Subgroups — C₂₃×#61446 #19209072

Order 5888.

1830 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3482	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3402	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3390	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3377	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3352	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3343	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3327	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3312	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3308	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3277	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3270	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3172	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3108	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3104	C₂	1	2	yes	maximal, complemented
16	C₂₃×#3102	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₂₃×#137	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₂₃×#137	C₂²	1	2	yes	—
21	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
22	C₂₃×#557	C₂²	1	2	yes	—
23	C₂₃×#556	—	2	2	no	—
24	C₂₃×#556	C₂²	1	2	yes	—
25	C₂₃×#552	—	2	2	no	—
26	C₂₃×#552	—	2	2	no	—
27	C₂₃×#552	C₂²	1	2	yes	—
28	C₂₃×#552	C₂²	1	2	yes	—
29	D₄×Q₈×C₂₃	C₂²	1	2	yes	—
30	C₂₃×#548	C₂²	1	2	yes	—
31	C₂₃×#548	C₂²	1	2	yes	—
32	C₂₃×#547	—	2	2	no	—
33	C₂₃×#547	C₂²	1	2	yes	—
34	C₂₃×#533	—	2	2	no	—
35	C₂₃×#533	C₂²	1	2	yes	—
36	C₂₃×#529	—	2	2	no	—
37	C₂₃×#529	—	2	2	no	—
38	C₂₃×#529	C₂²	1	2	yes	—
39	C₂₃×#529	C₂²	1	2	yes	—
40	C₄×#41×C₂₃	—	2	2	no	—
41	C₄×#41×C₂₃	C₂²	1	2	yes	—
42	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
45	C₂₃×#501	C₂²	1	2	yes	—
46	C₂₃×#499	C₂²	1	1	yes	characteristic
47	C₂₃×#497	C₂²	1	2	yes	—
48	C₂₃×#495	C₂²	1	1	yes	characteristic
49	C₂₃×#491	C₂²	1	2	yes	—
50	C₂₃×#489	C₂²	1	2	yes	—
51	C₂₃×#488	C₂²	1	2	yes	—
52	C₂₃×#485	C₂²	1	2	yes	—
53	C₂₃×#484	C₂²	1	2	yes	—
54	C₂₃×#484	C₂²	1	2	yes	—
55	C₂₃×#483	C₂²	1	2	yes	—
56	C₂₃×#482	C₂²	1	2	yes	—
57	C₂₃×#480	C₂²	1	2	yes	—
58	C₂₃×#479	C₂²	1	2	yes	—
59	C₂₃×#479	C₂²	1	2	yes	—
60	C₂₃×#479	C₂²	1	2	yes	—
61	C₂₃×#478	C₂²	1	2	yes	—
62	C₂₃×#477	C₂²	1	2	yes	—
63	C₂₃×#477	C₂²	1	2	yes	—
64	C₂₃×#470	C₂²	1	2	yes	—
65	C₂₃×#470	C₂²	1	2	yes	—
66	C₂₃×#468	C₂²	1	2	yes	—
67	C₂₃×#468	C₂²	1	2	yes	—
68	C₂₃×#467	C₂²	1	1	yes	characteristic
69	C₂₃×#466	C₂²	1	1	yes	characteristic
70	C₂₃×#465	C₂²	1	2	yes	—
71	C₂₃×#464	C₂²	1	2	yes	—
72	C₂₃×#464	C₂²	1	2	yes	—
73	C₂₃×#464	C₂²	1	2	yes	—
74	C₂₃×#463	C₂²	1	2	yes	—
75	C₂₃×#462	C₂²	1	2	yes	—
76	C₂₃×#462	C₂²	1	2	yes	—
77	C₂₃×#452	C₂²	1	2	yes	—
78	C₂₃×#451	C₂²	1	2	yes	—
79	C₂₃×#451	C₂²	1	2	yes	—
80	C₂₃×#451	C₂²	1	2	yes	—
81	C₂₃×#449	C₂²	1	2	yes	—
82	C₂₃×#448	C₂²	1	2	yes	—
83	C₂₃×#446	C₂²	1	1	yes	characteristic
84	C₂₃×#446	C₂²	1	1	yes	characteristic
85	C₂₃×#441	C₂²	1	2	yes	—
86	C₂₃×#441	C₂²	1	2	yes	—
87	C₂₃×#440	C₂²	1	2	yes	—
88	C₂₃×#440	C₂²	1	2	yes	—
89	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
90	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
91	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
92	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
93	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
94	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
95	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
96	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
97	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
98	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
99	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
100	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
101	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
102	C₂₃×#436	C₂²	1	1	yes	characteristic
103	C₂₃×#436	C₂²	1	1	yes	characteristic
104	C₂₃×#435	C₂²	1	2	yes	—
105	C₂₃×#435	C₂²	1	2	yes	—
106	C₂₃×#431	C₂²	1	2	yes	—
107	C₂₃×#431	C₂²	1	1	yes	characteristic
108	C₂₃×#428	C₂²	1	2	yes	—
109	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
110	C₂₃×#419	C₂²	1	2	yes	—
111	C₂₃×#417	C₂²	1	2	yes	—
112	C₂×C₂₃×#103	C₂²	1	2	yes	—
