Subgroups — C₂₃×#34406 #19182032

Order 5888.

2874 conjugacy classes of subgroups.

The subgroup lattice has 1060 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#535	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2380	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2379	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2377	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#2366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2364	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2358	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2358	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2343	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2339	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2337	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2333	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2328	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2325	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2321	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2308	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₂₃×#120	C₂	1	2	yes	maximal, complemented
19	C₂×C₂₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
21	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
23	C₂₃×#535	C₄	1	16	yes	complemented
24	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#121	C₂²	1	2	yes	—
29	C₂×C₂₃×#121	C₂²	1	2	yes	—
30	C₂×C₂₃×#120	C₂²	1	2	yes	—
31	C₂×C₂₃×#120	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
35	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
36	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
37	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
38	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
41	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
43	C₂₃×#391	C₂²	1	2	yes	complemented
44	C₂₃×#391	C₂²	1	2	yes	complemented
45	C₂₃×#390	C₂²	1	2	yes	complemented
46	C₂₃×#390	C₂²	1	2	yes	complemented
47	C₂₃×#390	C₂²	1	2	yes	complemented
48	C₂₃×#390	C₂²	1	2	yes	complemented
49	C₂₃×#388	C₂²	1	2	yes	complemented
50	C₂₃×#388	C₂²	1	2	yes	complemented
51	C₂₃×#388	C₂²	1	2	yes	complemented
52	C₂₃×#388	C₂²	1	2	yes	complemented
53	C₂₃×#388	C₂²	1	2	yes	complemented
54	C₂₃×#388	C₂²	1	2	yes	complemented
55	C₂₃×#388	C₂²	1	2	yes	complemented
56	C₂₃×#388	C₂²	1	2	yes	complemented
57	C₂₃×#387	C₂²	1	2	yes	complemented
58	C₂₃×#387	C₂²	1	2	yes	complemented
59	C₂₃×#387	C₂²	1	2	yes	complemented
60	C₂₃×#387	C₂²	1	2	yes	complemented
61	C₂₃×#386	C₂²	1	2	yes	—
62	C₂₃×#386	C₂²	1	2	yes	—
63	C₂₃×#386	C₂²	1	1	yes	characteristic
64	C₂₃×#386	C₂²	1	1	yes	characteristic
65	C₂₃×#386	C₂²	1	1	yes	characteristic
66	C₂₃×#386	C₂²	1	1	yes	characteristic
67	C₂₃×#386	C₂²	1	2	yes	—
68	C₂₃×#386	C₂²	1	1	yes	characteristic
69	C₂₃×#386	C₂²	1	2	yes	—
70	C₂₃×#386	C₂²	1	1	yes	characteristic
71	C₂₃×#386	C₂²	1	2	yes	—
72	C₂₃×#386	C₂²	1	1	yes	characteristic
73	C₂₃×#386	C₂²	1	1	yes	characteristic
74	C₂₃×#386	C₂²	1	2	yes	—
75	C₂₃×#386	C₂²	1	2	yes	complemented
76	C₂₃×#386	C₂²	1	2	yes	complemented
77	C₂₃×#386	C₂²	1	2	yes	complemented
78	C₂₃×#386	C₂²	1	2	yes	complemented
79	C₂₃×#386	C₂²	1	2	yes	complemented
80	C₂₃×#386	C₂²	1	2	yes	complemented
81	C₂₃×#386	C₂²	1	2	yes	complemented
82	C₂₃×#386	C₂²	1	2	yes	complemented
83	C₂₃×#386	C₂²	1	2	yes	complemented
84	C₂₃×#386	C₂²	1	2	yes	complemented
85	C₂₃×#385	C₂²	1	2	yes	—
86	C₂₃×#385	C₂²	1	2	yes	—
87	C₂₃×#385	C₂²	1	2	yes	complemented
88	C₂₃×#385	C₂²	1	2	yes	complemented
89	C₂₃×#385	C₂²	1	2	yes	complemented
90	C₂₃×#385	C₂²	1	2	yes	complemented
91	C₂₃×#383	C₂²	1	2	yes	complemented
92	C₂₃×#382	C₂²	1	2	yes	complemented
93	C₂₃×#381	C₂²	1	2	yes	—
94	C₂₃×#381	C₂²	1	2	yes	complemented
95	C₂₃×#380	C₂²	1	2	yes	complemented
96	C₂₃×#379	C₂²	1	2	yes	—
97	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
98	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
99	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
100	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
101	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
102	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
103	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
105	C₂₃×#376	C₂²	1	2	yes	complemented
106	C₂×C₂₃×#95	C₂²	1	2	yes	—
107	C₂×C₂₃×#95	C₂²	1	2	yes	complemented
108	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
109	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
110	C₂×#41×C₂₃	—	4	2	no	—
111	C₂×#41×C₂₃	—	4	2	no	—
112	C₂×#41×C₂₃	C₂×C₄	1	8	yes	complemented
113	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₂₃	—	4	2	no	—
115	C₂²×D₄×C₂₃	—	4	2	no	—
116	C₂²×D₄×C₂₃	C₂×C₄	1	8	yes	complemented
117	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
118	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
119	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
120	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
122	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
123	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
124	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
