Subgroups — C₂₃×#34466 #19182092

Order 5888.

2240 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#553	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2377	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2376	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2373	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2363	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2354	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2352	C₂	1	2	yes	maximal, complemented
10	D₄×C₄⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2346	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2344	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2334	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2330	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2324	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2324	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2322	C₂	1	2	yes	maximal, complemented
18	C₂₃×#2319	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂₃×#2319	C₂	1	2	yes	maximal, complemented
20	C₂₃×#2316	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂₃×#2290	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂₃×#553	C₄	1	16	yes	complemented
25	C₂×C₂₃×#126	C₂²	1	2	yes	—
26	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#123	C₂²	1	2	yes	—
28	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#121	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
37	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#117	C₂²	1	2	yes	—
41	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
42	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
43	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
45	C₂₃×#390	C₂²	1	1	yes	characteristic
46	C₂₃×#390	C₂²	1	2	yes	—
47	C₂₃×#390	C₂²	1	1	yes	characteristic
48	C₂₃×#390	C₂²	1	2	yes	—
49	C₂₃×#390	C₂²	1	2	yes	—
50	C₂₃×#390	C₂²	1	2	yes	—
51	C₂₃×#389	C₂²	1	1	yes	characteristic
52	C₂₃×#389	C₂²	1	1	yes	characteristic
53	C₂₃×#389	C₂²	1	1	yes	characteristic
54	C₂₃×#389	C₂²	1	1	yes	characteristic
55	C₂₃×#389	C₂²	1	1	yes	characteristic
56	C₂₃×#389	C₂²	1	2	yes	—
57	C₂₃×#389	C₂²	1	1	yes	characteristic
58	C₂₃×#389	C₂²	1	1	yes	characteristic
59	C₂₃×#389	C₂²	1	2	yes	—
60	C₂₃×#389	C₂²	1	2	yes	—
61	C₂₃×#389	C₂²	1	1	yes	characteristic
62	C₂₃×#389	C₂²	1	2	yes	—
63	C₂₃×#389	C₂²	1	2	yes	—
64	C₂₃×#388	C₂²	1	1	yes	characteristic
65	C₂₃×#388	C₂²	1	1	yes	characteristic
66	C₂₃×#388	C₂²	1	2	yes	—
67	C₂₃×#388	C₂²	1	2	yes	—
68	C₂₃×#388	C₂²	1	2	yes	—
69	C₂₃×#388	C₂²	1	2	yes	—
70	C₂₃×#388	C₂²	1	2	yes	—
71	C₂₃×#388	C₂²	1	2	yes	—
72	C₂₃×#388	C₂²	1	2	yes	—
73	C₂₃×#388	C₂²	1	2	yes	—
74	C₂₃×#388	C₂²	1	2	yes	—
75	C₂₃×#388	C₂²	1	2	yes	—
76	C₂₃×#387	C₂²	1	1	yes	characteristic
77	C₂₃×#387	C₂²	1	1	yes	characteristic
78	C₂₃×#387	C₂²	1	2	yes	—
79	C₂₃×#387	C₂²	1	2	yes	—
80	C₂₃×#387	C₂²	1	2	yes	—
81	C₂₃×#387	C₂²	1	2	yes	—
82	C₂₃×#387	C₂²	1	2	yes	—
83	C₂₃×#387	C₂²	1	2	yes	—
84	C₂₃×#386	C₂²	1	1	yes	characteristic
85	C₂₃×#386	C₂²	1	1	yes	characteristic
86	C₂₃×#386	C₂²	1	2	yes	—
87	C₂₃×#386	C₂²	1	2	yes	—
88	C₂₃×#386	C₂²	1	2	yes	—
89	C₂₃×#386	C₂²	1	2	yes	—
90	C₂₃×#385	C₂²	1	1	yes	characteristic
91	C₂₃×#385	C₂²	1	1	yes	characteristic
92	C₂₃×#385	C₂²	1	2	yes	—
93	C₂₃×#385	C₂²	1	2	yes	—
94	C₂₃×#385	C₂²	1	2	yes	—
95	C₂₃×#385	C₂²	1	2	yes	—
96	C₂₃×#385	C₂²	1	2	yes	—
97	C₂₃×#384	C₂²	1	1	yes	characteristic
98	C₂₃×#382	C₂²	1	2	yes	—
99	C₂₃×#381	C₂²	1	2	yes	—
100	C₂₃×#381	C₂²	1	2	yes	—
101	C₂₃×#380	C₂²	1	1	yes	characteristic
102	C₂₃×#380	C₂²	1	2	yes	—
103	C₂₃×#380	C₂²	1	2	yes	—
104	C₂₃×#380	C₂²	1	2	yes	—
105	C₂₃×#380	C₂²	1	2	yes	—
106	C₂₃×#380	C₂²	1	1	yes	characteristic
107	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
108	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
109	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
110	C₄×C₄⋊C₄×C₂₃	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	2	yes	—
114	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
115	C₄×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
116	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
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	2	yes	—
120	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
122	C₂₃×#376	C₂²	1	1	yes	characteristic
123	C₂₃×#376	C₂²	1	2	yes	—
124	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
127	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
128	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
131	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
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×#126	C₂×C₄	1	16	yes	complemented
137	C₂₃×#125	C₂×C₄	1	8	yes	complemented
138	C₂₃×#123	C₂×C₄	1	16	yes	complemented
139	C₂₃×#121	C₂×C₄	1	8	yes	—
