Subgroups — C₂₃×#24429 #19172055

Order 5888.

1508 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#448	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₂₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2416	C₂	1	1	yes	maximal, characteristic
7	C₂₃×#2043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2035	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2013	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1872	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1787	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
17	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
21	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
22	D₄×Q₈×C₂₃	—	2	4	no	—
23	D₄×Q₈×C₂₃	—	2	4	no	—
24	C₂×C₂₃×C₄⋊Q₈	—	2	1	no	—
25	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
27	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
28	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#121	—	2	1	no	—
31	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
33	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₂₃	—	2	1	no	—
35	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂₃×#465	—	2	4	no	—
38	C₂₃×#448	—	2	4	no	—
39	C₂₃×#448	—	2	4	no	—
40	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#103	—	2	4	no	—
42	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
48	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
49	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
50	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
51	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
52	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
53	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
54	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
55	C₂₃×#396	—	2	1	no	—
56	C₂₃×#394	—	2	1	no	—
57	C₂₃×#390	C₂²	1	1	yes	characteristic
58	C₂₃×#389	C₂²	1	1	yes	characteristic
59	C₂₃×#386	—	2	1	no	—
60	C₂₃×#380	C₂²	1	1	yes	characteristic
61	C₂₃×#340	C₂²	1	1	yes	characteristic
62	C₂₃×#340	C₂²	1	1	yes	characteristic
63	C₂₃×#336	C₂²	1	1	yes	characteristic
64	C₂₃×#336	C₂²	1	1	yes	characteristic
65	C₂²×Q₈×C₂₃	—	2	2	no	—
66	C₂²×Q₈×C₂₃	—	2	2	no	—
67	C₂²×Q₈×C₂₃	—	2	2	no	—
68	C₂²×Q₈×C₂₃	—	2	1	no	—
69	C₂²×Q₈×C₂₃	—	2	1	no	—
70	C₂²×Q₈×C₂₃	—	2	2	no	—
71	C₂²×Q₈×C₂₃	—	2	2	no	—
72	C₂²×Q₈×C₂₃	—	2	2	no	—
73	C₂²×Q₈×C₂₃	—	2	2	no	—
74	C₂²×Q₈×C₂₃	—	4	1	no	—
75	C₂²×Q₈×C₂₃	—	4	1	no	—
76	C₂²×Q₈×C₂₃	—	4	1	no	—
77	C₂²×Q₈×C₂₃	—	4	1	no	—
78	C₂²×Q₈×C₂₃	D₄	1	4	yes	complemented
79	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
81	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₂₃	—	2	1	no	—
83	C₂²×D₄×C₂₃	—	2	1	no	—
84	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
85	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₂₃	—	2	1	no	—
87	C₂³×C₄×C₂₃	—	2	1	no	—
88	C₂³×C₄×C₂₃	—	2	1	no	—
89	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
91	C₂×SD₁₆×C₂₃	—	2	2	no	—
92	C₂×SD₁₆×C₂₃	—	2	2	no	—
93	C₂×SD₁₆×C₂₃	—	2	2	no	—
94	C₂×SD₁₆×C₂₃	—	2	2	no	—
95	C₂×SD₁₆×C₂₃	—	2	2	no	—
96	C₂×SD₁₆×C₂₃	—	2	2	no	—
97	C₂×SD₁₆×C₂₃	—	4	1	no	—
98	C₂×SD₁₆×C₂₃	—	4	1	no	—
99	C₂×SD₁₆×C₂₃	—	4	1	no	—
100	C₂²×C₈×C₂₃	—	2	2	no	—
101	C₂²×C₈×C₂₃	—	2	2	no	—
102	C₂²×C₈×C₂₃	—	4	1	no	—
103	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
107	C₂₃×C₄⋊Q₈	—	2	8	no	—
108	C₂₃×C₄⋊Q₈	—	2	2	no	—
109	C₂₃×C₄⋊Q₈	—	2	2	no	—
110	C₂₃×C₂²⋊Q₈	—	2	8	no	—
111	C₂₃×C₂²⋊Q₈	—	2	8	no	—