113	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
114	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
115	C₂×#41×C₂₃	—	2	2	no	—
116	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
117	C₂×#41×C₂₃	C₂³	1	2	yes	—
118	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
119	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
120	C₂₃×#137	—	2	8	no	—
121	C₂×Q₁₆×C₂₃	—	2	4	no	—
122	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
123	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
124	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
125	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
126	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
127	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
128	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
129	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
130	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
131	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
132	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
133	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
134	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
136	C₂₃×C₄⋊Q₈	—	2	2	no	—
137	C₂₃×C₄⋊Q₈	—	2	2	no	—
138	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
139	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
140	C₂₃×#126	—	2	2	no	—
141	C₂₃×#126	—	2	2	no	—
142	C₂₃×#126	—	2	2	no	—
143	C₂₃×#126	—	2	2	no	—
144	C₂₃×#126	—	2	2	no	—
145	C₂₃×#126	—	2	2	no	—
146	C₂₃×#125	—	2	2	no	—
147	C₂₃×#125	—	2	2	no	—
148	C₂₃×#125	—	2	2	no	—
149	C₂₃×#125	—	2	2	no	—
150	C₂₃×#125	—	2	2	no	—
151	C₂₃×#125	C₂³	1	2	yes	—
152	C₂₃×#125	C₂³	1	2	yes	—
153	C₂₃×#124	—	2	2	no	—
154	C₂₃×#124	—	2	2	no	—
155	C₂₃×#124	C₂³	1	2	yes	—
156	C₂₃×#124	C₂³	1	2	yes	—
157	C₂₃×#123	—	2	2	no	—
158	C₂₃×#123	—	2	2	no	—
159	C₂₃×#123	—	2	2	no	—
160	C₂₃×#123	—	2	2	no	—
161	C₂₃×#123	—	2	2	no	—
162	C₂₃×#123	—	2	2	no	—
163	C₂₃×C₂²⋊Q₈	—	2	2	no	—
164	C₂₃×C₂²⋊Q₈	—	2	2	no	—
165	C₂₃×C₂²⋊Q₈	—	2	2	no	—
166	C₂₃×C₂²⋊Q₈	—	2	2	no	—
167	C₂₃×C₂²⋊Q₈	—	2	2	no	—
168	C₂₃×C₂²⋊Q₈	—	2	2	no	—
169	C₂₃×C₂²⋊Q₈	—	2	2	no	—
170	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
171	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
172	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
173	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
174	C₂₃×#121	—	2	2	no	—
175	C₂₃×#121	—	2	2	no	—
176	C₂₃×#121	C₂³	1	2	yes	—
177	C₂₃×#121	C₂³	1	2	yes	—
178	C₄×Q₈×C₂₃	—	2	2	no	—
179	C₄×Q₈×C₂₃	—	2	2	no	—
180	C₄×Q₈×C₂₃	—	2	2	no	—
181	C₄×Q₈×C₂₃	—	2	2	no	—
182	C₄×Q₈×C₂₃	—	2	2	no	—
183	C₄×Q₈×C₂₃	—	2	2	no	—
184	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
185	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
186	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
187	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
188	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
189	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
190	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
191	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
192	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
193	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
194	C₄×D₄×C₂₃	—	2	2	no	—
195	C₄×D₄×C₂₃	—	2	2	no	—
196	C₄×D₄×C₂₃	—	2	2	no	—
197	C₄×D₄×C₂₃	—	2	2	no	—
198	C₄×D₄×C₂₃	—	2	2	no	—
199	C₄×D₄×C₂₃	—	2	2	no	—
200	C₄×D₄×C₂₃	—	2	2	no	—
201	C₄×D₄×C₂₃	D₄	1	2	yes	—
202	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
203	C₄×D₄×C₂₃	C₂³	1	2	yes	—
204	C₄×D₄×C₂₃	C₂³	1	2	yes	—
205	C₄×D₄×C₂₃	C₂³	1	2	yes	—
206	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
207	C₂₃×#117	—	2	2	no	—
208	C₂₃×#117	—	2	2	no	—
209	C₂₃×#117	—	2	2	no	—
210	C₂₃×#117	—	2	2	no	—
211	C₂₃×#117	—	2	2	no	—
212	C₂₃×#117	—	2	2	no	—
213	C₂₃×#117	—	2	2	no	—
214	C₂₃×#117	D₄	1	1	yes	characteristic
215	C₂₃×#117	D₄	1	2	yes	—
216	C₂₃×#117	C₂³	1	2	yes	—
217	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
218	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
219	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
220	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
