Subgroups — C₂₃×#60942 #19208568

Order 5888.

1856 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3248	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3247	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3233	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3232	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3212	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3211	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3190	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3188	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3168	C₂	1	4	yes	maximal, complemented
12	C₂₃×#3104	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3103	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3102	C₂	1	4	yes	maximal, complemented
15	C₂₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₂₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#533	C₂²	1	1	yes	characteristic
19	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
20	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
21	C₂₃×#532	C₂²	1	1	yes	characteristic
22	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
23	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
24	C₂₃×#529	—	2	1	no	—
25	C₂₃×#529	—	2	1	no	—
26	C₂₃×#529	—	2	1	no	—
27	C₂₃×#529	—	2	1	no	—
28	C₂₃×#529	—	2	1	no	—
29	C₂₃×#529	—	2	1	no	—
30	C₂₃×#529	—	2	1	no	—
31	C₂₃×#529	—	2	1	no	—
32	C₂₃×#529	C₂²	1	2	yes	—
33	C₂₃×#529	C₂²	1	2	yes	—
34	C₂₃×#529	C₂²	1	2	yes	—
35	C₂₃×#529	C₂²	1	2	yes	—
36	C₂₃×#529	C₂²	1	2	yes	—
37	C₂₃×#529	C₂²	1	2	yes	complemented
38	C₂×C₂₃×#126	—	2	1	no	—
39	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
41	C₂₃×#525	—	2	1	no	—
42	C₂₃×#525	—	2	1	no	—
43	C₂₃×#525	C₂²	1	2	yes	—
44	C₂×C₂₃×#123	—	2	1	no	—
45	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
47	C₄×#41×C₂₃	—	2	1	no	—
48	C₄×#41×C₂₃	—	2	1	no	—
49	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
50	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₂₃	—	2	1	no	—
52	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
53	C₂×C₂₃×#117	—	2	1	no	—
54	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
55	C₂₃×#499	C₂²	1	4	yes	complemented
56	C₂₃×#495	C₂²	1	4	yes	complemented
57	C₂₃×#488	C₂²	1	4	yes	complemented
58	C₂₃×#488	C₂²	1	4	yes	complemented
59	C₂₃×#485	C₂²	1	4	yes	complemented
60	C₂₃×#484	C₂²	1	2	yes	—
61	C₂₃×#483	C₂²	1	2	yes	—
62	C₂₃×#482	C₂²	1	4	yes	—
63	C₂₃×#481	C₂²	1	2	yes	—
64	C₂₃×#480	C₂²	1	2	yes	—
65	C₂₃×#479	C₂²	1	4	yes	complemented
66	C₂₃×#478	C₂²	1	4	yes	complemented
67	C₂₃×#477	C₂²	1	2	yes	complemented
68	C₂₃×#476	C₂²	1	2	yes	complemented
69	C₂₃×#475	C₂²	1	2	yes	complemented
70	C₂₃×#474	C₂²	1	2	yes	complemented
71	C₂₃×#467	C₂²	1	4	yes	complemented
72	C₂₃×#466	C₂²	1	4	yes	—
73	C₂₃×#465	C₂²	1	4	yes	—
74	C₂₃×#465	C₂²	1	4	yes	complemented
75	C₂₃×#464	C₂²	1	4	yes	complemented
76	C₂₃×#463	C₂²	1	4	yes	complemented
77	C₂₃×#462	C₂²	1	2	yes	complemented
78	C₂₃×#461	C₂²	1	2	yes	complemented
79	C₂₃×#460	C₂²	1	2	yes	complemented
80	C₂₃×#459	C₂²	1	2	yes	complemented
81	C₂₃×#452	C₂²	1	4	yes	complemented
82	C₂₃×#451	C₂²	1	2	yes	—
83	C₂₃×#450	C₂²	1	2	yes	—
84	C₂₃×#449	C₂²	1	4	yes	—
85	C₂₃×#448	C₂²	1	2	yes	—
86	C₂₃×#447	C₂²	1	2	yes	—
87	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	complemented
88	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
89	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	complemented
90	C₄×D₈×C₂₃	C₂²	1	4	yes	complemented
91	C₂₃×#431	C₂²	1	2	yes	—
92	C₂₃×#431	C₂²	1	1	yes	characteristic
93	C₂₃×#431	C₂²	1	1	yes	characteristic
94	C₂₃×#431	C₂²	1	2	yes	complemented
95	C₂₃×#431	C₂²	1	2	yes	complemented
96	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	complemented
97	C₂×C₂₃×C₂²⋊C₈	C₂²	1	2	yes	—
98	C₂×C₄×C₈×C₂₃	C₂²	1	2	yes	complemented
99	C₂×#41×C₂₃	—	2	1	no	—
100	C₂×#41×C₂₃	—	2	1	no	—
101	C₂×#41×C₂₃	C₂³	1	2	yes	—
102	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
103	C₂²×D₄×C₂₃	—	2	1	no	—
104	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₂₃	—	2	1	no	—
106	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
107	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
108	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
109	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
110	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
