Subgroups — C₂₃×#34223 #19181849

Order 5888.

2698 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#525	C₂	1	1	yes	maximal, characteristic
2	C₂₃×#2374	C₂	1	4	yes	maximal, complemented
3	C₂₃×#2363	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2362	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2357	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2353	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2347	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#2346	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#2341	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2339	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2321	C₂	1	4	yes	maximal, complemented
12	C₂₃×#2318	C₂	1	2	yes	maximal, complemented
13	C₄×C₂₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
14	C₄×C₂₃×#121	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2280	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2275	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#525	C₄	1	16	yes	complemented
21	C₂×C₂₃×#123	C₂²	1	2	yes	—
22	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
26	C₂×C₂₃×#120	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	complemented
28	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
29	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
32	C₂×C₂₃×#117	C₂²	1	2	yes	—
33	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
35	C₂²×C₄²×C₂₃	C₂²	1	2	yes	—
36	C₂₃×#391	C₂²	1	2	yes	complemented
37	C₂₃×#390	C₂²	1	4	yes	—
38	C₂₃×#390	C₂²	1	4	yes	—
39	C₂₃×#390	C₂²	1	2	yes	complemented
40	C₂₃×#389	C₂²	1	2	yes	complemented
41	C₂₃×#389	C₂²	1	2	yes	complemented
42	C₂₃×#388	C₂²	1	4	yes	—
43	C₂₃×#388	C₂²	1	4	yes	—
44	C₂₃×#388	C₂²	1	4	yes	—
45	C₂₃×#388	C₂²	1	4	yes	—
46	C₂₃×#388	C₂²	1	4	yes	complemented
47	C₂₃×#388	C₂²	1	4	yes	complemented
48	C₂₃×#387	C₂²	1	4	yes	complemented
49	C₂₃×#387	C₂²	1	4	yes	complemented
50	C₂₃×#386	C₂²	1	4	yes	—
51	C₂₃×#386	C₂²	1	4	yes	—
52	C₂₃×#386	C₂²	1	4	yes	—
53	C₂₃×#385	C₂²	1	4	yes	—
54	C₂₃×#383	C₂²	1	2	yes	complemented
55	C₂₃×#382	C₂²	1	2	yes	complemented
56	C₂₃×#381	C₂²	1	2	yes	—
57	C₂₃×#381	C₂²	1	2	yes	complemented
58	C₂₃×#380	C₂²	1	2	yes	—
59	C₂₃×#380	C₂²	1	1	yes	characteristic
60	C₂₃×#380	C₂²	1	1	yes	characteristic
61	C₂₃×#380	C₂²	1	2	yes	complemented
62	C₂₃×#379	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
64	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	complemented
65	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
66	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
67	C₄×C₄⋊C₄×C₂₃	C₂²	1	4	yes	complemented
68	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
70	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
71	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
73	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
74	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
75	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	—
76	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
77	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
78	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	complemented
79	C₄×C₂²⋊C₄×C₂₃	C₂²	1	4	yes	complemented
80	C₂₃×#376	C₂²	1	2	yes	complemented
81	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
82	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
