Subgroups — C₂₃×#61576 #19209202

Order 5888.

2254 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#546	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3319	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3311	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3268	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3267	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3213	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3196	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3188	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3003	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3002	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2973	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
19	C₂×C₂₃×#135	C₂²	1	4	yes	complemented
20	C₂₃×#559	—	2	2	no	—
21	C₂₃×#556	C₂²	1	2	yes	complemented
22	C₂₃×#555	C₂²	1	2	yes	complemented
23	C₂₃×#553	—	2	2	no	—
24	C₂₃×#550	C₂²	1	2	yes	complemented
25	C₂₃×#547	C₂²	1	2	yes	complemented
26	C₂₃×#546	—	2	2	no	—
27	C₂₃×#546	—	2	2	no	—
28	C₂₃×#546	C₂²	1	4	yes	—
29	C₂₃×#546	C₂²	1	4	yes	—
30	C₂₃×#538	—	2	1	no	—
31	C₂₃×#538	—	2	1	no	—
32	C₂₃×#535	—	2	1	no	—
33	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
34	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
36	C₂₃×#525	C₂²	1	2	yes	—
37	C₂₃×#525	C₂²	1	2	yes	complemented
38	C₂×C₂₃×#123	—	2	1	no	—
39	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#121	—	2	1	no	—
41	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×#120	—	2	1	no	—
43	C₂₃×#520	—	2	1	no	—
44	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊C₄×C₂₃	—	2	1	no	—
47	C₂₃×#497	C₂²	1	2	yes	complemented
48	C₂₃×#496	C₂²	1	2	yes	complemented
49	C₂₃×#489	C₂²	1	2	yes	complemented
50	C₂₃×#489	C₂²	1	2	yes	complemented
51	C₂₃×#485	C₂²	1	4	yes	complemented
52	C₂₃×#484	C₂²	1	2	yes	complemented
53	C₂₃×#482	C₂²	1	4	yes	complemented
54	C₂₃×#481	C₂²	1	2	yes	complemented
55	C₂₃×#476	C₂²	1	2	yes	complemented
56	C₂₃×#474	C₂²	1	2	yes	complemented
57	C₂₃×#470	C₂²	1	4	yes	complemented
58	C₂₃×#468	C₂²	1	4	yes	complemented
59	C₂₃×#466	C₂²	1	4	yes	complemented
60	C₂₃×#465	C₂²	1	4	yes	complemented
61	C₂₃×#464	C₂²	1	4	yes	complemented
62	C₂₃×#463	C₂²	1	4	yes	complemented
63	C₂₃×#461	C₂²	1	2	yes	complemented
64	C₂₃×#459	C₂²	1	2	yes	complemented
65	C₂₃×#452	C₂²	1	4	yes	complemented
66	C₂₃×#452	C₂²	1	4	yes	complemented
67	C₂₃×#451	C₂²	1	2	yes	complemented
68	C₂₃×#450	C₂²	1	2	yes	—
69	C₂₃×#450	C₂²	1	2	yes	—
70	C₂₃×#450	C₂²	1	4	yes	complemented
71	C₂₃×#449	C₂²	1	4	yes	complemented
72	C₂₃×#449	C₂²	1	4	yes	complemented
73	C₂₃×#448	C₂²	1	2	yes	complemented
74	C₂₃×#447	C₂²	1	2	yes	—
75	C₂₃×#447	C₂²	1	2	yes	—
76	C₂₃×#447	C₂²	1	4	yes	complemented
77	C₂₃×#442	C₂²	1	4	yes	complemented
78	C₂₃×#440	C₂²	1	4	yes	complemented
79	C₂₃×#435	C₂²	1	4	yes	complemented
80	C₂₃×#435	C₂²	1	4	yes	complemented
81	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
82	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
83	C₂₃×#418	C₂²	1	4	yes	complemented
84	C₂₃×#416	C₂²	1	4	yes	complemented
85	C₂₃×#407	C₂²	1	2	yes	—
86	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
87	C₂⁵×C₂₃	—	2	1	no	—
88	C₂×#41×C₂₃	—	2	2	no	—
89	C₂×#41×C₂₃	—	2	1	no	—
90	C₂×#41×C₂₃	—	4	4	no	—
91	C₂×#41×C₂₃	C₂³	1	4	yes	—
92	C₂×#41×C₂₃	C₂³	1	2	yes	—
93	C₂×#41×C₂₃	C₂³	1	2	yes	complemented
94	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₂₃	—	2	1	no	—
96	C₂²×D₄×C₂₃	—	2	1	no	—
97	C₂²×D₄×C₂₃	—	2	1	no	—
98	C₂²×D₄×C₂₃	—	2	2	no	—
99	C₂²×D₄×C₂₃	—	4	4	no	—
100	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
101	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
102	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
103	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₂₃	—	2	1	no	—
105	C₂³×C₄×C₂₃	—	2	1	no	—
106	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
108	C₂₃×AGL(1,ℤ/8)	—	4	8	no	—
109	C₂₃×#135	—	4	8	no	—
110	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	complemented
111	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
113	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	complemented
114	C₂×D₈×C₂₃	C₂³	1	4	yes	—
115	C₂×D₈×C₂₃	C₂³	1	4	yes	—
116	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