140	C₂₃×#121	C₂×C₄	1	16	yes	complemented
141	C₂₃×#121	C₂×C₄	1	8	yes	complemented
142	C₄×D₄×C₂₃	—	4	2	no	—
143	C₄×D₄×C₂₃	—	4	2	no	—
144	C₄×D₄×C₂₃	—	4	4	no	—
145	C₄×D₄×C₂₃	C₂×C₄	1	16	yes	complemented
146	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	complemented
147	C₄×D₄×C₂₃	C₂×C₄	1	8	yes	complemented
148	C₂₃×#117	—	4	2	no	—
149	C₂₃×#117	—	4	4	no	—
150	C₂₃×#117	—	4	2	no	—
151	C₂₃×#117	—	4	2	no	—
152	C₂₃×#117	C₂×C₄	1	8	yes	complemented
153	C₂×C₄⋊C₄×C₂₃	—	4	4	no	—
154	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	8	yes	complemented
155	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
158	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
160	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
166	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
167	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
168	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
169	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
170	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
171	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
173	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
180	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
181	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
182	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
184	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
187	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
188	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
193	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
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	1	yes	characteristic
201	C₂×C₂²⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₂₃	—	4	2	no	—
203	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
206	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
209	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
210	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
211	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
212	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
213	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
214	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
215	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
217	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
218	C₂₃×#95	C₂³	1	1	yes	characteristic
219	C₂₃×#95	C₂³	1	2	yes	—
220	C₂₃×#95	C₂³	1	1	yes	characteristic
221	C₂₃×#95	C₂³	1	2	yes	—
222	C₂₃×#95	C₂³	1	1	yes	characteristic
223	C₂₃×#95	C₂³	1	2	yes	—
224	C₂₃×#95	C₂³	1	1	yes	characteristic
225	C₂₃×#95	C₂³	1	1	yes	characteristic
226	C₂₃×#95	C₂³	1	1	yes	characteristic
227	C₂₃×#95	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	1	yes	characteristic
232	C₂₃×#95	C₂³	1	1	yes	characteristic
233	C₂₃×#95	C₂³	1	2	yes	—
234	C₂₃×#95	C₂³	1	2	yes	—
235	C₂₃×#95	C₂³	1	2	yes	—
236	C₂₃×#95	C₂³	1	2	yes	—
237	C₂₃×#95	C₂³	1	2	yes	—
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	1	yes	characteristic
242	C₂₃×#95	C₂³	1	2	yes	—
243	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
244	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
245	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
246	C₂×D₄×C₂₃	—	2	2	no	—
247	C₂×D₄×C₂₃	—	2	2	no	—
248	C₂×D₄×C₂₃	—	4	2	no	—
249	C₂×D₄×C₂₃	—	4	1	no	—
250	C₂×D₄×C₂₃	—	4	2	no	—
251	C₂×D₄×C₂₃	—	4	2	no	—
252	C₂×D₄×C₂₃	—	4	1	no	—
253	C₂×D₄×C₂₃	—	4	2	no	—
254	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
255	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
256	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
257	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
258	C₂²×C₄×C₂₃	—	2	2	no	—
259	C₂²×C₄×C₂₃	—	2	2	no	—
260	C₂²×C₄×C₂₃	—	2	2	no	—
261	C₂²×C₄×C₂₃	—	2	2	no	—
262	C₂²×C₄×C₂₃	—	2	2	no	—
263	C₂²×C₄×C₂₃	—	2	4	no	—
264	C₂²×C₄×C₂₃	—	4	1	no	—
265	C₂²×C₄×C₂₃	—	4	1	no	—
266	C₂²×C₄×C₂₃	—	4	2	no	—
267	C₂²×C₄×C₂₃	—	4	2	no	—
268	C₂²×C₄×C₂₃	—	4	2	no	—
269	C₂²×C₄×C₂₃	—	4	2	no	—
270	C₂²×C₄×C₂₃	—	4	1	no	—
271	C₂²×C₄×C₂₃	—	4	1	no	—
272	C₂²×C₄×C₂₃	—	4	1	no	—
273	C₂²×C₄×C₂₃	—	4	2	no	—
274	C₂²×C₄×C₂₃	—	4	2	no	—
275	C₂²×C₄×C₂₃	—	4	2	no	—
276	C₂²×C₄×C₂₃	—	4	2	no	—
277	C₂²×C₄×C₂₃	—	4	2	no	—
278	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
279	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
280	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
281	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
282	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
285	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
286	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
295	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
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	1	yes	characteristic
