Subgroups — C₂₃×#60594 #19208220

Order 5888.

1990 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₂₃×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3127	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3120	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3116	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3113	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3107	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3104	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3097	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3011	C₂	1	2	yes	maximal
15	C₂₃×#2950	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2947	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
19	C₂×C₂₃×#137	C₂²	1	2	yes	—
20	C₂²×Q₁₆×C₂₃	C₂²	1	2	yes	—
21	C₂₃×#557	—	2	1	no	—
22	C₂₃×#557	—	2	1	no	—
23	C₂₃×#556	—	2	1	no	—
24	C₂₃×#556	—	2	1	no	—
25	C₂₃×#552	—	2	2	no	—
26	C₂₃×#552	—	2	2	no	—
27	C₂₃×#541	C₂²	1	4	yes	—
28	C₂₃×#536	C₂²	1	2	yes	—
29	C₂₃×#533	C₂²	1	2	yes	—
30	C₂₃×#533	C₂²	1	2	yes	—
31	C₂₃×#533	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂₃×#520	—	2	2	no	—
34	C₂₃×#520	—	2	1	no	—
35	C₂₃×#520	C₂²	1	1	yes	characteristic
36	C₂₃×#520	C₂²	1	2	yes	—
37	C₂₃×#520	C₂²	1	1	yes	characteristic
38	C₂₃×#519	—	2	1	no	—
39	C₂₃×#519	C₂²	1	1	yes	characteristic
40	C₂₃×#519	C₂²	1	2	yes	—
41	C₂₃×#519	C₂²	1	2	yes	—
42	C₄×#41×C₂₃	—	2	2	no	—
43	C₄×#41×C₂₃	—	2	1	no	—
44	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
45	C₄×#41×C₂₃	C₂²	1	2	yes	—
46	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
47	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
48	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
50	C₂₃×#485	C₂²	1	4	yes	—
51	C₂₃×#485	C₂²	1	4	yes	—
52	C₂₃×#484	C₂²	1	4	yes	—
53	C₂₃×#483	C₂²	1	4	yes	—
54	C₂₃×#479	C₂²	1	2	yes	—
55	C₂₃×#479	C₂²	1	4	yes	—
56	C₂₃×#478	C₂²	1	2	yes	—
57	C₂₃×#477	C₂²	1	1	yes	characteristic
58	C₂₃×#477	C₂²	1	2	yes	—
59	C₂₃×#476	C₂²	1	1	yes	characteristic
60	C₂₃×#475	C₂²	1	1	yes	characteristic
61	C₂₃×#475	C₂²	1	2	yes	—
62	C₂₃×#474	C₂²	1	1	yes	characteristic
63	C₂₃×#462	C₂²	1	2	yes	—
64	C₂₃×#462	C₂²	1	2	yes	—
65	C₂₃×#462	C₂²	1	4	yes	—
66	C₂₃×#462	C₂²	1	2	yes	—
67	C₂₃×#462	C₂²	1	2	yes	—
68	C₂₃×#461	C₂²	1	2	yes	—
69	C₂₃×#461	C₂²	1	2	yes	—
70	C₂₃×#452	C₂²	1	4	yes	—
71	C₂₃×#452	C₂²	1	4	yes	—
72	C₂₃×#451	C₂²	1	4	yes	—
73	C₂₃×#451	C₂²	1	4	yes	—
74	C₂₃×#441	C₂²	1	4	yes	—
75	C₂₃×#441	C₂²	1	4	yes	—
76	C₂₃×#441	C₂²	1	4	yes	—
77	C₂₃×#440	C₂²	1	4	yes	—
78	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	—
79	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	—
80	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	—
81	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	—
82	C₂₃×#433	C₂²	1	4	yes	—
83	C₂₃×#432	C₂²	1	2	yes	—
84	C₂₃×#431	C₂²	1	2	yes	—
85	C₂₃×#428	C₂²	1	2	yes	—
86	C₂₃×#427	C₂²	1	2	yes	—
87	C₂₃×#423	C₂²	1	1	yes	characteristic
88	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
89	C₂₃×#419	C₂²	1	2	yes	—
90	C₂₃×#419	C₂²	1	2	yes	—
91	C₂₃×#416	C₂²	1	2	yes	—
92	C₂×C₂₃×#103	C₂²	1	2	yes	—
93	C₂₃×#408	C₂²	1	2	yes	—
94	C₂₃×#405	C₂²	1	2	yes	—
95	C₂₃×2₋¹⁺⁴	—	2	4	no	—
96	C₂₃×2₋¹⁺⁴	—	2	4	no	—
97	C₂×#41×C₂₃	—	2	2	no	—
98	C₂×#41×C₂₃	—	2	1	no	—
99	C₂×#41×C₂₃	C₂³	1	2	yes	—
100	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
101	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
102	C₂²×Q₈×C₂₃	—	2	1	no	—
103	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
104	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
105	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
106	C₂₃×#137	—	2	8	no	—
107	C₂×Q₁₆×C₂₃	—	2	8	no	—
