Subgroups — C₂₃×#61604 #19209230

Order 5888.

2180 conjugacy classes of subgroups.

The subgroup lattice has 942 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×#3331	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3307	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3303	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3284	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3272	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3267	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3218	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3196	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3187	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×#3006	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3002	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₂₃	C₂²	1	2	yes	complemented
19	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
20	C₂×C₂₃×#135	C₂²	1	4	yes	complemented
21	C₂₃×#555	C₂²	1	1	yes	characteristic, complemented
22	C₂₃×#554	C₂²	1	1	yes	characteristic, complemented
23	C₂₃×#553	—	2	1	no	—
24	C₂₃×#553	C₂²	1	2	yes	complemented
25	C₂₃×#550	C₂²	1	1	yes	characteristic, complemented
26	C₂₃×#547	—	2	1	no	—
27	C₂₃×#547	—	2	1	no	—
28	C₂₃×#547	—	2	2	no	—
29	C₂₃×#547	C₂²	1	2	yes	—
30	C₂₃×#547	C₂²	1	4	yes	complemented
31	C₂₃×#547	C₂²	1	2	yes	complemented
32	C₂₃×#546	—	2	2	no	—
33	C₂₃×#546	C₂²	1	2	yes	complemented
34	D₄²×C₂₃	—	2	1	no	—
35	D₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
36	C₂₃×#540	—	2	1	no	—
37	C₂₃×#538	—	2	2	no	—
38	C₂₃×#532	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂₃×#529	C₂²	1	1	yes	characteristic
41	C₂₃×#525	C₂²	1	2	yes	—
42	C₂×C₂₃×#123	—	2	2	no	—
43	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
44	C₂×C₂₃×#121	—	2	1	no	—
45	C₂×C₂₃×#121	C₂²	1	2	yes	—
46	C₂₃×#518	—	2	1	no	—
47	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
49	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
50	C₂₃×#497	C₂²	1	2	yes	complemented
51	C₂₃×#492	C₂²	1	2	yes	complemented
52	C₂₃×#491	C₂²	1	2	yes	complemented
53	C₂₃×#487	C₂²	1	2	yes	complemented
54	C₂₃×#485	C₂²	1	4	yes	complemented
55	C₂₃×#484	C₂²	1	1	yes	characteristic, complemented
56	C₂₃×#483	C₂²	1	4	yes	complemented
57	C₂₃×#481	C₂²	1	1	yes	characteristic
58	C₂₃×#481	C₂²	1	2	yes	complemented
59	C₂₃×#478	C₂²	1	2	yes	complemented
60	C₂₃×#476	C₂²	1	2	yes	complemented
61	C₂₃×#470	C₂²	1	4	yes	complemented
62	C₂₃×#468	C₂²	1	4	yes	complemented
63	C₂₃×#465	C₂²	1	4	yes	complemented
64	C₂₃×#465	C₂²	1	4	yes	complemented
65	C₂₃×#463	C₂²	1	2	yes	complemented
66	C₂₃×#462	C₂²	1	2	yes	complemented
67	C₂₃×#461	C₂²	1	4	yes	complemented
68	C₂₃×#461	C₂²	1	2	yes	complemented
69	C₂₃×#459	C₂²	1	2	yes	complemented
70	C₂₃×#452	C₂²	1	4	yes	complemented
71	C₂₃×#452	C₂²	1	4	yes	complemented
72	C₂₃×#451	C₂²	1	2	yes	complemented
73	C₂₃×#450	C₂²	1	4	yes	complemented
74	C₂₃×#450	C₂²	1	1	yes	characteristic, complemented
75	C₂₃×#449	C₂²	1	4	yes	complemented
76	C₂₃×#449	C₂²	1	4	yes	complemented
77	C₂₃×#449	C₂²	1	4	yes	complemented
78	C₂₃×#448	C₂²	1	2	yes	—
79	C₂₃×#448	C₂²	1	2	yes	complemented
80	C₂₃×#448	C₂²	1	2	yes	complemented
81	C₂₃×#447	C₂²	1	1	yes	characteristic
82	C₂₃×#447	C₂²	1	2	yes	complemented
83	C₂₃×#442	C₂²	1	4	yes	complemented
84	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
85	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
86	C₂₃×#436	C₂²	1	2	yes	complemented
87	C₂₃×#435	C₂²	1	4	yes	complemented
88	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
89	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
90	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#417	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	2	no	—
96	C₂×#41×C₂₃	—	2	2	no	—
97	C₂×#41×C₂₃	—	2	1	no	—
98	C₂×#41×C₂₃	—	4	8	no	—
99	C₂×#41×C₂₃	C₂³	1	4	yes	—
100	C₂×#41×C₂₃	C₂³	1	4	yes	—
101	C₂×#41×C₂₃	C₂³	1	2	yes	—
102	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
103	C₂²×D₄×C₂₃	—	2	2	no	—
104	C₂²×D₄×C₂₃	—	2	2	no	—
105	C₂²×D₄×C₂₃	—	2	1	no	—
106	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
107	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
109	C₂³×C₄×C₂₃	—	2	2	no	—
110	C₂³×C₄×C₂₃	—	2	1	no	—
111	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
112	C₂₃×AGL(1,ℤ/8)	—	4	8	no	—
113	C₂₃×#135	—	4	8	no	—
114	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
115	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
116	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
