Subgroups — C₂₃×#60600 #19208226

Order 5888.

2046 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₂₃×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3124	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3121	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3116	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3112	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3106	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3104	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3098	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3079	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3013	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2951	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	C₂×C₂₃×#135	C₂²	1	2	yes	—
21	C₂₃×#556	—	2	1	no	—
22	C₂₃×#555	—	2	1	no	—
23	C₂₃×#554	—	2	1	no	—
24	C₂₃×#553	—	2	2	no	—
25	C₂₃×#548	—	2	2	no	—
26	C₂₃×#547	—	2	1	no	—
27	C₂₃×#542	C₂²	1	4	yes	—
28	C₂₃×#537	C₂²	1	2	yes	—
29	C₂₃×#533	C₂²	1	2	yes	—
30	C₂₃×#532	C₂²	1	1	yes	characteristic
31	C₂₃×#532	C₂²	1	2	yes	—
32	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
33	C₂₃×#520	—	2	1	no	—
34	C₂₃×#520	—	2	2	no	—
35	C₂₃×#520	C₂²	1	1	yes	characteristic
36	C₂₃×#520	C₂²	1	2	yes	—
37	C₂₃×#520	C₂²	1	2	yes	—
38	C₂₃×#520	C₂²	1	1	yes	characteristic
39	C₂₃×#519	—	2	1	no	—
40	C₂₃×#519	C₂²	1	1	yes	characteristic
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×#484	C₂²	1	4	yes	—
52	C₂₃×#482	C₂²	1	4	yes	—
53	C₂₃×#480	C₂²	1	4	yes	—
54	C₂₃×#477	C₂²	1	2	yes	—
55	C₂₃×#477	C₂²	1	2	yes	—
56	C₂₃×#477	C₂²	1	4	yes	—
57	C₂₃×#477	C₂²	1	2	yes	—
58	C₂₃×#476	C₂²	1	2	yes	—
59	C₂₃×#475	C₂²	1	2	yes	—
60	C₂₃×#474	C₂²	1	2	yes	—
61	C₂₃×#464	C₂²	1	2	yes	—
62	C₂₃×#464	C₂²	1	4	yes	—
63	C₂₃×#463	C₂²	1	2	yes	—
64	C₂₃×#462	C₂²	1	1	yes	characteristic
65	C₂₃×#462	C₂²	1	2	yes	—
66	C₂₃×#461	C₂²	1	1	yes	characteristic
67	C₂₃×#460	C₂²	1	1	yes	characteristic
68	C₂₃×#460	C₂²	1	2	yes	—
69	C₂₃×#459	C₂²	1	1	yes	characteristic
70	C₂₃×#452	C₂²	1	4	yes	—
71	C₂₃×#451	C₂²	1	4	yes	—
72	C₂₃×#449	C₂²	1	4	yes	—
73	C₂₃×#448	C₂²	1	4	yes	—
74	C₂₃×#441	C₂²	1	4	yes	—
75	C₂₃×#440	C₂²	1	4	yes	—
76	C₂₃×#440	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×SD₁₆×C₂₃	C₂²	1	4	yes	—
81	C₄×D₈×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	C₂×C₂₃×#107	C₂²	1	2	yes	—
87	C₂₃×#423	C₂²	1	1	yes	characteristic
88	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
89	C₂₃×#417	C₂²	1	2	yes	—
90	C₂₃×#417	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	1	no	—
98	C₂×#41×C₂₃	—	2	2	no	—
99	C₂×#41×C₂₃	—	2	2	no	—
100	C₂×#41×C₂₃	C₂³	1	2	yes	—
101	C₂×#41×C₂₃	C₂³	1	2	yes	—
102	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
103	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
104	C₂²×Q₈×C₂₃	—	2	1	no	—
105	C₂²×Q₈×C₂₃	—	2	1	no	—
106	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
107	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
108	C₂₃×#137	—	2	8	no	—
109	C₂₃×#135	—	2	8	no	—
110	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
111	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
112	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
113	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
114	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
115	C₂×D₈×C₂₃	C₂³	1	2	yes	—
116	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
117	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
118	C₂₃×C₄⋊Q₈	—	2	1	no	—
119	C₂₃×C₄⋊Q₈	—	2	1	no	—
120	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
123	C₂₃×#127	C₂³	1	1	yes	characteristic
124	C₂₃×#126	—	2	4	no	—
125	C₂₃×#125	—	2	2	no	—
126	C₂₃×#124	—	2	4	no	—
