Subgroups — C₂₃×#35008 #19182634

Order 5888.

2284 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#539	C₂	1	2	yes	maximal, complemented
2	C₂₃×#2860	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2664	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2663	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2556	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2553	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2506	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2501	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2496	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2488	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2486	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2452	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2440	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2425	C₂	1	2	yes	maximal, complemented
18	C₂₃×#2422	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2416	C₂	1	1	yes	maximal, characteristic
20	C₂₃×#2322	C₂	1	2	yes	maximal, complemented
21	C₄×C₂₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₂₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄²×D₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#539	—	2	16	no	—
25	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#126	C₂²	1	2	yes	—
27	C₂×C₂₃×#126	C₂²	1	2	yes	—
28	C₂×C₂₃×#125	C₂²	1	2	yes	—
29	C₂×C₂₃×#125	C₂²	1	2	yes	—
30	C₂×C₂₃×#123	C₂²	1	2	yes	—
31	C₂×C₂₃×#123	C₂²	1	2	yes	—
32	C₂×C₂₃×#123	C₂²	1	2	yes	—
33	C₂×C₂₃×#123	C₂²	1	2	yes	—
34	C₂×C₂₃×#123	C₂²	1	2	yes	—
35	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
36	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
37	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
38	C₂×C₂₃×#121	C₂²	1	2	yes	—
39	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
44	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
46	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
47	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
48	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
49	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
50	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
51	C₂₃×#400	C₂²	1	2	yes	—
52	C₂₃×#400	C₂²	1	2	yes	—
53	C₂₃×#399	C₂²	1	2	yes	—
54	C₂₃×#399	C₂²	1	2	yes	—
55	C₂₃×#398	C₂²	1	2	yes	—
56	C₂₃×#398	C₂²	1	2	yes	—
57	C₂₃×#398	C₂²	1	2	yes	—
58	C₂₃×#397	C₂²	1	2	yes	—
59	C₂₃×#397	C₂²	1	2	yes	—
60	C₂₃×#397	C₂²	1	2	yes	—
61	C₂₃×#396	C₂²	1	2	yes	—
62	C₂₃×#396	C₂²	1	2	yes	—
63	C₂₃×#395	C₂²	1	2	yes	—
64	C₂₃×#394	C₂²	1	2	yes	—
65	C₂₃×#394	C₂²	1	2	yes	—
66	C₂₃×#393	C₂²	1	2	yes	—
67	C₂₃×#391	C₂²	1	2	yes	—
68	C₂₃×#390	C₂²	1	1	yes	characteristic
69	C₂₃×#390	C₂²	1	1	yes	characteristic
70	C₂₃×#390	C₂²	1	1	yes	characteristic
71	C₂₃×#390	C₂²	1	1	yes	characteristic
72	C₂₃×#389	C₂²	1	2	yes	—
73	C₂₃×#389	C₂²	1	2	yes	—
74	C₂₃×#389	C₂²	1	2	yes	—
75	C₂₃×#389	C₂²	1	1	yes	characteristic
76	C₂₃×#389	C₂²	1	1	yes	characteristic
77	C₂₃×#389	C₂²	1	2	yes	—
78	C₂₃×#389	C₂²	1	1	yes	characteristic
79	C₂₃×#389	C₂²	1	1	yes	characteristic
80	C₂₃×#389	C₂²	1	1	yes	characteristic
81	C₂₃×#389	C₂²	1	1	yes	characteristic
82	C₂₃×#389	C₂²	1	1	yes	characteristic
83	C₂₃×#389	C₂²	1	2	yes	—
84	C₂₃×#389	C₂²	1	1	yes	characteristic
85	C₂₃×#389	C₂²	1	1	yes	characteristic
86	C₂₃×#389	C₂²	1	1	yes	characteristic
87	C₂₃×#388	C₂²	1	2	yes	—
88	C₂₃×#388	C₂²	1	2	yes	—
89	C₂₃×#388	C₂²	1	2	yes	—
90	C₂₃×#388	C₂²	1	2	yes	—
91	C₂₃×#388	C₂²	1	2	yes	—
92	C₂₃×#388	C₂²	1	2	yes	—
93	C₂₃×#387	C₂²	1	2	yes	—
94	C₂₃×#387	C₂²	1	2	yes	—
95	C₂₃×#386	C₂²	1	2	yes	—
96	C₂₃×#386	C₂²	1	2	yes	—
97	C₂₃×#386	C₂²	1	2	yes	—
98	C₂₃×#385	C₂²	1	2	yes	—
99	C₂₃×#385	C₂²	1	2	yes	—
100	C₂₃×#385	C₂²	1	2	yes	—
101	C₂₃×#384	C₂²	1	1	yes	characteristic
102	C₂₃×#384	C₂²	1	1	yes	characteristic
103	C₂₃×#384	C₂²	1	1	yes	characteristic
104	C₂₃×#382	C₂²	1	2	yes	—
105	C₂₃×#381	C₂²	1	2	yes	—
106	C₂₃×#380	C₂²	1	1	yes	characteristic
107	C₂₃×#380	C₂²	1	1	yes	characteristic
108	C₂₃×#380	C₂²	1	2	yes	—
109	C₂₃×#380	C₂²	1	1	yes	characteristic
110	C₂₃×#380	C₂²	1	1	yes	characteristic
111	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
112	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
113	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
114	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
115	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
116	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
117	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
