Subgroups — C₂₃×#61735 #19209361

Order 5888.

1796 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3520	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3356	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3344	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3335	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3331	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3316	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3299	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3238	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3229	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3195	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3190	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3113	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#3092	C₂	1	2	yes	maximal, complemented
16	C₂×C₂₃×#483	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#556	C₂²	1	1	yes	characteristic
19	C₂₃×#554	—	2	1	no	—
20	C₂₃×#554	—	2	2	no	—
21	C₂₃×#554	—	2	1	no	—
22	C₂₃×#554	—	2	1	no	—
23	C₂₃×#554	C₂²	1	2	yes	—
24	C₂₃×#554	C₂²	1	4	yes	—
25	C₂₃×#554	C₂²	1	2	yes	—
26	C₂₃×#552	C₂²	1	2	yes	—
27	C₂₃×#551	—	2	2	no	—
28	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₂₃×#548	C₂²	1	2	yes	—
30	C₂₃×#547	C₂²	1	1	yes	characteristic
31	C₂₃×#547	C₂²	1	1	yes	characteristic
32	C₂₃×#546	—	2	1	no	—
33	C₂₃×#542	—	2	1	no	—
34	C₂₃×#539	—	2	2	no	—
35	C₂₃×#533	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
37	C₂₃×#529	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#125	—	2	1	no	—
39	C₂₃×#525	C₂²	1	2	yes	—
40	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
41	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
42	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
43	C₂₃×#520	—	2	1	no	—
44	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₂₃	—	2	1	no	—
46	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
48	C₂₃×#501	C₂²	1	2	yes	complemented
49	C₂₃×#498	C₂²	1	2	yes	complemented
50	C₂₃×#489	C₂²	1	2	yes	complemented
51	C₂₃×#487	C₂²	1	2	yes	complemented
52	C₂₃×#485	C₂²	1	4	yes	complemented
53	C₂₃×#484	C₂²	1	4	yes	complemented
54	C₂₃×#483	C₂²	1	2	yes	—
55	C₂₃×#483	C₂²	1	2	yes	—
56	C₂₃×#483	C₂²	1	2	yes	—
57	C₂₃×#483	C₂²	1	1	yes	characteristic
58	C₂₃×#483	C₂²	1	2	yes	—
59	C₂₃×#483	C₂²	1	4	yes	complemented
60	C₂₃×#483	C₂²	1	4	yes	complemented
61	C₂₃×#483	C₂²	1	4	yes	complemented
62	C₂₃×#481	C₂²	1	4	yes	complemented
63	C₂₃×#480	C₂²	1	2	yes	—
64	C₂₃×#480	C₂²	1	1	yes	characteristic
65	C₂₃×#479	C₂²	1	2	yes	complemented
66	C₂₃×#477	C₂²	1	2	yes	complemented
67	C₂₃×#476	C₂²	1	2	yes	complemented
68	C₂₃×#475	C₂²	1	4	yes	complemented
69	C₂₃×#475	C₂²	1	2	yes	complemented
70	C₂₃×#470	C₂²	1	4	yes	complemented
71	C₂₃×#470	C₂²	1	4	yes	complemented
72	C₂₃×#467	C₂²	1	4	yes	complemented
73	C₂₃×#465	C₂²	1	4	yes	complemented
74	C₂₃×#464	C₂²	1	2	yes	complemented
75	C₂₃×#462	C₂²	1	2	yes	complemented
76	C₂₃×#452	C₂²	1	4	yes	complemented
77	C₂₃×#451	C₂²	1	2	yes	—
78	C₂₃×#451	C₂²	1	1	yes	characteristic
79	C₂₃×#451	C₂²	1	4	yes	complemented
80	C₂₃×#448	C₂²	1	1	yes	characteristic
81	C₂₃×#441	C₂²	1	4	yes	complemented
82	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
83	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
84	C₂₃×#436	C₂²	1	2	yes	—
85	C₂₃×#435	C₂²	1	4	yes	—
86	C₈×D₄×C₂₃	C₂²	1	2	yes	—
87	C₂₃×#432	C₂²	1	1	yes	characteristic
88	C₂₃×#431	C₂²	1	1	yes	characteristic
89	C₂₃×#428	C₂²	1	4	yes	complemented
90	C₂×C₂₃×#106	C₂²	1	4	yes	complemented
91	C₂₃×#417	C₂²	1	4	yes	complemented
92	C₂×C₂₃×#103	C₂²	1	4	yes	complemented
93	C₂₃×#407	C₂²	1	2	yes	—
94	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
95	C₂×#41×C₂₃	—	2	1	no	—
96	C₂×#41×C₂₃	C₂³	1	2	yes	—
97	C₂²×Q₈×C₂₃	—	2	1	no	—
98	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