111	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
112	C₂×D₈×C₂₃	C₂³	1	4	yes	—
113	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
114	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₂₃×#127	C₂³	1	1	yes	characteristic
118	C₂₃×#126	—	2	2	no	—
119	C₂₃×#126	—	2	2	no	—
120	C₂₃×#126	—	2	2	no	—
121	C₂₃×#126	—	2	2	no	—
122	C₂₃×#126	—	2	2	no	—
123	C₂₃×#126	—	2	2	no	—
124	C₂₃×#125	—	2	1	no	—
125	C₂₃×#125	—	2	1	no	—
126	C₂₃×#125	—	2	1	no	—
127	C₂₃×#125	—	2	1	no	—
128	C₂₃×#125	C₂³	1	2	yes	—
129	C₂₃×#125	C₂³	1	2	yes	—
130	C₂₃×#125	C₂³	1	2	yes	—
131	C₂₃×#124	—	2	1	no	—
132	C₂₃×#124	—	2	1	no	—
133	C₂₃×#124	—	2	1	no	—
134	C₂₃×#124	—	2	1	no	—
135	C₂₃×#124	C₂³	1	2	yes	—
136	C₂₃×#124	C₂³	1	2	yes	—
137	C₂₃×#124	C₂³	1	2	yes	—
138	C₂₃×#123	—	2	2	no	—
139	C₂₃×#123	—	2	2	no	—
140	C₂₃×#123	—	2	2	no	—
141	C₂₃×#123	—	2	2	no	—
142	C₂₃×#123	—	2	2	no	—
143	C₂₃×#123	—	2	2	no	—
144	C₂₃×#123	—	2	2	no	—
145	C₂₃×C₂²⋊Q₈	—	2	1	no	—
146	C₂₃×C₂²⋊Q₈	—	2	1	no	—
147	C₂₃×C₂²⋊Q₈	—	2	1	no	—
148	C₂₃×C₂²⋊Q₈	—	2	1	no	—
149	C₂₃×C₂²⋊Q₈	—	2	1	no	—
150	C₂₃×C₂²⋊Q₈	—	2	1	no	—
151	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
152	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
153	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
154	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
155	C₂₃×#121	—	2	1	no	—
156	C₂₃×#121	—	2	1	no	—
157	C₂₃×#121	—	2	1	no	—
158	C₂₃×#121	—	2	1	no	—
159	C₂₃×#121	—	2	1	no	—
160	C₂₃×#121	—	2	1	no	—
161	C₂₃×#121	C₂³	1	2	yes	—
162	C₂₃×#121	C₂³	1	2	yes	—
163	C₂₃×#121	C₂³	1	2	yes	—
164	C₂₃×#121	C₂³	1	2	yes	—
165	C₂₃×#120	—	2	2	no	—
166	C₄×Q₈×C₂₃	—	2	1	no	—
167	C₄×Q₈×C₂₃	—	2	1	no	—
168	C₄×Q₈×C₂₃	—	2	1	no	—
169	C₄×Q₈×C₂₃	—	2	1	no	—
170	C₄×Q₈×C₂₃	—	2	1	no	—
171	C₄×Q₈×C₂₃	—	2	1	no	—
172	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
173	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
174	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
175	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
176	C₄×D₄×C₂₃	—	2	2	no	—
177	C₄×D₄×C₂₃	—	2	2	no	—
178	C₄×D₄×C₂₃	—	2	2	no	—
179	C₄×D₄×C₂₃	—	2	2	no	—
180	C₄×D₄×C₂₃	—	2	2	no	—
181	C₄×D₄×C₂₃	—	2	2	no	—
182	C₄×D₄×C₂₃	—	2	2	no	—
183	C₄×D₄×C₂₃	—	2	2	no	—
184	C₄×D₄×C₂₃	—	2	2	no	—
185	C₄×D₄×C₂₃	—	2	2	no	—
186	C₄×D₄×C₂₃	—	2	1	no	—
187	C₄×D₄×C₂₃	—	2	1	no	—
188	C₄×D₄×C₂₃	—	2	1	no	—
189	C₄×D₄×C₂₃	—	2	1	no	—
190	C₄×D₄×C₂₃	—	2	1	no	—
191	C₄×D₄×C₂₃	—	2	1	no	—
192	C₄×D₄×C₂₃	C₂³	1	2	yes	—
193	C₄×D₄×C₂₃	C₂³	1	2	yes	—
194	C₄×D₄×C₂₃	C₂³	1	2	yes	—
195	C₄×D₄×C₂₃	C₂³	1	2	yes	—
196	C₂₃×#117	—	2	1	no	—
197	C₂₃×#117	—	2	1	no	—
198	C₂₃×#117	—	2	2	no	—
199	C₂₃×#117	—	2	2	no	—
200	C₂₃×#117	—	2	2	no	—
201	C₂₃×#117	—	2	2	no	—
202	C₂₃×#117	—	2	2	no	—
203	C₂₃×#117	—	2	2	no	—
204	C₂₃×#117	—	2	2	no	—
205	C₂₃×#117	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
207	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
208	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
209	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
210	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
213	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
214	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
215	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
216	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
217	C₂×C₄²×C₂₃	—	2	1	no	—
218	C₂×C₄²×C₂₃	—	2	2	no	—
219	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
220	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
221	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
222	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
223	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
224	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
225	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
226	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
227	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
228	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
229	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
230	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
231	C₂₃×#107	C₂³	1	4	yes	—
232	C₂₃×#107	C₂³	1	4	yes	—
233	C₂₃×#106	C₂³	1	4	yes	—
234	C₂₃×#106	C₂³	1	4	yes	—
235	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
236	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
237	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
238	C₂₃×#103	C₂³	1	4	yes	—
