Subgroups — C₂₃×#61369 #19208995

Order 5888.

1750 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#41×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#557	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3390	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3388	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3387	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3386	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3383	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3381	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3166	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3080	C₂	1	2	yes	maximal
12	C₂₃×#3079	C₂	1	1	yes	maximal, characteristic
13	C₂₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3078	C₂	1	2	yes	maximal, complemented
15	Q₈×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₂₃×#137	C₂	1	1	yes	maximal, characteristic
17	C₄×C₂₃×#137	C₂	1	2	yes	maximal
18	C₂×C₂₃×#137	C₂²	1	1	yes	characteristic
19	Q₈²×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#557	—	2	1	no	—
21	C₂₃×#557	—	2	2	no	—
22	C₂₃×#557	—	2	1	no	—
23	C₂₃×#557	C₂²	1	2	yes	—
24	C₂₃×#557	C₂²	1	2	yes	—
25	C₂₃×#557	C₂²	1	4	yes	—
26	C₂₃×#557	C₂²	1	1	yes	characteristic
27	C₂₃×#557	C₂²	1	2	yes	—
28	C₂₃×#554	—	2	1	no	—
29	C₂₃×#554	—	2	2	no	—
30	C₂₃×#554	C₂²	1	1	yes	characteristic
31	C₂₃×#554	C₂²	1	2	yes	—
32	D₄×Q₈×C₂₃	—	2	1	no	—
33	D₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
34	C₂₃×#533	—	2	2	no	—
35	C₂₃×#533	—	2	1	no	—
36	C₂₃×#533	C₂²	1	1	yes	characteristic
37	C₂₃×#533	C₂²	1	2	yes	—
38	C₂×C₂₃×C₄⋊Q₈	—	2	1	no	—
39	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#125	—	2	2	no	—
41	C₂×C₂₃×#125	C₂²	1	2	yes	—
42	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic
43	C₄×#41×C₂₃	C₂²	1	2	yes	—
44	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
45	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
46	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
47	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
49	C₂₃×#501	C₂²	1	4	yes	—
50	C₂₃×#501	C₂²	1	4	yes	—
51	C₂₃×#501	C₂²	1	4	yes	—
52	C₂₃×#500	C₂²	1	2	yes	—
53	C₂₃×#499	C₂²	1	4	yes	—
54	C₂₃×#499	C₂²	1	4	yes	—
55	C₂₃×#498	C₂²	1	2	yes	—
56	C₂₃×#479	C₂²	1	4	yes	—
57	C₂₃×#479	C₂²	1	4	yes	—
58	C₂₃×#479	C₂²	1	4	yes	—
59	C₂₃×#479	C₂²	1	4	yes	—
60	C₂₃×#479	C₂²	1	4	yes	—
61	C₂₃×#478	C₂²	1	4	yes	—
62	C₂₃×#478	C₂²	1	4	yes	—
63	C₂₃×#477	C₂²	1	2	yes	—
64	C₂₃×#477	C₂²	1	4	yes	—
65	C₂₃×#477	C₂²	1	2	yes	—
66	C₂₃×#476	C₂²	1	2	yes	—
67	C₂₃×#475	C₂²	1	2	yes	—
68	C₂₃×#475	C₂²	1	4	yes	—
69	C₂₃×#475	C₂²	1	2	yes	—
70	C₂₃×#474	C₂²	1	2	yes	—
71	C₂₃×#446	C₂²	1	2	yes	—
72	C₂₃×#446	C₂²	1	4	yes	—
73	C₈×Q₈×C₂₃	C₂²	1	2	yes	—
74	C₂₃×#441	C₂²	1	4	yes	—
75	C₂₃×#441	C₂²	1	2	yes	—
76	C₂₃×#440	C₂²	1	4	yes	—
77	C₂₃×#440	C₂²	1	2	yes	—
78	C₄×Q₁₆×C₂₃	C₂²	1	2	yes	—
79	C₄×Q₁₆×C₂₃	C₂²	1	4	yes	—
80	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	—
81	C₄×SD₁₆×C₂₃	C₂²	1	4	yes	—
82	C₂₃×#428	C₂²	1	2	yes	—
83	C₂₃×#428	C₂²	1	2	yes	—
84	C₂₃×#428	C₂²	1	1	yes	characteristic
85	C₂₃×#428	C₂²	1	2	yes	—
86	C₂₃×#428	C₂²	1	2	yes	—
87	C₂₃×#423	C₂²	1	1	yes	characteristic
88	C₂₃×#423	C₂²	1	2	yes	—
89	C₂₃×#419	C₂²	1	2	yes	—
90	C₂₃×#419	C₂²	1	1	yes	characteristic
91	C₂₃×#417	C₂²	1	2	yes	—
92	C₂₃×#417	C₂²	1	1	yes	characteristic
93	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
94	C₄×M₁₆×C₂₃	C₂²	1	2	yes	—
95	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²×Q₈×C₂₃	—	2	1	no	—
97	C₂²×Q₈×C₂₃	—	2	1	no	—
98	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