108	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
109	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
110	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
112	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
113	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
114	C₂₃×C₄⋊Q₈	—	2	2	no	—
115	C₂₃×C₄⋊Q₈	—	2	1	no	—
116	C₂₃×C₄⋊Q₈	—	2	1	no	—
117	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₂₃×#126	—	2	4	no	—
122	C₂₃×#126	—	2	4	no	—
123	C₂₃×#125	—	2	4	no	—
124	C₂₃×#125	—	2	4	no	—
125	C₂₃×#125	—	2	2	no	—
126	C₂₃×#125	—	2	2	no	—
127	C₂₃×#125	C₂³	1	2	yes	—
128	C₂₃×#124	—	2	2	no	—
129	C₂₃×#123	—	2	4	no	—
130	C₂₃×C₂²⋊Q₈	—	2	1	no	—
131	C₂₃×C₂²⋊Q₈	—	2	1	no	—
132	C₂₃×C₂²⋊Q₈	—	2	2	no	—
133	C₂₃×C₂²⋊Q₈	—	2	2	no	—
134	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
135	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
136	C₄×Q₈×C₂₃	—	2	1	no	—
137	C₄×Q₈×C₂₃	—	2	2	no	—
138	C₄×Q₈×C₂₃	—	2	2	no	—
139	C₄×Q₈×C₂₃	—	2	1	no	—
140	C₄×Q₈×C₂₃	—	2	2	no	—
141	C₄×Q₈×C₂₃	—	2	1	no	—
142	C₄×Q₈×C₂₃	—	2	2	no	—
143	C₄×Q₈×C₂₃	—	2	2	no	—
144	C₄×Q₈×C₂₃	—	2	2	no	—
145	C₄×Q₈×C₂₃	—	2	1	no	—
146	C₄×Q₈×C₂₃	—	2	1	no	—
147	C₄×Q₈×C₂₃	—	2	2	no	—
148	C₄×Q₈×C₂₃	—	2	1	no	—
149	C₄×Q₈×C₂₃	—	2	2	no	—
150	C₄×Q₈×C₂₃	—	2	1	no	—
151	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
152	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
153	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
154	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
155	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
156	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
157	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
158	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
160	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
161	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
162	C₄×D₄×C₂₃	—	2	2	no	—
163	C₄×D₄×C₂₃	—	2	1	no	—
164	C₄×D₄×C₂₃	—	2	1	no	—
165	C₄×D₄×C₂₃	—	2	2	no	—
166	C₄×D₄×C₂₃	—	2	1	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	D₄	1	2	yes	—
172	C₄×D₄×C₂₃	D₄	1	2	yes	—
173	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
174	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
175	C₄×D₄×C₂₃	C₂³	1	2	yes	—
176	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
178	C₂₃×#117	—	2	2	no	—
179	C₂₃×#117	—	2	2	no	—
180	C₂₃×#117	—	2	1	no	—
181	C₂₃×#117	—	2	2	no	—
182	C₂₃×#117	—	2	4	no	—
183	C₂₃×#117	—	2	2	no	—
184	C₂₃×#117	—	2	2	no	—
185	C₂₃×#117	—	2	2	no	—
186	C₂₃×#117	—	2	2	no	—
187	C₂₃×#117	—	2	1	no	—
188	C₂₃×#117	C₂³	1	2	yes	—
189	C₂₃×#117	C₂³	1	1	yes	characteristic
190	C₂₃×#117	C₂³	1	2	yes	—
191	C₂₃×#117	C₂³	1	1	yes	characteristic
192	C₂₃×#117	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
194	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
195	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
196	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
197	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
198	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
199	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
201	C₂×C₄²×C₂₃	—	2	1	no	—
202	C₂×C₄²×C₂₃	—	2	2	no	—
203	C₂×C₄²×C₂₃	—	2	2	no	—
204	C₂×C₄²×C₂₃	—	2	1	no	—
205	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
207	C₂₃×#107	C₂³	1	2	yes	—
208	C₂₃×#107	C₂³	1	2	yes	—
209	C₂₃×#107	C₂³	1	4	yes	—
210	C₂₃×#106	C₂³	1	2	yes	—
211	C₂₃×#106	C₂³	1	2	yes	—
212	C₂₃×#106	C₂³	1	4	yes	—
213	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
216	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
217	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
218	C₂₃×#103	C₂³	1	4	yes	—
219	C₂₃×#103	C₂³	1	4	yes	—