118	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
121	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
122	C₂×C₂₃×#95	C₂²	1	2	yes	—
123	C₄³×C₂₃	C₂²	1	1	yes	characteristic
124	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
125	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
126	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
127	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
128	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
129	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
130	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
135	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
136	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
138	C₂₃×C₄⋊Q₈	—	4	2	no	—
139	C₂₃×#126	—	2	8	no	—
140	C₂₃×#126	—	2	8	no	—
141	C₂₃×#125	—	2	8	no	—
142	C₂₃×#125	—	2	8	no	—
143	C₂₃×#123	—	2	8	no	—
144	C₂₃×#123	—	2	8	no	—
145	C₂₃×#123	—	2	8	no	—
146	C₂₃×#123	—	2	8	no	—
147	C₂₃×#123	—	2	8	no	—
148	C₂₃×C₂²⋊Q₈	—	2	8	no	—
149	C₂₃×C₂²⋊Q₈	—	2	8	no	—
150	C₂₃×C₂²⋊Q₈	—	2	8	no	—
151	C₂₃×#121	—	2	8	no	—
152	C₂₃×#121	—	2	4	no	—
153	C₂₃×#121	—	4	2	no	—
154	C₄×D₄×C₂₃	—	2	8	no	—
155	C₄×D₄×C₂₃	—	2	4	no	—
156	C₄×D₄×C₂₃	—	2	4	no	—
157	C₄×D₄×C₂₃	—	4	2	no	—
158	C₄×D₄×C₂₃	D₄	1	8	yes	complemented
159	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
160	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
161	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
162	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
163	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
172	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
174	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
176	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
178	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
182	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
185	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
191	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₂₃	—	4	2	no	—
213	C₂×C₄²×C₂₃	—	4	2	no	—
214	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
222	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
223	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
224	C₂×C₄²×C₂₃	C₂³	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	C₂₃×#95	C₂³	1	2	yes	—
229	C₂₃×#95	C₂³	1	2	yes	—
230	C₂₃×#95	C₂³	1	2	yes	—
231	C₂₃×#95	C₂³	1	2	yes	—
232	C₂₃×#95	C₂³	1	1	yes	characteristic
233	C₂₃×#95	C₂³	1	1	yes	characteristic
234	C₂₃×#95	C₂³	1	1	yes	characteristic
235	C₂₃×#95	C₂³	1	1	yes	characteristic
236	C₂₃×#95	C₂³	1	1	yes	characteristic
237	C₂₃×#95	C₂³	1	1	yes	characteristic
238	C₂₃×#95	C₂³	1	2	yes	—
239	C₂₃×#95	C₂³	1	2	yes	—
240	C₂₃×#95	C₂³	1	2	yes	—
241	C₂₃×#95	C₂³	1	2	yes	—
242	C₂₃×#95	C₂³	1	2	yes	—
243	C₂₃×#95	C₂³	1	2	yes	—
244	C₂₃×#95	C₂³	1	2	yes	—
245	C₂₃×#95	C₂³	1	2	yes	—
246	C₂₃×#95	C₂³	1	2	yes	—
247	C₂₃×#95	C₂³	1	2	yes	—
248	C₂₃×#95	C₂³	1	2	yes	—
249	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
250	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
251	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
252	C₂×Q₈×C₂₃	—	2	4	no	—
253	C₂×Q₈×C₂₃	—	4	2	no	—
254	C₂×Q₈×C₂₃	—	4	2	no	—
255	C₂×D₄×C₂₃	—	2	2	no	—
256	C₂×D₄×C₂₃	—	2	2	no	—
257	C₂×D₄×C₂₃	—	2	4	no	—
258	C₂×D₄×C₂₃	—	2	4	no	—
259	C₂×D₄×C₂₃	—	2	4	no	—
260	C₂×D₄×C₂₃	—	2	4	no	—
261	C₂×D₄×C₂₃	—	2	2	no	—
262	C₂×D₄×C₂₃	—	2	2	no	—
263	C₂×D₄×C₂₃	—	2	2	no	—
264	C₂×D₄×C₂₃	—	4	2	no	—
265	C₂×D₄×C₂₃	—	4	2	no	—
266	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
267	C₂²×C₄×C₂₃	—	2	2	no	—
268	C₂²×C₄×C₂₃	—	2	2	no	—
269	C₂²×C₄×C₂₃	—	2	4	no	—
270	C₂²×C₄×C₂₃	—	2	4	no	—
271	C₂²×C₄×C₂₃	—	2	2	no	—
272	C₂²×C₄×C₂₃	—	2	4	no	—
273	C₂²×C₄×C₂₃	—	2	4	no	—
274	C₂²×C₄×C₂₃	—	2	2	no	—
275	C₂²×C₄×C₂₃	—	2	2	no	—
276	C₂²×C₄×C₂₃	—	2	2	no	—
277	C₂²×C₄×C₂₃	—	2	2	no	—
278	C₂²×C₄×C₂₃	—	2	2	no	—
279	C₂²×C₄×C₂₃	—	2	2	no	—
280	C₂²×C₄×C₂₃	—	2	4	no	—
281	C₂²×C₄×C₂₃	—	4	1	no	—
282	C₂²×C₄×C₂₃	—	4	1	no	—
283	C₂²×C₄×C₂₃	—	4	1	no	—
284	C₂²×C₄×C₂₃	—	4	1	no	—
285	C₂²×C₄×C₂₃	—	4	1	no	—
286	C₂²×C₄×C₂₃	—	4	1	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	—	4	2	no	—
291	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
292	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
293	C₂²×C₄×C₂₃	#41	1	4	yes	—
294	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
298	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
314	C₄⋊C₄×C₂₃	—	2	4	no	—
315	C₄⋊C₄×C₂₃	—	2	4	no	—
316	C₄⋊C₄×C₂₃	—	2	4	no	—