300	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
301	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
302	C₄⋊C₄×C₂₃	—	2	2	no	—
303	C₄⋊C₄×C₂₃	—	2	4	no	—
304	C₄⋊C₄×C₂₃	—	2	2	no	—
305	C₄⋊C₄×C₂₃	—	2	2	no	—
306	C₄⋊C₄×C₂₃	—	2	2	no	—
307	C₄⋊C₄×C₂₃	—	2	2	no	—
308	C₄⋊C₄×C₂₃	—	4	2	no	—
309	C₄⋊C₄×C₂₃	—	4	2	no	—
310	C₄⋊C₄×C₂₃	—	4	2	no	—
311	C₄⋊C₄×C₂₃	—	4	2	no	—
312	C₄⋊C₄×C₂₃	—	4	2	no	—
313	C₄⋊C₄×C₂₃	—	4	2	no	—
314	C₄⋊C₄×C₂₃	—	4	1	no	—
315	C₄⋊C₄×C₂₃	—	4	2	no	—
316	C₄⋊C₄×C₂₃	—	4	1	no	—
317	C₄⋊C₄×C₂₃	—	4	1	no	—
318	C₄⋊C₄×C₂₃	—	4	2	no	—
319	C₄⋊C₄×C₂₃	—	4	2	no	—
320	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
321	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
322	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
323	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
324	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
325	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
326	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
327	C₂²⋊C₄×C₂₃	—	2	2	no	—
328	C₂²⋊C₄×C₂₃	—	4	1	no	—
329	C₂²⋊C₄×C₂₃	—	4	2	no	—
330	C₂²⋊C₄×C₂₃	—	4	1	no	—
331	C₂²⋊C₄×C₂₃	—	4	2	no	—
332	C₂²⋊C₄×C₂₃	—	4	2	no	—
333	C₂²⋊C₄×C₂₃	—	4	1	no	—
334	C₂²⋊C₄×C₂₃	—	4	1	no	—
335	C₂²⋊C₄×C₂₃	—	4	1	no	—
336	C₂²⋊C₄×C₂₃	—	4	2	no	—
337	C₂²⋊C₄×C₂₃	—	4	2	no	—
338	C₂²⋊C₄×C₂₃	—	4	2	no	—
339	C₂²⋊C₄×C₂₃	—	4	2	no	—
340	C₂²⋊C₄×C₂₃	—	4	2	no	—
341	C₂²⋊C₄×C₂₃	—	4	2	no	—
342	C₂²⋊C₄×C₂₃	—	4	2	no	—
343	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
344	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
345	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
346	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
347	C₂²⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
348	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
349	C₄²×C₂₃	—	2	2	no	—
350	C₄²×C₂₃	—	2	2	no	—
351	C₄²×C₂₃	—	2	4	no	—
352	C₄²×C₂₃	—	2	2	no	—
353	C₄²×C₂₃	—	2	2	no	—
354	C₄²×C₂₃	—	4	1	no	—
355	C₄²×C₂₃	—	4	1	no	—
356	C₄²×C₂₃	—	4	2	no	—
357	C₄²×C₂₃	—	4	2	no	—
358	C₄²×C₂₃	—	4	2	no	—
359	C₄²×C₂₃	—	4	2	no	—
360	C₄²×C₂₃	—	4	2	no	—
361	C₄²×C₂₃	—	4	2	no	—
362	C₄²×C₂₃	C₂²×C₄	1	8	yes	—
363	C₄²×C₂₃	C₂²×C₄	1	4	yes	—
364	#34466	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
365	C₂³×C₂₃	—	2	1	no	—
366	C₂³×C₂₃	—	2	1	no	—
367	C₂³×C₂₃	—	2	1	no	—
368	C₂³×C₂₃	—	2	1	no	—
369	C₂³×C₂₃	—	2	2	no	—
370	C₂³×C₂₃	—	2	2	no	—
371	C₂³×C₂₃	—	2	1	no	—
372	C₂³×C₂₃	—	2	1	no	—
373	C₂³×C₂₃	—	2	2	no	—
374	C₂³×C₂₃	—	2	2	no	—
375	C₂³×C₂₃	—	2	1	no	—
376	C₂³×C₂₃	—	2	1	no	—
377	C₂³×C₂₃	—	2	1	no	—
378	C₂³×C₂₃	—	2	2	no	—
379	C₂³×C₂₃	—	2	2	no	—
380	C₂³×C₂₃	—	2	1	no	—
381	C₂³×C₂₃	—	2	1	no	—
382	C₂³×C₂₃	—	2	1	no	—
383	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
384	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
385	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
386	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
387	D₄×C₂₃	—	2	8	no	—
388	D₄×C₂₃	—	4	4	no	—
389	D₄×C₂₃	—	4	8	no	—
390	D₄×C₂₃	—	4	8	no	—
391	C₂×C₄×C₂₃	—	2	2	no	—
392	C₂×C₄×C₂₃	—	2	1	no	—
393	C₂×C₄×C₂₃	—	2	1	no	—
394	C₂×C₄×C₂₃	—	2	1	no	—
395	C₂×C₄×C₂₃	—	2	1	no	—
396	C₂×C₄×C₂₃	—	2	2	no	—
397	C₂×C₄×C₂₃	—	2	1	no	—
398	C₂×C₄×C₂₃	—	2	1	no	—
399	C₂×C₄×C₂₃	—	2	1	no	—
400	C₂×C₄×C₂₃	—	2	2	no	—
401	C₂×C₄×C₂₃	—	2	2	no	—
402	C₂×C₄×C₂₃	—	2	1	no	—
403	C₂×C₄×C₂₃	—	2	2	no	—
404	C₂×C₄×C₂₃	—	2	1	no	—
405	C₂×C₄×C₂₃	—	2	2	no	—
406	C₂×C₄×C₂₃	—	2	1	no	—
407	C₂×C₄×C₂₃	—	2	8	no	—
408	C₂×C₄×C₂₃	—	2	8	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	2	no	—
414	C₂×C₄×C₂₃	—	2	1	no	—
415	C₂×C₄×C₂₃	—	2	1	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	1	no	—
421	C₂×C₄×C₂₃	—	2	2	no	—
422	C₂×C₄×C₂₃	—	2	1	no	—
423	C₂×C₄×C₂₃	—	2	1	no	—
424	C₂×C₄×C₂₃	—	2	1	no	—
425	C₂×C₄×C₂₃	—	2	2	no	—
426	C₂×C₄×C₂₃	—	2	1	no	—
427	C₂×C₄×C₂₃	—	2	2	no	—
428	C₂×C₄×C₂₃	—	2	1	no	—
429	C₂×C₄×C₂₃	—	2	2	no	—
430	C₂×C₄×C₂₃	—	2	2	no	—
431	C₂×C₄×C₂₃	—	2	1	no	—
432	C₂×C₄×C₂₃	—	2	1	no	—
433	C₂×C₄×C₂₃	—	2	1	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	1	no	—
438	C₂×C₄×C₂₃	—	2	1	no	—
439	C₂×C₄×C₂₃	—	2	1	no	—
440	C₂×C₄×C₂₃	—	2	1	no	—
441	C₂×C₄×C₂₃	—	2	2	no	—
442	C₂×C₄×C₂₃	—	4	8	no	—
443	C₂×C₄×C₂₃	—	4	8	no	—
444	C₂×C₄×C₂₃	—	4	4	no	—
445	C₂×C₄×C₂₃	—	4	4	no	—
446	C₂×C₄×C₂₃	—	8	4	no	—
447	C₂×C₄×C₂₃	—	8	4	no	—
448	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
449	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
450	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
451	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
452	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
453	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
454	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
455	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