239	C₂₃×#103	C₂³	1	4	yes	—
240	C₂₃×#103	C₂³	1	4	yes	—
241	C₂₃×#103	C₂³	1	4	yes	—
242	C₂₃×#102	C₂³	1	4	yes	—
243	C₂₃×#102	C₂³	1	4	yes	—
244	C₂₃×#102	C₂³	1	4	yes	—
245	C₂₃×#102	C₂³	1	4	yes	—
246	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
247	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
248	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
249	C₄×C₈×C₂₃	C₂³	1	2	yes	—
250	C₄×C₈×C₂₃	C₂³	1	2	yes	—
251	C₄×C₈×C₂₃	C₂³	1	4	yes	—
252	C₂⁴×C₂₃	—	2	1	no	—
253	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
254	#41×C₂₃	—	4	4	no	—
255	#41×C₂₃	—	4	4	no	—
256	#41×C₂₃	—	4	4	no	—
257	C₂×Q₈×C₂₃	—	2	1	no	—
258	C₂×Q₈×C₂₃	—	2	1	no	—
259	C₂×Q₈×C₂₃	—	2	1	no	—
260	C₂×Q₈×C₂₃	—	4	2	no	—
261	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
262	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
263	C₂×D₄×C₂₃	—	2	2	no	—
264	C₂×D₄×C₂₃	—	2	2	no	—
265	C₂×D₄×C₂₃	—	2	2	no	—
266	C₂×D₄×C₂₃	—	2	2	no	—
267	C₂×D₄×C₂₃	—	2	2	no	—
268	C₂×D₄×C₂₃	—	2	1	no	—
269	C₂×D₄×C₂₃	—	2	1	no	—
270	C₂×D₄×C₂₃	—	2	1	no	—
271	C₂×D₄×C₂₃	—	4	2	no	—
272	C₂×D₄×C₂₃	—	4	4	no	—
273	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
274	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₂₃	—	2	4	no	—
276	C₂²×C₄×C₂₃	—	2	1	no	—
277	C₂²×C₄×C₂₃	—	2	1	no	—
278	C₂²×C₄×C₂₃	—	2	1	no	—
279	C₂²×C₄×C₂₃	—	2	2	no	—
280	C₂²×C₄×C₂₃	—	2	2	no	—
281	C₂²×C₄×C₂₃	—	2	2	no	—
282	C₂²×C₄×C₂₃	—	2	2	no	—
283	C₂²×C₄×C₂₃	—	2	2	no	—
284	C₂²×C₄×C₂₃	—	4	2	no	—
285	C₂²×C₄×C₂₃	—	4	2	no	—
286	C₂²×C₄×C₂₃	—	4	4	no	—
287	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
293	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
297	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
298	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
300	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
305	Q₁₆×C₂₃	—	4	4	no	—
306	SD₁₆×C₂₃	—	4	4	no	—
307	SD₁₆×C₂₃	—	4	4	no	—
308	D₈×C₂₃	—	4	4	no	—
309	C₂×C₈×C₂₃	—	4	4	no	—
310	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
311	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
312	C₄⋊C₄×C₂₃	—	2	2	no	—
313	C₄⋊C₄×C₂₃	—	2	2	no	—
314	C₄⋊C₄×C₂₃	—	2	2	no	—
315	C₄⋊C₄×C₂₃	—	2	2	no	—
316	C₄⋊C₄×C₂₃	—	2	2	no	—
317	C₄⋊C₄×C₂₃	—	2	2	no	—
318	C₄⋊C₄×C₂₃	—	2	2	no	—
319	C₄⋊C₄×C₂₃	—	2	2	no	—
320	C₄⋊C₄×C₂₃	—	2	1	no	—
321	C₄⋊C₄×C₂₃	—	2	1	no	—
322	C₄⋊C₄×C₂₃	—	2	1	no	—
323	C₄⋊C₄×C₂₃	—	2	1	no	—
324	C₄⋊C₄×C₂₃	—	2	1	no	—
325	C₄⋊C₄×C₂₃	—	2	1	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	C₂⁴	1	2	yes	—
333	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
334	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
335	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
336	C₂²⋊C₄×C₂₃	—	2	2	no	—
337	C₂²⋊C₄×C₂₃	—	2	2	no	—
338	C₂²⋊C₄×C₂₃	—	2	2	no	—
339	C₂²⋊C₄×C₂₃	—	2	2	no	—
340	C₂²⋊C₄×C₂₃	—	2	2	no	—
341	C₂²⋊C₄×C₂₃	—	2	2	no	—
342	C₂²⋊C₄×C₂₃	—	2	2	no	—
343	C₂²⋊C₄×C₂₃	—	2	2	no	—
344	C₂²⋊C₄×C₂₃	—	2	2	no	—
345	C₂²⋊C₄×C₂₃	—	2	2	no	—
346	C₂²⋊C₄×C₂₃	—	2	2	no	—
347	C₂²⋊C₄×C₂₃	—	2	2	no	—
348	C₂²⋊C₄×C₂₃	—	2	2	no	—
349	C₂²⋊C₄×C₂₃	—	2	2	no	—
350	C₂²⋊C₄×C₂₃	—	2	2	no	—
351	C₂²⋊C₄×C₂₃	—	2	2	no	—
352	C₂²⋊C₄×C₂₃	—	2	2	no	—
353	C₂²⋊C₄×C₂₃	—	2	2	no	—
354	C₂²⋊C₄×C₂₃	—	2	2	no	—
355	C₄²×C₂₃	—	2	2	no	—
356	C₄²×C₂₃	—	2	2	no	—
357	C₄²×C₂₃	—	2	2	no	—
358	C₄²×C₂₃	—	2	2	no	—
359	C₄²×C₂₃	—	2	2	no	—
360	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
361	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
362	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
363	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
364	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
365	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
366	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
367	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
368	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
369	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
370	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
371	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
372	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
373	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
374	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
375	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
376	#60942	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
377	C₂³×C₂₃	—	2	2	no	—
378	C₂³×C₂₃	—	2	2	no	—