220	C₂₃×#103	C₂³	1	2	yes	—
221	C₂₃×#103	C₂³	1	2	yes	—
222	C₂₃×#103	C₂³	1	4	yes	—
223	C₂₃×#103	C₂³	1	4	yes	—
224	C₂₃×#103	C₂³	1	4	yes	—
225	C₂₃×#103	C₂³	1	4	yes	—
226	C₂₃×#102	C₂³	1	2	yes	—
227	C₂₃×#102	C₂³	1	2	yes	—
228	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
229	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
230	C₂₃×#97	C₂³	1	4	yes	—
231	C₄×C₈×C₂₃	C₂³	1	4	yes	—
232	#41×C₂₃	—	2	16	no	—
233	#41×C₂₃	—	2	8	no	—
234	#41×C₂₃	—	2	4	no	—
235	#41×C₂₃	—	2	4	no	—
236	#41×C₂₃	—	2	2	no	—
237	#41×C₂₃	—	2	2	no	—
238	#41×C₂₃	—	2	2	no	—
239	#41×C₂₃	#41	1	4	yes	—
240	C₂×Q₈×C₂₃	—	2	8	no	—
241	C₂×Q₈×C₂₃	—	2	4	no	—
242	C₂×Q₈×C₂₃	—	2	4	no	—
243	C₂×Q₈×C₂₃	—	2	2	no	—
244	C₂×Q₈×C₂₃	—	2	1	no	—
245	C₂×Q₈×C₂₃	—	2	1	no	—
246	C₂×Q₈×C₂₃	—	2	1	no	—
247	C₂×Q₈×C₂₃	—	2	2	no	—
248	C₂×Q₈×C₂₃	—	2	2	no	—
249	C₂×Q₈×C₂₃	—	2	4	no	—
250	C₂×Q₈×C₂₃	—	2	4	no	—
251	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
252	C₂×Q₈×C₂₃	#41	1	4	yes	—
253	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
254	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
255	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
256	C₂×D₄×C₂₃	—	2	2	no	—
257	C₂×D₄×C₂₃	—	2	1	no	—
258	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
259	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
260	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₂₃	—	2	2	no	—
262	C₂²×C₄×C₂₃	—	2	1	no	—
263	C₂²×C₄×C₂₃	—	2	2	no	—
264	C₂²×C₄×C₂₃	—	2	1	no	—
265	C₂²×C₄×C₂₃	—	2	2	no	—
266	C₂²×C₄×C₂₃	—	2	2	no	—
267	C₂²×C₄×C₂₃	—	2	1	no	—
268	C₂²×C₄×C₂₃	—	2	1	no	—
269	C₂²×C₄×C₂₃	—	2	2	no	—
270	C₂²×C₄×C₂₃	—	2	1	no	—
271	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
273	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
275	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
277	Q₁₆×C₂₃	—	2	8	no	—
278	Q₁₆×C₂₃	—	2	8	no	—
279	Q₁₆×C₂₃	—	2	8	no	—
280	SD₁₆×C₂₃	—	2	8	no	—
281	M₁₆×C₂₃	—	2	4	no	—
282	C₂×C₈×C₂₃	—	2	4	no	—
283	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
284	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
285	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
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	1	no	—
291	C₄⋊C₄×C₂₃	—	2	2	no	—
292	C₄⋊C₄×C₂₃	—	2	1	no	—
293	C₄⋊C₄×C₂₃	—	2	2	no	—
294	C₄⋊C₄×C₂₃	—	2	2	no	—
295	C₄⋊C₄×C₂₃	—	2	2	no	—
296	C₄⋊C₄×C₂₃	—	2	2	no	—
297	C₄⋊C₄×C₂₃	—	2	2	no	—
298	C₄⋊C₄×C₂₃	—	2	1	no	—
299	C₄⋊C₄×C₂₃	—	2	1	no	—
300	C₄⋊C₄×C₂₃	—	2	1	no	—
301	C₄⋊C₄×C₂₃	—	2	4	no	—
302	C₄⋊C₄×C₂₃	—	2	4	no	—
303	C₄⋊C₄×C₂₃	—	2	2	no	—
304	C₄⋊C₄×C₂₃	—	2	2	no	—
305	C₄⋊C₄×C₂₃	—	2	4	no	—
306	C₄⋊C₄×C₂₃	—	2	4	no	—
307	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
308	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
309	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
310	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
311	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
312	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
313	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
314	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
315	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
316	C₂²⋊C₄×C₂₃	—	2	2	no	—
317	C₂²⋊C₄×C₂₃	—	2	1	no	—
318	C₂²⋊C₄×C₂₃	—	2	2	no	—
319	C₂²⋊C₄×C₂₃	—	2	4	no	—
320	C₂²⋊C₄×C₂₃	—	2	4	no	—
321	C₂²⋊C₄×C₂₃	—	2	1	no	—
322	C₂²⋊C₄×C₂₃	—	2	2	no	—
323	C₂²⋊C₄×C₂₃	—	2	1	no	—
324	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
325	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
326	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
327	C₄²×C₂₃	—	2	2	no	—
328	C₄²×C₂₃	—	2	1	no	—
329	C₄²×C₂₃	—	2	2	no	—
330	C₄²×C₂₃	—	2	1	no	—
331	C₄²×C₂₃	—	2	2	no	—