99	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
100	C₂₃×#137	Q₈	1	8	yes	complemented
101	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
102	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
103	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
104	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
105	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
106	C₂₃×C₄⋊Q₈	—	2	1	no	—
107	C₂₃×C₄⋊Q₈	—	2	2	no	—
108	C₂₃×C₄⋊Q₈	—	2	2	no	—
109	C₂₃×C₄⋊Q₈	—	2	2	no	—
110	C₂₃×C₄⋊Q₈	—	2	4	no	—
111	C₂₃×C₄⋊Q₈	—	2	1	no	—
112	C₂₃×C₄⋊Q₈	—	2	2	no	—
113	C₂₃×C₄⋊Q₈	—	2	1	no	—
114	C₂₃×C₄⋊Q₈	—	2	1	no	—
115	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
119	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
120	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
121	C₂₃×#125	—	2	2	no	—
122	C₂₃×#125	—	2	2	no	—
123	C₂₃×#125	—	2	2	no	—
124	C₂₃×#125	—	2	4	no	—
125	C₂₃×#125	—	2	4	no	—
126	C₂₃×#125	—	2	4	no	—
127	C₂₃×#125	—	2	4	no	—
128	C₂₃×#125	—	2	2	no	—
129	C₂₃×#125	—	2	2	no	—
130	C₂₃×#125	C₂³	1	2	yes	—
131	C₂₃×#125	C₂³	1	2	yes	—
132	C₂₃×#125	C₂³	1	2	yes	—
133	C₂₃×#125	C₂³	1	4	yes	—
134	C₂₃×#125	C₂³	1	4	yes	—
135	C₂₃×C₂²⋊Q₈	—	2	1	no	—
136	C₂₃×C₂²⋊Q₈	—	2	2	no	—
137	C₂₃×C₂²⋊Q₈	—	2	1	no	—
138	C₂₃×C₂²⋊Q₈	—	2	2	no	—
139	C₂₃×C₂²⋊Q₈	—	2	2	no	—
140	C₂₃×C₂²⋊Q₈	—	2	1	no	—
141	C₂₃×C₂²⋊Q₈	—	2	1	no	—
142	C₂₃×C₂²⋊Q₈	—	2	2	no	—
143	C₂₃×C₂²⋊Q₈	—	2	2	no	—
144	C₂₃×C₂²⋊Q₈	—	2	2	no	—
145	C₂₃×C₂²⋊Q₈	—	2	2	no	—
146	C₄×Q₈×C₂₃	—	2	1	no	—
147	C₄×Q₈×C₂₃	—	2	1	no	—
148	C₄×Q₈×C₂₃	—	2	2	no	—
149	C₄×Q₈×C₂₃	—	2	2	no	—
150	C₄×Q₈×C₂₃	—	2	4	no	—
151	C₄×Q₈×C₂₃	—	2	2	no	—
152	C₄×Q₈×C₂₃	—	2	2	no	—
153	C₄×Q₈×C₂₃	—	2	2	no	—
154	C₄×Q₈×C₂₃	—	2	1	no	—
155	C₄×Q₈×C₂₃	—	2	1	no	—
156	C₄×Q₈×C₂₃	—	2	2	no	—
157	C₄×Q₈×C₂₃	—	2	1	no	—
158	C₄×Q₈×C₂₃	—	2	2	no	—
159	C₄×Q₈×C₂₃	—	2	1	no	—
160	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
161	C₄×Q₈×C₂₃	D₄	1	2	yes	—
162	C₄×Q₈×C₂₃	D₄	1	1	yes	characteristic
163	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
164	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
165	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
166	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
167	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
168	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
169	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
170	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
171	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
172	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
173	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
174	C₄×D₄×C₂₃	—	2	1	no	—
175	C₄×D₄×C₂₃	—	2	2	no	—
176	C₄×D₄×C₂₃	—	2	2	no	—
177	C₄×D₄×C₂₃	—	2	1	no	—
178	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
179	C₄×D₄×C₂₃	C₂³	1	2	yes	—
180	C₄×D₄×C₂₃	C₂³	1	2	yes	—
181	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
182	C₂₃×#117	—	2	2	no	—
183	C₂₃×#117	—	2	1	no	—
184	C₂₃×#117	C₂³	1	2	yes	—
185	C₂₃×#117	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
187	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
188	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
189	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
190	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
191	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
192	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
193	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
194	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
195	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
