Subgroups — C₂₃×#60536 #19208162

Order 5888.

2192 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3108	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3107	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3106	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3105	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3102	C₂	1	4	yes	maximal, complemented
10	C₂₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3091	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3076	C₂	1	2	yes	maximal, complemented
14	C₂₃×#3035	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3002	C₂	1	2	yes	maximal, complemented
16	C₄×C₂₃×#135	C₂	1	4	yes	maximal, complemented
17	C₂×C₂₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#135	C₂²	1	4	yes	—
20	C₂₃×#533	C₂²	1	1	yes	characteristic
21	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
22	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
23	C₂₃×#532	C₂²	1	1	yes	characteristic
24	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
25	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
26	C₂₃×#529	—	2	1	no	—
27	C₂₃×#529	—	2	1	no	—
28	C₂₃×#529	—	2	1	no	—
29	C₂₃×#529	—	2	1	no	—
30	C₂₃×#529	C₂²	1	2	yes	—
31	C₂₃×#529	C₂²	1	2	yes	complemented
32	C₂₃×#525	—	2	1	no	—
33	C₂₃×#525	—	2	1	no	—
34	C₂₃×#525	C₂²	1	2	yes	—
35	C₄×#41×C₂₃	—	2	1	no	—
36	C₄×#41×C₂₃	—	2	1	no	—
37	C₄×#41×C₂₃	—	2	1	no	—
38	C₄×#41×C₂₃	—	2	1	no	—
39	C₄×#41×C₂₃	—	2	1	no	—
40	C₄×#41×C₂₃	—	2	1	no	—
41	C₄×#41×C₂₃	C₂²	1	2	yes	—
42	C₄×#41×C₂₃	C₂²	1	2	yes	—
43	C₄×#41×C₂₃	C₂²	1	2	yes	—
44	C₄×#41×C₂₃	C₂²	1	2	yes	—
45	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
46	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₂₃	—	2	1	no	—
49	C₂×C₄×D₄×C₂₃	—	2	1	no	—
50	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
52	C₂×C₂₃×#117	—	2	1	no	—
53	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
54	C₂²×C₄²×C₂₃	—	2	1	no	—
55	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
56	C₂₃×#485	C₂²	1	4	yes	complemented
57	C₂₃×#484	C₂²	1	2	yes	—
58	C₂₃×#483	C₂²	1	2	yes	—
59	C₂₃×#482	C₂²	1	4	yes	complemented
60	C₂₃×#481	C₂²	1	2	yes	—
61	C₂₃×#480	C₂²	1	2	yes	—
62	C₂₃×#479	C₂²	1	4	yes	complemented
63	C₂₃×#478	C₂²	1	4	yes	complemented
64	C₂₃×#477	C₂²	1	2	yes	complemented
65	C₂₃×#476	C₂²	1	2	yes	complemented
66	C₂₃×#475	C₂²	1	2	yes	complemented
67	C₂₃×#474	C₂²	1	2	yes	complemented
68	C₂₃×#464	C₂²	1	4	yes	complemented
69	C₂₃×#463	C₂²	1	4	yes	complemented
70	C₂₃×#462	C₂²	1	2	yes	complemented
71	C₂₃×#461	C₂²	1	2	yes	complemented
72	C₂₃×#460	C₂²	1	2	yes	complemented
73	C₂₃×#459	C₂²	1	2	yes	complemented
74	C₂₃×#452	C₂²	1	4	yes	—
75	C₂₃×#451	C₂²	1	2	yes	—
76	C₂₃×#450	C₂²	1	2	yes	—
77	C₂₃×#449	C₂²	1	4	yes	—
78	C₂₃×#448	C₂²	1	2	yes	—
79	C₂₃×#447	C₂²	1	2	yes	—
80	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	complemented
81	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	complemented
82	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
83	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
84	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
85	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
86	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
87	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
88	C₂₃×#431	C₂²	1	1	yes	characteristic
89	C₂₃×#431	C₂²	1	1	yes	characteristic
90	C₂₃×#431	C₂²	1	2	yes	—
91	C₂₃×#431	C₂²	1	2	yes	complemented
92	C₂₃×#431	C₂²	1	2	yes	complemented
93	C₂₃×#427	C₂²	1	4	yes	complemented
94	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	complemented
95	C₂₃×#416	C₂²	1	4	yes	—
96	C₂₃×#416	C₂²	1	4	yes	complemented
97	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
98	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	complemented
99	C₂×#41×C₂₃	—	2	8	no	—
100	C₂×#41×C₂₃	—	2	1	no	—
101	C₂×#41×C₂₃	—	2	1	no	—
102	C₂×#41×C₂₃	—	2	1	no	—
103	C₂×#41×C₂₃	—	2	1	no	—
104	C₂×#41×C₂₃	C₂³	1	2	yes	—
105	C₂×#41×C₂₃	C₂³	1	2	yes	—
106	C₂×#41×C₂₃	C₂³	1	2	yes	—
107	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
108	C₂²×D₄×C₂₃	—	2	1	no	—
109	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₂₃	—	2	1	no	—
111	C₂³×C₄×C₂₃	—	2	1	no	—
112	C₂³×C₄×C₂₃	—	2	1	no	—
113	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
114	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
115	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
116	C₂₃×#135	—	2	16	no	—
117	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
118	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