127	C₂₃×#124	—	2	2	no	—
128	C₂₃×#124	C₂³	1	2	yes	—
129	C₂₃×#123	—	2	4	no	—
130	C₂₃×C₂²⋊Q₈	—	2	2	no	—
131	C₂₃×C₂²⋊Q₈	—	2	2	no	—
132	C₂₃×C₂²⋊Q₈	—	2	4	no	—
133	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₂₃×#121	—	2	2	no	—
135	C₂₃×#121	—	2	4	no	—
136	C₂₃×#121	—	2	1	no	—
137	C₂₃×#121	—	2	1	no	—
138	C₂₃×#121	—	2	2	no	—
139	C₂₃×#121	C₂³	1	4	yes	—
140	C₄×Q₈×C₂₃	—	2	1	no	—
141	C₄×Q₈×C₂₃	—	2	1	no	—
142	C₄×Q₈×C₂₃	—	2	2	no	—
143	C₄×Q₈×C₂₃	—	2	1	no	—
144	C₄×Q₈×C₂₃	—	2	2	no	—
145	C₄×Q₈×C₂₃	—	2	2	no	—
146	C₄×Q₈×C₂₃	—	2	2	no	—
147	C₄×Q₈×C₂₃	—	2	1	no	—
148	C₄×Q₈×C₂₃	—	2	1	no	—
149	C₄×Q₈×C₂₃	—	2	2	no	—
150	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
151	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
152	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
153	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
154	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
155	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
156	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
157	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
158	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
159	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
160	C₄×D₄×C₂₃	—	2	2	no	—
161	C₄×D₄×C₂₃	—	2	1	no	—
162	C₄×D₄×C₂₃	—	2	1	no	—
163	C₄×D₄×C₂₃	—	2	2	no	—
164	C₄×D₄×C₂₃	—	2	1	no	—
165	C₄×D₄×C₂₃	—	2	2	no	—
166	C₄×D₄×C₂₃	—	2	4	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	1	no	—
171	C₄×D₄×C₂₃	—	2	2	no	—
172	C₄×D₄×C₂₃	—	2	1	no	—
173	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
174	C₄×D₄×C₂₃	D₄	1	2	yes	—
175	C₄×D₄×C₂₃	D₄	1	2	yes	—
176	C₄×D₄×C₂₃	D₄	1	1	yes	characteristic
177	C₄×D₄×C₂₃	C₂³	1	2	yes	—
178	C₄×D₄×C₂₃	C₂³	1	4	yes	—
179	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
180	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
181	C₂₃×#117	—	2	2	no	—
182	C₂₃×#117	—	2	2	no	—
183	C₂₃×#117	—	2	1	no	—
184	C₂₃×#117	—	2	2	no	—
185	C₂₃×#117	—	2	2	no	—
186	C₂₃×#117	—	2	2	no	—
187	C₂₃×#117	—	2	2	no	—
188	C₂₃×#117	—	2	1	no	—
189	C₂₃×#117	—	2	2	no	—
190	C₂₃×#117	C₂³	1	1	yes	characteristic
191	C₂₃×#117	C₂³	1	2	yes	—
192	C₂₃×#117	C₂³	1	1	yes	characteristic
193	C₂₃×#117	C₂³	1	2	yes	—
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	2	no	—
198	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
199	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
200	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
201	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
203	C₂×C₄²×C₂₃	—	2	1	no	—
204	C₂×C₄²×C₂₃	—	2	2	no	—
205	C₂×C₄²×C₂₃	—	2	2	no	—
206	C₂×C₄²×C₂₃	—	2	1	no	—
207	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
209	C₂₃×#107	C₂³	1	4	yes	—
210	C₂₃×#107	C₂³	1	4	yes	—
211	C₂₃×#107	C₂³	1	4	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×#102	C₂³	1	2	yes	—
225	C₂₃×#102	C₂³	1	2	yes	—
226	C₂₃×#102	C₂³	1	4	yes	—
227	C₂₃×#102	C₂³	1	4	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	—	2	4	no	—
240	#41×C₂₃	—	2	4	no	—
241	#41×C₂₃	—	8	4	no	—
242	#41×C₂₃	#41	1	4	yes	complemented
243	C₂×Q₈×C₂₃	—	2	8	no	—
244	C₂×Q₈×C₂₃	—	2	4	no	—
245	C₂×Q₈×C₂₃	—	2	4	no	—
246	C₂×Q₈×C₂₃	—	2	2	no	—
247	C₂×Q₈×C₂₃	—	2	1	no	—
248	C₂×Q₈×C₂₃	—	2	2	no	—
249	C₂×Q₈×C₂₃	—	2	2	no	—
250	C₂×Q₈×C₂₃	—	2	2	no	—
251	C₂×Q₈×C₂₃	—	8	2	no	—
252	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
253	C₂×Q₈×C₂₃	#41	1	4	yes	complemented
254	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
255	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
256	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
257	C₂×D₄×C₂₃	—	2	2	no	—
258	C₂×D₄×C₂₃	—	2	1	no	—
259	C₂×D₄×C₂₃	—	2	2	no	—
260	C₂×D₄×C₂₃	—	2	4	no	—
261	C₂×D₄×C₂₃	—	2	1	no	—