196	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
197	C₂×C₄²×C₂₃	—	2	2	no	—
198	C₂×C₄²×C₂₃	—	2	1	no	—
199	C₂×C₄²×C₂₃	—	2	2	no	—
200	C₂×C₄²×C₂₃	—	2	1	no	—
201	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
202	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
203	C₂₃×#107	C₂³	1	2	yes	—
204	C₂₃×#107	C₂³	1	4	yes	—
205	C₂₃×#107	C₂³	1	4	yes	—
206	C₂₃×#107	C₂³	1	4	yes	—
207	C₂₃×#107	C₂³	1	4	yes	—
208	C₂₃×#106	C₂³	1	4	yes	—
209	C₂₃×#106	C₂³	1	2	yes	—
210	C₂₃×#106	C₂³	1	4	yes	—
211	C₂₃×#106	C₂³	1	4	yes	—
212	C₂₃×#106	C₂³	1	4	yes	—
213	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
214	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
215	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
216	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
217	C₂₃×#103	C₂³	1	4	yes	—
218	C₂₃×#103	C₂³	1	2	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×#102	C₂³	1	4	yes	—
224	C₂₃×#102	C₂³	1	2	yes	—
225	C₂₃×#97	C₂³	1	2	yes	—
226	C₂₃×#97	C₂³	1	4	yes	—
227	C₄×C₈×C₂₃	C₂³	1	2	yes	—
228	C₄×C₈×C₂₃	C₂³	1	4	yes	—
229	#41×C₂₃	—	2	2	no	—
230	#41×C₂₃	C₂×Q₈	1	4	yes	—
231	C₂×Q₈×C₂₃	—	2	1	no	—
232	C₂×Q₈×C₂₃	—	2	2	no	—
233	C₂×Q₈×C₂₃	—	2	1	no	—
234	C₂×Q₈×C₂₃	—	2	2	no	—
235	C₂×Q₈×C₂₃	—	2	2	no	—
236	C₂×Q₈×C₂₃	—	2	2	no	—
237	C₂×Q₈×C₂₃	—	2	1	no	—
238	C₂×Q₈×C₂₃	—	2	2	no	—
239	C₂×Q₈×C₂₃	—	4	2	no	—
240	C₂×Q₈×C₂₃	—	4	4	no	—
241	C₂×Q₈×C₂₃	—	4	4	no	—
242	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
243	C₂×Q₈×C₂₃	C₂×D₄	1	1	yes	characteristic
244	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
245	C₂×Q₈×C₂₃	C₂×Q₈	1	4	yes	complemented
246	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
247	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
248	C₂×D₄×C₂₃	—	2	1	no	—
249	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
250	C₂²×C₄×C₂₃	—	2	1	no	—
251	C₂²×C₄×C₂₃	—	2	1	no	—
252	C₂²×C₄×C₂₃	—	2	1	no	—
253	C₂²×C₄×C₂₃	—	2	2	no	—
254	C₂²×C₄×C₂₃	—	2	2	no	—
255	C₂²×C₄×C₂₃	—	2	1	no	—
256	C₂²×C₄×C₂₃	—	2	2	no	—
257	C₂²×C₄×C₂₃	—	2	1	no	—
258	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
260	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
262	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
263	Q₁₆×C₂₃	C₂×Q₈	1	8	yes	complemented
264	SD₁₆×C₂₃	C₂×Q₈	1	8	yes	complemented
265	M₁₆×C₂₃	—	2	2	no	—
266	M₁₆×C₂₃	—	2	4	no	—
267	M₁₆×C₂₃	C₂×Q₈	1	4	yes	complemented
268	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
269	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
270	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
271	C₄⋊C₄×C₂₃	—	2	2	no	—
272	C₄⋊C₄×C₂₃	—	2	2	no	—
273	C₄⋊C₄×C₂₃	—	2	2	no	—
274	C₄⋊C₄×C₂₃	—	2	2	no	—
275	C₄⋊C₄×C₂₃	—	2	1	no	—
276	C₄⋊C₄×C₂₃	—	2	4	no	—
277	C₄⋊C₄×C₂₃	—	2	4	no	—
278	C₄⋊C₄×C₂₃	—	2	2	no	—
279	C₄⋊C₄×C₂₃	—	2	2	no	—
280	C₄⋊C₄×C₂₃	—	2	4	no	—
281	C₄⋊C₄×C₂₃	—	2	4	no	—
282	C₄⋊C₄×C₂₃	—	2	2	no	—
283	C₄⋊C₄×C₂₃	—	2	2	no	—
284	C₄⋊C₄×C₂₃	—	2	4	no	—
285	C₄⋊C₄×C₂₃	—	2	4	no	—
286	C₄⋊C₄×C₂₃	—	2	1	no	—
287	C₄⋊C₄×C₂₃	—	2	2	no	—
288	C₄⋊C₄×C₂₃	—	2	2	no	—
289	C₄⋊C₄×C₂₃	—	2	1	no	—
290	C₄⋊C₄×C₂₃	—	2	2	no	—
291	C₄⋊C₄×C₂₃	—	2	1	no	—
292	C₄⋊C₄×C₂₃	—	2	2	no	—
293	C₄⋊C₄×C₂₃	—	2	1	no	—
294	C₄⋊C₄×C₂₃	—	2	2	no	—
295	C₄⋊C₄×C₂₃	—	2	2	no	—
296	C₄⋊C₄×C₂₃	—	2	2	no	—
297	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
298	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
299	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
300	C₄⋊C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
301	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
303	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