117	C₂²×C₈×C₂₃	C₂³	1	4	yes	complemented
118	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
119	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
120	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
121	C₂₃×#127	—	2	2	no	—
122	C₂₃×#127	C₂³	1	1	yes	characteristic, complemented
123	C₂₃×#126	—	2	2	no	—
124	C₂₃×#126	—	2	2	no	—
125	C₂₃×#125	—	2	1	no	—
126	C₂₃×#124	—	2	2	no	—
127	C₂₃×#124	—	2	2	no	—
128	C₂₃×#124	—	2	2	no	—
129	C₂₃×#124	—	2	1	no	—
130	C₂₃×#124	—	2	1	no	—
131	C₂₃×#124	—	2	1	no	—
132	C₂₃×#124	C₂³	1	2	yes	—
133	C₂₃×#124	C₂³	1	2	yes	—
134	C₂₃×#123	—	2	2	no	—
135	C₂₃×#123	—	2	2	no	—
136	C₂₃×#123	—	2	4	no	—
137	C₂₃×#123	—	2	4	no	—
138	C₂₃×#123	—	2	2	no	—
139	C₂₃×#123	—	2	2	no	—
140	C₂₃×C₂²⋊Q₈	—	2	2	no	—
141	C₂₃×C₂²⋊Q₈	—	2	1	no	—
142	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
143	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
144	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
145	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	complemented
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	2	no	—
152	C₂₃×#121	—	2	4	no	—
153	C₂₃×#121	—	2	4	no	—
154	C₂₃×#121	C₂³	1	2	yes	—
155	C₂₃×#121	C₂³	1	2	yes	—
156	C₂₃×#121	C₂³	1	4	yes	—
157	C₂₃×#121	C₂³	1	2	yes	complemented
158	C₂₃×#120	—	2	2	no	—
159	C₂₃×#120	—	2	2	no	—
160	C₂₃×#120	—	2	4	no	—
161	C₂₃×#120	—	2	4	no	—
162	C₄×Q₈×C₂₃	—	2	2	no	—
163	C₄×Q₈×C₂₃	—	2	1	no	—
164	C₄×Q₈×C₂₃	C₂³	1	2	yes	complemented
165	C₄×D₄×C₂₃	—	2	2	no	—
166	C₄×D₄×C₂₃	—	2	2	no	—
167	C₄×D₄×C₂₃	—	2	2	no	—
168	C₄×D₄×C₂₃	—	2	2	no	—
169	C₄×D₄×C₂₃	—	2	2	no	—
170	C₄×D₄×C₂₃	—	2	1	no	—
171	C₄×D₄×C₂₃	—	2	1	no	—
172	C₄×D₄×C₂₃	—	2	1	no	—
173	C₄×D₄×C₂₃	D₄	1	2	yes	—
174	C₄×D₄×C₂₃	D₄	1	2	yes	—
175	C₄×D₄×C₂₃	C₂³	1	2	yes	—
176	C₄×D₄×C₂₃	C₂³	1	2	yes	—
177	C₄×D₄×C₂₃	C₂³	1	2	yes	—
178	C₄×D₄×C₂₃	C₂³	1	2	yes	—
179	C₄×D₄×C₂₃	C₂³	1	2	yes	complemented
180	C₂₃×#117	—	2	1	no	—
181	C₂₃×#117	—	2	2	no	—
182	C₂₃×#117	C₂³	1	2	yes	—
183	C₂₃×#117	C₂³	1	2	yes	complemented
184	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
185	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
186	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
187	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
189	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
190	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
191	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
192	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
193	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
194	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
195	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
196	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
197	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
198	C₂₃×#107	C₂³	1	4	yes	complemented
199	C₂₃×#106	C₂³	1	4	yes	complemented
200	C₂₃×C₄⋊C₈	C₂³	1	2	yes	complemented
201	C₂₃×C₄⋊C₈	C₂³	1	2	yes	complemented
202	C₂₃×#103	C₂³	1	4	yes	complemented
203	C₂₃×#103	C₂³	1	4	yes	complemented
204	C₂₃×#103	C₂³	1	4	yes	complemented
205	C₂₃×#102	C₂³	1	4	yes	—
206	C₂₃×#102	C₂³	1	4	yes	—
207	C₂₃×#102	C₂³	1	4	yes	—
208	C₂₃×#102	C₂³	1	4	yes	—
209	C₂₃×#102	C₂³	1	4	yes	complemented
210	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
211	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
212	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
213	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	complemented
214	C₂₃×#97	C₂³	1	2	yes	complemented
215	C₂₃×#97	C₂³	1	2	yes	complemented
216	C₂⁴×C₂₃	—	2	1	no	—
217	C₂⁴×C₂₃	—	2	1	no	—
218	C₂⁴×C₂₃	—	2	4	no	—
219	C₂⁴×C₂₃	—	4	4	no	—
220	C₂⁴×C₂₃	—	4	4	no	—
221	C₂⁴×C₂₃	—	8	2	no	—
222	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
223	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
224	#41×C₂₃	—	2	8	no	—
225	#41×C₂₃	—	4	4	no	—
226	#41×C₂₃	—	4	4	no	—
227	#41×C₂₃	—	4	4	no	—
228	#41×C₂₃	—	4	4	no	—
229	#41×C₂₃	—	4	8	no	—
230	C₂×Q₈×C₂₃	—	2	1	no	—
231	C₂×Q₈×C₂₃	—	2	1	no	—
232	C₂×Q₈×C₂₃	—	2	1	no	—
233	C₂×Q₈×C₂₃	—	4	2	no	—
234	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
235	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
236	C₂×D₄×C₂₃	—	2	4	no	—
237	C₂×D₄×C₂₃	—	2	8	no	—