99	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
100	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
101	C₂³×C₄×C₂₃	—	2	2	no	—
102	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
103	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
104	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
105	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
106	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
107	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
108	C₂₃×C₄⋊Q₈	—	2	1	no	—
109	C₂₃×C₄⋊Q₈	—	2	1	no	—
110	C₂₃×C₄⋊Q₈	—	2	1	no	—
111	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₂₃×#126	—	2	2	no	—
116	C₂₃×#126	—	2	2	no	—
117	C₂₃×#126	—	2	1	no	—
118	C₂₃×#125	—	2	2	no	—
119	C₂₃×#125	—	2	2	no	—
120	C₂₃×#125	—	2	4	no	—
121	C₂₃×#125	—	2	2	no	—
122	C₂₃×#125	—	2	1	no	—
123	C₂₃×#125	C₂³	1	1	yes	characteristic
124	C₂₃×#124	—	2	1	no	—
125	C₂₃×#124	—	2	2	no	—
126	C₂₃×#124	C₂³	1	1	yes	characteristic
127	C₂₃×#123	—	2	2	no	—
128	C₂₃×#123	—	2	1	no	—
129	C₂₃×#123	—	2	2	no	—
130	C₂₃×#123	—	2	2	no	—
131	C₂₃×#123	—	2	2	no	—
132	C₂₃×C₂²⋊Q₈	—	2	2	no	—
133	C₂₃×C₂²⋊Q₈	—	2	2	no	—
134	C₂₃×C₂²⋊Q₈	—	2	2	no	—
135	C₂₃×C₂²⋊Q₈	—	2	1	no	—
136	C₂₃×C₂²⋊Q₈	—	2	2	no	—
137	C₂₃×C₂²⋊Q₈	—	2	1	no	—
138	C₂₃×C₂²⋊Q₈	—	2	2	no	—
139	C₂₃×C₂²⋊Q₈	—	2	2	no	—
140	C₂₃×C₂²⋊Q₈	—	2	4	no	—
141	C₂₃×C₂²⋊Q₈	—	2	4	no	—
142	C₂₃×C₂²⋊Q₈	—	2	4	no	—
143	C₂₃×C₂²⋊Q₈	—	2	4	no	—
144	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
145	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
148	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
149	C₂₃×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
150	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
151	C₂₃×#121	—	2	1	no	—
152	C₂₃×#121	—	2	2	no	—
153	C₂₃×#121	C₂³	1	2	yes	—
154	C₂₃×#121	C₂³	1	1	yes	characteristic
155	C₂₃×#120	—	2	2	no	—
156	C₄×Q₈×C₂₃	—	2	1	no	—
157	C₄×Q₈×C₂₃	—	2	1	no	—
158	C₄×Q₈×C₂₃	—	2	1	no	—
159	C₄×Q₈×C₂₃	—	2	1	no	—
160	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
161	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
162	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
163	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
164	C₄×D₄×C₂₃	—	2	1	no	—
165	C₄×D₄×C₂₃	—	2	4	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	1	no	—
170	C₄×D₄×C₂₃	—	2	2	no	—
171	C₄×D₄×C₂₃	—	2	2	no	—
172	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
173	C₄×D₄×C₂₃	D₄	1	2	yes	—
174	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
175	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₂₃	C₂³	1	2	yes	—
179	C₂₃×#117	—	2	1	no	—
180	C₂₃×#117	—	2	2	no	—
181	C₂₃×#117	—	2	1	no	—
182	C₂₃×#117	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
184	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
185	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
186	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
187	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
188	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
189	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
190	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
191	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
192	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
194	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
195	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
198	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
199	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
200	C₂×C₄²×C₂₃	—	2	1	no	—
201	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
202	C₂₃×#107	C₂³	1	2	yes	—
203	C₂₃×#107	C₂³	1	4	yes	—
204	C₂₃×#106	C₂³	1	2	yes	—
205	C₂₃×#106	C₂³	1	4	yes	—
206	C₂₃×#106	C₂³	1	4	yes	—
207	C₂₃×#106	C₂³	1	4	yes	—
208	C₂₃×#106	C₂³	1	4	yes	—
209	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