117	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
118	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
119	C₂×D₈×C₂₃	C₂³	1	4	yes	—
120	C₂×D₈×C₂₃	C₂³	1	2	yes	—
121	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
122	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
123	C₂₃×C₄⋊Q₈	—	2	1	no	—
124	C₂₃×C₄⋊Q₈	—	2	1	no	—
125	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
126	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
127	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
128	C₂₃×#127	—	2	1	no	—
129	C₂₃×#127	C₂³	1	1	yes	characteristic
130	C₂₃×#126	—	2	2	no	—
131	C₂₃×#126	—	2	1	no	—
132	C₂₃×#125	—	2	1	no	—
133	C₂₃×#125	C₂³	1	1	yes	characteristic
134	C₂₃×#124	—	2	2	no	—
135	C₂₃×#124	—	2	1	no	—
136	C₂₃×#124	C₂³	1	1	yes	characteristic
137	C₂₃×#123	—	2	2	no	—
138	C₂₃×#123	—	2	1	no	—
139	C₂₃×#123	—	2	2	no	—
140	C₂₃×#123	—	2	4	no	—
141	C₂₃×#123	—	2	4	no	—
142	C₂₃×#123	—	2	4	no	—
143	C₂₃×#123	—	2	4	no	—
144	C₂₃×#123	—	2	2	no	—
145	C₂₃×C₂²⋊Q₈	—	2	2	no	—
146	C₂₃×C₂²⋊Q₈	—	2	2	no	—
147	C₂₃×C₂²⋊Q₈	—	2	2	no	—
148	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
149	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
150	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
152	C₂₃×#121	—	2	2	no	—
153	C₂₃×#121	—	2	2	no	—
154	C₂₃×#121	—	2	4	no	—
155	C₂₃×#121	—	2	2	no	—
156	C₂₃×#121	—	2	1	no	—
157	C₂₃×#121	—	2	2	no	—
158	C₂₃×#121	—	2	1	no	—
159	C₂₃×#121	—	2	2	no	—
160	C₂₃×#121	—	2	1	no	—
161	C₂₃×#121	—	2	2	no	—
162	C₂₃×#121	—	2	2	no	—
163	C₂₃×#121	C₂³	1	2	yes	—
164	C₂₃×#121	C₂³	1	2	yes	—
165	C₂₃×#121	C₂³	1	2	yes	—
166	C₂₃×#121	C₂³	1	1	yes	characteristic
167	C₂₃×#121	C₂³	1	2	yes	—
168	C₂₃×#120	—	2	2	no	—
169	C₂₃×#120	—	2	2	no	—
170	C₂₃×#120	—	2	2	no	—
171	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
172	C₄×D₄×C₂₃	—	2	1	no	—
173	C₄×D₄×C₂₃	—	2	2	no	—
174	C₄×D₄×C₂₃	—	2	1	no	—
175	C₄×D₄×C₂₃	—	2	2	no	—
176	C₄×D₄×C₂₃	—	2	1	no	—
177	C₄×D₄×C₂₃	—	2	2	no	—
178	C₄×D₄×C₂₃	—	2	1	no	—
179	C₄×D₄×C₂₃	—	2	1	no	—
180	C₄×D₄×C₂₃	—	2	1	no	—
181	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
182	C₄×D₄×C₂₃	D₄	1	2	yes	—
183	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
184	C₄×D₄×C₂₃	C₂³	1	2	yes	—
185	C₄×D₄×C₂₃	C₂³	1	2	yes	—
186	C₄×D₄×C₂₃	C₂³	1	2	yes	—
187	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₂₃	C₂³	1	2	yes	—
191	C₂₃×#117	—	2	1	no	—
192	C₂₃×#117	—	2	1	no	—
193	C₂₃×#117	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
195	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
196	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
197	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
198	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
199	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
200	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
201	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
202	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
204	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
205	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
206	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
207	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
208	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
209	C₂₃×#107	C₂³	1	2	yes	—
210	C₂₃×#106	C₂³	1	2	yes	—
211	C₂₃×#106	C₂³	1	4	yes	—
212	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
213	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
214	C₂₃×#103	C₂³	1	4	yes	—
215	C₂₃×#103	C₂³	1	4	yes	—
216	C₂₃×#103	C₂³	1	4	yes	—
217	C₂₃×#103	C₂³	1	4	yes	—
218	C₂₃×#103	C₂³	1	2	yes	—
219	C₂₃×#102	C₂³	1	2	yes	—
220	C₂₃×#102	C₂³	1	4	yes	—
221	C₂₃×#102	C₂³	1	2	yes	—
222	C₂₃×#102	C₂³	1	2	yes	—
223	C₂₃×#102	C₂³	1	4	yes	—
224	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
225	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
226	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
227	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
228	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₂₃×#97	C₂³	1	2	yes	—
230	C₄×C₈×C₂₃	C₂³	1	2	yes	—
231	C₂⁴×C₂₃	—	2	1	no	—
232	C₂⁴×C₂₃	—	2	2	no	—
233	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
234	#41×C₂₃	—	2	8	no	—
235	#41×C₂₃	—	2	8	no	—
236	#41×C₂₃	—	4	4	no	—
237	#41×C₂₃	—	4	4	no	—
238	#41×C₂₃	—	4	4	no	—
239	#41×C₂₃	—	4	8	no	—
240	#41×C₂₃	—	4	8	no	—
241	#41×C₂₃	—	8	2	no	—
242	C₂×Q₈×C₂₃	—	2	2	no	—
243	C₂×Q₈×C₂₃	—	2	1	no	—
