Subgroups — C₂₃×#61442 #19209068

Order 5888.

1868 conjugacy classes of subgroups.

The subgroup lattice has 962 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3475	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3402	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3389	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3376	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3352	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#3348	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3323	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3319	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3315	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3273	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3267	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×#3107	C₂	1	2	yes	maximal, complemented
15	C₂₃×#3105	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×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
19	C₄×C₂₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
21	C₂×C₂₃×#135	C₂²	1	1	yes	characteristic
22	C₂₃×#556	C₂²	1	2	yes	complemented
23	C₂₃×#555	C₂²	1	2	yes	—
24	C₂₃×#554	C₂²	1	2	yes	complemented
25	C₂₃×#553	—	2	2	no	—
26	C₂₃×#552	—	2	2	no	—
27	C₂₃×#552	C₂²	1	2	yes	—
28	C₂₃×#552	C₂²	1	2	yes	complemented
29	C₂₃×#551	—	2	2	no	—
30	C₂₃×#551	—	2	2	no	—
31	C₂₃×#547	C₂²	1	2	yes	—
32	C₂₃×#546	C₂²	1	2	yes	—
33	C₂₃×#546	C₂²	1	2	yes	complemented
34	C₂₃×#533	C₂²	1	2	yes	complemented
35	C₂₃×#529	—	2	2	no	—
36	C₂₃×#529	—	2	2	no	—
37	C₂₃×#529	C₂²	1	2	yes	—
38	C₂₃×#529	C₂²	1	2	yes	complemented
39	C₂₃×#525	—	2	2	no	—
40	C₄×#41×C₂₃	C₂²	1	2	yes	—
41	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
42	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
43	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
44	C₂×C₂₃×#117	—	2	2	no	—
45	C₂₃×#501	C₂²	1	2	yes	complemented
46	C₂₃×#499	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#497	C₂²	1	2	yes	complemented
48	C₂₃×#495	C₂²	1	1	yes	characteristic
49	C₂₃×#491	C₂²	1	2	yes	complemented
50	C₂₃×#489	C₂²	1	2	yes	complemented
51	C₂₃×#488	C₂²	1	2	yes	complemented
52	C₂₃×#485	C₂²	1	2	yes	complemented
53	C₂₃×#485	C₂²	1	2	yes	complemented
54	C₂₃×#485	C₂²	1	2	yes	complemented
55	C₂₃×#484	C₂²	1	2	yes	complemented
56	C₂₃×#482	C₂²	1	2	yes	complemented
57	C₂₃×#481	C₂²	1	2	yes	—
58	C₂₃×#479	C₂²	1	2	yes	complemented
59	C₂₃×#478	C₂²	1	2	yes	complemented
60	C₂₃×#478	C₂²	1	2	yes	complemented
61	C₂₃×#478	C₂²	1	2	yes	complemented
62	C₂₃×#475	C₂²	1	2	yes	complemented
63	C₂₃×#474	C₂²	1	2	yes	complemented
64	C₂₃×#470	C₂²	1	2	yes	complemented
65	C₂₃×#470	C₂²	1	2	yes	complemented
66	C₂₃×#468	C₂²	1	2	yes	—
67	C₂₃×#468	C₂²	1	2	yes	—
68	C₂₃×#467	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×#466	C₂²	1	1	yes	characteristic
70	C₂₃×#465	C₂²	1	2	yes	complemented
71	C₂₃×#464	C₂²	1	2	yes	complemented
72	C₂₃×#463	C₂²	1	2	yes	—
73	C₂₃×#463	C₂²	1	2	yes	—
74	C₂₃×#463	C₂²	1	2	yes	—
75	C₂₃×#462	C₂²	1	2	yes	complemented
76	C₂₃×#461	C₂²	1	2	yes	complemented
77	C₂₃×#452	C₂²	1	2	yes	—
78	C₂₃×#452	C₂²	1	2	yes	—
79	C₂₃×#452	C₂²	1	2	yes	complemented
80	C₂₃×#450	C₂²	1	2	yes	complemented
81	C₂₃×#449	C₂²	1	2	yes	—
82	C₂₃×#447	C₂²	1	2	yes	—
83	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
84	C₂₃×#446	C₂²	1	1	yes	characteristic, complemented
85	C₂₃×#442	C₂²	1	2	yes	—
86	C₂₃×#442	C₂²	1	2	yes	—
87	C₂₃×#440	C₂²	1	2	yes	complemented
88	C₂₃×#440	C₂²	1	2	yes	complemented
89	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
90	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
91	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	complemented
92	C₄×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
93	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
94	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
95	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
96	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
97	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
98	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
99	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
100	C₄×D₈×C₂₃	C₂²	1	1	yes	characteristic
101	C₄×D₈×C₂₃	C₂²	1	2	yes	—