304	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
305	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
306	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
307	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
308	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
309	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
310	C₂²⋊C₄×C₂₃	—	2	2	no	—
311	C₂²⋊C₄×C₂₃	—	2	1	no	—
312	C₂²⋊C₄×C₂₃	—	2	2	no	—
313	C₂²⋊C₄×C₂₃	—	2	1	no	—
314	C₂²⋊C₄×C₂₃	—	2	2	no	—
315	C₂²⋊C₄×C₂₃	—	2	1	no	—
316	C₄²×C₂₃	—	2	2	no	—
317	C₄²×C₂₃	—	2	1	no	—
318	C₄²×C₂₃	—	2	2	no	—
319	C₄²×C₂₃	—	2	1	no	—
320	C₄²×C₂₃	—	2	2	no	—
321	C₄²×C₂₃	—	2	1	no	—
322	C₄²×C₂₃	—	2	4	no	—
323	C₄²×C₂₃	—	2	4	no	—
324	C₄²×C₂₃	—	2	2	no	—
325	C₄²×C₂₃	—	2	2	no	—
326	C₄²×C₂₃	C₂×D₄	1	2	yes	—
327	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₂₃	C₂×D₄	1	2	yes	—
329	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₂₃	C₂⁴	1	2	yes	—
331	C₄²×C₂₃	C₂⁴	1	2	yes	—
332	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
333	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
334	#61369	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
335	C₂³×C₂₃	—	2	1	no	—
336	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
337	Q₈×C₂₃	—	2	4	no	—
338	Q₈×C₂₃	—	2	2	no	—
339	Q₈×C₂₃	—	2	2	no	—
340	Q₈×C₂₃	—	2	2	no	—
341	Q₈×C₂₃	—	2	1	no	—
342	Q₈×C₂₃	—	4	2	no	—
343	Q₈×C₂₃	—	4	4	no	—
344	Q₈×C₂₃	—	4	4	no	—
345	Q₈×C₂₃	—	4	2	no	—
346	Q₈×C₂₃	—	4	4	no	—
347	Q₈×C₂₃	—	8	2	no	—
348	Q₈×C₂₃	—	8	1	no	—
349	Q₈×C₂₃	C₂²×Q₈	1	4	yes	—
350	Q₈×C₂₃	C₂²×Q₈	1	2	yes	—
351	D₄×C₂₃	—	2	4	no	—
352	D₄×C₂₃	—	2	1	no	—
353	D₄×C₂₃	C₂²×Q₈	1	2	yes	—
354	C₂×C₄×C₂₃	—	2	4	no	—
355	C₂×C₄×C₂₃	—	2	1	no	—
356	C₂×C₄×C₂₃	—	2	2	no	—
357	C₂×C₄×C₂₃	—	2	4	no	—
358	C₂×C₄×C₂₃	—	2	2	no	—
359	C₂×C₄×C₂₃	—	2	2	no	—
360	C₂×C₄×C₂₃	—	2	1	no	—
361	C₂×C₄×C₂₃	—	2	2	no	—
362	C₂×C₄×C₂₃	—	2	1	no	—
363	C₂×C₄×C₂₃	—	2	2	no	—
364	C₂×C₄×C₂₃	—	2	4	no	—
365	C₂×C₄×C₂₃	—	4	2	no	—
366	C₂×C₄×C₂₃	—	4	1	no	—
367	C₂×C₄×C₂₃	—	4	2	no	—
368	C₂×C₄×C₂₃	—	4	4	no	—
369	C₂×C₄×C₂₃	—	4	2	no	—
370	C₂×C₄×C₂₃	—	4	4	no	—
371	C₂×C₄×C₂₃	—	4	2	no	—
372	C₂×C₄×C₂₃	—	8	2	no	—
373	C₂×C₄×C₂₃	—	8	1	no	—
374	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
375	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
378	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
380	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
384	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
385	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
386	C₈×C₂₃	—	2	4	no	—
387	C₈×C₂₃	—	2	2	no	—
388	C₈×C₂₃	C₂²×Q₈	1	4	yes	—
389	Q₈×#41	C₂×C₂₃	1	1	yes	characteristic
390	C₂×#557	C₂×C₂₃	1	1	yes	characteristic, complemented
391	#3390	C₂×C₂₃	1	4	yes	complemented
392	#3388	C₂×C₂₃	1	4	yes	complemented
393	#3387	C₂×C₂₃	1	2	yes	complemented
394	#3386	C₂×C₂₃	1	2	yes	complemented
395	#3383	C₂×C₂₃	1	2	yes	complemented
396	#3381	C₂×C₂₃	1	2	yes	complemented
397	#3166	C₂×C₂₃	1	2	yes	complemented
398	#3165	C₂×C₂₃	1	1	yes	characteristic, complemented
399	#3080	C₂×C₂₃	1	2	yes	—
400	#3079	C₂×C₂₃	1	1	yes	characteristic
401	#3078	C₂×C₂₃	1	1	yes	characteristic, complemented
402	#3078	C₂×C₂₃	1	2	yes	complemented
403	Q₈×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
404	C₄×#137	C₂×C₂₃	1	1	yes	characteristic
405	C₄×#137	C₂×C₂₃	1	2	yes	—
406	C₂²×C₂₃	—	2	1	no	—
407	C₂²×C₂₃	—	2	1	no	—
408	C₂²×C₂₃	—	2	2	no	—
409	C₂²×C₂₃	—	4	1	no	—
410	C₂²×C₂₃	—	4	1	no	—
411	C₂²×C₂₃	D₄×Q₈	1	2	yes	—
412	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
413	C₄×C₂₃	—	2	2	no	—
414	C₄×C₂₃	—	2	1	no	—