238	C₂×D₄×C₂₃	—	2	2	no	—
239	C₂×D₄×C₂₃	—	2	4	no	—
240	C₂×D₄×C₂₃	—	2	2	no	—
241	C₂×D₄×C₂₃	—	2	2	no	—
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	1	no	—
247	C₂×D₄×C₂₃	—	2	4	no	—
248	C₂×D₄×C₂₃	—	2	1	no	—
249	C₂×D₄×C₂₃	—	2	1	no	—
250	C₂×D₄×C₂₃	—	4	4	no	—
251	C₂×D₄×C₂₃	—	4	2	no	—
252	C₂×D₄×C₂₃	—	4	2	no	—
253	C₂×D₄×C₂₃	—	4	8	no	—
254	C₂×D₄×C₂₃	—	4	4	no	—
255	C₂×D₄×C₂₃	—	4	4	no	—
256	C₂×D₄×C₂₃	—	8	2	no	—
257	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
258	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
260	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
261	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₂₃	—	2	1	no	—
263	C₂²×C₄×C₂₃	—	2	1	no	—
264	C₂²×C₄×C₂₃	—	2	4	no	—
265	C₂²×C₄×C₂₃	—	2	2	no	—
266	C₂²×C₄×C₂₃	—	2	2	no	—
267	C₂²×C₄×C₂₃	—	2	2	no	—
268	C₂²×C₄×C₂₃	—	2	2	no	—
269	C₂²×C₄×C₂₃	—	2	2	no	—
270	C₂²×C₄×C₂₃	—	4	2	no	—
271	C₂²×C₄×C₂₃	—	4	2	no	—
272	C₂²×C₄×C₂₃	—	4	4	no	—
273	C₂²×C₄×C₂₃	—	8	2	no	—
274	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
279	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
280	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
282	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
283	Q₁₆×C₂₃	—	4	4	no	—
284	SD₁₆×C₂₃	—	2	8	no	—
285	SD₁₆×C₂₃	—	4	4	no	—
286	SD₁₆×C₂₃	—	4	4	no	—
287	D₈×C₂₃	—	2	8	no	—
288	D₈×C₂₃	—	4	4	no	—
289	M₁₆×C₂₃	—	4	4	no	—
290	C₂×C₈×C₂₃	—	4	4	no	—
291	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
292	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
293	C₄⋊C₄×C₂₃	—	2	1	no	—
294	C₄⋊C₄×C₂₃	—	2	2	no	—
295	C₄⋊C₄×C₂₃	—	2	2	no	—
296	C₄⋊C₄×C₂₃	—	2	4	no	—
297	C₄⋊C₄×C₂₃	—	2	1	no	—
298	C₄⋊C₄×C₂₃	—	2	1	no	—
299	C₄⋊C₄×C₂₃	—	2	2	no	—
300	C₄⋊C₄×C₂₃	—	2	1	no	—
301	C₄⋊C₄×C₂₃	—	2	1	no	—
302	C₄⋊C₄×C₂₃	—	2	2	no	—
303	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
304	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
305	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
306	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
307	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
308	C₂²⋊C₄×C₂₃	—	2	4	no	—
309	C₂²⋊C₄×C₂₃	—	2	2	no	—
310	C₂²⋊C₄×C₂₃	—	2	2	no	—
311	C₂²⋊C₄×C₂₃	—	2	2	no	—
312	C₂²⋊C₄×C₂₃	—	2	2	no	—
313	C₂²⋊C₄×C₂₃	—	2	2	no	—
314	C₂²⋊C₄×C₂₃	—	2	2	no	—
315	C₂²⋊C₄×C₂₃	—	2	2	no	—
316	C₂²⋊C₄×C₂₃	—	2	4	no	—
317	C₂²⋊C₄×C₂₃	—	2	2	no	—
318	C₂²⋊C₄×C₂₃	—	2	2	no	—
319	C₂²⋊C₄×C₂₃	—	2	2	no	—
320	C₂²⋊C₄×C₂₃	—	2	2	no	—
321	C₂²⋊C₄×C₂₃	—	2	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	C₂×D₄	1	2	yes	—
326	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
327	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
328	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
329	C₄²×C₂₃	—	2	2	no	—
330	C₄²×C₂₃	—	2	2	no	—
331	C₄²×C₂₃	—	2	2	no	—
332	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
335	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
336	#61576	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
337	C₂³×C₂₃	—	2	4	no	—
338	C₂³×C₂₃	—	2	2	no	—
339	C₂³×C₂₃	—	2	2	no	—
340	C₂³×C₂₃	—	2	2	no	—
341	C₂³×C₂₃	—	2	2	no	—
342	C₂³×C₂₃	—	2	2	no	—
343	C₂³×C₂₃	—	4	1	no	—
344	C₂³×C₂₃	—	4	1	no	—
345	C₂³×C₂₃	—	4	1	no	—
346	C₂³×C₂₃	—	4	1	no	—
347	C₂³×C₂₃	—	4	8	no	—
348	C₂³×C₂₃	—	4	2	no	—
349	C₂³×C₂₃	—	4	2	no	—
350	C₂³×C₂₃	—	4	2	no	—
351	C₂³×C₂₃	—	4	8	no	—
352	C₂³×C₂₃	—	4	2	no	—
353	C₂³×C₂₃	—	4	2	no	—
354	C₂³×C₂₃	—	8	4	no	—
355	C₂³×C₂₃	—	8	16	no	—
356	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
357	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
358	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
359	Q₈×C₂₃	—	2	4	no	—
360	Q₈×C₂₃	—	2	4	no	—
361	Q₈×C₂₃	—	4	2	no	—
362	Q₈×C₂₃	—	4	2	no	—
363	Q₈×C₂₃	—	8	1	no	—
364	D₄×C₂₃	—	2	4	no	—
365	D₄×C₂₃	—	2	2	no	—
366	D₄×C₂₃	—	2	4	no	—
367	D₄×C₂₃	—	2	4	no	—
368	D₄×C₂₃	—	4	2	no	—
369	D₄×C₂₃	—	4	2	no	—
370	D₄×C₂₃	—	4	8	no	—
371	D₄×C₂₃	—	4	2	no	—
372	D₄×C₂₃	—	4	2	no	—
373	D₄×C₂₃	—	4	8	no	—
374	D₄×C₂₃	—	4	4	no	—
375	D₄×C₂₃	—	8	1	no	—
376	D₄×C₂₃	—	8	2	no	—
377	D₄×C₂₃	—	8	2	no	—
378	D₄×C₂₃	—	8	4	no	—
379	D₄×C₂₃	—	8	2	no	—
380	D₄×C₂₃	—	8	2	no	—
381	D₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
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	2	no	—
387	C₂×C₄×C₂₃	—	2	2	no	—