119	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
120	C₂×D₈×C₂₃	C₂³	1	4	yes	—
121	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
122	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
124	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
125	C₂₃×#127	C₂³	1	1	yes	characteristic
126	C₂₃×#126	—	2	2	no	—
127	C₂₃×#126	—	2	2	no	—
128	C₂₃×#125	—	2	1	no	—
129	C₂₃×#125	—	2	1	no	—
130	C₂₃×#125	C₂³	1	2	yes	—
131	C₂₃×#124	—	2	1	no	—
132	C₂₃×#124	—	2	1	no	—
133	C₂₃×#124	C₂³	1	2	yes	—
134	C₂₃×#123	—	2	2	no	—
135	C₂₃×#123	—	2	2	no	—
136	C₂₃×#123	—	2	2	no	—
137	C₂₃×C₂²⋊Q₈	—	2	1	no	—
138	C₂₃×C₂²⋊Q₈	—	2	1	no	—
139	C₂₃×C₂²⋊Q₈	—	2	1	no	—
140	C₂₃×C₂²⋊Q₈	—	2	1	no	—
141	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
142	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
143	C₂₃×#121	—	2	1	no	—
144	C₂₃×#121	—	2	1	no	—
145	C₂₃×#121	—	2	1	no	—
146	C₂₃×#121	—	2	1	no	—
147	C₂₃×#121	C₂³	1	2	yes	—
148	C₂₃×#121	C₂³	1	2	yes	—
149	C₂₃×#120	—	2	2	no	—
150	C₄×Q₈×C₂₃	—	2	1	no	—
151	C₄×Q₈×C₂₃	—	2	1	no	—
152	C₄×Q₈×C₂₃	—	2	1	no	—
153	C₄×Q₈×C₂₃	—	2	1	no	—
154	C₄×Q₈×C₂₃	—	2	1	no	—
155	C₄×Q₈×C₂₃	—	2	1	no	—
156	C₄×Q₈×C₂₃	—	2	1	no	—
157	C₄×Q₈×C₂₃	—	2	1	no	—
158	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
160	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
161	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
162	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
163	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
164	C₄×D₄×C₂₃	—	2	2	no	—
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	2	no	—
171	C₄×D₄×C₂₃	—	2	2	no	—
172	C₄×D₄×C₂₃	—	2	2	no	—
173	C₄×D₄×C₂₃	—	2	2	no	—
174	C₄×D₄×C₂₃	—	2	2	no	—
175	C₄×D₄×C₂₃	—	2	2	no	—
176	C₄×D₄×C₂₃	—	2	2	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	—	2	1	no	—
182	C₄×D₄×C₂₃	—	2	1	no	—
183	C₄×D₄×C₂₃	—	2	1	no	—
184	C₄×D₄×C₂₃	—	2	1	no	—
185	C₄×D₄×C₂₃	—	2	1	no	—
186	C₄×D₄×C₂₃	C₂³	1	2	yes	—
187	C₄×D₄×C₂₃	C₂³	1	2	yes	—
188	C₄×D₄×C₂₃	C₂³	1	2	yes	—
189	C₄×D₄×C₂₃	C₂³	1	2	yes	—
190	C₄×D₄×C₂₃	C₂³	1	2	yes	—
191	C₄×D₄×C₂₃	C₂³	1	2	yes	—
192	C₂₃×#117	—	2	1	no	—
193	C₂₃×#117	—	2	1	no	—
194	C₂₃×#117	—	2	1	no	—
195	C₂₃×#117	—	2	1	no	—
196	C₂₃×#117	—	2	2	no	—
197	C₂₃×#117	—	2	2	no	—
198	C₂₃×#117	—	2	2	no	—
199	C₂₃×#117	—	2	2	no	—
200	C₂₃×#117	—	2	2	no	—
201	C₂₃×#117	—	2	2	no	—
202	C₂₃×#117	—	2	2	no	—
203	C₂₃×#117	C₂³	1	2	yes	—
204	C₂₃×#117	C₂³	1	2	yes	—
205	C₂₃×#117	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
207	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
208	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
211	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
212	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
213	C₂×C₄²×C₂₃	—	2	1	no	—
214	C₂×C₄²×C₂₃	—	2	1	no	—
215	C₂×C₄²×C₂₃	—	2	1	no	—
216	C₂×C₄²×C₂₃	—	2	2	no	—
217	C₂×C₄²×C₂₃	—	2	2	no	—
218	C₂×C₄²×C₂₃	—	2	2	no	—
219	C₂×C₄²×C₂₃	—	2	2	no	—
220	C₂×C₄²×C₂₃	—	2	2	no	—
221	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
222	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
223	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
224	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
225	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
226	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
227	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
232	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
233	C₂₃×#107	C₂³	1	4	yes	—
234	C₂₃×#107	C₂³	1	4	yes	—
235	C₂₃×#106	C₂³	1	4	yes	—
236	C₂₃×#106	C₂³	1	4	yes	—
237	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
238	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
239	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
240	C₂₃×#103	C₂³	1	4	yes	—
241	C₂₃×#103	C₂³	1	4	yes	—
242	C₂₃×#103	C₂³	1	4	yes	—
243	C₂₃×#103	C₂³	1	4	yes	—
244	C₂₃×#102	C₂³	1	4	yes	—
245	C₂₃×#102	C₂³	1	4	yes	—
246	C₂₃×#102	C₂³	1	4	yes	—
247	C₂₃×#102	C₂³	1	4	yes	—
248	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
249	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
250	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
251	C₄×C₈×C₂₃	C₂³	1	2	yes	—
252	C₄×C₈×C₂₃	C₂³	1	4	yes	—
253	C₄×C₈×C₂₃	C₂³	1	2	yes	—
254	C₂⁴×C₂₃	—	2	1	no	—
255	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
256	#41×C₂₃	—	2	8	no	—
257	#41×C₂₃	—	2	8	no	—
258	#41×C₂₃	—	2	4	no	—
259	#41×C₂₃	—	2	4	no	—
260	#41×C₂₃	—	2	4	no	—
261	#41×C₂₃	—	2	8	no	—
262	#41×C₂₃	—	4	4	no	—
263	#41×C₂₃	—	4	4	no	—
264	#41×C₂₃	#41	1	8	yes	complemented
265	C₂×Q₈×C₂₃	—	2	4	no	—