332	C₄²×C₂₃	—	2	2	no	—
333	C₄²×C₂₃	—	2	2	no	—
334	C₄²×C₂₃	—	2	2	no	—
335	C₄²×C₂₃	—	2	1	no	—
336	C₄²×C₂₃	—	2	4	no	—
337	C₄²×C₂₃	—	2	4	no	—
338	C₄²×C₂₃	—	2	2	no	—
339	C₄²×C₂₃	C₂×D₄	1	2	yes	—
340	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₂₃	C₂×D₄	1	2	yes	—
342	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
343	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
344	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
345	C₄²×C₂₃	C₂⁴	1	2	yes	—
346	#60594	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
347	C₂³×C₂₃	—	2	1	no	—
348	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
349	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
350	Q₈×C₂₃	—	2	8	no	—
351	Q₈×C₂₃	—	2	2	no	—
352	Q₈×C₂₃	—	2	4	no	—
353	Q₈×C₂₃	—	2	1	no	—
354	Q₈×C₂₃	—	2	2	no	—
355	Q₈×C₂₃	—	2	4	no	—
356	Q₈×C₂₃	—	2	4	no	—
357	Q₈×C₂₃	—	4	2	no	—
358	Q₈×C₂₃	—	4	4	no	—
359	Q₈×C₂₃	—	4	2	no	—
360	Q₈×C₂₃	C₂×#41	1	2	yes	—
361	Q₈×C₂₃	C₂×#41	1	4	yes	—
362	D₄×C₂₃	—	2	8	no	—
363	D₄×C₂₃	—	2	4	no	—
364	D₄×C₂₃	—	2	4	no	—
365	D₄×C₂₃	—	2	2	no	—
366	D₄×C₂₃	—	2	1	no	—
367	D₄×C₂₃	C₂×#41	1	2	yes	—
368	C₂×C₄×C₂₃	—	2	8	no	—
369	C₂×C₄×C₂₃	—	2	8	no	—
370	C₂×C₄×C₂₃	—	2	4	no	—
371	C₂×C₄×C₂₃	—	2	2	no	—
372	C₂×C₄×C₂₃	—	2	1	no	—
373	C₂×C₄×C₂₃	—	2	4	no	—
374	C₂×C₄×C₂₃	—	2	2	no	—
375	C₂×C₄×C₂₃	—	2	4	no	—
376	C₂×C₄×C₂₃	—	2	2	no	—
377	C₂×C₄×C₂₃	—	2	2	no	—
378	C₂×C₄×C₂₃	—	2	1	no	—
379	C₂×C₄×C₂₃	—	2	1	no	—
380	C₂×C₄×C₂₃	—	2	2	no	—
381	C₂×C₄×C₂₃	—	2	2	no	—
382	C₂×C₄×C₂₃	—	2	2	no	—
383	C₂×C₄×C₂₃	—	2	4	no	—
384	C₂×C₄×C₂₃	—	4	1	no	—
385	C₂×C₄×C₂₃	—	4	2	no	—
386	C₂×C₄×C₂₃	—	4	4	no	—
387	C₂×C₄×C₂₃	—	4	2	no	—
388	C₂×C₄×C₂₃	—	8	2	no	—
389	C₂×C₄×C₂₃	—	8	1	no	—
390	C₂×C₄×C₂₃	—	8	1	no	—
391	C₂×C₄×C₂₃	—	8	2	no	—
392	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
393	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
394	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
397	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
401	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
402	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
403	C₈×C₂₃	—	2	2	no	—
404	C₈×C₂₃	—	2	2	no	—
405	C₈×C₂₃	—	2	4	no	—
406	#3509	C₂×C₂₃	1	1	yes	characteristic, complemented
407	C₄×2₋¹⁺⁴	C₂×C₂₃	1	1	yes	characteristic
408	#3127	C₂×C₂₃	1	4	yes	complemented
409	#3120	C₂×C₂₃	1	4	yes	complemented
410	#3116	C₂×C₂₃	1	2	yes	complemented
411	#3113	C₂×C₂₃	1	2	yes	complemented
412	#3107	C₂×C₂₃	1	2	yes	complemented
413	#3104	C₂×C₂₃	1	2	yes	complemented
414	#3097	C₂×C₂₃	1	2	yes	complemented
415	#3078	C₂×C₂₃	1	1	yes	characteristic, complemented
416	#3076	C₂×C₂₃	1	1	yes	characteristic, complemented
417	#3039	C₂×C₂₃	1	1	yes	characteristic, complemented
418	C₂×#462	C₂×C₂₃	1	1	yes	characteristic, complemented
419	#3011	C₂×C₂₃	1	2	yes	—
420	#2950	C₂×C₂₃	1	2	yes	complemented
421	#2947	C₂×C₂₃	1	2	yes	complemented
422	#2925	C₂×C₂₃	1	1	yes	characteristic, complemented
423	C₂²×C₂₃	—	2	1	no	—
424	C₂²×C₂₃	—	2	1	no	—
425	C₂²×C₂₃	—	2	2	no	—
426	C₂²×C₂₃	—	2	2	no	—
427	C₂²×C₂₃	—	2	2	no	—
428	C₂²×C₂₃	—	2	2	no	—
429	C₂²×C₂₃	—	4	1	no	—
430	C₂²×C₂₃	—	4	1	no	—
431	C₂²×C₂₃	#525	1	2	yes	—
432	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
433	C₄×C₂₃	—	2	1	no	—
434	C₄×C₂₃	—	2	2	no	—
435	C₄×C₂₃	—	2	1	no	—
436	C₄×C₂₃	—	2	4	no	—
437	C₄×C₂₃	—	2	2	no	—
438	C₄×C₂₃	—	2	2	no	—
439	C₄×C₂₃	—	2	2	no	—
440	C₄×C₂₃	—	2	1	no	—
441	C₄×C₂₃	—	4	2	no	—
442	C₄×C₂₃	—	4	1	no	—
443	C₄×C₂₃	—	4	2	no	—
444	C₄×C₂₃	—	4	4	no	—
445	C₄×C₂₃	—	4	1	no	—
446	C₄×C₂₃	—	4	2	no	—
447	C₄×C₂₃	#525	1	2	yes	—
448	C₄×C₂₃	#578	1	2	yes	—
449	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