415	C₄×C₂₃	—	2	2	no	—
416	C₄×C₂₃	—	2	1	no	—
417	C₄×C₂₃	—	2	2	no	—
418	C₄×C₂₃	—	2	4	no	—
419	C₄×C₂₃	—	2	1	no	—
420	C₄×C₂₃	—	2	2	no	—
421	C₄×C₂₃	—	2	2	no	—
422	C₄×C₂₃	—	4	2	no	—
423	C₄×C₂₃	—	4	2	no	—
424	C₄×C₂₃	—	4	1	no	—
425	C₄×C₂₃	—	4	2	no	—
426	C₄×C₂₃	—	4	1	no	—
427	C₄×C₂₃	—	4	4	no	—
428	C₄×C₂₃	D₄×Q₈	1	2	yes	—
429	C₄×C₂₃	#575	1	2	yes	—
430	C₄×C₂₃	C₂³×Q₈	1	1	yes	characteristic
431	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
432	C₂×#137	C₂²×C₂₃	1	1	yes	characteristic
433	Q₈²	C₂²×C₂₃	1	1	yes	characteristic
434	#557	—	2	1	no	—
435	#557	—	2	2	no	—
436	#557	—	2	1	no	—
437	#557	C₂²×C₂₃	1	2	yes	—
438	#557	C₂²×C₂₃	1	1	yes	characteristic
439	#557	C₂²×C₂₃	1	2	yes	—
440	#557	C₂²×C₂₃	1	4	yes	—
441	#557	C₂²×C₂₃	1	2	yes	—
442	#554	—	2	1	no	—
443	#554	—	2	2	no	—
444	#554	C₂²×C₂₃	1	1	yes	characteristic
445	#554	C₂²×C₂₃	1	2	yes	—
446	D₄×Q₈	—	2	1	no	—
447	D₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
448	#533	—	2	2	no	—
449	#533	—	2	1	no	—
450	#533	C₂²×C₂₃	1	1	yes	characteristic
451	#533	C₂²×C₂₃	1	2	yes	—
452	C₂×C₄⋊Q₈	—	2	1	no	—
453	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
454	C₂×#125	—	2	2	no	—
455	C₂×#125	C₂²×C₂₃	1	2	yes	—
456	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic
457	C₄×#41	C₂²×C₂₃	1	2	yes	—
458	C₂×C₄×Q₈	—	2	1	no	—
459	C₂×C₄×Q₈	—	2	1	no	—
460	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
461	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
462	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
463	#501	C₂²×C₂₃	1	4	yes	—
464	#501	C₂²×C₂₃	1	4	yes	—
465	#501	C₂²×C₂₃	1	4	yes	—
466	#500	C₂²×C₂₃	1	2	yes	—
467	#499	C₂²×C₂₃	1	4	yes	—
468	#499	C₂²×C₂₃	1	4	yes	—
469	#498	C₂²×C₂₃	1	2	yes	—
470	#479	C₂²×C₂₃	1	4	yes	—
471	#479	C₂²×C₂₃	1	4	yes	—
472	#479	C₂²×C₂₃	1	4	yes	—
473	#479	C₂²×C₂₃	1	4	yes	—
474	#479	C₂²×C₂₃	1	4	yes	—
475	#478	C₂²×C₂₃	1	4	yes	—
476	#478	C₂²×C₂₃	1	4	yes	—
477	#477	C₂²×C₂₃	1	2	yes	—
478	#477	C₂²×C₂₃	1	4	yes	—
479	#477	C₂²×C₂₃	1	2	yes	—
480	#476	C₂²×C₂₃	1	2	yes	—
481	#475	C₂²×C₂₃	1	2	yes	—
482	#475	C₂²×C₂₃	1	4	yes	—
483	#475	C₂²×C₂₃	1	2	yes	—
484	#474	C₂²×C₂₃	1	2	yes	—
485	#446	C₂²×C₂₃	1	2	yes	—
486	#446	C₂²×C₂₃	1	4	yes	—
487	C₈×Q₈	C₂²×C₂₃	1	2	yes	—
488	#441	C₂²×C₂₃	1	4	yes	—
489	#441	C₂²×C₂₃	1	2	yes	—
490	#440	C₂²×C₂₃	1	4	yes	—
491	#440	C₂²×C₂₃	1	2	yes	—
492	C₄×Q₁₆	C₂²×C₂₃	1	2	yes	—
493	C₄×Q₁₆	C₂²×C₂₃	1	4	yes	—
494	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	—
495	C₄×SD₁₆	C₂²×C₂₃	1	4	yes	—
496	#428	C₂²×C₂₃	1	2	yes	—
497	#428	C₂²×C₂₃	1	2	yes	—
498	#428	C₂²×C₂₃	1	2	yes	—
499	#428	C₂²×C₂₃	1	2	yes	—
500	#428	C₂²×C₂₃	1	1	yes	characteristic
501	#423	C₂²×C₂₃	1	1	yes	characteristic
502	#423	C₂²×C₂₃	1	2	yes	—
503	#419	C₂²×C₂₃	1	2	yes	—
504	#419	C₂²×C₂₃	1	1	yes	characteristic
505	#417	C₂²×C₂₃	1	2	yes	—
506	#417	C₂²×C₂₃	1	1	yes	characteristic
507	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
508	C₄×M₁₆	C₂²×C₂₃	1	2	yes	—
509	C₂×C₂₃	—	2	2	no	—
510	C₂×C₂₃	—	4	2	no	—
511	C₂×C₂₃	C₂×D₄×Q₈	1	1	yes	characteristic
512	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
513	C₂×C₂₃	#3586	1	1	yes	characteristic
514	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
515	C₂²×Q₈	—	2	1	no	—
516	C₂²×Q₈	—	2	1	no	—
517	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
518	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
519	#137	Q₈×C₂₃	1	8	yes	complemented
520	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
521	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
522	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
523	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