210	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
211	C₂₃×#103	C₂³	1	2	yes	—
212	C₂₃×#103	C₂³	1	4	yes	—
213	C₂₃×#103	C₂³	1	4	yes	—
214	C₂₃×#103	C₂³	1	4	yes	—
215	C₂₃×#103	C₂³	1	4	yes	—
216	C₂₃×#103	C₂³	1	2	yes	—
217	C₂₃×#103	C₂³	1	2	yes	—
218	C₂₃×#103	C₂³	1	4	yes	—
219	C₂₃×#102	C₂³	1	2	yes	—
220	C₂₃×#102	C₂³	1	4	yes	—
221	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
222	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
223	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
224	C₂₃×C₂²⋊C₈	C₂³	1	1	yes	characteristic
225	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₂₃×#97	C₂³	1	2	yes	—
227	C₄×C₈×C₂₃	C₂³	1	2	yes	—
228	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
229	#41×C₂₃	—	4	4	no	—
230	#41×C₂₃	—	4	4	no	—
231	C₂×Q₈×C₂₃	—	2	1	no	—
232	C₂×Q₈×C₂₃	—	2	1	no	—
233	C₂×Q₈×C₂₃	—	2	2	no	—
234	C₂×Q₈×C₂₃	—	2	2	no	—
235	C₂×Q₈×C₂₃	—	2	2	no	—
236	C₂×Q₈×C₂₃	—	4	2	no	—
237	C₂×Q₈×C₂₃	—	4	4	no	—
238	C₂×Q₈×C₂₃	—	8	2	no	—
239	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
241	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
242	C₂×D₄×C₂₃	—	2	4	no	—
243	C₂×D₄×C₂₃	—	2	1	no	—
244	C₂×D₄×C₂₃	—	2	2	no	—
245	C₂×D₄×C₂₃	—	2	2	no	—
246	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
247	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
248	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
249	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₂₃	—	2	1	no	—
251	C₂²×C₄×C₂₃	—	2	1	no	—
252	C₂²×C₄×C₂₃	—	2	2	no	—
253	C₂²×C₄×C₂₃	—	2	2	no	—
254	C₂²×C₄×C₂₃	—	2	2	no	—
255	C₂²×C₄×C₂₃	—	2	4	no	—
256	C₂²×C₄×C₂₃	—	2	4	no	—
257	C₂²×C₄×C₂₃	—	2	1	no	—
258	C₂²×C₄×C₂₃	—	2	2	no	—
259	C₂²×C₄×C₂₃	—	4	4	no	—
260	C₂²×C₄×C₂₃	—	8	4	no	—
261	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
264	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
265	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
266	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
269	Q₁₆×C₂₃	—	4	4	no	—
270	Q₁₆×C₂₃	—	4	2	no	—
271	SD₁₆×C₂₃	—	4	2	no	—
272	M₁₆×C₂₃	—	4	4	no	—
273	C₂×C₈×C₂₃	—	4	4	no	—
274	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
275	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
276	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₂₃	—	2	1	no	—
278	C₄⋊C₄×C₂₃	—	2	4	no	—
279	C₄⋊C₄×C₂₃	—	2	4	no	—
280	C₄⋊C₄×C₂₃	—	2	2	no	—
281	C₄⋊C₄×C₂₃	—	2	1	no	—
282	C₄⋊C₄×C₂₃	—	2	2	no	—
283	C₄⋊C₄×C₂₃	—	2	2	no	—
284	C₄⋊C₄×C₂₃	—	2	2	no	—
285	C₄⋊C₄×C₂₃	—	2	1	no	—
286	C₄⋊C₄×C₂₃	—	2	2	no	—
287	C₄⋊C₄×C₂₃	—	2	2	no	—
288	C₄⋊C₄×C₂₃	—	2	2	no	—
289	C₄⋊C₄×C₂₃	—	2	2	no	—
290	C₄⋊C₄×C₂₃	—	2	4	no	—
291	C₄⋊C₄×C₂₃	—	2	4	no	—
292	C₄⋊C₄×C₂₃	—	2	2	no	—
293	C₄⋊C₄×C₂₃	—	2	1	no	—
294	C₄⋊C₄×C₂₃	—	2	1	no	—
295	C₄⋊C₄×C₂₃	—	2	1	no	—
296	C₄⋊C₄×C₂₃	—	2	2	no	—
297	C₄⋊C₄×C₂₃	—	2	1	no	—
298	C₄⋊C₄×C₂₃	—	2	2	no	—
299	C₄⋊C₄×C₂₃	—	2	1	no	—
300	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
301	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
303	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
304	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
305	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
307	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
308	C₂²⋊C₄×C₂₃	—	2	1	no	—
309	C₂²⋊C₄×C₂₃	—	2	2	no	—
310	C₂²⋊C₄×C₂₃	—	2	4	no	—
311	C₂²⋊C₄×C₂₃	—	2	4	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	1	no	—
317	C₂²⋊C₄×C₂₃	—	2	1	no	—
318	C₂²⋊C₄×C₂₃	—	2	1	no	—
319	C₂²⋊C₄×C₂₃	—	2	2	no	—
320	C₂²⋊C₄×C₂₃	—	2	1	no	—
321	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
322	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
323	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
324	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
325	C₄²×C₂₃	—	2	2	no	—
326	C₄²×C₂₃	—	2	2	no	—
327	C₄²×C₂₃	—	2	2	no	—
328	C₄²×C₂₃	—	2	2	no	—
329	C₄²×C₂₃	—	2	1	no	—