112	C₂₃×C₂²⋊Q₈	—	2	2	no	—
113	C₂₃×C₂²⋊Q₈	—	2	2	no	—
114	C₂₃×C₂²⋊Q₈	—	2	2	no	—
115	C₂₃×C₂²⋊Q₈	D₄	1	4	yes	complemented
116	C₂₃×#121	—	2	2	no	—
117	C₂₃×#121	—	2	2	no	—
118	C₂₃×#121	—	2	2	no	—
119	C₂₃×#121	—	4	1	no	—
120	C₂₃×#121	—	4	4	no	—
121	C₄×Q₈×C₂₃	—	2	2	no	—
122	C₄×Q₈×C₂₃	—	2	2	no	—
123	C₄×D₄×C₂₃	—	2	8	no	—
124	C₄×D₄×C₂₃	—	2	2	no	—
125	C₄×D₄×C₂₃	—	2	2	no	—
126	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
127	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
128	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
129	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
130	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
131	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
132	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
133	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
134	C₂×C₄⋊C₄×C₂₃	—	4	1	no	—
135	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
141	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
142	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
143	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
144	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
145	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
146	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
148	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
149	C₂×C₄²×C₂₃	—	2	1	no	—
150	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
151	C₂₃×#106	—	2	2	no	—
152	C₂₃×#103	—	2	2	no	—
153	C₂₃×#103	—	2	2	no	—
154	C₂₃×#103	—	2	2	no	—
155	C₂₃×#103	—	2	2	no	—
156	C₂₃×#103	—	2	2	no	—
157	C₂₃×#103	—	2	2	no	—
158	C₂₃×#103	—	2	2	no	—
159	C₂₃×#103	—	4	1	no	—
160	C₂₃×#103	D₄	1	4	yes	complemented
161	C₂₃×#102	—	2	2	no	—
162	C₂₃×C₂²⋊C₈	—	2	2	no	—
163	C₂₃×C₂²⋊C₈	—	2	2	no	—
164	C₂₃×C₂²⋊C₈	—	4	1	no	—
165	C₂₃×#95	—	2	1	no	—
166	C₂₃×#95	—	2	1	no	—
167	C₂⁴×C₂₃	—	2	1	no	—
168	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
169	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
170	C₂×Q₈×C₂₃	—	2	4	no	—
171	C₂×Q₈×C₂₃	—	2	4	no	—
172	C₂×Q₈×C₂₃	—	2	1	no	—
173	C₂×Q₈×C₂₃	—	2	1	no	—
174	C₂×Q₈×C₂₃	—	2	1	no	—
175	C₂×Q₈×C₂₃	—	2	1	no	—
176	C₂×Q₈×C₂₃	—	2	1	no	—
177	C₂×Q₈×C₂₃	—	2	8	no	—
178	C₂×Q₈×C₂₃	—	2	1	no	—
179	C₂×Q₈×C₂₃	—	2	1	no	—
180	C₂×Q₈×C₂₃	—	2	1	no	—
181	C₂×Q₈×C₂₃	—	2	1	no	—
182	C₂×Q₈×C₂₃	—	2	1	no	—
183	C₂×Q₈×C₂₃	—	2	1	no	—
184	C₂×Q₈×C₂₃	—	2	1	no	—
185	C₂×Q₈×C₂₃	—	2	1	no	—
186	C₂×Q₈×C₂₃	—	4	2	no	—
187	C₂×Q₈×C₂₃	—	4	2	no	—
188	C₂×Q₈×C₂₃	—	4	2	no	—
189	C₂×Q₈×C₂₃	—	4	2	no	—
190	C₂×Q₈×C₂₃	—	4	4	no	—
191	C₂×Q₈×C₂₃	—	4	4	no	—
192	C₂×Q₈×C₂₃	—	4	4	no	—
193	C₂×Q₈×C₂₃	—	4	4	no	—
194	C₂×Q₈×C₂₃	—	4	4	no	—
195	C₂×Q₈×C₂₃	—	4	4	no	—
196	C₂×Q₈×C₂₃	—	4	4	no	—
197	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
198	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
199	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
200	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
201	C₂×Q₈×C₂₃	#41	1	2	yes	—
202	C₂×D₄×C₂₃	—	2	2	no	—
203	C₂×D₄×C₂₃	—	2	2	no	—
204	C₂×D₄×C₂₃	—	2	1	no	—
205	C₂×D₄×C₂₃	—	2	1	no	—
206	C₂×D₄×C₂₃	—	2	1	no	—
207	C₂×D₄×C₂₃	—	2	1	no	—
208	C₂×D₄×C₂₃	—	2	1	no	—
209	C₂×D₄×C₂₃	—	2	1	no	—
210	C₂×D₄×C₂₃	—	4	2	no	—
211	C₂×D₄×C₂₃	—	4	2	no	—
212	C₂×D₄×C₂₃	—	4	2	no	—
213	C₂×D₄×C₂₃	—	4	2	no	—
214	C₂×D₄×C₂₃	—	4	2	no	—
215	C₂×D₄×C₂₃	—	8	1	no	—
216	C₂×D₄×C₂₃	SD₁₆	1	4	yes	complemented
217	C₂²×C₄×C₂₃	—	2	1	no	—