126	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
127	C₂³×C₄×C₂₃	—	4	4	no	—
128	C₂³×C₄×C₂₃	—	4	2	no	—
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	2	yes	—
133	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
135	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
137	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
139	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
141	C₂₃×#127	C₂×C₄	1	8	yes	complemented
142	C₂₃×#127	C₂×C₄	1	8	yes	complemented
143	C₂₃×#124	C₂×C₄	1	8	yes	complemented
144	C₂₃×#124	C₂×C₄	1	8	yes	complemented
145	C₂₃×#121	C₂×C₄	1	16	yes	complemented
146	C₂₃×#121	C₂×C₄	1	16	yes	complemented
147	C₂₃×#120	C₂×C₄	1	16	yes	complemented
148	C₂₃×#120	C₂×C₄	1	16	yes	complemented
149	C₄×D₄×C₂₃	—	4	4	no	—
150	C₄×D₄×C₂₃	—	4	4	no	—
151	C₄×D₄×C₂₃	—	4	4	no	—
152	C₄×D₄×C₂₃	—	4	4	no	—
153	C₄×D₄×C₂₃	—	4	4	no	—
154	C₄×D₄×C₂₃	—	4	4	no	—
155	C₂₃×#117	C₂×C₄	1	8	yes	complemented
156	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
157	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
158	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
159	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
160	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
162	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
164	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
165	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
166	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
167	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
168	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
169	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
170	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
171	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
173	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
175	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
176	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
177	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
179	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
180	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
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	1	yes	characteristic
185	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
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×C₄²×C₂₃	C₂³	1	2	yes	—
195	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
196	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
197	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
198	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
199	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
200	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
202	C₂₃×#95	C₂³	1	2	yes	—
203	C₂₃×#95	C₂³	1	2	yes	—
204	C₂₃×#95	C₂³	1	2	yes	—
205	C₂₃×#95	C₂³	1	2	yes	—
206	C₂₃×#95	C₂³	1	2	yes	—
207	C₂₃×#95	C₂³	1	2	yes	—
208	C₂₃×#95	C₂³	1	2	yes	—
209	C₂₃×#95	C₂³	1	2	yes	—
210	C₂₃×#95	C₂³	1	2	yes	—
211	C₂₃×#95	C₂³	1	2	yes	—
212	C₂₃×#95	C₂³	1	2	yes	—
213	C₂₃×#95	C₂³	1	2	yes	—
214	C₂₃×#95	C₂³	1	2	yes	—
215	C₂₃×#95	C₂³	1	2	yes	—
216	C₂₃×#95	C₂³	1	2	yes	—
217	C₂₃×#95	C₂³	1	2	yes	—
218	C₂₃×#95	C₂³	1	2	yes	—
219	C₂₃×#95	C₂³	1	2	yes	—
220	C₂₃×#95	C₂³	1	2	yes	—
221	C₂₃×#95	C₂³	1	2	yes	—
222	C₂⁴×C₂₃	—	2	2	no	—
223	C₂⁴×C₂₃	—	2	2	no	—
224	C₂⁴×C₂₃	—	2	2	no	—
225	C₂⁴×C₂₃	—	2	2	no	—
226	C₂⁴×C₂₃	—	4	2	no	—
227	C₂⁴×C₂₃	—	4	2	no	—
228	C₂⁴×C₂₃	—	4	2	no	—
229	C₂⁴×C₂₃	—	4	2	no	—
230	C₂⁴×C₂₃	C₂²×C₄	1	4	yes	—
231	C₂⁴×C₂₃	C₂²×C₄	1	4	yes	—
232	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
233	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
234	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
235	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
236	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
237	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
238	#41×C₂₃	—	4	16	no	—
239	C₂×Q₈×C₂₃	—	4	1	no	—
240	C₂×Q₈×C₂₃	—	4	1	no	—
241	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	complemented
242	C₂×D₄×C₂₃	—	2	4	no	—
243	C₂×D₄×C₂₃	—	2	4	no	—
244	C₂×D₄×C₂₃	—	4	2	no	—
245	C₂×D₄×C₂₃	—	4	2	no	—
246	C₂×D₄×C₂₃	—	4	2	no	—
247	C₂×D₄×C₂₃	—	4	2	no	—
248	C₂×D₄×C₂₃	—	4	16	no	—
249	C₂×D₄×C₂₃	—	4	1	no	—
250	C₂×D₄×C₂₃	—	4	1	no	—
251	C₂×D₄×C₂₃	—	4	1	no	—
252	C₂×D₄×C₂₃	—	4	1	no	—
253	C₂×D₄×C₂₃	—	4	1	no	—
254	C₂×D₄×C₂₃	—	4	1	no	—
255	C₂×D₄×C₂₃	—	4	1	no	—
256	C₂×D₄×C₂₃	—	4	1	no	—
257	C₂×D₄×C₂₃	—	4	2	no	—
258	C₂×D₄×C₂₃	—	4	2	no	—
259	C₂×D₄×C₂₃	—	4	2	no	—
260	C₂×D₄×C₂₃	—	4	2	no	—
261	C₂×D₄×C₂₃	—	4	1	no	—
262	C₂×D₄×C₂₃	—	4	1	no	—
263	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
264	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
265	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
266	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
267	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
268	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
269	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
270	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	complemented
271	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	complemented