262	C₂×D₄×C₂₃	—	2	1	no	—
263	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
264	C₂×D₄×C₂₃	C₂×D₄	1	1	yes	characteristic
265	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
266	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₂₃	—	2	2	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	—	2	2	no	—
272	C₂²×C₄×C₂₃	—	2	1	no	—
273	C₂²×C₄×C₂₃	—	2	2	no	—
274	C₂²×C₄×C₂₃	—	2	1	no	—
275	C₂²×C₄×C₂₃	—	2	2	no	—
276	C₂²×C₄×C₂₃	—	2	1	no	—
277	C₂²×C₄×C₂₃	—	2	2	no	—
278	C₂²×C₄×C₂₃	—	2	4	no	—
279	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
281	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
283	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
285	Q₁₆×C₂₃	—	2	4	no	—
286	Q₁₆×C₂₃	—	2	8	no	—
287	SD₁₆×C₂₃	—	2	4	no	—
288	SD₁₆×C₂₃	—	2	8	no	—
289	SD₁₆×C₂₃	—	2	4	no	—
290	D₈×C₂₃	—	2	4	no	—
291	M₁₆×C₂₃	—	2	4	no	—
292	C₂×C₈×C₂₃	—	2	4	no	—
293	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
294	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
295	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
296	C₄⋊C₄×C₂₃	—	2	2	no	—
297	C₄⋊C₄×C₂₃	—	2	2	no	—
298	C₄⋊C₄×C₂₃	—	2	2	no	—
299	C₄⋊C₄×C₂₃	—	2	2	no	—
300	C₄⋊C₄×C₂₃	—	2	1	no	—
301	C₄⋊C₄×C₂₃	—	2	2	no	—
302	C₄⋊C₄×C₂₃	—	2	1	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	2	no	—
307	C₄⋊C₄×C₂₃	—	2	2	no	—
308	C₄⋊C₄×C₂₃	—	2	1	no	—
309	C₄⋊C₄×C₂₃	—	2	1	no	—
310	C₄⋊C₄×C₂₃	—	2	1	no	—
311	C₄⋊C₄×C₂₃	—	2	4	no	—
312	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
313	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
314	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
315	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
316	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
317	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
318	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
319	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
320	C₂²⋊C₄×C₂₃	—	2	2	no	—
321	C₂²⋊C₄×C₂₃	—	2	1	no	—
322	C₂²⋊C₄×C₂₃	—	2	4	no	—
323	C₂²⋊C₄×C₂₃	—	2	1	no	—
324	C₂²⋊C₄×C₂₃	—	2	2	no	—
325	C₂²⋊C₄×C₂₃	—	2	1	no	—
326	C₂²⋊C₄×C₂₃	—	2	4	no	—
327	C₂²⋊C₄×C₂₃	—	2	4	no	—
328	C₂²⋊C₄×C₂₃	—	2	2	no	—
329	C₂²⋊C₄×C₂₃	—	2	2	no	—
330	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
331	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
332	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
333	C₄²×C₂₃	—	2	2	no	—
334	C₄²×C₂₃	—	2	1	no	—
335	C₄²×C₂₃	—	2	1	no	—
336	C₄²×C₂₃	—	2	2	no	—
337	C₄²×C₂₃	—	2	2	no	—
338	C₄²×C₂₃	—	2	2	no	—
339	C₄²×C₂₃	—	2	2	no	—
340	C₄²×C₂₃	—	2	2	no	—
341	C₄²×C₂₃	—	2	1	no	—
342	C₄²×C₂₃	—	2	4	no	—
343	C₄²×C₂₃	C₂×D₄	1	2	yes	—
344	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
345	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
346	C₄²×C₂₃	C₂×D₄	1	2	yes	—
347	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
348	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
349	C₄²×C₂₃	C₂⁴	1	2	yes	—
350	#60600	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
351	C₂³×C₂₃	—	2	1	no	—
352	C₂³×C₂₃	—	2	2	no	—
353	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
354	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
355	Q₈×C₂₃	—	2	8	no	—
356	Q₈×C₂₃	—	2	2	no	—
357	Q₈×C₂₃	—	2	4	no	—
358	Q₈×C₂₃	—	2	1	no	—
359	Q₈×C₂₃	—	2	2	no	—
360	Q₈×C₂₃	—	2	2	no	—
361	Q₈×C₂₃	—	2	2	no	—
362	Q₈×C₂₃	—	4	4	no	—
363	Q₈×C₂₃	—	8	2	no	—
364	Q₈×C₂₃	C₂×#41	1	2	yes	—
365	Q₈×C₂₃	C₂×#41	1	4	yes	—
366	D₄×C₂₃	—	2	8	no	—
367	D₄×C₂₃	—	2	4	no	—
368	D₄×C₂₃	—	2	4	no	—
369	D₄×C₂₃	—	2	2	no	—
370	D₄×C₂₃	—	2	1	no	—
371	D₄×C₂₃	—	2	2	no	—
372	D₄×C₂₃	—	2	2	no	—
373	D₄×C₂₃	—	4	2	no	—
374	D₄×C₂₃	—	4	4	no	—
375	D₄×C₂₃	—	4	2	no	—
376	D₄×C₂₃	—	8	4	no	—