266	C₂×Q₈×C₂₃	—	2	1	no	—
267	C₂×Q₈×C₂₃	—	2	1	no	—
268	C₂×Q₈×C₂₃	—	2	1	no	—
269	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
270	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
271	C₂×D₄×C₂₃	—	2	8	no	—
272	C₂×D₄×C₂₃	—	2	2	no	—
273	C₂×D₄×C₂₃	—	2	2	no	—
274	C₂×D₄×C₂₃	—	2	4	no	—
275	C₂×D₄×C₂₃	—	2	2	no	—
276	C₂×D₄×C₂₃	—	2	2	no	—
277	C₂×D₄×C₂₃	—	2	2	no	—
278	C₂×D₄×C₂₃	—	2	1	no	—
279	C₂×D₄×C₂₃	—	2	1	no	—
280	C₂×D₄×C₂₃	—	2	1	no	—
281	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
282	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₂₃	—	2	8	no	—
284	C₂²×C₄×C₂₃	—	2	1	no	—
285	C₂²×C₄×C₂₃	—	2	4	no	—
286	C₂²×C₄×C₂₃	—	2	2	no	—
287	C₂²×C₄×C₂₃	—	2	2	no	—
288	C₂²×C₄×C₂₃	—	2	4	no	—
289	C₂²×C₄×C₂₃	—	2	1	no	—
290	C₂²×C₄×C₂₃	—	2	1	no	—
291	C₂²×C₄×C₂₃	—	2	2	no	—
292	C₂²×C₄×C₂₃	—	2	2	no	—
293	C₂²×C₄×C₂₃	—	2	2	no	—
294	C₂²×C₄×C₂₃	—	2	2	no	—
295	C₂²×C₄×C₂₃	—	2	2	no	—
296	C₂²×C₄×C₂₃	—	2	2	no	—
297	C₂²×C₄×C₂₃	—	2	2	no	—
298	C₂²×C₄×C₂₃	—	4	2	no	—
299	C₂²×C₄×C₂₃	—	4	4	no	—
300	C₂²×C₄×C₂₃	—	4	4	no	—
301	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
307	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
310	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
313	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
314	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
315	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
319	Q₁₆×C₂₃	—	2	8	no	—
320	SD₁₆×C₂₃	—	2	8	no	—
321	SD₁₆×C₂₃	—	2	8	no	—
322	D₈×C₂₃	—	2	8	no	—
323	C₂×C₈×C₂₃	—	2	8	no	—
324	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
325	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
326	C₄⋊C₄×C₂₃	—	2	2	no	—
327	C₄⋊C₄×C₂₃	—	2	2	no	—
328	C₄⋊C₄×C₂₃	—	2	2	no	—
329	C₄⋊C₄×C₂₃	—	2	2	no	—
330	C₄⋊C₄×C₂₃	—	2	1	no	—
331	C₄⋊C₄×C₂₃	—	2	1	no	—
332	C₄⋊C₄×C₂₃	—	2	1	no	—
333	C₄⋊C₄×C₂₃	—	2	1	no	—
334	C₄⋊C₄×C₂₃	—	2	1	no	—
335	C₄⋊C₄×C₂₃	—	2	1	no	—
336	C₄⋊C₄×C₂₃	—	2	2	no	—
337	C₄⋊C₄×C₂₃	—	2	2	no	—
338	C₄⋊C₄×C₂₃	—	2	2	no	—
339	C₄⋊C₄×C₂₃	—	2	2	no	—
340	C₄⋊C₄×C₂₃	—	2	2	no	—
341	C₄⋊C₄×C₂₃	—	2	2	no	—
342	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
343	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
346	C₂²⋊C₄×C₂₃	—	2	2	no	—
347	C₂²⋊C₄×C₂₃	—	2	2	no	—
348	C₂²⋊C₄×C₂₃	—	2	2	no	—
349	C₂²⋊C₄×C₂₃	—	2	2	no	—
350	C₂²⋊C₄×C₂₃	—	2	2	no	—
351	C₂²⋊C₄×C₂₃	—	2	2	no	—
352	C₂²⋊C₄×C₂₃	—	2	2	no	—
353	C₂²⋊C₄×C₂₃	—	2	2	no	—
354	C₂²⋊C₄×C₂₃	—	2	2	no	—
355	C₂²⋊C₄×C₂₃	—	2	2	no	—
356	C₂²⋊C₄×C₂₃	—	2	2	no	—
357	C₂²⋊C₄×C₂₃	—	2	2	no	—
358	C₂²⋊C₄×C₂₃	—	2	2	no	—
359	C₂²⋊C₄×C₂₃	—	2	2	no	—
360	C₂²⋊C₄×C₂₃	—	2	2	no	—
361	C₄²×C₂₃	—	2	2	no	—
362	C₄²×C₂₃	—	2	2	no	—
363	C₄²×C₂₃	—	2	2	no	—
364	C₄²×C₂₃	—	2	2	no	—
365	C₄²×C₂₃	—	2	2	no	—
366	C₄²×C₂₃	—	2	2	no	—
367	C₄²×C₂₃	—	2	2	no	—
368	C₄²×C₂₃	—	2	2	no	—
369	C₄²×C₂₃	—	2	2	no	—
370	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
371	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
372	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
373	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
374	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
375	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
376	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
377	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
378	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
379	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
380	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
381	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
382	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
383	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
384	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
385	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
386	#60536	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
387	C₂³×C₂₃	—	2	4	no	—
388	C₂³×C₂₃	—	2	2	no	—
389	C₂³×C₂₃	—	2	2	no	—
390	C₂³×C₂₃	—	2	2	no	—
391	C₂³×C₂₃	—	2	2	no	—
392	C₂³×C₂₃	—	4	1	no	—
393	C₂³×C₂₃	—	4	2	no	—
394	C₂³×C₂₃	—	4	2	no	—
395	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
396	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
397	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
398	Q₈×C₂₃	—	2	4	no	—
399	Q₈×C₂₃	—	2	2	no	—
400	Q₈×C₂₃	—	2	4	no	—
401	Q₈×C₂₃	—	4	2	no	—
402	Q₈×C₂₃	—	4	2	no	—
403	Q₈×C₂₃	C₂×#41	1	4	yes	—
404	D₄×C₂₃	—	2	8	no	—
405	D₄×C₂₃	—	2	4	no	—
406	D₄×C₂₃	—	2	8	no	—
407	D₄×C₂₃	—	2	2	no	—
408	D₄×C₂₃	—	2	4	no	—
409	D₄×C₂₃	—	4	2	no	—
410	D₄×C₂₃	—	4	4	no	—
411	D₄×C₂₃	—	4	4	no	—
412	D₄×C₂₃	—	4	4	no	—
