Subgroups — C₂₃×#61752 #19209378

Order 5888.

1862 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3537	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3494	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3355	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3347	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3345	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3339	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3325	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3318	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3318	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3294	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3241	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3199	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3192	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3186	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3122	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3096	C₂	1	2	yes	maximal, complemented
17	C₂₃×#3094	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2976	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂₃×#560	—	2	2	no	—
21	C₂₃×#555	C₂²	1	2	yes	complemented
22	C₂₃×#553	C₂²	1	2	yes	complemented
23	C₂₃×#553	C₂²	1	2	yes	complemented
24	C₂₃×#553	C₂²	1	2	yes	complemented
25	C₂₃×#553	C₂²	1	2	yes	complemented
26	C₂₃×#551	—	2	2	no	—
27	C₂₃×#547	C₂²	1	2	yes	complemented
28	C₂₃×#546	—	2	2	no	—
29	D₄²×C₂₃	—	2	2	no	—
30	D₄²×C₂₃	C₂²	1	2	yes	complemented
31	D₄²×C₂₃	C₂²	1	2	yes	complemented
32	C₂₃×#544	C₂²	1	1	yes	characteristic, complemented
33	C₂₃×#542	—	2	1	no	—
34	C₂₃×#540	—	2	1	no	—
35	C₂₃×#540	C₂²	1	2	yes	—
36	C₂₃×#538	—	2	1	no	—
37	C₂₃×#538	—	2	1	no	—
38	C₂₃×#535	C₂²	1	2	yes	—
39	C₂₃×#535	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#534	—	2	1	no	—
41	C₂₃×#534	—	2	1	no	—
42	C₂₃×#532	—	2	1	no	—
43	C₂₃×#529	—	2	1	no	—
44	C₂₃×#525	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
48	C₂₃×#520	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#518	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#501	C₂²	1	2	yes	complemented
52	C₂₃×#499	C₂²	1	2	yes	complemented
53	C₂₃×#490	C₂²	1	2	yes	complemented
54	C₂₃×#486	C₂²	1	2	yes	complemented
55	C₂₃×#482	C₂²	1	2	yes	complemented
56	C₂₃×#482	C₂²	1	2	yes	complemented
57	C₂₃×#482	C₂²	1	2	yes	complemented
58	C₂₃×#482	C₂²	1	2	yes	complemented
59	C₂₃×#482	C₂²	1	2	yes	complemented
60	C₂₃×#482	C₂²	1	2	yes	complemented
61	C₂₃×#482	C₂²	1	2	yes	complemented
62	C₂₃×#482	C₂²	1	2	yes	complemented
63	C₂₃×#482	C₂²	1	2	yes	complemented
64	C₂₃×#482	C₂²	1	2	yes	complemented
65	C₂₃×#481	C₂²	1	2	yes	complemented
66	C₂₃×#481	C₂²	1	2	yes	complemented
67	C₂₃×#481	C₂²	1	2	yes	complemented
68	C₂₃×#481	C₂²	1	2	yes	complemented
69	C₂₃×#480	C₂²	1	2	yes	complemented
70	C₂₃×#480	C₂²	1	2	yes	complemented
71	C₂₃×#480	C₂²	1	2	yes	complemented
72	C₂₃×#480	C₂²	1	2	yes	complemented
73	C₂₃×#478	C₂²	1	2	yes	complemented
74	C₂₃×#478	C₂²	1	2	yes	complemented
75	C₂₃×#478	C₂²	1	2	yes	complemented
76	C₂₃×#478	C₂²	1	2	yes	complemented
77	C₂₃×#476	C₂²	1	2	yes	complemented
78	C₂₃×#474	C₂²	1	2	yes	complemented
79	C₂₃×#469	C₂²	1	2	yes	complemented
80	C₂₃×#469	C₂²	1	2	yes	complemented
81	C₂₃×#469	C₂²	1	2	yes	complemented
82	C₂₃×#469	C₂²	1	2	yes	complemented
83	C₂₃×#466	C₂²	1	2	yes	complemented
84	C₂₃×#466	C₂²	1	2	yes	complemented
85	C₂₃×#466	C₂²	1	2	yes	complemented
86	C₂₃×#466	C₂²	1	2	yes	complemented
87	C₂₃×#459	C₂²	1	2	yes	complemented
88	C₂₃×#459	C₂²	1	2	yes	complemented
89	C₂₃×#447	C₂²	1	2	yes	complemented
90	C₂₃×#447	C₂²	1	2	yes	complemented
91	C₂₃×#447	C₂²	1	2	yes	complemented
92	C₂₃×#447	C₂²	1	2	yes	complemented
93	C₂₃×#447	C₂²	1	2	yes	complemented
94	C₂₃×#447	C₂²	1	2	yes	complemented
95	C₂₃×#442	C₂²	1	2	yes	complemented
96	C₂₃×#442	C₂²	1	2	yes	complemented
97	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
98	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
99	C₂₃×#436	C₂²	1	2	yes	complemented
100	C₂₃×#435	C₂²	1	2	yes	complemented
101	C₂₃×#435	C₂²	1	2	yes	complemented
102	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
103	C₂₃×#433	C₂²	1	2	yes	complemented
104	C₂₃×#428	C₂²	1	2	yes	complemented
105	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
106	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
107	C₂₃×#427	C₂²	1	2	yes	complemented
108	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic, complemented
109	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic, complemented
110	C₂₃×#418	C₂²	1	1	yes	characteristic, complemented
111	C₂₃×#418	C₂²	1	2	yes	complemented
112	C₂₃×#418	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₂₃×#102	C₂²	1	2	yes	complemented
115	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic, complemented
116	C₂₃×#408	C₂²	1	2	yes	complemented
117	C₂₃×#407	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
119	C₂×#41×C₂₃	—	2	2	no	—
120	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
121	C₂²×D₄×C₂₃	—	2	1	no	—
122	C₂²×D₄×C₂₃	—	2	1	no	—
123	C₂²×D₄×C₂₃	—	2	1	no	—
124	C₂²×D₄×C₂₃	—	2	2	no	—
125	C₂²×D₄×C₂₃	—	2	2	no	—