221	C₂×C₄²×C₂₃	—	2	2	no	—
222	C₂×C₄²×C₂₃	—	2	2	no	—
223	C₂×C₄²×C₂₃	—	2	2	no	—
224	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
225	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
226	C₂₃×#107	C₂³	1	1	yes	characteristic
227	C₂₃×#107	C₂³	1	1	yes	characteristic
228	C₂₃×#107	C₂³	1	2	yes	—
229	C₂₃×#107	C₂³	1	2	yes	—
230	C₂₃×#107	C₂³	1	1	yes	characteristic
231	C₂₃×#107	C₂³	1	1	yes	characteristic
232	C₂₃×#107	C₂³	1	2	yes	—
233	C₂₃×#106	C₂³	1	2	yes	—
234	C₂₃×#106	C₂³	1	2	yes	—
235	C₂₃×#106	C₂³	1	2	yes	—
236	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
237	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
238	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
239	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
240	C₂₃×#103	C₂³	1	2	yes	—
241	C₂₃×#103	C₂³	1	2	yes	—
242	C₂₃×#103	C₂³	1	2	yes	—
243	C₂₃×#103	C₂³	1	2	yes	—
244	C₂₃×#103	C₂³	1	2	yes	—
245	C₂₃×#103	C₂³	1	2	yes	—
246	C₂₃×#103	C₂³	1	2	yes	—
247	C₂₃×#103	C₂³	1	2	yes	—
248	C₂₃×#103	C₂³	1	2	yes	—
249	C₂₃×#103	C₂³	1	2	yes	—
250	C₂₃×#103	C₂³	1	2	yes	—
251	C₂₃×#103	C₂³	1	2	yes	—
252	C₂₃×#102	C₂³	1	2	yes	—
253	C₂₃×#102	C₂³	1	2	yes	—
254	C₂₃×#102	C₂³	1	2	yes	—
255	C₂₃×#102	C₂³	1	2	yes	—
256	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
258	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
259	C₂₃×#97	C₂³	1	2	yes	—
260	C₂₃×#97	C₂³	1	2	yes	—
261	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
262	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
263	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
264	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₂₃	C₂³	1	2	yes	—
266	#41×C₂₃	—	2	4	no	—
267	#41×C₂₃	—	4	2	no	—
268	#41×C₂₃	—	4	2	no	—
269	#41×C₂₃	—	4	8	no	—
270	C₂×Q₈×C₂₃	—	2	2	no	—
271	C₂×Q₈×C₂₃	—	2	2	no	—
272	C₂×Q₈×C₂₃	—	2	2	no	—
273	C₂×Q₈×C₂₃	—	2	4	no	—
274	C₂×Q₈×C₂₃	—	2	4	no	—
275	C₂×Q₈×C₂₃	—	4	2	no	—
276	C₂×Q₈×C₂₃	—	4	2	no	—
277	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
278	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
279	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
280	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
281	C₂×D₄×C₂₃	—	2	2	no	—
282	C₂×D₄×C₂₃	—	2	2	no	—
283	C₂×D₄×C₂₃	—	2	2	no	—
284	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
285	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
286	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₂₃	—	2	2	no	—
288	C₂²×C₄×C₂₃	—	2	2	no	—
289	C₂²×C₄×C₂₃	—	2	2	no	—
290	C₂²×C₄×C₂₃	—	2	2	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	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
297	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
298	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
300	Q₁₆×C₂₃	—	2	4	no	—
301	Q₁₆×C₂₃	—	2	4	no	—
302	Q₁₆×C₂₃	—	2	2	no	—
303	Q₁₆×C₂₃	—	4	1	no	—
304	Q₁₆×C₂₃	—	4	2	no	—
305	Q₁₆×C₂₃	#41	1	4	yes	complemented
306	SD₁₆×C₂₃	—	2	4	no	—
307	SD₁₆×C₂₃	—	2	4	no	—
308	SD₁₆×C₂₃	—	4	2	no	—
309	D₈×C₂₃	—	4	1	no	—
310	M₁₆×C₂₃	—	2	4	no	—
311	M₁₆×C₂₃	—	4	2	no	—
312	C₂×C₈×C₂₃	—	2	2	no	—
313	C₂×C₈×C₂₃	—	4	1	no	—
314	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
315	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
316	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
317	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
318	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
319	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
320	C₄⋊C₄×C₂₃	—	2	2	no	—
321	C₄⋊C₄×C₂₃	—	2	2	no	—
322	C₄⋊C₄×C₂₃	—	2	2	no	—
323	C₄⋊C₄×C₂₃	—	2	2	no	—
324	C₄⋊C₄×C₂₃	—	2	2	no	—
325	C₄⋊C₄×C₂₃	—	2	2	no	—
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	2	no	—
331	C₄⋊C₄×C₂₃	—	2	2	no	—
332	C₄⋊C₄×C₂₃	—	2	2	no	—
333	C₄⋊C₄×C₂₃	—	2	2	no	—
334	C₄⋊C₄×C₂₃	—	2	2	no	—
335	C₄⋊C₄×C₂₃	—	2	2	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	C₂×D₄	1	2	yes	—
342	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
343	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
344	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
345	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
346	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