102	C₂₃×#436	C₂²	1	1	yes	characteristic
103	C₂₃×#436	C₂²	1	1	yes	characteristic
104	C₂₃×#435	C₂²	1	2	yes	complemented
105	C₂₃×#435	C₂²	1	2	yes	complemented
106	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
107	C₂₃×#431	C₂²	1	2	yes	complemented
108	C₂₃×#428	C₂²	1	2	yes	complemented
109	C₂₃×#427	C₂²	1	1	yes	characteristic, complemented
110	C₂₃×#418	C₂²	1	2	yes	complemented
111	C₂₃×#417	C₂²	1	2	yes	—
112	C₂₃×#416	C₂²	1	2	yes	complemented
113	C₄×M₁₆×C₂₃	C₂²	1	2	yes	complemented
114	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
115	C₂×#41×C₂₃	D₄	1	1	yes	characteristic
116	C₂×#41×C₂₃	C₂³	1	2	yes	—
117	C₂×#41×C₂₃	C₂³	1	2	yes	—
118	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₂₃	—	2	2	no	—
120	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
121	C₂₃×#135	—	2	4	no	—
122	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
123	C₂×Q₁₆×C₂₃	C₂³	1	1	yes	characteristic
124	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
126	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
128	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
129	C₂×D₈×C₂₃	C₂³	1	2	yes	—
130	C₂×D₈×C₂₃	C₂³	1	1	yes	characteristic
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	C₂³	1	2	yes	—
137	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₂₃×#126	—	2	2	no	—
139	C₂₃×#126	—	2	2	no	—
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×#125	—	2	2	no	—
145	C₂₃×#125	—	2	2	no	—
146	C₂₃×#125	—	2	2	no	—
147	C₂₃×#125	C₂³	1	2	yes	—
148	C₂₃×#125	C₂³	1	2	yes	—
149	C₂₃×#124	—	2	2	no	—
150	C₂₃×#124	—	2	2	no	—
151	C₂₃×#124	C₂³	1	2	yes	—
152	C₂₃×#124	C₂³	1	2	yes	—
153	C₂₃×#123	—	2	2	no	—
154	C₂₃×#123	—	2	2	no	—
155	C₂₃×#123	—	2	2	no	—
156	C₂₃×#123	—	2	2	no	—
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×C₂²⋊Q₈	—	2	2	no	—
162	C₂₃×C₂²⋊Q₈	—	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	C₂³	1	2	yes	—
167	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
168	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
169	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
170	C₂₃×#121	—	2	2	no	—
171	C₂₃×#121	—	2	2	no	—
172	C₂₃×#121	—	2	2	no	—
173	C₂₃×#121	—	2	2	no	—
174	C₂₃×#121	C₂³	1	2	yes	—
175	C₂₃×#121	C₂³	1	2	yes	—
176	C₂₃×#120	—	2	2	no	—
177	C₂₃×#120	—	2	2	no	—
178	C₄×Q₈×C₂₃	—	2	2	no	—
179	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
180	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
181	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
182	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
183	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
184	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
185	C₄×D₄×C₂₃	—	2	2	no	—
186	C₄×D₄×C₂₃	—	2	2	no	—
187	C₄×D₄×C₂₃	—	2	2	no	—
188	C₄×D₄×C₂₃	—	2	2	no	—
189	C₄×D₄×C₂₃	—	2	2	no	—
190	C₄×D₄×C₂₃	—	2	2	no	—
191	C₄×D₄×C₂₃	—	2	2	no	—
192	C₄×D₄×C₂₃	—	2	2	no	—
193	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
194	C₄×D₄×C₂₃	D₄	1	2	yes	—
195	C₄×D₄×C₂₃	C₂³	1	2	yes	—
196	C₄×D₄×C₂₃	C₂³	1	2	yes	—
197	C₄×D₄×C₂₃	C₂³	1	2	yes	—
198	C₄×D₄×C₂₃	C₂³	1	2	yes	—
199	C₄×D₄×C₂₃	C₂³	1	2	yes	—
200	C₄×D₄×C₂₃	C₂³	1	2	yes	—
201	C₄×D₄×C₂₃	C₂³	1	2	yes	—
202	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
203	C₂₃×#117	—	2	2	no	—
204	C₂₃×#117	—	2	2	no	—
205	C₂₃×#117	—	2	2	no	—
206	C₂₃×#117	—	2	2	no	—
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	D₄	1	2	yes	—
213	C₂₃×#117	D₄	1	1	yes	characteristic
214	C₂₃×#117	C₂³	1	2	yes	—
215	C₂₃×#117	C₂³	1	2	yes	—
216	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
217	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
218	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
220	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
221	C₂×C₂²⋊C₄×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	1	yes	characteristic
230	C₂₃×#107	C₂³	1	1	yes	characteristic
231	C₂₃×#107	C₂³	1	2	yes	—
232	C₂₃×#106	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×#102	C₂³	1	2	yes	—
249	C₂₃×#102	C₂³	1	2	yes	—
250	C₂₃×#102	C₂³	1	2	yes	—
251	C₂₃×#102	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	C₂⁴×C₂₃	—	2	2	no	—
267	#41×C₂₃	—	2	4	no	—
268	#41×C₂₃	—	2	4	no	—
269	#41×C₂₃	—	4	2	no	—
270	#41×C₂₃	—	4	2	no	—