317	C₄⋊C₄×C₂₃	—	2	4	no	—
318	C₄⋊C₄×C₂₃	—	2	4	no	—
319	C₄⋊C₄×C₂₃	—	2	4	no	—
320	C₄⋊C₄×C₂₃	—	2	4	no	—
321	C₄⋊C₄×C₂₃	—	2	4	no	—
322	C₄⋊C₄×C₂₃	—	2	4	no	—
323	C₄⋊C₄×C₂₃	—	2	4	no	—
324	C₄⋊C₄×C₂₃	—	2	4	no	—
325	C₄⋊C₄×C₂₃	—	2	4	no	—
326	C₄⋊C₄×C₂₃	—	2	4	no	—
327	C₄⋊C₄×C₂₃	—	2	4	no	—
328	C₄⋊C₄×C₂₃	—	2	2	no	—
329	C₄⋊C₄×C₂₃	—	2	2	no	—
330	C₄⋊C₄×C₂₃	—	2	2	no	—
331	C₄⋊C₄×C₂₃	—	2	2	no	—
332	C₄⋊C₄×C₂₃	—	2	2	no	—
333	C₄⋊C₄×C₂₃	—	2	4	no	—
334	C₄⋊C₄×C₂₃	—	2	4	no	—
335	C₄⋊C₄×C₂₃	—	2	2	no	—
336	C₄⋊C₄×C₂₃	—	2	2	no	—
337	C₄⋊C₄×C₂₃	—	2	2	no	—
338	C₄⋊C₄×C₂₃	—	2	2	no	—
339	C₄⋊C₄×C₂₃	—	4	2	no	—
340	C₄⋊C₄×C₂₃	—	4	2	no	—
341	C₄⋊C₄×C₂₃	—	4	2	no	—
342	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
343	C₂²⋊C₄×C₂₃	—	2	4	no	—
344	C₂²⋊C₄×C₂₃	—	2	4	no	—
345	C₂²⋊C₄×C₂₃	—	2	4	no	—
346	C₂²⋊C₄×C₂₃	—	2	4	no	—
347	C₂²⋊C₄×C₂₃	—	2	2	no	—
348	C₂²⋊C₄×C₂₃	—	2	4	no	—
349	C₂²⋊C₄×C₂₃	—	2	4	no	—
350	C₂²⋊C₄×C₂₃	—	2	4	no	—
351	C₂²⋊C₄×C₂₃	—	2	4	no	—
352	C₂²⋊C₄×C₂₃	—	2	2	no	—
353	C₂²⋊C₄×C₂₃	—	2	2	no	—
354	C₂²⋊C₄×C₂₃	—	2	4	no	—
355	C₂²⋊C₄×C₂₃	—	2	4	no	—
356	C₂²⋊C₄×C₂₃	—	2	4	no	—
357	C₂²⋊C₄×C₂₃	—	2	4	no	—
358	C₂²⋊C₄×C₂₃	—	4	2	no	—
359	C₂²⋊C₄×C₂₃	—	4	2	no	—
360	C₂²⋊C₄×C₂₃	—	4	2	no	—
361	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
362	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
363	C₂²⋊C₄×C₂₃	#41	1	4	yes	—
364	C₄²×C₂₃	—	2	4	no	—
365	C₄²×C₂₃	—	2	2	no	—
366	C₄²×C₂₃	—	2	2	no	—
367	C₄²×C₂₃	—	2	2	no	—
368	C₄²×C₂₃	—	2	2	no	—
369	C₄²×C₂₃	—	2	2	no	—
370	C₄²×C₂₃	—	2	2	no	—
371	C₄²×C₂₃	—	2	2	no	—
372	C₄²×C₂₃	—	4	1	no	—
373	C₄²×C₂₃	—	4	1	no	—
374	C₄²×C₂₃	—	4	1	no	—
375	C₄²×C₂₃	—	4	1	no	—
376	C₄²×C₂₃	—	4	1	no	—
377	C₄²×C₂₃	C₂×D₄	1	4	yes	—
378	#35008	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
379	C₂³×C₂₃	—	2	1	no	—
380	C₂³×C₂₃	—	2	1	no	—
381	C₂³×C₂₃	—	2	1	no	—
382	C₂³×C₂₃	—	2	1	no	—
383	C₂³×C₂₃	—	2	1	no	—
384	C₂³×C₂₃	—	2	1	no	—
385	C₂³×C₂₃	—	2	1	no	—
386	C₂³×C₂₃	—	2	1	no	—
387	C₂³×C₂₃	—	2	1	no	—
388	C₂³×C₂₃	—	2	1	no	—
389	C₂³×C₂₃	—	2	2	no	—
390	C₂³×C₂₃	—	2	2	no	—
391	C₂³×C₂₃	—	2	2	no	—
392	C₂³×C₂₃	—	2	2	no	—
393	C₂³×C₂₃	—	2	2	no	—
394	C₂³×C₂₃	—	2	2	no	—
395	C₂³×C₂₃	—	2	2	no	—
396	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
397	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
398	C₂³×C₂₃	C₂×#41	1	2	yes	—
399	C₂³×C₂₃	C₂×#41	1	2	yes	—
400	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
401	Q₈×C₂₃	—	8	4	no	—
402	D₄×C₂₃	—	2	8	no	—
403	D₄×C₂₃	—	4	8	no	—
404	D₄×C₂₃	—	4	4	no	—
405	D₄×C₂₃	—	8	4	no	—
406	C₂×C₄×C₂₃	—	2	1	no	—
407	C₂×C₄×C₂₃	—	2	1	no	—
408	C₂×C₄×C₂₃	—	2	1	no	—
409	C₂×C₄×C₂₃	—	2	1	no	—
410	C₂×C₄×C₂₃	—	2	1	no	—
411	C₂×C₄×C₂₃	—	2	1	no	—
412	C₂×C₄×C₂₃	—	2	1	no	—
413	C₂×C₄×C₂₃	—	2	1	no	—
414	C₂×C₄×C₂₃	—	2	1	no	—
415	C₂×C₄×C₂₃	—	2	1	no	—
416	C₂×C₄×C₂₃	—	2	1	no	—
417	C₂×C₄×C₂₃	—	2	1	no	—
418	C₂×C₄×C₂₃	—	2	1	no	—
419	C₂×C₄×C₂₃	—	2	1	no	—
420	C₂×C₄×C₂₃	—	2	1	no	—
421	C₂×C₄×C₂₃	—	2	1	no	—
422	C₂×C₄×C₂₃	—	2	1	no	—
423	C₂×C₄×C₂₃	—	2	1	no	—
424	C₂×C₄×C₂₃	—	2	8	no	—
425	C₂×C₄×C₂₃	—	2	2	no	—
426	C₂×C₄×C₂₃	—	2	2	no	—
427	C₂×C₄×C₂₃	—	2	2	no	—
428	C₂×C₄×C₂₃	—	2	2	no	—
429	C₂×C₄×C₂₃	—	2	2	no	—
430	C₂×C₄×C₂₃	—	2	2	no	—
431	C₂×C₄×C₂₃	—	2	2	no	—
432	C₂×C₄×C₂₃	—	2	1	no	—
433	C₂×C₄×C₂₃	—	2	2	no	—
434	C₂×C₄×C₂₃	—	2	2	no	—
435	C₂×C₄×C₂₃	—	2	1	no	—
436	C₂×C₄×C₂₃	—	2	1	no	—
437	C₂×C₄×C₂₃	—	2	2	no	—
438	C₂×C₄×C₂₃	—	2	2	no	—
439	C₂×C₄×C₂₃	—	2	2	no	—
440	C₂×C₄×C₂₃	—	2	2	no	—
441	C₂×C₄×C₂₃	—	2	1	no	—
442	C₂×C₄×C₂₃	—	2	1	no	—
443	C₂×C₄×C₂₃	—	2	2	no	—
444	C₂×C₄×C₂₃	—	2	2	no	—
445	C₂×C₄×C₂₃	—	2	2	no	—
446	C₂×C₄×C₂₃	—	2	1	no	—
447	C₂×C₄×C₂₃	—	2	2	no	—
448	C₂×C₄×C₂₃	—	2	2	no	—
449	C₂×C₄×C₂₃	—	2	1	no	—
450	C₂×C₄×C₂₃	—	2	1	no	—
451	C₂×C₄×C₂₃	—	2	1	no	—
452	C₂×C₄×C₂₃	—	2	2	no	—
453	C₂×C₄×C₂₃	—	2	2	no	—
454	C₂×C₄×C₂₃	—	2	2	no	—
455	C₂×C₄×C₂₃	—	4	4	no	—
456	C₂×C₄×C₂₃	—	4	4	no	—
457	C₂×C₄×C₂₃	—	4	4	no	—
458	C₂×C₄×C₂₃	—	4	4	no	—
459	C₂×C₄×C₂₃	—	4	8	no	—
460	C₂×C₄×C₂₃	—	4	4	no	—
461	C₂×C₄×C₂₃	—	8	4	no	—
462	C₂×C₄×C₂₃	—	8	4	no	—
463	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
464	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
465	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
466	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
467	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
468	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
469	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
470	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
471	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