126	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
128	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
129	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
131	C₂×D₈×C₂₃	C₂³	1	2	yes	—
132	C₂×D₈×C₂₃	C₂³	1	2	yes	—
133	C₂×D₈×C₂₃	C₂³	1	2	yes	—
134	C₂×D₈×C₂₃	C₂³	1	2	yes	—
135	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
136	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
137	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
138	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
139	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
141	C₂₃×C₄⋊Q₈	—	2	1	no	—
142	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
143	C₂₃×#127	—	2	2	no	—
144	C₂₃×#127	—	2	1	no	—
145	C₂₃×#127	C₂³	1	2	yes	—
146	C₂₃×#126	—	2	2	no	—
147	C₂₃×#126	—	2	2	no	—
148	C₂₃×#126	—	2	2	no	—
149	C₂₃×#126	—	2	2	no	—
150	C₂₃×#125	—	2	1	no	—
151	C₂₃×#125	C₂³	1	2	yes	—
152	C₂₃×#125	C₂³	1	2	yes	—
153	C₂₃×#124	—	2	1	no	—
154	C₂₃×#124	—	2	2	no	—
155	C₂₃×#124	—	2	2	no	—
156	C₂₃×#124	—	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×#123	—	2	2	no	—
164	C₂₃×#123	—	2	2	no	—
165	C₂₃×#123	D₄	1	2	yes	—
166	C₂₃×C₂²⋊Q₈	—	2	2	no	—
167	C₂₃×C₂²⋊Q₈	—	2	2	no	—
168	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
169	C₂₃×C₂²⋊Q₈	D₄	1	1	yes	characteristic
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	1	no	—
176	C₂₃×#121	—	2	1	no	—
177	C₂₃×#121	—	2	1	no	—
178	C₂₃×#121	—	2	1	no	—
179	C₂₃×#121	—	2	1	no	—
180	C₂₃×#121	—	2	1	no	—
181	C₂₃×#121	—	2	2	no	—
182	C₂₃×#121	—	2	2	no	—
183	C₂₃×#121	—	2	2	no	—
184	C₂₃×#121	—	2	2	no	—
185	C₂₃×#121	D₄	1	1	yes	characteristic
186	C₂₃×#121	D₄	1	1	yes	characteristic
187	C₂₃×#121	C₂³	1	2	yes	—
188	C₂₃×#121	C₂³	1	2	yes	—
189	C₂₃×#121	C₂³	1	2	yes	—
190	C₂₃×#121	C₂³	1	2	yes	—
191	C₂₃×#121	C₂³	1	2	yes	—
192	C₂₃×#121	C₂³	1	2	yes	—
193	C₂₃×#121	C₂³	1	2	yes	—
194	C₂₃×#121	C₂³	1	2	yes	—
195	C₂₃×#121	C₂³	1	2	yes	—
196	C₂₃×#121	C₂³	1	2	yes	—
197	C₂₃×#120	—	2	2	no	—
198	C₂₃×#120	—	2	2	no	—
199	C₂₃×#120	—	2	2	no	—
200	C₂₃×#120	—	2	2	no	—
201	C₂₃×#120	—	2	2	no	—
202	C₂₃×#120	—	2	2	no	—
203	C₂₃×#120	—	2	2	no	—
204	C₂₃×#120	D₄	1	2	yes	—
205	C₄×Q₈×C₂₃	—	2	1	no	—
206	C₄×D₄×C₂₃	—	2	2	no	—
207	C₄×D₄×C₂₃	—	2	1	no	—
208	C₄×D₄×C₂₃	—	2	1	no	—
209	C₄×D₄×C₂₃	—	2	1	no	—
210	C₄×D₄×C₂₃	—	2	2	no	—
211	C₄×D₄×C₂₃	—	2	2	no	—
212	C₄×D₄×C₂₃	—	2	2	no	—
213	C₄×D₄×C₂₃	—	2	2	no	—
214	C₄×D₄×C₂₃	C₂³	1	2	yes	—
215	C₄×D₄×C₂₃	C₂³	1	2	yes	—
216	C₄×D₄×C₂₃	C₂³	1	2	yes	—
217	C₄×D₄×C₂₃	C₂³	1	2	yes	—
218	C₄×D₄×C₂₃	C₂³	1	2	yes	—
219	C₄×D₄×C₂₃	C₂³	1	2	yes	—
220	C₂₃×#117	—	2	1	no	—
221	C₂₃×#117	—	2	1	no	—
222	C₂₃×#117	—	2	2	no	—
223	C₂₃×#117	C₂³	1	1	yes	characteristic
224	C₂₃×#117	C₂³	1	2	yes	—
225	C₂₃×#117	C₂³	1	2	yes	—
226	C₂₃×#117	C₂³	1	1	yes	characteristic
227	C₂₃×#117	C₂³	1	1	yes	characteristic
228	C₂₃×#117	C₂³	1	1	yes	characteristic
229	C₂₃×#117	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
232	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
236	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
237	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
239	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
240	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
241	C₂×C₄²×C₂₃	—	2	1	no	—
242	C₂₃×#107	C₂³	1	2	yes	—
243	C₂₃×#107	C₂³	1	2	yes	—
244	C₂₃×#107	C₂³	1	2	yes	—
245	C₂₃×#107	C₂³	1	2	yes	—
246	C₂₃×#107	C₂³	1	2	yes	—
247	C₂₃×#107	C₂³	1	2	yes	—
248	C₂₃×#106	C₂³	1	2	yes	—
249	C₂₃×#106	C₂³	1	2	yes	—
250	C₂₃×#106	C₂³	1	2	yes	—
251	C₂₃×#106	C₂³	1	2	yes	—
252	C₂₃×#106	C₂³	1	2	yes	—
253	C₂₃×#106	C₂³	1	2	yes	—
254	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
255	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
256	C₂₃×#102	C₂³	1	2	yes	—
257	C₂₃×#102	C₂³	1	2	yes	—
258	C₂₃×#102	C₂³	1	2	yes	—
259	C₂₃×#102	C₂³	1	2	yes	—
260	C₂₃×#102	C₂³	1	2	yes	—
261	C₂₃×#102	C₂³	1	2	yes	—
262	C₂₃×#102	C₂³	1	2	yes	—
263	C₂₃×#102	C₂³	1	2	yes	—
264	C₂₃×#102	C₂³	1	2	yes	—
265	C₂₃×#102	C₂³	1	2	yes	—
266	C₂₃×#102	C₂³	1	2	yes	—
267	C₂₃×#102	C₂³	1	2	yes	—
268	C₂₃×#102	C₂³	1	2	yes	—
269	C₂₃×#102	C₂³	1	2	yes	—
270	C₂₃×#102	C₂³	1	2	yes	—
271	C₂₃×#102	C₂³	1	2	yes	—
272	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
273	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
274	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
275	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
276	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
277	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
278	C₂₃×#97	C₂³	1	2	yes	—
279	C₄×C₈×C₂₃	C₂³	1	2	yes	—
280	C₂⁴×C₂₃	—	2	1	no	—
281	C₂⁴×C₂₃	—	2	1	no	—
282	C₂⁴×C₂₃	—	2	1	no	—
283	C₂⁴×C₂₃	—	2	2	no	—
284	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
285	#41×C₂₃	—	4	1	no	—
286	#41×C₂₃	—	4	1	no	—
287	#41×C₂₃	—	8	4	no	—
288	C₂×Q₈×C₂₃	—	2	2	no	—
289	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
290	C₂×D₄×C₂₃	—	2	2	no	—
291	C₂×D₄×C₂₃	—	2	2	no	—
292	C₂×D₄×C₂₃	—	2	2	no	—
293	C₂×D₄×C₂₃	—	2	2	no	—
294	C₂×D₄×C₂₃	—	2	2	no	—
295	C₂×D₄×C₂₃	—	2	2	no	—
296	C₂×D₄×C₂₃	—	2	2	no	—
297	C₂×D₄×C₂₃	—	2	2	no	—
298	C₂×D₄×C₂₃	—	2	2	no	—
299	C₂×D₄×C₂₃	—	2	2	no	—
300	C₂×D₄×C₂₃	—	2	1	no	—