272	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	complemented
273	C₂²×C₄×C₂₃	—	2	2	no	—
274	C₂²×C₄×C₂₃	—	2	2	no	—
275	C₂²×C₄×C₂₃	—	2	4	no	—
276	C₂²×C₄×C₂₃	—	2	4	no	—
277	C₂²×C₄×C₂₃	—	2	4	no	—
278	C₂²×C₄×C₂₃	—	2	4	no	—
279	C₂²×C₄×C₂₃	—	2	4	no	—
280	C₂²×C₄×C₂₃	—	2	4	no	—
281	C₂²×C₄×C₂₃	—	4	1	no	—
282	C₂²×C₄×C₂₃	—	4	2	no	—
283	C₂²×C₄×C₂₃	—	4	2	no	—
284	C₂²×C₄×C₂₃	—	4	2	no	—
285	C₂²×C₄×C₂₃	—	4	2	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	1	no	—
290	C₂²×C₄×C₂₃	—	4	2	no	—
291	C₂²×C₄×C₂₃	—	4	2	no	—
292	C₂²×C₄×C₂₃	—	4	1	no	—
293	C₂²×C₄×C₂₃	—	4	2	no	—
294	C₂²×C₄×C₂₃	—	4	2	no	—
295	C₂²×C₄×C₂₃	—	4	2	no	—
296	C₂²×C₄×C₂₃	—	4	2	no	—
297	C₂²×C₄×C₂₃	—	4	2	no	—
298	C₂²×C₄×C₂₃	—	4	2	no	—
299	C₂²×C₄×C₂₃	—	4	2	no	—
300	C₂²×C₄×C₂₃	—	4	2	no	—
301	C₂²×C₄×C₂₃	—	4	2	no	—
302	C₂²×C₄×C₂₃	—	4	2	no	—
303	C₂²×C₄×C₂₃	—	4	16	no	—
304	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
305	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	complemented
306	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
307	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
311	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
313	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
314	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
319	C₄⋊C₄×C₂₃	—	2	4	no	—
320	C₄⋊C₄×C₂₃	—	4	2	no	—
321	C₄⋊C₄×C₂₃	—	4	2	no	—
322	C₄⋊C₄×C₂₃	—	4	2	no	—
323	C₄⋊C₄×C₂₃	—	4	2	no	—
324	C₄⋊C₄×C₂₃	—	4	2	no	—
325	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	complemented
326	C₂²⋊C₄×C₂₃	—	2	4	no	—
327	C₂²⋊C₄×C₂₃	—	2	4	no	—
328	C₂²⋊C₄×C₂₃	—	2	4	no	—
329	C₂²⋊C₄×C₂₃	—	2	4	no	—
330	C₂²⋊C₄×C₂₃	—	2	4	no	—
331	C₂²⋊C₄×C₂₃	—	4	1	no	—
332	C₂²⋊C₄×C₂₃	—	4	2	no	—
333	C₂²⋊C₄×C₂₃	—	4	2	no	—
334	C₂²⋊C₄×C₂₃	—	4	1	no	—
335	C₂²⋊C₄×C₂₃	—	4	2	no	—
336	C₂²⋊C₄×C₂₃	—	4	1	no	—
337	C₂²⋊C₄×C₂₃	—	4	2	no	—
338	C₂²⋊C₄×C₂₃	—	4	1	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	—	4	2	no	—
344	C₂²⋊C₄×C₂₃	—	4	2	no	—
345	C₂²⋊C₄×C₂₃	—	4	2	no	—
346	C₂²⋊C₄×C₂₃	—	4	2	no	—
347	C₂²⋊C₄×C₂₃	—	4	2	no	—
348	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
349	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
350	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
351	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	complemented
352	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	complemented
353	C₄²×C₂₃	—	2	4	no	—
354	C₄²×C₂₃	—	4	2	no	—
355	C₄²×C₂₃	—	4	2	no	—
356	C₄²×C₂₃	—	4	2	no	—
357	C₄²×C₂₃	—	4	2	no	—
358	C₄²×C₂₃	—	4	2	no	—
359	C₄²×C₂₃	C₂²×C₄	1	4	yes	complemented
360	C₄²×C₂₃	C₂²×C₄	1	4	yes	complemented
361	#34406	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
362	C₂³×C₂₃	—	2	2	no	—
363	C₂³×C₂₃	—	2	2	no	—
364	C₂³×C₂₃	—	2	8	no	—
365	C₂³×C₂₃	—	2	2	no	—
366	C₂³×C₂₃	—	2	2	no	—
367	C₂³×C₂₃	—	2	2	no	—
368	C₂³×C₂₃	—	2	2	no	—
369	C₂³×C₂₃	—	2	1	no	—
370	C₂³×C₂₃	—	2	1	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	2	no	—
376	C₂³×C₂₃	—	2	2	no	—
377	C₂³×C₂₃	—	2	1	no	—
378	C₂³×C₂₃	—	2	1	no	—
379	C₂³×C₂₃	—	2	1	no	—
380	C₂³×C₂₃	—	2	1	no	—
381	C₂³×C₂₃	—	2	2	no	—
382	C₂³×C₂₃	—	2	2	no	—
383	C₂³×C₂₃	—	2	2	no	—
384	C₂³×C₂₃	—	2	2	no	—
385	C₂³×C₂₃	—	2	2	no	—
386	C₂³×C₂₃	—	2	2	no	—
387	C₂³×C₂₃	—	2	8	no	—
388	C₂³×C₂₃	—	4	8	no	—
389	C₂³×C₂₃	—	4	8	no	—
390	C₂³×C₂₃	—	4	4	no	—
391	C₂³×C₂₃	—	4	4	no	—
392	C₂³×C₂₃	—	4	8	no	—
393	C₂³×C₂₃	—	8	2	no	—
394	C₂³×C₂₃	—	8	2	no	—
395	C₂³×C₂₃	—	8	4	no	—
396	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
397	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
398	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
399	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
400	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
401	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
402	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
403	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
404	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
405	Q₈×C₂₃	—	4	4	no	—
406	D₄×C₂₃	—	2	16	no	—
407	D₄×C₂₃	—	4	4	no	—
408	D₄×C₂₃	—	4	4	no	—
409	D₄×C₂₃	—	4	4	no	—
410	D₄×C₂₃	—	4	4	no	—
411	D₄×C₂₃	—	4	8	no	—
412	D₄×C₂₃	—	4	8	no	—
413	D₄×C₂₃	—	4	8	no	—
414	D₄×C₂₃	—	4	8	no	—
415	D₄×C₂₃	—	4	4	no	—
416	C₂×C₄×C₂₃	—	2	8	no	—
417	C₂×C₄×C₂₃	—	2	2	no	—
418	C₂×C₄×C₂₃	—	2	2	no	—
419	C₂×C₄×C₂₃	—	2	2	no	—
420	C₂×C₄×C₂₃	—	2	2	no	—
421	C₂×C₄×C₂₃	—	2	2	no	—
422	C₂×C₄×C₂₃	—	2	2	no	—
423	C₂×C₄×C₂₃	—	2	1	no	—
424	C₂×C₄×C₂₃	—	2	1	no	—
425	C₂×C₄×C₂₃	—	2	1	no	—
426	C₂×C₄×C₂₃	—	2	1	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	2	no	—
433	C₂×C₄×C₂₃	—	2	2	no	—
434	C₂×C₄×C₂₃	—	2	2	no	—
435	C₂×C₄×C₂₃	—	2	2	no	—
436	C₂×C₄×C₂₃	—	2	2	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	2	no	—
442	C₂×C₄×C₂₃	—	2	2	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	2	no	—
447	C₂×C₄×C₂₃	—	2	2	no	—
448	C₂×C₄×C₂₃	—	2	2	no	—
449	C₂×C₄×C₂₃	—	2	2	no	—
450	C₂×C₄×C₂₃	—	4	8	no	—
451	C₂×C₄×C₂₃	—	4	4	no	—
452	C₂×C₄×C₂₃	—	4	8	no	—
453	C₂×C₄×C₂₃	—	4	8	no	—
454	C₂×C₄×C₂₃	—	4	4	no	—
455	C₂×C₄×C₂₃	—	8	4	no	—
456	C₂×C₄×C₂₃	—	8	4	no	—
457	C₂×C₄×C₂₃	—	8	2	no	—
458	C₂×C₄×C₂₃	—	8	2	no	—
459	C₂×C₄×C₂₃	—	8	4	no	—
460	C₂×C₄×C₂₃	—	8	4	no	—
