303	C₄⋊C₄×C₂₃	—	2	1	no	—
304	C₄⋊C₄×C₂₃	—	2	1	no	—
305	C₄⋊C₄×C₂₃	—	2	1	no	—
306	C₄⋊C₄×C₂₃	—	2	2	no	—
307	C₄⋊C₄×C₂₃	—	2	1	no	—
308	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
309	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
310	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
312	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
313	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
314	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
315	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
316	C₂²⋊C₄×C₂₃	—	2	2	no	—
317	C₂²⋊C₄×C₂₃	—	2	2	no	—
318	C₂²⋊C₄×C₂₃	—	2	1	no	—
319	C₂²⋊C₄×C₂₃	—	2	1	no	—
320	C₂²⋊C₄×C₂₃	—	2	1	no	—
321	C₂²⋊C₄×C₂₃	—	2	2	no	—
322	C₂²⋊C₄×C₂₃	—	2	2	no	—
323	C₂²⋊C₄×C₂₃	—	2	2	no	—
324	C₂²⋊C₄×C₂₃	—	2	2	no	—
325	C₂²⋊C₄×C₂₃	—	2	2	no	—
326	C₂²⋊C₄×C₂₃	—	2	4	no	—
327	C₂²⋊C₄×C₂₃	—	2	4	no	—
328	C₂²⋊C₄×C₂₃	—	2	1	no	—
329	C₂²⋊C₄×C₂₃	—	2	2	no	—
330	C₂²⋊C₄×C₂₃	—	2	1	no	—
331	C₂²⋊C₄×C₂₃	—	2	2	no	—
332	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
333	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
334	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
335	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
336	C₄²×C₂₃	—	2	2	no	—
337	C₄²×C₂₃	—	2	1	no	—
338	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
341	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
342	#61728	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
343	C₂³×C₂₃	—	2	4	no	—
344	C₂³×C₂₃	—	2	4	no	—
345	C₂³×C₂₃	—	2	2	no	—
346	C₂³×C₂₃	—	2	1	no	—
347	C₂³×C₂₃	—	2	2	no	—
348	C₂³×C₂₃	—	4	2	no	—
349	C₂³×C₂₃	—	4	2	no	—
350	C₂³×C₂₃	—	4	2	no	—
351	C₂³×C₂₃	—	4	2	no	—
352	C₂³×C₂₃	—	4	4	no	—
353	C₂³×C₂₃	—	8	2	no	—
354	C₂³×C₂₃	—	8	2	no	—
355	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
356	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
357	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
358	Q₈×C₂₃	—	2	2	no	—
359	Q₈×C₂₃	—	4	4	no	—
360	Q₈×C₂₃	—	4	4	no	—
361	Q₈×C₂₃	—	8	1	no	—
362	D₄×C₂₃	—	2	4	no	—
363	D₄×C₂₃	—	2	2	no	—
364	D₄×C₂₃	—	2	2	no	—
365	D₄×C₂₃	—	2	2	no	—
366	D₄×C₂₃	—	2	2	no	—
367	D₄×C₂₃	—	2	4	no	—
368	D₄×C₂₃	—	4	2	no	—
369	D₄×C₂₃	—	4	8	no	—
370	D₄×C₂₃	—	4	4	no	—
371	D₄×C₂₃	—	4	8	no	—
372	D₄×C₂₃	—	4	2	no	—
373	D₄×C₂₃	—	4	4	no	—
374	D₄×C₂₃	—	4	2	no	—
375	D₄×C₂₃	—	8	2	no	—
376	D₄×C₂₃	—	8	1	no	—
377	D₄×C₂₃	—	8	2	no	—
378	D₄×C₂₃	—	8	2	no	—
379	D₄×C₂₃	—	8	2	no	—
380	D₄×C₂₃	AGL(1,ℤ/8)	1	4	yes	—
381	C₂×C₄×C₂₃	—	2	2	no	—
382	C₂×C₄×C₂₃	—	2	2	no	—
383	C₂×C₄×C₂₃	—	2	4	no	—
384	C₂×C₄×C₂₃	—	2	4	no	—
385	C₂×C₄×C₂₃	—	2	2	no	—
386	C₂×C₄×C₂₃	—	2	1	no	—
387	C₂×C₄×C₂₃	—	2	1	no	—
388	C₂×C₄×C₂₃	—	2	2	no	—
389	C₂×C₄×C₂₃	—	2	1	no	—
390	C₂×C₄×C₂₃	—	2	2	no	—
391	C₂×C₄×C₂₃	—	2	4	no	—
392	C₂×C₄×C₂₃	—	4	2	no	—
393	C₂×C₄×C₂₃	—	4	2	no	—
394	C₂×C₄×C₂₃	—	4	2	no	—
395	C₂×C₄×C₂₃	—	4	4	no	—
396	C₂×C₄×C₂₃	—	4	2	no	—
397	C₂×C₄×C₂₃	—	4	4	no	—
398	C₂×C₄×C₂₃	—	4	8	no	—
399	C₂×C₄×C₂₃	—	4	8	no	—
400	C₂×C₄×C₂₃	—	4	4	no	—