218	C₂²×C₄×C₂₃	—	2	1	no	—
219	C₂²×C₄×C₂₃	—	2	1	no	—
220	C₂²×C₄×C₂₃	—	2	1	no	—
221	C₂²×C₄×C₂₃	—	2	1	no	—
222	C₂²×C₄×C₂₃	—	2	4	no	—
223	C₂²×C₄×C₂₃	—	2	4	no	—
224	C₂²×C₄×C₂₃	—	2	1	no	—
225	C₂²×C₄×C₂₃	—	2	1	no	—
226	C₂²×C₄×C₂₃	—	2	1	no	—
227	C₂²×C₄×C₂₃	—	2	1	no	—
228	C₂²×C₄×C₂₃	—	2	1	no	—
229	C₂²×C₄×C₂₃	—	2	1	no	—
230	C₂²×C₄×C₂₃	—	2	1	no	—
231	C₂²×C₄×C₂₃	—	2	1	no	—
232	C₂²×C₄×C₂₃	—	2	1	no	—
233	C₂²×C₄×C₂₃	—	2	1	no	—
234	C₂²×C₄×C₂₃	—	2	1	no	—
235	C₂²×C₄×C₂₃	—	2	1	no	—
236	C₂²×C₄×C₂₃	—	4	2	no	—
237	C₂²×C₄×C₂₃	—	4	2	no	—
238	C₂²×C₄×C₂₃	—	4	2	no	—
239	C₂²×C₄×C₂₃	—	4	2	no	—
240	C₂²×C₄×C₂₃	—	4	2	no	—
241	C₂²×C₄×C₂₃	—	4	2	no	—
242	C₂²×C₄×C₂₃	—	8	1	no	—
243	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
247	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
248	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
249	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
250	SD₁₆×C₂₃	—	4	4	no	—
251	SD₁₆×C₂₃	—	4	4	no	—
252	SD₁₆×C₂₃	—	4	4	no	—
253	C₂×C₈×C₂₃	—	2	1	no	—
254	C₂×C₈×C₂₃	—	2	1	no	—
255	C₂×C₈×C₂₃	—	2	1	no	—
256	C₂×C₈×C₂₃	—	2	1	no	—
257	C₂×C₈×C₂₃	—	2	1	no	—
258	C₂×C₈×C₂₃	—	2	1	no	—
259	C₂×C₈×C₂₃	—	2	1	no	—
260	C₂×C₈×C₂₃	—	2	1	no	—
261	C₂×C₈×C₂₃	—	2	1	no	—
262	C₂×C₈×C₂₃	—	2	1	no	—
263	C₂×C₈×C₂₃	—	2	1	no	—
264	C₂×C₈×C₂₃	—	4	4	no	—
265	C₂×C₈×C₂₃	C₂×D₄	1	2	yes	—
266	C₄⋊C₄×C₂₃	—	2	4	no	—
267	C₄⋊C₄×C₂₃	—	2	4	no	—
268	C₄⋊C₄×C₂₃	—	2	4	no	—
269	C₄⋊C₄×C₂₃	—	2	4	no	—
270	C₄⋊C₄×C₂₃	—	2	4	no	—
271	C₄⋊C₄×C₂₃	—	2	2	no	—
272	C₄⋊C₄×C₂₃	—	2	1	no	—
273	C₄⋊C₄×C₂₃	—	2	1	no	—
274	C₄⋊C₄×C₂₃	—	2	1	no	—
275	C₄⋊C₄×C₂₃	—	2	1	no	—
276	C₄⋊C₄×C₂₃	—	2	1	no	—
277	C₄⋊C₄×C₂₃	—	2	1	no	—
278	C₄⋊C₄×C₂₃	—	4	2	no	—
279	C₄⋊C₄×C₂₃	—	4	2	no	—
280	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
281	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
282	C₂²⋊C₄×C₂₃	—	2	4	no	—
283	C₂²⋊C₄×C₂₃	—	2	4	no	—
284	C₂²⋊C₄×C₂₃	—	2	2	no	—
285	C₂²⋊C₄×C₂₃	—	2	2	no	—
286	C₂²⋊C₄×C₂₃	—	4	2	no	—
287	C₂²⋊C₄×C₂₃	—	4	2	no	—
288	C₂²⋊C₄×C₂₃	—	4	2	no	—
289	C₂²⋊C₄×C₂₃	—	4	2	no	—
290	C₂²⋊C₄×C₂₃	—	8	1	no	—
291	C₄²×C₂₃	—	2	4	no	—
292	C₄²×C₂₃	—	2	1	no	—
293	C₄²×C₂₃	—	2	1	no	—
294	#24429	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
295	C₂³×C₂₃	—	2	1	no	—
296	C₂³×C₂₃	—	2	1	no	—
297	C₂³×C₂₃	—	2	1	no	—
298	C₂³×C₂₃	—	2	1	no	—
299	C₂³×C₂₃	—	2	1	no	—
300	C₂³×C₂₃	—	2	1	no	—
301	C₂³×C₂₃	—	2	1	no	—
302	C₂³×C₂₃	—	2	1	no	—
303	C₂³×C₂₃	—	2	1	no	—
304	C₂³×C₂₃	—	2	1	no	—
305	C₂³×C₂₃	—	4	1	no	—
306	C₂³×C₂₃	—	4	1	no	—
307	C₂³×C₂₃	—	4	1	no	—
308	C₂³×C₂₃	—	4	1	no	—
309	C₂³×C₂₃	—	4	1	no	—
310	C₂³×C₂₃	—	4	1	no	—
311	C₂³×C₂₃	—	4	1	no	—
312	C₂³×C₂₃	#120	1	2	yes	—
313	C₂³×C₂₃	C₂×SD₁₆	1	2	yes	—
314	C₂³×C₂₃	C₂×SD₁₆	1	2	yes	—
315	C₂³×C₂₃	#137	1	2	yes	—
316	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
317	Q₈×C₂₃	—	2	2	no	—
318	Q₈×C₂₃	—	2	2	no	—
319	Q₈×C₂₃	—	2	2	no	—
320	Q₈×C₂₃	—	2	2	no	—
321	Q₈×C₂₃	—	2	2	no	—
322	Q₈×C₂₃	—	2	2	no	—
323	Q₈×C₂₃	—	2	2	no	—
324	Q₈×C₂₃	—	4	8	no	—
325	Q₈×C₂₃	—	4	8	no	—
326	Q₈×C₂₃	—	4	1	no	—
327	Q₈×C₂₃	—	4	1	no	—
328	Q₈×C₂₃	—	4	1	no	—
329	Q₈×C₂₃	—	4	1	no	—
330	Q₈×C₂₃	#121	1	4	yes	complemented
331	D₄×C₂₃	—	2	8	no	—
332	D₄×C₂₃	—	4	1	no	—
333	D₄×C₂₃	—	4	1	no	—
334	D₄×C₂₃	—	4	1	no	—
335	D₄×C₂₃	—	4	1	no	—
336	D₄×C₂₃	—	8	4	no	—
337	D₄×C₂₃	—	8	4	no	—
338	C₂×C₄×C₂₃	—	2	1	no	—
339	C₂×C₄×C₂₃	—	2	2	no	—
340	C₂×C₄×C₂₃	—	2	1	no	—
341	C₂×C₄×C₂₃	—	2	2	no	—
342	C₂×C₄×C₂₃	—	2	1	no	—