472	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
473	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
474	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
475	C₂×#539	C₂×C₂₃	1	2	yes	complemented
476	#2860	C₂×C₂₃	1	1	yes	characteristic, complemented
477	#2859	C₂×C₂₃	1	1	yes	characteristic, complemented
478	#2857	C₂×C₂₃	1	1	yes	characteristic, complemented
479	#2854	C₂×C₂₃	1	1	yes	characteristic, complemented
480	#2664	C₂×C₂₃	1	2	yes	complemented
481	#2663	C₂×C₂₃	1	2	yes	complemented
482	#2556	C₂×C₂₃	1	2	yes	complemented
483	#2553	C₂×C₂₃	1	2	yes	complemented
484	#2506	C₂×C₂₃	1	1	yes	characteristic, complemented
485	#2501	C₂×C₂₃	1	1	yes	characteristic, complemented
486	#2496	C₂×C₂₃	1	1	yes	characteristic, complemented
487	#2488	C₂×C₂₃	1	2	yes	complemented
488	#2486	C₂×C₂₃	1	1	yes	characteristic, complemented
489	#2452	C₂×C₂₃	1	1	yes	characteristic, complemented
490	#2440	C₂×C₂₃	1	1	yes	characteristic, complemented
491	#2425	C₂×C₂₃	1	2	yes	complemented
492	#2422	C₂×C₂₃	1	1	yes	characteristic, complemented
493	#2416	C₂×C₂₃	1	1	yes	characteristic
494	#2322	C₂×C₂₃	1	2	yes	complemented
495	C₄×#121	C₂×C₂₃	1	1	yes	characteristic, complemented
496	C₂×#389	C₂×C₂₃	1	1	yes	characteristic, complemented
497	C₄²×D₄	C₂×C₂₃	1	1	yes	characteristic, complemented
498	C₂²×C₂₃	—	2	2	no	—
499	C₂²×C₂₃	—	2	2	no	—
500	C₂²×C₂₃	—	2	2	no	—
501	C₂²×C₂₃	—	2	2	no	—
502	C₂²×C₂₃	—	2	2	no	—
503	C₂²×C₂₃	—	2	2	no	—
504	C₂²×C₂₃	—	2	2	no	—
505	C₂²×C₂₃	—	2	2	no	—
506	C₂²×C₂₃	—	2	2	no	—
507	C₂²×C₂₃	—	4	1	no	—
508	C₂²×C₂₃	—	4	1	no	—
509	C₂²×C₂₃	—	4	1	no	—
510	C₂²×C₂₃	—	4	1	no	—
511	C₂²×C₂₃	—	4	2	no	—
512	C₂²×C₂₃	—	4	2	no	—
513	C₂²×C₂₃	—	4	2	no	—
514	C₂²×C₂₃	—	4	2	no	—
515	C₂²×C₂₃	—	4	2	no	—
516	C₂²×C₂₃	—	4	2	no	—
517	C₂²×C₂₃	—	4	2	no	—
518	C₂²×C₂₃	#532	1	4	yes	—
519	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
520	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
521	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
522	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
523	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
524	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
525	C₂²×C₂₃	#585	1	1	yes	characteristic
526	C₄×C₂₃	—	2	2	no	—
527	C₄×C₂₃	—	2	2	no	—
528	C₄×C₂₃	—	2	2	no	—
529	C₄×C₂₃	—	2	2	no	—
530	C₄×C₂₃	—	2	2	no	—
531	C₄×C₂₃	—	2	2	no	—
532	C₄×C₂₃	—	2	2	no	—
533	C₄×C₂₃	—	2	2	no	—
534	C₄×C₂₃	—	2	2	no	—
535	C₄×C₂₃	—	4	2	no	—
536	C₄×C₂₃	—	4	2	no	—
537	C₄×C₂₃	—	4	2	no	—
538	C₄×C₂₃	—	4	1	no	—
539	C₄×C₂₃	—	4	1	no	—
540	C₄×C₂₃	—	4	2	no	—
541	C₄×C₂₃	—	4	2	no	—
542	C₄×C₂₃	—	4	2	no	—
543	C₄×C₂₃	—	4	2	no	—
544	C₄×C₂₃	—	4	1	no	—
545	C₄×C₂₃	#539	1	4	yes	complemented
546	#539	—	2	16	no	—
547	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
548	C₂×#126	C₂²×C₂₃	1	2	yes	—
549	C₂×#126	C₂²×C₂₃	1	2	yes	—
550	C₂×#125	C₂²×C₂₃	1	2	yes	—
551	C₂×#125	C₂²×C₂₃	1	2	yes	—
552	C₂×#123	C₂²×C₂₃	1	2	yes	—
553	C₂×#123	C₂²×C₂₃	1	2	yes	—
554	C₂×#123	C₂²×C₂₃	1	2	yes	—
555	C₂×#123	C₂²×C₂₃	1	2	yes	—
556	C₂×#123	C₂²×C₂₃	1	2	yes	—
557	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
558	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
559	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
560	C₂×#121	C₂²×C₂₃	1	2	yes	—
561	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
562	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
563	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
564	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
565	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
566	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
567	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
568	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
569	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
570	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
571	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
572	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
573	#400	C₂²×C₂₃	1	2	yes	—
574	#400	C₂²×C₂₃	1	2	yes	—
575	#399	C₂²×C₂₃	1	2	yes	—
576	#399	C₂²×C₂₃	1	2	yes	—
577	#398	C₂²×C₂₃	1	2	yes	—
578	#398	C₂²×C₂₃	1	2	yes	—
579	#398	C₂²×C₂₃	1	2	yes	—
580	#397	C₂²×C₂₃	1	2	yes	—
581	#397	C₂²×C₂₃	1	2	yes	—
582	#397	C₂²×C₂₃	1	2	yes	—
583	#396	C₂²×C₂₃	1	2	yes	—
584	#396	C₂²×C₂₃	1	2	yes	—
585	#395	C₂²×C₂₃	1	2	yes	—
586	#394	C₂²×C₂₃	1	2	yes	—
587	#394	C₂²×C₂₃	1	2	yes	—
588	#393	C₂²×C₂₃	1	2	yes	—
589	#391	C₂²×C₂₃	1	2	yes	—
590	#390	C₂²×C₂₃	1	1	yes	characteristic