347	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
348	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
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	C₂²⋊C₄×C₂₃	—	2	2	no	—
362	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
363	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
364	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
371	C₄²×C₂₃	—	2	2	no	—
372	C₄²×C₂₃	—	2	2	no	—
373	C₄²×C₂₃	—	2	2	no	—
374	C₄²×C₂₃	C₂×D₄	1	2	yes	—
375	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
376	C₄²×C₂₃	C₂×D₄	1	2	yes	—
377	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
378	C₄²×C₂₃	C₂⁴	1	2	yes	—
379	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
380	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
381	#61446	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
382	C₂³×C₂₃	—	2	2	no	—
383	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
384	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
385	Q₈×C₂₃	—	2	2	no	—
386	Q₈×C₂₃	—	2	2	no	—
387	Q₈×C₂₃	—	2	2	no	—
388	Q₈×C₂₃	—	2	2	no	—
389	Q₈×C₂₃	—	2	2	no	—
390	Q₈×C₂₃	—	4	1	no	—
391	Q₈×C₂₃	—	4	4	no	—
392	Q₈×C₂₃	—	4	4	no	—
393	Q₈×C₂₃	—	4	4	no	—
394	Q₈×C₂₃	C₂×#41	1	4	yes	—
395	D₄×C₂₃	—	2	4	no	—
396	D₄×C₂₃	—	2	2	no	—
397	D₄×C₂₃	—	2	2	no	—
398	D₄×C₂₃	—	4	1	no	—
399	D₄×C₂₃	—	4	4	no	—
400	D₄×C₂₃	—	4	4	no	—
401	D₄×C₂₃	—	4	4	no	—
402	C₂×C₄×C₂₃	—	2	2	no	—
403	C₂×C₄×C₂₃	—	2	2	no	—
404	C₂×C₄×C₂₃	—	2	2	no	—
405	C₂×C₄×C₂₃	—	2	4	no	—
406	C₂×C₄×C₂₃	—	2	1	no	—
407	C₂×C₄×C₂₃	—	2	2	no	—
408	C₂×C₄×C₂₃	—	2	1	no	—
409	C₂×C₄×C₂₃	—	2	2	no	—
410	C₂×C₄×C₂₃	—	2	2	no	—
411	C₂×C₄×C₂₃	—	2	2	no	—
412	C₂×C₄×C₂₃	—	2	2	no	—
413	C₂×C₄×C₂₃	—	2	2	no	—
414	C₂×C₄×C₂₃	—	2	2	no	—
415	C₂×C₄×C₂₃	—	2	2	no	—
416	C₂×C₄×C₂₃	—	4	2	no	—
417	C₂×C₄×C₂₃	—	4	4	no	—
418	C₂×C₄×C₂₃	—	4	4	no	—
419	C₂×C₄×C₂₃	—	4	4	no	—
420	C₂×C₄×C₂₃	—	4	4	no	—
421	C₂×C₄×C₂₃	—	4	4	no	—
422	C₂×C₄×C₂₃	—	4	4	no	—
423	C₂×C₄×C₂₃	—	4	4	no	—
424	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
426	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
427	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
428	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
429	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
430	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
433	C₈×C₂₃	—	2	1	no	—
434	C₈×C₂₃	—	2	2	no	—
435	C₈×C₂₃	—	2	1	no	—
436	C₈×C₂₃	—	2	1	no	—
437	C₈×C₂₃	—	2	2	no	—
438	C₈×C₂₃	C₂×#41	1	2	yes	—
439	#3482	C₂×C₂₃	1	2	yes	complemented
440	#3402	C₂×C₂₃	1	1	yes	characteristic, complemented
441	#3390	C₂×C₂₃	1	1	yes	characteristic, complemented
442	#3377	C₂×C₂₃	1	2	yes	complemented
443	#3352	C₂×C₂₃	1	1	yes	characteristic, complemented
444	#3343	C₂×C₂₃	1	2	yes	complemented
445	#3327	C₂×C₂₃	1	2	yes	complemented
446	#3312	C₂×C₂₃	1	2	yes	complemented
447	#3308	C₂×C₂₃	1	2	yes	complemented
448	#3277	C₂×C₂₃	1	1	yes	characteristic, complemented
449	#3270	C₂×C₂₃	1	2	yes	complemented
450	#3172	C₂×C₂₃	1	2	yes	complemented
451	#3168	C₂×C₂₃	1	1	yes	characteristic, complemented
452	#3108	C₂×C₂₃	1	2	yes	complemented
453	#3104	C₂×C₂₃	1	2	yes	complemented
454	#3102	C₂×C₂₃	1	2	yes	complemented
455	#2965	C₂×C₂₃	1	1	yes	characteristic, complemented
456	C₄×#137	C₂×C₂₃	1	2	yes	complemented
457	C₂×C₄×Q₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
458	C₂²×C₂₃	—	2	1	no	—
459	C₂²×C₂₃	—	2	1	no	—
460	C₂²×C₂₃	—	2	2	no	—
461	C₂²×C₂₃	—	2	2	no	—
462	C₂²×C₂₃	—	2	2	no	—
463	C₂²×C₂₃	—	4	2	no	—
464	C₂²×C₂₃	—	4	2	no	—
465	C₂²×C₂₃	—	4	2	no	—
466	C₂²×C₂₃	#575	1	2	yes	—
467	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
468	C₄×C₂₃	—	2	2	no	—
469	C₄×C₂₃	—	2	1	no	—
470	C₄×C₂₃	—	2	4	no	—
471	C₄×C₂₃	—	2	1	no	—
472	C₄×C₂₃	—	2	1	no	—
473	C₄×C₂₃	—	2	2	no	—
474	C₄×C₂₃	—	2	1	no	—
475	C₄×C₂₃	—	2	2	no	—
476	C₄×C₂₃	—	4	2	no	—
477	C₄×C₂₃	—	4	2	no	—
478	C₄×C₂₃	—	4	2	no	—
479	C₄×C₂₃	—	4	2	no	—
480	C₄×C₂₃	—	4	2	no	—
481	C₄×C₂₃	—	4	2	no	—
482	C₄×C₂₃	#578	1	2	yes	—
483	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
484	C₄×C₂₃	#585	1	1	yes	characteristic
485	C₂×#137	C₂²×C₂₃	1	2	yes	—
486	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