343	C₂×C₄×C₂₃	—	2	2	no	—
344	C₂×C₄×C₂₃	—	2	1	no	—
345	C₂×C₄×C₂₃	—	2	2	no	—
346	C₂×C₄×C₂₃	—	2	2	no	—
347	C₂×C₄×C₂₃	—	2	2	no	—
348	C₂×C₄×C₂₃	—	2	2	no	—
349	C₂×C₄×C₂₃	—	2	1	no	—
350	C₂×C₄×C₂₃	—	2	2	no	—
351	C₂×C₄×C₂₃	—	2	2	no	—
352	C₂×C₄×C₂₃	—	2	2	no	—
353	C₂×C₄×C₂₃	—	2	1	no	—
354	C₂×C₄×C₂₃	—	2	1	no	—
355	C₂×C₄×C₂₃	—	2	2	no	—
356	C₂×C₄×C₂₃	—	2	1	no	—
357	C₂×C₄×C₂₃	—	2	1	no	—
358	C₂×C₄×C₂₃	—	2	1	no	—
359	C₂×C₄×C₂₃	—	4	8	no	—
360	C₂×C₄×C₂₃	—	4	8	no	—
361	C₂×C₄×C₂₃	—	4	1	no	—
362	C₂×C₄×C₂₃	—	4	1	no	—
363	C₂×C₄×C₂₃	—	4	1	no	—
364	C₂×C₄×C₂₃	—	4	1	no	—
365	C₂×C₄×C₂₃	—	4	1	no	—
366	C₂×C₄×C₂₃	—	4	1	no	—
367	C₂×C₄×C₂₃	—	4	1	no	—
368	C₂×C₄×C₂₃	—	4	1	no	—
369	C₂×C₄×C₂₃	—	4	1	no	—
370	C₂×C₄×C₂₃	—	4	1	no	—
371	C₂×C₄×C₂₃	—	4	1	no	—
372	C₂×C₄×C₂₃	—	4	1	no	—
373	C₂×C₄×C₂₃	—	4	1	no	—
374	C₂×C₄×C₂₃	—	4	1	no	—
375	C₂×C₄×C₂₃	—	4	1	no	—
376	C₂×C₄×C₂₃	—	4	1	no	—
377	C₂×C₄×C₂₃	—	4	1	no	—
378	C₂×C₄×C₂₃	—	4	1	no	—
379	C₂×C₄×C₂₃	—	8	4	no	—
380	C₂×C₄×C₂₃	#120	1	2	yes	—
381	C₂×C₄×C₂₃	C₂×SD₁₆	1	2	yes	—
382	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₂₃	C₂×#41	1	1	yes	characteristic
386	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
387	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
388	C₈×C₂₃	—	2	2	no	—
389	C₈×C₂₃	—	4	1	no	—
390	C₈×C₂₃	—	4	1	no	—
391	C₈×C₂₃	—	4	1	no	—
392	C₂×D₄×Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
393	C₂×#465	C₂×C₂₃	1	1	yes	characteristic, complemented
394	C₂×#448	C₂×C₂₃	1	1	yes	characteristic, complemented
395	C₂×#448	C₂×C₂₃	1	1	yes	characteristic, complemented
396	C₂²×#103	C₂×C₂₃	1	1	yes	characteristic, complemented
397	#2416	C₂×C₂₃	1	1	yes	characteristic
398	#2043	C₂×C₂₃	1	1	yes	characteristic, complemented
399	#2035	C₂×C₂₃	1	1	yes	characteristic, complemented
400	#2013	C₂×C₂₃	1	1	yes	characteristic, complemented
401	#2000	C₂×C₂₃	1	1	yes	characteristic, complemented
402	#1880	C₂×C₂₃	1	1	yes	characteristic, complemented
403	#1872	C₂×C₂₃	1	1	yes	characteristic, complemented
404	#1869	C₂×C₂₃	1	1	yes	characteristic, complemented
405	#1865	C₂×C₂₃	1	1	yes	characteristic, complemented
406	#1787	C₂×C₂₃	1	1	yes	characteristic, complemented
407	C₂²×C₂₃	—	2	2	no	—
408	C₂²×C₂₃	—	2	2	no	—
409	C₂²×C₂₃	—	2	2	no	—
410	C₂²×C₂₃	—	2	2	no	—
411	C₂²×C₂₃	—	2	2	no	—
412	C₂²×C₂₃	—	2	2	no	—
413	C₂²×C₂₃	—	2	2	no	—
414	C₂²×C₂₃	—	2	2	no	—
415	C₂²×C₂₃	—	2	2	no	—
416	C₂²×C₂₃	—	4	1	no	—
417	C₂²×C₂₃	—	4	1	no	—
418	C₂²×C₂₃	—	4	1	no	—
419	C₂²×C₂₃	—	4	1	no	—
420	C₂²×C₂₃	—	8	1	no	—
421	C₂²×C₂₃	—	8	1	no	—
422	C₂²×C₂₃	—	8	1	no	—
423	C₂²×C₂₃	—	8	1	no	—
424	C₂²×C₂₃	—	8	1	no	—
425	C₂²×C₂₃	—	8	1	no	—
426	C₂²×C₂₃	—	8	1	no	—
427	C₂²×C₂₃	#448	1	4	yes	complemented
428	C₂²×C₂₃	C₂×#120	1	1	yes	characteristic
429	C₂²×C₂₃	D₄²	1	1	yes	characteristic
430	C₂²×C₂₃	#546	1	1	yes	characteristic
431	C₂²×C₂₃	C₂²×SD₁₆	1	1	yes	characteristic
432	C₂²×C₂₃	C₂×#137	1	1	yes	characteristic
433	C₂²×C₂₃	#577	1	1	yes	characteristic
434	C₂²×C₂₃	#578	1	1	yes	characteristic
435	C₄×C₂₃	—	2	2	no	—
436	C₄×C₂₃	—	2	4	no	—
437	C₄×C₂₃	—	2	2	no	—
438	C₄×C₂₃	—	4	1	no	—
439	C₄×C₂₃	—	4	2	no	—
440	C₄×C₂₃	—	4	2	no	—
441	C₄×C₂₃	—	4	1	no	—
442	C₄×C₂₃	—	4	2	no	—
443	C₄×C₂₃	—	4	2	no	—
444	C₄×C₂₃	—	8	1	no	—
445	C₄×C₂₃	—	8	1	no	—
446	C₄×C₂₃	C₂×#121	1	1	yes	characteristic
447	C₄×C₂₃	#534	1	1	yes	characteristic
448	C₄×C₂₃	D₄²	1	1	yes	characteristic
449	C₄×C₂₃	#546	1	1	yes	characteristic