591	#390	C₂²×C₂₃	1	1	yes	characteristic
592	#390	C₂²×C₂₃	1	1	yes	characteristic
593	#390	C₂²×C₂₃	1	1	yes	characteristic
594	#389	C₂²×C₂₃	1	2	yes	—
595	#389	C₂²×C₂₃	1	2	yes	—
596	#389	C₂²×C₂₃	1	1	yes	characteristic
597	#389	C₂²×C₂₃	1	1	yes	characteristic
598	#389	C₂²×C₂₃	1	1	yes	characteristic
599	#389	C₂²×C₂₃	1	1	yes	characteristic
600	#389	C₂²×C₂₃	1	1	yes	characteristic
601	#389	C₂²×C₂₃	1	2	yes	—
602	#389	C₂²×C₂₃	1	1	yes	characteristic
603	#389	C₂²×C₂₃	1	1	yes	characteristic
604	#389	C₂²×C₂₃	1	1	yes	characteristic
605	#389	C₂²×C₂₃	1	2	yes	—
606	#389	C₂²×C₂₃	1	1	yes	characteristic
607	#389	C₂²×C₂₃	1	1	yes	characteristic
608	#389	C₂²×C₂₃	1	2	yes	—
609	#388	C₂²×C₂₃	1	2	yes	—
610	#388	C₂²×C₂₃	1	2	yes	—
611	#388	C₂²×C₂₃	1	2	yes	—
612	#388	C₂²×C₂₃	1	2	yes	—
613	#388	C₂²×C₂₃	1	2	yes	—
614	#388	C₂²×C₂₃	1	2	yes	—
615	#387	C₂²×C₂₃	1	2	yes	—
616	#387	C₂²×C₂₃	1	2	yes	—
617	#386	C₂²×C₂₃	1	2	yes	—
618	#386	C₂²×C₂₃	1	2	yes	—
619	#386	C₂²×C₂₃	1	2	yes	—
620	#385	C₂²×C₂₃	1	2	yes	—
621	#385	C₂²×C₂₃	1	2	yes	—
622	#385	C₂²×C₂₃	1	2	yes	—
623	#384	C₂²×C₂₃	1	1	yes	characteristic
624	#384	C₂²×C₂₃	1	1	yes	characteristic
625	#384	C₂²×C₂₃	1	1	yes	characteristic
626	#382	C₂²×C₂₃	1	2	yes	—
627	#381	C₂²×C₂₃	1	2	yes	—
628	#380	C₂²×C₂₃	1	1	yes	characteristic
629	#380	C₂²×C₂₃	1	1	yes	characteristic
630	#380	C₂²×C₂₃	1	1	yes	characteristic
631	#380	C₂²×C₂₃	1	2	yes	—
632	#380	C₂²×C₂₃	1	1	yes	characteristic
633	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
634	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
635	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
636	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
637	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
638	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
639	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
640	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
641	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
642	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
643	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
644	C₂×#95	C₂²×C₂₃	1	2	yes	—
645	C₄³	C₂²×C₂₃	1	1	yes	characteristic
646	C₂×C₂₃	—	2	4	no	—
647	C₂×C₂₃	—	4	2	no	—
648	C₂×C₂₃	—	8	2	no	—
649	C₂×C₂₃	C₂×#532	1	1	yes	characteristic
650	C₂×C₂₃	C₂×#539	1	1	yes	characteristic
651	C₂×C₂₃	#3461	1	1	yes	characteristic
652	C₂×C₂₃	#3496	1	1	yes	characteristic
653	C₂×C₂₃	#3499	1	1	yes	characteristic
654	C₂×C₂₃	#3515	1	1	yes	characteristic
655	C₂×C₂₃	#3520	1	1	yes	characteristic
656	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
657	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
658	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
659	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
660	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
661	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
662	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
663	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
664	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
665	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
666	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
667	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
668	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
669	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
670	C₄⋊Q₈	—	4	2	no	—
671	#126	—	2	8	no	—
672	#126	—	2	8	no	—
673	#125	—	2	8	no	—
674	#125	—	2	8	no	—
675	#123	—	2	8	no	—
676	#123	—	2	8	no	—
677	#123	—	2	8	no	—
678	#123	—	2	8	no	—
679	#123	—	2	8	no	—
680	C₂²⋊Q₈	—	2	8	no	—
681	C₂²⋊Q₈	—	2	8	no	—
682	C₂²⋊Q₈	—	2	8	no	—
683	#121	—	2	8	no	—
684	#121	—	2	4	no	—
685	#121	—	4	2	no	—
686	C₄×D₄	—	2	8	no	—
687	C₄×D₄	—	2	4	no	—
688	C₄×D₄	—	2	4	no	—
689	C₄×D₄	—	4	2	no	—
690	C₄×D₄	D₄×C₂₃	1	8	yes	complemented
691	C₂×C₄⋊C₄	—	2	8	no	—
692	C₂×C₄⋊C₄	—	2	4	no	—
693	C₂×C₄⋊C₄	—	4	2	no	—
694	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
696	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
697	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
698	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
700	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
701	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
702	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
703	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
704	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
705	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