377	D₄×C₂₃	C₂×#41	1	2	yes	—
378	C₂×C₄×C₂₃	—	2	8	no	—
379	C₂×C₄×C₂₃	—	2	8	no	—
380	C₂×C₄×C₂₃	—	2	4	no	—
381	C₂×C₄×C₂₃	—	2	2	no	—
382	C₂×C₄×C₂₃	—	2	1	no	—
383	C₂×C₄×C₂₃	—	2	4	no	—
384	C₂×C₄×C₂₃	—	2	2	no	—
385	C₂×C₄×C₂₃	—	2	4	no	—
386	C₂×C₄×C₂₃	—	2	2	no	—
387	C₂×C₄×C₂₃	—	2	2	no	—
388	C₂×C₄×C₂₃	—	2	1	no	—
389	C₂×C₄×C₂₃	—	2	1	no	—
390	C₂×C₄×C₂₃	—	2	2	no	—
391	C₂×C₄×C₂₃	—	2	2	no	—
392	C₂×C₄×C₂₃	—	2	4	no	—
393	C₂×C₄×C₂₃	—	4	1	no	—
394	C₂×C₄×C₂₃	—	4	2	no	—
395	C₂×C₄×C₂₃	—	4	4	no	—
396	C₂×C₄×C₂₃	—	4	2	no	—
397	C₂×C₄×C₂₃	—	8	2	no	—
398	C₂×C₄×C₂₃	—	8	1	no	—
399	C₂×C₄×C₂₃	—	8	4	no	—
400	C₂×C₄×C₂₃	—	8	1	no	—
401	C₂×C₄×C₂₃	—	8	2	no	—
402	C₂×C₄×C₂₃	—	8	2	no	—
403	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
404	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
406	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
407	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
408	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
409	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
410	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
411	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
412	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
413	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
414	C₈×C₂₃	—	2	2	no	—
415	C₈×C₂₃	—	2	2	no	—
416	C₈×C₂₃	—	2	4	no	—
417	#3511	C₂×C₂₃	1	1	yes	characteristic, complemented
418	C₄×2₋¹⁺⁴	C₂×C₂₃	1	1	yes	characteristic, complemented
419	#3124	C₂×C₂₃	1	4	yes	complemented
420	#3121	C₂×C₂₃	1	4	yes	complemented
421	#3116	C₂×C₂₃	1	2	yes	complemented
422	#3112	C₂×C₂₃	1	2	yes	complemented
423	#3106	C₂×C₂₃	1	2	yes	complemented
424	#3104	C₂×C₂₃	1	2	yes	complemented
425	#3098	C₂×C₂₃	1	2	yes	complemented
426	#3079	C₂×C₂₃	1	1	yes	characteristic, complemented
427	C₂×#477	C₂×C₂₃	1	1	yes	characteristic, complemented
428	#3037	C₂×C₂₃	1	1	yes	characteristic, complemented
429	#3035	C₂×C₂₃	1	1	yes	characteristic, complemented
430	#3013	C₂×C₂₃	1	2	yes	complemented
431	#2951	C₂×C₂₃	1	2	yes	complemented
432	#2947	C₂×C₂₃	1	2	yes	complemented
433	#2925	C₂×C₂₃	1	1	yes	characteristic, complemented
434	C₂²×C₂₃	—	2	1	no	—
435	C₂²×C₂₃	—	2	1	no	—
436	C₂²×C₂₃	—	2	2	no	—
437	C₂²×C₂₃	—	2	2	no	—
438	C₂²×C₂₃	—	2	2	no	—
439	C₂²×C₂₃	—	2	2	no	—
440	C₂²×C₂₃	—	4	1	no	—
441	C₂²×C₂₃	—	4	1	no	—
442	C₂²×C₂₃	—	4	2	no	—
443	C₂²×C₂₃	—	4	2	no	—
444	C₂²×C₂₃	—	4	2	no	—
445	C₂²×C₂₃	#525	1	2	yes	—
446	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
447	C₄×C₂₃	—	2	1	no	—
448	C₄×C₂₃	—	2	2	no	—
449	C₄×C₂₃	—	2	1	no	—
450	C₄×C₂₃	—	2	4	no	—
451	C₄×C₂₃	—	2	2	no	—
452	C₄×C₂₃	—	2	2	no	—
453	C₄×C₂₃	—	2	2	no	—
454	C₄×C₂₃	—	2	1	no	—
455	C₄×C₂₃	—	4	2	no	—
456	C₄×C₂₃	—	4	1	no	—
457	C₄×C₂₃	—	4	4	no	—
458	C₄×C₂₃	—	4	2	no	—
459	C₄×C₂₃	—	4	1	no	—
460	C₄×C₂₃	#525	1	2	yes	—
461	C₄×C₂₃	#578	1	2	yes	—
462	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
463	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
464	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	1	yes	characteristic
465	C₂×#137	C₂²×C₂₃	1	2	yes	—
466	C₂×#135	C₂²×C₂₃	1	2	yes	—
467	#556	—	2	1	no	—
468	#555	—	2	1	no	—
469	#554	—	2	1	no	—
470	#553	—	2	2	no	—
471	#548	—	2	2	no	—
472	#547	—	2	1	no	—
473	#542	C₂²×C₂₃	1	4	yes	—
474	#537	C₂²×C₂₃	1	2	yes	—
475	#533	C₂²×C₂₃	1	2	yes	—
476	#532	C₂²×C₂₃	1	1	yes	characteristic
477	#532	C₂²×C₂₃	1	2	yes	—
478	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
479	#520	—	2	1	no	—
480	#520	—	2	2	no	—
481	#520	C₂²×C₂₃	1	2	yes	—
482	#520	C₂²×C₂₃	1	1	yes	characteristic
483	#520	C₂²×C₂₃	1	2	yes	—
484	#520	C₂²×C₂₃	1	1	yes	characteristic
485	#519	—	2	1	no	—
486	#519	C₂²×C₂₃	1	2	yes	—
487	#519	C₂²×C₂₃	1	1	yes	characteristic