301	C₂×D₄×C₂₃	—	2	1	no	—
302	C₂×D₄×C₂₃	—	2	1	no	—
303	C₂×D₄×C₂₃	—	2	2	no	—
304	C₂×D₄×C₂₃	—	2	2	no	—
305	C₂×D₄×C₂₃	—	2	2	no	—
306	C₂×D₄×C₂₃	—	4	1	no	—
307	C₂×D₄×C₂₃	—	4	1	no	—
308	C₂×D₄×C₂₃	—	4	1	no	—
309	C₂×D₄×C₂₃	—	4	1	no	—
310	C₂×D₄×C₂₃	—	4	2	no	—
311	C₂×D₄×C₂₃	—	4	1	no	—
312	C₂×D₄×C₂₃	—	4	1	no	—
313	C₂×D₄×C₂₃	—	4	2	no	—
314	C₂×D₄×C₂₃	—	8	4	no	—
315	C₂×D₄×C₂₃	—	8	2	no	—
316	C₂×D₄×C₂₃	—	8	2	no	—
317	C₂×D₄×C₂₃	—	8	4	no	—
318	C₂×D₄×C₂₃	—	8	2	no	—
319	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
320	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
321	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
322	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
323	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
324	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
325	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
326	C₂²×C₄×C₂₃	—	2	1	no	—
327	C₂²×C₄×C₂₃	—	2	1	no	—
328	C₂²×C₄×C₂₃	—	2	1	no	—
329	C₂²×C₄×C₂₃	—	2	1	no	—
330	C₂²×C₄×C₂₃	—	2	1	no	—
331	C₂²×C₄×C₂₃	—	2	2	no	—
332	C₂²×C₄×C₂₃	—	2	2	no	—
333	C₂²×C₄×C₂₃	—	2	2	no	—
334	C₂²×C₄×C₂₃	—	2	2	no	—
335	C₂²×C₄×C₂₃	—	2	2	no	—
336	C₂²×C₄×C₂₃	—	4	1	no	—
337	C₂²×C₄×C₂₃	—	4	1	no	—
338	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
339	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
340	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
342	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
343	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
344	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
345	D₈×C₂₃	—	4	2	no	—
346	D₈×C₂₃	—	4	2	no	—
347	D₈×C₂₃	—	4	2	no	—
348	D₈×C₂₃	—	4	2	no	—
349	M₁₆×C₂₃	—	4	1	no	—
350	M₁₆×C₂₃	—	4	2	no	—
351	M₁₆×C₂₃	—	4	1	no	—
352	C₂×C₈×C₂₃	—	4	1	no	—
353	C₂×C₈×C₂₃	—	4	2	no	—
354	C₂×C₈×C₂₃	—	4	1	no	—
355	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
356	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
357	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
358	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
359	C₄⋊C₄×C₂₃	—	2	1	no	—
360	C₄⋊C₄×C₂₃	—	2	1	no	—
361	C₄⋊C₄×C₂₃	—	2	1	no	—
362	C₄⋊C₄×C₂₃	—	2	2	no	—
363	C₄⋊C₄×C₂₃	—	2	1	no	—
364	C₄⋊C₄×C₂₃	—	2	1	no	—
365	C₄⋊C₄×C₂₃	—	2	2	no	—
366	C₄⋊C₄×C₂₃	—	2	2	no	—
367	C₄⋊C₄×C₂₃	—	2	2	no	—
368	C₄⋊C₄×C₂₃	—	2	2	no	—
369	C₄⋊C₄×C₂₃	—	2	2	no	—
370	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
371	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
372	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
373	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
375	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
376	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
377	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
379	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
380	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
381	C₂²⋊C₄×C₂₃	—	2	1	no	—
382	C₂²⋊C₄×C₂₃	—	2	1	no	—
383	C₂²⋊C₄×C₂₃	—	2	1	no	—
384	C₂²⋊C₄×C₂₃	—	2	1	no	—
385	C₂²⋊C₄×C₂₃	—	2	2	no	—
386	C₂²⋊C₄×C₂₃	—	2	2	no	—
387	C₂²⋊C₄×C₂₃	—	2	2	no	—
388	C₂²⋊C₄×C₂₃	—	2	2	no	—
389	C₂²⋊C₄×C₂₃	—	2	2	no	—
390	C₂²⋊C₄×C₂₃	—	2	2	no	—
391	C₂²⋊C₄×C₂₃	—	2	2	no	—
392	C₂²⋊C₄×C₂₃	—	2	2	no	—
393	C₂²⋊C₄×C₂₃	—	2	2	no	—
394	C₂²⋊C₄×C₂₃	—	2	2	no	—
395	C₂²⋊C₄×C₂₃	—	2	2	no	—
396	C₂²⋊C₄×C₂₃	—	2	2	no	—
397	C₂²⋊C₄×C₂₃	—	2	2	no	—
398	C₂²⋊C₄×C₂₃	—	2	2	no	—
399	C₂²⋊C₄×C₂₃	—	2	2	no	—
400	C₂²⋊C₄×C₂₃	—	2	2	no	—
401	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
402	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
403	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
404	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
405	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
406	C₄²×C₂₃	—	2	1	no	—
407	C₄²×C₂₃	—	2	1	no	—
408	C₄²×C₂₃	—	2	1	no	—
409	C₄²×C₂₃	—	2	1	no	—
410	C₄²×C₂₃	—	2	2	no	—
411	C₄²×C₂₃	—	2	2	no	—
412	C₄²×C₂₃	C₂⁴	1	2	yes	—
413	#61752	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
414	C₂³×C₂₃	—	2	2	no	—
415	C₂³×C₂₃	—	2	2	no	—
416	C₂³×C₂₃	—	2	2	no	—
417	C₂³×C₂₃	—	2	2	no	—
418	C₂³×C₂₃	—	4	1	no	—
419	C₂³×C₂₃	—	4	1	no	—
420	C₂³×C₂₃	—	4	2	no	—
421	C₂³×C₂₃	—	4	2	no	—
422	C₂³×C₂₃	—	4	2	no	—
423	C₂³×C₂₃	—	8	1	no	—
424	C₂³×C₂₃	—	8	1	no	—
425	C₂³×C₂₃	—	8	2	no	—
426	C₂³×C₂₃	—	8	1	no	—
427	C₂³×C₂₃	—	8	2	no	—
428	C₂³×C₂₃	—	8	2	no	—
429	C₂³×C₂₃	—	8	1	no	—
430	C₂³×C₂₃	—	8	1	no	—
431	C₂³×C₂₃	—	8	1	no	—
432	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
433	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
434	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
435	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
436	Q₈×C₂₃	—	4	1	no	—
437	Q₈×C₂₃	—	8	2	no	—
438	D₄×C₂₃	—	2	4	no	—
439	D₄×C₂₃	—	2	2	no	—
440	D₄×C₂₃	—	2	2	no	—
441	D₄×C₂₃	—	2	2	no	—
442	D₄×C₂₃	—	2	2	no	—
443	D₄×C₂₃	—	2	2	no	—
444	D₄×C₂₃	—	2	2	no	—
445	D₄×C₂₃	—	4	2	no	—
446	D₄×C₂₃	—	4	1	no	—
447	D₄×C₂₃	—	4	2	no	—
448	D₄×C₂₃	—	4	2	no	—
449	D₄×C₂₃	—	4	4	no	—
450	D₄×C₂₃	—	4	4	no	—
451	D₄×C₂₃	—	4	4	no	—
452	D₄×C₂₃	—	8	1	no	—
453	D₄×C₂₃	—	8	1	no	—
454	D₄×C₂₃	—	8	2	no	—
455	D₄×C₂₃	—	8	2	no	—
456	D₄×C₂₃	—	8	2	no	—
457	D₄×C₂₃	—	8	2	no	—
458	D₄×C₂₃	—	8	2	no	—