706	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
707	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
708	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
709	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
710	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
711	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
712	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
713	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
714	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
715	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
716	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
717	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
718	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
719	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
720	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
721	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
722	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
723	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
724	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
725	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
726	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
727	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
728	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
729	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
730	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
731	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
732	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
733	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
734	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
735	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
736	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
737	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
738	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
739	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
740	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
741	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
742	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
743	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
744	C₂×C₄²	—	4	2	no	—
745	C₂×C₄²	—	4	2	no	—
746	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
747	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
748	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
749	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
750	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
751	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
752	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
753	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
754	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
755	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
756	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
757	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
758	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
759	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
760	#95	C₂³×C₂₃	1	2	yes	—
761	#95	C₂³×C₂₃	1	2	yes	—
762	#95	C₂³×C₂₃	1	2	yes	—
763	#95	C₂³×C₂₃	1	2	yes	—
764	#95	C₂³×C₂₃	1	1	yes	characteristic
765	#95	C₂³×C₂₃	1	1	yes	characteristic
766	#95	C₂³×C₂₃	1	1	yes	characteristic
767	#95	C₂³×C₂₃	1	1	yes	characteristic
768	#95	C₂³×C₂₃	1	1	yes	characteristic
769	#95	C₂³×C₂₃	1	1	yes	characteristic
770	#95	C₂³×C₂₃	1	2	yes	—
771	#95	C₂³×C₂₃	1	2	yes	—
772	#95	C₂³×C₂₃	1	2	yes	—
773	#95	C₂³×C₂₃	1	2	yes	—
774	#95	C₂³×C₂₃	1	2	yes	—
775	#95	C₂³×C₂₃	1	2	yes	—
776	#95	C₂³×C₂₃	1	2	yes	—
777	#95	C₂³×C₂₃	1	2	yes	—
778	#95	C₂³×C₂₃	1	2	yes	—
779	#95	C₂³×C₂₃	1	2	yes	—
780	#95	C₂³×C₂₃	1	2	yes	—
781	C₂₃	#35008	1	1	yes	characteristic, direct product factor, Sylow
782	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
783	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
784	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
785	C₂×Q₈	—	2	4	no	—
786	C₂×Q₈	—	4	2	no	—
787	C₂×Q₈	—	4	2	no	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	2	4	no	—
791	C₂×D₄	—	2	4	no	—
792	C₂×D₄	—	2	4	no	—
793	C₂×D₄	—	2	4	no	—
794	C₂×D₄	—	2	2	no	—
795	C₂×D₄	—	2	2	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	4	2	no	—
798	C₂×D₄	—	4	2	no	—
799	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
800	C₂²×C₄	—	2	2	no	—
801	C₂²×C₄	—	2	2	no	—
802	C₂²×C₄	—	2	4	no	—