450	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
451	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic
452	C₂×#137	C₂²×C₂₃	1	2	yes	—
453	C₂²×Q₁₆	C₂²×C₂₃	1	2	yes	—
454	#557	—	2	1	no	—
455	#557	—	2	1	no	—
456	#556	—	2	1	no	—
457	#556	—	2	1	no	—
458	#552	—	2	2	no	—
459	#552	—	2	2	no	—
460	#541	C₂²×C₂₃	1	4	yes	—
461	#536	C₂²×C₂₃	1	2	yes	—
462	#533	C₂²×C₂₃	1	2	yes	—
463	#533	C₂²×C₂₃	1	2	yes	—
464	#533	C₂²×C₂₃	1	1	yes	characteristic
465	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
466	#520	—	2	2	no	—
467	#520	—	2	1	no	—
468	#520	C₂²×C₂₃	1	2	yes	—
469	#520	C₂²×C₂₃	1	1	yes	characteristic
470	#520	C₂²×C₂₃	1	1	yes	characteristic
471	#519	—	2	1	no	—
472	#519	C₂²×C₂₃	1	2	yes	—
473	#519	C₂²×C₂₃	1	1	yes	characteristic
474	#519	C₂²×C₂₃	1	2	yes	—
475	C₄×#41	—	2	2	no	—
476	C₄×#41	—	2	1	no	—
477	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
478	C₄×#41	C₂²×C₂₃	1	2	yes	—
479	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
480	C₂×C₄×Q₈	—	2	1	no	—
481	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
482	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
483	#485	C₂²×C₂₃	1	4	yes	—
484	#485	C₂²×C₂₃	1	4	yes	—
485	#484	C₂²×C₂₃	1	4	yes	—
486	#483	C₂²×C₂₃	1	4	yes	—
487	#479	C₂²×C₂₃	1	2	yes	—
488	#479	C₂²×C₂₃	1	4	yes	—
489	#478	C₂²×C₂₃	1	2	yes	—
490	#477	C₂²×C₂₃	1	1	yes	characteristic
491	#477	C₂²×C₂₃	1	2	yes	—
492	#476	C₂²×C₂₃	1	1	yes	characteristic
493	#475	C₂²×C₂₃	1	1	yes	characteristic
494	#475	C₂²×C₂₃	1	2	yes	—
495	#474	C₂²×C₂₃	1	1	yes	characteristic
496	#462	C₂²×C₂₃	1	2	yes	—
497	#462	C₂²×C₂₃	1	2	yes	—
498	#462	C₂²×C₂₃	1	2	yes	—
499	#462	C₂²×C₂₃	1	4	yes	—
500	#462	C₂²×C₂₃	1	2	yes	—
501	#461	C₂²×C₂₃	1	2	yes	—
502	#461	C₂²×C₂₃	1	2	yes	—
503	#452	C₂²×C₂₃	1	4	yes	—
504	#452	C₂²×C₂₃	1	4	yes	—
505	#451	C₂²×C₂₃	1	4	yes	—
506	#451	C₂²×C₂₃	1	4	yes	—
507	#441	C₂²×C₂₃	1	4	yes	—
508	#441	C₂²×C₂₃	1	4	yes	—
509	#441	C₂²×C₂₃	1	4	yes	—
510	#440	C₂²×C₂₃	1	4	yes	—
511	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	—
512	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	—
513	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	—
514	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	—
515	#433	C₂²×C₂₃	1	4	yes	—
516	#432	C₂²×C₂₃	1	2	yes	—
517	#431	C₂²×C₂₃	1	2	yes	—
518	#428	C₂²×C₂₃	1	2	yes	—
519	#427	C₂²×C₂₃	1	2	yes	—
520	#423	C₂²×C₂₃	1	1	yes	characteristic
521	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
522	#419	C₂²×C₂₃	1	2	yes	—
523	#419	C₂²×C₂₃	1	2	yes	—
524	#416	C₂²×C₂₃	1	2	yes	—
525	C₂×#103	C₂²×C₂₃	1	2	yes	—
526	#408	C₂²×C₂₃	1	2	yes	—
527	#405	C₂²×C₂₃	1	2	yes	—
528	C₂×C₂₃	—	2	2	no	—
529	C₂×C₂₃	—	4	2	no	—
530	C₂×C₂₃	—	4	2	no	—
531	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
532	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
533	C₂×C₂₃	#3586	1	1	yes	characteristic
534	2₋¹⁺⁴	—	2	4	no	—
535	2₋¹⁺⁴	—	2	4	no	—
536	C₂×#41	—	2	2	no	—
537	C₂×#41	—	2	1	no	—
538	C₂×#41	C₂³×C₂₃	1	2	yes	—
539	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
540	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
541	C₂²×Q₈	—	2	1	no	—
542	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
543	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
544	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
545	#137	—	2	8	no	—
546	C₂×Q₁₆	—	2	8	no	—
547	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
548	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
549	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
550	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
551	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
552	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