456	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
457	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
458	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
459	C₂×#553	C₂×C₂₃	1	1	yes	characteristic
460	#2377	C₂×C₂₃	1	2	yes	complemented
461	#2376	C₂×C₂₃	1	2	yes	complemented
462	#2373	C₂×C₂₃	1	2	yes	complemented
463	#2370	C₂×C₂₃	1	1	yes	characteristic, complemented
464	#2363	C₂×C₂₃	1	1	yes	characteristic, complemented
465	#2363	C₂×C₂₃	1	1	yes	characteristic, complemented
466	#2354	C₂×C₂₃	1	1	yes	characteristic, complemented
467	#2352	C₂×C₂₃	1	2	yes	complemented
468	D₄×C₄⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
469	#2346	C₂×C₂₃	1	1	yes	characteristic, complemented
470	#2344	C₂×C₂₃	1	1	yes	characteristic, complemented
471	#2334	C₂×C₂₃	1	2	yes	complemented
472	#2330	C₂×C₂₃	1	1	yes	characteristic, complemented
473	#2324	C₂×C₂₃	1	1	yes	characteristic, complemented
474	#2324	C₂×C₂₃	1	2	yes	complemented
475	#2322	C₂×C₂₃	1	2	yes	complemented
476	#2319	C₂×C₂₃	1	1	yes	characteristic, complemented
477	#2319	C₂×C₂₃	1	2	yes	complemented
478	#2316	C₂×C₂₃	1	1	yes	characteristic, complemented
479	C₄×#121	C₂×C₂₃	1	1	yes	characteristic, complemented
480	#2296	C₂×C₂₃	1	1	yes	characteristic, complemented
481	#2290	C₂×C₂₃	1	1	yes	characteristic, complemented
482	C₂²×C₂₃	—	2	2	no	—
483	C₂²×C₂₃	—	2	2	no	—
484	C₂²×C₂₃	—	2	4	no	—
485	C₂²×C₂₃	—	2	2	no	—
486	C₂²×C₂₃	—	2	4	no	—
487	C₂²×C₂₃	—	2	2	no	—
488	C₂²×C₂₃	—	2	2	no	—
489	C₂²×C₂₃	—	2	4	no	—
490	C₂²×C₂₃	—	2	2	no	—
491	C₂²×C₂₃	—	4	1	no	—
492	C₂²×C₂₃	—	4	1	no	—
493	C₂²×C₂₃	—	4	2	no	—
494	C₂²×C₂₃	—	4	1	no	—
495	C₂²×C₂₃	—	4	2	no	—
496	C₂²×C₂₃	—	4	1	no	—
497	C₂²×C₂₃	—	4	1	no	—
498	C₂²×C₂₃	—	4	1	no	—
499	C₂²×C₂₃	—	4	2	no	—
500	C₂²×C₂₃	—	4	1	no	—
501	C₂²×C₂₃	—	4	1	no	—
502	C₂²×C₂₃	—	4	2	no	—
503	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
504	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
505	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
506	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
507	C₂²×C₂₃	#585	1	1	yes	characteristic
508	C₂²×C₂₃	#585	1	1	yes	characteristic
509	C₂²×C₂₃	#585	1	1	yes	characteristic
510	C₄×C₂₃	—	2	2	no	—
511	C₄×C₂₃	—	2	2	no	—
512	C₄×C₂₃	—	2	2	no	—
513	C₄×C₂₃	—	2	4	no	—
514	C₄×C₂₃	—	2	2	no	—
515	C₄×C₂₃	—	2	4	no	—
516	C₄×C₂₃	—	2	4	no	—
517	C₄×C₂₃	—	2	2	no	—
518	C₄×C₂₃	—	4	1	no	—
519	C₄×C₂₃	—	4	2	no	—
520	C₄×C₂₃	—	4	1	no	—
521	C₄×C₂₃	—	4	1	no	—
522	C₄×C₂₃	—	4	1	no	—
523	C₄×C₂₃	—	4	2	no	—
524	C₄×C₂₃	—	4	2	no	—
525	C₄×C₂₃	—	4	1	no	—
526	C₄×C₂₃	—	4	2	no	—
527	C₄×C₂₃	—	4	1	no	—
528	C₄×C₂₃	—	4	1	no	—
529	C₄×C₂₃	#520	1	4	yes	—
530	#553	C₄×C₂₃	1	16	yes	complemented
531	C₂×#126	C₂²×C₂₃	1	2	yes	—
532	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
533	C₂×#123	C₂²×C₂₃	1	2	yes	—
534	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
535	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
536	C₂×#121	C₂²×C₂₃	1	2	yes	—
537	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
538	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
539	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
540	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
541	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
542	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
543	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
544	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
545	C₂×#117	C₂²×C₂₃	1	2	yes	—
546	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
547	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
548	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
549	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
550	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
551	#390	C₂²×C₂₃	1	2	yes	—
552	#390	C₂²×C₂₃	1	1	yes	characteristic
553	#390	C₂²×C₂₃	1	1	yes	characteristic
554	#390	C₂²×C₂₃	1	2	yes	—
555	#390	C₂²×C₂₃	1	2	yes	—
556	#390	C₂²×C₂₃	1	2	yes	—
557	#389	C₂²×C₂₃	1	1	yes	characteristic
558	#389	C₂²×C₂₃	1	2	yes	—
559	#389	C₂²×C₂₃	1	1	yes	characteristic
560	#389	C₂²×C₂₃	1	1	yes	characteristic
561	#389	C₂²×C₂₃	1	1	yes	characteristic
562	#389	C₂²×C₂₃	1	2	yes	—
563	#389	C₂²×C₂₃	1	2	yes	—
564	#389	C₂²×C₂₃	1	1	yes	characteristic
565	#389	C₂²×C₂₃	1	2	yes	—
566	#389	C₂²×C₂₃	1	2	yes	—
567	#389	C₂²×C₂₃	1	1	yes	characteristic
568	#389	C₂²×C₂₃	1	1	yes	characteristic
569	#389	C₂²×C₂₃	1	1	yes	characteristic
570	#388	C₂²×C₂₃	1	1	yes	characteristic
571	#388	C₂²×C₂₃	1	2	yes	—
572	#388	C₂²×C₂₃	1	2	yes	—
573	#388	C₂²×C₂₃	1	2	yes	—
574	#388	C₂²×C₂₃	1	2	yes	—
575	#388	C₂²×C₂₃	1	2	yes	—
576	#388	C₂²×C₂₃	1	2	yes	—
577	#388	C₂²×C₂₃	1	2	yes	—
578	#388	C₂²×C₂₃	1	2	yes	—
579	#388	C₂²×C₂₃	1	2	yes	—