379	C₂³×C₂₃	—	2	2	no	—
380	C₂³×C₂₃	—	2	2	no	—
381	C₂³×C₂₃	—	4	1	no	—
382	C₂³×C₂₃	—	4	2	no	—
383	C₂³×C₂₃	—	4	2	no	—
384	C₂³×C₂₃	—	4	2	no	—
385	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
386	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
387	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
388	Q₈×C₂₃	—	2	2	no	—
389	Q₈×C₂₃	—	2	4	no	—
390	Q₈×C₂₃	—	2	2	no	—
391	Q₈×C₂₃	—	4	2	no	—
392	Q₈×C₂₃	—	4	2	no	—
393	Q₈×C₂₃	—	4	2	no	—
394	D₄×C₂₃	—	2	2	no	—
395	D₄×C₂₃	—	2	4	no	—
396	D₄×C₂₃	—	2	2	no	—
397	D₄×C₂₃	—	4	2	no	—
398	D₄×C₂₃	—	4	2	no	—
399	D₄×C₂₃	—	4	4	no	—
400	D₄×C₂₃	—	4	4	no	—
401	D₄×C₂₃	—	4	4	no	—
402	D₄×C₂₃	—	4	4	no	—
403	D₄×C₂₃	—	4	4	no	—
404	D₄×C₂₃	—	4	2	no	—
405	C₂×C₄×C₂₃	—	2	2	no	—
406	C₂×C₄×C₂₃	—	2	2	no	—
407	C₂×C₄×C₂₃	—	2	2	no	—
408	C₂×C₄×C₂₃	—	2	2	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	—	2	2	no	—
417	C₂×C₄×C₂₃	—	2	2	no	—
418	C₂×C₄×C₂₃	—	2	2	no	—
419	C₂×C₄×C₂₃	—	2	2	no	—
420	C₂×C₄×C₂₃	—	2	2	no	—
421	C₂×C₄×C₂₃	—	4	1	no	—
422	C₂×C₄×C₂₃	—	4	1	no	—
423	C₂×C₄×C₂₃	—	4	1	no	—
424	C₂×C₄×C₂₃	—	4	1	no	—
425	C₂×C₄×C₂₃	—	4	1	no	—
426	C₂×C₄×C₂₃	—	4	1	no	—
427	C₂×C₄×C₂₃	—	4	1	no	—
428	C₂×C₄×C₂₃	—	4	4	no	—
429	C₂×C₄×C₂₃	—	4	4	no	—
430	C₂×C₄×C₂₃	—	4	2	no	—
431	C₂×C₄×C₂₃	—	4	2	no	—
432	C₂×C₄×C₂₃	—	4	2	no	—
433	C₂×C₄×C₂₃	—	4	4	no	—
434	C₂×C₄×C₂₃	—	4	4	no	—
435	C₂×C₄×C₂₃	—	4	4	no	—
436	C₂×C₄×C₂₃	#135	1	4	yes	—
437	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
440	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
441	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
442	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
443	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
449	C₈×C₂₃	—	2	4	no	—
450	C₈×C₂₃	—	2	4	no	—
451	#3444	C₂×C₂₃	1	1	yes	characteristic, complemented
452	C₂×#529	C₂×C₂₃	1	1	yes	characteristic, complemented
453	#3248	C₂×C₂₃	1	2	yes	complemented
454	#3247	C₂×C₂₃	1	2	yes	complemented
455	#3233	C₂×C₂₃	1	2	yes	complemented
456	#3232	C₂×C₂₃	1	2	yes	complemented
457	#3212	C₂×C₂₃	1	2	yes	complemented
458	#3211	C₂×C₂₃	1	2	yes	complemented
459	#3190	C₂×C₂₃	1	2	yes	complemented
460	#3188	C₂×C₂₃	1	2	yes	complemented
461	#3168	C₂×C₂₃	1	4	yes	complemented
462	#3104	C₂×C₂₃	1	1	yes	characteristic, complemented
463	#3103	C₂×C₂₃	1	1	yes	characteristic, complemented
464	#3102	C₂×C₂₃	1	4	yes	complemented
465	#3101	C₂×C₂₃	1	1	yes	characteristic, complemented
466	#3100	C₂×C₂₃	1	1	yes	characteristic, complemented
467	C₂×#431	C₂×C₂₃	1	1	yes	characteristic, complemented
468	C₂²×C₂₃	—	2	1	no	—
469	C₂²×C₂₃	—	2	1	no	—
470	C₂²×C₂₃	—	2	1	no	—
471	C₂²×C₂₃	—	2	1	no	—
472	C₂²×C₂₃	—	2	1	no	—
473	C₂²×C₂₃	—	2	1	no	—
474	C₂²×C₂₃	—	2	1	no	—
475	C₂²×C₂₃	—	4	4	no	—
476	C₂²×C₂₃	—	4	2	no	—
477	C₂²×C₂₃	—	4	2	no	—
478	C₂²×C₂₃	—	4	2	no	—
479	C₂²×C₂₃	—	4	2	no	—
480	C₂²×C₂₃	—	4	2	no	—
481	C₂²×C₂₃	—	4	2	no	—
482	C₂²×C₂₃	—	8	4	no	—
483	C₂²×C₂₃	C₂×#135	1	2	yes	—
484	C₂²×C₂₃	#575	1	2	yes	—
485	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
486	C₄×C₂₃	—	2	1	no	—
487	C₄×C₂₃	—	2	1	no	—
488	C₄×C₂₃	—	2	1	no	—
489	C₄×C₂₃	—	2	1	no	—
490	C₄×C₂₃	—	2	1	no	—
491	C₄×C₂₃	—	2	1	no	—
492	C₄×C₂₃	—	2	1	no	—
493	C₄×C₂₃	—	2	1	no	—
494	C₄×C₂₃	—	2	1	no	—
495	C₄×C₂₃	—	4	2	no	—
496	C₄×C₂₃	—	4	2	no	—
497	C₄×C₂₃	—	4	2	no	—
498	C₄×C₂₃	—	4	2	no	—
499	C₄×C₂₃	—	4	2	no	—
500	C₄×C₂₃	—	4	2	no	—
501	C₄×C₂₃	C₂×#135	1	2	yes	—
502	C₄×C₂₃	C₂×#135	1	2	yes	—
503	C₄×C₂₃	#585	1	2	yes	—
504	#533	C₂²×C₂₃	1	1	yes	characteristic
505	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
506	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
507	#532	C₂²×C₂₃	1	1	yes	characteristic
508	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
509	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
510	#529	—	2	1	no	—
511	#529	—	2	1	no	—
512	#529	—	2	1	no	—
513	#529	—	2	1	no	—
514	#529	—	2	1	no	—
515	#529	—	2	1	no	—
516	#529	—	2	1	no	—
517	#529	—	2	1	no	—
518	#529	C₂²×C₂₃	1	2	yes	—
519	#529	C₂²×C₂₃	1	2	yes	—
520	#529	C₂²×C₂₃	1	2	yes	—
521	#529	C₂²×C₂₃	1	2	yes	—
522	#529	C₂²×C₂₃	1	2	yes	—
523	#529	C₂²×C₂₃	1	2	yes	complemented
524	C₂×#126	—	2	1	no	—
525	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
526	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
527	#525	—	2	1	no	—
528	#525	—	2	1	no	—
529	#525	C₂²×C₂₃	1	2	yes	—
530	C₂×#123	—	2	1	no	—
531	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