459	D₄×C₂₃	—	8	2	no	—
460	D₄×C₂₃	—	8	2	no	—
461	D₄×C₂₃	—	8	2	no	—
462	D₄×C₂₃	—	8	2	no	—
463	D₄×C₂₃	—	8	2	no	—
464	C₂×C₄×C₂₃	—	2	1	no	—
465	C₂×C₄×C₂₃	—	2	1	no	—
466	C₂×C₄×C₂₃	—	2	2	no	—
467	C₂×C₄×C₂₃	—	2	1	no	—
468	C₂×C₄×C₂₃	—	2	1	no	—
469	C₂×C₄×C₂₃	—	2	2	no	—
470	C₂×C₄×C₂₃	—	2	1	no	—
471	C₂×C₄×C₂₃	—	2	1	no	—
472	C₂×C₄×C₂₃	—	2	1	no	—
473	C₂×C₄×C₂₃	—	2	1	no	—
474	C₂×C₄×C₂₃	—	2	1	no	—
475	C₂×C₄×C₂₃	—	2	1	no	—
476	C₂×C₄×C₂₃	—	2	2	no	—
477	C₂×C₄×C₂₃	—	2	2	no	—
478	C₂×C₄×C₂₃	—	2	2	no	—
479	C₂×C₄×C₂₃	—	4	1	no	—
480	C₂×C₄×C₂₃	—	4	1	no	—
481	C₂×C₄×C₂₃	—	4	1	no	—
482	C₂×C₄×C₂₃	—	4	2	no	—
483	C₂×C₄×C₂₃	—	8	2	no	—
484	C₂×C₄×C₂₃	—	8	2	no	—
485	C₂×C₄×C₂₃	—	8	2	no	—
486	C₂×C₄×C₂₃	—	8	2	no	—
487	C₂×C₄×C₂₃	—	8	1	no	—
488	C₂×C₄×C₂₃	—	8	1	no	—
489	C₂×C₄×C₂₃	—	8	1	no	—
490	C₂×C₄×C₂₃	—	8	1	no	—
491	C₂×C₄×C₂₃	—	8	2	no	—
492	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
499	C₈×C₂₃	—	2	2	no	—
500	C₈×C₂₃	—	2	2	no	—
501	C₈×C₂₃	—	2	2	no	—
502	C₈×C₂₃	—	2	2	no	—
503	#3537	C₂×C₂₃	1	1	yes	characteristic, complemented
504	#3494	C₂×C₂₃	1	1	yes	characteristic, complemented
505	#3355	C₂×C₂₃	1	2	yes	complemented
506	#3347	C₂×C₂₃	1	2	yes	complemented
507	#3345	C₂×C₂₃	1	2	yes	complemented
508	#3339	C₂×C₂₃	1	2	yes	complemented
509	#3325	C₂×C₂₃	1	2	yes	complemented
510	#3318	C₂×C₂₃	1	2	yes	complemented
511	#3318	C₂×C₂₃	1	2	yes	complemented
512	#3294	C₂×C₂₃	1	2	yes	complemented
513	#3241	C₂×C₂₃	1	2	yes	complemented
514	#3199	C₂×C₂₃	1	2	yes	complemented
515	#3192	C₂×C₂₃	1	1	yes	characteristic, complemented
516	#3186	C₂×C₂₃	1	1	yes	characteristic, complemented
517	#3122	C₂×C₂₃	1	2	yes	complemented
518	#3096	C₂×C₂₃	1	2	yes	complemented
519	#3094	C₂×C₂₃	1	1	yes	characteristic, complemented
520	C₂×#482	C₂×C₂₃	1	1	yes	characteristic, complemented
521	#2976	C₂×C₂₃	1	1	yes	characteristic, complemented
522	C₂²×C₂₃	—	2	1	no	—
523	C₂²×C₂₃	—	2	1	no	—
524	C₂²×C₂₃	—	2	1	no	—
525	C₂²×C₂₃	—	2	2	no	—
526	C₂²×C₂₃	—	2	1	no	—
527	C₂²×C₂₃	—	2	1	no	—
528	C₂²×C₂₃	—	2	1	no	—
529	C₂²×C₂₃	—	2	2	no	—
530	C₂²×C₂₃	—	2	2	no	—
531	C₂²×C₂₃	—	2	1	no	—
532	C₂²×C₂₃	—	2	1	no	—
533	C₂²×C₂₃	—	4	2	no	—
534	C₂²×C₂₃	—	4	2	no	—
535	C₂²×C₂₃	—	4	2	no	—
536	C₂²×C₂₃	—	4	2	no	—
537	C₂²×C₂₃	—	4	2	no	—
538	C₂²×C₂₃	—	4	2	no	—
539	C₂²×C₂₃	—	4	2	no	—
540	C₂²×C₂₃	—	4	2	no	—
541	C₂²×C₂₃	—	4	2	no	—
542	C₂²×C₂₃	—	8	2	no	—
543	C₂²×C₂₃	—	16	2	no	—
544	C₂²×C₂₃	—	16	2	no	—
545	C₂²×C₂₃	—	16	2	no	—
546	C₂²×C₂₃	—	16	4	no	—
547	C₂²×C₂₃	#576	1	2	yes	—
548	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
549	C₄×C₂₃	—	2	2	no	—
550	C₄×C₂₃	—	2	1	no	—
551	C₄×C₂₃	—	2	1	no	—
552	C₄×C₂₃	—	2	1	no	—
553	C₄×C₂₃	—	2	2	no	—
554	C₄×C₂₃	—	2	2	no	—
555	C₄×C₂₃	—	4	1	no	—
556	C₄×C₂₃	—	4	2	no	—
557	C₄×C₂₃	—	4	1	no	—
558	C₄×C₂₃	—	4	1	no	—
559	C₄×C₂₃	—	4	1	no	—
560	C₄×C₂₃	—	4	2	no	—
561	C₄×C₂₃	—	4	2	no	—
562	C₄×C₂₃	#585	1	1	yes	characteristic
563	C₄×C₂₃	#585	1	1	yes	characteristic
564	#560	—	2	2	no	—
565	#555	C₂²×C₂₃	1	2	yes	complemented
566	#553	C₂²×C₂₃	1	2	yes	complemented
567	#553	C₂²×C₂₃	1	2	yes	complemented
568	#553	C₂²×C₂₃	1	2	yes	complemented
569	#553	C₂²×C₂₃	1	2	yes	complemented
570	#551	—	2	2	no	—
571	#547	C₂²×C₂₃	1	2	yes	complemented
572	#546	—	2	2	no	—
573	D₄²	—	2	2	no	—
574	D₄²	C₂²×C₂₃	1	2	yes	complemented
575	D₄²	C₂²×C₂₃	1	2	yes	complemented
576	#544	C₂²×C₂₃	1	1	yes	characteristic, complemented
577	#542	—	2	1	no	—
578	#540	—	2	1	no	—
579	#540	C₂²×C₂₃	1	2	yes	—
580	#538	—	2	1	no	—
581	#538	—	2	1	no	—
582	#535	C₂²×C₂₃	1	2	yes	—
583	#535	C₂²×C₂₃	1	1	yes	characteristic, complemented
584	#534	—	2	1	no	—
585	#534	—	2	1	no	—
586	#532	—	2	1	no	—
587	#529	—	2	1	no	—
588	#525	C₂²×C₂₃	1	1	yes	characteristic
589	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
590	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
591	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic, complemented
592	#520	C₂²×C₂₃	1	1	yes	characteristic, complemented
593	#518	C₂²×C₂₃	1	1	yes	characteristic, complemented
594	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic, complemented
595	#501	C₂²×C₂₃	1	2	yes	complemented
596	#499	C₂²×C₂₃	1	2	yes	complemented
597	#490	C₂²×C₂₃	1	2	yes	complemented
598	#486	C₂²×C₂₃	1	2	yes	complemented
599	#482	C₂²×C₂₃	1	2	yes	complemented
600	#482	C₂²×C₂₃	1	2	yes	complemented
601	#482	C₂²×C₂₃	1	2	yes	complemented
602	#482	C₂²×C₂₃	1	2	yes	complemented
603	#482	C₂²×C₂₃	1	2	yes	complemented
604	#482	C₂²×C₂₃	1	2	yes	complemented
605	#482	C₂²×C₂₃	1	2	yes	complemented
606	#482	C₂²×C₂₃	1	2	yes	complemented
607	#482	C₂²×C₂₃	1	2	yes	complemented
608	#482	C₂²×C₂₃	1	2	yes	complemented
609	#481	C₂²×C₂₃	1	2	yes	complemented
610	#481	C₂²×C₂₃	1	2	yes	complemented
611	#481	C₂²×C₂₃	1	2	yes	complemented
612	#481	C₂²×C₂₃	1	2	yes	complemented
613	#480	C₂²×C₂₃	1	2	yes	complemented
614	#480	C₂²×C₂₃	1	2	yes	complemented
615	#480	C₂²×C₂₃	1	2	yes	complemented
616	#480	C₂²×C₂₃	1	2	yes	complemented
617	#478	C₂²×C₂₃	1	2	yes	complemented
618	#478	C₂²×C₂₃	1	2	yes	complemented
619	#478	C₂²×C₂₃	1	2	yes	complemented
620	#478	C₂²×C₂₃	1	2	yes	complemented
621	#476	C₂²×C₂₃	1	2	yes	complemented
622	#474	C₂²×C₂₃	1	2	yes	complemented