401	C₂×C₄×C₂₃	—	4	2	no	—
402	C₂×C₄×C₂₃	—	8	2	no	—
403	C₂×C₄×C₂₃	—	8	2	no	—
404	C₂×C₄×C₂₃	—	8	2	no	—
405	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
408	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
411	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
413	C₈×C₂₃	—	2	2	no	—
414	C₈×C₂₃	—	2	4	no	—
415	C₈×C₂₃	—	2	2	no	—
416	#3519	C₂×C₂₃	1	1	yes	characteristic, complemented
417	C₂×#547	C₂×C₂₃	1	1	yes	characteristic, complemented
418	#3354	C₂×C₂₃	1	2	yes	complemented
419	#3345	C₂×C₂₃	1	4	yes	complemented
420	#3335	C₂×C₂₃	1	2	yes	complemented
421	#3332	C₂×C₂₃	1	2	yes	complemented
422	#3306	C₂×C₂₃	1	4	yes	complemented
423	#3294	C₂×C₂₃	1	2	yes	complemented
424	#3239	C₂×C₂₃	1	1	yes	characteristic, complemented
425	#3227	C₂×C₂₃	1	1	yes	characteristic, complemented
426	#3192	C₂×C₂₃	1	2	yes	complemented
427	#3188	C₂×C₂₃	1	2	yes	complemented
428	#3109	C₂×C₂₃	1	1	yes	characteristic, complemented
429	#3105	C₂×C₂₃	1	1	yes	characteristic, complemented
430	#3092	C₂×C₂₃	1	2	yes	complemented
431	C₂×#481	C₂×C₂₃	1	2	yes	complemented
432	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
433	C₂²×C₂₃	—	2	1	no	—
434	C₂²×C₂₃	—	2	2	no	—
435	C₂²×C₂₃	—	2	1	no	—
436	C₂²×C₂₃	—	2	2	no	—
437	C₂²×C₂₃	—	2	2	no	—
438	C₂²×C₂₃	—	2	2	no	—
439	C₂²×C₂₃	—	2	2	no	—
440	C₂²×C₂₃	—	4	8	no	—
441	C₂²×C₂₃	—	4	2	no	—
442	C₂²×C₂₃	—	4	2	no	—
443	C₂²×C₂₃	—	4	1	no	—
444	C₂²×C₂₃	—	4	2	no	—
445	C₂²×C₂₃	—	4	1	no	—
446	C₂²×C₂₃	—	4	2	no	—
447	C₂²×C₂₃	—	4	2	no	—
448	C₂²×C₂₃	—	4	1	no	—
449	C₂²×C₂₃	—	4	2	no	—
450	C₂²×C₂₃	—	8	4	no	—
451	C₂²×C₂₃	—	16	4	no	—
452	C₂²×C₂₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
453	C₂²×C₂₃	#577	1	2	yes	—
454	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
455	C₄×C₂₃	—	2	1	no	—
456	C₄×C₂₃	—	2	2	no	—
457	C₄×C₂₃	—	2	2	no	—
458	C₄×C₂₃	—	2	1	no	—
459	C₄×C₂₃	—	2	1	no	—
460	C₄×C₂₃	—	2	1	no	—
461	C₄×C₂₃	—	4	1	no	—
462	C₄×C₂₃	—	4	2	no	—
463	C₄×C₂₃	—	4	4	no	—
464	C₄×C₂₃	—	4	1	no	—
465	C₄×C₂₃	—	4	1	no	—
466	C₄×C₂₃	—	4	2	no	—
467	C₄×C₂₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
468	C₄×C₂₃	#585	1	2	yes	—
469	C₂²×#41	—	2	1	no	—
470	#555	C₂²×C₂₃	1	1	yes	characteristic, complemented
471	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
472	#553	—	2	1	no	—
473	#553	C₂²×C₂₃	1	2	yes	complemented
474	#550	C₂²×C₂₃	1	1	yes	characteristic, complemented
475	#547	—	2	1	no	—
476	#547	—	2	2	no	—
477	#547	—	2	1	no	—
478	#547	C₂²×C₂₃	1	2	yes	—
479	#547	C₂²×C₂₃	1	2	yes	complemented
480	#547	C₂²×C₂₃	1	4	yes	complemented
481	#546	—	2	2	no	—
482	#546	C₂²×C₂₃	1	2	yes	complemented
483	D₄²	—	2	1	no	—
484	D₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
485	#540	—	2	1	no	—
486	#538	—	2	2	no	—
487	#532	C₂²×C₂₃	1	1	yes	characteristic
488	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
489	#529	C₂²×C₂₃	1	1	yes	characteristic
490	#525	C₂²×C₂₃	1	2	yes	—
491	C₂×#123	—	2	2	no	—
492	C₂×C₂²⋊Q₈	—	2	1	no	—
493	C₂×#121	C₂²×C₂₃	1	2	yes	—