330	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
333	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
334	#61735	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
335	C₂³×C₂₃	—	2	4	no	—
336	C₂³×C₂₃	—	2	4	no	—
337	C₂³×C₂₃	—	2	1	no	—
338	C₂³×C₂₃	—	4	2	no	—
339	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
340	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
341	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
342	Q₈×C₂₃	—	2	2	no	—
343	Q₈×C₂₃	—	2	2	no	—
344	Q₈×C₂₃	—	2	2	no	—
345	Q₈×C₂₃	—	2	4	no	—
346	Q₈×C₂₃	—	4	2	no	—
347	Q₈×C₂₃	—	4	2	no	—
348	Q₈×C₂₃	—	8	2	no	—
349	Q₈×C₂₃	—	8	2	no	—
350	Q₈×C₂₃	—	8	2	no	—
351	D₄×C₂₃	—	2	4	no	—
352	D₄×C₂₃	—	2	2	no	—
353	D₄×C₂₃	—	2	2	no	—
354	D₄×C₂₃	—	4	4	no	—
355	D₄×C₂₃	—	4	2	no	—
356	D₄×C₂₃	—	8	2	no	—
357	D₄×C₂₃	#137	1	4	yes	—
358	C₂×C₄×C₂₃	—	2	2	no	—
359	C₂×C₄×C₂₃	—	2	2	no	—
360	C₂×C₄×C₂₃	—	2	4	no	—
361	C₂×C₄×C₂₃	—	2	4	no	—
362	C₂×C₄×C₂₃	—	2	2	no	—
363	C₂×C₄×C₂₃	—	2	1	no	—
364	C₂×C₄×C₂₃	—	2	2	no	—
365	C₂×C₄×C₂₃	—	2	2	no	—
366	C₂×C₄×C₂₃	—	2	2	no	—
367	C₂×C₄×C₂₃	—	2	1	no	—
368	C₂×C₄×C₂₃	—	2	2	no	—
369	C₂×C₄×C₂₃	—	2	1	no	—
370	C₂×C₄×C₂₃	—	2	4	no	—
371	C₂×C₄×C₂₃	—	4	2	no	—
372	C₂×C₄×C₂₃	—	4	2	no	—
373	C₂×C₄×C₂₃	—	4	2	no	—
374	C₂×C₄×C₂₃	—	4	2	no	—
375	C₂×C₄×C₂₃	—	4	4	no	—
376	C₂×C₄×C₂₃	—	4	2	no	—
377	C₂×C₄×C₂₃	—	4	4	no	—
378	C₂×C₄×C₂₃	—	4	2	no	—
379	C₂×C₄×C₂₃	—	8	2	no	—
380	C₂×C₄×C₂₃	—	8	4	no	—
381	C₂×C₄×C₂₃	—	8	4	no	—
382	C₂×C₄×C₂₃	—	8	2	no	—
383	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
386	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
389	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
391	C₈×C₂₃	—	2	2	no	—
392	C₈×C₂₃	—	2	4	no	—
393	C₈×C₂₃	—	2	2	no	—
394	#3520	C₂×C₂₃	1	1	yes	characteristic
395	C₂×#554	C₂×C₂₃	1	1	yes	characteristic, complemented
396	#3356	C₂×C₂₃	1	2	yes	complemented
397	#3344	C₂×C₂₃	1	4	yes	complemented
398	#3335	C₂×C₂₃	1	2	yes	complemented
399	#3331	C₂×C₂₃	1	2	yes	complemented
400	#3316	C₂×C₂₃	1	4	yes	complemented
401	#3299	C₂×C₂₃	1	2	yes	complemented
402	#3238	C₂×C₂₃	1	1	yes	characteristic, complemented
403	#3229	C₂×C₂₃	1	1	yes	characteristic, complemented
404	#3195	C₂×C₂₃	1	2	yes	complemented
405	#3190	C₂×C₂₃	1	2	yes	complemented
406	#3113	C₂×C₂₃	1	1	yes	characteristic, complemented
407	#3108	C₂×C₂₃	1	1	yes	characteristic, complemented
408	#3092	C₂×C₂₃	1	2	yes	complemented
409	C₂×#483	C₂×C₂₃	1	2	yes	complemented
410	#2974	C₂×C₂₃	1	1	yes	characteristic, complemented
411	C₂²×C₂₃	—	2	1	no	—
412	C₂²×C₂₃	—	2	2	no	—
413	C₂²×C₂₃	—	2	1	no	—
414	C₂²×C₂₃	—	2	2	no	—
415	C₂²×C₂₃	—	2	2	no	—
416	C₂²×C₂₃	—	2	2	no	—
417	C₂²×C₂₃	—	2	2	no	—
418	C₂²×C₂₃	—	4	8	no	—
419	C₂²×C₂₃	—	4	1	no	—
420	C₂²×C₂₃	—	4	1	no	—
421	C₂²×C₂₃	—	4	1	no	—
422	C₂²×C₂₃	C₂×#137	1	4	yes	—
423	C₂²×C₂₃	#577	1	2	yes	—
424	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
425	C₄×C₂₃	—	2	1	no	—
426	C₄×C₂₃	—	2	2	no	—
427	C₄×C₂₃	—	2	2	no	—
428	C₄×C₂₃	—	2	1	no	—
429	C₄×C₂₃	—	2	1	no	—
430	C₄×C₂₃	—	2	1	no	—
431	C₄×C₂₃	—	4	2	no	—
432	C₄×C₂₃	—	4	2	no	—
433	C₄×C₂₃	—	4	1	no	—
434	C₄×C₂₃	—	4	1	no	—
435	C₄×C₂₃	—	4	2	no	—
436	C₄×C₂₃	—	4	2	no	—
437	C₄×C₂₃	—	4	4	no	—
438	C₄×C₂₃	—	4	1	no	—
439	C₄×C₂₃	C₂×#137	1	2	yes	—
440	C₄×C₂₃	#585	1	2	yes	—
441	#556	C₂²×C₂₃	1	1	yes	characteristic
442	#554	—	2	1	no	—
443	#554	—	2	2	no	—
444	#554	—	2	1	no	—
445	#554	—	2	1	no	—
446	#554	C₂²×C₂₃	1	2	yes	—
447	#554	C₂²×C₂₃	1	2	yes	—
448	#554	C₂²×C₂₃	1	4	yes	—
449	#552	C₂²×C₂₃	1	2	yes	—
450	#551	—	2	2	no	—
451	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
452	#548	C₂²×C₂₃	1	2	yes	—
453	#547	C₂²×C₂₃	1	1	yes	characteristic
454	#547	C₂²×C₂₃	1	1	yes	characteristic
455	#546	—	2	1	no	—
456	#542	—	2	1	no	—
457	#539	—	2	2	no	—
458	#533	C₂²×C₂₃	1	1	yes	characteristic
459	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