388	C₂×C₄×C₂₃	—	2	2	no	—
389	C₂×C₄×C₂₃	—	2	2	no	—
390	C₂×C₄×C₂₃	—	2	2	no	—
391	C₂×C₄×C₂₃	—	4	1	no	—
392	C₂×C₄×C₂₃	—	4	2	no	—
393	C₂×C₄×C₂₃	—	4	1	no	—
394	C₂×C₄×C₂₃	—	4	2	no	—
395	C₂×C₄×C₂₃	—	4	1	no	—
396	C₂×C₄×C₂₃	—	4	8	no	—
397	C₂×C₄×C₂₃	—	4	4	no	—
398	C₂×C₄×C₂₃	—	4	2	no	—
399	C₂×C₄×C₂₃	—	4	2	no	—
400	C₂×C₄×C₂₃	—	8	2	no	—
401	C₂×C₄×C₂₃	—	8	2	no	—
402	C₂×C₄×C₂₃	—	8	2	no	—
403	C₂×C₄×C₂₃	—	8	2	no	—
404	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
411	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
412	C₈×C₂₃	—	2	4	no	—
413	C₈×C₂₃	—	2	4	no	—
414	#3506	C₂×C₂₃	1	1	yes	characteristic, complemented
415	C₂×#546	C₂×C₂₃	1	1	yes	characteristic, complemented
416	#3319	C₂×C₂₃	1	4	yes	complemented
417	#3311	C₂×C₂₃	1	4	yes	complemented
418	#3268	C₂×C₂₃	1	4	yes	complemented
419	#3267	C₂×C₂₃	1	4	yes	complemented
420	#3215	C₂×C₂₃	1	1	yes	characteristic, complemented
421	#3213	C₂×C₂₃	1	1	yes	characteristic, complemented
422	#3196	C₂×C₂₃	1	2	yes	complemented
423	#3188	C₂×C₂₃	1	2	yes	complemented
424	#3110	C₂×C₂₃	1	1	yes	characteristic, complemented
425	#3109	C₂×C₂₃	1	1	yes	characteristic, complemented
426	#3003	C₂×C₂₃	1	2	yes	complemented
427	#3002	C₂×C₂₃	1	2	yes	complemented
428	#2973	C₂×C₂₃	1	1	yes	characteristic, complemented
429	C₂²×C₂₃	—	2	1	no	—
430	C₂²×C₂₃	—	2	1	no	—
431	C₂²×C₂₃	—	2	2	no	—
432	C₂²×C₂₃	—	2	2	no	—
433	C₂²×C₂₃	—	2	2	no	—
434	C₂²×C₂₃	—	2	2	no	—
435	C₂²×C₂₃	—	2	4	no	—
436	C₂²×C₂₃	—	2	2	no	—
437	C₂²×C₂₃	—	2	2	no	—
438	C₂²×C₂₃	—	4	8	no	—
439	C₂²×C₂₃	—	4	4	no	—
440	C₂²×C₂₃	—	4	2	no	—
441	C₂²×C₂₃	—	4	2	no	—
442	C₂²×C₂₃	—	4	2	no	—
443	C₂²×C₂₃	—	4	2	no	—
444	C₂²×C₂₃	—	4	2	no	—
445	C₂²×C₂₃	—	4	2	no	—
446	C₂²×C₂₃	—	4	2	no	—
447	C₂²×C₂₃	—	4	2	no	—
448	C₂²×C₂₃	—	8	2	no	—
449	C₂²×C₂₃	—	8	4	no	—
450	C₂²×C₂₃	—	8	16	no	—
451	C₂²×C₂₃	#575	1	2	yes	—
452	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
453	C₄×C₂₃	—	2	1	no	—
454	C₄×C₂₃	—	2	1	no	—
455	C₄×C₂₃	—	2	2	no	—
456	C₄×C₂₃	—	2	1	no	—
457	C₄×C₂₃	—	2	2	no	—
458	C₄×C₂₃	—	2	1	no	—
459	C₄×C₂₃	—	2	1	no	—
460	C₄×C₂₃	—	4	2	no	—
461	C₄×C₂₃	—	4	2	no	—
462	C₄×C₂₃	—	4	2	no	—
463	C₄×C₂₃	—	4	2	no	—
464	C₄×C₂₃	—	4	2	no	—
465	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
466	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
467	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
468	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	4	yes	complemented
469	C₂×#135	C₂²×C₂₃	1	4	yes	complemented
470	#559	—	2	2	no	—
471	#556	C₂²×C₂₃	1	2	yes	complemented
472	#555	C₂²×C₂₃	1	2	yes	complemented
473	#553	—	2	2	no	—
474	#550	C₂²×C₂₃	1	2	yes	complemented
475	#547	C₂²×C₂₃	1	2	yes	complemented
476	#546	—	2	2	no	—
477	#546	—	2	2	no	—
478	#546	C₂²×C₂₃	1	4	yes	—
479	#546	C₂²×C₂₃	1	4	yes	—
480	#538	—	2	1	no	—
481	#538	—	2	1	no	—
482	#535	—	2	1	no	—
483	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
484	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
485	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
486	#525	C₂²×C₂₃	1	2	yes	—
487	#525	C₂²×C₂₃	1	2	yes	complemented
488	C₂×#123	—	2	1	no	—
489	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
490	C₂×#121	—	2	1	no	—
491	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
492	C₂×#120	—	2	1	no	—
493	#520	—	2	1	no	—
494	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
495	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
496	C₂²×C₂²⋊C₄	—	2	1	no	—
497	#497	C₂²×C₂₃	1	2	yes	complemented
498	#496	C₂²×C₂₃	1	2	yes	complemented
499	#489	C₂²×C₂₃	1	2	yes	complemented
500	#489	C₂²×C₂₃	1	2	yes	complemented
501	#485	C₂²×C₂₃	1	4	yes	complemented
502	#484	C₂²×C₂₃	1	2	yes	complemented
503	#482	C₂²×C₂₃	1	4	yes	complemented
504	#481	C₂²×C₂₃	1	2	yes	complemented
505	#476	C₂²×C₂₃	1	2	yes	complemented
506	#474	C₂²×C₂₃	1	2	yes	complemented
507	#470	C₂²×C₂₃	1	4	yes	complemented
508	#468	C₂²×C₂₃	1	4	yes	complemented
509	#466	C₂²×C₂₃	1	4	yes	complemented
510	#465	C₂²×C₂₃	1	4	yes	complemented
511	#464	C₂²×C₂₃	1	4	yes	complemented
512	#463	C₂²×C₂₃	1	4	yes	complemented
513	#461	C₂²×C₂₃	1	2	yes	complemented
514	#459	C₂²×C₂₃	1	2	yes	complemented
515	#452	C₂²×C₂₃	1	4	yes	complemented
516	#452	C₂²×C₂₃	1	4	yes	complemented
517	#451	C₂²×C₂₃	1	2	yes	complemented