623	#469	C₂²×C₂₃	1	2	yes	complemented
624	#469	C₂²×C₂₃	1	2	yes	complemented
625	#469	C₂²×C₂₃	1	2	yes	complemented
626	#469	C₂²×C₂₃	1	2	yes	complemented
627	#466	C₂²×C₂₃	1	2	yes	complemented
628	#466	C₂²×C₂₃	1	2	yes	complemented
629	#466	C₂²×C₂₃	1	2	yes	complemented
630	#466	C₂²×C₂₃	1	2	yes	complemented
631	#459	C₂²×C₂₃	1	2	yes	complemented
632	#459	C₂²×C₂₃	1	2	yes	complemented
633	#447	C₂²×C₂₃	1	2	yes	complemented
634	#447	C₂²×C₂₃	1	2	yes	complemented
635	#447	C₂²×C₂₃	1	2	yes	complemented
636	#447	C₂²×C₂₃	1	2	yes	complemented
637	#447	C₂²×C₂₃	1	2	yes	complemented
638	#447	C₂²×C₂₃	1	2	yes	complemented
639	#442	C₂²×C₂₃	1	2	yes	complemented
640	#442	C₂²×C₂₃	1	2	yes	complemented
641	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
642	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
643	#436	C₂²×C₂₃	1	2	yes	complemented
644	#435	C₂²×C₂₃	1	2	yes	complemented
645	#435	C₂²×C₂₃	1	2	yes	complemented
646	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
647	#433	C₂²×C₂₃	1	2	yes	complemented
648	#428	C₂²×C₂₃	1	2	yes	complemented
649	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
650	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
651	#427	C₂²×C₂₃	1	2	yes	complemented
652	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic, complemented
653	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic, complemented
654	#418	C₂²×C₂₃	1	1	yes	characteristic, complemented
655	#418	C₂²×C₂₃	1	1	yes	characteristic, complemented
656	#418	C₂²×C₂₃	1	2	yes	complemented
657	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
658	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic, complemented
659	C₂×#102	C₂²×C₂₃	1	2	yes	complemented
660	#408	C₂²×C₂₃	1	2	yes	complemented
661	#407	C₂²×C₂₃	1	1	yes	characteristic, complemented
662	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
663	C₂×C₂₃	—	2	2	no	—
664	C₂×C₂₃	—	4	1	no	—
665	C₂×C₂₃	—	4	1	no	—
666	C₂×C₂₃	—	4	2	no	—
667	C₂×C₂₃	—	8	2	no	—
668	C₂×C₂₃	—	8	2	no	—
669	C₂×C₂₃	—	8	2	no	—
670	C₂×C₂₃	#3485	1	1	yes	characteristic
671	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
672	C₂×C₂₃	#3585	1	1	yes	characteristic
673	C₂×#41	—	2	2	no	—
674	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
675	C₂²×D₄	—	2	1	no	—
676	C₂²×D₄	—	2	1	no	—
677	C₂²×D₄	—	2	1	no	—
678	C₂²×D₄	—	2	2	no	—
679	C₂²×D₄	—	2	2	no	—
680	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
681	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
682	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
683	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
684	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
685	C₂×D₈	C₂³×C₂₃	1	2	yes	—
686	C₂×D₈	C₂³×C₂₃	1	2	yes	—
687	C₂×D₈	C₂³×C₂₃	1	2	yes	—
688	C₂×D₈	C₂³×C₂₃	1	2	yes	—
689	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
690	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
691	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
692	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
693	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
694	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
695	C₄⋊Q₈	—	2	1	no	—
696	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
697	#127	—	2	1	no	—
698	#127	—	2	2	no	—
699	#127	C₂³×C₂₃	1	2	yes	—
700	#126	—	2	2	no	—
701	#126	—	2	2	no	—
702	#126	—	2	2	no	—
703	#126	—	2	2	no	—
704	#125	—	2	1	no	—
705	#125	C₂³×C₂₃	1	2	yes	—
706	#125	C₂³×C₂₃	1	2	yes	—
707	#124	—	2	1	no	—
708	#124	—	2	2	no	—
709	#124	—	2	2	no	—
710	#124	—	2	2	no	—
711	#123	—	2	2	no	—
712	#123	—	2	2	no	—
713	#123	—	2	2	no	—
714	#123	—	2	2	no	—
715	#123	—	2	2	no	—
716	#123	—	2	2	no	—
717	#123	—	2	2	no	—
718	#123	—	2	2	no	—
719	#123	D₄×C₂₃	1	2	yes	—
720	C₂²⋊Q₈	—	2	2	no	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
723	C₂²⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
724	#121	—	2	2	no	—
725	#121	—	2	2	no	—
726	#121	—	2	2	no	—
727	#121	—	2	2	no	—
728	#121	—	2	2	no	—
729	#121	—	2	1	no	—
730	#121	—	2	1	no	—
731	#121	—	2	1	no	—
732	#121	—	2	1	no	—
733	#121	—	2	1	no	—
734	#121	—	2	1	no	—
735	#121	—	2	2	no	—
736	#121	—	2	2	no	—
737	#121	—	2	2	no	—
738	#121	—	2	2	no	—
739	#121	D₄×C₂₃	1	1	yes	characteristic
740	#121	D₄×C₂₃	1	1	yes	characteristic
741	#121	C₂³×C₂₃	1	2	yes	—
742	#121	C₂³×C₂₃	1	2	yes	—
743	#121	C₂³×C₂₃	1	2	yes	—
744	#121	C₂³×C₂₃	1	2	yes	—
745	#121	C₂³×C₂₃	1	2	yes	—
746	#121	C₂³×C₂₃	1	2	yes	—
747	#121	C₂³×C₂₃	1	2	yes	—
748	#121	C₂³×C₂₃	1	2	yes	—
749	#121	C₂³×C₂₃	1	2	yes	—
750	#121	C₂³×C₂₃	1	2	yes	—
751	#120	—	2	2	no	—
752	#120	—	2	2	no	—
753	#120	—	2	2	no	—
754	#120	—	2	2	no	—
755	#120	—	2	2	no	—
756	#120	—	2	2	no	—
757	#120	—	2	2	no	—
758	#120	D₄×C₂₃	1	2	yes	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×D₄	—	2	1	no	—
761	C₄×D₄	—	2	2	no	—
762	C₄×D₄	—	2	1	no	—
763	C₄×D₄	—	2	1	no	—
764	C₄×D₄	—	2	2	no	—
765	C₄×D₄	—	2	2	no	—
766	C₄×D₄	—	2	2	no	—
767	C₄×D₄	—	2	2	no	—
768	C₄×D₄	C₂³×C₂₃	1	2	yes	—
769	C₄×D₄	C₂³×C₂₃	1	2	yes	—
770	C₄×D₄	C₂³×C₂₃	1	2	yes	—
771	C₄×D₄	C₂³×C₂₃	1	2	yes	—
772	C₄×D₄	C₂³×C₂₃	1	2	yes	—
773	C₄×D₄	C₂³×C₂₃	1	2	yes	—
774	#117	—	2	1	no	—
775	#117	—	2	1	no	—