460	#529	C₂²×C₂₃	1	1	yes	characteristic
461	C₂×#125	—	2	1	no	—
462	#525	C₂²×C₂₃	1	2	yes	—
463	C₂×C₂²⋊Q₈	—	2	2	no	—
464	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
465	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
466	#520	—	2	1	no	—
467	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
468	C₂×C₄×D₄	—	2	1	no	—
469	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
470	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
471	#501	C₂²×C₂₃	1	2	yes	complemented
472	#498	C₂²×C₂₃	1	2	yes	complemented
473	#489	C₂²×C₂₃	1	2	yes	complemented
474	#487	C₂²×C₂₃	1	2	yes	complemented
475	#485	C₂²×C₂₃	1	4	yes	complemented
476	#484	C₂²×C₂₃	1	4	yes	complemented
477	#483	C₂²×C₂₃	1	1	yes	characteristic
478	#483	C₂²×C₂₃	1	2	yes	—
479	#483	C₂²×C₂₃	1	2	yes	—
480	#483	C₂²×C₂₃	1	2	yes	—
481	#483	C₂²×C₂₃	1	2	yes	—
482	#483	C₂²×C₂₃	1	4	yes	complemented
483	#483	C₂²×C₂₃	1	4	yes	complemented
484	#483	C₂²×C₂₃	1	4	yes	complemented
485	#481	C₂²×C₂₃	1	4	yes	complemented
486	#480	C₂²×C₂₃	1	1	yes	characteristic
487	#480	C₂²×C₂₃	1	2	yes	—
488	#479	C₂²×C₂₃	1	2	yes	complemented
489	#477	C₂²×C₂₃	1	2	yes	complemented
490	#476	C₂²×C₂₃	1	2	yes	complemented
491	#475	C₂²×C₂₃	1	2	yes	complemented
492	#475	C₂²×C₂₃	1	4	yes	complemented
493	#470	C₂²×C₂₃	1	4	yes	complemented
494	#470	C₂²×C₂₃	1	4	yes	complemented
495	#467	C₂²×C₂₃	1	4	yes	complemented
496	#465	C₂²×C₂₃	1	4	yes	complemented
497	#464	C₂²×C₂₃	1	2	yes	complemented
498	#462	C₂²×C₂₃	1	2	yes	complemented
499	#452	C₂²×C₂₃	1	4	yes	complemented
500	#451	C₂²×C₂₃	1	1	yes	characteristic
501	#451	C₂²×C₂₃	1	2	yes	—
502	#451	C₂²×C₂₃	1	4	yes	complemented
503	#448	C₂²×C₂₃	1	1	yes	characteristic
504	#441	C₂²×C₂₃	1	4	yes	complemented
505	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
506	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
507	#436	C₂²×C₂₃	1	2	yes	—
508	#435	C₂²×C₂₃	1	4	yes	—
509	C₈×D₄	C₂²×C₂₃	1	2	yes	—
510	#432	C₂²×C₂₃	1	1	yes	characteristic
511	#431	C₂²×C₂₃	1	1	yes	characteristic
512	#428	C₂²×C₂₃	1	4	yes	complemented
513	C₂×#106	C₂²×C₂₃	1	4	yes	complemented
514	#417	C₂²×C₂₃	1	4	yes	complemented
515	C₂×#103	C₂²×C₂₃	1	4	yes	complemented
516	#407	C₂²×C₂₃	1	2	yes	—
517	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
518	C₂×C₂₃	—	2	2	no	—
519	C₂×C₂₃	—	2	4	no	—
520	C₂×C₂₃	—	4	2	no	—
521	C₂×C₂₃	—	8	1	no	—
522	C₂×C₂₃	#3485	1	1	yes	characteristic
523	C₂×C₂₃	C₂²×#137	1	1	yes	characteristic
524	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
525	C₂×#41	—	2	1	no	—
526	C₂×#41	C₂³×C₂₃	1	2	yes	—
527	C₂²×Q₈	—	2	1	no	—
528	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
529	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
530	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
531	C₂³×C₄	—	2	2	no	—
532	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
533	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
534	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
535	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
536	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
537	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
538	C₄⋊Q₈	—	2	1	no	—
539	C₄⋊Q₈	—	2	1	no	—
540	C₄⋊Q₈	—	2	1	no	—
541	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
542	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
543	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
544	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
545	#126	—	2	2	no	—
546	#126	—	2	2	no	—
547	#126	—	2	1	no	—
548	#125	—	2	2	no	—
549	#125	—	2	4	no	—
550	#125	—	2	2	no	—
551	#125	—	2	2	no	—
552	#125	—	2	1	no	—
553	#125	C₂³×C₂₃	1	1	yes	characteristic
554	#124	—	2	1	no	—
555	#124	—	2	2	no	—
556	#124	C₂³×C₂₃	1	1	yes	characteristic
557	#123	—	2	2	no	—
558	#123	—	2	2	no	—
559	#123	—	2	1	no	—
560	#123	—	2	2	no	—