244	C₂×Q₈×C₂₃	—	4	4	no	—
245	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
246	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
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	1	no	—
251	C₂×D₄×C₂₃	—	2	4	no	—
252	C₂×D₄×C₂₃	—	2	4	no	—
253	C₂×D₄×C₂₃	—	2	2	no	—
254	C₂×D₄×C₂₃	—	2	2	no	—
255	C₂×D₄×C₂₃	—	2	2	no	—
256	C₂×D₄×C₂₃	—	2	1	no	—
257	C₂×D₄×C₂₃	—	2	1	no	—
258	C₂×D₄×C₂₃	—	2	1	no	—
259	C₂×D₄×C₂₃	—	2	2	no	—
260	C₂×D₄×C₂₃	—	4	2	no	—
261	C₂×D₄×C₂₃	—	4	4	no	—
262	C₂×D₄×C₂₃	—	4	4	no	—
263	C₂×D₄×C₂₃	—	4	8	no	—
264	C₂×D₄×C₂₃	—	8	4	no	—
265	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
266	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
267	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
268	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
269	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
270	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
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	—	2	4	no	—
277	C₂²×C₄×C₂₃	—	2	4	no	—
278	C₂²×C₄×C₂₃	—	2	1	no	—
279	C₂²×C₄×C₂₃	—	2	2	no	—
280	C₂²×C₄×C₂₃	—	2	2	no	—
281	C₂²×C₄×C₂₃	—	4	4	no	—
282	C₂²×C₄×C₂₃	—	4	4	no	—
283	C₂²×C₄×C₂₃	—	4	8	no	—
284	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
287	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
288	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
289	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
291	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
292	Q₁₆×C₂₃	—	4	4	no	—
293	SD₁₆×C₂₃	—	2	4	no	—
294	SD₁₆×C₂₃	—	4	4	no	—
295	SD₁₆×C₂₃	—	4	4	no	—
296	SD₁₆×C₂₃	—	4	4	no	—
297	D₈×C₂₃	—	2	8	no	—
298	D₈×C₂₃	—	2	4	no	—
299	M₁₆×C₂₃	—	4	4	no	—
300	C₂×C₈×C₂₃	—	4	4	no	—
301	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
302	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
303	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
304	C₄⋊C₄×C₂₃	—	2	2	no	—
305	C₄⋊C₄×C₂₃	—	2	2	no	—
306	C₄⋊C₄×C₂₃	—	2	4	no	—
307	C₄⋊C₄×C₂₃	—	2	4	no	—
308	C₄⋊C₄×C₂₃	—	2	2	no	—
309	C₄⋊C₄×C₂₃	—	2	2	no	—
310	C₄⋊C₄×C₂₃	—	2	1	no	—
311	C₄⋊C₄×C₂₃	—	2	2	no	—
312	C₄⋊C₄×C₂₃	—	2	1	no	—
313	C₄⋊C₄×C₂₃	—	2	1	no	—
314	C₄⋊C₄×C₂₃	—	2	1	no	—
315	C₄⋊C₄×C₂₃	—	2	1	no	—
316	C₄⋊C₄×C₂₃	—	2	2	no	—
317	C₄⋊C₄×C₂₃	—	2	1	no	—
318	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
319	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
320	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
321	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
322	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
323	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
324	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
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	2	no	—
329	C₂²⋊C₄×C₂₃	—	2	1	no	—
330	C₂²⋊C₄×C₂₃	—	2	1	no	—
331	C₂²⋊C₄×C₂₃	—	2	1	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	—	2	2	no	—
337	C₂²⋊C₄×C₂₃	—	2	1	no	—
338	C₂²⋊C₄×C₂₃	—	2	2	no	—
339	C₂²⋊C₄×C₂₃	—	2	1	no	—
340	C₂²⋊C₄×C₂₃	—	2	2	no	—
341	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
342	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
343	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
344	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
345	C₄²×C₂₃	—	2	2	no	—
346	C₄²×C₂₃	—	2	1	no	—
347	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
349	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
350	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
351	#61604	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
352	C₂³×C₂₃	—	2	4	no	—
353	C₂³×C₂₃	—	2	2	no	—
354	C₂³×C₂₃	—	2	4	no	—
355	C₂³×C₂₃	—	2	1	no	—
356	C₂³×C₂₃	—	2	2	no	—
357	C₂³×C₂₃	—	4	2	no	—
358	C₂³×C₂₃	—	4	2	no	—
359	C₂³×C₂₃	—	4	2	no	—
360	C₂³×C₂₃	—	4	4	no	—
361	C₂³×C₂₃	—	4	2	no	—
362	C₂³×C₂₃	—	8	2	no	—
363	C₂³×C₂₃	—	8	2	no	—
364	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
365	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
366	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
367	Q₈×C₂₃	—	2	2	no	—
368	Q₈×C₂₃	—	2	4	no	—
369	Q₈×C₂₃	—	2	4	no	—
370	Q₈×C₂₃	—	4	4	no	—
371	Q₈×C₂₃	—	8	1	no	—
372	D₄×C₂₃	—	2	4	no	—
373	D₄×C₂₃	—	2	2	no	—
374	D₄×C₂₃	—	2	2	no	—
375	D₄×C₂₃	—	2	2	no	—
376	D₄×C₂₃	—	2	2	no	—
377	D₄×C₂₃	—	2	4	no	—
378	D₄×C₂₃	—	4	2	no	—
379	D₄×C₂₃	—	4	8	no	—
380	D₄×C₂₃	—	4	8	no	—
381	D₄×C₂₃	—	4	4	no	—
382	D₄×C₂₃	—	4	2	no	—
383	D₄×C₂₃	—	4	4	no	—
384	D₄×C₂₃	—	4	2	no	—
385	D₄×C₂₃	—	8	2	no	—
386	D₄×C₂₃	—	8	1	no	—
387	D₄×C₂₃	—	8	2	no	—
388	D₄×C₂₃	—	8	2	no	—
389	D₄×C₂₃	—	8	2	no	—