271	#41×C₂₃	—	4	2	no	—
272	C₂×Q₈×C₂₃	—	2	2	no	—
273	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
274	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
275	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
276	C₂×D₄×C₂₃	—	2	4	no	—
277	C₂×D₄×C₂₃	—	2	2	no	—
278	C₂×D₄×C₂₃	—	2	2	no	—
279	C₂×D₄×C₂₃	—	2	2	no	—
280	C₂×D₄×C₂₃	—	2	2	no	—
281	C₂×D₄×C₂₃	—	2	2	no	—
282	C₂×D₄×C₂₃	—	4	2	no	—
283	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
284	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
285	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
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	—	2	2	no	—
295	C₂²×C₄×C₂₃	—	2	2	no	—
296	C₂²×C₄×C₂₃	—	4	8	no	—
297	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
298	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
300	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
303	Q₁₆×C₂₃	—	2	2	no	—
304	Q₁₆×C₂₃	—	4	1	no	—
305	Q₁₆×C₂₃	—	4	2	no	—
306	SD₁₆×C₂₃	—	2	4	no	—
307	SD₁₆×C₂₃	—	2	4	no	—
308	SD₁₆×C₂₃	—	2	4	no	—
309	SD₁₆×C₂₃	—	4	2	no	—
310	D₈×C₂₃	—	2	4	no	—
311	D₈×C₂₃	—	4	1	no	—
312	D₈×C₂₃	#41	1	4	yes	complemented
313	M₁₆×C₂₃	—	2	4	no	—
314	M₁₆×C₂₃	—	4	2	no	—
315	C₂×C₈×C₂₃	—	2	2	no	—
316	C₂×C₈×C₂₃	—	4	1	no	—
317	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
318	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
319	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
320	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
321	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
322	C₂×C₈×C₂₃	C₂⁴	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
340	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
341	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
342	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
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	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
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	C₂²⋊C₄×C₂₃	—	2	2	no	—
362	C₂²⋊C₄×C₂₃	—	2	2	no	—
363	C₂²⋊C₄×C₂₃	—	2	2	no	—
364	C₂²⋊C₄×C₂₃	—	2	2	no	—
365	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
366	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
367	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
375	C₄²×C₂₃	C₂×D₄	1	2	yes	—
376	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
377	C₄²×C₂₃	C₂×D₄	1	2	yes	—
378	C₄²×C₂₃	C₂⁴	1	2	yes	—
379	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
380	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
381	#61442	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
382	C₂³×C₂₃	—	2	2	no	—
383	C₂³×C₂₃	—	2	2	no	—
384	C₂³×C₂₃	—	4	4	no	—
385	C₂³×C₂₃	—	4	4	no	—
386	C₂³×C₂₃	—	8	2	no	—
387	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
388	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
389	Q₈×C₂₃	—	2	2	no	—
390	Q₈×C₂₃	—	2	2	no	—
391	Q₈×C₂₃	—	2	2	no	—
392	Q₈×C₂₃	—	2	2	no	—
393	Q₈×C₂₃	—	4	1	no	—
394	Q₈×C₂₃	—	8	2	no	—
395	D₄×C₂₃	—	2	2	no	—
396	D₄×C₂₃	—	2	2	no	—
397	D₄×C₂₃	—	2	2	no	—
398	D₄×C₂₃	—	4	2	no	—
399	D₄×C₂₃	—	4	1	no	—
400	D₄×C₂₃	—	4	4	no	—
401	D₄×C₂₃	—	4	4	no	—
402	D₄×C₂₃	—	4	4	no	—
403	D₄×C₂₃	—	8	2	no	—
404	D₄×C₂₃	—	8	2	no	—
405	D₄×C₂₃	C₂×#41	1	4	yes	—
406	C₂×C₄×C₂₃	—	2	4	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	1	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	—	2	2	no	—
417	C₂×C₄×C₂₃	—	2	2	no	—
418	C₂×C₄×C₂₃	—	4	1	no	—
419	C₂×C₄×C₂₃	—	4	2	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	—	4	4	no	—
425	C₂×C₄×C₂₃	—	4	4	no	—
426	C₂×C₄×C₂₃	—	4	4	no	—
427	C₂×C₄×C₂₃	—	8	2	no	—
428	C₂×C₄×C₂₃	—	8	2	no	—
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	2	yes	—
432	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
433	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
436	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
438	C₈×C₂₃	—	2	1	no	—
439	C₈×C₂₃	—	2	2	no	—
440	C₈×C₂₃	—	2	1	no	—
441	C₈×C₂₃	—	2	1	no	—
442	C₈×C₂₃	—	2	2	no	—
443	C₈×C₂₃	C₂×#41	1	2	yes	—
444	#3475	C₂×C₂₃	1	2	yes	complemented
445	#3402	C₂×C₂₃	1	1	yes	characteristic, complemented
446	#3389	C₂×C₂₃	1	1	yes	characteristic, complemented
447	#3376	C₂×C₂₃	1	2	yes	complemented
448	#3352	C₂×C₂₃	1	1	yes	characteristic, complemented