488	C₄×#41	—	2	2	no	—
489	C₄×#41	—	2	1	no	—
490	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
491	C₄×#41	C₂²×C₂₃	1	2	yes	—
492	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
493	C₂×C₄×Q₈	—	2	1	no	—
494	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
495	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
496	#485	C₂²×C₂₃	1	4	yes	—
497	#484	C₂²×C₂₃	1	4	yes	—
498	#482	C₂²×C₂₃	1	4	yes	—
499	#480	C₂²×C₂₃	1	4	yes	—
500	#477	C₂²×C₂₃	1	2	yes	—
501	#477	C₂²×C₂₃	1	2	yes	—
502	#477	C₂²×C₂₃	1	4	yes	—
503	#477	C₂²×C₂₃	1	2	yes	—
504	#476	C₂²×C₂₃	1	2	yes	—
505	#475	C₂²×C₂₃	1	2	yes	—
506	#474	C₂²×C₂₃	1	2	yes	—
507	#464	C₂²×C₂₃	1	2	yes	—
508	#464	C₂²×C₂₃	1	4	yes	—
509	#463	C₂²×C₂₃	1	2	yes	—
510	#462	C₂²×C₂₃	1	1	yes	characteristic
511	#462	C₂²×C₂₃	1	2	yes	—
512	#461	C₂²×C₂₃	1	1	yes	characteristic
513	#460	C₂²×C₂₃	1	2	yes	—
514	#460	C₂²×C₂₃	1	1	yes	characteristic
515	#459	C₂²×C₂₃	1	1	yes	characteristic
516	#452	C₂²×C₂₃	1	4	yes	—
517	#451	C₂²×C₂₃	1	4	yes	—
518	#449	C₂²×C₂₃	1	4	yes	—
519	#448	C₂²×C₂₃	1	4	yes	—
520	#441	C₂²×C₂₃	1	4	yes	—
521	#440	C₂²×C₂₃	1	4	yes	—
522	#440	C₂²×C₂₃	1	4	yes	—
523	#440	C₂²×C₂₃	1	4	yes	—
524	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	—
525	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	—
526	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	—
527	C₄×D₈	C₂²×C₂₃	1	4	yes	—
528	#433	C₂²×C₂₃	1	4	yes	—
529	#432	C₂²×C₂₃	1	2	yes	—
530	#431	C₂²×C₂₃	1	2	yes	—
531	#428	C₂²×C₂₃	1	2	yes	—
532	C₂×#107	C₂²×C₂₃	1	2	yes	—
533	#423	C₂²×C₂₃	1	1	yes	characteristic
534	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
535	#417	C₂²×C₂₃	1	2	yes	—
536	#417	C₂²×C₂₃	1	2	yes	—
537	#416	C₂²×C₂₃	1	2	yes	—
538	C₂×#103	C₂²×C₂₃	1	2	yes	—
539	#408	C₂²×C₂₃	1	2	yes	—
540	#405	C₂²×C₂₃	1	2	yes	—
541	C₂×C₂₃	—	2	2	no	—
542	C₂×C₂₃	—	4	2	no	—
543	C₂×C₂₃	—	4	2	no	—
544	C₂×C₂₃	—	8	2	no	—
545	C₂×C₂₃	C₂×#525	1	1	yes	characteristic
546	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
547	C₂×C₂₃	#3585	1	1	yes	characteristic
548	2₋¹⁺⁴	—	2	4	no	—
549	2₋¹⁺⁴	—	2	4	no	—
550	C₂×#41	—	2	1	no	—
551	C₂×#41	—	2	2	no	—
552	C₂×#41	—	2	2	no	—
553	C₂×#41	C₂³×C₂₃	1	2	yes	—
554	C₂×#41	C₂³×C₂₃	1	2	yes	—
555	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
556	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
557	C₂²×Q₈	—	2	1	no	—
558	C₂²×Q₈	—	2	1	no	—
559	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
560	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
561	#137	—	2	8	no	—
562	#135	—	2	8	no	—
563	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
564	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
565	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
566	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
567	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
568	C₂×D₈	C₂³×C₂₃	1	2	yes	—
569	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
570	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
571	C₄⋊Q₈	—	2	1	no	—
572	C₄⋊Q₈	—	2	1	no	—
573	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
574	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
575	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
576	#127	C₂³×C₂₃	1	1	yes	characteristic
577	#126	—	2	4	no	—
578	#125	—	2	2	no	—
579	#124	—	2	4	no	—
580	#124	—	2	2	no	—
581	#124	C₂³×C₂₃	1	2	yes	—
582	#123	—	2	4	no	—
583	C₂²⋊Q₈	—	2	2	no	—
584	C₂²⋊Q₈	—	2	2	no	—
585	C₂²⋊Q₈	—	2	4	no	—
586	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
587	#121	—	2	2	no	—
588	#121	—	2	4	no	—
589	#121	—	2	1	no	—
590	#121	—	2	1	no	—
591	#121	—	2	2	no	—
592	#121	C₂³×C₂₃	1	4	yes	—
593	C₄×Q₈	—	2	1	no	—