83	C₂×C₂₃×#95	C₂²	1	2	yes	complemented
84	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
85	C₂×#41×C₂₃	—	4	4	no	—
86	C₂×#41×C₂₃	C₂×C₄	1	8	yes	complemented
87	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
88	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
89	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
90	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
91	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
92	C₂³×C₄×C₂₃	—	4	4	no	—
93	C₂³×C₄×C₂₃	C₂×C₄	1	8	yes	complemented
94	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
98	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
99	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
103	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
104	C₂₃×#123	C₂×C₄	1	16	yes	complemented
105	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
106	C₂₃×C₂²⋊Q₈	C₂×C₄	1	8	yes	complemented
107	C₂₃×#121	C₂×C₄	1	8	yes	—
108	C₂₃×#121	C₂×C₄	1	8	yes	complemented
109	C₂₃×#120	C₂×C₄	1	16	yes	complemented
110	C₄×Q₈×C₂₃	—	4	4	no	—
111	C₄×D₄×C₂₃	—	2	16	no	—
112	C₄×D₄×C₂₃	—	4	4	no	—
113	C₄×D₄×C₂₃	C₂×C₄	1	16	yes	complemented
114	C₄×D₄×C₂₃	C₂×C₄	1	16	yes	complemented
115	C₂₃×#117	—	4	4	no	—
116	C₂₃×#117	C₂×C₄	1	8	yes	complemented
117	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
121	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
123	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
124	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂×C₂²⋊C₄×C₂₃	—	2	8	no	—
127	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
143	C₂×C₄²×C₂₃	—	4	4	no	—
144	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
145	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
146	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
147	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
148	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
149	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
150	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
151	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
152	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
153	C₂₃×#95	C₂³	1	1	yes	characteristic
154	C₂₃×#95	C₂³	1	2	yes	—
155	C₂₃×#95	C₂³	1	1	yes	characteristic
156	C₂₃×#95	C₂³	1	1	yes	characteristic
157	C₂₃×#95	C₂³	1	1	yes	characteristic
158	C₂₃×#95	C₂³	1	2	yes	—
159	C₂₃×#95	C₂³	1	2	yes	—
160	C₂₃×#95	C₂³	1	4	yes	—
161	C₂₃×#95	C₂³	1	2	yes	—
162	C₂₃×#95	C₂³	1	4	yes	—
163	C₂₃×#95	C₂³	1	4	yes	—
164	C₂₃×#95	C₂³	1	4	yes	—
165	C₂₃×#95	C₂³	1	4	yes	—
166	C₂₃×#95	C₂³	1	4	yes	—
167	C₂₃×#95	C₂³	1	4	yes	—
168	C₂⁴×C₂₃	—	2	4	no	—
169	C₂⁴×C₂₃	—	4	2	no	—
170	C₂⁴×C₂₃	—	4	1	no	—
171	C₂⁴×C₂₃	—	4	1	no	—
172	C₂⁴×C₂₃	C₂²×C₄	1	4	yes	—
173	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
174	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
175	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
176	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
177	#41×C₂₃	—	4	16	no	—
178	C₂×Q₈×C₂₃	—	2	4	no	—
179	C₂×Q₈×C₂₃	C₂²×C₄	1	4	yes	—
180	C₂×D₄×C₂₃	—	2	8	no	—
181	C₂×D₄×C₂₃	—	2	4	no	—
182	C₂×D₄×C₂₃	—	4	2	no	—
183	C₂×D₄×C₂₃	—	4	2	no	—
184	C₂×D₄×C₂₃	—	4	4	no	—
185	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
186	C₂×D₄×C₂₃	C₂²×C₄	1	4	yes	—
187	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
188	C₂×D₄×C₂₃	C₂²×C₄	1	8	yes	—
189	C₂²×C₄×C₂₃	—	2	4	no	—
190	C₂²×C₄×C₂₃	—	2	4	no	—