487	#557	C₂²×C₂₃	1	2	yes	—
488	#556	—	2	2	no	—
489	#556	C₂²×C₂₃	1	2	yes	—
490	#552	—	2	2	no	—
491	#552	—	2	2	no	—
492	#552	C₂²×C₂₃	1	2	yes	—
493	#552	C₂²×C₂₃	1	2	yes	—
494	D₄×Q₈	C₂²×C₂₃	1	2	yes	—
495	#548	C₂²×C₂₃	1	2	yes	—
496	#548	C₂²×C₂₃	1	2	yes	—
497	#547	—	2	2	no	—
498	#547	C₂²×C₂₃	1	2	yes	—
499	#533	—	2	2	no	—
500	#533	C₂²×C₂₃	1	2	yes	—
501	#529	—	2	2	no	—
502	#529	—	2	2	no	—
503	#529	C₂²×C₂₃	1	2	yes	—
504	#529	C₂²×C₂₃	1	2	yes	—
505	C₄×#41	—	2	2	no	—
506	C₄×#41	C₂²×C₂₃	1	2	yes	—
507	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
508	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
509	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
510	#501	C₂²×C₂₃	1	2	yes	—
511	#499	C₂²×C₂₃	1	1	yes	characteristic
512	#497	C₂²×C₂₃	1	2	yes	—
513	#495	C₂²×C₂₃	1	1	yes	characteristic
514	#491	C₂²×C₂₃	1	2	yes	—
515	#489	C₂²×C₂₃	1	2	yes	—
516	#488	C₂²×C₂₃	1	2	yes	—
517	#485	C₂²×C₂₃	1	2	yes	—
518	#484	C₂²×C₂₃	1	2	yes	—
519	#484	C₂²×C₂₃	1	2	yes	—
520	#483	C₂²×C₂₃	1	2	yes	—
521	#482	C₂²×C₂₃	1	2	yes	—
522	#480	C₂²×C₂₃	1	2	yes	—
523	#479	C₂²×C₂₃	1	2	yes	—
524	#479	C₂²×C₂₃	1	2	yes	—
525	#479	C₂²×C₂₃	1	2	yes	—
526	#478	C₂²×C₂₃	1	2	yes	—
527	#477	C₂²×C₂₃	1	2	yes	—
528	#477	C₂²×C₂₃	1	2	yes	—
529	#470	C₂²×C₂₃	1	2	yes	—
530	#470	C₂²×C₂₃	1	2	yes	—
531	#468	C₂²×C₂₃	1	2	yes	—
532	#468	C₂²×C₂₃	1	2	yes	—
533	#467	C₂²×C₂₃	1	1	yes	characteristic
534	#466	C₂²×C₂₃	1	1	yes	characteristic
535	#465	C₂²×C₂₃	1	2	yes	—
536	#464	C₂²×C₂₃	1	2	yes	—
537	#464	C₂²×C₂₃	1	2	yes	—
538	#464	C₂²×C₂₃	1	2	yes	—
539	#463	C₂²×C₂₃	1	2	yes	—
540	#462	C₂²×C₂₃	1	2	yes	—
541	#462	C₂²×C₂₃	1	2	yes	—
542	#452	C₂²×C₂₃	1	2	yes	—
543	#451	C₂²×C₂₃	1	2	yes	—
544	#451	C₂²×C₂₃	1	2	yes	—
545	#451	C₂²×C₂₃	1	2	yes	—
546	#449	C₂²×C₂₃	1	2	yes	—
547	#448	C₂²×C₂₃	1	2	yes	—
548	#446	C₂²×C₂₃	1	1	yes	characteristic
549	#446	C₂²×C₂₃	1	1	yes	characteristic
550	#441	C₂²×C₂₃	1	2	yes	—
551	#441	C₂²×C₂₃	1	2	yes	—
552	#440	C₂²×C₂₃	1	2	yes	—
553	#440	C₂²×C₂₃	1	2	yes	—
554	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
555	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
556	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
557	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
558	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
559	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
560	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
561	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
562	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
563	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
564	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
565	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
566	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
567	#436	C₂²×C₂₃	1	1	yes	characteristic
568	#436	C₂²×C₂₃	1	1	yes	characteristic
569	#435	C₂²×C₂₃	1	2	yes	—
570	#435	C₂²×C₂₃	1	2	yes	—
571	#431	C₂²×C₂₃	1	2	yes	—
572	#431	C₂²×C₂₃	1	1	yes	characteristic
573	#428	C₂²×C₂₃	1	2	yes	—
574	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
575	#419	C₂²×C₂₃	1	2	yes	—
576	#417	C₂²×C₂₃	1	2	yes	—
577	C₂×#103	C₂²×C₂₃	1	2	yes	—
578	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
579	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
580	C₂×C₂₃	—	2	2	no	—
581	C₂×C₂₃	—	4	2	no	—
582	C₂×C₂₃	—	8	2	no	—
583	C₂×C₂₃	D₄×#41	1	1	yes	characteristic
584	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
585	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
586	C₂×#41	—	2	2	no	—
587	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
588	C₂×#41	C₂³×C₂₃	1	2	yes	—
589	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
590	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
591	#137	—	2	8	no	—
592	C₂×Q₁₆	—	2	4	no	—
593	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
594	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
595	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
596	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
597	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
598	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