524	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
525	C₄⋊Q₈	—	2	2	no	—
526	C₄⋊Q₈	—	2	2	no	—
527	C₄⋊Q₈	—	2	4	no	—
528	C₄⋊Q₈	—	2	1	no	—
529	C₄⋊Q₈	—	2	2	no	—
530	C₄⋊Q₈	—	2	1	no	—
531	C₄⋊Q₈	—	2	2	no	—
532	C₄⋊Q₈	—	2	1	no	—
533	C₄⋊Q₈	—	2	1	no	—
534	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
535	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
536	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
537	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
538	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
539	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
540	#125	—	2	4	no	—
541	#125	—	2	4	no	—
542	#125	—	2	4	no	—
543	#125	—	2	4	no	—
544	#125	—	2	2	no	—
545	#125	—	2	2	no	—
546	#125	—	2	2	no	—
547	#125	—	2	2	no	—
548	#125	—	2	2	no	—
549	#125	C₂³×C₂₃	1	4	yes	—
550	#125	C₂³×C₂₃	1	4	yes	—
551	#125	C₂³×C₂₃	1	2	yes	—
552	#125	C₂³×C₂₃	1	2	yes	—
553	#125	C₂³×C₂₃	1	2	yes	—
554	C₂²⋊Q₈	—	2	1	no	—
555	C₂²⋊Q₈	—	2	2	no	—
556	C₂²⋊Q₈	—	2	1	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	—	2	1	no	—
560	C₂²⋊Q₈	—	2	1	no	—
561	C₂²⋊Q₈	—	2	2	no	—
562	C₂²⋊Q₈	—	2	2	no	—
563	C₂²⋊Q₈	—	2	2	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₄×Q₈	—	2	1	no	—
566	C₄×Q₈	—	2	1	no	—
567	C₄×Q₈	—	2	2	no	—
568	C₄×Q₈	—	2	2	no	—
569	C₄×Q₈	—	2	4	no	—
570	C₄×Q₈	—	2	2	no	—
571	C₄×Q₈	—	2	2	no	—
572	C₄×Q₈	—	2	1	no	—
573	C₄×Q₈	—	2	2	no	—
574	C₄×Q₈	—	2	2	no	—
575	C₄×Q₈	—	2	1	no	—
576	C₄×Q₈	—	2	1	no	—
577	C₄×Q₈	—	2	2	no	—
578	C₄×Q₈	—	2	1	no	—
579	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
580	C₄×Q₈	D₄×C₂₃	1	2	yes	—
581	C₄×Q₈	D₄×C₂₃	1	1	yes	characteristic
582	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
583	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
584	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
585	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
586	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
587	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
588	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
589	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
590	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
591	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
592	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	—	2	2	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
598	C₄×D₄	C₂³×C₂₃	1	2	yes	—
599	C₄×D₄	C₂³×C₂₃	1	2	yes	—
600	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
601	#117	—	2	2	no	—
602	#117	—	2	1	no	—
603	#117	C₂³×C₂₃	1	1	yes	characteristic
604	#117	C₂³×C₂₃	1	2	yes	—
605	C₂×C₄⋊C₄	—	2	2	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	—	2	2	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	—	2	2	no	—
610	C₂×C₄⋊C₄	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	2	no	—
612	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
613	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
616	C₂×C₄²	—	2	2	no	—
617	C₂×C₄²	—	2	1	no	—
618	C₂×C₄²	—	2	2	no	—
619	C₂×C₄²	—	2	1	no	—
620	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
621	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
622	#107	C₂³×C₂₃	1	2	yes	—
623	#107	C₂³×C₂₃	1	4	yes	—
624	#107	C₂³×C₂₃	1	4	yes	—
625	#107	C₂³×C₂₃	1	4	yes	—
626	#107	C₂³×C₂₃	1	4	yes	—
627	#106	C₂³×C₂₃	1	4	yes	—
628	#106	C₂³×C₂₃	1	2	yes	—
629	#106	C₂³×C₂₃	1	4	yes	—
630	#106	C₂³×C₂₃	1	4	yes	—
631	#106	C₂³×C₂₃	1	4	yes	—
632	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
633	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