191	C₂²×C₄×C₂₃	—	2	4	no	—
192	C₂²×C₄×C₂₃	—	2	4	no	—
193	C₂²×C₄×C₂₃	—	2	8	no	—
194	C₂²×C₄×C₂₃	—	4	16	no	—
195	C₂²×C₄×C₂₃	—	4	2	no	—
196	C₂²×C₄×C₂₃	—	4	2	no	—
197	C₂²×C₄×C₂₃	—	4	2	no	—
198	C₂²×C₄×C₂₃	—	4	2	no	—
199	C₂²×C₄×C₂₃	—	4	2	no	—
200	C₂²×C₄×C₂₃	—	4	2	no	—
201	C₂²×C₄×C₂₃	—	4	2	no	—
202	C₂²×C₄×C₂₃	—	4	4	no	—
203	C₂²×C₄×C₂₃	—	4	4	no	—
204	C₂²×C₄×C₂₃	—	4	4	no	—
205	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
206	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
207	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
208	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
209	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
210	C₂²×C₄×C₂₃	C₂²×C₄	1	8	yes	—
211	C₂²×C₄×C₂₃	C₂²×C₄	1	4	yes	—
212	C₂²×C₄×C₂₃	#41	1	8	yes	complemented
213	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
217	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
218	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
226	C₄⋊C₄×C₂₃	—	2	8	no	—
227	C₄⋊C₄×C₂₃	—	2	4	no	—
228	C₄⋊C₄×C₂₃	—	2	4	no	—
229	C₄⋊C₄×C₂₃	—	4	4	no	—
230	C₄⋊C₄×C₂₃	—	4	4	no	—
231	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
232	C₄⋊C₄×C₂₃	C₂²×C₄	1	4	yes	—
233	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
234	C₄⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
235	C₂²⋊C₄×C₂₃	—	2	8	no	—
236	C₂²⋊C₄×C₂₃	—	2	4	no	—
237	C₂²⋊C₄×C₂₃	—	2	4	no	—
238	C₂²⋊C₄×C₂₃	—	2	4	no	—
239	C₂²⋊C₄×C₂₃	—	2	4	no	—
240	C₂²⋊C₄×C₂₃	—	2	8	no	—
241	C₂²⋊C₄×C₂₃	—	4	2	no	—
242	C₂²⋊C₄×C₂₃	—	4	2	no	—
243	C₂²⋊C₄×C₂₃	—	4	4	no	—
244	C₂²⋊C₄×C₂₃	—	4	4	no	—
245	C₂²⋊C₄×C₂₃	—	4	4	no	—
246	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
247	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
248	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
249	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
250	C₂²⋊C₄×C₂₃	C₂²×C₄	1	8	yes	—
251	C₄²×C₂₃	—	2	8	no	—
252	C₄²×C₂₃	—	2	4	no	—
253	C₄²×C₂₃	—	2	4	no	—
254	C₄²×C₂₃	—	4	2	no	—
255	C₄²×C₂₃	—	4	2	no	—
256	C₄²×C₂₃	—	4	4	no	—
257	C₄²×C₂₃	—	4	4	no	—
258	C₄²×C₂₃	—	4	4	no	—
259	C₄²×C₂₃	C₂²×C₄	1	8	yes	—
260	#34223	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₂³×C₂₃	—	2	2	no	—
262	C₂³×C₂₃	—	2	1	no	—
263	C₂³×C₂₃	—	2	1	no	—
264	C₂³×C₂₃	—	2	8	no	—
265	C₂³×C₂₃	—	2	2	no	—
266	C₂³×C₂₃	—	2	2	no	—
267	C₂³×C₂₃	—	2	4	no	—
268	C₂³×C₂₃	—	2	2	no	—
269	C₂³×C₂₃	—	2	4	no	—
270	C₂³×C₂₃	—	2	2	no	—
271	C₂³×C₂₃	—	2	2	no	—
272	C₂³×C₂₃	—	2	1	no	—
273	C₂³×C₂₃	—	2	1	no	—
274	C₂³×C₂₃	—	2	2	no	—
275	C₂³×C₂₃	—	2	1	no	—
276	C₂³×C₂₃	—	2	1	no	—
277	C₂³×C₂₃	—	4	4	no	—
278	C₂³×C₂₃	—	4	4	no	—
279	C₂³×C₂₃	—	4	8	no	—
280	C₂³×C₂₃	—	4	8	no	—
281	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
282	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
283	C₂³×C₂₃	C₂³×C₄	1	4	yes	—
284	C₂³×C₂₃	C₂³×C₄	1	2	yes	—
285	C₂³×C₂₃	C₂×#41	1	4	yes	—
286	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
287	Q₈×C₂₃	—	2	8	no	—
288	D₄×C₂₃	—	2	16	no	—
289	D₄×C₂₃	—	2	8	no	—
290	D₄×C₂₃	—	4	8	no	—
291	D₄×C₂₃	—	4	8	no	—
292	C₂×C₄×C₂₃	—	2	4	no	—
293	C₂×C₄×C₂₃	—	2	2	no	—
294	C₂×C₄×C₂₃	—	2	2	no	—
295	C₂×C₄×C₂₃	—	2	2	no	—
296	C₂×C₄×C₂₃	—	2	2	no	—
297	C₂×C₄×C₂₃	—	2	4	no	—
298	C₂×C₄×C₂₃	—	2	2	no	—
299	C₂×C₄×C₂₃	—	2	2	no	—
300	C₂×C₄×C₂₃	—	2	2	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	2	no	—
303	C₂×C₄×C₂₃	—	2	8	no	—
304	C₂×C₄×C₂₃	—	2	8	no	—
305	C₂×C₄×C₂₃	—	2	8	no	—