494	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
495	#518	—	2	1	no	—
496	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
497	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
498	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
499	#501	C₂²×C₂₃	1	2	yes	complemented
500	#498	C₂²×C₂₃	1	2	yes	complemented
501	#489	C₂²×C₂₃	1	2	yes	complemented
502	#486	C₂²×C₂₃	1	2	yes	complemented
503	#484	C₂²×C₂₃	1	1	yes	characteristic, complemented
504	#484	C₂²×C₂₃	1	2	yes	complemented
505	#483	C₂²×C₂₃	1	4	yes	complemented
506	#482	C₂²×C₂₃	1	4	yes	complemented
507	#481	C₂²×C₂₃	1	1	yes	characteristic
508	#481	C₂²×C₂₃	1	2	yes	—
509	#481	C₂²×C₂₃	1	4	yes	complemented
510	#481	C₂²×C₂₃	1	4	yes	complemented
511	#481	C₂²×C₂₃	1	2	yes	complemented
512	#481	C₂²×C₂₃	1	4	yes	complemented
513	#481	C₂²×C₂₃	1	2	yes	complemented
514	#481	C₂²×C₂₃	1	2	yes	complemented
515	#480	C₂²×C₂₃	1	4	yes	complemented
516	#478	C₂²×C₂₃	1	2	yes	complemented
517	#476	C₂²×C₂₃	1	2	yes	complemented
518	#476	C₂²×C₂₃	1	4	yes	complemented
519	#475	C₂²×C₂₃	1	2	yes	complemented
520	#474	C₂²×C₂₃	1	2	yes	complemented
521	#469	C₂²×C₂₃	1	4	yes	complemented
522	#469	C₂²×C₂₃	1	4	yes	complemented
523	#466	C₂²×C₂₃	1	4	yes	complemented
524	#465	C₂²×C₂₃	1	4	yes	complemented
525	#463	C₂²×C₂₃	1	2	yes	complemented
526	#459	C₂²×C₂₃	1	2	yes	complemented
527	#450	C₂²×C₂₃	1	1	yes	characteristic, complemented
528	#449	C₂²×C₂₃	1	4	yes	complemented
529	#447	C₂²×C₂₃	1	1	yes	characteristic
530	#447	C₂²×C₂₃	1	2	yes	complemented
531	#447	C₂²×C₂₃	1	4	yes	complemented
532	#442	C₂²×C₂₃	1	4	yes	complemented
533	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
534	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
535	#436	C₂²×C₂₃	1	2	yes	complemented
536	#435	C₂²×C₂₃	1	4	yes	complemented
537	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
538	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
539	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
540	#428	C₂²×C₂₃	1	4	yes	complemented
541	C₂×#106	C₂²×C₂₃	1	4	yes	complemented
542	#417	C₂²×C₂₃	1	4	yes	complemented
543	C₂×#102	C₂²×C₂₃	1	4	yes	complemented
544	#407	C₂²×C₂₃	1	2	yes	complemented
545	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
546	C₂×C₂₃	—	2	2	no	—
547	C₂×C₂₃	—	2	4	no	—
548	C₂×C₂₃	—	4	2	no	—
549	C₂×C₂₃	—	8	2	no	—
550	C₂×C₂₃	—	8	2	no	—
551	C₂×C₂₃	—	8	1	no	—
552	C₂×C₂₃	#3485	1	1	yes	characteristic
553	C₂×C₂₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
554	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
555	C₂×#41	—	2	2	no	—
556	C₂×#41	—	2	4	no	—
557	C₂×#41	—	2	2	no	—
558	C₂×#41	—	2	1	no	—
559	C₂×#41	—	4	8	no	—
560	C₂×#41	C₂³×C₂₃	1	2	yes	—
561	C₂²×Q₈	—	2	1	no	—
562	C₂²×D₄	—	2	2	no	—
563	C₂²×D₄	—	2	2	no	—
564	C₂²×D₄	—	2	1	no	—
565	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
566	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
567	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