580	#388	C₂²×C₂₃	1	2	yes	—
581	#388	C₂²×C₂₃	1	1	yes	characteristic
582	#387	C₂²×C₂₃	1	2	yes	—
583	#387	C₂²×C₂₃	1	2	yes	—
584	#387	C₂²×C₂₃	1	2	yes	—
585	#387	C₂²×C₂₃	1	2	yes	—
586	#387	C₂²×C₂₃	1	1	yes	characteristic
587	#387	C₂²×C₂₃	1	2	yes	—
588	#387	C₂²×C₂₃	1	2	yes	—
589	#387	C₂²×C₂₃	1	1	yes	characteristic
590	#386	C₂²×C₂₃	1	2	yes	—
591	#386	C₂²×C₂₃	1	1	yes	characteristic
592	#386	C₂²×C₂₃	1	2	yes	—
593	#386	C₂²×C₂₃	1	2	yes	—
594	#386	C₂²×C₂₃	1	2	yes	—
595	#386	C₂²×C₂₃	1	1	yes	characteristic
596	#385	C₂²×C₂₃	1	1	yes	characteristic
597	#385	C₂²×C₂₃	1	2	yes	—
598	#385	C₂²×C₂₃	1	2	yes	—
599	#385	C₂²×C₂₃	1	2	yes	—
600	#385	C₂²×C₂₃	1	2	yes	—
601	#385	C₂²×C₂₃	1	1	yes	characteristic
602	#385	C₂²×C₂₃	1	2	yes	—
603	#384	C₂²×C₂₃	1	1	yes	characteristic
604	#382	C₂²×C₂₃	1	2	yes	—
605	#381	C₂²×C₂₃	1	2	yes	—
606	#381	C₂²×C₂₃	1	2	yes	—
607	#380	C₂²×C₂₃	1	2	yes	—
608	#380	C₂²×C₂₃	1	2	yes	—
609	#380	C₂²×C₂₃	1	2	yes	—
610	#380	C₂²×C₂₃	1	2	yes	—
611	#380	C₂²×C₂₃	1	1	yes	characteristic
612	#380	C₂²×C₂₃	1	1	yes	characteristic
613	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
614	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
615	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
616	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
617	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
618	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
619	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
620	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
621	C₄×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
622	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	—
623	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
624	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
625	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
626	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
627	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
628	#376	C₂²×C₂₃	1	1	yes	characteristic
629	#376	C₂²×C₂₃	1	2	yes	—
630	C₂×C₂₃	—	4	2	no	—
631	C₂×C₂₃	—	4	2	no	—
632	C₂×C₂₃	—	4	4	no	—
633	C₂×C₂₃	C₂×#520	1	1	yes	characteristic
634	C₂×C₂₃	#3428	1	1	yes	characteristic
635	C₂×C₂₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
636	C₂×C₂₃	#3539	1	1	yes	characteristic
637	C₂×C₂₃	#3542	1	1	yes	characteristic
638	C₂×C₂₃	#3547	1	1	yes	characteristic
639	C₂×C₂₃	#3565	1	1	yes	characteristic
640	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
641	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
642	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
643	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
644	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
645	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
646	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
647	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
648	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
649	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
650	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
651	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
652	#126	C₂×C₄×C₂₃	1	16	yes	complemented
653	#125	C₂×C₄×C₂₃	1	8	yes	complemented
654	#123	C₂×C₄×C₂₃	1	16	yes	complemented
655	#121	C₂×C₄×C₂₃	1	8	yes	—
656	#121	C₂×C₄×C₂₃	1	16	yes	complemented
657	#121	C₂×C₄×C₂₃	1	8	yes	complemented
658	C₄×D₄	—	4	2	no	—
659	C₄×D₄	—	4	2	no	—
660	C₄×D₄	—	4	4	no	—
661	C₄×D₄	C₂×C₄×C₂₃	1	16	yes	complemented
662	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	complemented
663	C₄×D₄	C₂×C₄×C₂₃	1	8	yes	complemented
664	#117	—	4	2	no	—
665	#117	—	4	4	no	—
666	#117	—	4	2	no	—
667	#117	—	4	2	no	—
668	#117	C₂×C₄×C₂₃	1	8	yes	complemented
669	C₂×C₄⋊C₄	—	4	4	no	—
670	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	8	yes	complemented
671	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
672	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
673	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
674	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
675	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
676	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
677	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
678	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
679	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
680	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
681	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
682	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
683	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
684	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
685	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
686	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