461	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
462	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
463	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
464	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
465	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
466	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
467	C₂×#535	C₂×C₂₃	1	1	yes	characteristic
468	#2380	C₂×C₂₃	1	1	yes	characteristic, complemented
469	#2379	C₂×C₂₃	1	1	yes	characteristic, complemented
470	#2377	C₂×C₂₃	1	2	yes	complemented
471	#2372	C₂×C₂₃	1	1	yes	characteristic, complemented
472	#2366	C₂×C₂₃	1	1	yes	characteristic, complemented
473	#2364	C₂×C₂₃	1	2	yes	complemented
474	#2358	C₂×C₂₃	1	2	yes	complemented
475	#2358	C₂×C₂₃	1	2	yes	complemented
476	#2343	C₂×C₂₃	1	2	yes	complemented
477	#2339	C₂×C₂₃	1	2	yes	complemented
478	#2337	C₂×C₂₃	1	2	yes	complemented
479	#2333	C₂×C₂₃	1	2	yes	complemented
480	#2328	C₂×C₂₃	1	2	yes	complemented
481	#2325	C₂×C₂₃	1	2	yes	complemented
482	#2321	C₂×C₂₃	1	2	yes	complemented
483	#2308	C₂×C₂₃	1	1	yes	characteristic, complemented
484	C₄×#120	C₂×C₂₃	1	2	yes	complemented
485	C₂×#386	C₂×C₂₃	1	1	yes	characteristic, complemented
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	4	no	—
491	C₂²×C₂₃	—	2	2	no	—
492	C₂²×C₂₃	—	2	2	no	—
493	C₂²×C₂₃	—	2	2	no	—
494	C₂²×C₂₃	—	2	2	no	—
495	C₂²×C₂₃	—	2	4	no	—
496	C₂²×C₂₃	—	2	4	no	—
497	C₂²×C₂₃	—	2	4	no	—
498	C₂²×C₂₃	—	2	4	no	—
499	C₂²×C₂₃	—	2	4	no	—
500	C₂²×C₂₃	—	2	4	no	—
501	C₂²×C₂₃	—	4	16	no	—
502	C₂²×C₂₃	—	4	1	no	—
503	C₂²×C₂₃	—	4	1	no	—
504	C₂²×C₂₃	—	4	2	no	—
505	C₂²×C₂₃	—	4	1	no	—
506	C₂²×C₂₃	—	4	1	no	—
507	C₂²×C₂₃	—	4	1	no	—
508	C₂²×C₂₃	—	4	2	no	—
509	C₂²×C₂₃	—	4	1	no	—
510	C₂²×C₂₃	—	4	1	no	—
511	C₂²×C₂₃	—	4	1	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	—	8	8	no	—
519	C₂²×C₂₃	#518	1	4	yes	—
520	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
521	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
522	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
523	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
524	C₂²×C₂₃	#585	1	2	yes	—
525	C₄×C₂₃	—	2	2	no	—
526	C₄×C₂₃	—	2	2	no	—
527	C₄×C₂₃	—	2	4	no	—
528	C₄×C₂₃	—	2	4	no	—
529	C₄×C₂₃	—	2	4	no	—
530	C₄×C₂₃	—	2	4	no	—
531	C₄×C₂₃	—	4	2	no	—
532	C₄×C₂₃	—	4	2	no	—
533	C₄×C₂₃	—	4	2	no	—
534	C₄×C₂₃	—	4	2	no	—
535	C₄×C₂₃	—	4	2	no	—
536	C₄×C₂₃	—	4	2	no	—
537	C₄×C₂₃	—	4	2	no	—
538	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
539	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
540	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
541	#535	C₄×C₂₃	1	16	yes	complemented
542	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
543	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
544	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
545	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
546	C₂×#121	C₂²×C₂₃	1	2	yes	—
547	C₂×#121	C₂²×C₂₃	1	2	yes	—
548	C₂×#120	C₂²×C₂₃	1	2	yes	—
549	C₂×#120	C₂²×C₂₃	1	2	yes	—
550	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
551	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
552	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
553	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
554	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
555	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
556	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
557	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
558	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
559	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
560	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
561	#391	C₂²×C₂₃	1	2	yes	complemented
562	#391	C₂²×C₂₃	1	2	yes	complemented
563	#390	C₂²×C₂₃	1	2	yes	complemented
564	#390	C₂²×C₂₃	1	2	yes	complemented
565	#390	C₂²×C₂₃	1	2	yes	complemented
566	#390	C₂²×C₂₃	1	2	yes	complemented
567	#388	C₂²×C₂₃	1	2	yes	complemented
568	#388	C₂²×C₂₃	1	2	yes	complemented
569	#388	C₂²×C₂₃	1	2	yes	complemented
570	#388	C₂²×C₂₃	1	2	yes	complemented
571	#388	C₂²×C₂₃	1	2	yes	complemented
572	#388	C₂²×C₂₃	1	2	yes	complemented
573	#388	C₂²×C₂₃	1	2	yes	complemented
574	#388	C₂²×C₂₃	1	2	yes	complemented
575	#387	C₂²×C₂₃	1	2	yes	complemented
576	#387	C₂²×C₂₃	1	2	yes	complemented
577	#387	C₂²×C₂₃	1	2	yes	complemented
578	#387	C₂²×C₂₃	1	2	yes	complemented
579	#386	C₂²×C₂₃	1	1	yes	characteristic
580	#386	C₂²×C₂₃	1	2	yes	—
581	#386	C₂²×C₂₃	1	1	yes	characteristic
582	#386	C₂²×C₂₃	1	2	yes	—
583	#386	C₂²×C₂₃	1	1	yes	characteristic
584	#386	C₂²×C₂₃	1	1	yes	characteristic
585	#386	C₂²×C₂₃	1	2	yes	—
586	#386	C₂²×C₂₃	1	2	yes	—
587	#386	C₂²×C₂₃	1	2	yes	—
588	#386	C₂²×C₂₃	1	2	yes	—
589	#386	C₂²×C₂₃	1	1	yes	characteristic
590	#386	C₂²×C₂₃	1	1	yes	characteristic
591	#386	C₂²×C₂₃	1	1	yes	characteristic
592	#386	C₂²×C₂₃	1	1	yes	characteristic
593	#386	C₂²×C₂₃	1	2	yes	complemented
594	#386	C₂²×C₂₃	1	2	yes	complemented
595	#386	C₂²×C₂₃	1	2	yes	complemented
596	#386	C₂²×C₂₃	1	2	yes	complemented
597	#386	C₂²×C₂₃	1	2	yes	complemented
598	#386	C₂²×C₂₃	1	2	yes	complemented