306	C₂×C₄×C₂₃	—	2	4	no	—
307	C₂×C₄×C₂₃	—	2	2	no	—
308	C₂×C₄×C₂₃	—	2	2	no	—
309	C₂×C₄×C₂₃	—	2	4	no	—
310	C₂×C₄×C₂₃	—	2	2	no	—
311	C₂×C₄×C₂₃	—	2	2	no	—
312	C₂×C₄×C₂₃	—	2	4	no	—
313	C₂×C₄×C₂₃	—	2	4	no	—
314	C₂×C₄×C₂₃	—	2	4	no	—
315	C₂×C₄×C₂₃	—	2	4	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	2	no	—
318	C₂×C₄×C₂₃	—	4	4	no	—
319	C₂×C₄×C₂₃	—	4	4	no	—
320	C₂×C₄×C₂₃	—	4	4	no	—
321	C₂×C₄×C₂₃	—	4	8	no	—
322	C₂×C₄×C₂₃	—	4	8	no	—
323	C₂×C₄×C₂₃	—	4	8	no	—
324	C₂×C₄×C₂₃	—	8	8	no	—
325	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
326	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
327	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
328	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
329	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
330	C₂×C₄×C₂₃	C₂³×C₄	1	4	yes	—
331	C₂×C₄×C₂₃	C₂³×C₄	1	2	yes	—
332	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
333	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
334	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
335	C₂×#525	C₂×C₂₃	1	1	yes	characteristic
336	#2374	C₂×C₂₃	1	4	yes	complemented
337	#2363	C₂×C₂₃	1	2	yes	complemented
338	#2362	C₂×C₂₃	1	2	yes	complemented
339	#2357	C₂×C₂₃	1	2	yes	complemented
340	#2353	C₂×C₂₃	1	2	yes	complemented
341	#2347	C₂×C₂₃	1	1	yes	characteristic, complemented
342	#2346	C₂×C₂₃	1	1	yes	characteristic, complemented
343	#2341	C₂×C₂₃	1	1	yes	characteristic, complemented
344	#2339	C₂×C₂₃	1	1	yes	characteristic, complemented
345	#2321	C₂×C₂₃	1	4	yes	complemented
346	#2318	C₂×C₂₃	1	2	yes	complemented
347	C₄×C₂²⋊Q₈	C₂×C₂₃	1	2	yes	complemented
348	C₄×#121	C₂×C₂₃	1	2	yes	complemented
349	#2280	C₂×C₂₃	1	1	yes	characteristic, complemented
350	#2275	C₂×C₂₃	1	2	yes	complemented
351	C₂×C₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
352	C₂²×C₂₃	—	2	2	no	—
353	C₂²×C₂₃	—	2	2	no	—
354	C₂²×C₂₃	—	2	4	no	—
355	C₂²×C₂₃	—	2	4	no	—
356	C₂²×C₂₃	—	2	4	no	—
357	C₂²×C₂₃	—	2	2	no	—
358	C₂²×C₂₃	—	2	2	no	—
359	C₂²×C₂₃	—	2	2	no	—
360	C₂²×C₂₃	—	2	2	no	—
361	C₂²×C₂₃	—	2	4	no	—
362	C₂²×C₂₃	—	2	2	no	—
363	C₂²×C₂₃	—	2	4	no	—
364	C₂²×C₂₃	—	2	2	no	—
365	C₂²×C₂₃	—	4	16	no	—
366	C₂²×C₂₃	—	4	4	no	—
367	C₂²×C₂₃	—	4	2	no	—
368	C₂²×C₂₃	—	4	2	no	—
369	C₂²×C₂₃	—	4	4	no	—
370	C₂²×C₂₃	—	4	2	no	—
371	C₂²×C₂₃	—	4	2	no	—
372	C₂²×C₂₃	C₄×#41	1	4	yes	—
373	C₂²×C₂₃	C₂⁴×C₄	1	1	yes	characteristic
374	C₂²×C₂₃	C₂²×#41	1	2	yes	—
375	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
376	C₂²×C₂₃	#585	1	1	yes	characteristic
377	C₂²×C₂₃	#585	1	1	yes	characteristic
378	C₄×C₂₃	—	2	4	no	—
379	C₄×C₂₃	—	2	2	no	—
380	C₄×C₂₃	—	2	2	no	—
381	C₄×C₂₃	—	2	2	no	—
382	C₄×C₂₃	—	2	4	no	—
383	C₄×C₂₃	—	2	4	no	—
384	C₄×C₂₃	—	2	4	no	—
385	C₄×C₂₃	—	2	4	no	—
386	C₄×C₂₃	—	4	4	no	—
387	C₄×C₂₃	—	4	4	no	—
388	C₄×C₂₃	—	4	2	no	—
389	C₄×C₂₃	—	4	2	no	—
390	C₄×C₂₃	#518	1	4	yes	—
391	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
392	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
393	#525	C₄×C₂₃	1	16	yes	complemented
394	C₂×#123	C₂²×C₂₃	1	2	yes	—
395	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
396	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
397	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
398	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
399	C₂×#120	C₂²×C₂₃	1	2	yes	—
400	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	complemented