390	D₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
391	C₂×C₄×C₂₃	—	2	2	no	—
392	C₂×C₄×C₂₃	—	2	2	no	—
393	C₂×C₄×C₂₃	—	2	4	no	—
394	C₂×C₄×C₂₃	—	2	4	no	—
395	C₂×C₄×C₂₃	—	2	2	no	—
396	C₂×C₄×C₂₃	—	2	1	no	—
397	C₂×C₄×C₂₃	—	2	1	no	—
398	C₂×C₄×C₂₃	—	2	2	no	—
399	C₂×C₄×C₂₃	—	2	1	no	—
400	C₂×C₄×C₂₃	—	2	2	no	—
401	C₂×C₄×C₂₃	—	2	4	no	—
402	C₂×C₄×C₂₃	—	4	2	no	—
403	C₂×C₄×C₂₃	—	4	2	no	—
404	C₂×C₄×C₂₃	—	4	2	no	—
405	C₂×C₄×C₂₃	—	4	8	no	—
406	C₂×C₄×C₂₃	—	4	8	no	—
407	C₂×C₄×C₂₃	—	4	4	no	—
408	C₂×C₄×C₂₃	—	4	2	no	—
409	C₂×C₄×C₂₃	—	4	4	no	—
410	C₂×C₄×C₂₃	—	4	4	no	—
411	C₂×C₄×C₂₃	—	4	2	no	—
412	C₂×C₄×C₂₃	—	8	2	no	—
413	C₂×C₄×C₂₃	—	8	2	no	—
414	C₂×C₄×C₂₃	—	8	2	no	—
415	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
416	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
417	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
418	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
419	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
420	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
421	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
423	C₈×C₂₃	—	2	2	no	—
424	C₈×C₂₃	—	2	4	no	—
425	C₈×C₂₃	—	2	2	no	—
426	#3519	C₂×C₂₃	1	1	yes	characteristic, complemented
427	C₂×#547	C₂×C₂₃	1	1	yes	characteristic, complemented
428	#3331	C₂×C₂₃	1	2	yes	complemented
429	#3307	C₂×C₂₃	1	4	yes	complemented
430	#3303	C₂×C₂₃	1	2	yes	complemented
431	#3284	C₂×C₂₃	1	2	yes	complemented
432	#3272	C₂×C₂₃	1	2	yes	complemented
433	#3267	C₂×C₂₃	1	4	yes	complemented
434	#3218	C₂×C₂₃	1	1	yes	characteristic, complemented
435	#3206	C₂×C₂₃	1	1	yes	characteristic, complemented
436	#3196	C₂×C₂₃	1	2	yes	complemented
437	#3187	C₂×C₂₃	1	2	yes	complemented
438	#3109	C₂×C₂₃	1	1	yes	characteristic, complemented
439	#3105	C₂×C₂₃	1	1	yes	characteristic, complemented
440	#3006	C₂×C₂₃	1	2	yes	complemented
441	#3002	C₂×C₂₃	1	2	yes	complemented
442	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
443	C₂²×C₂₃	—	2	1	no	—
444	C₂²×C₂₃	—	2	1	no	—
445	C₂²×C₂₃	—	2	2	no	—
446	C₂²×C₂₃	—	2	2	no	—
447	C₂²×C₂₃	—	2	4	no	—
448	C₂²×C₂₃	—	2	2	no	—
449	C₂²×C₂₃	—	2	2	no	—
450	C₂²×C₂₃	—	2	2	no	—
451	C₂²×C₂₃	—	2	2	no	—
452	C₂²×C₂₃	—	4	8	no	—
453	C₂²×C₂₃	—	4	2	no	—
454	C₂²×C₂₃	—	4	2	no	—
455	C₂²×C₂₃	—	4	2	no	—
456	C₂²×C₂₃	—	4	1	no	—
457	C₂²×C₂₃	—	4	1	no	—
458	C₂²×C₂₃	—	4	2	no	—
459	C₂²×C₂₃	—	4	2	no	—
460	C₂²×C₂₃	—	4	1	no	—
461	C₂²×C₂₃	—	8	4	no	—
462	C₂²×C₂₃	—	16	4	no	—
463	C₂²×C₂₃	#577	1	2	yes	—
464	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
465	C₄×C₂₃	—	2	2	no	—
466	C₄×C₂₃	—	2	2	no	—
467	C₄×C₂₃	—	2	1	no	—
468	C₄×C₂₃	—	2	1	no	—
469	C₄×C₂₃	—	2	1	no	—
470	C₄×C₂₃	—	2	1	no	—
471	C₄×C₂₃	—	4	4	no	—
472	C₄×C₂₃	—	4	1	no	—
473	C₄×C₂₃	—	4	2	no	—
474	C₄×C₂₃	—	4	1	no	—
475	C₄×C₂₃	—	4	1	no	—
476	C₄×C₂₃	—	4	2	no	—
477	C₄×C₂₃	#575	1	2	yes	—
478	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
479	C₂²×#41	C₂²×C₂₃	1	2	yes	complemented
480	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	4	yes	complemented
481	C₂×#135	C₂²×C₂₃	1	4	yes	complemented
482	#555	C₂²×C₂₃	1	1	yes	characteristic, complemented
483	#554	C₂²×C₂₃	1	1	yes	characteristic, complemented
484	#553	—	2	1	no	—
485	#553	C₂²×C₂₃	1	2	yes	complemented
486	#550	C₂²×C₂₃	1	1	yes	characteristic, complemented
487	#547	—	2	1	no	—
488	#547	—	2	1	no	—
489	#547	—	2	2	no	—
490	#547	C₂²×C₂₃	1	2	yes	—
491	#547	C₂²×C₂₃	1	4	yes	complemented
492	#547	C₂²×C₂₃	1	2	yes	complemented
493	#546	—	2	2	no	—
494	#546	C₂²×C₂₃	1	2	yes	complemented
495	D₄²	—	2	1	no	—
496	D₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
497	#540	—	2	1	no	—
498	#538	—	2	2	no	—
499	#532	C₂²×C₂₃	1	1	yes	characteristic
500	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
501	#529	C₂²×C₂₃	1	1	yes	characteristic
502	#525	C₂²×C₂₃	1	2	yes	—
503	C₂×#123	—	2	2	no	—
504	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
505	C₂×#121	—	2	1	no	—
506	C₂×#121	C₂²×C₂₃	1	2	yes	—
507	#518	—	2	1	no	—
508	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
509	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
510	C₂²×C₄⋊C₄	—	2	1	no	—
511	#497	C₂²×C₂₃	1	2	yes	complemented
512	#492	C₂²×C₂₃	1	2	yes	complemented
513	#491	C₂²×C₂₃	1	2	yes	complemented
514	#487	C₂²×C₂₃	1	2	yes	complemented
515	#485	C₂²×C₂₃	1	4	yes	complemented
516	#484	C₂²×C₂₃	1	1	yes	characteristic, complemented
517	#483	C₂²×C₂₃	1	4	yes	complemented
518	#481	C₂²×C₂₃	1	1	yes	characteristic
519	#481	C₂²×C₂₃	1	2	yes	complemented