553	C₄⋊Q₈	—	2	2	no	—
554	C₄⋊Q₈	—	2	1	no	—
555	C₄⋊Q₈	—	2	1	no	—
556	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
557	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
558	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
559	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
560	#126	—	2	4	no	—
561	#126	—	2	4	no	—
562	#125	—	2	4	no	—
563	#125	—	2	4	no	—
564	#125	—	2	2	no	—
565	#125	—	2	2	no	—
566	#125	C₂³×C₂₃	1	2	yes	—
567	#124	—	2	2	no	—
568	#123	—	2	4	no	—
569	C₂²⋊Q₈	—	2	1	no	—
570	C₂²⋊Q₈	—	2	1	no	—
571	C₂²⋊Q₈	—	2	2	no	—
572	C₂²⋊Q₈	—	2	2	no	—
573	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
574	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
575	C₄×Q₈	—	2	1	no	—
576	C₄×Q₈	—	2	1	no	—
577	C₄×Q₈	—	2	2	no	—
578	C₄×Q₈	—	2	1	no	—
579	C₄×Q₈	—	2	2	no	—
580	C₄×Q₈	—	2	2	no	—
581	C₄×Q₈	—	2	2	no	—
582	C₄×Q₈	—	2	2	no	—
583	C₄×Q₈	—	2	1	no	—
584	C₄×Q₈	—	2	2	no	—
585	C₄×Q₈	—	2	1	no	—
586	C₄×Q₈	—	2	2	no	—
587	C₄×Q₈	—	2	2	no	—
588	C₄×Q₈	—	2	1	no	—
589	C₄×Q₈	—	2	1	no	—
590	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
591	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
592	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
593	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
594	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
595	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
596	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
597	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
598	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
599	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
600	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
601	C₄×D₄	—	2	2	no	—
602	C₄×D₄	—	2	1	no	—
603	C₄×D₄	—	2	1	no	—
604	C₄×D₄	—	2	2	no	—
605	C₄×D₄	—	2	1	no	—
606	C₄×D₄	—	2	2	no	—
607	C₄×D₄	—	2	2	no	—
608	C₄×D₄	—	2	2	no	—
609	C₄×D₄	—	2	2	no	—
610	C₄×D₄	D₄×C₂₃	1	2	yes	—
611	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
612	C₄×D₄	D₄×C₂₃	1	2	yes	—
613	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
614	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
615	C₄×D₄	C₂³×C₂₃	1	2	yes	—
616	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
617	#117	—	2	2	no	—
618	#117	—	2	2	no	—
619	#117	—	2	1	no	—
620	#117	—	2	2	no	—
621	#117	—	2	2	no	—
622	#117	—	2	2	no	—
623	#117	—	2	2	no	—
624	#117	—	2	4	no	—
625	#117	—	2	2	no	—
626	#117	—	2	1	no	—
627	#117	C₂³×C₂₃	1	1	yes	characteristic
628	#117	C₂³×C₂₃	1	2	yes	—
629	#117	C₂³×C₂₃	1	2	yes	—
630	#117	C₂³×C₂₃	1	1	yes	characteristic
631	#117	C₂³×C₂₃	1	2	yes	—
632	C₂×C₄⋊C₄	—	2	1	no	—
633	C₂×C₄⋊C₄	—	2	2	no	—
634	C₂×C₄⋊C₄	—	2	1	no	—
635	C₂×C₄⋊C₄	—	2	1	no	—
636	C₂×C₄⋊C₄	—	2	1	no	—
637	C₂×C₄⋊C₄	—	2	2	no	—
638	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
639	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
640	C₂×C₄²	—	2	1	no	—
641	C₂×C₄²	—	2	2	no	—
642	C₂×C₄²	—	2	2	no	—
643	C₂×C₄²	—	2	1	no	—
644	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
646	#107	C₂³×C₂₃	1	2	yes	—
647	#107	C₂³×C₂₃	1	2	yes	—
648	#107	C₂³×C₂₃	1	4	yes	—
649	#106	C₂³×C₂₃	1	2	yes	—
650	#106	C₂³×C₂₃	1	2	yes	—
651	#106	C₂³×C₂₃	1	4	yes	—
652	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
653	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
654	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
655	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
656	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
657	#103	C₂³×C₂₃	1	4	yes	—
658	#103	C₂³×C₂₃	1	4	yes	—
659	#103	C₂³×C₂₃	1	2	yes	—
660	#103	C₂³×C₂₃	1	2	yes	—
661	#103	C₂³×C₂₃	1	4	yes	—
662	#103	C₂³×C₂₃	1	4	yes	—
663	#103	C₂³×C₂₃	1	4	yes	—