599	#386	C₂²×C₂₃	1	2	yes	complemented
600	#386	C₂²×C₂₃	1	2	yes	complemented
601	#386	C₂²×C₂₃	1	2	yes	complemented
602	#386	C₂²×C₂₃	1	2	yes	complemented
603	#385	C₂²×C₂₃	1	2	yes	—
604	#385	C₂²×C₂₃	1	2	yes	—
605	#385	C₂²×C₂₃	1	2	yes	complemented
606	#385	C₂²×C₂₃	1	2	yes	complemented
607	#385	C₂²×C₂₃	1	2	yes	complemented
608	#385	C₂²×C₂₃	1	2	yes	complemented
609	#383	C₂²×C₂₃	1	2	yes	complemented
610	#382	C₂²×C₂₃	1	2	yes	complemented
611	#381	C₂²×C₂₃	1	2	yes	—
612	#381	C₂²×C₂₃	1	2	yes	complemented
613	#380	C₂²×C₂₃	1	2	yes	complemented
614	#379	C₂²×C₂₃	1	2	yes	—
615	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
616	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
617	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
618	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
619	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
620	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
621	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
622	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
623	#376	C₂²×C₂₃	1	2	yes	complemented
624	C₂×#95	C₂²×C₂₃	1	2	yes	—
625	C₂×#95	C₂²×C₂₃	1	2	yes	complemented
626	C₂×C₂₃	—	2	4	no	—
627	C₂×C₂₃	—	4	4	no	—
628	C₂×C₂₃	—	4	2	no	—
629	C₂×C₂₃	—	4	2	no	—
630	C₂×C₂₃	—	4	2	no	—
631	C₂×C₂₃	—	4	2	no	—
632	C₂×C₂₃	C₂×#518	1	1	yes	characteristic
633	C₂×C₂₃	C₄×H(5,𝔽₂)	1	2	yes	—
634	C₂×C₂₃	#3532	1	1	yes	characteristic
635	C₂×C₂₃	#3533	1	1	yes	characteristic
636	C₂×C₂₃	#3542	1	2	yes	—
637	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
638	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
639	C₂×#41	—	4	2	no	—
640	C₂×#41	—	4	2	no	—
641	C₂×#41	C₂×C₄×C₂₃	1	8	yes	complemented
642	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
643	C₂²×D₄	—	4	2	no	—
644	C₂²×D₄	—	4	2	no	—
645	C₂²×D₄	C₂×C₄×C₂₃	1	8	yes	complemented
646	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
647	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
648	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
649	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
650	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
651	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
652	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
653	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
654	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
655	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
656	C₂³×C₄	—	4	4	no	—
657	C₂³×C₄	—	4	2	no	—
658	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
659	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
660	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
661	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
662	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
663	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
664	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
665	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
666	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
667	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
668	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
669	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
670	#127	C₂×C₄×C₂₃	1	8	yes	complemented
671	#127	C₂×C₄×C₂₃	1	8	yes	complemented
672	#124	C₂×C₄×C₂₃	1	8	yes	complemented
673	#124	C₂×C₄×C₂₃	1	8	yes	complemented
674	#121	C₂×C₄×C₂₃	1	16	yes	complemented
675	#121	C₂×C₄×C₂₃	1	16	yes	complemented
676	#120	C₂×C₄×C₂₃	1	16	yes	complemented
677	#120	C₂×C₄×C₂₃	1	16	yes	complemented
678	C₄×D₄	—	4	4	no	—
679	C₄×D₄	—	4	4	no	—
680	C₄×D₄	—	4	4	no	—
681	C₄×D₄	—	4	4	no	—
682	C₄×D₄	—	4	4	no	—
683	C₄×D₄	—	4	4	no	—
684	#117	C₂×C₄×C₂₃	1	8	yes	complemented
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	2	yes	—
690	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
691	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
692	C₂×C₂²⋊C₄	—	4	4	no	—
693	C₂×C₂²⋊C₄	—	4	2	no	—
694	C₂×C₂²⋊C₄	—	4	2	no	—
695	C₂×C₂²⋊C₄	—	4	2	no	—
696	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
697	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
698	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
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	1	yes	characteristic
704	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
711	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
712	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
713	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
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	2	yes	—
717	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
718	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
719	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
720	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
721	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
722	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
723	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
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	1	yes	characteristic
731	#95	C₂³×C₂₃	1	2	yes	—
732	#95	C₂³×C₂₃	1	2	yes	—