520	#478	C₂²×C₂₃	1	2	yes	complemented
521	#476	C₂²×C₂₃	1	2	yes	complemented
522	#470	C₂²×C₂₃	1	4	yes	complemented
523	#468	C₂²×C₂₃	1	4	yes	complemented
524	#465	C₂²×C₂₃	1	4	yes	complemented
525	#465	C₂²×C₂₃	1	4	yes	complemented
526	#463	C₂²×C₂₃	1	2	yes	complemented
527	#462	C₂²×C₂₃	1	2	yes	complemented
528	#461	C₂²×C₂₃	1	4	yes	complemented
529	#461	C₂²×C₂₃	1	2	yes	complemented
530	#459	C₂²×C₂₃	1	2	yes	complemented
531	#452	C₂²×C₂₃	1	4	yes	complemented
532	#452	C₂²×C₂₃	1	4	yes	complemented
533	#451	C₂²×C₂₃	1	2	yes	complemented
534	#450	C₂²×C₂₃	1	1	yes	characteristic, complemented
535	#450	C₂²×C₂₃	1	4	yes	complemented
536	#449	C₂²×C₂₃	1	4	yes	complemented
537	#449	C₂²×C₂₃	1	4	yes	complemented
538	#449	C₂²×C₂₃	1	4	yes	complemented
539	#448	C₂²×C₂₃	1	2	yes	—
540	#448	C₂²×C₂₃	1	2	yes	complemented
541	#448	C₂²×C₂₃	1	2	yes	complemented
542	#447	C₂²×C₂₃	1	1	yes	characteristic
543	#447	C₂²×C₂₃	1	2	yes	complemented
544	#442	C₂²×C₂₃	1	4	yes	complemented
545	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
546	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
547	#436	C₂²×C₂₃	1	2	yes	complemented
548	#435	C₂²×C₂₃	1	4	yes	complemented
549	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
550	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
551	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
552	#417	C₂²×C₂₃	1	4	yes	complemented
553	#416	C₂²×C₂₃	1	4	yes	complemented
554	#407	C₂²×C₂₃	1	2	yes	complemented
555	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
556	C₂×C₂₃	—	2	2	no	—
557	C₂×C₂₃	—	4	2	no	—
558	C₂×C₂₃	—	4	2	no	—
559	C₂×C₂₃	—	4	4	no	—
560	C₂×C₂₃	—	8	2	no	—
561	C₂×C₂₃	—	8	1	no	—
562	C₂×C₂₃	#3484	1	1	yes	characteristic
563	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
564	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
565	C₂×#41	—	2	2	no	—
566	C₂×#41	—	2	2	no	—
567	C₂×#41	—	2	1	no	—
568	C₂×#41	—	4	8	no	—
569	C₂×#41	C₂³×C₂₃	1	4	yes	—
570	C₂×#41	C₂³×C₂₃	1	4	yes	—
571	C₂×#41	C₂³×C₂₃	1	2	yes	—
572	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
573	C₂²×D₄	—	2	2	no	—
574	C₂²×D₄	—	2	2	no	—
575	C₂²×D₄	—	2	1	no	—
576	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
577	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
578	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
579	C₂³×C₄	—	2	1	no	—
580	C₂³×C₄	—	2	2	no	—
581	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
582	AGL(1,ℤ/8)	—	4	8	no	—
583	#135	—	4	8	no	—
584	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
585	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
586	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
587	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
588	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
589	C₂×D₈	C₂³×C₂₃	1	4	yes	—
590	C₂×D₈	C₂³×C₂₃	1	2	yes	—
591	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
592	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
593	C₄⋊Q₈	—	2	1	no	—
594	C₄⋊Q₈	—	2	1	no	—
595	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
596	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
597	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
598	#127	—	2	1	no	—
599	#127	C₂³×C₂₃	1	1	yes	characteristic
600	#126	—	2	2	no	—
601	#126	—	2	1	no	—
602	#125	—	2	1	no	—
603	#125	C₂³×C₂₃	1	1	yes	characteristic
604	#124	—	2	2	no	—
605	#124	—	2	1	no	—
606	#124	C₂³×C₂₃	1	1	yes	characteristic
607	#123	—	2	2	no	—
608	#123	—	2	1	no	—
609	#123	—	2	2	no	—
610	#123	—	2	4	no	—
611	#123	—	2	4	no	—
612	#123	—	2	4	no	—
613	#123	—	2	4	no	—
614	#123	—	2	2	no	—
615	C₂²⋊Q₈	—	2	2	no	—
616	C₂²⋊Q₈	—	2	2	no	—
617	C₂²⋊Q₈	—	2	2	no	—
618	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
619	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
620	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
621	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
622	#121	—	2	2	no	—
623	#121	—	2	2	no	—
624	#121	—	2	4	no	—
625	#121	—	2	2	no	—
626	#121	—	2	1	no	—
627	#121	—	2	2	no	—
628	#121	—	2	2	no	—
629	#121	—	2	1	no	—
630	#121	—	2	1	no	—
631	#121	—	2	2	no	—
632	#121	—	2	2	no	—
633	#121	C₂³×C₂₃	1	1	yes	characteristic
634	#121	C₂³×C₂₃	1	2	yes	—
635	#121	C₂³×C₂₃	1	2	yes	—
636	#121	C₂³×C₂₃	1	2	yes	—
637	#121	C₂³×C₂₃	1	2	yes	—
638	#120	—	2	2	no	—
639	#120	—	2	2	no	—
640	#120	—	2	2	no	—
641	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
642	C₄×D₄	—	2	1	no	—
643	C₄×D₄	—	2	2	no	—
644	C₄×D₄	—	2	2	no	—
645	C₄×D₄	—	2	1	no	—