687	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
688	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
689	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
690	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
691	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
692	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
693	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
694	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
695	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
696	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
697	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
698	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
699	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
700	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
701	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
702	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
703	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
704	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
705	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
706	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
707	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
708	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
709	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
710	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
711	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
712	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
714	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
715	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
716	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
717	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
718	C₂×C₄²	—	4	2	no	—
719	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
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	2	yes	—
725	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
726	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
727	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
728	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
729	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
730	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
731	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
732	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
733	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
734	#95	C₂³×C₂₃	1	1	yes	characteristic
735	#95	C₂³×C₂₃	1	2	yes	—
736	#95	C₂³×C₂₃	1	1	yes	characteristic
737	#95	C₂³×C₂₃	1	2	yes	—
738	#95	C₂³×C₂₃	1	1	yes	characteristic
739	#95	C₂³×C₂₃	1	2	yes	—
740	#95	C₂³×C₂₃	1	1	yes	characteristic
741	#95	C₂³×C₂₃	1	1	yes	characteristic
742	#95	C₂³×C₂₃	1	1	yes	characteristic
743	#95	C₂³×C₂₃	1	1	yes	characteristic
744	#95	C₂³×C₂₃	1	2	yes	—
745	#95	C₂³×C₂₃	1	2	yes	—
746	#95	C₂³×C₂₃	1	2	yes	—
747	#95	C₂³×C₂₃	1	1	yes	characteristic
748	#95	C₂³×C₂₃	1	1	yes	characteristic
749	#95	C₂³×C₂₃	1	2	yes	—
750	#95	C₂³×C₂₃	1	2	yes	—
751	#95	C₂³×C₂₃	1	2	yes	—
752	#95	C₂³×C₂₃	1	2	yes	—
753	#95	C₂³×C₂₃	1	2	yes	—
754	#95	C₂³×C₂₃	1	2	yes	—
755	#95	C₂³×C₂₃	1	2	yes	—
756	#95	C₂³×C₂₃	1	2	yes	—
757	#95	C₂³×C₂₃	1	1	yes	characteristic
758	#95	C₂³×C₂₃	1	2	yes	—
759	C₂₃	#34466	1	1	yes	characteristic, direct product factor, Sylow
760	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
761	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
762	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
763	C₂×D₄	—	2	2	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	4	2	no	—
766	C₂×D₄	—	4	1	no	—
767	C₂×D₄	—	4	2	no	—
768	C₂×D₄	—	4	2	no	—
769	C₂×D₄	—	4	1	no	—
770	C₂×D₄	—	4	2	no	—
771	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
772	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
773	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
774	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
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	—	2	2	no	—
780	C₂²×C₄	—	2	4	no	—
781	C₂²×C₄	—	4	1	no	—
782	C₂²×C₄	—	4	1	no	—
783	C₂²×C₄	—	4	2	no	—
784	C₂²×C₄	—	4	2	no	—
785	C₂²×C₄	—	4	2	no	—
786	C₂²×C₄	—	4	2	no	—
787	C₂²×C₄	—	4	1	no	—
788	C₂²×C₄	—	4	1	no	—
789	C₂²×C₄	—	4	1	no	—
790	C₂²×C₄	—	4	2	no	—
791	C₂²×C₄	—	4	2	no	—
792	C₂²×C₄	—	4	2	no	—
793	C₂²×C₄	—	4	2	no	—
794	C₂²×C₄	—	4	2	no	—
795	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
796	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
797	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
798	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
799	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
800	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