518	#450	C₂²×C₂₃	1	2	yes	—
519	#450	C₂²×C₂₃	1	2	yes	—
520	#450	C₂²×C₂₃	1	4	yes	complemented
521	#449	C₂²×C₂₃	1	4	yes	complemented
522	#449	C₂²×C₂₃	1	4	yes	complemented
523	#448	C₂²×C₂₃	1	2	yes	complemented
524	#447	C₂²×C₂₃	1	2	yes	—
525	#447	C₂²×C₂₃	1	2	yes	—
526	#447	C₂²×C₂₃	1	4	yes	complemented
527	#442	C₂²×C₂₃	1	4	yes	complemented
528	#440	C₂²×C₂₃	1	4	yes	complemented
529	#435	C₂²×C₂₃	1	4	yes	complemented
530	#435	C₂²×C₂₃	1	4	yes	complemented
531	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
532	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
533	#418	C₂²×C₂₃	1	4	yes	complemented
534	#416	C₂²×C₂₃	1	4	yes	complemented
535	#407	C₂²×C₂₃	1	2	yes	—
536	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	complemented
537	C₂×C₂₃	—	2	2	no	—
538	C₂×C₂₃	—	4	2	no	—
539	C₂×C₂₃	—	4	2	no	—
540	C₂×C₂₃	—	4	4	no	—
541	C₂×C₂₃	—	8	2	no	—
542	C₂×C₂₃	—	8	2	no	—
543	C₂×C₂₃	#3484	1	1	yes	characteristic
544	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
545	C₂×C₂₃	#3585	1	1	yes	characteristic
546	C₂⁵	—	2	1	no	—
547	C₂×#41	—	2	1	no	—
548	C₂×#41	—	2	2	no	—
549	C₂×#41	—	4	4	no	—
550	C₂×#41	C₂³×C₂₃	1	4	yes	—
551	C₂×#41	C₂³×C₂₃	1	2	yes	—
552	C₂×#41	C₂³×C₂₃	1	2	yes	complemented
553	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
554	C₂²×D₄	—	2	1	no	—
555	C₂²×D₄	—	2	1	no	—
556	C₂²×D₄	—	2	1	no	—
557	C₂²×D₄	—	2	2	no	—
558	C₂²×D₄	—	4	4	no	—
559	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
560	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
561	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
562	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
563	C₂³×C₄	—	2	1	no	—
564	C₂³×C₄	—	2	1	no	—
565	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
566	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
567	AGL(1,ℤ/8)	—	4	8	no	—
568	#135	—	4	8	no	—
569	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	complemented
570	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
571	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
572	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	complemented
573	C₂×D₈	C₂³×C₂₃	1	4	yes	—
574	C₂×D₈	C₂³×C₂₃	1	4	yes	—
575	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
576	C₂²×C₈	C₂³×C₂₃	1	4	yes	complemented
577	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic, complemented
578	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic, complemented
579	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic, complemented
580	#127	—	2	2	no	—
581	#127	C₂³×C₂₃	1	1	yes	characteristic, complemented
582	#126	—	2	2	no	—
583	#126	—	2	2	no	—
584	#125	—	2	1	no	—
585	#124	—	2	2	no	—
586	#124	—	2	2	no	—
587	#124	—	2	2	no	—
588	#124	—	2	1	no	—
589	#124	—	2	1	no	—
590	#124	—	2	1	no	—
591	#124	C₂³×C₂₃	1	2	yes	—
592	#124	C₂³×C₂₃	1	2	yes	—
593	#123	—	2	2	no	—
594	#123	—	2	2	no	—
595	#123	—	2	4	no	—
596	#123	—	2	4	no	—
597	#123	—	2	2	no	—
598	#123	—	2	2	no	—
599	C₂²⋊Q₈	—	2	2	no	—
600	C₂²⋊Q₈	—	2	1	no	—
601	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
602	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
603	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
604	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	complemented
605	#121	—	2	2	no	—
606	#121	—	2	2	no	—
607	#121	—	2	2	no	—
608	#121	—	2	1	no	—
609	#121	—	2	4	no	—
610	#121	—	2	4	no	—
611	#121	—	2	2	no	—
612	#121	—	2	2	no	—
613	#121	C₂³×C₂₃	1	4	yes	—
614	#121	C₂³×C₂₃	1	2	yes	—
615	#121	C₂³×C₂₃	1	2	yes	—
616	#121	C₂³×C₂₃	1	2	yes	complemented
617	#120	—	2	2	no	—
618	#120	—	2	2	no	—
619	#120	—	2	4	no	—
620	#120	—	2	4	no	—
621	C₄×Q₈	—	2	2	no	—
622	C₄×Q₈	—	2	1	no	—
623	C₄×Q₈	C₂³×C₂₃	1	2	yes	complemented
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	—	2	2	no	—
626	C₄×D₄	—	2	2	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	1	no	—
630	C₄×D₄	—	2	1	no	—
631	C₄×D₄	—	2	1	no	—
632	C₄×D₄	D₄×C₂₃	1	2	yes	—
633	C₄×D₄	D₄×C₂₃	1	2	yes	—
634	C₄×D₄	C₂³×C₂₃	1	2	yes	—
635	C₄×D₄	C₂³×C₂₃	1	2	yes	—
636	C₄×D₄	C₂³×C₂₃	1	2	yes	—
637	C₄×D₄	C₂³×C₂₃	1	2	yes	—
638	C₄×D₄	C₂³×C₂₃	1	2	yes	complemented
639	#117	—	2	1	no	—
640	#117	—	2	2	no	—
641	#117	C₂³×C₂₃	1	2	yes	—
642	#117	C₂³×C₂₃	1	2	yes	complemented
643	C₂×C₄⋊C₄	—	2	1	no	—