646	C₄×D₄	—	2	1	no	—
647	C₄×D₄	—	2	2	no	—
648	C₄×D₄	—	2	1	no	—
649	C₄×D₄	—	2	1	no	—
650	C₄×D₄	—	2	1	no	—
651	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
652	C₄×D₄	D₄×C₂₃	1	2	yes	—
653	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
654	C₄×D₄	C₂³×C₂₃	1	2	yes	—
655	C₄×D₄	C₂³×C₂₃	1	2	yes	—
656	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
657	C₄×D₄	C₂³×C₂₃	1	2	yes	—
658	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
659	C₄×D₄	C₂³×C₂₃	1	2	yes	—
660	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
661	#117	—	2	1	no	—
662	#117	—	2	1	no	—
663	#117	C₂³×C₂₃	1	2	yes	—
664	C₂×C₄⋊C₄	—	2	1	no	—
665	C₂×C₄⋊C₄	—	2	2	no	—
666	C₂×C₄⋊C₄	—	2	1	no	—
667	C₂×C₄⋊C₄	—	2	2	no	—
668	C₂×C₄⋊C₄	—	2	2	no	—
669	C₂×C₄⋊C₄	—	2	4	no	—
670	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
671	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
672	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
673	C₂×C₂²⋊C₄	—	2	2	no	—
674	C₂×C₂²⋊C₄	—	2	1	no	—
675	C₂×C₂²⋊C₄	—	2	2	no	—
676	C₂×C₂²⋊C₄	—	2	2	no	—
677	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
678	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
679	#107	C₂³×C₂₃	1	2	yes	—
680	#106	C₂³×C₂₃	1	2	yes	—
681	#106	C₂³×C₂₃	1	4	yes	—
682	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
683	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
684	#103	C₂³×C₂₃	1	4	yes	—
685	#103	C₂³×C₂₃	1	4	yes	—
686	#103	C₂³×C₂₃	1	4	yes	—
687	#103	C₂³×C₂₃	1	4	yes	—
688	#103	C₂³×C₂₃	1	2	yes	—
689	#102	C₂³×C₂₃	1	2	yes	—
690	#102	C₂³×C₂₃	1	4	yes	—
691	#102	C₂³×C₂₃	1	2	yes	—
692	#102	C₂³×C₂₃	1	2	yes	—
693	#102	C₂³×C₂₃	1	4	yes	—
694	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
695	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
696	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
697	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
698	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
699	#97	C₂³×C₂₃	1	2	yes	—
700	C₄×C₈	C₂³×C₂₃	1	2	yes	—
701	C₂₃	#61604	1	1	yes	characteristic, direct product factor, Sylow
702	C₂⁴	—	2	1	no	—
703	C₂⁴	—	2	2	no	—
704	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
705	#41	—	2	8	no	—
706	#41	—	2	8	no	—
707	#41	—	4	4	no	—
708	#41	—	4	4	no	—
709	#41	—	4	4	no	—
710	#41	—	4	8	no	—
711	#41	—	4	8	no	—
712	#41	—	8	2	no	—
713	C₂×Q₈	—	2	2	no	—
714	C₂×Q₈	—	2	1	no	—
715	C₂×Q₈	—	4	4	no	—
716	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
717	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	2	2	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	1	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	1	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	1	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	4	2	no	—
732	C₂×D₄	—	4	4	no	—
733	C₂×D₄	—	4	4	no	—
734	C₂×D₄	—	4	8	no	—
735	C₂×D₄	—	8	4	no	—
736	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
737	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
738	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
739	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
740	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
741	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
742	C₂²×C₄	—	2	1	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	4	no	—
748	C₂²×C₄	—	2	4	no	—
749	C₂²×C₄	—	2	1	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	4	4	no	—
753	C₂²×C₄	—	4	4	no	—
754	C₂²×C₄	—	4	8	no	—
755	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
756	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
757	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
758	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
759	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
760	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
761	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
763	Q₁₆	—	4	4	no	—
764	SD₁₆	—	2	4	no	—
765	SD₁₆	—	4	4	no	—
766	SD₁₆	—	4	4	no	—
767	SD₁₆	—	4	4	no	—
768	D₈	—	2	8	no	—
769	D₈	—	2	4	no	—
770	M₁₆	—	4	4	no	—
771	C₂×C₈	—	4	4	no	—
772	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
773	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
774	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	4	no	—
778	C₄⋊C₄	—	2	4	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	1	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	—	2	1	no	—
784	C₄⋊C₄	—	2	1	no	—
785	C₄⋊C₄	—	2	1	no	—
786	C₄⋊C₄	—	2	1	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	1	no	—