450	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
451	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
452	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
453	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
454	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
455	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
456	D₄×Q₈	—	2	4	no	—
457	D₄×Q₈	—	2	4	no	—
458	C₂×C₄⋊Q₈	—	2	1	no	—
459	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
460	C₂×C₂²⋊Q₈	—	2	1	no	—
461	C₂×C₂²⋊Q₈	—	2	1	no	—
462	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
463	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
464	C₂×#121	—	2	1	no	—
465	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
466	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
467	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
468	C₂×C₄×D₄	—	2	1	no	—
469	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
470	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
471	#465	—	2	4	no	—
472	#448	—	2	4	no	—
473	#448	—	2	4	no	—
474	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
475	C₂×#103	—	2	4	no	—
476	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
477	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
478	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
479	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
480	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
481	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
482	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
483	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
484	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
485	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
486	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
487	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
488	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
489	#396	—	2	1	no	—
490	#394	—	2	1	no	—
491	#390	C₂²×C₂₃	1	1	yes	characteristic
492	#389	C₂²×C₂₃	1	1	yes	characteristic
493	#386	—	2	1	no	—
494	#380	C₂²×C₂₃	1	1	yes	characteristic
495	#340	C₂²×C₂₃	1	1	yes	characteristic
496	#340	C₂²×C₂₃	1	1	yes	characteristic
497	#336	C₂²×C₂₃	1	1	yes	characteristic
498	#336	C₂²×C₂₃	1	1	yes	characteristic
499	C₂×C₂₃	—	2	4	no	—
500	C₂×C₂₃	—	4	2	no	—
501	C₂×C₂₃	—	16	1	no	—
502	C₂×C₂₃	#2410	1	1	yes	characteristic
503	C₂×C₂₃	C₂×#448	1	1	yes	characteristic
504	C₂×C₂₃	#3013	1	1	yes	characteristic
505	C₂×C₂₃	#3270	1	1	yes	characteristic
506	C₂×C₂₃	D₄×SD₁₆	1	1	yes	characteristic
507	C₂×C₂₃	#3298	1	1	yes	characteristic
508	C₂×C₂₃	#3320	1	1	yes	characteristic
509	C₂²×Q₈	—	2	2	no	—
510	C₂²×Q₈	—	2	2	no	—
511	C₂²×Q₈	—	2	1	no	—
512	C₂²×Q₈	—	2	1	no	—
513	C₂²×Q₈	—	2	2	no	—
514	C₂²×Q₈	—	2	2	no	—
515	C₂²×Q₈	—	2	2	no	—
516	C₂²×Q₈	—	2	2	no	—
517	C₂²×Q₈	—	2	2	no	—
518	C₂²×Q₈	—	4	1	no	—
519	C₂²×Q₈	—	4	1	no	—
520	C₂²×Q₈	—	4	1	no	—
521	C₂²×Q₈	—	4	1	no	—
522	C₂²×Q₈	D₄×C₂₃	1	4	yes	complemented
523	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
524	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
525	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
526	C₂²×D₄	—	2	1	no	—
527	C₂²×D₄	—	2	1	no	—
528	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
529	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
530	C₂³×C₄	—	2	1	no	—
531	C₂³×C₄	—	2	1	no	—
532	C₂³×C₄	—	2	1	no	—
533	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