776	#117	—	2	2	no	—
777	#117	C₂³×C₂₃	1	1	yes	characteristic
778	#117	C₂³×C₂₃	1	1	yes	characteristic
779	#117	C₂³×C₂₃	1	1	yes	characteristic
780	#117	C₂³×C₂₃	1	1	yes	characteristic
781	#117	C₂³×C₂₃	1	2	yes	—
782	#117	C₂³×C₂₃	1	2	yes	—
783	#117	C₂³×C₂₃	1	1	yes	characteristic
784	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
785	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
786	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
787	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
788	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
789	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
790	C₂×C₂²⋊C₄	—	2	1	no	—
791	C₂×C₂²⋊C₄	—	2	1	no	—
792	C₂×C₂²⋊C₄	—	2	1	no	—
793	C₂×C₂²⋊C₄	—	2	1	no	—
794	C₂×C₂²⋊C₄	—	2	2	no	—
795	C₂×C₄²	—	2	1	no	—
796	#107	C₂³×C₂₃	1	2	yes	—
797	#107	C₂³×C₂₃	1	2	yes	—
798	#107	C₂³×C₂₃	1	2	yes	—
799	#107	C₂³×C₂₃	1	2	yes	—
800	#107	C₂³×C₂₃	1	2	yes	—
801	#107	C₂³×C₂₃	1	2	yes	—
802	#106	C₂³×C₂₃	1	2	yes	—
803	#106	C₂³×C₂₃	1	2	yes	—
804	#106	C₂³×C₂₃	1	2	yes	—
805	#106	C₂³×C₂₃	1	2	yes	—
806	#106	C₂³×C₂₃	1	2	yes	—
807	#106	C₂³×C₂₃	1	2	yes	—
808	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
809	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
810	#102	C₂³×C₂₃	1	2	yes	—
811	#102	C₂³×C₂₃	1	2	yes	—
812	#102	C₂³×C₂₃	1	2	yes	—
813	#102	C₂³×C₂₃	1	2	yes	—
814	#102	C₂³×C₂₃	1	2	yes	—
815	#102	C₂³×C₂₃	1	2	yes	—
816	#102	C₂³×C₂₃	1	2	yes	—
817	#102	C₂³×C₂₃	1	2	yes	—
818	#102	C₂³×C₂₃	1	2	yes	—
819	#102	C₂³×C₂₃	1	2	yes	—
820	#102	C₂³×C₂₃	1	2	yes	—
821	#102	C₂³×C₂₃	1	2	yes	—
822	#102	C₂³×C₂₃	1	2	yes	—
823	#102	C₂³×C₂₃	1	2	yes	—
824	#102	C₂³×C₂₃	1	2	yes	—
825	#102	C₂³×C₂₃	1	2	yes	—
826	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
827	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
828	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
829	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
830	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
831	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
832	#97	C₂³×C₂₃	1	2	yes	—
833	C₄×C₈	C₂³×C₂₃	1	2	yes	—
834	C₂₃	#61752	1	1	yes	characteristic, direct product factor, Sylow
835	C₂⁴	—	2	1	no	—
836	C₂⁴	—	2	1	no	—
837	C₂⁴	—	2	1	no	—
838	C₂⁴	—	2	2	no	—
839	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
840	#41	—	4	1	no	—
841	#41	—	4	1	no	—
842	#41	—	8	4	no	—
843	C₂×Q₈	—	2	2	no	—
844	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	2	2	no	—
850	C₂×D₄	—	2	2	no	—
851	C₂×D₄	—	2	2	no	—
852	C₂×D₄	—	2	2	no	—
853	C₂×D₄	—	2	2	no	—
854	C₂×D₄	—	2	2	no	—
855	C₂×D₄	—	2	1	no	—
856	C₂×D₄	—	2	1	no	—
857	C₂×D₄	—	2	1	no	—
858	C₂×D₄	—	2	2	no	—
859	C₂×D₄	—	2	2	no	—
860	C₂×D₄	—	2	2	no	—
861	C₂×D₄	—	4	1	no	—
862	C₂×D₄	—	4	1	no	—
863	C₂×D₄	—	4	1	no	—
864	C₂×D₄	—	4	1	no	—
865	C₂×D₄	—	4	2	no	—
866	C₂×D₄	—	4	1	no	—
867	C₂×D₄	—	4	1	no	—
868	C₂×D₄	—	4	2	no	—
869	C₂×D₄	—	8	4	no	—
870	C₂×D₄	—	8	2	no	—
871	C₂×D₄	—	8	2	no	—
872	C₂×D₄	—	8	4	no	—
873	C₂×D₄	—	8	2	no	—
874	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
875	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
876	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
877	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
878	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
879	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
880	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	2	1	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	1	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	2	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	4	1	no	—
892	C₂²×C₄	—	4	1	no	—
893	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
894	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
895	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
896	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
897	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
898	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
899	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
900	D₈	—	4	2	no	—
901	D₈	—	4	2	no	—
902	D₈	—	4	2	no	—
903	D₈	—	4	2	no	—
904	M₁₆	—	4	1	no	—
905	M₁₆	—	4	2	no	—
906	M₁₆	—	4	1	no	—
907	C₂×C₈	—	4	1	no	—
908	C₂×C₈	—	4	2	no	—
909	C₂×C₈	—	4	1	no	—
910	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
911	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
912	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
913	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	2	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
926	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
927	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
928	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
929	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
930	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
931	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
932	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
933	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
934	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
935	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
936	C₂²⋊C₄	—	2	1	no	—