413	D₄×C₂₃	—	4	2	no	—
414	D₄×C₂₃	C₂×#41	1	4	yes	—
415	C₂×C₄×C₂₃	—	2	4	no	—
416	C₂×C₄×C₂₃	—	2	8	no	—
417	C₂×C₄×C₂₃	—	2	2	no	—
418	C₂×C₄×C₂₃	—	2	2	no	—
419	C₂×C₄×C₂₃	—	2	2	no	—
420	C₂×C₄×C₂₃	—	2	2	no	—
421	C₂×C₄×C₂₃	—	2	8	no	—
422	C₂×C₄×C₂₃	—	2	2	no	—
423	C₂×C₄×C₂₃	—	2	2	no	—
424	C₂×C₄×C₂₃	—	2	2	no	—
425	C₂×C₄×C₂₃	—	2	2	no	—
426	C₂×C₄×C₂₃	—	2	2	no	—
427	C₂×C₄×C₂₃	—	2	2	no	—
428	C₂×C₄×C₂₃	—	2	2	no	—
429	C₂×C₄×C₂₃	—	2	2	no	—
430	C₂×C₄×C₂₃	—	2	2	no	—
431	C₂×C₄×C₂₃	—	2	2	no	—
432	C₂×C₄×C₂₃	—	2	2	no	—
433	C₂×C₄×C₂₃	—	2	2	no	—
434	C₂×C₄×C₂₃	—	2	2	no	—
435	C₂×C₄×C₂₃	—	2	2	no	—
436	C₂×C₄×C₂₃	—	2	2	no	—
437	C₂×C₄×C₂₃	—	4	1	no	—
438	C₂×C₄×C₂₃	—	4	1	no	—
439	C₂×C₄×C₂₃	—	4	1	no	—
440	C₂×C₄×C₂₃	—	4	4	no	—
441	C₂×C₄×C₂₃	—	4	2	no	—
442	C₂×C₄×C₂₃	—	4	2	no	—
443	C₂×C₄×C₂₃	—	4	4	no	—
444	C₂×C₄×C₂₃	—	4	4	no	—
445	C₂×C₄×C₂₃	—	4	4	no	—
446	C₂×C₄×C₂₃	—	4	4	no	—
447	C₂×C₄×C₂₃	—	4	4	no	—
448	C₂×C₄×C₂₃	—	4	4	no	—
449	C₂×C₄×C₂₃	#135	1	4	yes	complemented
450	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
462	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
463	C₈×C₂₃	—	2	4	no	—
464	C₈×C₂₃	—	2	4	no	—
465	#3444	C₂×C₂₃	1	1	yes	characteristic, complemented
466	C₂×C₄×#41	C₂×C₂₃	1	1	yes	characteristic, complemented
467	#3108	C₂×C₂₃	1	2	yes	complemented
468	#3107	C₂×C₂₃	1	2	yes	complemented
469	#3106	C₂×C₂₃	1	2	yes	complemented
470	#3105	C₂×C₂₃	1	2	yes	complemented
471	#3104	C₂×C₂₃	1	1	yes	characteristic, complemented
472	#3103	C₂×C₂₃	1	1	yes	characteristic, complemented
473	#3102	C₂×C₂₃	1	4	yes	complemented
474	#3101	C₂×C₂₃	1	1	yes	characteristic, complemented
475	#3100	C₂×C₂₃	1	1	yes	characteristic, complemented
476	#3091	C₂×C₂₃	1	2	yes	complemented
477	#3076	C₂×C₂₃	1	2	yes	complemented
478	#3035	C₂×C₂₃	1	2	yes	complemented
479	#3002	C₂×C₂₃	1	2	yes	complemented
480	C₄×#135	C₂×C₂₃	1	4	yes	complemented
481	C₂×#431	C₂×C₂₃	1	1	yes	characteristic, complemented
482	C₂²×C₂₃	—	2	1	no	—
483	C₂²×C₂₃	—	2	1	no	—
484	C₂²×C₂₃	—	2	1	no	—
485	C₂²×C₂₃	—	2	1	no	—
486	C₂²×C₂₃	—	2	1	no	—
487	C₂²×C₂₃	—	2	4	no	—
488	C₂²×C₂₃	—	2	1	no	—
489	C₂²×C₂₃	—	2	1	no	—
490	C₂²×C₂₃	—	4	4	no	—
491	C₂²×C₂₃	—	4	8	no	—
492	C₂²×C₂₃	—	4	2	no	—
493	C₂²×C₂₃	—	4	2	no	—
494	C₂²×C₂₃	—	4	2	no	—
495	C₂²×C₂₃	—	4	2	no	—
496	C₂²×C₂₃	—	4	2	no	—
497	C₂²×C₂₃	#525	1	2	yes	—
498	C₂²×C₂₃	C₂×#135	1	2	yes	—
499	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
500	C₄×C₂₃	—	2	1	no	—
501	C₄×C₂₃	—	2	4	no	—
502	C₄×C₂₃	—	2	1	no	—
503	C₄×C₂₃	—	2	1	no	—
504	C₄×C₂₃	—	2	1	no	—
505	C₄×C₂₃	—	2	1	no	—
506	C₄×C₂₃	—	2	1	no	—
507	C₄×C₂₃	—	2	1	no	—
508	C₄×C₂₃	—	4	2	no	—
509	C₄×C₂₃	—	4	2	no	—
510	C₄×C₂₃	—	4	2	no	—
511	C₄×C₂₃	—	4	2	no	—
512	C₄×C₂₃	—	4	2	no	—
513	C₄×C₂₃	#525	1	2	yes	—
514	C₄×C₂₃	C₂×#135	1	2	yes	—
515	C₄×C₂₃	C₂×#135	1	2	yes	—
516	C₄×C₂₃	#575	1	2	yes	—
517	C₄×C₂₃	C₂²×#41	1	2	yes	—
518	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
519	C₂×#135	C₂²×C₂₃	1	4	yes	—
520	#533	C₂²×C₂₃	1	1	yes	characteristic
521	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
522	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
523	#532	C₂²×C₂₃	1	1	yes	characteristic
524	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
525	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
526	#529	—	2	1	no	—
527	#529	—	2	1	no	—
528	#529	—	2	1	no	—
529	#529	—	2	1	no	—
530	#529	C₂²×C₂₃	1	2	yes	—
531	#529	C₂²×C₂₃	1	2	yes	complemented
532	#525	—	2	1	no	—
533	#525	—	2	1	no	—
534	#525	C₂²×C₂₃	1	2	yes	—
535	C₄×#41	—	2	1	no	—
536	C₄×#41	—	2	1	no	—
537	C₄×#41	—	2	1	no	—
538	C₄×#41	—	2	1	no	—
539	C₄×#41	—	2	1	no	—
540	C₄×#41	—	2	1	no	—
541	C₄×#41	C₂²×C₂₃	1	2	yes	—
542	C₄×#41	C₂²×C₂₃	1	2	yes	—
543	C₄×#41	C₂²×C₂₃	1	2	yes	—
544	C₄×#41	C₂²×C₂₃	1	2	yes	—
545	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
546	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
547	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
548	C₂×C₄×D₄	—	2	1	no	—
549	C₂×C₄×D₄	—	2	1	no	—
550	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
551	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
552	C₂×#117	—	2	1	no	—
553	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
554	C₂²×C₄²	—	2	1	no	—
555	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
556	#485	C₂²×C₂₃	1	4	yes	complemented
557	#484	C₂²×C₂₃	1	2	yes	—
558	#483	C₂²×C₂₃	1	2	yes	—
559	#482	C₂²×C₂₃	1	4	yes	complemented
560	#481	C₂²×C₂₃	1	2	yes	—
561	#480	C₂²×C₂₃	1	2	yes	—
562	#479	C₂²×C₂₃	1	4	yes	complemented
563	#478	C₂²×C₂₃	1	4	yes	complemented
564	#477	C₂²×C₂₃	1	2	yes	complemented