535	C₂×SD₁₆	—	2	2	no	—
536	C₂×SD₁₆	—	2	2	no	—
537	C₂×SD₁₆	—	2	2	no	—
538	C₂×SD₁₆	—	2	2	no	—
539	C₂×SD₁₆	—	2	2	no	—
540	C₂×SD₁₆	—	2	2	no	—
541	C₂×SD₁₆	—	4	1	no	—
542	C₂×SD₁₆	—	4	1	no	—
543	C₂×SD₁₆	—	4	1	no	—
544	C₂²×C₈	—	2	2	no	—
545	C₂²×C₈	—	2	2	no	—
546	C₂²×C₈	—	4	1	no	—
547	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
548	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
549	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
550	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
551	C₄⋊Q₈	—	2	8	no	—
552	C₄⋊Q₈	—	2	2	no	—
553	C₄⋊Q₈	—	2	2	no	—
554	C₂²⋊Q₈	—	2	8	no	—
555	C₂²⋊Q₈	—	2	8	no	—
556	C₂²⋊Q₈	—	2	2	no	—
557	C₂²⋊Q₈	—	2	2	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	D₄×C₂₃	1	4	yes	complemented
560	#121	—	2	2	no	—
561	#121	—	2	2	no	—
562	#121	—	2	2	no	—
563	#121	—	4	1	no	—
564	#121	—	4	4	no	—
565	C₄×Q₈	—	2	2	no	—
566	C₄×Q₈	—	2	2	no	—
567	C₄×D₄	—	2	8	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	2	no	—
570	C₂×C₄⋊C₄	—	2	1	no	—
571	C₂×C₄⋊C₄	—	2	1	no	—
572	C₂×C₄⋊C₄	—	2	1	no	—
573	C₂×C₄⋊C₄	—	2	1	no	—
574	C₂×C₄⋊C₄	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	2	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	4	1	no	—
579	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
584	C₂×C₂²⋊C₄	—	2	1	no	—
585	C₂×C₂²⋊C₄	—	2	1	no	—
586	C₂×C₂²⋊C₄	—	2	1	no	—
587	C₂×C₂²⋊C₄	—	2	1	no	—
588	C₂×C₂²⋊C₄	—	2	1	no	—
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₂²⋊C₄	—	2	1	no	—
591	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
592	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
593	C₂×C₄²	—	2	1	no	—
594	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
595	#106	—	2	2	no	—
596	#103	—	2	2	no	—
597	#103	—	2	2	no	—
598	#103	—	2	2	no	—
599	#103	—	2	2	no	—
600	#103	—	2	2	no	—
601	#103	—	2	2	no	—
602	#103	—	2	2	no	—
603	#103	—	4	1	no	—
604	#103	D₄×C₂₃	1	4	yes	complemented
605	#102	—	2	2	no	—
606	C₂²⋊C₈	—	2	2	no	—
607	C₂²⋊C₈	—	2	2	no	—
608	C₂²⋊C₈	—	4	1	no	—
609	#95	—	2	1	no	—
610	#95	—	2	1	no	—
611	C₂₃	#24429	1	1	yes	characteristic, direct product factor, Sylow
612	C₂⁴	—	2	1	no	—
613	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
614	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
615	C₂×Q₈	—	2	4	no	—
616	C₂×Q₈	—	2	4	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	—	2	1	no	—
619	C₂×Q₈	—	2	1	no	—
620	C₂×Q₈	—	2	1	no	—
621	C₂×Q₈	—	2	1	no	—
622	C₂×Q₈	—	2	8	no	—
623	C₂×Q₈	—	2	1	no	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	1	no	—
626	C₂×Q₈	—	2	1	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	—	4	2	no	—
632	C₂×Q₈	—	4	2	no	—
633	C₂×Q₈	—	4	2	no	—
634	C₂×Q₈	—	4	2	no	—
635	C₂×Q₈	—	4	4	no	—
636	C₂×Q₈	—	4	4	no	—
637	C₂×Q₈	—	4	4	no	—
638	C₂×Q₈	—	4	4	no	—
639	C₂×Q₈	—	4	4	no	—
640	C₂×Q₈	—	4	4	no	—
641	C₂×Q₈	—	4	4	no	—
642	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
643	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
644	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
645	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
646	C₂×Q₈	#41×C₂₃	1	2	yes	—
647	C₂×D₄	—	2	2	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	1	no	—
650	C₂×D₄	—	2	1	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	1	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	4	2	no	—
656	C₂×D₄	—	4	2	no	—
657	C₂×D₄	—	4	2	no	—
658	C₂×D₄	—	4	2	no	—