803	C₂²×C₄	—	2	4	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	4	no	—
806	C₂²×C₄	—	2	4	no	—
807	C₂²×C₄	—	2	2	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	2	no	—
810	C₂²×C₄	—	2	2	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	2	2	no	—
813	C₂²×C₄	—	2	4	no	—
814	C₂²×C₄	—	4	1	no	—
815	C₂²×C₄	—	4	1	no	—
816	C₂²×C₄	—	4	1	no	—
817	C₂²×C₄	—	4	1	no	—
818	C₂²×C₄	—	4	1	no	—
819	C₂²×C₄	—	4	1	no	—
820	C₂²×C₄	—	4	2	no	—
821	C₂²×C₄	—	4	2	no	—
822	C₂²×C₄	—	4	2	no	—
823	C₂²×C₄	—	4	2	no	—
824	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
825	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
826	C₂²×C₄	#41×C₂₃	1	4	yes	—
827	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
828	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
829	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
830	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
831	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
832	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
833	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
834	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
835	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
836	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
840	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
843	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
846	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
847	C₄⋊C₄	—	2	4	no	—
848	C₄⋊C₄	—	2	4	no	—
849	C₄⋊C₄	—	2	4	no	—
850	C₄⋊C₄	—	2	4	no	—
851	C₄⋊C₄	—	2	4	no	—
852	C₄⋊C₄	—	2	4	no	—
853	C₄⋊C₄	—	2	4	no	—
854	C₄⋊C₄	—	2	4	no	—
855	C₄⋊C₄	—	2	4	no	—
856	C₄⋊C₄	—	2	4	no	—
857	C₄⋊C₄	—	2	4	no	—
858	C₄⋊C₄	—	2	4	no	—
859	C₄⋊C₄	—	2	4	no	—
860	C₄⋊C₄	—	2	4	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	4	no	—
867	C₄⋊C₄	—	2	4	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	2	no	—
870	C₄⋊C₄	—	2	2	no	—
871	C₄⋊C₄	—	2	2	no	—
872	C₄⋊C₄	—	4	2	no	—
873	C₄⋊C₄	—	4	2	no	—
874	C₄⋊C₄	—	4	2	no	—
875	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
876	C₂²⋊C₄	—	2	4	no	—
877	C₂²⋊C₄	—	2	4	no	—
878	C₂²⋊C₄	—	2	4	no	—
879	C₂²⋊C₄	—	2	4	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	4	no	—
882	C₂²⋊C₄	—	2	4	no	—
883	C₂²⋊C₄	—	2	4	no	—
884	C₂²⋊C₄	—	2	4	no	—
885	C₂²⋊C₄	—	2	2	no	—
886	C₂²⋊C₄	—	2	2	no	—
887	C₂²⋊C₄	—	2	4	no	—
888	C₂²⋊C₄	—	2	4	no	—
889	C₂²⋊C₄	—	2	4	no	—
890	C₂²⋊C₄	—	2	4	no	—
891	C₂²⋊C₄	—	4	2	no	—
892	C₂²⋊C₄	—	4	2	no	—
893	C₂²⋊C₄	—	4	2	no	—
894	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
895	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
896	C₂²⋊C₄	#41×C₂₃	1	4	yes	—
897	C₄²	—	2	4	no	—
898	C₄²	—	2	2	no	—
899	C₄²	—	2	2	no	—
900	C₄²	—	2	2	no	—
901	C₄²	—	2	2	no	—
902	C₄²	—	2	2	no	—
903	C₄²	—	2	2	no	—
904	C₄²	—	2	2	no	—
905	C₄²	—	4	1	no	—
906	C₄²	—	4	1	no	—
907	C₄²	—	4	1	no	—
908	C₄²	—	4	1	no	—
909	C₄²	—	4	1	no	—
910	C₄²	C₂×D₄×C₂₃	1	4	yes	—
911	C₂³	—	2	1	no	—
912	C₂³	—	2	1	no	—
913	C₂³	—	2	1	no	—
914	C₂³	—	2	1	no	—
915	C₂³	—	2	1	no	—
916	C₂³	—	2	1	no	—
917	C₂³	—	2	1	no	—
918	C₂³	—	2	1	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	2	1	no	—
921	C₂³	—	2	2	no	—
922	C₂³	—	2	2	no	—
923	C₂³	—	2	2	no	—
924	C₂³	—	2	2	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	2	no	—
927	C₂³	—	2	2	no	—
928	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
929	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
930	C₂³	C₂×#41×C₂₃	1	2	yes	—
931	C₂³	C₂×#41×C₂₃	1	2	yes	—
932	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
933	Q₈	—	8	4	no	—
934	D₄	—	2	8	no	—
935	D₄	—	4	8	no	—
936	D₄	—	4	4	no	—
937	D₄	—	8	4	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	1	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	1	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	1	no	—
946	C₂×C₄	—	2	1	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	1	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	1	no	—
954	C₂×C₄	—	2	1	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	8	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	2	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	2	no	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	2	no	—
964	C₂×C₄	—	2	1	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	1	no	—
968	C₂×C₄	—	2	1	no	—
969	C₂×C₄	—	2	2	no	—
970	C₂×C₄	—	2	2	no	—
971	C₂×C₄	—	2	2	no	—
972	C₂×C₄	—	2	2	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	2	no	—
985	C₂×C₄	—	2	2	no	—
986	C₂×C₄	—	2	2	no	—
987	C₂×C₄	—	4	4	no	—
988	C₂×C₄	—	4	4	no	—
989	C₂×C₄	—	4	4	no	—