565	#476	C₂²×C₂₃	1	2	yes	complemented
566	#475	C₂²×C₂₃	1	2	yes	complemented
567	#474	C₂²×C₂₃	1	2	yes	complemented
568	#464	C₂²×C₂₃	1	4	yes	complemented
569	#463	C₂²×C₂₃	1	4	yes	complemented
570	#462	C₂²×C₂₃	1	2	yes	complemented
571	#461	C₂²×C₂₃	1	2	yes	complemented
572	#460	C₂²×C₂₃	1	2	yes	complemented
573	#459	C₂²×C₂₃	1	2	yes	complemented
574	#452	C₂²×C₂₃	1	4	yes	—
575	#451	C₂²×C₂₃	1	2	yes	—
576	#450	C₂²×C₂₃	1	2	yes	—
577	#449	C₂²×C₂₃	1	4	yes	—
578	#448	C₂²×C₂₃	1	2	yes	—
579	#447	C₂²×C₂₃	1	2	yes	—
580	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	complemented
581	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	complemented
582	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
583	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
584	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
585	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
586	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
587	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
588	#431	C₂²×C₂₃	1	1	yes	characteristic
589	#431	C₂²×C₂₃	1	1	yes	characteristic
590	#431	C₂²×C₂₃	1	2	yes	—
591	#431	C₂²×C₂₃	1	2	yes	complemented
592	#431	C₂²×C₂₃	1	2	yes	complemented
593	#427	C₂²×C₂₃	1	4	yes	complemented
594	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	complemented
595	#416	C₂²×C₂₃	1	4	yes	—
596	#416	C₂²×C₂₃	1	4	yes	complemented
597	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
598	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	complemented
599	C₂×C₂₃	—	2	2	no	—
600	C₂×C₂₃	—	2	2	no	—
601	C₂×C₂₃	—	4	1	no	—
602	C₂×C₂₃	—	4	4	no	—
603	C₂×C₂₃	—	8	2	no	—
604	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
605	C₂×C₂₃	C₂²×#135	1	1	yes	characteristic
606	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
607	C₂×#41	—	2	8	no	—
608	C₂×#41	—	2	1	no	—
609	C₂×#41	—	2	1	no	—
610	C₂×#41	—	2	1	no	—
611	C₂×#41	—	2	1	no	—
612	C₂×#41	C₂³×C₂₃	1	2	yes	—
613	C₂×#41	C₂³×C₂₃	1	2	yes	—
614	C₂×#41	C₂³×C₂₃	1	2	yes	—
615	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
616	C₂²×D₄	—	2	1	no	—
617	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
618	C₂³×C₄	—	2	1	no	—
619	C₂³×C₄	—	2	1	no	—
620	C₂³×C₄	—	2	1	no	—
621	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
622	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
623	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
624	#135	—	2	16	no	—
625	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
626	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
627	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
628	C₂×D₈	C₂³×C₂₃	1	4	yes	—
629	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
630	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
631	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
632	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
633	#127	C₂³×C₂₃	1	1	yes	characteristic
634	#126	—	2	2	no	—
635	#126	—	2	2	no	—
636	#125	—	2	1	no	—
637	#125	—	2	1	no	—
638	#125	C₂³×C₂₃	1	2	yes	—
639	#124	—	2	1	no	—
640	#124	—	2	1	no	—
641	#124	C₂³×C₂₃	1	2	yes	—
642	#123	—	2	2	no	—
643	#123	—	2	2	no	—
644	#123	—	2	2	no	—
645	C₂²⋊Q₈	—	2	1	no	—
646	C₂²⋊Q₈	—	2	1	no	—
647	C₂²⋊Q₈	—	2	1	no	—
648	C₂²⋊Q₈	—	2	1	no	—
649	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
650	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
651	#121	—	2	1	no	—
652	#121	—	2	1	no	—
653	#121	—	2	1	no	—
654	#121	—	2	1	no	—
655	#121	C₂³×C₂₃	1	2	yes	—
656	#121	C₂³×C₂₃	1	2	yes	—
657	#120	—	2	2	no	—
658	C₄×Q₈	—	2	1	no	—
659	C₄×Q₈	—	2	1	no	—
660	C₄×Q₈	—	2	1	no	—
661	C₄×Q₈	—	2	1	no	—
662	C₄×Q₈	—	2	1	no	—
663	C₄×Q₈	—	2	1	no	—
664	C₄×Q₈	—	2	1	no	—
665	C₄×Q₈	—	2	1	no	—
666	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
667	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
668	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
669	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
670	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
671	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	—	2	2	no	—
680	C₄×D₄	—	2	2	no	—
681	C₄×D₄	—	2	2	no	—
682	C₄×D₄	—	2	2	no	—
683	C₄×D₄	—	2	2	no	—
684	C₄×D₄	—	2	2	no	—
685	C₄×D₄	—	2	2	no	—
686	C₄×D₄	—	2	1	no	—
687	C₄×D₄	—	2	1	no	—
688	C₄×D₄	—	2	1	no	—
689	C₄×D₄	—	2	1	no	—
690	C₄×D₄	—	2	1	no	—
691	C₄×D₄	—	2	1	no	—
692	C₄×D₄	—	2	1	no	—
693	C₄×D₄	—	2	1	no	—
694	C₄×D₄	C₂³×C₂₃	1	2	yes	—
695	C₄×D₄	C₂³×C₂₃	1	2	yes	—
696	C₄×D₄	C₂³×C₂₃	1	2	yes	—
697	C₄×D₄	C₂³×C₂₃	1	2	yes	—
698	C₄×D₄	C₂³×C₂₃	1	2	yes	—
699	C₄×D₄	C₂³×C₂₃	1	2	yes	—