659	C₂×D₄	—	4	2	no	—
660	C₂×D₄	—	8	1	no	—
661	C₂×D₄	SD₁₆×C₂₃	1	4	yes	complemented
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	2	1	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	2	4	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	1	no	—
672	C₂²×C₄	—	2	1	no	—
673	C₂²×C₄	—	2	1	no	—
674	C₂²×C₄	—	2	1	no	—
675	C₂²×C₄	—	2	1	no	—
676	C₂²×C₄	—	2	1	no	—
677	C₂²×C₄	—	2	1	no	—
678	C₂²×C₄	—	2	1	no	—
679	C₂²×C₄	—	2	1	no	—
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	4	2	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	—	4	2	no	—
685	C₂²×C₄	—	4	2	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	—	8	1	no	—
688	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
689	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
690	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
691	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
692	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
693	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
695	SD₁₆	—	4	4	no	—
696	SD₁₆	—	4	4	no	—
697	SD₁₆	—	4	4	no	—
698	C₂×C₈	—	2	1	no	—
699	C₂×C₈	—	2	1	no	—
700	C₂×C₈	—	2	1	no	—
701	C₂×C₈	—	2	1	no	—
702	C₂×C₈	—	2	1	no	—
703	C₂×C₈	—	2	1	no	—
704	C₂×C₈	—	2	1	no	—
705	C₂×C₈	—	2	1	no	—
706	C₂×C₈	—	2	1	no	—
707	C₂×C₈	—	2	1	no	—
708	C₂×C₈	—	2	1	no	—
709	C₂×C₈	—	4	4	no	—
710	C₂×C₈	C₂×D₄×C₂₃	1	2	yes	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	2	4	no	—
715	C₄⋊C₄	—	2	4	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	1	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
726	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	4	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	4	2	no	—
732	C₂²⋊C₄	—	4	2	no	—
733	C₂²⋊C₄	—	4	2	no	—
734	C₂²⋊C₄	—	4	2	no	—
735	C₂²⋊C₄	—	8	1	no	—
736	C₄²	—	2	4	no	—
737	C₄²	—	2	1	no	—
738	C₄²	—	2	1	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	2	1	no	—
741	C₂³	—	2	1	no	—
742	C₂³	—	2	1	no	—
743	C₂³	—	2	1	no	—
744	C₂³	—	2	1	no	—
745	C₂³	—	2	1	no	—
746	C₂³	—	2	1	no	—
747	C₂³	—	2	1	no	—
748	C₂³	—	2	1	no	—
749	C₂³	—	4	1	no	—
750	C₂³	—	4	1	no	—
751	C₂³	—	4	1	no	—
752	C₂³	—	4	1	no	—
753	C₂³	—	4	1	no	—
754	C₂³	—	4	1	no	—
755	C₂³	—	4	1	no	—
756	C₂³	C₂₃×#120	1	2	yes	—
757	C₂³	C₂×SD₁₆×C₂₃	1	2	yes	—
758	C₂³	C₂×SD₁₆×C₂₃	1	2	yes	—
759	C₂³	C₂₃×#137	1	2	yes	—
760	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
761	Q₈	—	2	2	no	—
762	Q₈	—	2	2	no	—
763	Q₈	—	2	2	no	—
764	Q₈	—	2	2	no	—
765	Q₈	—	2	2	no	—
766	Q₈	—	2	2	no	—
767	Q₈	—	2	2	no	—
768	Q₈	—	4	8	no	—
769	Q₈	—	4	8	no	—
770	Q₈	—	4	1	no	—
771	Q₈	—	4	1	no	—
772	Q₈	—	4	1	no	—
773	Q₈	—	4	1	no	—
774	Q₈	C₂₃×#121	1	4	yes	complemented
775	D₄	—	2	8	no	—
776	D₄	—	4	1	no	—
777	D₄	—	4	1	no	—
778	D₄	—	4	1	no	—
779	D₄	—	4	1	no	—
780	D₄	—	8	4	no	—
781	D₄	—	8	4	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	4	8	no	—
804	C₂×C₄	—	4	8	no	—
805	C₂×C₄	—	4	1	no	—
806	C₂×C₄	—	4	1	no	—
807	C₂×C₄	—	4	1	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	1	no	—
810	C₂×C₄	—	4	1	no	—
811	C₂×C₄	—	4	1	no	—
812	C₂×C₄	—	4	1	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	4	1	no	—
815	C₂×C₄	—	4	1	no	—
816	C₂×C₄	—	4	1	no	—
817	C₂×C₄	—	4	1	no	—
818	C₂×C₄	—	4	1	no	—
819	C₂×C₄	—	4	1	no	—
820	C₂×C₄	—	4	1	no	—
821	C₂×C₄	—	4	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	8	4	no	—
824	C₂×C₄	C₂₃×#120	1	2	yes	—
825	C₂×C₄	C₂×SD₁₆×C₂₃	1	2	yes	—