449	#3348	C₂×C₂₃	1	2	yes	complemented
450	#3323	C₂×C₂₃	1	2	yes	complemented
451	#3319	C₂×C₂₃	1	2	yes	complemented
452	#3315	C₂×C₂₃	1	2	yes	complemented
453	#3273	C₂×C₂₃	1	1	yes	characteristic, complemented
454	#3267	C₂×C₂₃	1	2	yes	complemented
455	#3172	C₂×C₂₃	1	2	yes	complemented
456	#3168	C₂×C₂₃	1	1	yes	characteristic, complemented
457	#3107	C₂×C₂₃	1	2	yes	complemented
458	#3105	C₂×C₂₃	1	2	yes	complemented
459	#3102	C₂×C₂₃	1	2	yes	complemented
460	#2965	C₂×C₂₃	1	1	yes	characteristic, complemented
461	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	2	yes	complemented
462	C₄×#135	C₂×C₂₃	1	1	yes	characteristic, complemented
463	C₂²×C₂₃	—	2	1	no	—
464	C₂²×C₂₃	—	2	2	no	—
465	C₂²×C₂₃	—	2	1	no	—
466	C₂²×C₂₃	—	2	2	no	—
467	C₂²×C₂₃	—	2	4	no	—
468	C₂²×C₂₃	—	2	2	no	—
469	C₂²×C₂₃	—	2	1	no	—
470	C₂²×C₂₃	—	4	2	no	—
471	C₂²×C₂₃	—	4	2	no	—
472	C₂²×C₂₃	—	4	2	no	—
473	C₂²×C₂₃	—	4	2	no	—
474	C₂²×C₂₃	—	4	2	no	—
475	C₂²×C₂₃	—	8	8	no	—
476	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
477	C₄×C₂₃	—	2	1	no	—
478	C₄×C₂₃	—	2	1	no	—
479	C₄×C₂₃	—	2	2	no	—
480	C₄×C₂₃	—	2	1	no	—
481	C₄×C₂₃	—	2	2	no	—
482	C₄×C₂₃	—	2	2	no	—
483	C₄×C₂₃	—	2	1	no	—
484	C₄×C₂₃	—	4	2	no	—
485	C₄×C₂₃	—	4	2	no	—
486	C₄×C₂₃	—	4	2	no	—
487	C₄×C₂₃	—	4	2	no	—
488	C₄×C₂₃	—	4	2	no	—
489	C₄×C₂₃	—	4	2	no	—
490	C₄×C₂₃	#575	1	2	yes	—
491	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
492	C₄×C₂₃	#585	1	1	yes	characteristic
493	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
494	C₂×#135	C₂²×C₂₃	1	1	yes	characteristic
495	#556	C₂²×C₂₃	1	2	yes	complemented
496	#555	C₂²×C₂₃	1	2	yes	—
497	#554	C₂²×C₂₃	1	2	yes	complemented
498	#553	—	2	2	no	—
499	#552	—	2	2	no	—
500	#552	C₂²×C₂₃	1	2	yes	—
501	#552	C₂²×C₂₃	1	2	yes	complemented
502	#551	—	2	2	no	—
503	#551	—	2	2	no	—
504	#547	C₂²×C₂₃	1	2	yes	—
505	#546	C₂²×C₂₃	1	2	yes	—
506	#546	C₂²×C₂₃	1	2	yes	complemented
507	#533	C₂²×C₂₃	1	2	yes	complemented
508	#529	—	2	2	no	—
509	#529	—	2	2	no	—
510	#529	C₂²×C₂₃	1	2	yes	—
511	#529	C₂²×C₂₃	1	2	yes	complemented
512	#525	—	2	2	no	—
513	C₄×#41	C₂²×C₂₃	1	2	yes	—
514	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
515	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
516	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
517	C₂×#117	—	2	2	no	—
518	#501	C₂²×C₂₃	1	2	yes	complemented
519	#499	C₂²×C₂₃	1	1	yes	characteristic, complemented
520	#497	C₂²×C₂₃	1	2	yes	complemented
521	#495	C₂²×C₂₃	1	1	yes	characteristic
522	#491	C₂²×C₂₃	1	2	yes	complemented
523	#489	C₂²×C₂₃	1	2	yes	complemented
524	#488	C₂²×C₂₃	1	2	yes	complemented
525	#485	C₂²×C₂₃	1	2	yes	complemented
526	#485	C₂²×C₂₃	1	2	yes	complemented
527	#485	C₂²×C₂₃	1	2	yes	complemented
528	#484	C₂²×C₂₃	1	2	yes	complemented
529	#482	C₂²×C₂₃	1	2	yes	complemented
530	#481	C₂²×C₂₃	1	2	yes	—
531	#479	C₂²×C₂₃	1	2	yes	complemented
532	#478	C₂²×C₂₃	1	2	yes	complemented
533	#478	C₂²×C₂₃	1	2	yes	complemented
534	#478	C₂²×C₂₃	1	2	yes	complemented
535	#475	C₂²×C₂₃	1	2	yes	complemented
536	#474	C₂²×C₂₃	1	2	yes	complemented
537	#470	C₂²×C₂₃	1	2	yes	complemented
538	#470	C₂²×C₂₃	1	2	yes	complemented
539	#468	C₂²×C₂₃	1	2	yes	—
540	#468	C₂²×C₂₃	1	2	yes	—
541	#467	C₂²×C₂₃	1	1	yes	characteristic, complemented
542	#466	C₂²×C₂₃	1	1	yes	characteristic
543	#465	C₂²×C₂₃	1	2	yes	complemented
544	#464	C₂²×C₂₃	1	2	yes	complemented
545	#463	C₂²×C₂₃	1	2	yes	—
546	#463	C₂²×C₂₃	1	2	yes	—
547	#463	C₂²×C₂₃	1	2	yes	—
548	#462	C₂²×C₂₃	1	2	yes	complemented
549	#461	C₂²×C₂₃	1	2	yes	complemented
550	#452	C₂²×C₂₃	1	2	yes	—
551	#452	C₂²×C₂₃	1	2	yes	—
552	#452	C₂²×C₂₃	1	2	yes	complemented
553	#450	C₂²×C₂₃	1	2	yes	complemented
554	#449	C₂²×C₂₃	1	2	yes	—
555	#447	C₂²×C₂₃	1	2	yes	—
556	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
557	#446	C₂²×C₂₃	1	1	yes	characteristic, complemented
558	#442	C₂²×C₂₃	1	2	yes	—
559	#442	C₂²×C₂₃	1	2	yes	—
560	#440	C₂²×C₂₃	1	2	yes	complemented
561	#440	C₂²×C₂₃	1	2	yes	complemented
562	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
563	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	complemented
564	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
565	C₄×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