664	#103	C₂³×C₂₃	1	4	yes	—
665	#102	C₂³×C₂₃	1	2	yes	—
666	#102	C₂³×C₂₃	1	2	yes	—
667	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
668	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
669	#97	C₂³×C₂₃	1	4	yes	—
670	C₄×C₈	C₂³×C₂₃	1	4	yes	—
671	C₂₃	#60594	1	1	yes	characteristic, direct product factor, Sylow
672	#41	—	2	16	no	—
673	#41	—	2	8	no	—
674	#41	—	2	4	no	—
675	#41	—	2	4	no	—
676	#41	—	2	2	no	—
677	#41	—	2	2	no	—
678	#41	—	2	2	no	—
679	#41	#41×C₂₃	1	4	yes	—
680	C₂×Q₈	—	2	8	no	—
681	C₂×Q₈	—	2	4	no	—
682	C₂×Q₈	—	2	4	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	2	1	no	—
685	C₂×Q₈	—	2	1	no	—
686	C₂×Q₈	—	2	1	no	—
687	C₂×Q₈	—	2	2	no	—
688	C₂×Q₈	—	2	2	no	—
689	C₂×Q₈	—	2	4	no	—
690	C₂×Q₈	—	2	4	no	—
691	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
692	C₂×Q₈	#41×C₂₃	1	4	yes	—
693	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
694	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
695	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
699	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
700	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
712	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
713	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
714	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
715	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
716	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
717	Q₁₆	—	2	8	no	—
718	Q₁₆	—	2	8	no	—
719	Q₁₆	—	2	8	no	—
720	SD₁₆	—	2	8	no	—
721	M₁₆	—	2	4	no	—
722	C₂×C₈	—	2	4	no	—
723	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
724	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
725	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	1	no	—
739	C₄⋊C₄	—	2	1	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	4	no	—
743	C₄⋊C₄	—	2	2	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	4	no	—
746	C₄⋊C₄	—	2	4	no	—
747	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
748	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
749	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
750	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
751	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
752	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
753	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
754	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
755	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	4	no	—
760	C₂²⋊C₄	—	2	4	no	—
761	C₂²⋊C₄	—	2	1	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	1	no	—
764	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
765	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
766	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
767	C₄²	—	2	2	no	—
768	C₄²	—	2	1	no	—
769	C₄²	—	2	2	no	—
770	C₄²	—	2	1	no	—
771	C₄²	—	2	2	no	—
772	C₄²	—	2	2	no	—
773	C₄²	—	2	2	no	—
774	C₄²	—	2	2	no	—
775	C₄²	—	2	1	no	—
776	C₄²	—	2	4	no	—
777	C₄²	—	2	4	no	—
778	C₄²	—	2	2	no	—
779	C₄²	C₂×D₄×C₂₃	1	2	yes	—
780	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
781	C₄²	C₂×D₄×C₂₃	1	2	yes	—
782	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
783	C₄²	C₂⁴×C₂₃	1	2	yes	—
784	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
785	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
786	C₂³	—	2	1	no	—
787	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
788	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
789	Q₈	—	2	8	no	—
790	Q₈	—	2	1	no	—
791	Q₈	—	2	2	no	—
792	Q₈	—	2	2	no	—
793	Q₈	—	2	4	no	—
794	Q₈	—	2	4	no	—
795	Q₈	—	2	4	no	—
796	Q₈	—	4	2	no	—
797	Q₈	—	4	2	no	—
798	Q₈	—	4	4	no	—
799	Q₈	C₂×#41×C₂₃	1	2	yes	—