401	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
402	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
403	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
404	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
405	C₂×#117	C₂²×C₂₃	1	2	yes	—
406	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
407	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
408	C₂²×C₄²	C₂²×C₂₃	1	2	yes	—
409	#391	C₂²×C₂₃	1	2	yes	complemented
410	#390	C₂²×C₂₃	1	4	yes	—
411	#390	C₂²×C₂₃	1	4	yes	—
412	#390	C₂²×C₂₃	1	2	yes	complemented
413	#389	C₂²×C₂₃	1	2	yes	complemented
414	#389	C₂²×C₂₃	1	2	yes	complemented
415	#388	C₂²×C₂₃	1	4	yes	—
416	#388	C₂²×C₂₃	1	4	yes	—
417	#388	C₂²×C₂₃	1	4	yes	—
418	#388	C₂²×C₂₃	1	4	yes	—
419	#388	C₂²×C₂₃	1	4	yes	complemented
420	#388	C₂²×C₂₃	1	4	yes	complemented
421	#387	C₂²×C₂₃	1	4	yes	complemented
422	#387	C₂²×C₂₃	1	4	yes	complemented
423	#386	C₂²×C₂₃	1	4	yes	—
424	#386	C₂²×C₂₃	1	4	yes	—
425	#386	C₂²×C₂₃	1	4	yes	—
426	#385	C₂²×C₂₃	1	4	yes	—
427	#383	C₂²×C₂₃	1	2	yes	complemented
428	#382	C₂²×C₂₃	1	2	yes	complemented
429	#381	C₂²×C₂₃	1	2	yes	—
430	#381	C₂²×C₂₃	1	2	yes	complemented
431	#380	C₂²×C₂₃	1	1	yes	characteristic
432	#380	C₂²×C₂₃	1	1	yes	characteristic
433	#380	C₂²×C₂₃	1	2	yes	—
434	#380	C₂²×C₂₃	1	2	yes	complemented
435	#379	C₂²×C₂₃	1	2	yes	—
436	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
437	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
438	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
439	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	complemented
440	C₄×C₄⋊C₄	C₂²×C₂₃	1	4	yes	complemented
441	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
442	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	—
443	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
444	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
445	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
446	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
447	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
448	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
449	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
450	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
451	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	complemented
452	C₄×C₂²⋊C₄	C₂²×C₂₃	1	4	yes	complemented
453	#376	C₂²×C₂₃	1	2	yes	complemented
454	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
455	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
456	C₂×#95	C₂²×C₂₃	1	2	yes	complemented
457	C₂×C₂₃	—	2	4	no	—
458	C₂×C₂₃	—	4	4	no	—
459	C₂×C₂₃	—	4	2	no	—
460	C₂×C₂₃	—	4	2	no	—
461	C₂×C₂₃	C₂×C₄×#41	1	1	yes	characteristic
462	C₂×C₂₃	C₂×#518	1	1	yes	characteristic
463	C₂×C₂₃	#3428	1	1	yes	characteristic
464	C₂×C₂₃	#3505	1	2	yes	—
465	C₂×C₂₃	#3506	1	2	yes	—
466	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
467	C₂×#41	—	4	4	no	—
468	C₂×#41	C₂×C₄×C₂₃	1	8	yes	complemented
469	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
470	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
471	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
472	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
473	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
474	C₂³×C₄	—	4	4	no	—
475	C₂³×C₄	C₂×C₄×C₂₃	1	8	yes	complemented
476	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