789	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
790	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
791	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
792	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
793	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
794	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
795	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	1	no	—
801	C₂²⋊C₄	—	2	1	no	—
802	C₂²⋊C₄	—	2	1	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	—	2	2	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	1	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	1	no	—
811	C₂²⋊C₄	—	2	2	no	—
812	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
813	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
814	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
815	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
816	C₄²	—	2	2	no	—
817	C₄²	—	2	1	no	—
818	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
819	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
820	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
821	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
822	C₂³	—	2	4	no	—
823	C₂³	—	2	2	no	—
824	C₂³	—	2	4	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	4	2	no	—
828	C₂³	—	4	2	no	—
829	C₂³	—	4	2	no	—
830	C₂³	—	4	4	no	—
831	C₂³	—	4	2	no	—
832	C₂³	—	8	2	no	—
833	C₂³	—	8	2	no	—
834	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
835	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
836	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
837	Q₈	—	2	2	no	—
838	Q₈	—	2	4	no	—
839	Q₈	—	2	4	no	—
840	Q₈	—	4	4	no	—
841	Q₈	—	8	1	no	—
842	D₄	—	2	4	no	—
843	D₄	—	2	2	no	—
844	D₄	—	2	2	no	—
845	D₄	—	2	2	no	—
846	D₄	—	2	2	no	—
847	D₄	—	2	4	no	—
848	D₄	—	4	2	no	—
849	D₄	—	4	8	no	—
850	D₄	—	4	8	no	—
851	D₄	—	4	4	no	—
852	D₄	—	4	2	no	—
853	D₄	—	4	4	no	—
854	D₄	—	4	2	no	—
855	D₄	—	8	2	no	—
856	D₄	—	8	1	no	—
857	D₄	—	8	2	no	—
858	D₄	—	8	2	no	—
859	D₄	—	8	2	no	—
860	D₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	4	no	—
864	C₂×C₄	—	2	4	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	1	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	4	no	—
872	C₂×C₄	—	4	2	no	—
873	C₂×C₄	—	4	2	no	—
874	C₂×C₄	—	4	2	no	—
875	C₂×C₄	—	4	8	no	—
876	C₂×C₄	—	4	8	no	—
877	C₂×C₄	—	4	4	no	—
878	C₂×C₄	—	4	4	no	—
879	C₂×C₄	—	4	2	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	—	4	2	no	—
882	C₂×C₄	—	8	2	no	—
883	C₂×C₄	—	8	2	no	—
884	C₂×C₄	—	8	2	no	—
885	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
886	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
887	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
888	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
889	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
890	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
891	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
892	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
893	C₈	—	2	2	no	—
894	C₈	—	2	4	no	—
895	C₈	—	2	2	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	2	no	—
899	C₂²	—	2	2	no	—
900	C₂²	—	2	4	no	—
901	C₂²	—	2	2	no	—
902	C₂²	—	2	2	no	—
903	C₂²	—	2	2	no	—
904	C₂²	—	2	2	no	—
905	C₂²	—	4	8	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	1	no	—
910	C₂²	—	4	1	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	4	2	no	—
913	C₂²	—	4	1	no	—
914	C₂²	—	8	4	no	—
915	C₂²	—	16	4	no	—
916	C₂²	C₂₃×#577	1	2	yes	—
917	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	1	no	—
924	C₄	—	4	4	no	—
925	C₄	—	4	1	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	1	no	—
928	C₄	—	4	1	no	—
929	C₄	—	4	2	no	—
930	C₄	C₂₃×#575	1	2	yes	—
931	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
932	C₂	—	2	2	no	—
933	C₂	—	4	2	no	—
934	C₂	—	4	2	no	—
935	C₂	—	4	4	no	—
936	C₂	—	8	1	no	—
937	C₂	—	8	2	no	—
938	C₂	C₂₃×#3484	1	1	yes	characteristic
939	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
940	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×#3331	C₂	semidirect
4. C₂₃×#3307	C₂	semidirect
5. C₂₃×#3303	C₂	semidirect
6. C₂₃×#3284	C₂	semidirect
7. C₂₃×#3272	C₂	semidirect
8. C₂₃×#3267	C₂	semidirect
9. C₂₃×#3218	C₂	semidirect
10. C₂₃×#3206	C₂	semidirect
11. C₂₃×#3196	C₂	semidirect
12. C₂₃×#3187	C₂	semidirect
13. C₂₃×#3109	C₂	semidirect
14. C₂₃×#3105	C₂	semidirect
15. C₂₃×#3006	C₂	semidirect
16. C₂₃×#3002	C₂	semidirect
17. C₂₃×#2974	C₂	semidirect