826	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
829	C₂×C₄	C₂×#41×C₂₃	1	1	yes	characteristic
830	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
831	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
832	C₈	—	2	2	no	—
833	C₈	—	4	1	no	—
834	C₈	—	4	1	no	—
835	C₈	—	4	1	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	2	2	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	2	2	no	—
842	C₂²	—	2	2	no	—
843	C₂²	—	2	2	no	—
844	C₂²	—	2	2	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	8	1	no	—
850	C₂²	—	8	1	no	—
851	C₂²	—	8	1	no	—
852	C₂²	—	8	1	no	—
853	C₂²	—	8	1	no	—
854	C₂²	—	8	1	no	—
855	C₂²	—	8	1	no	—
856	C₂²	C₂₃×#448	1	4	yes	complemented
857	C₂²	C₂×C₂₃×#120	1	1	yes	characteristic
858	C₂²	D₄²×C₂₃	1	1	yes	characteristic
859	C₂²	C₂₃×#546	1	1	yes	characteristic
860	C₂²	C₂²×SD₁₆×C₂₃	1	1	yes	characteristic
861	C₂²	C₂×C₂₃×#137	1	1	yes	characteristic
862	C₂²	C₂₃×#577	1	1	yes	characteristic
863	C₂²	C₂₃×#578	1	1	yes	characteristic
864	C₄	—	2	2	no	—
865	C₄	—	2	4	no	—
866	C₄	—	2	2	no	—
867	C₄	—	4	1	no	—
868	C₄	—	4	2	no	—
869	C₄	—	4	2	no	—
870	C₄	—	4	1	no	—
871	C₄	—	4	2	no	—
872	C₄	—	4	2	no	—
873	C₄	—	8	1	no	—
874	C₄	—	8	1	no	—
875	C₄	C₂×C₂₃×#121	1	1	yes	characteristic
876	C₄	C₂₃×#534	1	1	yes	characteristic
877	C₄	D₄²×C₂₃	1	1	yes	characteristic
878	C₄	C₂₃×#546	1	1	yes	characteristic
879	C₂	—	2	4	no	—
880	C₂	—	4	2	no	—
881	C₂	—	16	1	no	—
882	C₂	C₂₃×#2410	1	1	yes	characteristic
883	C₂	C₂×C₂₃×#448	1	1	yes	characteristic
884	C₂	C₂₃×#3013	1	1	yes	characteristic
885	C₂	C₂₃×#3270	1	1	yes	characteristic
886	C₂	D₄×SD₁₆×C₂₃	1	1	yes	characteristic
887	C₂	C₂₃×#3298	1	1	yes	characteristic
888	C₂	C₂₃×#3320	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
prime radical	C₂₃×#2416	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×Q₈×C₂₃	C₂	semidirect
2. C₂×C₂₃×#465	C₂	semidirect
3. C₂×C₂₃×#448	C₂	semidirect
4. C₂×C₂₃×#448	C₂	semidirect
5. C₂²×C₂₃×#103	C₂	semidirect
7. C₂₃×#2043	C₂	semidirect
8. C₂₃×#2035	C₂	semidirect
9. C₂₃×#2013	C₂	semidirect
10. C₂₃×#2000	C₂	semidirect
11. C₂₃×#1880	C₂	semidirect
12. C₂₃×#1872	C₂	semidirect
13. C₂₃×#1869	C₂	semidirect
14. C₂₃×#1865	C₂	semidirect
15. C₂₃×#1787	C₂	semidirect
78. C₂²×Q₈×C₂₃	D₄	semidirect
115. C₂₃×C₂²⋊Q₈	D₄	semidirect
160. C₂₃×#103	D₄	semidirect
216. C₂×D₄×C₂₃	SD₁₆	semidirect
294. #24429	C₂₃	direct (N × H)
330. Q₈×C₂₃	#121	semidirect
392. C₂×D₄×Q₈	C₂×C₂₃	semidirect
393. C₂×#465	C₂×C₂₃	semidirect
394. C₂×#448	C₂×C₂₃	semidirect
395. C₂×#448	C₂×C₂₃	semidirect
396. C₂²×#103	C₂×C₂₃	semidirect
398. #2043	C₂×C₂₃	semidirect
399. #2035	C₂×C₂₃	semidirect
400. #2013	C₂×C₂₃	semidirect
401. #2000	C₂×C₂₃	semidirect
402. #1880	C₂×C₂₃	semidirect
403. #1872	C₂×C₂₃	semidirect
404. #1869	C₂×C₂₃	semidirect
405. #1865	C₂×C₂₃	semidirect
406. #1787	C₂×C₂₃	semidirect
427. C₂²×C₂₃	#448	semidirect
522. C₂²×Q₈	D₄×C₂₃	semidirect
559. C₂²⋊Q₈	D₄×C₂₃	semidirect
604. #103	D₄×C₂₃	semidirect
611. C₂₃	#24429	direct (N × H)
661. C₂×D₄	SD₁₆×C₂₃	semidirect
774. Q₈	C₂₃×#121	semidirect
856. C₂²	C₂₃×#448	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₂₃	2
C₂×C₂₃×#465	2
C₂×C₂₃×#448	2
C₂²×C₂₃×#103	2
C₂₃×#2416	2
C₂₃×#2043	2
C₂₃×#2035	2
C₂₃×#2013	2
C₂₃×#2000	2
C₂₃×#1880	2
C₂₃×#1872	2
C₂₃×#1869	2
C₂₃×#1865	2
C₂₃×#1787	2
#24429	23

Subgroups — C23×#24429 #19172055

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#24429 #19172055