644	C₂×C₄⋊C₄	—	2	2	no	—
645	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
646	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	—	2	1	no	—
648	C₂×C₂²⋊C₄	—	2	1	no	—
649	C₂×C₂²⋊C₄	—	2	1	no	—
650	C₂×C₂²⋊C₄	—	2	1	no	—
651	C₂×C₂²⋊C₄	—	2	1	no	—
652	C₂×C₂²⋊C₄	—	2	4	no	—
653	C₂×C₂²⋊C₄	—	2	4	no	—
654	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
655	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
657	#107	C₂³×C₂₃	1	4	yes	complemented
658	#106	C₂³×C₂₃	1	4	yes	complemented
659	C₄⋊C₈	C₂³×C₂₃	1	2	yes	complemented
660	C₄⋊C₈	C₂³×C₂₃	1	2	yes	complemented
661	#103	C₂³×C₂₃	1	4	yes	complemented
662	#103	C₂³×C₂₃	1	4	yes	complemented
663	#103	C₂³×C₂₃	1	4	yes	complemented
664	#102	C₂³×C₂₃	1	4	yes	—
665	#102	C₂³×C₂₃	1	4	yes	—
666	#102	C₂³×C₂₃	1	4	yes	—
667	#102	C₂³×C₂₃	1	4	yes	—
668	#102	C₂³×C₂₃	1	4	yes	complemented
669	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
670	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
671	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
672	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	complemented
673	#97	C₂³×C₂₃	1	2	yes	complemented
674	#97	C₂³×C₂₃	1	2	yes	complemented
675	C₂₃	#61576	1	1	yes	characteristic, direct product factor, Sylow
676	C₂⁴	—	2	1	no	—
677	C₂⁴	—	2	1	no	—
678	C₂⁴	—	2	4	no	—
679	C₂⁴	—	4	4	no	—
680	C₂⁴	—	4	4	no	—
681	C₂⁴	—	8	2	no	—
682	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
683	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
684	#41	—	2	8	no	—
685	#41	—	4	4	no	—
686	#41	—	4	4	no	—
687	#41	—	4	4	no	—
688	#41	—	4	4	no	—
689	#41	—	4	8	no	—
690	C₂×Q₈	—	2	1	no	—
691	C₂×Q₈	—	2	1	no	—
692	C₂×Q₈	—	2	1	no	—
693	C₂×Q₈	—	4	2	no	—
694	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
695	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	8	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	2	no	—
701	C₂×D₄	—	2	2	no	—
702	C₂×D₄	—	2	4	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	2	no	—
705	C₂×D₄	—	2	1	no	—
706	C₂×D₄	—	2	1	no	—
707	C₂×D₄	—	2	4	no	—
708	C₂×D₄	—	2	1	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	4	4	no	—
711	C₂×D₄	—	4	2	no	—
712	C₂×D₄	—	4	2	no	—
713	C₂×D₄	—	4	8	no	—
714	C₂×D₄	—	4	4	no	—
715	C₂×D₄	—	4	4	no	—
716	C₂×D₄	—	8	2	no	—
717	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
718	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
719	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
720	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
721	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	1	no	—
724	C₂²×C₄	—	2	4	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	4	2	no	—
731	C₂²×C₄	—	4	2	no	—
732	C₂²×C₄	—	4	4	no	—
733	C₂²×C₄	—	8	2	no	—
734	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
735	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
736	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
737	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
738	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
739	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
742	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
743	Q₁₆	—	4	4	no	—
744	SD₁₆	—	2	8	no	—
745	SD₁₆	—	4	4	no	—
746	SD₁₆	—	4	4	no	—
747	D₈	—	2	8	no	—
748	D₈	—	4	4	no	—
749	M₁₆	—	4	4	no	—
750	C₂×C₈	—	4	4	no	—
751	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
752	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
753	C₄⋊C₄	—	2	1	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	1	no	—
758	C₄⋊C₄	—	2	1	no	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	1	no	—
761	C₄⋊C₄	—	2	1	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
764	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
765	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
766	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
767	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
768	C₂²⋊C₄	—	2	4	no	—
769	C₂²⋊C₄	—	2	2	no	—
770	C₂²⋊C₄	—	2	2	no	—
771	C₂²⋊C₄	—	2	2	no	—
772	C₂²⋊C₄	—	2	2	no	—
773	C₂²⋊C₄	—	2	2	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	2	no	—
780	C₂²⋊C₄	—	2	2	no	—
781	C₂²⋊C₄	—	2	2	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
786	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