532	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
533	C₄×#41	—	2	1	no	—
534	C₄×#41	—	2	1	no	—
535	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
536	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
537	C₂×C₄×D₄	—	2	1	no	—
538	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
539	C₂×#117	—	2	1	no	—
540	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
541	#499	C₂²×C₂₃	1	4	yes	complemented
542	#495	C₂²×C₂₃	1	4	yes	complemented
543	#488	C₂²×C₂₃	1	4	yes	complemented
544	#488	C₂²×C₂₃	1	4	yes	complemented
545	#485	C₂²×C₂₃	1	4	yes	complemented
546	#484	C₂²×C₂₃	1	2	yes	—
547	#483	C₂²×C₂₃	1	2	yes	—
548	#482	C₂²×C₂₃	1	4	yes	—
549	#481	C₂²×C₂₃	1	2	yes	—
550	#480	C₂²×C₂₃	1	2	yes	—
551	#479	C₂²×C₂₃	1	4	yes	complemented
552	#478	C₂²×C₂₃	1	4	yes	complemented
553	#477	C₂²×C₂₃	1	2	yes	complemented
554	#476	C₂²×C₂₃	1	2	yes	complemented
555	#475	C₂²×C₂₃	1	2	yes	complemented
556	#474	C₂²×C₂₃	1	2	yes	complemented
557	#467	C₂²×C₂₃	1	4	yes	complemented
558	#466	C₂²×C₂₃	1	4	yes	—
559	#465	C₂²×C₂₃	1	4	yes	—
560	#465	C₂²×C₂₃	1	4	yes	complemented
561	#464	C₂²×C₂₃	1	4	yes	complemented
562	#463	C₂²×C₂₃	1	4	yes	complemented
563	#462	C₂²×C₂₃	1	2	yes	complemented
564	#461	C₂²×C₂₃	1	2	yes	complemented
565	#460	C₂²×C₂₃	1	2	yes	complemented
566	#459	C₂²×C₂₃	1	2	yes	complemented
567	#452	C₂²×C₂₃	1	4	yes	complemented
568	#451	C₂²×C₂₃	1	2	yes	—
569	#450	C₂²×C₂₃	1	2	yes	—
570	#449	C₂²×C₂₃	1	4	yes	—
571	#448	C₂²×C₂₃	1	2	yes	—
572	#447	C₂²×C₂₃	1	2	yes	—
573	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	complemented
574	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
575	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	complemented
576	C₄×D₈	C₂²×C₂₃	1	4	yes	complemented
577	#431	C₂²×C₂₃	1	1	yes	characteristic
578	#431	C₂²×C₂₃	1	1	yes	characteristic
579	#431	C₂²×C₂₃	1	2	yes	—
580	#431	C₂²×C₂₃	1	2	yes	complemented
581	#431	C₂²×C₂₃	1	2	yes	complemented
582	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	complemented
583	C₂×C₂²⋊C₈	C₂²×C₂₃	1	2	yes	—
584	C₂×C₄×C₈	C₂²×C₂₃	1	2	yes	complemented
585	C₂×C₂₃	—	2	2	no	—
586	C₂×C₂₃	—	2	2	no	—
587	C₂×C₂₃	—	4	1	no	—
588	C₂×C₂₃	—	8	2	no	—
589	C₂×C₂₃	—	8	2	no	—
590	C₂×C₂₃	#3449	1	1	yes	characteristic
591	C₂×C₂₃	C₂²×#135	1	1	yes	characteristic
592	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
593	C₂×#41	—	2	1	no	—
594	C₂×#41	—	2	1	no	—
595	C₂×#41	C₂³×C₂₃	1	2	yes	—
596	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
597	C₂²×D₄	—	2	1	no	—
598	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
599	C₂³×C₄	—	2	1	no	—
600	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
601	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
602	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
603	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
604	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
605	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
606	C₂×D₈	C₂³×C₂₃	1	4	yes	—
607	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
608	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
609	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
610	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
611	#127	C₂³×C₂₃	1	1	yes	characteristic
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	#126	—	2	2	no	—
618	#125	—	2	1	no	—
619	#125	—	2	1	no	—
620	#125	—	2	1	no	—
621	#125	—	2	1	no	—
622	#125	C₂³×C₂₃	1	2	yes	—
623	#125	C₂³×C₂₃	1	2	yes	—
624	#125	C₂³×C₂₃	1	2	yes	—
625	#124	—	2	1	no	—
626	#124	—	2	1	no	—
627	#124	—	2	1	no	—
628	#124	—	2	1	no	—
629	#124	C₂³×C₂₃	1	2	yes	—
630	#124	C₂³×C₂₃	1	2	yes	—
631	#124	C₂³×C₂₃	1	2	yes	—
632	#123	—	2	2	no	—
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	C₂²⋊Q₈	—	2	1	no	—
640	C₂²⋊Q₈	—	2	1	no	—
641	C₂²⋊Q₈	—	2	1	no	—
642	C₂²⋊Q₈	—	2	1	no	—
643	C₂²⋊Q₈	—	2	1	no	—
644	C₂²⋊Q₈	—	2	1	no	—
645	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
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	#121	—	2	1	no	—
650	#121	—	2	1	no	—
651	#121	—	2	1	no	—
652	#121	—	2	1	no	—
653	#121	—	2	1	no	—
654	#121	—	2	1	no	—
655	#121	C₂³×C₂₃	1	2	yes	—
656	#121	C₂³×C₂₃	1	2	yes	—
657	#121	C₂³×C₂₃	1	2	yes	—
658	#121	C₂³×C₂₃	1	2	yes	—
659	#120	—	2	2	no	—
660	C₄×Q₈	—	2	1	no	—
661	C₄×Q₈	—	2	1	no	—
662	C₄×Q₈	—	2	1	no	—
663	C₄×Q₈	—	2	1	no	—
664	C₄×Q₈	—	2	1	no	—