733	#95	C₂³×C₂₃	1	2	yes	—
734	#95	C₂³×C₂₃	1	2	yes	—
735	#95	C₂³×C₂₃	1	2	yes	—
736	#95	C₂³×C₂₃	1	2	yes	—
737	#95	C₂³×C₂₃	1	2	yes	—
738	#95	C₂³×C₂₃	1	2	yes	—
739	#95	C₂³×C₂₃	1	2	yes	—
740	#95	C₂³×C₂₃	1	2	yes	—
741	#95	C₂³×C₂₃	1	2	yes	—
742	#95	C₂³×C₂₃	1	2	yes	—
743	#95	C₂³×C₂₃	1	2	yes	—
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	2	yes	—
748	#95	C₂³×C₂₃	1	2	yes	—
749	#95	C₂³×C₂₃	1	2	yes	—
750	#95	C₂³×C₂₃	1	2	yes	—
751	C₂₃	#34406	1	1	yes	characteristic, direct product factor, Sylow
752	C₂⁴	—	2	2	no	—
753	C₂⁴	—	2	2	no	—
754	C₂⁴	—	2	2	no	—
755	C₂⁴	—	2	2	no	—
756	C₂⁴	—	4	2	no	—
757	C₂⁴	—	4	2	no	—
758	C₂⁴	—	4	2	no	—
759	C₂⁴	—	4	2	no	—
760	C₂⁴	C₂²×C₄×C₂₃	1	4	yes	—
761	C₂⁴	C₂²×C₄×C₂₃	1	4	yes	—
762	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
763	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
764	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
765	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
766	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
767	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
768	#41	—	4	16	no	—
769	C₂×Q₈	—	4	1	no	—
770	C₂×Q₈	—	4	1	no	—
771	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	complemented
772	C₂×D₄	—	2	4	no	—
773	C₂×D₄	—	2	4	no	—
774	C₂×D₄	—	4	2	no	—
775	C₂×D₄	—	4	2	no	—
776	C₂×D₄	—	4	2	no	—
777	C₂×D₄	—	4	2	no	—
778	C₂×D₄	—	4	16	no	—
779	C₂×D₄	—	4	1	no	—
780	C₂×D₄	—	4	1	no	—
781	C₂×D₄	—	4	1	no	—
782	C₂×D₄	—	4	1	no	—
783	C₂×D₄	—	4	1	no	—
784	C₂×D₄	—	4	1	no	—
785	C₂×D₄	—	4	1	no	—
786	C₂×D₄	—	4	1	no	—
787	C₂×D₄	—	4	1	no	—
788	C₂×D₄	—	4	1	no	—
789	C₂×D₄	—	4	2	no	—
790	C₂×D₄	—	4	2	no	—
791	C₂×D₄	—	4	2	no	—
792	C₂×D₄	—	4	2	no	—
793	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
794	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
795	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
796	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
797	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
798	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
799	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
800	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	complemented
801	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	complemented
802	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	complemented
803	C₂²×C₄	—	2	2	no	—
804	C₂²×C₄	—	2	2	no	—
805	C₂²×C₄	—	2	4	no	—
806	C₂²×C₄	—	2	4	no	—
807	C₂²×C₄	—	2	4	no	—
808	C₂²×C₄	—	2	4	no	—
809	C₂²×C₄	—	2	4	no	—
810	C₂²×C₄	—	2	4	no	—
811	C₂²×C₄	—	4	1	no	—
812	C₂²×C₄	—	4	2	no	—
813	C₂²×C₄	—	4	2	no	—
814	C₂²×C₄	—	4	2	no	—
815	C₂²×C₄	—	4	2	no	—
816	C₂²×C₄	—	4	1	no	—
817	C₂²×C₄	—	4	2	no	—
818	C₂²×C₄	—	4	2	no	—
819	C₂²×C₄	—	4	1	no	—
820	C₂²×C₄	—	4	2	no	—
821	C₂²×C₄	—	4	2	no	—
822	C₂²×C₄	—	4	1	no	—
823	C₂²×C₄	—	4	2	no	—
824	C₂²×C₄	—	4	2	no	—
825	C₂²×C₄	—	4	2	no	—
826	C₂²×C₄	—	4	2	no	—
827	C₂²×C₄	—	4	2	no	—
828	C₂²×C₄	—	4	2	no	—
829	C₂²×C₄	—	4	2	no	—
830	C₂²×C₄	—	4	2	no	—
831	C₂²×C₄	—	4	2	no	—
832	C₂²×C₄	—	4	2	no	—
833	C₂²×C₄	—	4	16	no	—
834	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
835	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	complemented
836	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
837	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
838	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
839	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
840	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
841	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
842	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
843	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
845	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
846	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
847	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
848	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
849	C₄⋊C₄	—	2	4	no	—
850	C₄⋊C₄	—	4	2	no	—
851	C₄⋊C₄	—	4	2	no	—
852	C₄⋊C₄	—	4	2	no	—
853	C₄⋊C₄	—	4	2	no	—
854	C₄⋊C₄	—	4	2	no	—
855	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	complemented
856	C₂²⋊C₄	—	2	4	no	—
857	C₂²⋊C₄	—	2	4	no	—
858	C₂²⋊C₄	—	2	4	no	—
859	C₂²⋊C₄	—	2	4	no	—
860	C₂²⋊C₄	—	2	4	no	—
861	C₂²⋊C₄	—	4	1	no	—
862	C₂²⋊C₄	—	4	2	no	—
863	C₂²⋊C₄	—	4	2	no	—
864	C₂²⋊C₄	—	4	1	no	—
865	C₂²⋊C₄	—	4	2	no	—
866	C₂²⋊C₄	—	4	1	no	—
867	C₂²⋊C₄	—	4	2	no	—
868	C₂²⋊C₄	—	4	1	no	—
869	C₂²⋊C₄	—	4	2	no	—
870	C₂²⋊C₄	—	4	2	no	—
871	C₂²⋊C₄	—	4	2	no	—
872	C₂²⋊C₄	—	4	2	no	—
873	C₂²⋊C₄	—	4	2	no	—
874	C₂²⋊C₄	—	4	2	no	—
875	C₂²⋊C₄	—	4	2	no	—
876	C₂²⋊C₄	—	4	2	no	—
877	C₂²⋊C₄	—	4	2	no	—
878	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
879	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
880	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
881	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	complemented
882	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	complemented
883	C₄²	—	2	4	no	—
884	C₄²	—	4	2	no	—
885	C₄²	—	4	2	no	—
886	C₄²	—	4	2	no	—
887	C₄²	—	4	2	no	—
888	C₄²	—	4	2	no	—
889	C₄²	C₂²×C₄×C₂₃	1	4	yes	complemented
890	C₄²	C₂²×C₄×C₂₃	1	4	yes	complemented
891	C₂³	—	2	2	no	—