568	C₂³×C₄	—	2	2	no	—
569	C₂³×C₄	—	2	1	no	—
570	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
571	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
572	C₂×D₈	C₂³×C₂₃	1	2	yes	—
573	C₂×D₈	C₂³×C₂₃	1	4	yes	—
574	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
575	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
576	C₄⋊Q₈	—	2	1	no	—
577	C₄⋊Q₈	—	2	1	no	—
578	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
579	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
580	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
581	#127	—	2	1	no	—
582	#127	C₂³×C₂₃	1	1	yes	characteristic
583	#126	—	2	2	no	—
584	#126	—	2	1	no	—
585	#125	—	2	1	no	—
586	#125	C₂³×C₂₃	1	1	yes	characteristic
587	#124	—	2	2	no	—
588	#124	—	2	1	no	—
589	#124	C₂³×C₂₃	1	1	yes	characteristic
590	#123	—	2	2	no	—
591	#123	—	2	1	no	—
592	#123	—	2	2	no	—
593	#123	—	2	4	no	—
594	#123	—	2	4	no	—
595	#123	—	2	4	no	—
596	#123	—	2	4	no	—
597	#123	—	2	2	no	—
598	C₂²⋊Q₈	—	2	2	no	—
599	C₂²⋊Q₈	—	2	2	no	—
600	C₂²⋊Q₈	—	2	4	no	—
601	C₂²⋊Q₈	—	2	2	no	—
602	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
603	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
604	#121	—	2	2	no	—
605	#121	—	2	1	no	—
606	#121	—	2	2	no	—
607	#121	—	2	2	no	—
608	#121	—	2	2	no	—
609	#121	—	2	2	no	—
610	#121	—	2	1	no	—
611	#121	—	2	1	no	—
612	#121	—	2	2	no	—
613	#121	—	2	2	no	—
614	#121	C₂³×C₂₃	1	1	yes	characteristic
615	#121	C₂³×C₂₃	1	2	yes	—
616	#121	C₂³×C₂₃	1	2	yes	—
617	#121	C₂³×C₂₃	1	2	yes	—
618	#121	C₂³×C₂₃	1	4	yes	—
619	#121	C₂³×C₂₃	1	4	yes	—
620	#121	C₂³×C₂₃	1	2	yes	—
621	#120	—	2	2	no	—
622	#120	—	2	2	no	—
623	#120	—	2	2	no	—
624	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	1	no	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	1	no	—
632	C₄×D₄	—	2	1	no	—
633	C₄×D₄	—	2	1	no	—
634	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
635	C₄×D₄	D₄×C₂₃	1	2	yes	—
636	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
637	C₄×D₄	C₂³×C₂₃	1	2	yes	—
638	C₄×D₄	C₂³×C₂₃	1	2	yes	—
639	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
640	C₄×D₄	C₂³×C₂₃	1	2	yes	—
641	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
642	C₄×D₄	C₂³×C₂₃	1	2	yes	—
643	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
644	#117	—	2	1	no	—
645	#117	—	2	1	no	—
646	#117	C₂³×C₂₃	1	2	yes	—
647	C₂×C₄⋊C₄	—	2	2	no	—
648	C₂×C₄⋊C₄	—	2	2	no	—
649	C₂×C₄⋊C₄	—	2	2	no	—
650	C₂×C₄⋊C₄	—	2	1	no	—
651	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
652	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
653	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
654	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
655	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
656	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
657	C₂×C₂²⋊C₄	—	2	1	no	—
658	C₂×C₂²⋊C₄	—	2	2	no	—
659	C₂×C₂²⋊C₄	—	2	2	no	—
660	C₂×C₂²⋊C₄	—	2	2	no	—