566	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
567	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
568	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
569	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
570	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
571	C₄×D₈	C₂²×C₂₃	1	2	yes	—
572	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
573	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
574	C₄×D₈	C₂²×C₂₃	1	1	yes	characteristic
575	#436	C₂²×C₂₃	1	1	yes	characteristic
576	#436	C₂²×C₂₃	1	1	yes	characteristic
577	#435	C₂²×C₂₃	1	2	yes	complemented
578	#435	C₂²×C₂₃	1	2	yes	complemented
579	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
580	#431	C₂²×C₂₃	1	2	yes	complemented
581	#428	C₂²×C₂₃	1	2	yes	complemented
582	#427	C₂²×C₂₃	1	1	yes	characteristic, complemented
583	#418	C₂²×C₂₃	1	2	yes	complemented
584	#417	C₂²×C₂₃	1	2	yes	—
585	#416	C₂²×C₂₃	1	2	yes	complemented
586	C₄×M₁₆	C₂²×C₂₃	1	2	yes	complemented
587	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
588	C₂×C₂₃	—	4	1	no	—
589	C₂×C₂₃	—	4	2	no	—
590	C₂×C₂₃	—	4	4	no	—
591	C₂×C₂₃	—	8	2	no	—
592	C₂×C₂₃	D₄×#41	1	1	yes	characteristic
593	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
594	C₂×C₂₃	#3584	1	1	yes	characteristic
595	C₂×#41	D₄×C₂₃	1	1	yes	characteristic
596	C₂×#41	C₂³×C₂₃	1	2	yes	—
597	C₂×#41	C₂³×C₂₃	1	2	yes	—
598	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
599	C₂³×C₄	—	2	2	no	—
600	AGL(1,ℤ/8)	—	2	8	no	—
601	#135	—	2	4	no	—
602	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
603	C₂×Q₁₆	C₂³×C₂₃	1	1	yes	characteristic
604	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
605	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
606	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
607	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
608	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
609	C₂×D₈	C₂³×C₂₃	1	2	yes	—
610	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
611	C₂×D₈	C₂³×C₂₃	1	1	yes	characteristic
612	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
613	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
614	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
615	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
616	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
617	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
618	#126	—	2	2	no	—
619	#126	—	2	2	no	—
620	#126	—	2	2	no	—
621	#126	—	2	2	no	—
622	#126	—	2	2	no	—
623	#126	—	2	2	no	—
624	#125	—	2	2	no	—
625	#125	—	2	2	no	—
626	#125	—	2	2	no	—
627	#125	C₂³×C₂₃	1	2	yes	—
628	#125	C₂³×C₂₃	1	2	yes	—
629	#124	—	2	2	no	—
630	#124	—	2	2	no	—
631	#124	C₂³×C₂₃	1	2	yes	—
632	#124	C₂³×C₂₃	1	2	yes	—
633	#123	—	2	2	no	—
634	#123	—	2	2	no	—
635	#123	—	2	2	no	—
636	#123	—	2	2	no	—
637	#123	—	2	2	no	—
638	#123	—	2	2	no	—
639	#123	—	2	2	no	—
640	#123	—	2	2	no	—
641	C₂²⋊Q₈	—	2	2	no	—
642	C₂²⋊Q₈	—	2	2	no	—
643	C₂²⋊Q₈	—	2	2	no	—
644	C₂²⋊Q₈	—	2	2	no	—
645	C₂²⋊Q₈	—	2	2	no	—
646	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
647	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
648	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
649	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
650	#121	—	2	2	no	—
651	#121	—	2	2	no	—
652	#121	—	2	2	no	—
653	#121	—	2	2	no	—
654	#121	C₂³×C₂₃	1	2	yes	—
655	#121	C₂³×C₂₃	1	2	yes	—
656	#120	—	2	2	no	—
657	#120	—	2	2	no	—
658	C₄×Q₈	—	2	2	no	—
659	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
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	—	2	2	no	—
673	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
674	C₄×D₄	D₄×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	2	yes	—
678	C₄×D₄	C₂³×C₂₃	1	2	yes	—
679	C₄×D₄	C₂³×C₂₃	1	2	yes	—
680	C₄×D₄	C₂³×C₂₃	1	2	yes	—
681	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
682	C₄×D₄	C₂³×C₂₃	1	2	yes	—
683	#117	—	2	2	no	—
684	#117	—	2	2	no	—
685	#117	—	2	2	no	—
686	#117	—	2	2	no	—
687	#117	—	2	2	no	—
688	#117	—	2	2	no	—
689	#117	—	2	2	no	—
690	#117	—	2	2	no	—
691	#117	—	2	2	no	—
692	#117	D₄×C₂₃	1	2	yes	—
693	#117	D₄×C₂₃	1	1	yes	characteristic
694	#117	C₂³×C₂₃	1	2	yes	—
695	#117	C₂³×C₂₃	1	2	yes	—
696	C₂×C₄⋊C₄	—	2	2	no	—