700	#117	—	2	1	no	—
701	#117	—	2	1	no	—
702	#117	—	2	1	no	—
703	#117	—	2	1	no	—
704	#117	—	2	2	no	—
705	#117	—	2	2	no	—
706	#117	—	2	2	no	—
707	#117	—	2	2	no	—
708	#117	—	2	2	no	—
709	#117	—	2	2	no	—
710	#117	—	2	2	no	—
711	#117	C₂³×C₂₃	1	2	yes	—
712	#117	C₂³×C₂₃	1	2	yes	—
713	#117	C₂³×C₂₃	1	2	yes	—
714	C₂×C₄⋊C₄	—	2	1	no	—
715	C₂×C₄⋊C₄	—	2	1	no	—
716	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
717	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
718	C₂×C₂²⋊C₄	—	2	1	no	—
719	C₂×C₂²⋊C₄	—	2	1	no	—
720	C₂×C₂²⋊C₄	—	2	1	no	—
721	C₂×C₄²	—	2	1	no	—
722	C₂×C₄²	—	2	1	no	—
723	C₂×C₄²	—	2	1	no	—
724	C₂×C₄²	—	2	2	no	—
725	C₂×C₄²	—	2	2	no	—
726	C₂×C₄²	—	2	2	no	—
727	C₂×C₄²	—	2	2	no	—
728	C₂×C₄²	—	2	2	no	—
729	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
730	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
731	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
732	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
733	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
734	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
735	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
736	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
737	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
738	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
739	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
740	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
741	#107	C₂³×C₂₃	1	4	yes	—
742	#107	C₂³×C₂₃	1	4	yes	—
743	#106	C₂³×C₂₃	1	4	yes	—
744	#106	C₂³×C₂₃	1	4	yes	—
745	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
746	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
747	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
748	#103	C₂³×C₂₃	1	4	yes	—
749	#103	C₂³×C₂₃	1	4	yes	—
750	#103	C₂³×C₂₃	1	4	yes	—
751	#103	C₂³×C₂₃	1	4	yes	—
752	#102	C₂³×C₂₃	1	4	yes	—
753	#102	C₂³×C₂₃	1	4	yes	—
754	#102	C₂³×C₂₃	1	4	yes	—
755	#102	C₂³×C₂₃	1	4	yes	—
756	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
757	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
758	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
759	C₄×C₈	C₂³×C₂₃	1	2	yes	—
760	C₄×C₈	C₂³×C₂₃	1	4	yes	—
761	C₄×C₈	C₂³×C₂₃	1	2	yes	—
762	C₂₃	#60536	1	1	yes	characteristic, direct product factor, Sylow
763	C₂⁴	—	2	1	no	—
764	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
765	#41	—	2	8	no	—
766	#41	—	2	8	no	—
767	#41	—	2	4	no	—
768	#41	—	2	4	no	—
769	#41	—	2	4	no	—
770	#41	—	2	8	no	—
771	#41	—	4	4	no	—
772	#41	—	4	4	no	—
773	#41	#41×C₂₃	1	8	yes	complemented
774	C₂×Q₈	—	2	4	no	—
775	C₂×Q₈	—	2	1	no	—
776	C₂×Q₈	—	2	1	no	—
777	C₂×Q₈	—	2	1	no	—
778	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
779	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
780	C₂×D₄	—	2	8	no	—
781	C₂×D₄	—	2	2	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	4	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	—	2	2	no	—
787	C₂×D₄	—	2	1	no	—
788	C₂×D₄	—	2	1	no	—
789	C₂×D₄	—	2	1	no	—
790	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
791	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
792	C₂²×C₄	—	2	8	no	—
793	C₂²×C₄	—	2	1	no	—
794	C₂²×C₄	—	2	4	no	—
795	C₂²×C₄	—	2	2	no	—
796	C₂²×C₄	—	2	2	no	—
797	C₂²×C₄	—	2	4	no	—
798	C₂²×C₄	—	2	1	no	—
799	C₂²×C₄	—	2	1	no	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	2	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	—	4	2	no	—
808	C₂²×C₄	—	4	4	no	—
809	C₂²×C₄	—	4	4	no	—
810	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
811	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
812	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
813	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
814	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
815	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
816	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
817	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
818	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
819	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
820	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
821	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
822	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
823	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
824	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
825	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
826	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
827	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