892	C₂³	—	2	2	no	—
893	C₂³	—	2	2	no	—
894	C₂³	—	2	2	no	—
895	C₂³	—	2	2	no	—
896	C₂³	—	2	2	no	—
897	C₂³	—	2	1	no	—
898	C₂³	—	2	1	no	—
899	C₂³	—	2	1	no	—
900	C₂³	—	2	1	no	—
901	C₂³	—	2	2	no	—
902	C₂³	—	2	2	no	—
903	C₂³	—	2	2	no	—
904	C₂³	—	2	2	no	—
905	C₂³	—	2	1	no	—
906	C₂³	—	2	1	no	—
907	C₂³	—	2	1	no	—
908	C₂³	—	2	1	no	—
909	C₂³	—	2	2	no	—
910	C₂³	—	2	2	no	—
911	C₂³	—	2	2	no	—
912	C₂³	—	2	2	no	—
913	C₂³	—	2	2	no	—
914	C₂³	—	2	2	no	—
915	C₂³	—	2	8	no	—
916	C₂³	—	2	8	no	—
917	C₂³	—	4	8	no	—
918	C₂³	—	4	8	no	—
919	C₂³	—	4	4	no	—
920	C₂³	—	4	4	no	—
921	C₂³	—	4	8	no	—
922	C₂³	—	8	2	no	—
923	C₂³	—	8	2	no	—
924	C₂³	—	8	4	no	—
925	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
926	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
927	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
928	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
929	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
930	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
931	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
932	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
933	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
934	Q₈	—	4	4	no	—
935	D₄	—	2	16	no	—
936	D₄	—	4	4	no	—
937	D₄	—	4	4	no	—
938	D₄	—	4	4	no	—
939	D₄	—	4	4	no	—
940	D₄	—	4	8	no	—
941	D₄	—	4	8	no	—
942	D₄	—	4	4	no	—
943	D₄	—	4	8	no	—
944	D₄	—	4	8	no	—
945	C₂×C₄	—	2	2	no	—
946	C₂×C₄	—	2	2	no	—
947	C₂×C₄	—	2	2	no	—
948	C₂×C₄	—	2	2	no	—
949	C₂×C₄	—	2	2	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	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	8	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	2	no	—
965	C₂×C₄	—	2	2	no	—
966	C₂×C₄	—	2	2	no	—
967	C₂×C₄	—	2	2	no	—
968	C₂×C₄	—	2	2	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	2	no	—
974	C₂×C₄	—	2	2	no	—
975	C₂×C₄	—	2	2	no	—
976	C₂×C₄	—	2	2	no	—
977	C₂×C₄	—	2	2	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	4	8	no	—
980	C₂×C₄	—	4	4	no	—
981	C₂×C₄	—	4	8	no	—
982	C₂×C₄	—	4	8	no	—
983	C₂×C₄	—	4	4	no	—
984	C₂×C₄	—	8	4	no	—
985	C₂×C₄	—	8	4	no	—
986	C₂×C₄	—	8	2	no	—
987	C₂×C₄	—	8	2	no	—
988	C₂×C₄	—	8	4	no	—
989	C₂×C₄	—	8	4	no	—
990	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
991	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
992	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
993	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
994	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
995	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
996	C₂²	—	2	4	no	—
997	C₂²	—	2	2	no	—
998	C₂²	—	2	2	no	—
999	C₂²	—	2	4	no	—
1000	C₂²	—	2	4	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	2	no	—
1003	C₂²	—	2	2	no	—
1004	C₂²	—	2	2	no	—
1005	C₂²	—	2	4	no	—
1006	C₂²	—	2	4	no	—
1007	C₂²	—	2	4	no	—
1008	C₂²	—	2	4	no	—
1009	C₂²	—	2	4	no	—
1010	C₂²	—	2	4	no	—
1011	C₂²	—	4	16	no	—
1012	C₂²	—	4	1	no	—
1013	C₂²	—	4	1	no	—
1014	C₂²	—	4	1	no	—
1015	C₂²	—	4	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	1	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	—	4	2	no	—
1028	C₂²	—	8	8	no	—
1029	C₂²	C₂₃×#518	1	4	yes	—
1030	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
1031	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1032	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1033	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
1034	C₂²	C₂₃×#585	1	2	yes	—
1035	C₄	—	2	2	no	—
1036	C₄	—	2	2	no	—
1037	C₄	—	2	4	no	—
1038	C₄	—	2	4	no	—
1039	C₄	—	2	4	no	—
1040	C₄	—	2	4	no	—
1041	C₄	—	4	2	no	—
1042	C₄	—	4	2	no	—
1043	C₄	—	4	2	no	—
1044	C₄	—	4	2	no	—
1045	C₄	—	4	2	no	—
1046	C₄	—	4	2	no	—
1047	C₄	—	4	2	no	—
1048	C₂	—	2	4	no	—
1049	C₂	—	4	2	no	—
1050	C₂	—	4	2	no	—
1051	C₂	—	4	2	no	—
1052	C₂	—	4	2	no	—
1053	C₂	—	4	4	no	—
1054	C₂	C₂×C₂₃×#518	1	1	yes	characteristic
1055	C₂	C₄×C₂₃×H(5,𝔽₂)	1	2	yes	—
1056	C₂	C₂₃×#3532	1	1	yes	characteristic
1057	C₂	C₂₃×#3533	1	1	yes	characteristic
1058	C₂	C₂₃×#3542	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#535	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×#2380	C₂	semidirect
3. C₂₃×#2379	C₂	semidirect
4. C₂₃×#2377	C₂	semidirect
5. C₂₃×#2372	C₂	semidirect
6. C₂₃×#2366	C₂	semidirect
7. C₂₃×#2364	C₂	semidirect
8. C₂₃×#2358	C₂	semidirect
9. C₂₃×#2358	C₂	semidirect
10. C₂₃×#2343	C₂	semidirect
11. C₂₃×#2339	C₂	semidirect
12. C₂₃×#2337	C₂	semidirect
13. C₂₃×#2333	C₂	semidirect
14. C₂₃×#2328	C₂	semidirect
15. C₂₃×#2325	C₂	semidirect
16. C₂₃×#2321	C₂	semidirect
17. C₂₃×#2308	C₂	semidirect
18. C₄×C₂₃×#120	C₂	semidirect
19. C₂×C₂₃×#386	C₂	semidirect
23. C₂₃×#535	C₄	semidirect
34. C₂×C₄×D₄×C₂₃	C₂²	semidirect
35. C₂×C₄×D₄×C₂₃	C₂²	semidirect
36. C₂×C₄×D₄×C₂₃	C₂²	semidirect
37. C₂×C₄×D₄×C₂₃	C₂²	semidirect
43. C₂₃×#391	C₂²	semidirect
44. C₂₃×#391	C₂²	semidirect
45. C₂₃×#390	C₂²	semidirect
46. C₂₃×#390	C₂²	semidirect
47. C₂₃×#390	C₂²	semidirect
48. C₂₃×#390	C₂²	semidirect
49. C₂₃×#388	C₂²	semidirect
50. C₂₃×#388	C₂²	semidirect
51. C₂₃×#388	C₂²	semidirect
52. C₂₃×#388	C₂²	semidirect
53. C₂₃×#388	C₂²	semidirect
54. C₂₃×#388	C₂²	semidirect
55. C₂₃×#388	C₂²	semidirect