594	C₄×Q₈	—	2	1	no	—
595	C₄×Q₈	—	2	2	no	—
596	C₄×Q₈	—	2	1	no	—
597	C₄×Q₈	—	2	2	no	—
598	C₄×Q₈	—	2	2	no	—
599	C₄×Q₈	—	2	1	no	—
600	C₄×Q₈	—	2	1	no	—
601	C₄×Q₈	—	2	2	no	—
602	C₄×Q₈	—	2	2	no	—
603	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
604	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
605	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
606	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
607	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
608	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
609	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
610	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
611	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
612	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
613	C₄×D₄	—	2	2	no	—
614	C₄×D₄	—	2	1	no	—
615	C₄×D₄	—	2	1	no	—
616	C₄×D₄	—	2	2	no	—
617	C₄×D₄	—	2	1	no	—
618	C₄×D₄	—	2	2	no	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	4	no	—
623	C₄×D₄	—	2	1	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	D₄×C₂₃	1	2	yes	—
627	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
628	C₄×D₄	D₄×C₂₃	1	1	yes	characteristic
629	C₄×D₄	D₄×C₂₃	1	2	yes	—
630	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
631	C₄×D₄	C₂³×C₂₃	1	2	yes	—
632	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
633	C₄×D₄	C₂³×C₂₃	1	4	yes	—
634	#117	—	2	2	no	—
635	#117	—	2	1	no	—
636	#117	—	2	2	no	—
637	#117	—	2	2	no	—
638	#117	—	2	2	no	—
639	#117	—	2	2	no	—
640	#117	—	2	2	no	—
641	#117	—	2	1	no	—
642	#117	—	2	2	no	—
643	#117	C₂³×C₂₃	1	1	yes	characteristic
644	#117	C₂³×C₂₃	1	2	yes	—
645	#117	C₂³×C₂₃	1	1	yes	characteristic
646	#117	C₂³×C₂₃	1	2	yes	—
647	C₂×C₄⋊C₄	—	2	1	no	—
648	C₂×C₄⋊C₄	—	2	2	no	—
649	C₂×C₄⋊C₄	—	2	1	no	—
650	C₂×C₄⋊C₄	—	2	1	no	—
651	C₂×C₄⋊C₄	—	2	2	no	—
652	C₂×C₄⋊C₄	—	2	2	no	—
653	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
654	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
655	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
656	C₂×C₄²	—	2	1	no	—
657	C₂×C₄²	—	2	2	no	—
658	C₂×C₄²	—	2	2	no	—
659	C₂×C₄²	—	2	1	no	—
660	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
662	#107	C₂³×C₂₃	1	4	yes	—
663	#107	C₂³×C₂₃	1	4	yes	—
664	#107	C₂³×C₂₃	1	4	yes	—
665	#106	C₂³×C₂₃	1	4	yes	—
666	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
667	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
668	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
669	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
670	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
671	#103	C₂³×C₂₃	1	4	yes	—
672	#103	C₂³×C₂₃	1	4	yes	—
673	#103	C₂³×C₂₃	1	2	yes	—
674	#103	C₂³×C₂₃	1	2	yes	—
675	#103	C₂³×C₂₃	1	4	yes	—
676	#103	C₂³×C₂₃	1	4	yes	—
677	#102	C₂³×C₂₃	1	2	yes	—
678	#102	C₂³×C₂₃	1	2	yes	—
679	#102	C₂³×C₂₃	1	4	yes	—
680	#102	C₂³×C₂₃	1	4	yes	—
681	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
682	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
683	#97	C₂³×C₂₃	1	4	yes	—
684	C₄×C₈	C₂³×C₂₃	1	4	yes	—
685	C₂₃	#60600	1	1	yes	characteristic, direct product factor, Sylow
686	#41	—	2	16	no	—
687	#41	—	2	8	no	—
688	#41	—	2	4	no	—
689	#41	—	2	4	no	—
690	#41	—	2	2	no	—
691	#41	—	2	2	no	—
692	#41	—	2	2	no	—
693	#41	—	2	4	no	—
694	#41	—	2	4	no	—
695	#41	—	8	4	no	—
696	#41	#41×C₂₃	1	4	yes	complemented
697	C₂×Q₈	—	2	8	no	—
698	C₂×Q₈	—	2	4	no	—
699	C₂×Q₈	—	2	4	no	—
700	C₂×Q₈	—	2	2	no	—
701	C₂×Q₈	—	2	1	no	—
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	—	2	2	no	—
704	C₂×Q₈	—	2	2	no	—
705	C₂×Q₈	—	8	2	no	—
706	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
707	C₂×Q₈	#41×C₂₃	1	4	yes	complemented