787	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
788	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
789	C₄²	—	2	2	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	2	no	—
792	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
793	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
794	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
795	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
796	C₂³	—	2	4	no	—
797	C₂³	—	2	2	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	2	2	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	4	1	no	—
803	C₂³	—	4	1	no	—
804	C₂³	—	4	1	no	—
805	C₂³	—	4	1	no	—
806	C₂³	—	4	8	no	—
807	C₂³	—	4	2	no	—
808	C₂³	—	4	2	no	—
809	C₂³	—	4	2	no	—
810	C₂³	—	4	8	no	—
811	C₂³	—	4	2	no	—
812	C₂³	—	4	2	no	—
813	C₂³	—	8	4	no	—
814	C₂³	—	8	16	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	4	no	—
819	Q₈	—	2	4	no	—
820	Q₈	—	4	2	no	—
821	Q₈	—	4	2	no	—
822	Q₈	—	8	1	no	—
823	D₄	—	2	4	no	—
824	D₄	—	2	2	no	—
825	D₄	—	2	4	no	—
826	D₄	—	2	4	no	—
827	D₄	—	4	2	no	—
828	D₄	—	4	2	no	—
829	D₄	—	4	8	no	—
830	D₄	—	4	2	no	—
831	D₄	—	4	2	no	—
832	D₄	—	4	8	no	—
833	D₄	—	4	4	no	—
834	D₄	—	8	1	no	—
835	D₄	—	8	4	no	—
836	D₄	—	8	2	no	—
837	D₄	—	8	2	no	—
838	D₄	—	8	2	no	—
839	D₄	—	8	2	no	—
840	D₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	4	no	—
843	C₂×C₄	—	2	4	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	4	1	no	—
851	C₂×C₄	—	4	2	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	2	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	8	no	—
856	C₂×C₄	—	4	4	no	—
857	C₂×C₄	—	4	2	no	—
858	C₂×C₄	—	4	2	no	—
859	C₂×C₄	—	8	2	no	—
860	C₂×C₄	—	8	2	no	—
861	C₂×C₄	—	8	2	no	—
862	C₂×C₄	—	8	2	no	—
863	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
864	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
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	C₂⁵×C₂₃	1	1	yes	characteristic
871	C₈	—	2	4	no	—
872	C₈	—	2	4	no	—
873	C₂²	—	2	1	no	—
874	C₂²	—	2	1	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	2	2	no	—
877	C₂²	—	2	4	no	—
878	C₂²	—	2	2	no	—
879	C₂²	—	2	2	no	—
880	C₂²	—	2	2	no	—
881	C₂²	—	2	2	no	—
882	C₂²	—	4	4	no	—
883	C₂²	—	4	8	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	4	2	no	—
890	C₂²	—	4	2	no	—
891	C₂²	—	4	2	no	—
892	C₂²	—	8	2	no	—
893	C₂²	—	8	4	no	—
894	C₂²	—	8	16	no	—
895	C₂²	C₂₃×#575	1	2	yes	—
896	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
897	C₄	—	2	2	no	—
898	C₄	—	2	1	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	1	no	—
901	C₄	—	2	1	no	—
902	C₄	—	2	1	no	—
903	C₄	—	2	1	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	2	no	—
907	C₄	—	4	2	no	—
908	C₄	—	4	2	no	—
909	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
910	C₂	—	2	2	no	—
911	C₂	—	4	2	no	—
912	C₂	—	4	2	no	—
913	C₂	—	4	4	no	—
914	C₂	—	8	2	no	—
915	C₂	—	8	2	no	—
916	C₂	C₂₃×#3484	1	1	yes	characteristic
917	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
918	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 ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3506	C₂	semidirect
2. C₂×C₂₃×#546	C₂	semidirect
3. C₂₃×#3319	C₂	semidirect
4. C₂₃×#3311	C₂	semidirect
5. C₂₃×#3268	C₂	semidirect
6. C₂₃×#3267	C₂	semidirect
7. C₂₃×#3215	C₂	semidirect
8. C₂₃×#3213	C₂	semidirect
9. C₂₃×#3196	C₂	semidirect
10. C₂₃×#3188	C₂	semidirect
11. C₂₃×#3110	C₂	semidirect
12. C₂₃×#3109	C₂	semidirect
13. C₂₃×#3003	C₂	semidirect
14. C₂₃×#3002	C₂	semidirect
15. C₂₃×#2973	C₂	semidirect
18. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
19. C₂×C₂₃×#135	C₂²	semidirect
21. C₂₃×#556	C₂²	semidirect
22. C₂₃×#555	C₂²	semidirect
24. C₂₃×#550	C₂²	semidirect
25. C₂₃×#547	C₂²	semidirect
33. C₂₃×#533	C₂²	semidirect
34. C₂₃×#532	C₂²	semidirect
37. C₂₃×#525	C₂²	semidirect
47. C₂₃×#497	C₂²	semidirect
48. C₂₃×#496	C₂²	semidirect
49. C₂₃×#489	C₂²	semidirect
50. C₂₃×#489	C₂²	semidirect
51. C₂₃×#485	C₂²	semidirect
52. C₂₃×#484	C₂²	semidirect
53. C₂₃×#482	C₂²	semidirect
54. C₂₃×#481	C₂²	semidirect
55. C₂₃×#476	C₂²	semidirect
56. C₂₃×#474	C₂²	semidirect
57. C₂₃×#470	C₂²	semidirect
58. C₂₃×#468	C₂²	semidirect
59. C₂₃×#466	C₂²	semidirect
60. C₂₃×#465	C₂²	semidirect
61. C₂₃×#464	C₂²	semidirect
62. C₂₃×#463	C₂²	semidirect