828	Q₁₆	—	2	8	no	—
829	SD₁₆	—	2	8	no	—
830	SD₁₆	—	2	8	no	—
831	D₈	—	2	8	no	—
832	C₂×C₈	—	2	8	no	—
833	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
834	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
835	C₄⋊C₄	—	2	2	no	—
836	C₄⋊C₄	—	2	2	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	1	no	—
840	C₄⋊C₄	—	2	1	no	—
841	C₄⋊C₄	—	2	1	no	—
842	C₄⋊C₄	—	2	1	no	—
843	C₄⋊C₄	—	2	1	no	—
844	C₄⋊C₄	—	2	1	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	2	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
852	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
853	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
854	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
855	C₂²⋊C₄	—	2	2	no	—
856	C₂²⋊C₄	—	2	2	no	—
857	C₂²⋊C₄	—	2	2	no	—
858	C₂²⋊C₄	—	2	2	no	—
859	C₂²⋊C₄	—	2	2	no	—
860	C₂²⋊C₄	—	2	2	no	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	2	no	—
864	C₂²⋊C₄	—	2	2	no	—
865	C₂²⋊C₄	—	2	2	no	—
866	C₂²⋊C₄	—	2	2	no	—
867	C₂²⋊C₄	—	2	2	no	—
868	C₂²⋊C₄	—	2	2	no	—
869	C₂²⋊C₄	—	2	2	no	—
870	C₄²	—	2	2	no	—
871	C₄²	—	2	2	no	—
872	C₄²	—	2	2	no	—
873	C₄²	—	2	2	no	—
874	C₄²	—	2	2	no	—
875	C₄²	—	2	2	no	—
876	C₄²	—	2	2	no	—
877	C₄²	—	2	2	no	—
878	C₄²	—	2	2	no	—
879	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
880	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
881	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
882	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
883	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
884	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
885	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
886	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
887	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
888	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
889	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
890	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
891	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
892	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
893	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
894	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
895	C₂³	—	2	4	no	—
896	C₂³	—	2	2	no	—
897	C₂³	—	2	2	no	—
898	C₂³	—	2	2	no	—
899	C₂³	—	2	2	no	—
900	C₂³	—	4	1	no	—
901	C₂³	—	4	2	no	—
902	C₂³	—	4	2	no	—
903	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
904	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
905	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
906	Q₈	—	2	4	no	—
907	Q₈	—	2	2	no	—
908	Q₈	—	2	4	no	—
909	Q₈	—	4	2	no	—
910	Q₈	—	4	2	no	—
911	Q₈	C₂×#41×C₂₃	1	4	yes	—
912	D₄	—	2	8	no	—
913	D₄	—	2	4	no	—
914	D₄	—	2	8	no	—
915	D₄	—	2	2	no	—
916	D₄	—	2	4	no	—
917	D₄	—	4	2	no	—
918	D₄	—	4	4	no	—
919	D₄	—	4	4	no	—
920	D₄	—	4	4	no	—
921	D₄	—	4	2	no	—
922	D₄	C₂×#41×C₂₃	1	4	yes	—
923	C₂×C₄	—	2	4	no	—
924	C₂×C₄	—	2	8	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	2	no	—
931	C₂×C₄	—	2	2	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	8	no	—
939	C₂×C₄	—	2	2	no	—
940	C₂×C₄	—	2	2	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	2	no	—
945	C₂×C₄	—	4	1	no	—
946	C₂×C₄	—	4	1	no	—
947	C₂×C₄	—	4	1	no	—
948	C₂×C₄	—	4	4	no	—
949	C₂×C₄	—	4	2	no	—
950	C₂×C₄	—	4	2	no	—
951	C₂×C₄	—	4	4	no	—
952	C₂×C₄	—	4	4	no	—
953	C₂×C₄	—	4	4	no	—
954	C₂×C₄	—	4	4	no	—
955	C₂×C₄	—	4	4	no	—
956	C₂×C₄	—	4	4	no	—
957	C₂×C₄	C₂₃×#135	1	4	yes	complemented
958	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
959	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
960	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
961	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
962	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
963	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
964	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
965	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
966	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
967	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
968	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
969	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
970	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
971	C₈	—	2	4	no	—
972	C₈	—	2	4	no	—
973	C₂²	—	2	1	no	—
974	C₂²	—	2	1	no	—
975	C₂²	—	2	1	no	—
976	C₂²	—	2	1	no	—
977	C₂²	—	2	1	no	—
978	C₂²	—	2	4	no	—
979	C₂²	—	2	1	no	—
980	C₂²	—	2	1	no	—
981	C₂²	—	4	4	no	—
982	C₂²	—	4	8	no	—
983	C₂²	—	4	2	no	—
984	C₂²	—	4	2	no	—
985	C₂²	—	4	2	no	—