634	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
635	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
636	#103	C₂³×C₂₃	1	4	yes	—
637	#103	C₂³×C₂₃	1	2	yes	—
638	#103	C₂³×C₂₃	1	4	yes	—
639	#103	C₂³×C₂₃	1	2	yes	—
640	#103	C₂³×C₂₃	1	2	yes	—
641	#103	C₂³×C₂₃	1	4	yes	—
642	#102	C₂³×C₂₃	1	4	yes	—
643	#102	C₂³×C₂₃	1	2	yes	—
644	#97	C₂³×C₂₃	1	2	yes	—
645	#97	C₂³×C₂₃	1	4	yes	—
646	C₄×C₈	C₂³×C₂₃	1	2	yes	—
647	C₄×C₈	C₂³×C₂₃	1	4	yes	—
648	C₂₃	#61369	1	1	yes	characteristic, direct product factor, Sylow
649	#41	—	2	2	no	—
650	#41	C₂×Q₈×C₂₃	1	4	yes	—
651	C₂×Q₈	—	2	1	no	—
652	C₂×Q₈	—	2	2	no	—
653	C₂×Q₈	—	2	1	no	—
654	C₂×Q₈	—	2	2	no	—
655	C₂×Q₈	—	2	2	no	—
656	C₂×Q₈	—	2	2	no	—
657	C₂×Q₈	—	2	1	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	4	2	no	—
660	C₂×Q₈	—	4	4	no	—
661	C₂×Q₈	—	4	4	no	—
662	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
663	C₂×Q₈	C₂×D₄×C₂₃	1	1	yes	characteristic
664	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
665	C₂×Q₈	C₂×Q₈×C₂₃	1	4	yes	complemented
666	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
667	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
679	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
680	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
683	Q₁₆	C₂×Q₈×C₂₃	1	8	yes	complemented
684	SD₁₆	C₂×Q₈×C₂₃	1	8	yes	complemented
685	M₁₆	—	2	2	no	—
686	M₁₆	—	2	4	no	—
687	M₁₆	C₂×Q₈×C₂₃	1	4	yes	complemented
688	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
689	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
690	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	—	2	2	no	—
694	C₄⋊C₄	—	2	2	no	—
695	C₄⋊C₄	—	2	1	no	—
696	C₄⋊C₄	—	2	4	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	2	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	2	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
718	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
719	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
720	C₄⋊C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
721	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
722	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
723	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
724	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
725	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
726	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
727	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
728	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
729	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
730	C₂²⋊C₄	—	2	1	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	1	no	—
736	C₄²	—	2	2	no	—
737	C₄²	—	2	1	no	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	1	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	1	no	—
742	C₄²	—	2	4	no	—
743	C₄²	—	2	4	no	—
744	C₄²	—	2	2	no	—
745	C₄²	—	2	2	no	—
746	C₄²	C₂×D₄×C₂₃	1	2	yes	—
747	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
748	C₄²	C₂×D₄×C₂₃	1	2	yes	—
749	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
750	C₄²	C₂⁴×C₂₃	1	2	yes	—
751	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
752	C₄²	C₂⁴×C₂₃	1	2	yes	—
753	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
754	C₂³	—	2	1	no	—
755	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
756	Q₈	—	2	4	no	—
757	Q₈	—	2	2	no	—
758	Q₈	—	2	2	no	—
759	Q₈	—	2	2	no	—
760	Q₈	—	2	1	no	—
761	Q₈	—	4	2	no	—
762	Q₈	—	4	4	no	—
763	Q₈	—	4	4	no	—
764	Q₈	—	4	2	no	—
765	Q₈	—	4	4	no	—
766	Q₈	—	8	2	no	—
767	Q₈	—	8	1	no	—
768	Q₈	C₂²×Q₈×C₂₃	1	4	yes	—
769	Q₈	C₂²×Q₈×C₂₃	1	2	yes	—