661	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
662	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
663	#107	C₂³×C₂₃	1	2	yes	—
664	#107	C₂³×C₂₃	1	4	yes	—
665	#106	C₂³×C₂₃	1	2	yes	—
666	#106	C₂³×C₂₃	1	4	yes	—
667	#106	C₂³×C₂₃	1	4	yes	—
668	#106	C₂³×C₂₃	1	4	yes	—
669	#106	C₂³×C₂₃	1	4	yes	—
670	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
671	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
672	#103	C₂³×C₂₃	1	2	yes	—
673	#103	C₂³×C₂₃	1	4	yes	—
674	#102	C₂³×C₂₃	1	2	yes	—
675	#102	C₂³×C₂₃	1	4	yes	—
676	#102	C₂³×C₂₃	1	4	yes	—
677	#102	C₂³×C₂₃	1	4	yes	—
678	#102	C₂³×C₂₃	1	4	yes	—
679	#102	C₂³×C₂₃	1	2	yes	—
680	#102	C₂³×C₂₃	1	2	yes	—
681	#102	C₂³×C₂₃	1	4	yes	—
682	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
683	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
684	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
685	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
686	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
687	#97	C₂³×C₂₃	1	2	yes	—
688	C₄×C₈	C₂³×C₂₃	1	2	yes	—
689	C₂₃	#61728	1	1	yes	characteristic, direct product factor, Sylow
690	C₂⁴	—	2	1	no	—
691	C₂⁴	—	2	2	no	—
692	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
693	#41	—	4	4	no	—
694	#41	—	4	16	no	—
695	#41	—	4	8	no	—
696	#41	—	4	8	no	—
697	#41	—	8	2	no	—
698	C₂×Q₈	—	2	2	no	—
699	C₂×Q₈	—	2	2	no	—
700	C₂×Q₈	—	2	1	no	—
701	C₂×Q₈	—	4	4	no	—
702	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
703	C₂×D₄	—	2	4	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	2	no	—
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	4	no	—
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	2	2	no	—
710	C₂×D₄	—	2	2	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	1	no	—
714	C₂×D₄	—	2	1	no	—
715	C₂×D₄	—	2	2	no	—
716	C₂×D₄	—	4	2	no	—
717	C₂×D₄	—	4	4	no	—
718	C₂×D₄	—	4	8	no	—
719	C₂×D₄	—	4	4	no	—
720	C₂×D₄	—	8	4	no	—
721	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
722	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
723	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
724	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
725	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
726	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
727	C₂²×C₄	—	2	1	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	4	no	—
730	C₂²×C₄	—	2	4	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	2	no	—
736	C₂²×C₄	—	2	2	no	—
737	C₂²×C₄	—	4	4	no	—
738	C₂²×C₄	—	4	4	no	—
739	C₂²×C₄	—	4	8	no	—
740	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
741	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
742	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
743	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
744	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
748	SD₁₆	—	4	2	no	—
749	D₈	—	4	4	no	—
750	D₈	—	4	2	no	—
751	M₁₆	—	4	4	no	—
752	C₂×C₈	—	4	4	no	—
753	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