986	C₂²	—	4	2	no	—
987	C₂²	—	4	2	no	—
988	C₂²	C₂₃×#525	1	2	yes	—
989	C₂²	C₂×C₂₃×#135	1	2	yes	—
990	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
991	C₄	—	2	1	no	—
992	C₄	—	2	4	no	—
993	C₄	—	2	1	no	—
994	C₄	—	2	1	no	—
995	C₄	—	2	1	no	—
996	C₄	—	2	1	no	—
997	C₄	—	2	1	no	—
998	C₄	—	2	1	no	—
999	C₄	—	4	2	no	—
1000	C₄	—	4	2	no	—
1001	C₄	—	4	2	no	—
1002	C₄	—	4	2	no	—
1003	C₄	—	4	2	no	—
1004	C₄	C₂₃×#525	1	2	yes	—
1005	C₄	C₂×C₂₃×#135	1	2	yes	—
1006	C₄	C₂×C₂₃×#135	1	2	yes	—
1007	C₄	C₂₃×#575	1	2	yes	—
1008	C₄	C₂²×#41×C₂₃	1	2	yes	—
1009	C₂	—	2	2	no	—
1010	C₂	—	2	2	no	—
1011	C₂	—	4	1	no	—
1012	C₂	—	4	4	no	—
1013	C₂	—	8	2	no	—
1014	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
1015	C₂	C₂²×C₂₃×#135	1	1	yes	characteristic
1016	C₂	C₂×C₂₃×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₂₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3444	C₂	semidirect
2. C₂×C₄×#41×C₂₃	C₂	semidirect
3. C₂₃×#3108	C₂	semidirect
4. C₂₃×#3107	C₂	semidirect
5. C₂₃×#3106	C₂	semidirect
6. C₂₃×#3105	C₂	semidirect
7. C₂₃×#3104	C₂	semidirect
8. C₂₃×#3103	C₂	semidirect
9. C₂₃×#3102	C₂	semidirect
10. C₂₃×#3101	C₂	semidirect
11. C₂₃×#3100	C₂	semidirect
12. C₂₃×#3091	C₂	semidirect
13. C₂₃×#3076	C₂	semidirect
14. C₂₃×#3035	C₂	semidirect
15. C₂₃×#3002	C₂	semidirect
16. C₄×C₂₃×#135	C₂	semidirect
17. C₂×C₂₃×#431	C₂	semidirect
21. C₂₃×#533	C₂²	semidirect
22. C₂₃×#533	C₂²	semidirect
24. C₂₃×#532	C₂²	semidirect
25. C₂₃×#532	C₂²	semidirect
31. C₂₃×#529	C₂²	semidirect
45. C₄×#41×C₂₃	C₂²	semidirect
56. C₂₃×#485	C₂²	semidirect
59. C₂₃×#482	C₂²	semidirect
62. C₂₃×#479	C₂²	semidirect
63. C₂₃×#478	C₂²	semidirect
64. C₂₃×#477	C₂²	semidirect
65. C₂₃×#476	C₂²	semidirect
66. C₂₃×#475	C₂²	semidirect
67. C₂₃×#474	C₂²	semidirect
68. C₂₃×#464	C₂²	semidirect
69. C₂₃×#463	C₂²	semidirect
70. C₂₃×#462	C₂²	semidirect
71. C₂₃×#461	C₂²	semidirect
72. C₂₃×#460	C₂²	semidirect
73. C₂₃×#459	C₂²	semidirect
80. C₄×Q₁₆×C₂₃	C₂²	semidirect
81. C₄×Q₁₆×C₂₃	C₂²	semidirect
82. C₄×SD₁₆×C₂₃	C₂²	semidirect
83. C₄×SD₁₆×C₂₃	C₂²	semidirect
84. C₄×SD₁₆×C₂₃	C₂²	semidirect
85. C₄×SD₁₆×C₂₃	C₂²	semidirect
86. C₄×D₈×C₂₃	C₂²	semidirect
87. C₄×D₈×C₂₃	C₂²	semidirect
91. C₂₃×#431	C₂²	semidirect
92. C₂₃×#431	C₂²	semidirect
93. C₂₃×#427	C₂²	semidirect
94. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
96. C₂₃×#416	C₂²	semidirect
98. C₂×C₄×C₈×C₂₃	C₂²	semidirect
264. #41×C₂₃	#41	semidirect
386. #60536	C₂₃	direct (N × H)
449. C₂×C₄×C₂₃	#135	semidirect
465. #3444	C₂×C₂₃	semidirect
466. C₂×C₄×#41	C₂×C₂₃	semidirect
467. #3108	C₂×C₂₃	semidirect
468. #3107	C₂×C₂₃	semidirect
469. #3106	C₂×C₂₃	semidirect
470. #3105	C₂×C₂₃	semidirect
471. #3104	C₂×C₂₃	semidirect
472. #3103	C₂×C₂₃	semidirect
473. #3102	C₂×C₂₃	semidirect
474. #3101	C₂×C₂₃	semidirect
475. #3100	C₂×C₂₃	semidirect
476. #3091	C₂×C₂₃	semidirect
477. #3076	C₂×C₂₃	semidirect
478. #3035	C₂×C₂₃	semidirect
479. #3002	C₂×C₂₃	semidirect
480. C₄×#135	C₂×C₂₃	semidirect
481. C₂×#431	C₂×C₂₃	semidirect
521. #533	C₂²×C₂₃	semidirect
522. #533	C₂²×C₂₃	semidirect
524. #532	C₂²×C₂₃	semidirect
525. #532	C₂²×C₂₃	semidirect
531. #529	C₂²×C₂₃	semidirect
545. C₄×#41	C₂²×C₂₃	semidirect
556. #485	C₂²×C₂₃	semidirect
559. #482	C₂²×C₂₃	semidirect
562. #479	C₂²×C₂₃	semidirect
563. #478	C₂²×C₂₃	semidirect
564. #477	C₂²×C₂₃	semidirect
565. #476	C₂²×C₂₃	semidirect
566. #475	C₂²×C₂₃	semidirect
567. #474	C₂²×C₂₃	semidirect
568. #464	C₂²×C₂₃	semidirect
569. #463	C₂²×C₂₃	semidirect
570. #462	C₂²×C₂₃	semidirect
571. #461	C₂²×C₂₃	semidirect
572. #460	C₂²×C₂₃	semidirect
573. #459	C₂²×C₂₃	semidirect
580. C₄×Q₁₆	C₂²×C₂₃	semidirect
581. C₄×Q₁₆	C₂²×C₂₃	semidirect
582. C₄×SD₁₆	C₂²×C₂₃	semidirect
583. C₄×SD₁₆	C₂²×C₂₃	semidirect
584. C₄×SD₁₆	C₂²×C₂₃	semidirect
585. C₄×SD₁₆	C₂²×C₂₃	semidirect
586. C₄×D₈	C₂²×C₂₃	semidirect
587. C₄×D₈	C₂²×C₂₃	semidirect
591. #431	C₂²×C₂₃	semidirect
592. #431	C₂²×C₂₃	semidirect
593. #427	C₂²×C₂₃	semidirect
594. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
596. #416	C₂²×C₂₃	semidirect
598. C₂×C₄×C₈	C₂²×C₂₃	semidirect
762. C₂₃	#60536	direct (N × H)
773. #41	#41×C₂₃	semidirect
957. C₂×C₄	C₂₃×#135	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3444	2
C₂×C₄×#41×C₂₃	2
C₂₃×#3108	2
C₂₃×#3107	2
C₂₃×#3106	2
C₂₃×#3105	2
C₂₃×#3104	2
C₂₃×#3103	2
C₂₃×#3102	2
C₂₃×#3101	2
C₂₃×#3100	2
C₂₃×#3091	2
C₂₃×#3076	2
C₂₃×#3035	2
C₂₃×#3002	2
C₄×C₂₃×#135	2
C₂×C₂₃×#431	2
#60536	23

Subgroups — C23×#60536 #19208162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60536 #19208162