990	C₂×C₄	—	4	4	no	—
991	C₂×C₄	—	4	8	no	—
992	C₂×C₄	—	4	4	no	—
993	C₂×C₄	—	8	4	no	—
994	C₂×C₄	—	8	4	no	—
995	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
996	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
997	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
998	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
999	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
1000	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1001	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1002	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1003	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
1004	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
1005	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
1006	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	2	no	—
1009	C₂²	—	2	2	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	2	no	—
1012	C₂²	—	2	2	no	—
1013	C₂²	—	2	2	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	4	1	no	—
1017	C₂²	—	4	1	no	—
1018	C₂²	—	4	1	no	—
1019	C₂²	—	4	1	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	4	2	no	—
1022	C₂²	—	4	2	no	—
1023	C₂²	—	4	2	no	—
1024	C₂²	—	4	2	no	—
1025	C₂²	—	4	2	no	—
1026	C₂²	—	4	2	no	—
1027	C₂²	C₂₃×#532	1	4	yes	—
1028	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
1029	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1030	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
1031	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1032	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1033	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1034	C₂²	C₂₃×#585	1	1	yes	characteristic
1035	C₄	—	2	2	no	—
1036	C₄	—	2	2	no	—
1037	C₄	—	2	2	no	—
1038	C₄	—	2	2	no	—
1039	C₄	—	2	2	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	2	2	no	—
1044	C₄	—	4	2	no	—
1045	C₄	—	4	2	no	—
1046	C₄	—	4	2	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	1	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	2	no	—
1051	C₄	—	4	2	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	1	no	—
1054	C₄	C₂₃×#539	1	4	yes	complemented
1055	C₂	—	2	4	no	—
1056	C₂	—	4	2	no	—
1057	C₂	—	8	2	no	—
1058	C₂	C₂×C₂₃×#532	1	1	yes	characteristic
1059	C₂	C₂×C₂₃×#539	1	1	yes	characteristic
1060	C₂	C₂₃×#3461	1	1	yes	characteristic
1061	C₂	C₂₃×#3496	1	1	yes	characteristic
1062	C₂	C₂₃×#3499	1	1	yes	characteristic
1063	C₂	C₂₃×#3515	1	1	yes	characteristic
1064	C₂	C₂₃×#3520	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂₃×#2416	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#539	C₂	semidirect
2. C₂₃×#2860	C₂	semidirect
3. C₂₃×#2859	C₂	semidirect
4. C₂₃×#2857	C₂	semidirect
5. C₂₃×#2854	C₂	semidirect
6. C₂₃×#2664	C₂	semidirect
7. C₂₃×#2663	C₂	semidirect
8. C₂₃×#2556	C₂	semidirect
9. C₂₃×#2553	C₂	semidirect
10. C₂₃×#2506	C₂	semidirect
11. C₂₃×#2501	C₂	semidirect
12. C₂₃×#2496	C₂	semidirect
13. C₂₃×#2488	C₂	semidirect
14. C₂₃×#2486	C₂	semidirect
15. C₂₃×#2452	C₂	semidirect
16. C₂₃×#2440	C₂	semidirect
17. C₂₃×#2425	C₂	semidirect
18. C₂₃×#2422	C₂	semidirect
20. C₂₃×#2322	C₂	semidirect
21. C₄×C₂₃×#121	C₂	semidirect
22. C₂×C₂₃×#389	C₂	semidirect
23. C₄²×D₄×C₂₃	C₂	semidirect
158. C₄×D₄×C₂₃	D₄	semidirect
378. #35008	C₂₃	direct (N × H)
475. C₂×#539	C₂×C₂₃	semidirect
476. #2860	C₂×C₂₃	semidirect
477. #2859	C₂×C₂₃	semidirect
478. #2857	C₂×C₂₃	semidirect
479. #2854	C₂×C₂₃	semidirect
480. #2664	C₂×C₂₃	semidirect
481. #2663	C₂×C₂₃	semidirect
482. #2556	C₂×C₂₃	semidirect
483. #2553	C₂×C₂₃	semidirect
484. #2506	C₂×C₂₃	semidirect
485. #2501	C₂×C₂₃	semidirect
486. #2496	C₂×C₂₃	semidirect
487. #2488	C₂×C₂₃	semidirect
488. #2486	C₂×C₂₃	semidirect
489. #2452	C₂×C₂₃	semidirect
490. #2440	C₂×C₂₃	semidirect
491. #2425	C₂×C₂₃	semidirect
492. #2422	C₂×C₂₃	semidirect
494. #2322	C₂×C₂₃	semidirect
495. C₄×#121	C₂×C₂₃	semidirect
496. C₂×#389	C₂×C₂₃	semidirect
497. C₄²×D₄	C₂×C₂₃	semidirect
545. C₄×C₂₃	#539	semidirect
690. C₄×D₄	D₄×C₂₃	semidirect
781. C₂₃	#35008	direct (N × H)
1054. C₄	C₂₃×#539	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#539	2
C₂₃×#2860	2
C₂₃×#2859	2
C₂₃×#2857	2
C₂₃×#2854	2
C₂₃×#2664	2
C₂₃×#2663	2
C₂₃×#2556	2
C₂₃×#2553	2
C₂₃×#2506	2
C₂₃×#2501	2
C₂₃×#2496	2
C₂₃×#2488	2
C₂₃×#2486	2
C₂₃×#2452	2
C₂₃×#2440	2
C₂₃×#2425	2
C₂₃×#2422	2
C₂₃×#2416	2
C₂₃×#2322	2
C₄×C₂₃×#121	2
C₂×C₂₃×#389	2
C₄²×D₄×C₂₃	2
#35008	23

Subgroups — C23×#35008 #19182634

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#35008 #19182634