800	Q₈	C₂×#41×C₂₃	1	4	yes	—
801	D₄	—	2	8	no	—
802	D₄	—	2	4	no	—
803	D₄	—	2	4	no	—
804	D₄	—	2	1	no	—
805	D₄	—	2	2	no	—
806	D₄	C₂×#41×C₂₃	1	2	yes	—
807	C₂×C₄	—	2	8	no	—
808	C₂×C₄	—	2	8	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	4	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	4	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	4	no	—
817	C₂×C₄	—	2	1	no	—
818	C₂×C₄	—	2	1	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	4	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	2	no	—
825	C₂×C₄	—	4	4	no	—
826	C₂×C₄	—	4	2	no	—
827	C₂×C₄	—	8	2	no	—
828	C₂×C₄	—	8	1	no	—
829	C₂×C₄	—	8	1	no	—
830	C₂×C₄	—	8	2	no	—
831	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
832	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
833	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
834	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
835	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
836	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
837	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
838	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
839	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
840	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
841	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
842	C₈	—	2	2	no	—
843	C₈	—	2	2	no	—
844	C₈	—	2	4	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	2	1	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	4	1	no	—
852	C₂²	—	4	1	no	—
853	C₂²	C₂₃×#525	1	2	yes	—
854	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
855	C₄	—	2	4	no	—
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	2	no	—
859	C₄	—	2	1	no	—
860	C₄	—	2	1	no	—
861	C₄	—	2	2	no	—
862	C₄	—	2	1	no	—
863	C₄	—	4	4	no	—
864	C₄	—	4	1	no	—
865	C₄	—	4	2	no	—
866	C₄	—	4	2	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	2	no	—
869	C₄	C₂₃×#525	1	2	yes	—
870	C₄	C₂₃×#578	1	2	yes	—
871	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
872	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
873	C₂	—	2	2	no	—
874	C₂	—	4	2	no	—
875	C₂	—	4	2	no	—
876	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
877	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
878	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂×C₂₃×2₋¹⁺⁴	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3509	C₂	semidirect
3. C₂₃×#3127	C₂	semidirect
4. C₂₃×#3120	C₂	semidirect
5. C₂₃×#3116	C₂	semidirect
6. C₂₃×#3113	C₂	semidirect
7. C₂₃×#3107	C₂	semidirect
8. C₂₃×#3104	C₂	semidirect
9. C₂₃×#3097	C₂	semidirect
10. C₂₃×#3078	C₂	semidirect
11. C₂₃×#3076	C₂	semidirect
12. C₂₃×#3039	C₂	semidirect
13. C₂×C₂₃×#462	C₂	semidirect
15. C₂₃×#2950	C₂	semidirect
16. C₂₃×#2947	C₂	semidirect
17. C₂₃×#2925	C₂	semidirect
346. #60594	C₂₃	direct (N × H)
406. #3509	C₂×C₂₃	semidirect
408. #3127	C₂×C₂₃	semidirect
409. #3120	C₂×C₂₃	semidirect
410. #3116	C₂×C₂₃	semidirect
411. #3113	C₂×C₂₃	semidirect
412. #3107	C₂×C₂₃	semidirect
413. #3104	C₂×C₂₃	semidirect
414. #3097	C₂×C₂₃	semidirect
415. #3078	C₂×C₂₃	semidirect
416. #3076	C₂×C₂₃	semidirect
417. #3039	C₂×C₂₃	semidirect
418. C₂×#462	C₂×C₂₃	semidirect
420. #2950	C₂×C₂₃	semidirect
421. #2947	C₂×C₂₃	semidirect
422. #2925	C₂×C₂₃	semidirect
671. C₂₃	#60594	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×#3509	2
C₄×C₂₃×2₋¹⁺⁴	2
C₂₃×#3127	2
C₂₃×#3120	2
C₂₃×#3116	2
C₂₃×#3113	2
C₂₃×#3107	2
C₂₃×#3104	2
C₂₃×#3097	2
C₂₃×#3078	2
C₂₃×#3076	2
C₂₃×#3039	2
C₂×C₂₃×#462	2
C₂₃×#3011	2
C₂₃×#2950	2
C₂₃×#2947	2
C₂₃×#2925	2
#60594	23

Subgroups — C23×#60594 #19208220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60594 #19208220