937	C₂²⋊C₄	—	2	1	no	—
938	C₂²⋊C₄	—	2	1	no	—
939	C₂²⋊C₄	—	2	1	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
957	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
958	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
959	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
960	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
961	C₄²	—	2	1	no	—
962	C₄²	—	2	1	no	—
963	C₄²	—	2	1	no	—
964	C₄²	—	2	1	no	—
965	C₄²	—	2	2	no	—
966	C₄²	—	2	2	no	—
967	C₄²	C₂⁴×C₂₃	1	2	yes	—
968	C₂³	—	2	2	no	—
969	C₂³	—	2	2	no	—
970	C₂³	—	2	2	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	4	1	no	—
973	C₂³	—	4	1	no	—
974	C₂³	—	4	2	no	—
975	C₂³	—	4	2	no	—
976	C₂³	—	4	2	no	—
977	C₂³	—	8	1	no	—
978	C₂³	—	8	1	no	—
979	C₂³	—	8	2	no	—
980	C₂³	—	8	1	no	—
981	C₂³	—	8	2	no	—
982	C₂³	—	8	1	no	—
983	C₂³	—	8	1	no	—
984	C₂³	—	8	2	no	—
985	C₂³	—	8	1	no	—
986	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
987	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
988	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
989	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
990	Q₈	—	4	1	no	—
991	Q₈	—	8	2	no	—
992	D₄	—	2	4	no	—
993	D₄	—	2	2	no	—
994	D₄	—	2	2	no	—
995	D₄	—	2	2	no	—
996	D₄	—	2	2	no	—
997	D₄	—	2	2	no	—
998	D₄	—	2	2	no	—
999	D₄	—	4	2	no	—
1000	D₄	—	4	1	no	—
1001	D₄	—	4	2	no	—
1002	D₄	—	4	2	no	—
1003	D₄	—	4	4	no	—
1004	D₄	—	4	4	no	—
1005	D₄	—	4	4	no	—
1006	D₄	—	8	1	no	—
1007	D₄	—	8	1	no	—
1008	D₄	—	8	2	no	—
1009	D₄	—	8	2	no	—
1010	D₄	—	8	2	no	—
1011	D₄	—	8	2	no	—
1012	D₄	—	8	2	no	—
1013	D₄	—	8	2	no	—
1014	D₄	—	8	2	no	—
1015	D₄	—	8	2	no	—
1016	D₄	—	8	2	no	—
1017	D₄	—	8	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	4	1	no	—
1034	C₂×C₄	—	4	1	no	—
1035	C₂×C₄	—	4	1	no	—
1036	C₂×C₄	—	4	2	no	—
1037	C₂×C₄	—	8	2	no	—
1038	C₂×C₄	—	8	2	no	—
1039	C₂×C₄	—	8	2	no	—
1040	C₂×C₄	—	8	2	no	—
1041	C₂×C₄	—	8	1	no	—
1042	C₂×C₄	—	8	1	no	—
1043	C₂×C₄	—	8	1	no	—
1044	C₂×C₄	—	8	2	no	—
1045	C₂×C₄	—	8	1	no	—
1046	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1047	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1048	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1049	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1050	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1051	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
1052	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
1053	C₈	—	2	2	no	—
1054	C₈	—	2	2	no	—
1055	C₈	—	2	2	no	—
1056	C₈	—	2	2	no	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	1	no	—
1061	C₂²	—	2	2	no	—
1062	C₂²	—	2	2	no	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	2	1	no	—
1066	C₂²	—	2	2	no	—
1067	C₂²	—	2	1	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	2	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	4	2	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	4	2	no	—
1077	C₂²	—	8	2	no	—
1078	C₂²	—	16	2	no	—
1079	C₂²	—	16	2	no	—
1080	C₂²	—	16	2	no	—
1081	C₂²	—	16	4	no	—
1082	C₂²	C₂₃×#576	1	2	yes	—
1083	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1084	C₄	—	2	1	no	—
1085	C₄	—	2	1	no	—
1086	C₄	—	2	1	no	—
1087	C₄	—	2	2	no	—
1088	C₄	—	2	2	no	—
1089	C₄	—	2	2	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	1	no	—
1092	C₄	—	4	2	no	—
1093	C₄	—	4	2	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	4	2	no	—
1096	C₄	—	4	1	no	—
1097	C₄	C₂₃×#585	1	1	yes	characteristic
1098	C₄	C₂₃×#585	1	1	yes	characteristic
1099	C₂	—	2	2	no	—
1100	C₂	—	4	1	no	—
1101	C₂	—	4	1	no	—
1102	C₂	—	4	2	no	—
1103	C₂	—	8	2	no	—
1104	C₂	—	8	2	no	—
1105	C₂	—	8	2	no	—
1106	C₂	C₂₃×#3485	1	1	yes	characteristic
1107	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
1108	C₂	C₂₃×#3585	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 ◁ C₂₃×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3537	C₂	semidirect
2. C₂₃×#3494	C₂	semidirect
3. C₂₃×#3355	C₂	semidirect
4. C₂₃×#3347	C₂	semidirect
5. C₂₃×#3345	C₂	semidirect
6. C₂₃×#3339	C₂	semidirect
7. C₂₃×#3325	C₂	semidirect
8. C₂₃×#3318	C₂	semidirect
9. C₂₃×#3318	C₂	semidirect
10. C₂₃×#3294	C₂	semidirect
11. C₂₃×#3241	C₂	semidirect
12. C₂₃×#3199	C₂	semidirect
13. C₂₃×#3192	C₂	semidirect
14. C₂₃×#3186	C₂	semidirect
15. C₂₃×#3122	C₂	semidirect
16. C₂₃×#3096	C₂	semidirect
17. C₂₃×#3094	C₂	semidirect
18. C₂×C₂₃×#482	C₂	semidirect
19. C₂₃×#2976	C₂	semidirect
21. C₂₃×#555	C₂²	semidirect
22. C₂₃×#553	C₂²	semidirect
23. C₂₃×#553	C₂²	semidirect
24. C₂₃×#553	C₂²	semidirect
25. C₂₃×#553	C₂²	semidirect
27. C₂₃×#547	C₂²	semidirect
30. D₄²×C₂₃	C₂²	semidirect
31. D₄²×C₂₃	C₂²	semidirect
32. C₂₃×#544	C₂²	semidirect
39. C₂₃×#535	C₂²	semidirect
47. C₂×C₂₃×#121	C₂²	semidirect
48. C₂₃×#520	C₂²	semidirect
49. C₂₃×#518	C₂²	semidirect
50. C₂×C₂₃×#117	C₂²	semidirect
51. C₂₃×#501	C₂²	semidirect
52. C₂₃×#499	C₂²	semidirect
53. C₂₃×#490	C₂²	semidirect
54. C₂₃×#486	C₂²	semidirect
55. C₂₃×#482	C₂²	semidirect
56. C₂₃×#482	C₂²	semidirect
57. C₂₃×#482	C₂²	semidirect
58. C₂₃×#482	C₂²	semidirect
59. C₂₃×#482	C₂²	semidirect
60. C₂₃×#482	C₂²	semidirect
61. C₂₃×#482	C₂²	semidirect
62. C₂₃×#482	C₂²	semidirect
63. C₂₃×#482	C₂²	semidirect
64. C₂₃×#482	C₂²	semidirect