697	C₂×C₄⋊C₄	—	2	2	no	—
698	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
699	C₂×C₂²⋊C₄	—	2	2	no	—
700	C₂×C₂²⋊C₄	—	2	2	no	—
701	C₂×C₂²⋊C₄	—	2	2	no	—
702	C₂×C₄²	—	2	2	no	—
703	C₂×C₄²	—	2	2	no	—
704	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
705	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
706	#107	C₂³×C₂₃	1	1	yes	characteristic
707	#107	C₂³×C₂₃	1	1	yes	characteristic
708	#107	C₂³×C₂₃	1	2	yes	—
709	#107	C₂³×C₂₃	1	1	yes	characteristic
710	#107	C₂³×C₂₃	1	1	yes	characteristic
711	#107	C₂³×C₂₃	1	2	yes	—
712	#106	C₂³×C₂₃	1	2	yes	—
713	#106	C₂³×C₂₃	1	2	yes	—
714	#106	C₂³×C₂₃	1	2	yes	—
715	#106	C₂³×C₂₃	1	2	yes	—
716	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
717	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
718	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
719	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
720	#103	C₂³×C₂₃	1	2	yes	—
721	#103	C₂³×C₂₃	1	2	yes	—
722	#103	C₂³×C₂₃	1	2	yes	—
723	#103	C₂³×C₂₃	1	2	yes	—
724	#103	C₂³×C₂₃	1	2	yes	—
725	#103	C₂³×C₂₃	1	2	yes	—
726	#103	C₂³×C₂₃	1	2	yes	—
727	#103	C₂³×C₂₃	1	2	yes	—
728	#102	C₂³×C₂₃	1	2	yes	—
729	#102	C₂³×C₂₃	1	2	yes	—
730	#102	C₂³×C₂₃	1	2	yes	—
731	#102	C₂³×C₂₃	1	2	yes	—
732	#102	C₂³×C₂₃	1	2	yes	—
733	#102	C₂³×C₂₃	1	2	yes	—
734	#102	C₂³×C₂₃	1	2	yes	—
735	#102	C₂³×C₂₃	1	2	yes	—
736	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
737	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
738	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
739	#97	C₂³×C₂₃	1	2	yes	—
740	#97	C₂³×C₂₃	1	2	yes	—
741	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
742	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
743	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
744	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
745	C₄×C₈	C₂³×C₂₃	1	2	yes	—
746	C₂₃	#61442	1	1	yes	characteristic, direct product factor, Sylow
747	C₂⁴	—	2	2	no	—
748	#41	—	2	4	no	—
749	#41	—	2	4	no	—
750	#41	—	4	2	no	—
751	#41	—	4	2	no	—
752	#41	—	4	2	no	—
753	C₂×Q₈	—	2	2	no	—
754	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
755	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
756	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
757	C₂×D₄	—	2	4	no	—
758	C₂×D₄	—	2	2	no	—
759	C₂×D₄	—	2	2	no	—
760	C₂×D₄	—	2	2	no	—
761	C₂×D₄	—	2	2	no	—
762	C₂×D₄	—	2	2	no	—
763	C₂×D₄	—	4	2	no	—
764	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
765	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
766	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
767	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
768	C₂²×C₄	—	2	2	no	—
769	C₂²×C₄	—	2	2	no	—
770	C₂²×C₄	—	2	2	no	—
771	C₂²×C₄	—	2	2	no	—
772	C₂²×C₄	—	2	2	no	—
773	C₂²×C₄	—	2	2	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	4	8	no	—
778	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
779	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
780	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
781	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
783	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
784	Q₁₆	—	2	2	no	—
785	Q₁₆	—	4	1	no	—
786	Q₁₆	—	4	2	no	—
787	SD₁₆	—	2	4	no	—
788	SD₁₆	—	2	4	no	—
789	SD₁₆	—	2	4	no	—
790	SD₁₆	—	4	2	no	—
791	D₈	—	2	4	no	—
792	D₈	—	4	1	no	—
793	D₈	#41×C₂₃	1	4	yes	complemented
794	M₁₆	—	2	4	no	—
795	M₁₆	—	4	2	no	—
796	C₂×C₈	—	2	2	no	—
797	C₂×C₈	—	4	1	no	—
798	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
799	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
800	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
801	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
802	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
803	C₂×C₈	C₂⁴×C₂₃	1	1	yes	characteristic
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	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
821	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
822	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
823	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
824	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
825	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
826	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