599	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
600	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
601	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
602	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
603	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
604	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
605	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
606	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
607	C₄⋊Q₈	—	2	2	no	—
608	C₄⋊Q₈	—	2	2	no	—
609	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
610	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
611	#126	—	2	2	no	—
612	#126	—	2	2	no	—
613	#126	—	2	2	no	—
614	#126	—	2	2	no	—
615	#126	—	2	2	no	—
616	#126	—	2	2	no	—
617	#125	—	2	2	no	—
618	#125	—	2	2	no	—
619	#125	—	2	2	no	—
620	#125	—	2	2	no	—
621	#125	—	2	2	no	—
622	#125	C₂³×C₂₃	1	2	yes	—
623	#125	C₂³×C₂₃	1	2	yes	—
624	#124	—	2	2	no	—
625	#124	—	2	2	no	—
626	#124	C₂³×C₂₃	1	2	yes	—
627	#124	C₂³×C₂₃	1	2	yes	—
628	#123	—	2	2	no	—
629	#123	—	2	2	no	—
630	#123	—	2	2	no	—
631	#123	—	2	2	no	—
632	#123	—	2	2	no	—
633	#123	—	2	2	no	—
634	C₂²⋊Q₈	—	2	2	no	—
635	C₂²⋊Q₈	—	2	2	no	—
636	C₂²⋊Q₈	—	2	2	no	—
637	C₂²⋊Q₈	—	2	2	no	—
638	C₂²⋊Q₈	—	2	2	no	—
639	C₂²⋊Q₈	—	2	2	no	—
640	C₂²⋊Q₈	—	2	2	no	—
641	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
642	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
643	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
644	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
645	#121	—	2	2	no	—
646	#121	—	2	2	no	—
647	#121	C₂³×C₂₃	1	2	yes	—
648	#121	C₂³×C₂₃	1	2	yes	—
649	C₄×Q₈	—	2	2	no	—
650	C₄×Q₈	—	2	2	no	—
651	C₄×Q₈	—	2	2	no	—
652	C₄×Q₈	—	2	2	no	—
653	C₄×Q₈	—	2	2	no	—
654	C₄×Q₈	—	2	2	no	—
655	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
656	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
657	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
658	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
659	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
660	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
661	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
662	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
663	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
664	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
665	C₄×D₄	—	2	2	no	—
666	C₄×D₄	—	2	2	no	—
667	C₄×D₄	—	2	2	no	—
668	C₄×D₄	—	2	2	no	—
669	C₄×D₄	—	2	2	no	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	D₄×C₂₃	1	2	yes	—
673	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
674	C₄×D₄	C₂³×C₂₃	1	2	yes	—
675	C₄×D₄	C₂³×C₂₃	1	2	yes	—
676	C₄×D₄	C₂³×C₂₃	1	2	yes	—
677	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
678	#117	—	2	2	no	—
679	#117	—	2	2	no	—
680	#117	—	2	2	no	—
681	#117	—	2	2	no	—
682	#117	—	2	2	no	—
683	#117	—	2	2	no	—
684	#117	—	2	2	no	—
685	#117	D₄×C₂₃	1	1	yes	characteristic
686	#117	D₄×C₂₃	1	2	yes	—
687	#117	C₂³×C₂₃	1	2	yes	—
688	C₂×C₄⋊C₄	—	2	2	no	—
689	C₂×C₄⋊C₄	—	2	2	no	—
690	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
692	C₂×C₄²	—	2	2	no	—
693	C₂×C₄²	—	2	2	no	—
694	C₂×C₄²	—	2	2	no	—
695	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
696	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
697	#107	C₂³×C₂₃	1	1	yes	characteristic
698	#107	C₂³×C₂₃	1	1	yes	characteristic
699	#107	C₂³×C₂₃	1	2	yes	—
700	#107	C₂³×C₂₃	1	2	yes	—
701	#107	C₂³×C₂₃	1	1	yes	characteristic
702	#107	C₂³×C₂₃	1	1	yes	characteristic
703	#107	C₂³×C₂₃	1	2	yes	—
704	#106	C₂³×C₂₃	1	2	yes	—
705	#106	C₂³×C₂₃	1	2	yes	—
706	#106	C₂³×C₂₃	1	2	yes	—
707	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
708	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
709	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
710	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
711	#103	C₂³×C₂₃	1	2	yes	—
712	#103	C₂³×C₂₃	1	2	yes	—
713	#103	C₂³×C₂₃	1	2	yes	—
714	#103	C₂³×C₂₃	1	2	yes	—
715	#103	C₂³×C₂₃	1	2	yes	—
716	#103	C₂³×C₂₃	1	2	yes	—
717	#103	C₂³×C₂₃	1	2	yes	—
718	#103	C₂³×C₂₃	1	2	yes	—
719	#103	C₂³×C₂₃	1	2	yes	—