18. C₂²×#41×C₂₃	C₂²	semidirect
19. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
20. C₂×C₂₃×#135	C₂²	semidirect
21. C₂₃×#555	C₂²	semidirect
22. C₂₃×#554	C₂²	semidirect
24. C₂₃×#553	C₂²	semidirect
25. C₂₃×#550	C₂²	semidirect
30. C₂₃×#547	C₂²	semidirect
31. C₂₃×#547	C₂²	semidirect
33. C₂₃×#546	C₂²	semidirect
35. D₄²×C₂₃	C₂²	semidirect
39. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
43. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
48. C₂×C₄×D₄×C₂₃	C₂²	semidirect
50. C₂₃×#497	C₂²	semidirect
51. C₂₃×#492	C₂²	semidirect
52. C₂₃×#491	C₂²	semidirect
53. C₂₃×#487	C₂²	semidirect
54. C₂₃×#485	C₂²	semidirect
55. C₂₃×#484	C₂²	semidirect
56. C₂₃×#483	C₂²	semidirect
58. C₂₃×#481	C₂²	semidirect
59. C₂₃×#478	C₂²	semidirect
60. C₂₃×#476	C₂²	semidirect
61. C₂₃×#470	C₂²	semidirect
62. C₂₃×#468	C₂²	semidirect
63. C₂₃×#465	C₂²	semidirect
64. C₂₃×#465	C₂²	semidirect
65. C₂₃×#463	C₂²	semidirect
66. C₂₃×#462	C₂²	semidirect
67. C₂₃×#461	C₂²	semidirect
68. C₂₃×#461	C₂²	semidirect
69. C₂₃×#459	C₂²	semidirect
70. C₂₃×#452	C₂²	semidirect
71. C₂₃×#452	C₂²	semidirect
72. C₂₃×#451	C₂²	semidirect
73. C₂₃×#450	C₂²	semidirect
74. C₂₃×#450	C₂²	semidirect
75. C₂₃×#449	C₂²	semidirect
76. C₂₃×#449	C₂²	semidirect
77. C₂₃×#449	C₂²	semidirect
79. C₂₃×#448	C₂²	semidirect
80. C₂₃×#448	C₂²	semidirect
82. C₂₃×#447	C₂²	semidirect
83. C₂₃×#442	C₂²	semidirect
84. C₄×SD₁₆×C₂₃	C₂²	semidirect
85. C₄×D₈×C₂₃	C₂²	semidirect
86. C₂₃×#436	C₂²	semidirect
87. C₂₃×#435	C₂²	semidirect
88. C₈×D₄×C₂₃	C₂²	semidirect
89. C₂₃×#432	C₂²	semidirect
90. C₂₃×#431	C₂²	semidirect
91. C₂₃×#417	C₂²	semidirect
92. C₂₃×#416	C₂²	semidirect
93. C₂₃×#407	C₂²	semidirect
94. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
351. #61604	C₂₃	direct (N × H)
426. #3519	C₂×C₂₃	semidirect
427. C₂×#547	C₂×C₂₃	semidirect
428. #3331	C₂×C₂₃	semidirect
429. #3307	C₂×C₂₃	semidirect
430. #3303	C₂×C₂₃	semidirect
431. #3284	C₂×C₂₃	semidirect
432. #3272	C₂×C₂₃	semidirect
433. #3267	C₂×C₂₃	semidirect
434. #3218	C₂×C₂₃	semidirect
435. #3206	C₂×C₂₃	semidirect
436. #3196	C₂×C₂₃	semidirect
437. #3187	C₂×C₂₃	semidirect
438. #3109	C₂×C₂₃	semidirect
439. #3105	C₂×C₂₃	semidirect
440. #3006	C₂×C₂₃	semidirect
441. #3002	C₂×C₂₃	semidirect
442. #2974	C₂×C₂₃	semidirect
479. C₂²×#41	C₂²×C₂₃	semidirect
480. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
481. C₂×#135	C₂²×C₂₃	semidirect
482. #555	C₂²×C₂₃	semidirect
483. #554	C₂²×C₂₃	semidirect
485. #553	C₂²×C₂₃	semidirect
486. #550	C₂²×C₂₃	semidirect
491. #547	C₂²×C₂₃	semidirect
492. #547	C₂²×C₂₃	semidirect
494. #546	C₂²×C₂₃	semidirect
496. D₄²	C₂²×C₂₃	semidirect
500. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
504. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
509. C₂×C₄×D₄	C₂²×C₂₃	semidirect
511. #497	C₂²×C₂₃	semidirect
512. #492	C₂²×C₂₃	semidirect
513. #491	C₂²×C₂₃	semidirect
514. #487	C₂²×C₂₃	semidirect
515. #485	C₂²×C₂₃	semidirect
516. #484	C₂²×C₂₃	semidirect
517. #483	C₂²×C₂₃	semidirect
519. #481	C₂²×C₂₃	semidirect
520. #478	C₂²×C₂₃	semidirect
521. #476	C₂²×C₂₃	semidirect
522. #470	C₂²×C₂₃	semidirect
523. #468	C₂²×C₂₃	semidirect
524. #465	C₂²×C₂₃	semidirect
525. #465	C₂²×C₂₃	semidirect
526. #463	C₂²×C₂₃	semidirect
527. #462	C₂²×C₂₃	semidirect
528. #461	C₂²×C₂₃	semidirect
529. #461	C₂²×C₂₃	semidirect
530. #459	C₂²×C₂₃	semidirect
531. #452	C₂²×C₂₃	semidirect
532. #452	C₂²×C₂₃	semidirect
533. #451	C₂²×C₂₃	semidirect
534. #450	C₂²×C₂₃	semidirect
535. #450	C₂²×C₂₃	semidirect
536. #449	C₂²×C₂₃	semidirect
537. #449	C₂²×C₂₃	semidirect
538. #449	C₂²×C₂₃	semidirect
540. #448	C₂²×C₂₃	semidirect
541. #448	C₂²×C₂₃	semidirect
543. #447	C₂²×C₂₃	semidirect
544. #442	C₂²×C₂₃	semidirect
545. C₄×SD₁₆	C₂²×C₂₃	semidirect
546. C₄×D₈	C₂²×C₂₃	semidirect
547. #436	C₂²×C₂₃	semidirect
548. #435	C₂²×C₂₃	semidirect
549. C₈×D₄	C₂²×C₂₃	semidirect
550. #432	C₂²×C₂₃	semidirect
551. #431	C₂²×C₂₃	semidirect
552. #417	C₂²×C₂₃	semidirect
553. #416	C₂²×C₂₃	semidirect
554. #407	C₂²×C₂₃	semidirect
555. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
701. C₂₃	#61604	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×#3331	2
C₂₃×#3307	2
C₂₃×#3303	2
C₂₃×#3284	2
C₂₃×#3272	2
C₂₃×#3267	2
C₂₃×#3218	2
C₂₃×#3206	2
C₂₃×#3196	2
C₂₃×#3187	2
C₂₃×#3109	2
C₂₃×#3105	2
C₂₃×#3006	2
C₂₃×#3002	2
C₂₃×#2974	2
#61604	23

Subgroups — C23×#61604 #19209230

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61604 #19209230