665	C₄×Q₈	—	2	1	no	—
666	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
667	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
668	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
669	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
670	C₄×D₄	—	2	2	no	—
671	C₄×D₄	—	2	2	no	—
672	C₄×D₄	—	2	2	no	—
673	C₄×D₄	—	2	2	no	—
674	C₄×D₄	—	2	2	no	—
675	C₄×D₄	—	2	2	no	—
676	C₄×D₄	—	2	2	no	—
677	C₄×D₄	—	2	2	no	—
678	C₄×D₄	—	2	2	no	—
679	C₄×D₄	—	2	2	no	—
680	C₄×D₄	—	2	1	no	—
681	C₄×D₄	—	2	1	no	—
682	C₄×D₄	—	2	1	no	—
683	C₄×D₄	—	2	1	no	—
684	C₄×D₄	—	2	1	no	—
685	C₄×D₄	—	2	1	no	—
686	C₄×D₄	C₂³×C₂₃	1	2	yes	—
687	C₄×D₄	C₂³×C₂₃	1	2	yes	—
688	C₄×D₄	C₂³×C₂₃	1	2	yes	—
689	C₄×D₄	C₂³×C₂₃	1	2	yes	—
690	#117	—	2	1	no	—
691	#117	—	2	1	no	—
692	#117	—	2	2	no	—
693	#117	—	2	2	no	—
694	#117	—	2	2	no	—
695	#117	—	2	2	no	—
696	#117	—	2	2	no	—
697	#117	—	2	2	no	—
698	#117	—	2	2	no	—
699	#117	C₂³×C₂₃	1	2	yes	—
700	C₂×C₄⋊C₄	—	2	1	no	—
701	C₂×C₄⋊C₄	—	2	1	no	—
702	C₂×C₄⋊C₄	—	2	1	no	—
703	C₂×C₄⋊C₄	—	2	1	no	—
704	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
705	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
706	C₂×C₂²⋊C₄	—	2	1	no	—
707	C₂×C₂²⋊C₄	—	2	1	no	—
708	C₂×C₂²⋊C₄	—	2	1	no	—
709	C₂×C₂²⋊C₄	—	2	1	no	—
710	C₂×C₂²⋊C₄	—	2	1	no	—
711	C₂×C₄²	—	2	1	no	—
712	C₂×C₄²	—	2	2	no	—
713	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
714	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
715	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
716	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
717	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
718	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
719	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
720	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
721	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
722	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
723	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
724	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
725	#107	C₂³×C₂₃	1	4	yes	—
726	#107	C₂³×C₂₃	1	4	yes	—
727	#106	C₂³×C₂₃	1	4	yes	—
728	#106	C₂³×C₂₃	1	4	yes	—
729	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
730	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
731	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
732	#103	C₂³×C₂₃	1	4	yes	—
733	#103	C₂³×C₂₃	1	4	yes	—
734	#103	C₂³×C₂₃	1	4	yes	—
735	#103	C₂³×C₂₃	1	4	yes	—
736	#102	C₂³×C₂₃	1	4	yes	—
737	#102	C₂³×C₂₃	1	4	yes	—
738	#102	C₂³×C₂₃	1	4	yes	—
739	#102	C₂³×C₂₃	1	4	yes	—
740	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
741	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
742	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
743	C₄×C₈	C₂³×C₂₃	1	2	yes	—
744	C₄×C₈	C₂³×C₂₃	1	2	yes	—
745	C₄×C₈	C₂³×C₂₃	1	4	yes	—
746	C₂₃	#60942	1	1	yes	characteristic, direct product factor, Sylow
747	C₂⁴	—	2	1	no	—
748	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
749	#41	—	4	4	no	—
750	#41	—	4	4	no	—
751	#41	—	4	4	no	—
752	C₂×Q₈	—	2	1	no	—
753	C₂×Q₈	—	2	1	no	—
754	C₂×Q₈	—	2	1	no	—
755	C₂×Q₈	—	4	2	no	—
756	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
757	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
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	—	2	1	no	—
764	C₂×D₄	—	2	1	no	—
765	C₂×D₄	—	2	1	no	—
766	C₂×D₄	—	4	2	no	—
767	C₂×D₄	—	4	4	no	—
768	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
769	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
770	C₂²×C₄	—	2	4	no	—
771	C₂²×C₄	—	2	1	no	—
772	C₂²×C₄	—	2	1	no	—
773	C₂²×C₄	—	2	1	no	—
774	C₂²×C₄	—	2	2	no	—
775	C₂²×C₄	—	2	2	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	2	no	—
779	C₂²×C₄	—	4	2	no	—
780	C₂²×C₄	—	4	2	no	—
781	C₂²×C₄	—	4	4	no	—
782	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
783	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
784	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
785	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
786	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
787	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
788	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
789	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
790	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
791	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