720	#103	C₂³×C₂₃	1	2	yes	—
721	#103	C₂³×C₂₃	1	2	yes	—
722	#103	C₂³×C₂₃	1	2	yes	—
723	#102	C₂³×C₂₃	1	2	yes	—
724	#102	C₂³×C₂₃	1	2	yes	—
725	#102	C₂³×C₂₃	1	2	yes	—
726	#102	C₂³×C₂₃	1	2	yes	—
727	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
728	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
729	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
730	#97	C₂³×C₂₃	1	2	yes	—
731	#97	C₂³×C₂₃	1	2	yes	—
732	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
733	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
734	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
735	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
736	C₄×C₈	C₂³×C₂₃	1	2	yes	—
737	C₂₃	#61446	1	1	yes	characteristic, direct product factor, Sylow
738	#41	—	2	4	no	—
739	#41	—	4	2	no	—
740	#41	—	4	2	no	—
741	#41	—	4	8	no	—
742	C₂×Q₈	—	2	2	no	—
743	C₂×Q₈	—	2	2	no	—
744	C₂×Q₈	—	2	2	no	—
745	C₂×Q₈	—	2	4	no	—
746	C₂×Q₈	—	2	4	no	—
747	C₂×Q₈	—	4	2	no	—
748	C₂×Q₈	—	4	2	no	—
749	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
750	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
751	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
752	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
753	C₂×D₄	—	2	2	no	—
754	C₂×D₄	—	2	2	no	—
755	C₂×D₄	—	2	2	no	—
756	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
757	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
758	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
759	C₂²×C₄	—	2	2	no	—
760	C₂²×C₄	—	2	2	no	—
761	C₂²×C₄	—	2	2	no	—
762	C₂²×C₄	—	2	2	no	—
763	C₂²×C₄	—	2	2	no	—
764	C₂²×C₄	—	2	2	no	—
765	C₂²×C₄	—	2	2	no	—
766	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
767	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
768	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
769	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
771	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
772	Q₁₆	—	2	4	no	—
773	Q₁₆	—	2	4	no	—
774	Q₁₆	—	2	2	no	—
775	Q₁₆	—	4	1	no	—
776	Q₁₆	—	4	2	no	—
777	Q₁₆	#41×C₂₃	1	4	yes	complemented
778	SD₁₆	—	2	4	no	—
779	SD₁₆	—	2	4	no	—
780	SD₁₆	—	4	2	no	—
781	D₈	—	4	1	no	—
782	M₁₆	—	2	4	no	—
783	M₁₆	—	4	2	no	—
784	C₂×C₈	—	2	2	no	—
785	C₂×C₈	—	4	1	no	—
786	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
787	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
788	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
789	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
790	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
791	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	—	2	2	no	—
795	C₄⋊C₄	—	2	2	no	—
796	C₄⋊C₄	—	2	2	no	—
797	C₄⋊C₄	—	2	2	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	2	no	—
801	C₄⋊C₄	—	2	2	no	—
802	C₄⋊C₄	—	2	2	no	—
803	C₄⋊C₄	—	2	2	no	—
804	C₄⋊C₄	—	2	2	no	—
805	C₄⋊C₄	—	2	2	no	—
806	C₄⋊C₄	—	2	2	no	—
807	C₄⋊C₄	—	2	2	no	—
808	C₄⋊C₄	—	2	2	no	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
814	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
815	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
816	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
817	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
818	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
819	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
820	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
821	C₂²⋊C₄	—	2	2	no	—
822	C₂²⋊C₄	—	2	2	no	—
823	C₂²⋊C₄	—	2	2	no	—
824	C₂²⋊C₄	—	2	2	no	—
825	C₂²⋊C₄	—	2	2	no	—
826	C₂²⋊C₄	—	2	2	no	—
827	C₂²⋊C₄	—	2	2	no	—
828	C₂²⋊C₄	—	2	2	no	—
829	C₂²⋊C₄	—	2	2	no	—
830	C₂²⋊C₄	—	2	2	no	—
831	C₂²⋊C₄	—	2	2	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
835	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
836	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	2	no	—
842	C₄²	—	2	2	no	—
843	C₄²	—	2	2	no	—
844	C₄²	—	2	2	no	—
845	C₄²	—	2	2	no	—
846	C₄²	C₂×D₄×C₂₃	1	2	yes	—
847	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
848	C₄²	C₂×D₄×C₂₃	1	2	yes	—
849	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
850	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