754	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
755	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	2	4	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	1	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	1	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	1	no	—
769	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
770	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
771	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
772	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
773	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
774	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
775	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
776	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	1	no	—
780	C₂²⋊C₄	—	2	1	no	—
781	C₂²⋊C₄	—	2	1	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	1	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	1	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
794	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
795	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
796	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	1	no	—
799	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
800	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
801	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
802	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
803	C₂³	—	2	4	no	—
804	C₂³	—	2	4	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	1	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	4	2	no	—
809	C₂³	—	4	2	no	—
810	C₂³	—	4	2	no	—
811	C₂³	—	4	2	no	—
812	C₂³	—	4	4	no	—
813	C₂³	—	8	2	no	—
814	C₂³	—	8	2	no	—
815	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
816	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
817	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
818	Q₈	—	2	2	no	—
819	Q₈	—	4	4	no	—
820	Q₈	—	4	4	no	—
821	Q₈	—	8	1	no	—
822	D₄	—	2	4	no	—
823	D₄	—	2	2	no	—
824	D₄	—	2	2	no	—
825	D₄	—	2	2	no	—
826	D₄	—	2	2	no	—
827	D₄	—	2	4	no	—
828	D₄	—	4	2	no	—
829	D₄	—	4	8	no	—
830	D₄	—	4	8	no	—
831	D₄	—	4	4	no	—
832	D₄	—	4	2	no	—
833	D₄	—	4	4	no	—
834	D₄	—	4	2	no	—
835	D₄	—	8	2	no	—
836	D₄	—	8	1	no	—
837	D₄	—	8	2	no	—
838	D₄	—	8	2	no	—
839	D₄	—	8	2	no	—
840	D₄	C₂₃×AGL(1,ℤ/8)	1	4	yes	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	4	no	—
844	C₂×C₄	—	2	4	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	1	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	4	2	no	—
853	C₂×C₄	—	4	2	no	—
854	C₂×C₄	—	4	2	no	—
855	C₂×C₄	—	4	4	no	—
856	C₂×C₄	—	4	2	no	—
857	C₂×C₄	—	4	4	no	—
858	C₂×C₄	—	4	8	no	—
859	C₂×C₄	—	4	8	no	—
860	C₂×C₄	—	4	4	no	—
861	C₂×C₄	—	4	2	no	—
862	C₂×C₄	—	8	2	no	—
863	C₂×C₄	—	8	2	no	—
864	C₂×C₄	—	8	2	no	—
865	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
866	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
867	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