708	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
709	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
710	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	4	no	—
715	C₂×D₄	—	2	1	no	—
716	C₂×D₄	—	2	1	no	—
717	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
718	C₂×D₄	C₂×D₄×C₂₃	1	1	yes	characteristic
719	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
720	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	1	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	1	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	1	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	1	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	4	no	—
733	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
734	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
735	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
736	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
739	Q₁₆	—	2	4	no	—
740	Q₁₆	—	2	8	no	—
741	SD₁₆	—	2	4	no	—
742	SD₁₆	—	2	8	no	—
743	SD₁₆	—	2	4	no	—
744	D₈	—	2	4	no	—
745	M₁₆	—	2	4	no	—
746	C₂×C₈	—	2	4	no	—
747	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
748	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
749	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	2	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	1	no	—
757	C₄⋊C₄	—	2	2	no	—
758	C₄⋊C₄	—	2	2	no	—
759	C₄⋊C₄	—	2	4	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	1	no	—
763	C₄⋊C₄	—	2	1	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	4	no	—
766	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
767	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
768	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
769	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
770	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
771	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
772	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
773	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	1	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	1	no	—
778	C₂²⋊C₄	—	2	2	no	—
779	C₂²⋊C₄	—	2	1	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	2	2	no	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
785	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
786	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
787	C₄²	—	2	2	no	—
788	C₄²	—	2	1	no	—
789	C₄²	—	2	1	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	2	2	no	—
792	C₄²	—	2	2	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	1	no	—
796	C₄²	—	2	4	no	—
797	C₄²	C₂×D₄×C₂₃	1	2	yes	—
798	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
799	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
800	C₄²	C₂×D₄×C₂₃	1	2	yes	—
801	C₄²	C₂⁴×C₂₃	1	2	yes	—
802	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
803	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
804	C₂³	—	2	1	no	—
805	C₂³	—	2	2	no	—
806	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
807	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
808	Q₈	—	2	8	no	—
809	Q₈	—	2	1	no	—
810	Q₈	—	2	2	no	—
811	Q₈	—	2	2	no	—
812	Q₈	—	2	4	no	—
813	Q₈	—	2	2	no	—
814	Q₈	—	2	2	no	—
815	Q₈	—	4	4	no	—
816	Q₈	—	8	2	no	—
817	Q₈	C₂×#41×C₂₃	1	2	yes	—
818	Q₈	C₂×#41×C₂₃	1	4	yes	—
819	D₄	—	2	8	no	—
820	D₄	—	2	4	no	—
821	D₄	—	2	4	no	—
822	D₄	—	2	1	no	—
823	D₄	—	2	2	no	—
824	D₄	—	2	2	no	—
825	D₄	—	2	2	no	—
826	D₄	—	4	2	no	—
827	D₄	—	4	4	no	—
828	D₄	—	4	2	no	—
829	D₄	—	8	4	no	—
830	D₄	C₂×#41×C₂₃	1	2	yes	—
831	C₂×C₄	—	2	8	no	—
832	C₂×C₄	—	2	8	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	4	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	4	no	—