801	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
802	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
803	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
804	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
805	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
806	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
807	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
808	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
809	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
810	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
811	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
812	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
813	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
814	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
815	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
816	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
817	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
818	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	4	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	—	4	2	no	—
826	C₄⋊C₄	—	4	2	no	—
827	C₄⋊C₄	—	4	1	no	—
828	C₄⋊C₄	—	4	1	no	—
829	C₄⋊C₄	—	4	2	no	—
830	C₄⋊C₄	—	4	2	no	—
831	C₄⋊C₄	—	4	2	no	—
832	C₄⋊C₄	—	4	2	no	—
833	C₄⋊C₄	—	4	2	no	—
834	C₄⋊C₄	—	4	2	no	—
835	C₄⋊C₄	—	4	1	no	—
836	C₄⋊C₄	—	4	2	no	—
837	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
838	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
839	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
840	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
841	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
842	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
843	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	4	1	no	—
846	C₂²⋊C₄	—	4	1	no	—
847	C₂²⋊C₄	—	4	2	no	—
848	C₂²⋊C₄	—	4	2	no	—
849	C₂²⋊C₄	—	4	2	no	—
850	C₂²⋊C₄	—	4	2	no	—
851	C₂²⋊C₄	—	4	2	no	—
852	C₂²⋊C₄	—	4	2	no	—
853	C₂²⋊C₄	—	4	2	no	—
854	C₂²⋊C₄	—	4	1	no	—
855	C₂²⋊C₄	—	4	2	no	—
856	C₂²⋊C₄	—	4	1	no	—
857	C₂²⋊C₄	—	4	2	no	—
858	C₂²⋊C₄	—	4	2	no	—
859	C₂²⋊C₄	—	4	1	no	—
860	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
861	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
862	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
863	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
864	C₂²⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
865	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
866	C₄²	—	2	2	no	—
867	C₄²	—	2	2	no	—
868	C₄²	—	2	4	no	—
869	C₄²	—	2	2	no	—
870	C₄²	—	2	2	no	—
871	C₄²	—	4	1	no	—
872	C₄²	—	4	1	no	—
873	C₄²	—	4	2	no	—
874	C₄²	—	4	2	no	—
875	C₄²	—	4	2	no	—
876	C₄²	—	4	2	no	—
877	C₄²	—	4	2	no	—
878	C₄²	—	4	2	no	—
879	C₄²	C₂²×C₄×C₂₃	1	8	yes	—
880	C₄²	C₂²×C₄×C₂₃	1	4	yes	—
881	C₂³	—	2	1	no	—
882	C₂³	—	2	1	no	—
883	C₂³	—	2	1	no	—
884	C₂³	—	2	1	no	—
885	C₂³	—	2	2	no	—
886	C₂³	—	2	2	no	—
887	C₂³	—	2	1	no	—
888	C₂³	—	2	1	no	—
889	C₂³	—	2	2	no	—
890	C₂³	—	2	2	no	—
891	C₂³	—	2	1	no	—
892	C₂³	—	2	1	no	—
893	C₂³	—	2	1	no	—
894	C₂³	—	2	2	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	2	1	no	—
897	C₂³	—	2	1	no	—
898	C₂³	—	2	1	no	—
899	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
900	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
901	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
902	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
903	D₄	—	2	8	no	—
904	D₄	—	4	4	no	—
905	D₄	—	4	8	no	—
906	D₄	—	4	8	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	1	no	—
909	C₂×C₄	—	2	1	no	—
910	C₂×C₄	—	2	1	no	—
911	C₂×C₄	—	2	1	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	1	no	—
914	C₂×C₄	—	2	1	no	—
915	C₂×C₄	—	2	1	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	1	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	1	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	1	no	—
923	C₂×C₄	—	2	8	no	—
924	C₂×C₄	—	2	8	no	—
925	C₂×C₄	—	2	1	no	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	1	no	—
928	C₂×C₄	—	2	1	no	—
929	C₂×C₄	—	2	2	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	2	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	1	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	2	1	no	—
939	C₂×C₄	—	2	1	no	—
940	C₂×C₄	—	2	1	no	—
941	C₂×C₄	—	2	2	no	—
942	C₂×C₄	—	2	1	no	—
943	C₂×C₄	—	2	2	no	—
944	C₂×C₄	—	2	1	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	1	no	—
948	C₂×C₄	—	2	1	no	—
949	C₂×C₄	—	2	1	no	—
950	C₂×C₄	—	2	2	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	1	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	4	8	no	—
959	C₂×C₄	—	4	8	no	—
960	C₂×C₄	—	4	4	no	—
961	C₂×C₄	—	4	4	no	—
962	C₂×C₄	—	8	4	no	—
963	C₂×C₄	—	8	4	no	—