792	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
793	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
794	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
795	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
796	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
797	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
798	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
799	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
800	Q₁₆	—	4	4	no	—
801	SD₁₆	—	4	4	no	—
802	SD₁₆	—	4	4	no	—
803	D₈	—	4	4	no	—
804	C₂×C₈	—	4	4	no	—
805	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
806	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
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	1	no	—
816	C₄⋊C₄	—	2	1	no	—
817	C₄⋊C₄	—	2	1	no	—
818	C₄⋊C₄	—	2	1	no	—
819	C₄⋊C₄	—	2	1	no	—
820	C₄⋊C₄	—	2	1	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	—	2	2	no	—
823	C₄⋊C₄	—	2	2	no	—
824	C₄⋊C₄	—	2	2	no	—
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
828	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
829	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
830	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
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	—	2	2	no	—
847	C₂²⋊C₄	—	2	2	no	—
848	C₂²⋊C₄	—	2	2	no	—
849	C₂²⋊C₄	—	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	1	yes	characteristic
857	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
858	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
859	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
860	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
861	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
862	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
863	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
864	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
865	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
866	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
867	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
868	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
869	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
870	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
871	C₂³	—	2	2	no	—
872	C₂³	—	2	2	no	—
873	C₂³	—	2	2	no	—
874	C₂³	—	2	2	no	—
875	C₂³	—	4	1	no	—
876	C₂³	—	4	2	no	—
877	C₂³	—	4	2	no	—
878	C₂³	—	4	2	no	—
879	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
880	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
881	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
882	Q₈	—	2	2	no	—
883	Q₈	—	2	4	no	—
884	Q₈	—	2	2	no	—
885	Q₈	—	4	2	no	—
886	Q₈	—	4	2	no	—
887	Q₈	—	4	2	no	—
888	D₄	—	2	2	no	—
889	D₄	—	2	4	no	—
890	D₄	—	2	2	no	—
891	D₄	—	4	2	no	—
892	D₄	—	4	2	no	—
893	D₄	—	4	4	no	—
894	D₄	—	4	4	no	—
895	D₄	—	4	4	no	—
896	D₄	—	4	4	no	—
897	D₄	—	4	4	no	—
898	D₄	—	4	2	no	—
899	C₂×C₄	—	2	2	no	—
900	C₂×C₄	—	2	2	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	2	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	4	1	no	—
916	C₂×C₄	—	4	1	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	1	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	4	1	no	—
922	C₂×C₄	—	4	4	no	—
923	C₂×C₄	—	4	4	no	—
924	C₂×C₄	—	4	2	no	—
925	C₂×C₄	—	4	2	no	—
926	C₂×C₄	—	4	2	no	—
927	C₂×C₄	—	4	4	no	—
928	C₂×C₄	—	4	4	no	—
929	C₂×C₄	—	4	4	no	—
930	C₂×C₄	C₂₃×#135	1	4	yes	—
931	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
932	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
933	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
934	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
935	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
936	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
937	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
938	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
939	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
940	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
941	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
942	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
943	C₈	—	2	4	no	—
944	C₈	—	2	4	no	—
945	C₂²	—	2	1	no	—
946	C₂²	—	2	1	no	—
947	C₂²	—	2	1	no	—
948	C₂²	—	2	1	no	—
949	C₂²	—	2	1	no	—
950	C₂²	—	2	1	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	4	4	no	—