65. C₂₃×#481	C₂²	semidirect
66. C₂₃×#481	C₂²	semidirect
67. C₂₃×#481	C₂²	semidirect
68. C₂₃×#481	C₂²	semidirect
69. C₂₃×#480	C₂²	semidirect
70. C₂₃×#480	C₂²	semidirect
71. C₂₃×#480	C₂²	semidirect
72. C₂₃×#480	C₂²	semidirect
73. C₂₃×#478	C₂²	semidirect
74. C₂₃×#478	C₂²	semidirect
75. C₂₃×#478	C₂²	semidirect
76. C₂₃×#478	C₂²	semidirect
77. C₂₃×#476	C₂²	semidirect
78. C₂₃×#474	C₂²	semidirect
79. C₂₃×#469	C₂²	semidirect
80. C₂₃×#469	C₂²	semidirect
81. C₂₃×#469	C₂²	semidirect
82. C₂₃×#469	C₂²	semidirect
83. C₂₃×#466	C₂²	semidirect
84. C₂₃×#466	C₂²	semidirect
85. C₂₃×#466	C₂²	semidirect
86. C₂₃×#466	C₂²	semidirect
87. C₂₃×#459	C₂²	semidirect
88. C₂₃×#459	C₂²	semidirect
89. C₂₃×#447	C₂²	semidirect
90. C₂₃×#447	C₂²	semidirect
91. C₂₃×#447	C₂²	semidirect
92. C₂₃×#447	C₂²	semidirect
93. C₂₃×#447	C₂²	semidirect
94. C₂₃×#447	C₂²	semidirect
95. C₂₃×#442	C₂²	semidirect
96. C₂₃×#442	C₂²	semidirect
97. C₄×D₈×C₂₃	C₂²	semidirect
98. C₄×D₈×C₂₃	C₂²	semidirect
99. C₂₃×#436	C₂²	semidirect
100. C₂₃×#435	C₂²	semidirect
101. C₂₃×#435	C₂²	semidirect
102. C₈×D₄×C₂₃	C₂²	semidirect
103. C₂₃×#433	C₂²	semidirect
104. C₂₃×#428	C₂²	semidirect
105. C₂₃×#428	C₂²	semidirect
106. C₂₃×#428	C₂²	semidirect
107. C₂₃×#427	C₂²	semidirect
108. C₂×C₂₃×#107	C₂²	semidirect
109. C₂×C₂₃×#106	C₂²	semidirect
110. C₂₃×#418	C₂²	semidirect
111. C₂₃×#418	C₂²	semidirect
112. C₂₃×#418	C₂²	semidirect
113. C₂×C₂₃×#102	C₂²	semidirect
114. C₂×C₂₃×#102	C₂²	semidirect
115. C₂×C₂₃×#102	C₂²	semidirect
116. C₂₃×#408	C₂²	semidirect
117. C₂₃×#407	C₂²	semidirect
118. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
413. #61752	C₂₃	direct (N × H)
503. #3537	C₂×C₂₃	semidirect
504. #3494	C₂×C₂₃	semidirect
505. #3355	C₂×C₂₃	semidirect
506. #3347	C₂×C₂₃	semidirect
507. #3345	C₂×C₂₃	semidirect
508. #3339	C₂×C₂₃	semidirect
509. #3325	C₂×C₂₃	semidirect
510. #3318	C₂×C₂₃	semidirect
511. #3318	C₂×C₂₃	semidirect
512. #3294	C₂×C₂₃	semidirect
513. #3241	C₂×C₂₃	semidirect
514. #3199	C₂×C₂₃	semidirect
515. #3192	C₂×C₂₃	semidirect
516. #3186	C₂×C₂₃	semidirect
517. #3122	C₂×C₂₃	semidirect
518. #3096	C₂×C₂₃	semidirect
519. #3094	C₂×C₂₃	semidirect
520. C₂×#482	C₂×C₂₃	semidirect
521. #2976	C₂×C₂₃	semidirect
565. #555	C₂²×C₂₃	semidirect
566. #553	C₂²×C₂₃	semidirect
567. #553	C₂²×C₂₃	semidirect
568. #553	C₂²×C₂₃	semidirect
569. #553	C₂²×C₂₃	semidirect
571. #547	C₂²×C₂₃	semidirect
574. D₄²	C₂²×C₂₃	semidirect
575. D₄²	C₂²×C₂₃	semidirect
576. #544	C₂²×C₂₃	semidirect
583. #535	C₂²×C₂₃	semidirect
591. C₂×#121	C₂²×C₂₃	semidirect
592. #520	C₂²×C₂₃	semidirect
593. #518	C₂²×C₂₃	semidirect
594. C₂×#117	C₂²×C₂₃	semidirect
595. #501	C₂²×C₂₃	semidirect
596. #499	C₂²×C₂₃	semidirect
597. #490	C₂²×C₂₃	semidirect
598. #486	C₂²×C₂₃	semidirect
599. #482	C₂²×C₂₃	semidirect
600. #482	C₂²×C₂₃	semidirect
601. #482	C₂²×C₂₃	semidirect
602. #482	C₂²×C₂₃	semidirect
603. #482	C₂²×C₂₃	semidirect
604. #482	C₂²×C₂₃	semidirect
605. #482	C₂²×C₂₃	semidirect
606. #482	C₂²×C₂₃	semidirect
607. #482	C₂²×C₂₃	semidirect
608. #482	C₂²×C₂₃	semidirect
609. #481	C₂²×C₂₃	semidirect
610. #481	C₂²×C₂₃	semidirect
611. #481	C₂²×C₂₃	semidirect
612. #481	C₂²×C₂₃	semidirect
613. #480	C₂²×C₂₃	semidirect
614. #480	C₂²×C₂₃	semidirect
615. #480	C₂²×C₂₃	semidirect
616. #480	C₂²×C₂₃	semidirect
617. #478	C₂²×C₂₃	semidirect
618. #478	C₂²×C₂₃	semidirect
619. #478	C₂²×C₂₃	semidirect
620. #478	C₂²×C₂₃	semidirect
621. #476	C₂²×C₂₃	semidirect
622. #474	C₂²×C₂₃	semidirect
623. #469	C₂²×C₂₃	semidirect
624. #469	C₂²×C₂₃	semidirect
625. #469	C₂²×C₂₃	semidirect
626. #469	C₂²×C₂₃	semidirect
627. #466	C₂²×C₂₃	semidirect
628. #466	C₂²×C₂₃	semidirect
629. #466	C₂²×C₂₃	semidirect
630. #466	C₂²×C₂₃	semidirect
631. #459	C₂²×C₂₃	semidirect
632. #459	C₂²×C₂₃	semidirect
633. #447	C₂²×C₂₃	semidirect
634. #447	C₂²×C₂₃	semidirect
635. #447	C₂²×C₂₃	semidirect
636. #447	C₂²×C₂₃	semidirect
637. #447	C₂²×C₂₃	semidirect
638. #447	C₂²×C₂₃	semidirect
639. #442	C₂²×C₂₃	semidirect
640. #442	C₂²×C₂₃	semidirect
641. C₄×D₈	C₂²×C₂₃	semidirect
642. C₄×D₈	C₂²×C₂₃	semidirect
643. #436	C₂²×C₂₃	semidirect
644. #435	C₂²×C₂₃	semidirect
645. #435	C₂²×C₂₃	semidirect
646. C₈×D₄	C₂²×C₂₃	semidirect
647. #433	C₂²×C₂₃	semidirect
648. #428	C₂²×C₂₃	semidirect
649. #428	C₂²×C₂₃	semidirect
650. #428	C₂²×C₂₃	semidirect
651. #427	C₂²×C₂₃	semidirect
652. C₂×#107	C₂²×C₂₃	semidirect
653. C₂×#106	C₂²×C₂₃	semidirect
654. #418	C₂²×C₂₃	semidirect
655. #418	C₂²×C₂₃	semidirect
656. #418	C₂²×C₂₃	semidirect
657. C₂×#102	C₂²×C₂₃	semidirect
658. C₂×#102	C₂²×C₂₃	semidirect
659. C₂×#102	C₂²×C₂₃	semidirect
660. #408	C₂²×C₂₃	semidirect
661. #407	C₂²×C₂₃	semidirect
662. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
834. C₂₃	#61752	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×#3537	2
C₂₃×#3494	2
C₂₃×#3355	2
C₂₃×#3347	2
C₂₃×#3345	2
C₂₃×#3339	2
C₂₃×#3325	2
C₂₃×#3318	2
C₂₃×#3294	2
C₂₃×#3241	2
C₂₃×#3199	2
C₂₃×#3192	2
C₂₃×#3186	2
C₂₃×#3122	2
C₂₃×#3096	2
C₂₃×#3094	2
C₂×C₂₃×#482	2
C₂₃×#2976	2
#61752	23

Subgroups — C23×#61752 #19209378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61752 #19209378