964	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
965	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
966	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
967	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
968	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
969	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
970	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
971	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
972	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
973	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
974	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
975	C₂²	—	2	2	no	—
976	C₂²	—	2	2	no	—
977	C₂²	—	2	4	no	—
978	C₂²	—	2	2	no	—
979	C₂²	—	2	4	no	—
980	C₂²	—	2	2	no	—
981	C₂²	—	2	2	no	—
982	C₂²	—	2	4	no	—
983	C₂²	—	2	2	no	—
984	C₂²	—	4	1	no	—
985	C₂²	—	4	1	no	—
986	C₂²	—	4	2	no	—
987	C₂²	—	4	1	no	—
988	C₂²	—	4	2	no	—
989	C₂²	—	4	1	no	—
990	C₂²	—	4	1	no	—
991	C₂²	—	4	1	no	—
992	C₂²	—	4	2	no	—
993	C₂²	—	4	1	no	—
994	C₂²	—	4	1	no	—
995	C₂²	—	4	2	no	—
996	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
997	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
998	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
999	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1000	C₂²	C₂₃×#585	1	1	yes	characteristic
1001	C₂²	C₂₃×#585	1	1	yes	characteristic
1002	C₂²	C₂₃×#585	1	1	yes	characteristic
1003	C₄	—	2	2	no	—
1004	C₄	—	2	2	no	—
1005	C₄	—	2	2	no	—
1006	C₄	—	2	4	no	—
1007	C₄	—	2	2	no	—
1008	C₄	—	2	4	no	—
1009	C₄	—	2	4	no	—
1010	C₄	—	2	2	no	—
1011	C₄	—	4	1	no	—
1012	C₄	—	4	1	no	—
1013	C₄	—	4	1	no	—
1014	C₄	—	4	2	no	—
1015	C₄	—	4	1	no	—
1016	C₄	—	4	1	no	—
1017	C₄	—	4	2	no	—
1018	C₄	—	4	2	no	—
1019	C₄	—	4	2	no	—
1020	C₄	—	4	1	no	—
1021	C₄	—	4	1	no	—
1022	C₄	C₂₃×#520	1	4	yes	—
1023	C₂	—	4	2	no	—
1024	C₂	—	4	2	no	—
1025	C₂	—	4	4	no	—
1026	C₂	C₂×C₂₃×#520	1	1	yes	characteristic
1027	C₂	C₂₃×#3428	1	1	yes	characteristic
1028	C₂	C₄×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1029	C₂	C₂₃×#3539	1	1	yes	characteristic
1030	C₂	C₂₃×#3542	1	1	yes	characteristic
1031	C₂	C₂₃×#3547	1	1	yes	characteristic
1032	C₂	C₂₃×#3565	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#553	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₃×#2377	C₂	semidirect
3. C₂₃×#2376	C₂	semidirect
4. C₂₃×#2373	C₂	semidirect
5. C₂₃×#2370	C₂	semidirect
6. C₂₃×#2363	C₂	semidirect
7. C₂₃×#2363	C₂	semidirect
8. C₂₃×#2354	C₂	semidirect
9. C₂₃×#2352	C₂	semidirect
10. D₄×C₄⋊C₄×C₂₃	C₂	semidirect
11. C₂₃×#2346	C₂	semidirect
12. C₂₃×#2344	C₂	semidirect
13. C₂₃×#2334	C₂	semidirect
14. C₂₃×#2330	C₂	semidirect
15. C₂₃×#2324	C₂	semidirect
16. C₂₃×#2324	C₂	semidirect
17. C₂₃×#2322	C₂	semidirect
18. C₂₃×#2319	C₂	semidirect
19. C₂₃×#2319	C₂	semidirect
20. C₂₃×#2316	C₂	semidirect
21. C₄×C₂₃×#121	C₂	semidirect
22. C₂₃×#2296	C₂	semidirect
23. C₂₃×#2290	C₂	semidirect
24. C₂₃×#553	C₄	semidirect
136. C₂₃×#126	C₂×C₄	semidirect
137. C₂₃×#125	C₂×C₄	semidirect
138. C₂₃×#123	C₂×C₄	semidirect
140. C₂₃×#121	C₂×C₄	semidirect
141. C₂₃×#121	C₂×C₄	semidirect
145. C₄×D₄×C₂₃	C₂×C₄	semidirect
146. C₄×D₄×C₂₃	C₂×C₄	semidirect
147. C₄×D₄×C₂₃	C₂×C₄	semidirect
152. C₂₃×#117	C₂×C₄	semidirect
154. C₂×C₄⋊C₄×C₂₃	C₂×C₄	semidirect
364. #34466	C₂₃	direct (N × H)
460. #2377	C₂×C₂₃	semidirect
461. #2376	C₂×C₂₃	semidirect
462. #2373	C₂×C₂₃	semidirect
463. #2370	C₂×C₂₃	semidirect
464. #2363	C₂×C₂₃	semidirect
465. #2363	C₂×C₂₃	semidirect
466. #2354	C₂×C₂₃	semidirect
467. #2352	C₂×C₂₃	semidirect
468. D₄×C₄⋊C₄	C₂×C₂₃	semidirect
469. #2346	C₂×C₂₃	semidirect
470. #2344	C₂×C₂₃	semidirect
471. #2334	C₂×C₂₃	semidirect
472. #2330	C₂×C₂₃	semidirect
473. #2324	C₂×C₂₃	semidirect
474. #2324	C₂×C₂₃	semidirect
475. #2322	C₂×C₂₃	semidirect
476. #2319	C₂×C₂₃	semidirect
477. #2319	C₂×C₂₃	semidirect
478. #2316	C₂×C₂₃	semidirect
479. C₄×#121	C₂×C₂₃	semidirect
480. #2296	C₂×C₂₃	semidirect
481. #2290	C₂×C₂₃	semidirect
530. #553	C₄×C₂₃	semidirect
652. #126	C₂×C₄×C₂₃	semidirect
653. #125	C₂×C₄×C₂₃	semidirect
654. #123	C₂×C₄×C₂₃	semidirect
656. #121	C₂×C₄×C₂₃	semidirect
657. #121	C₂×C₄×C₂₃	semidirect
661. C₄×D₄	C₂×C₄×C₂₃	semidirect
662. C₄×D₄	C₂×C₄×C₂₃	semidirect
663. C₄×D₄	C₂×C₄×C₂₃	semidirect
668. #117	C₂×C₄×C₂₃	semidirect
670. C₂×C₄⋊C₄	C₂×C₄×C₂₃	semidirect
759. C₂₃	#34466	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#553	2
C₂₃×#2377	2
C₂₃×#2376	2
C₂₃×#2373	2
C₂₃×#2370	2
C₂₃×#2363	2
C₂₃×#2354	2
C₂₃×#2352	2
D₄×C₄⋊C₄×C₂₃	2
C₂₃×#2346	2
C₂₃×#2344	2
C₂₃×#2334	2
C₂₃×#2330	2
C₂₃×#2324	2
C₂₃×#2322	2
C₂₃×#2319	2
C₂₃×#2316	2
C₄×C₂₃×#121	2
C₂₃×#2296	2
C₂₃×#2290	2
#34466	23

Subgroups — C23×#34466 #19182092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34466 #19182092