838	C₂×C₄	—	2	2	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	4	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	1	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	2	no	—
845	C₂×C₄	—	2	4	no	—
846	C₂×C₄	—	4	1	no	—
847	C₂×C₄	—	4	2	no	—
848	C₂×C₄	—	4	2	no	—
849	C₂×C₄	—	4	4	no	—
850	C₂×C₄	—	8	4	no	—
851	C₂×C₄	—	8	2	no	—
852	C₂×C₄	—	8	1	no	—
853	C₂×C₄	—	8	2	no	—
854	C₂×C₄	—	8	1	no	—
855	C₂×C₄	—	8	2	no	—
856	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
857	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
858	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
859	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
860	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
861	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
862	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
863	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
864	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
865	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
866	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
867	C₈	—	2	2	no	—
868	C₈	—	2	2	no	—
869	C₈	—	2	4	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	2	no	—
873	C₂²	—	2	2	no	—
874	C₂²	—	2	2	no	—
875	C₂²	—	2	2	no	—
876	C₂²	—	4	1	no	—
877	C₂²	—	4	1	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	C₂₃×#525	1	2	yes	—
882	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
883	C₄	—	2	4	no	—
884	C₄	—	2	2	no	—
885	C₄	—	2	2	no	—
886	C₄	—	2	2	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	2	no	—
890	C₄	—	2	1	no	—
891	C₄	—	4	2	no	—
892	C₄	—	4	1	no	—
893	C₄	—	4	2	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	4	no	—
896	C₄	C₂₃×#525	1	2	yes	—
897	C₄	C₂₃×#578	1	2	yes	—
898	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
899	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
900	C₂	—	2	2	no	—
901	C₂	—	4	2	no	—
902	C₂	—	4	2	no	—
903	C₂	—	8	2	no	—
904	C₂	C₂×C₂₃×#525	1	1	yes	characteristic
905	C₂	C₂×C₂₃×#578	1	1	yes	characteristic
906	C₂	C₂₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
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×#3511	C₂	semidirect
2. C₄×C₂₃×2₋¹⁺⁴	C₂	semidirect
3. C₂₃×#3124	C₂	semidirect
4. C₂₃×#3121	C₂	semidirect
5. C₂₃×#3116	C₂	semidirect
6. C₂₃×#3112	C₂	semidirect
7. C₂₃×#3106	C₂	semidirect
8. C₂₃×#3104	C₂	semidirect
9. C₂₃×#3098	C₂	semidirect
10. C₂₃×#3079	C₂	semidirect
11. C₂×C₂₃×#477	C₂	semidirect
12. C₂₃×#3037	C₂	semidirect
13. C₂₃×#3035	C₂	semidirect
14. C₂₃×#3013	C₂	semidirect
15. C₂₃×#2951	C₂	semidirect
16. C₂₃×#2947	C₂	semidirect
17. C₂₃×#2925	C₂	semidirect
242. #41×C₂₃	#41	semidirect
253. C₂×Q₈×C₂₃	#41	semidirect
350. #60600	C₂₃	direct (N × H)
417. #3511	C₂×C₂₃	semidirect
418. C₄×2₋¹⁺⁴	C₂×C₂₃	semidirect
419. #3124	C₂×C₂₃	semidirect
420. #3121	C₂×C₂₃	semidirect
421. #3116	C₂×C₂₃	semidirect
422. #3112	C₂×C₂₃	semidirect
423. #3106	C₂×C₂₃	semidirect
424. #3104	C₂×C₂₃	semidirect
425. #3098	C₂×C₂₃	semidirect
426. #3079	C₂×C₂₃	semidirect
427. C₂×#477	C₂×C₂₃	semidirect
428. #3037	C₂×C₂₃	semidirect
429. #3035	C₂×C₂₃	semidirect
430. #3013	C₂×C₂₃	semidirect
431. #2951	C₂×C₂₃	semidirect
432. #2947	C₂×C₂₃	semidirect
433. #2925	C₂×C₂₃	semidirect
685. C₂₃	#60600	direct (N × H)
696. #41	#41×C₂₃	semidirect
707. C₂×Q₈	#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×#3511	2
C₄×C₂₃×2₋¹⁺⁴	2
C₂₃×#3124	2
C₂₃×#3121	2
C₂₃×#3116	2
C₂₃×#3112	2
C₂₃×#3106	2
C₂₃×#3104	2
C₂₃×#3098	2
C₂₃×#3079	2
C₂×C₂₃×#477	2
C₂₃×#3037	2
C₂₃×#3035	2
C₂₃×#3013	2
C₂₃×#2951	2
C₂₃×#2947	2
C₂₃×#2925	2
#60600	23

Subgroups — C23×#60600 #19208226

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60600 #19208226