868	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
869	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
870	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
871	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
872	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
873	C₈	—	2	2	no	—
874	C₈	—	2	4	no	—
875	C₈	—	2	2	no	—
876	C₂²	—	2	1	no	—
877	C₂²	—	2	2	no	—
878	C₂²	—	2	1	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	4	8	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	1	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	1	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	1	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	8	4	no	—
894	C₂²	—	16	4	no	—
895	C₂²	C₂×C₂₃×AGL(1,ℤ/8)	1	4	yes	—
896	C₂²	C₂₃×#577	1	2	yes	—
897	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
898	C₄	—	2	1	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	1	no	—
902	C₄	—	2	1	no	—
903	C₄	—	2	1	no	—
904	C₄	—	4	1	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	4	no	—
907	C₄	—	4	1	no	—
908	C₄	—	4	1	no	—
909	C₄	—	4	2	no	—
910	C₄	C₂×C₂₃×AGL(1,ℤ/8)	1	2	yes	—
911	C₄	C₂₃×#585	1	2	yes	—
912	C₂	—	2	2	no	—
913	C₂	—	2	4	no	—
914	C₂	—	4	2	no	—
915	C₂	—	8	2	no	—
916	C₂	—	8	1	no	—
917	C₂	—	8	2	no	—
918	C₂	C₂₃×#3485	1	1	yes	characteristic
919	C₂	C₂²×C₂₃×AGL(1,ℤ/8)	1	1	yes	characteristic
920	C₂	C₂×C₂₃×#577	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×#547	C₂	semidirect
3. C₂₃×#3354	C₂	semidirect
4. C₂₃×#3345	C₂	semidirect
5. C₂₃×#3335	C₂	semidirect
6. C₂₃×#3332	C₂	semidirect
7. C₂₃×#3306	C₂	semidirect
8. C₂₃×#3294	C₂	semidirect
9. C₂₃×#3239	C₂	semidirect
10. C₂₃×#3227	C₂	semidirect
11. C₂₃×#3192	C₂	semidirect
12. C₂₃×#3188	C₂	semidirect
13. C₂₃×#3109	C₂	semidirect
14. C₂₃×#3105	C₂	semidirect
15. C₂₃×#3092	C₂	semidirect
16. C₂×C₂₃×#481	C₂	semidirect
17. C₂₃×#2974	C₂	semidirect
19. C₂₃×#555	C₂²	semidirect
20. C₂₃×#554	C₂²	semidirect
22. C₂₃×#553	C₂²	semidirect
23. C₂₃×#550	C₂²	semidirect
28. C₂₃×#547	C₂²	semidirect
29. C₂₃×#547	C₂²	semidirect
31. C₂₃×#546	C₂²	semidirect
33. D₄²×C₂₃	C₂²	semidirect
37. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
43. C₂×C₂₃×#121	C₂²	semidirect
46. C₂×C₄×D₄×C₂₃	C₂²	semidirect
47. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
48. C₂₃×#501	C₂²	semidirect
49. C₂₃×#498	C₂²	semidirect
50. C₂₃×#489	C₂²	semidirect
51. C₂₃×#486	C₂²	semidirect
52. C₂₃×#484	C₂²	semidirect
53. C₂₃×#484	C₂²	semidirect
54. C₂₃×#483	C₂²	semidirect
55. C₂₃×#482	C₂²	semidirect
58. C₂₃×#481	C₂²	semidirect
59. C₂₃×#481	C₂²	semidirect
60. C₂₃×#481	C₂²	semidirect
61. C₂₃×#481	C₂²	semidirect
62. C₂₃×#481	C₂²	semidirect
63. C₂₃×#481	C₂²	semidirect
64. C₂₃×#480	C₂²	semidirect
65. C₂₃×#478	C₂²	semidirect
66. C₂₃×#476	C₂²	semidirect
67. C₂₃×#476	C₂²	semidirect
68. C₂₃×#475	C₂²	semidirect
69. C₂₃×#474	C₂²	semidirect
70. C₂₃×#469	C₂²	semidirect
71. C₂₃×#469	C₂²	semidirect
72. C₂₃×#466	C₂²	semidirect