477	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
478	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
480	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
481	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
482	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
483	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
484	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
486	#123	C₂×C₄×C₂₃	1	16	yes	complemented
487	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
488	C₂²⋊Q₈	C₂×C₄×C₂₃	1	8	yes	complemented
489	#121	C₂×C₄×C₂₃	1	8	yes	—
490	#121	C₂×C₄×C₂₃	1	8	yes	complemented
491	#120	C₂×C₄×C₂₃	1	16	yes	complemented
492	C₄×Q₈	—	4	4	no	—
493	C₄×D₄	—	2	16	no	—
494	C₄×D₄	—	4	4	no	—
495	C₄×D₄	C₂×C₄×C₂₃	1	16	yes	complemented
496	C₄×D₄	C₂×C₄×C₂₃	1	16	yes	complemented
497	#117	—	4	4	no	—
498	#117	C₂×C₄×C₂₃	1	8	yes	complemented
499	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
500	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
501	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
502	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
503	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
504	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
508	C₂×C₂²⋊C₄	—	2	8	no	—
509	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
513	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
514	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
525	C₂×C₄²	—	4	4	no	—
526	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
527	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
528	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
529	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
530	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
531	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
532	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
533	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
534	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
535	#95	C₂³×C₂₃	1	1	yes	characteristic
536	#95	C₂³×C₂₃	1	1	yes	characteristic
537	#95	C₂³×C₂₃	1	2	yes	—
538	#95	C₂³×C₂₃	1	1	yes	characteristic
539	#95	C₂³×C₂₃	1	1	yes	characteristic
540	#95	C₂³×C₂₃	1	2	yes	—
541	#95	C₂³×C₂₃	1	2	yes	—
542	#95	C₂³×C₂₃	1	4	yes	—
543	#95	C₂³×C₂₃	1	2	yes	—
544	#95	C₂³×C₂₃	1	4	yes	—
545	#95	C₂³×C₂₃	1	4	yes	—
546	#95	C₂³×C₂₃	1	4	yes	—
547	#95	C₂³×C₂₃	1	4	yes	—
548	#95	C₂³×C₂₃	1	4	yes	—
549	#95	C₂³×C₂₃	1	4	yes	—
550	C₂₃	#34223	1	1	yes	characteristic, direct product factor, Sylow
551	C₂⁴	—	2	4	no	—
552	C₂⁴	—	4	2	no	—
553	C₂⁴	—	4	1	no	—
554	C₂⁴	—	4	1	no	—
555	C₂⁴	C₂²×C₄×C₂₃	1	4	yes	—
556	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
557	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
558	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
559	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
560	#41	—	4	16	no	—
561	C₂×Q₈	—	2	4	no	—
562	C₂×Q₈	C₂²×C₄×C₂₃	1	4	yes	—
563	C₂×D₄	—	2	8	no	—
564	C₂×D₄	—	2	4	no	—
565	C₂×D₄	—	4	4	no	—
566	C₂×D₄	—	4	2	no	—
567	C₂×D₄	—	4	2	no	—
568	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
569	C₂×D₄	C₂²×C₄×C₂₃	1	4	yes	—
570	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
571	C₂×D₄	C₂²×C₄×C₂₃	1	8	yes	—
572	C₂²×C₄	—	2	4	no	—
573	C₂²×C₄	—	2	4	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	2	4	no	—
576	C₂²×C₄	—	2	8	no	—