770	D₄	—	2	4	no	—
771	D₄	—	2	1	no	—
772	D₄	C₂²×Q₈×C₂₃	1	2	yes	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	4	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	1	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	4	no	—
784	C₂×C₄	—	4	2	no	—
785	C₂×C₄	—	4	2	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	4	4	no	—
789	C₂×C₄	—	4	2	no	—
790	C₂×C₄	—	4	2	no	—
791	C₂×C₄	—	8	2	no	—
792	C₂×C₄	—	8	1	no	—
793	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
794	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
795	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
796	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
797	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
798	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
799	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
800	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
801	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
802	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
803	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
804	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
805	C₈	—	2	2	no	—
806	C₈	—	2	4	no	—
807	C₈	C₂²×Q₈×C₂₃	1	4	yes	—
808	C₂²	—	2	1	no	—
809	C₂²	—	2	1	no	—
810	C₂²	—	2	2	no	—
811	C₂²	—	4	1	no	—
812	C₂²	—	4	1	no	—
813	C₂²	D₄×Q₈×C₂₃	1	2	yes	—
814	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
815	C₄	—	2	2	no	—
816	C₄	—	2	4	no	—
817	C₄	—	2	1	no	—
818	C₄	—	2	2	no	—
819	C₄	—	2	2	no	—
820	C₄	—	2	2	no	—
821	C₄	—	2	1	no	—
822	C₄	—	2	2	no	—
823	C₄	—	2	1	no	—
824	C₄	—	4	2	no	—
825	C₄	—	4	1	no	—
826	C₄	—	4	4	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	1	no	—
830	C₄	D₄×Q₈×C₂₃	1	2	yes	—
831	C₄	C₂₃×#575	1	2	yes	—
832	C₄	C₂³×Q₈×C₂₃	1	1	yes	characteristic
833	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
834	C₂	—	2	2	no	—
835	C₂	—	4	2	no	—
836	C₂	C₂×D₄×Q₈×C₂₃	1	1	yes	characteristic
837	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
838	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂×#41×C₂₃	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄×Q₈×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#557	C₂	semidirect
3. C₂₃×#3390	C₂	semidirect
4. C₂₃×#3388	C₂	semidirect
5. C₂₃×#3387	C₂	semidirect
6. C₂₃×#3386	C₂	semidirect
7. C₂₃×#3383	C₂	semidirect
8. C₂₃×#3381	C₂	semidirect
9. C₂₃×#3166	C₂	semidirect
10. C₂₃×#3165	C₂	semidirect
13. C₂₃×#3078	C₂	semidirect
14. C₂₃×#3078	C₂	semidirect
15. Q₈×M₁₆×C₂₃	C₂	semidirect
100. C₂₃×#137	Q₈	semidirect
245. C₂×Q₈×C₂₃	C₂×Q₈	semidirect
263. Q₁₆×C₂₃	C₂×Q₈	semidirect
264. SD₁₆×C₂₃	C₂×Q₈	semidirect
267. M₁₆×C₂₃	C₂×Q₈	semidirect
334. #61369	C₂₃	direct (N × H)
390. C₂×#557	C₂×C₂₃	semidirect
391. #3390	C₂×C₂₃	semidirect
392. #3388	C₂×C₂₃	semidirect
393. #3387	C₂×C₂₃	semidirect
394. #3386	C₂×C₂₃	semidirect
395. #3383	C₂×C₂₃	semidirect
396. #3381	C₂×C₂₃	semidirect
397. #3166	C₂×C₂₃	semidirect
398. #3165	C₂×C₂₃	semidirect
401. #3078	C₂×C₂₃	semidirect
402. #3078	C₂×C₂₃	semidirect
403. Q₈×M₁₆	C₂×C₂₃	semidirect
519. #137	Q₈×C₂₃	semidirect
648. C₂₃	#61369	direct (N × H)
665. C₂×Q₈	C₂×Q₈×C₂₃	semidirect
683. Q₁₆	C₂×Q₈×C₂₃	semidirect
684. SD₁₆	C₂×Q₈×C₂₃	semidirect
687. M₁₆	C₂×Q₈×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#41×C₂₃	2
C₂×C₂₃×#557	2
C₂₃×#3390	2
C₂₃×#3388	2
C₂₃×#3387	2
C₂₃×#3386	2
C₂₃×#3383	2
C₂₃×#3381	2
C₂₃×#3166	2
C₂₃×#3165	2
C₂₃×#3080	2
C₂₃×#3079	2
C₂₃×#3078	2
Q₈×M₁₆×C₂₃	2
C₄×C₂₃×#137	2
#61369	23

Subgroups — C23×#61369 #19208995

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61369 #19208995