56. C₂₃×#388	C₂²	semidirect
57. C₂₃×#387	C₂²	semidirect
58. C₂₃×#387	C₂²	semidirect
59. C₂₃×#387	C₂²	semidirect
60. C₂₃×#387	C₂²	semidirect
75. C₂₃×#386	C₂²	semidirect
76. C₂₃×#386	C₂²	semidirect
77. C₂₃×#386	C₂²	semidirect
78. C₂₃×#386	C₂²	semidirect
79. C₂₃×#386	C₂²	semidirect
80. C₂₃×#386	C₂²	semidirect
81. C₂₃×#386	C₂²	semidirect
82. C₂₃×#386	C₂²	semidirect
83. C₂₃×#386	C₂²	semidirect
84. C₂₃×#386	C₂²	semidirect
87. C₂₃×#385	C₂²	semidirect
88. C₂₃×#385	C₂²	semidirect
89. C₂₃×#385	C₂²	semidirect
90. C₂₃×#385	C₂²	semidirect
91. C₂₃×#383	C₂²	semidirect
92. C₂₃×#382	C₂²	semidirect
94. C₂₃×#381	C₂²	semidirect
95. C₂₃×#380	C₂²	semidirect
97. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
100. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
101. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
102. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
103. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
104. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
105. C₂₃×#376	C₂²	semidirect
107. C₂×C₂₃×#95	C₂²	semidirect
112. C₂×#41×C₂₃	C₂×C₄	semidirect
116. C₂²×D₄×C₂₃	C₂×C₄	semidirect
141. C₂₃×#127	C₂×C₄	semidirect
142. C₂₃×#127	C₂×C₄	semidirect
143. C₂₃×#124	C₂×C₄	semidirect
144. C₂₃×#124	C₂×C₄	semidirect
145. C₂₃×#121	C₂×C₄	semidirect
146. C₂₃×#121	C₂×C₄	semidirect
147. C₂₃×#120	C₂×C₄	semidirect
148. C₂₃×#120	C₂×C₄	semidirect
155. C₂₃×#117	C₂×C₄	semidirect
241. C₂×Q₈×C₂₃	C₂²×C₄	semidirect
270. C₂×D₄×C₂₃	C₂²×C₄	semidirect
271. C₂×D₄×C₂₃	C₂²×C₄	semidirect
272. C₂×D₄×C₂₃	C₂²×C₄	semidirect
305. C₂²×C₄×C₂₃	C₂²×C₄	semidirect
325. C₄⋊C₄×C₂₃	C₂²×C₄	semidirect
351. C₂²⋊C₄×C₂₃	C₂²×C₄	semidirect
352. C₂²⋊C₄×C₂₃	C₂²×C₄	semidirect
359. C₄²×C₂₃	C₂²×C₄	semidirect
360. C₄²×C₂₃	C₂²×C₄	semidirect
361. #34406	C₂₃	direct (N × H)
468. #2380	C₂×C₂₃	semidirect
469. #2379	C₂×C₂₃	semidirect
470. #2377	C₂×C₂₃	semidirect
471. #2372	C₂×C₂₃	semidirect
472. #2366	C₂×C₂₃	semidirect
473. #2364	C₂×C₂₃	semidirect
474. #2358	C₂×C₂₃	semidirect
475. #2358	C₂×C₂₃	semidirect
476. #2343	C₂×C₂₃	semidirect
477. #2339	C₂×C₂₃	semidirect
478. #2337	C₂×C₂₃	semidirect
479. #2333	C₂×C₂₃	semidirect
480. #2328	C₂×C₂₃	semidirect
481. #2325	C₂×C₂₃	semidirect
482. #2321	C₂×C₂₃	semidirect
483. #2308	C₂×C₂₃	semidirect
484. C₄×#120	C₂×C₂₃	semidirect
485. C₂×#386	C₂×C₂₃	semidirect
541. #535	C₄×C₂₃	semidirect
552. C₂×C₄×D₄	C₂²×C₂₃	semidirect
553. C₂×C₄×D₄	C₂²×C₂₃	semidirect
554. C₂×C₄×D₄	C₂²×C₂₃	semidirect
555. C₂×C₄×D₄	C₂²×C₂₃	semidirect
561. #391	C₂²×C₂₃	semidirect
562. #391	C₂²×C₂₃	semidirect
563. #390	C₂²×C₂₃	semidirect
564. #390	C₂²×C₂₃	semidirect
565. #390	C₂²×C₂₃	semidirect
566. #390	C₂²×C₂₃	semidirect
567. #388	C₂²×C₂₃	semidirect
568. #388	C₂²×C₂₃	semidirect
569. #388	C₂²×C₂₃	semidirect
570. #388	C₂²×C₂₃	semidirect
571. #388	C₂²×C₂₃	semidirect
572. #388	C₂²×C₂₃	semidirect
573. #388	C₂²×C₂₃	semidirect
574. #388	C₂²×C₂₃	semidirect
575. #387	C₂²×C₂₃	semidirect
576. #387	C₂²×C₂₃	semidirect
577. #387	C₂²×C₂₃	semidirect
578. #387	C₂²×C₂₃	semidirect
593. #386	C₂²×C₂₃	semidirect
594. #386	C₂²×C₂₃	semidirect
595. #386	C₂²×C₂₃	semidirect
596. #386	C₂²×C₂₃	semidirect
597. #386	C₂²×C₂₃	semidirect
598. #386	C₂²×C₂₃	semidirect
599. #386	C₂²×C₂₃	semidirect
600. #386	C₂²×C₂₃	semidirect
601. #386	C₂²×C₂₃	semidirect
602. #386	C₂²×C₂₃	semidirect
605. #385	C₂²×C₂₃	semidirect
606. #385	C₂²×C₂₃	semidirect
607. #385	C₂²×C₂₃	semidirect
608. #385	C₂²×C₂₃	semidirect
609. #383	C₂²×C₂₃	semidirect
610. #382	C₂²×C₂₃	semidirect
612. #381	C₂²×C₂₃	semidirect
613. #380	C₂²×C₂₃	semidirect
615. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
618. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
619. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
620. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
621. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
622. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
623. #376	C₂²×C₂₃	semidirect
625. C₂×#95	C₂²×C₂₃	semidirect
641. C₂×#41	C₂×C₄×C₂₃	semidirect
645. C₂²×D₄	C₂×C₄×C₂₃	semidirect
670. #127	C₂×C₄×C₂₃	semidirect
671. #127	C₂×C₄×C₂₃	semidirect
672. #124	C₂×C₄×C₂₃	semidirect
673. #124	C₂×C₄×C₂₃	semidirect
674. #121	C₂×C₄×C₂₃	semidirect
675. #121	C₂×C₄×C₂₃	semidirect
676. #120	C₂×C₄×C₂₃	semidirect
677. #120	C₂×C₄×C₂₃	semidirect
684. #117	C₂×C₄×C₂₃	semidirect
751. C₂₃	#34406	direct (N × H)
771. C₂×Q₈	C₂²×C₄×C₂₃	semidirect
800. C₂×D₄	C₂²×C₄×C₂₃	semidirect
801. C₂×D₄	C₂²×C₄×C₂₃	semidirect
802. C₂×D₄	C₂²×C₄×C₂₃	semidirect
835. C₂²×C₄	C₂²×C₄×C₂₃	semidirect
855. C₄⋊C₄	C₂²×C₄×C₂₃	semidirect
881. C₂²⋊C₄	C₂²×C₄×C₂₃	semidirect
882. C₂²⋊C₄	C₂²×C₄×C₂₃	semidirect
889. C₄²	C₂²×C₄×C₂₃	semidirect
890. C₄²	C₂²×C₄×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#535	2
C₂₃×#2380	2
C₂₃×#2379	2
C₂₃×#2377	2
C₂₃×#2372	2
C₂₃×#2366	2
C₂₃×#2364	2
C₂₃×#2358	2
C₂₃×#2343	2
C₂₃×#2339	2
C₂₃×#2337	2
C₂₃×#2333	2
C₂₃×#2328	2
C₂₃×#2325	2
C₂₃×#2321	2
C₂₃×#2308	2
C₄×C₂₃×#120	2
C₂×C₂₃×#386	2
#34406	23

Subgroups — C23×#34406 #19182032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34406 #19182032