73. C₂₃×#465	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. C₂×C₂₃×#106	C₂²	semidirect
91. C₂₃×#417	C₂²	semidirect
92. C₂×C₂₃×#102	C₂²	semidirect
93. C₂₃×#407	C₂²	semidirect
94. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
342. #61728	C₂₃	direct (N × H)
416. #3519	C₂×C₂₃	semidirect
417. C₂×#547	C₂×C₂₃	semidirect
418. #3354	C₂×C₂₃	semidirect
419. #3345	C₂×C₂₃	semidirect
420. #3335	C₂×C₂₃	semidirect
421. #3332	C₂×C₂₃	semidirect
422. #3306	C₂×C₂₃	semidirect
423. #3294	C₂×C₂₃	semidirect
424. #3239	C₂×C₂₃	semidirect
425. #3227	C₂×C₂₃	semidirect
426. #3192	C₂×C₂₃	semidirect
427. #3188	C₂×C₂₃	semidirect
428. #3109	C₂×C₂₃	semidirect
429. #3105	C₂×C₂₃	semidirect
430. #3092	C₂×C₂₃	semidirect
431. C₂×#481	C₂×C₂₃	semidirect
432. #2974	C₂×C₂₃	semidirect
470. #555	C₂²×C₂₃	semidirect
471. #554	C₂²×C₂₃	semidirect
473. #553	C₂²×C₂₃	semidirect
474. #550	C₂²×C₂₃	semidirect
479. #547	C₂²×C₂₃	semidirect
480. #547	C₂²×C₂₃	semidirect
482. #546	C₂²×C₂₃	semidirect
484. D₄²	C₂²×C₂₃	semidirect
488. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
494. C₂×#121	C₂²×C₂₃	semidirect
497. C₂×C₄×D₄	C₂²×C₂₃	semidirect
498. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
499. #501	C₂²×C₂₃	semidirect
500. #498	C₂²×C₂₃	semidirect
501. #489	C₂²×C₂₃	semidirect
502. #486	C₂²×C₂₃	semidirect
503. #484	C₂²×C₂₃	semidirect
504. #484	C₂²×C₂₃	semidirect
505. #483	C₂²×C₂₃	semidirect
506. #482	C₂²×C₂₃	semidirect
509. #481	C₂²×C₂₃	semidirect
510. #481	C₂²×C₂₃	semidirect
511. #481	C₂²×C₂₃	semidirect
512. #481	C₂²×C₂₃	semidirect
513. #481	C₂²×C₂₃	semidirect
514. #481	C₂²×C₂₃	semidirect
515. #480	C₂²×C₂₃	semidirect
516. #478	C₂²×C₂₃	semidirect
517. #476	C₂²×C₂₃	semidirect
518. #476	C₂²×C₂₃	semidirect
519. #475	C₂²×C₂₃	semidirect
520. #474	C₂²×C₂₃	semidirect
521. #469	C₂²×C₂₃	semidirect
522. #469	C₂²×C₂₃	semidirect
523. #466	C₂²×C₂₃	semidirect
524. #465	C₂²×C₂₃	semidirect
525. #463	C₂²×C₂₃	semidirect
526. #459	C₂²×C₂₃	semidirect
527. #450	C₂²×C₂₃	semidirect
528. #449	C₂²×C₂₃	semidirect
530. #447	C₂²×C₂₃	semidirect
531. #447	C₂²×C₂₃	semidirect
532. #442	C₂²×C₂₃	semidirect
533. C₄×SD₁₆	C₂²×C₂₃	semidirect
534. C₄×D₈	C₂²×C₂₃	semidirect
535. #436	C₂²×C₂₃	semidirect
536. #435	C₂²×C₂₃	semidirect
537. C₈×D₄	C₂²×C₂₃	semidirect
538. #432	C₂²×C₂₃	semidirect
539. #431	C₂²×C₂₃	semidirect
540. #428	C₂²×C₂₃	semidirect
541. C₂×#106	C₂²×C₂₃	semidirect
542. #417	C₂²×C₂₃	semidirect
543. C₂×#102	C₂²×C₂₃	semidirect
544. #407	C₂²×C₂₃	semidirect
545. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
689. C₂₃	#61728	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×#547	2
C₂₃×#3354	2
C₂₃×#3345	2
C₂₃×#3335	2
C₂₃×#3332	2
C₂₃×#3306	2
C₂₃×#3294	2
C₂₃×#3239	2
C₂₃×#3227	2
C₂₃×#3192	2
C₂₃×#3188	2
C₂₃×#3109	2
C₂₃×#3105	2
C₂₃×#3092	2
C₂×C₂₃×#481	2
C₂₃×#2974	2
#61728	23

Subgroups — C23×#61728 #19209354

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61728 #19209354