827	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
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	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
847	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
848	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
849	C₄²	—	2	2	no	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	—	2	2	no	—
855	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
856	C₄²	C₂×D₄×C₂₃	1	2	yes	—
857	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
858	C₄²	C₂×D₄×C₂₃	1	2	yes	—
859	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
860	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
861	C₄²	C₂⁴×C₂₃	1	2	yes	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	4	4	no	—
865	C₂³	—	4	4	no	—
866	C₂³	—	8	2	no	—
867	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
868	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
869	Q₈	—	2	2	no	—
870	Q₈	—	2	2	no	—
871	Q₈	—	2	2	no	—
872	Q₈	—	2	2	no	—
873	Q₈	—	4	1	no	—
874	Q₈	—	8	2	no	—
875	D₄	—	2	2	no	—
876	D₄	—	2	2	no	—
877	D₄	—	2	2	no	—
878	D₄	—	4	2	no	—
879	D₄	—	4	1	no	—
880	D₄	—	4	4	no	—
881	D₄	—	4	4	no	—
882	D₄	—	4	4	no	—
883	D₄	—	8	2	no	—
884	D₄	—	8	2	no	—
885	D₄	C₂×#41×C₂₃	1	4	yes	—
886	C₂×C₄	—	2	4	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	2	no	—
893	C₂×C₄	—	2	2	no	—
894	C₂×C₄	—	2	2	no	—
895	C₂×C₄	—	2	2	no	—
896	C₂×C₄	—	2	2	no	—
897	C₂×C₄	—	2	2	no	—
898	C₂×C₄	—	4	1	no	—
899	C₂×C₄	—	4	2	no	—
900	C₂×C₄	—	4	4	no	—
901	C₂×C₄	—	4	4	no	—
902	C₂×C₄	—	4	4	no	—
903	C₂×C₄	—	4	4	no	—
904	C₂×C₄	—	4	4	no	—
905	C₂×C₄	—	4	4	no	—
906	C₂×C₄	—	4	4	no	—
907	C₂×C₄	—	8	2	no	—
908	C₂×C₄	—	8	2	no	—
909	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
910	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
911	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
912	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
913	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
914	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
915	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
916	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
917	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
918	C₈	—	2	1	no	—
919	C₈	—	2	2	no	—
920	C₈	—	2	1	no	—
921	C₈	—	2	1	no	—
922	C₈	—	2	2	no	—
923	C₈	C₂×#41×C₂₃	1	2	yes	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	2	no	—
926	C₂²	—	2	4	no	—
927	C₂²	—	2	2	no	—
928	C₂²	—	2	1	no	—
929	C₂²	—	2	1	no	—
930	C₂²	—	2	2	no	—
931	C₂²	—	4	2	no	—
932	C₂²	—	4	2	no	—
933	C₂²	—	4	2	no	—
934	C₂²	—	4	2	no	—
935	C₂²	—	4	2	no	—
936	C₂²	—	8	8	no	—
937	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
938	C₄	—	2	1	no	—
939	C₄	—	2	2	no	—
940	C₄	—	2	2	no	—
941	C₄	—	2	1	no	—
942	C₄	—	2	1	no	—
943	C₄	—	2	1	no	—
944	C₄	—	2	2	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	2	no	—
947	C₄	—	4	2	no	—
948	C₄	—	4	2	no	—
949	C₄	—	4	2	no	—
950	C₄	—	4	2	no	—
951	C₄	C₂₃×#575	1	2	yes	—
952	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
953	C₄	C₂₃×#585	1	1	yes	characteristic
954	C₂	—	4	2	no	—
955	C₂	—	4	1	no	—
956	C₂	—	4	4	no	—
957	C₂	—	8	2	no	—
958	C₂	D₄×#41×C₂₃	1	1	yes	characteristic
959	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
960	C₂	C₂₃×#3584	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×#3475	C₂	semidirect
2. C₂₃×#3402	C₂	semidirect
3. C₂₃×#3389	C₂	semidirect
4. C₂₃×#3376	C₂	semidirect
5. C₂₃×#3352	C₂	semidirect
6. C₂₃×#3348	C₂	semidirect
7. C₂₃×#3323	C₂	semidirect
8. C₂₃×#3319	C₂	semidirect
9. C₂₃×#3315	C₂	semidirect
10. C₂₃×#3273	C₂	semidirect
11. C₂₃×#3267	C₂	semidirect
12. C₂₃×#3172	C₂	semidirect
13. C₂₃×#3168	C₂	semidirect
14. C₂₃×#3107	C₂	semidirect
15. C₂₃×#3105	C₂	semidirect
16. C₂₃×#3102	C₂	semidirect
17. C₂₃×#2965	C₂	semidirect
18. C₄×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
19. C₄×C₂₃×#135	C₂	semidirect
22. C₂₃×#556	C₂²	semidirect
24. C₂₃×#554	C₂²	semidirect
28. C₂₃×#552	C₂²	semidirect
33. C₂₃×#546	C₂²	semidirect
34. C₂₃×#533	C₂²	semidirect
38. C₂₃×#529	C₂²	semidirect
42. C₄×#41×C₂₃	C₂²	semidirect
43. C₂×C₄×D₄×C₂₃	C₂²	semidirect
45. C₂₃×#501	C₂²	semidirect
46. C₂₃×#499	C₂²	semidirect
47. C₂₃×#497	C₂²	semidirect