561	#123	—	2	2	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	—	2	1	no	—
567	C₂²⋊Q₈	—	2	2	no	—
568	C₂²⋊Q₈	—	2	1	no	—
569	C₂²⋊Q₈	—	2	4	no	—
570	C₂²⋊Q₈	—	2	4	no	—
571	C₂²⋊Q₈	—	2	4	no	—
572	C₂²⋊Q₈	—	2	4	no	—
573	C₂²⋊Q₈	—	2	2	no	—
574	C₂²⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
575	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
576	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
577	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
578	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
579	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
580	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
581	#121	—	2	2	no	—
582	#121	—	2	1	no	—
583	#121	C₂³×C₂₃	1	1	yes	characteristic
584	#121	C₂³×C₂₃	1	2	yes	—
585	#120	—	2	2	no	—
586	C₄×Q₈	—	2	1	no	—
587	C₄×Q₈	—	2	1	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	—	2	1	no	—
590	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
591	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
592	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
593	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
594	C₄×D₄	—	2	4	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	2	no	—
597	C₄×D₄	—	2	1	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	—	2	1	no	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
603	C₄×D₄	D₄×C₂₃	1	2	yes	—
604	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
605	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
606	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
607	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
608	C₄×D₄	C₂³×C₂₃	1	2	yes	—
609	#117	—	2	1	no	—
610	#117	—	2	2	no	—
611	#117	—	2	1	no	—
612	#117	C₂³×C₂₃	1	2	yes	—
613	C₂×C₄⋊C₄	—	2	2	no	—
614	C₂×C₄⋊C₄	—	2	2	no	—
615	C₂×C₄⋊C₄	—	2	2	no	—
616	C₂×C₄⋊C₄	—	2	1	no	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	—	2	2	no	—
619	C₂×C₄⋊C₄	—	2	2	no	—
620	C₂×C₄⋊C₄	—	2	1	no	—
621	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
622	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
623	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
624	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
625	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
626	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
627	C₂×C₂²⋊C₄	—	2	2	no	—
628	C₂×C₂²⋊C₄	—	2	2	no	—
629	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
630	C₂×C₄²	—	2	1	no	—
631	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
632	#107	C₂³×C₂₃	1	2	yes	—
633	#107	C₂³×C₂₃	1	4	yes	—
634	#106	C₂³×C₂₃	1	2	yes	—
635	#106	C₂³×C₂₃	1	4	yes	—
636	#106	C₂³×C₂₃	1	4	yes	—
637	#106	C₂³×C₂₃	1	4	yes	—
638	#106	C₂³×C₂₃	1	4	yes	—
639	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
640	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
641	#103	C₂³×C₂₃	1	2	yes	—
642	#103	C₂³×C₂₃	1	4	yes	—
643	#103	C₂³×C₂₃	1	4	yes	—
644	#103	C₂³×C₂₃	1	4	yes	—
645	#103	C₂³×C₂₃	1	4	yes	—
646	#103	C₂³×C₂₃	1	2	yes	—
647	#103	C₂³×C₂₃	1	2	yes	—
648	#103	C₂³×C₂₃	1	4	yes	—
649	#102	C₂³×C₂₃	1	2	yes	—
650	#102	C₂³×C₂₃	1	4	yes	—
651	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
652	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
653	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
654	C₂²⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
655	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
656	#97	C₂³×C₂₃	1	2	yes	—
657	C₄×C₈	C₂³×C₂₃	1	2	yes	—
658	C₂₃	#61735	1	1	yes	characteristic, direct product factor, Sylow
659	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
660	#41	—	4	4	no	—
661	#41	—	4	4	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	2	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	4	2	no	—
668	C₂×Q₈	—	4	4	no	—
669	C₂×Q₈	—	8	2	no	—
670	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