953	C₂²	—	4	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	8	4	no	—
960	C₂²	C₂×C₂₃×#135	1	2	yes	—
961	C₂²	C₂₃×#575	1	2	yes	—
962	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
963	C₄	—	2	1	no	—
964	C₄	—	2	1	no	—
965	C₄	—	2	1	no	—
966	C₄	—	2	1	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	1	no	—
969	C₄	—	2	1	no	—
970	C₄	—	2	1	no	—
971	C₄	—	2	1	no	—
972	C₄	—	4	2	no	—
973	C₄	—	4	2	no	—
974	C₄	—	4	2	no	—
975	C₄	—	4	2	no	—
976	C₄	—	4	2	no	—
977	C₄	—	4	2	no	—
978	C₄	C₂×C₂₃×#135	1	2	yes	—
979	C₄	C₂×C₂₃×#135	1	2	yes	—
980	C₄	C₂₃×#585	1	2	yes	—
981	C₂	—	2	2	no	—
982	C₂	—	2	2	no	—
983	C₂	—	4	1	no	—
984	C₂	—	8	2	no	—
985	C₂	—	8	2	no	—
986	C₂	C₂₃×#3449	1	1	yes	characteristic
987	C₂	C₂²×C₂₃×#135	1	1	yes	characteristic
988	C₂	C₂×C₂₃×#575	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 ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3444	C₂	semidirect
2. C₂×C₂₃×#529	C₂	semidirect
3. C₂₃×#3248	C₂	semidirect
4. C₂₃×#3247	C₂	semidirect
5. C₂₃×#3233	C₂	semidirect
6. C₂₃×#3232	C₂	semidirect
7. C₂₃×#3212	C₂	semidirect
8. C₂₃×#3211	C₂	semidirect
9. C₂₃×#3190	C₂	semidirect
10. C₂₃×#3188	C₂	semidirect
11. C₂₃×#3168	C₂	semidirect
12. C₂₃×#3104	C₂	semidirect
13. C₂₃×#3103	C₂	semidirect
14. C₂₃×#3102	C₂	semidirect
15. C₂₃×#3101	C₂	semidirect
16. C₂₃×#3100	C₂	semidirect
17. C₂×C₂₃×#431	C₂	semidirect
19. C₂₃×#533	C₂²	semidirect
20. C₂₃×#533	C₂²	semidirect
22. C₂₃×#532	C₂²	semidirect
23. C₂₃×#532	C₂²	semidirect
37. C₂₃×#529	C₂²	semidirect
49. C₄×#41×C₂₃	C₂²	semidirect
55. C₂₃×#499	C₂²	semidirect
56. C₂₃×#495	C₂²	semidirect
57. C₂₃×#488	C₂²	semidirect
58. C₂₃×#488	C₂²	semidirect
59. C₂₃×#485	C₂²	semidirect
65. C₂₃×#479	C₂²	semidirect
66. C₂₃×#478	C₂²	semidirect
67. C₂₃×#477	C₂²	semidirect
68. C₂₃×#476	C₂²	semidirect
69. C₂₃×#475	C₂²	semidirect
70. C₂₃×#474	C₂²	semidirect
71. C₂₃×#467	C₂²	semidirect
74. C₂₃×#465	C₂²	semidirect
75. C₂₃×#464	C₂²	semidirect
76. C₂₃×#463	C₂²	semidirect
77. C₂₃×#462	C₂²	semidirect
78. C₂₃×#461	C₂²	semidirect
79. C₂₃×#460	C₂²	semidirect
80. C₂₃×#459	C₂²	semidirect
81. C₂₃×#452	C₂²	semidirect
87. C₄×Q₁₆×C₂₃	C₂²	semidirect
88. C₄×SD₁₆×C₂₃	C₂²	semidirect
89. C₄×SD₁₆×C₂₃	C₂²	semidirect
90. C₄×D₈×C₂₃	C₂²	semidirect
94. C₂₃×#431	C₂²	semidirect
95. C₂₃×#431	C₂²	semidirect
96. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
98. C₂×C₄×C₈×C₂₃	C₂²	semidirect
376. #60942	C₂₃	direct (N × H)
451. #3444	C₂×C₂₃	semidirect
452. C₂×#529	C₂×C₂₃	semidirect
453. #3248	C₂×C₂₃	semidirect
454. #3247	C₂×C₂₃	semidirect
455. #3233	C₂×C₂₃	semidirect
456. #3232	C₂×C₂₃	semidirect
457. #3212	C₂×C₂₃	semidirect
458. #3211	C₂×C₂₃	semidirect
459. #3190	C₂×C₂₃	semidirect
460. #3188	C₂×C₂₃	semidirect
461. #3168	C₂×C₂₃	semidirect
462. #3104	C₂×C₂₃	semidirect
463. #3103	C₂×C₂₃	semidirect
464. #3102	C₂×C₂₃	semidirect
465. #3101	C₂×C₂₃	semidirect
466. #3100	C₂×C₂₃	semidirect
467. C₂×#431	C₂×C₂₃	semidirect
505. #533	C₂²×C₂₃	semidirect
506. #533	C₂²×C₂₃	semidirect
508. #532	C₂²×C₂₃	semidirect
509. #532	C₂²×C₂₃	semidirect
523. #529	C₂²×C₂₃	semidirect
535. C₄×#41	C₂²×C₂₃	semidirect
541. #499	C₂²×C₂₃	semidirect
542. #495	C₂²×C₂₃	semidirect
543. #488	C₂²×C₂₃	semidirect
544. #488	C₂²×C₂₃	semidirect
545. #485	C₂²×C₂₃	semidirect
551. #479	C₂²×C₂₃	semidirect
552. #478	C₂²×C₂₃	semidirect
553. #477	C₂²×C₂₃	semidirect
554. #476	C₂²×C₂₃	semidirect
555. #475	C₂²×C₂₃	semidirect
556. #474	C₂²×C₂₃	semidirect
557. #467	C₂²×C₂₃	semidirect
560. #465	C₂²×C₂₃	semidirect
561. #464	C₂²×C₂₃	semidirect
562. #463	C₂²×C₂₃	semidirect
563. #462	C₂²×C₂₃	semidirect
564. #461	C₂²×C₂₃	semidirect
565. #460	C₂²×C₂₃	semidirect
566. #459	C₂²×C₂₃	semidirect
567. #452	C₂²×C₂₃	semidirect
573. C₄×Q₁₆	C₂²×C₂₃	semidirect
574. C₄×SD₁₆	C₂²×C₂₃	semidirect
575. C₄×SD₁₆	C₂²×C₂₃	semidirect
576. C₄×D₈	C₂²×C₂₃	semidirect
580. #431	C₂²×C₂₃	semidirect
581. #431	C₂²×C₂₃	semidirect
582. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
584. C₂×C₄×C₈	C₂²×C₂₃	semidirect
746. C₂₃	#60942	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×#3444	2
C₂×C₂₃×#529	2
C₂₃×#3248	2
C₂₃×#3247	2
C₂₃×#3233	2
C₂₃×#3232	2
C₂₃×#3212	2
C₂₃×#3211	2
C₂₃×#3190	2
C₂₃×#3188	2
C₂₃×#3168	2
C₂₃×#3104	2
C₂₃×#3103	2
C₂₃×#3102	2
C₂₃×#3101	2
C₂₃×#3100	2
C₂×C₂₃×#431	2
#60942	23

Subgroups — C23×#60942 #19208568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60942 #19208568