851	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
852	C₄²	C₂⁴×C₂₃	1	2	yes	—
853	C₂³	—	2	2	no	—
854	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
855	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
856	Q₈	—	2	2	no	—
857	Q₈	—	2	2	no	—
858	Q₈	—	2	2	no	—
859	Q₈	—	2	2	no	—
860	Q₈	—	2	2	no	—
861	Q₈	—	4	1	no	—
862	Q₈	—	4	4	no	—
863	Q₈	—	4	4	no	—
864	Q₈	—	4	4	no	—
865	Q₈	C₂×#41×C₂₃	1	4	yes	—
866	D₄	—	2	4	no	—
867	D₄	—	2	2	no	—
868	D₄	—	2	2	no	—
869	D₄	—	4	1	no	—
870	D₄	—	4	4	no	—
871	D₄	—	4	4	no	—
872	D₄	—	4	4	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	4	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	1	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	2	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	2	no	—
887	C₂×C₄	—	4	2	no	—
888	C₂×C₄	—	4	4	no	—
889	C₂×C₄	—	4	4	no	—
890	C₂×C₄	—	4	4	no	—
891	C₂×C₄	—	4	4	no	—
892	C₂×C₄	—	4	4	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
896	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
897	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
898	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
899	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
900	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
901	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
902	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
903	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
904	C₈	—	2	1	no	—
905	C₈	—	2	2	no	—
906	C₈	—	2	1	no	—
907	C₈	—	2	1	no	—
908	C₈	—	2	2	no	—
909	C₈	C₂×#41×C₂₃	1	2	yes	—
910	C₂²	—	2	1	no	—
911	C₂²	—	2	1	no	—
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	4	2	no	—
916	C₂²	—	4	2	no	—
917	C₂²	—	4	2	no	—
918	C₂²	C₂₃×#575	1	2	yes	—
919	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
920	C₄	—	2	2	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	4	no	—
923	C₄	—	2	1	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	2	no	—
926	C₄	—	2	1	no	—
927	C₄	—	2	2	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	2	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	2	no	—
933	C₄	—	4	2	no	—
934	C₄	C₂₃×#578	1	2	yes	—
935	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
936	C₄	C₂₃×#585	1	1	yes	characteristic
937	C₂	—	2	2	no	—
938	C₂	—	4	2	no	—
939	C₂	—	8	2	no	—
940	C₂	D₄×#41×C₂₃	1	1	yes	characteristic
941	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
942	C₂	C₂×C₂₃×#578	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ C₄×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3482	C₂	semidirect
2. C₂₃×#3402	C₂	semidirect
3. C₂₃×#3390	C₂	semidirect
4. C₂₃×#3377	C₂	semidirect
5. C₂₃×#3352	C₂	semidirect
6. C₂₃×#3343	C₂	semidirect
7. C₂₃×#3327	C₂	semidirect
8. C₂₃×#3312	C₂	semidirect
9. C₂₃×#3308	C₂	semidirect
10. C₂₃×#3277	C₂	semidirect
11. C₂₃×#3270	C₂	semidirect
12. C₂₃×#3172	C₂	semidirect
13. C₂₃×#3168	C₂	semidirect
14. C₂₃×#3108	C₂	semidirect
15. C₂₃×#3104	C₂	semidirect
16. C₂₃×#3102	C₂	semidirect
17. C₂₃×#2965	C₂	semidirect
18. C₄×C₂₃×#137	C₂	semidirect
19. C₂×C₄×Q₁₆×C₂₃	C₂	semidirect
305. Q₁₆×C₂₃	#41	semidirect
381. #61446	C₂₃	direct (N × H)
439. #3482	C₂×C₂₃	semidirect
440. #3402	C₂×C₂₃	semidirect
441. #3390	C₂×C₂₃	semidirect
442. #3377	C₂×C₂₃	semidirect
443. #3352	C₂×C₂₃	semidirect
444. #3343	C₂×C₂₃	semidirect
445. #3327	C₂×C₂₃	semidirect
446. #3312	C₂×C₂₃	semidirect
447. #3308	C₂×C₂₃	semidirect
448. #3277	C₂×C₂₃	semidirect
449. #3270	C₂×C₂₃	semidirect
450. #3172	C₂×C₂₃	semidirect
451. #3168	C₂×C₂₃	semidirect
452. #3108	C₂×C₂₃	semidirect
453. #3104	C₂×C₂₃	semidirect
454. #3102	C₂×C₂₃	semidirect
455. #2965	C₂×C₂₃	semidirect
456. C₄×#137	C₂×C₂₃	semidirect
457. C₂×C₄×Q₁₆	C₂×C₂₃	semidirect
737. C₂₃	#61446	direct (N × H)
777. Q₁₆	#41×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3482	2
C₂₃×#3402	2
C₂₃×#3390	2
C₂₃×#3377	2
C₂₃×#3352	2
C₂₃×#3343	2
C₂₃×#3327	2
C₂₃×#3312	2
C₂₃×#3308	2
C₂₃×#3277	2
C₂₃×#3270	2
C₂₃×#3172	2
C₂₃×#3168	2
C₂₃×#3108	2
C₂₃×#3104	2
C₂₃×#3102	2
C₂₃×#2965	2
C₄×C₂₃×#137	2
C₂×C₄×Q₁₆×C₂₃	2
#61446	23

Subgroups — C23×#61446 #19209072

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61446 #19209072