671	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
672	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	2	1	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
678	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
679	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
680	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	—	2	4	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	4	4	no	—
691	C₂²×C₄	—	8	4	no	—
692	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
693	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
694	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
695	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
696	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
700	Q₁₆	—	4	4	no	—
701	Q₁₆	—	4	2	no	—
702	SD₁₆	—	4	2	no	—
703	M₁₆	—	4	4	no	—
704	C₂×C₈	—	4	4	no	—
705	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
706	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
707	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	4	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	1	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
732	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
733	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
734	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
735	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
736	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
737	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
738	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	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	1	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	1	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	1	no	—
752	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
753	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
754	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
755	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	2	no	—
760	C₄²	—	2	1	no	—
761	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
762	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
763	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
764	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
765	C₂³	—	2	4	no	—
766	C₂³	—	2	4	no	—
767	C₂³	—	2	1	no	—
768	C₂³	—	4	2	no	—
769	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
770	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
771	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
772	Q₈	—	2	2	no	—
773	Q₈	—	2	2	no	—
774	Q₈	—	2	2	no	—
775	Q₈	—	2	4	no	—
776	Q₈	—	4	2	no	—
777	Q₈	—	4	2	no	—
778	Q₈	—	8	2	no	—
779	Q₈	—	8	2	no	—
780	Q₈	—	8	2	no	—
781	D₄	—	2	4	no	—
782	D₄	—	2	2	no	—
783	D₄	—	2	2	no	—
784	D₄	—	4	4	no	—
785	D₄	—	4	2	no	—
786	D₄	—	8	2	no	—
787	D₄	C₂₃×#137	1	4	yes	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	4	no	—
791	C₂×C₄	—	2	4	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	4	2	no	—
802	C₂×C₄	—	4	2	no	—
803	C₂×C₄	—	4	2	no	—
804	C₂×C₄	—	4	2	no	—
805	C₂×C₄	—	4	4	no	—
806	C₂×C₄	—	4	2	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	4	2	no	—
809	C₂×C₄	—	8	2	no	—
810	C₂×C₄	—	8	4	no	—
811	C₂×C₄	—	8	4	no	—
812	C₂×C₄	—	8	2	no	—
813	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
814	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
815	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
817	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
818	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
819	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
820	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
821	C₈	—	2	2	no	—
822	C₈	—	2	4	no	—
823	C₈	—	2	2	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	4	8	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	C₂×C₂₃×#137	1	4	yes	—
836	C₂²	C₂₃×#577	1	2	yes	—