63. C₂₃×#461	C₂²	semidirect
64. C₂₃×#459	C₂²	semidirect
65. C₂₃×#452	C₂²	semidirect
66. C₂₃×#452	C₂²	semidirect
67. C₂₃×#451	C₂²	semidirect
70. C₂₃×#450	C₂²	semidirect
71. C₂₃×#449	C₂²	semidirect
72. C₂₃×#449	C₂²	semidirect
73. C₂₃×#448	C₂²	semidirect
76. C₂₃×#447	C₂²	semidirect
77. C₂₃×#442	C₂²	semidirect
78. C₂₃×#440	C₂²	semidirect
79. C₂₃×#435	C₂²	semidirect
80. C₂₃×#435	C₂²	semidirect
81. C₂₃×#432	C₂²	semidirect
82. C₂₃×#432	C₂²	semidirect
83. C₂₃×#418	C₂²	semidirect
84. C₂₃×#416	C₂²	semidirect
86. C₂×C₂₃×C₂²⋊C₈	C₂²	semidirect
93. C₂×#41×C₂₃	C₂³	semidirect
110. C₂×Q₁₆×C₂₃	C₂³	semidirect
113. C₂×SD₁₆×C₂₃	C₂³	semidirect
117. C₂²×C₈×C₂₃	C₂³	semidirect
118. C₂₃×C₄⋊Q₈	C₂³	semidirect
119. C₂₃×C₄⋊Q₈	C₂³	semidirect
120. C₂₃×C₄⋊Q₈	C₂³	semidirect
122. C₂₃×#127	C₂³	semidirect
145. C₂₃×C₂²⋊Q₈	C₂³	semidirect
157. C₂₃×#121	C₂³	semidirect
164. C₄×Q₈×C₂₃	C₂³	semidirect
179. C₄×D₄×C₂₃	C₂³	semidirect
183. C₂₃×#117	C₂³	semidirect
198. C₂₃×#107	C₂³	semidirect
199. C₂₃×#106	C₂³	semidirect
200. C₂₃×C₄⋊C₈	C₂³	semidirect
201. C₂₃×C₄⋊C₈	C₂³	semidirect
202. C₂₃×#103	C₂³	semidirect
203. C₂₃×#103	C₂³	semidirect
204. C₂₃×#103	C₂³	semidirect
209. C₂₃×#102	C₂³	semidirect
213. C₂₃×C₂²⋊C₈	C₂³	semidirect
214. C₂₃×#97	C₂³	semidirect
215. C₂₃×#97	C₂³	semidirect
336. #61576	C₂₃	direct (N × H)
414. #3506	C₂×C₂₃	semidirect
415. C₂×#546	C₂×C₂₃	semidirect
416. #3319	C₂×C₂₃	semidirect
417. #3311	C₂×C₂₃	semidirect
418. #3268	C₂×C₂₃	semidirect
419. #3267	C₂×C₂₃	semidirect
420. #3215	C₂×C₂₃	semidirect
421. #3213	C₂×C₂₃	semidirect
422. #3196	C₂×C₂₃	semidirect
423. #3188	C₂×C₂₃	semidirect
424. #3110	C₂×C₂₃	semidirect
425. #3109	C₂×C₂₃	semidirect
426. #3003	C₂×C₂₃	semidirect
427. #3002	C₂×C₂₃	semidirect
428. #2973	C₂×C₂₃	semidirect
468. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
469. C₂×#135	C₂²×C₂₃	semidirect
471. #556	C₂²×C₂₃	semidirect
472. #555	C₂²×C₂₃	semidirect
474. #550	C₂²×C₂₃	semidirect
475. #547	C₂²×C₂₃	semidirect
483. #533	C₂²×C₂₃	semidirect
484. #532	C₂²×C₂₃	semidirect
487. #525	C₂²×C₂₃	semidirect
497. #497	C₂²×C₂₃	semidirect
498. #496	C₂²×C₂₃	semidirect
499. #489	C₂²×C₂₃	semidirect
500. #489	C₂²×C₂₃	semidirect
501. #485	C₂²×C₂₃	semidirect
502. #484	C₂²×C₂₃	semidirect
503. #482	C₂²×C₂₃	semidirect
504. #481	C₂²×C₂₃	semidirect
505. #476	C₂²×C₂₃	semidirect
506. #474	C₂²×C₂₃	semidirect
507. #470	C₂²×C₂₃	semidirect
508. #468	C₂²×C₂₃	semidirect
509. #466	C₂²×C₂₃	semidirect
510. #465	C₂²×C₂₃	semidirect
511. #464	C₂²×C₂₃	semidirect
512. #463	C₂²×C₂₃	semidirect
513. #461	C₂²×C₂₃	semidirect
514. #459	C₂²×C₂₃	semidirect
515. #452	C₂²×C₂₃	semidirect
516. #452	C₂²×C₂₃	semidirect
517. #451	C₂²×C₂₃	semidirect
520. #450	C₂²×C₂₃	semidirect
521. #449	C₂²×C₂₃	semidirect
522. #449	C₂²×C₂₃	semidirect
523. #448	C₂²×C₂₃	semidirect
526. #447	C₂²×C₂₃	semidirect
527. #442	C₂²×C₂₃	semidirect
528. #440	C₂²×C₂₃	semidirect
529. #435	C₂²×C₂₃	semidirect
530. #435	C₂²×C₂₃	semidirect
531. #432	C₂²×C₂₃	semidirect
532. #432	C₂²×C₂₃	semidirect
533. #418	C₂²×C₂₃	semidirect
534. #416	C₂²×C₂₃	semidirect
536. C₂×C₂²⋊C₈	C₂²×C₂₃	semidirect
552. C₂×#41	C₂³×C₂₃	semidirect
569. C₂×Q₁₆	C₂³×C₂₃	semidirect
572. C₂×SD₁₆	C₂³×C₂₃	semidirect
576. C₂²×C₈	C₂³×C₂₃	semidirect
577. C₄⋊Q₈	C₂³×C₂₃	semidirect
578. C₄⋊Q₈	C₂³×C₂₃	semidirect
579. C₄⋊Q₈	C₂³×C₂₃	semidirect
581. #127	C₂³×C₂₃	semidirect
604. C₂²⋊Q₈	C₂³×C₂₃	semidirect
616. #121	C₂³×C₂₃	semidirect
623. C₄×Q₈	C₂³×C₂₃	semidirect
638. C₄×D₄	C₂³×C₂₃	semidirect
642. #117	C₂³×C₂₃	semidirect
657. #107	C₂³×C₂₃	semidirect
658. #106	C₂³×C₂₃	semidirect
659. C₄⋊C₈	C₂³×C₂₃	semidirect
660. C₄⋊C₈	C₂³×C₂₃	semidirect
661. #103	C₂³×C₂₃	semidirect
662. #103	C₂³×C₂₃	semidirect
663. #103	C₂³×C₂₃	semidirect
668. #102	C₂³×C₂₃	semidirect
672. C₂²⋊C₈	C₂³×C₂₃	semidirect
673. #97	C₂³×C₂₃	semidirect
674. #97	C₂³×C₂₃	semidirect
675. C₂₃	#61576	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×#3506	2
C₂×C₂₃×#546	2
C₂₃×#3319	2
C₂₃×#3311	2
C₂₃×#3268	2
C₂₃×#3267	2
C₂₃×#3215	2
C₂₃×#3213	2
C₂₃×#3196	2
C₂₃×#3188	2
C₂₃×#3110	2
C₂₃×#3109	2
C₂₃×#3003	2
C₂₃×#3002	2
C₂₃×#2973	2
#61576	23

Subgroups — C23×#61576 #19209202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61576 #19209202