49. C₂₃×#491	C₂²	semidirect
50. C₂₃×#489	C₂²	semidirect
51. C₂₃×#488	C₂²	semidirect
52. C₂₃×#485	C₂²	semidirect
53. C₂₃×#485	C₂²	semidirect
54. C₂₃×#485	C₂²	semidirect
55. C₂₃×#484	C₂²	semidirect
56. C₂₃×#482	C₂²	semidirect
58. C₂₃×#479	C₂²	semidirect
59. C₂₃×#478	C₂²	semidirect
60. C₂₃×#478	C₂²	semidirect
61. C₂₃×#478	C₂²	semidirect
62. C₂₃×#475	C₂²	semidirect
63. C₂₃×#474	C₂²	semidirect
64. C₂₃×#470	C₂²	semidirect
65. C₂₃×#470	C₂²	semidirect
68. C₂₃×#467	C₂²	semidirect
70. C₂₃×#465	C₂²	semidirect
71. C₂₃×#464	C₂²	semidirect
75. C₂₃×#462	C₂²	semidirect
76. C₂₃×#461	C₂²	semidirect
79. C₂₃×#452	C₂²	semidirect
80. C₂₃×#450	C₂²	semidirect
83. C₂₃×#446	C₂²	semidirect
84. C₂₃×#446	C₂²	semidirect
87. C₂₃×#440	C₂²	semidirect
88. C₂₃×#440	C₂²	semidirect
89. C₄×Q₁₆×C₂₃	C₂²	semidirect
90. C₄×Q₁₆×C₂₃	C₂²	semidirect
91. C₄×Q₁₆×C₂₃	C₂²	semidirect
92. C₄×Q₁₆×C₂₃	C₂²	semidirect
93. C₄×SD₁₆×C₂₃	C₂²	semidirect
94. C₄×SD₁₆×C₂₃	C₂²	semidirect
95. C₄×SD₁₆×C₂₃	C₂²	semidirect
96. C₄×SD₁₆×C₂₃	C₂²	semidirect
97. C₄×SD₁₆×C₂₃	C₂²	semidirect
104. C₂₃×#435	C₂²	semidirect
105. C₂₃×#435	C₂²	semidirect
106. C₂₃×#431	C₂²	semidirect
107. C₂₃×#431	C₂²	semidirect
108. C₂₃×#428	C₂²	semidirect
109. C₂₃×#427	C₂²	semidirect
110. C₂₃×#418	C₂²	semidirect
112. C₂₃×#416	C₂²	semidirect
113. C₄×M₁₆×C₂₃	C₂²	semidirect
114. C₂×C₄×C₈×C₂₃	C₂²	semidirect
312. D₈×C₂₃	#41	semidirect
381. #61442	C₂₃	direct (N × H)
444. #3475	C₂×C₂₃	semidirect
445. #3402	C₂×C₂₃	semidirect
446. #3389	C₂×C₂₃	semidirect
447. #3376	C₂×C₂₃	semidirect
448. #3352	C₂×C₂₃	semidirect
449. #3348	C₂×C₂₃	semidirect
450. #3323	C₂×C₂₃	semidirect
451. #3319	C₂×C₂₃	semidirect
452. #3315	C₂×C₂₃	semidirect
453. #3273	C₂×C₂₃	semidirect
454. #3267	C₂×C₂₃	semidirect
455. #3172	C₂×C₂₃	semidirect
456. #3168	C₂×C₂₃	semidirect
457. #3107	C₂×C₂₃	semidirect
458. #3105	C₂×C₂₃	semidirect
459. #3102	C₂×C₂₃	semidirect
460. #2965	C₂×C₂₃	semidirect
461. C₄×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
462. C₄×#135	C₂×C₂₃	semidirect
495. #556	C₂²×C₂₃	semidirect
497. #554	C₂²×C₂₃	semidirect
501. #552	C₂²×C₂₃	semidirect
506. #546	C₂²×C₂₃	semidirect
507. #533	C₂²×C₂₃	semidirect
511. #529	C₂²×C₂₃	semidirect
515. C₄×#41	C₂²×C₂₃	semidirect
516. C₂×C₄×D₄	C₂²×C₂₃	semidirect
518. #501	C₂²×C₂₃	semidirect
519. #499	C₂²×C₂₃	semidirect
520. #497	C₂²×C₂₃	semidirect
522. #491	C₂²×C₂₃	semidirect
523. #489	C₂²×C₂₃	semidirect
524. #488	C₂²×C₂₃	semidirect
525. #485	C₂²×C₂₃	semidirect
526. #485	C₂²×C₂₃	semidirect
527. #485	C₂²×C₂₃	semidirect
528. #484	C₂²×C₂₃	semidirect
529. #482	C₂²×C₂₃	semidirect
531. #479	C₂²×C₂₃	semidirect
532. #478	C₂²×C₂₃	semidirect
533. #478	C₂²×C₂₃	semidirect
534. #478	C₂²×C₂₃	semidirect
535. #475	C₂²×C₂₃	semidirect
536. #474	C₂²×C₂₃	semidirect
537. #470	C₂²×C₂₃	semidirect
538. #470	C₂²×C₂₃	semidirect
541. #467	C₂²×C₂₃	semidirect
543. #465	C₂²×C₂₃	semidirect
544. #464	C₂²×C₂₃	semidirect
548. #462	C₂²×C₂₃	semidirect
549. #461	C₂²×C₂₃	semidirect
552. #452	C₂²×C₂₃	semidirect
553. #450	C₂²×C₂₃	semidirect
556. #446	C₂²×C₂₃	semidirect
557. #446	C₂²×C₂₃	semidirect
560. #440	C₂²×C₂₃	semidirect
561. #440	C₂²×C₂₃	semidirect
562. C₄×Q₁₆	C₂²×C₂₃	semidirect
563. C₄×Q₁₆	C₂²×C₂₃	semidirect
564. C₄×Q₁₆	C₂²×C₂₃	semidirect
565. C₄×Q₁₆	C₂²×C₂₃	semidirect
566. C₄×SD₁₆	C₂²×C₂₃	semidirect
567. C₄×SD₁₆	C₂²×C₂₃	semidirect
568. C₄×SD₁₆	C₂²×C₂₃	semidirect
569. C₄×SD₁₆	C₂²×C₂₃	semidirect
570. C₄×SD₁₆	C₂²×C₂₃	semidirect
577. #435	C₂²×C₂₃	semidirect
578. #435	C₂²×C₂₃	semidirect
579. #431	C₂²×C₂₃	semidirect
580. #431	C₂²×C₂₃	semidirect
581. #428	C₂²×C₂₃	semidirect
582. #427	C₂²×C₂₃	semidirect
583. #418	C₂²×C₂₃	semidirect
585. #416	C₂²×C₂₃	semidirect
586. C₄×M₁₆	C₂²×C₂₃	semidirect
587. C₂×C₄×C₈	C₂²×C₂₃	semidirect
746. C₂₃	#61442	direct (N × H)
793. D₈	#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×#3475	2
C₂₃×#3402	2
C₂₃×#3389	2
C₂₃×#3376	2
C₂₃×#3352	2
C₂₃×#3348	2
C₂₃×#3323	2
C₂₃×#3319	2
C₂₃×#3315	2
C₂₃×#3273	2
C₂₃×#3267	2
C₂₃×#3172	2
C₂₃×#3168	2
C₂₃×#3107	2
C₂₃×#3105	2
C₂₃×#3102	2
C₂₃×#2965	2
C₄×C₂₃×AGL(1,ℤ/8)	2
C₄×C₂₃×#135	2
#61442	23

Subgroups — C23×#61442 #19209068

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61442 #19209068