837	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
838	C₄	—	2	1	no	—
839	C₄	—	2	2	no	—
840	C₄	—	2	2	no	—
841	C₄	—	2	1	no	—
842	C₄	—	2	1	no	—
843	C₄	—	2	1	no	—
844	C₄	—	4	2	no	—
845	C₄	—	4	2	no	—
846	C₄	—	4	1	no	—
847	C₄	—	4	1	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	4	no	—
851	C₄	—	4	1	no	—
852	C₄	C₂×C₂₃×#137	1	2	yes	—
853	C₄	C₂₃×#585	1	2	yes	—
854	C₂	—	2	2	no	—
855	C₂	—	2	4	no	—
856	C₂	—	4	2	no	—
857	C₂	—	8	1	no	—
858	C₂	C₂₃×#3485	1	1	yes	characteristic
859	C₂	C₂²×C₂₃×#137	1	1	yes	characteristic
860	C₂	C₂×C₂₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂₃×#3520	C₂
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
2. C₂×C₂₃×#554	C₂	semidirect
3. C₂₃×#3356	C₂	semidirect
4. C₂₃×#3344	C₂	semidirect
5. C₂₃×#3335	C₂	semidirect
6. C₂₃×#3331	C₂	semidirect
7. C₂₃×#3316	C₂	semidirect
8. C₂₃×#3299	C₂	semidirect
9. C₂₃×#3238	C₂	semidirect
10. C₂₃×#3229	C₂	semidirect
11. C₂₃×#3195	C₂	semidirect
12. C₂₃×#3190	C₂	semidirect
13. C₂₃×#3113	C₂	semidirect
14. C₂₃×#3108	C₂	semidirect
15. C₂₃×#3092	C₂	semidirect
16. C₂×C₂₃×#483	C₂	semidirect
17. C₂₃×#2974	C₂	semidirect
48. C₂₃×#501	C₂²	semidirect
49. C₂₃×#498	C₂²	semidirect
50. C₂₃×#489	C₂²	semidirect
51. C₂₃×#487	C₂²	semidirect
52. C₂₃×#485	C₂²	semidirect
53. C₂₃×#484	C₂²	semidirect
59. C₂₃×#483	C₂²	semidirect
60. C₂₃×#483	C₂²	semidirect
61. C₂₃×#483	C₂²	semidirect
62. C₂₃×#481	C₂²	semidirect
65. C₂₃×#479	C₂²	semidirect
66. C₂₃×#477	C₂²	semidirect
67. C₂₃×#476	C₂²	semidirect
68. C₂₃×#475	C₂²	semidirect
69. C₂₃×#475	C₂²	semidirect
70. C₂₃×#470	C₂²	semidirect
71. C₂₃×#470	C₂²	semidirect
72. C₂₃×#467	C₂²	semidirect
73. C₂₃×#465	C₂²	semidirect
74. C₂₃×#464	C₂²	semidirect
75. C₂₃×#462	C₂²	semidirect
76. C₂₃×#452	C₂²	semidirect
79. C₂₃×#451	C₂²	semidirect
81. C₂₃×#441	C₂²	semidirect
82. C₄×Q₁₆×C₂₃	C₂²	semidirect
83. C₄×SD₁₆×C₂₃	C₂²	semidirect
89. C₂₃×#428	C₂²	semidirect
90. C₂×C₂₃×#106	C₂²	semidirect
91. C₂₃×#417	C₂²	semidirect
92. C₂×C₂₃×#103	C₂²	semidirect
334. #61735	C₂₃	direct (N × H)
395. C₂×#554	C₂×C₂₃	semidirect
396. #3356	C₂×C₂₃	semidirect
397. #3344	C₂×C₂₃	semidirect
398. #3335	C₂×C₂₃	semidirect
399. #3331	C₂×C₂₃	semidirect
400. #3316	C₂×C₂₃	semidirect
401. #3299	C₂×C₂₃	semidirect
402. #3238	C₂×C₂₃	semidirect
403. #3229	C₂×C₂₃	semidirect
404. #3195	C₂×C₂₃	semidirect
405. #3190	C₂×C₂₃	semidirect
406. #3113	C₂×C₂₃	semidirect
407. #3108	C₂×C₂₃	semidirect
408. #3092	C₂×C₂₃	semidirect
409. C₂×#483	C₂×C₂₃	semidirect
410. #2974	C₂×C₂₃	semidirect
471. #501	C₂²×C₂₃	semidirect
472. #498	C₂²×C₂₃	semidirect
473. #489	C₂²×C₂₃	semidirect
474. #487	C₂²×C₂₃	semidirect
475. #485	C₂²×C₂₃	semidirect
476. #484	C₂²×C₂₃	semidirect
482. #483	C₂²×C₂₃	semidirect
483. #483	C₂²×C₂₃	semidirect
484. #483	C₂²×C₂₃	semidirect
485. #481	C₂²×C₂₃	semidirect
488. #479	C₂²×C₂₃	semidirect
489. #477	C₂²×C₂₃	semidirect
490. #476	C₂²×C₂₃	semidirect
491. #475	C₂²×C₂₃	semidirect
492. #475	C₂²×C₂₃	semidirect
493. #470	C₂²×C₂₃	semidirect
494. #470	C₂²×C₂₃	semidirect
495. #467	C₂²×C₂₃	semidirect
496. #465	C₂²×C₂₃	semidirect
497. #464	C₂²×C₂₃	semidirect
498. #462	C₂²×C₂₃	semidirect
499. #452	C₂²×C₂₃	semidirect
502. #451	C₂²×C₂₃	semidirect
504. #441	C₂²×C₂₃	semidirect
505. C₄×Q₁₆	C₂²×C₂₃	semidirect
506. C₄×SD₁₆	C₂²×C₂₃	semidirect
512. #428	C₂²×C₂₃	semidirect
513. C₂×#106	C₂²×C₂₃	semidirect
514. #417	C₂²×C₂₃	semidirect
515. C₂×#103	C₂²×C₂₃	semidirect
658. C₂₃	#61735	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×#3520	2
C₂×C₂₃×#554	2
C₂₃×#3356	2
C₂₃×#3344	2
C₂₃×#3335	2
C₂₃×#3331	2
C₂₃×#3316	2
C₂₃×#3299	2
C₂₃×#3238	2
C₂₃×#3229	2
C₂₃×#3195	2
C₂₃×#3190	2
C₂₃×#3113	2
C₂₃×#3108	2
C₂₃×#3092	2
C₂×C₂₃×#483	2
C₂₃×#2974	2
#61735	23

Subgroups — C23×#61735 #19209361

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61735 #19209361