577	C₂²×C₄	—	4	16	no	—
578	C₂²×C₄	—	4	2	no	—
579	C₂²×C₄	—	4	2	no	—
580	C₂²×C₄	—	4	2	no	—
581	C₂²×C₄	—	4	2	no	—
582	C₂²×C₄	—	4	2	no	—
583	C₂²×C₄	—	4	4	no	—
584	C₂²×C₄	—	4	2	no	—
585	C₂²×C₄	—	4	2	no	—
586	C₂²×C₄	—	4	4	no	—
587	C₂²×C₄	—	4	4	no	—
588	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
589	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
590	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
591	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
592	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
593	C₂²×C₄	C₂²×C₄×C₂₃	1	8	yes	—
594	C₂²×C₄	C₂²×C₄×C₂₃	1	4	yes	—
595	C₂²×C₄	#41×C₂₃	1	8	yes	complemented
596	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
597	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
598	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
599	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
600	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
601	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
609	C₄⋊C₄	—	2	8	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	4	4	no	—
613	C₄⋊C₄	—	4	4	no	—
614	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
615	C₄⋊C₄	C₂²×C₄×C₂₃	1	4	yes	—
616	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
617	C₄⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
618	C₂²⋊C₄	—	2	8	no	—
619	C₂²⋊C₄	—	2	4	no	—
620	C₂²⋊C₄	—	2	4	no	—
621	C₂²⋊C₄	—	2	4	no	—
622	C₂²⋊C₄	—	2	4	no	—
623	C₂²⋊C₄	—	2	8	no	—
624	C₂²⋊C₄	—	4	4	no	—
625	C₂²⋊C₄	—	4	4	no	—
626	C₂²⋊C₄	—	4	2	no	—
627	C₂²⋊C₄	—	4	2	no	—
628	C₂²⋊C₄	—	4	4	no	—
629	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
630	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
631	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
632	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
633	C₂²⋊C₄	C₂²×C₄×C₂₃	1	8	yes	—
634	C₄²	—	2	8	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	2	4	no	—
637	C₄²	—	4	2	no	—
638	C₄²	—	4	2	no	—
639	C₄²	—	4	4	no	—
640	C₄²	—	4	4	no	—
641	C₄²	—	4	4	no	—
642	C₄²	C₂²×C₄×C₂₃	1	8	yes	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	1	no	—
645	C₂³	—	2	1	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	2	2	no	—
648	C₂³	—	2	4	no	—
649	C₂³	—	2	2	no	—
650	C₂³	—	2	4	no	—
651	C₂³	—	2	2	no	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	1	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	1	no	—
658	C₂³	—	2	8	no	—
659	C₂³	—	4	4	no	—
660	C₂³	—	4	4	no	—
661	C₂³	—	4	8	no	—
662	C₂³	—	4	8	no	—
663	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
664	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
665	C₂³	C₂³×C₄×C₂₃	1	4	yes	—
666	C₂³	C₂³×C₄×C₂₃	1	2	yes	—
667	C₂³	C₂×#41×C₂₃	1	4	yes	—
668	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
669	Q₈	—	2	8	no	—
670	D₄	—	2	16	no	—
671	D₄	—	2	8	no	—
672	D₄	—	4	8	no	—
673	D₄	—	4	8	no	—
674	C₂×C₄	—	2	4	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	8	no	—
686	C₂×C₄	—	2	8	no	—
687	C₂×C₄	—	2	8	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	4	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	2	4	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	2	4	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	4	4	no	—
702	C₂×C₄	—	4	4	no	—
703	C₂×C₄	—	4	8	no	—
704	C₂×C₄	—	4	8	no	—
705	C₂×C₄	—	4	8	no	—
706	C₂×C₄	—	8	8	no	—
707	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
708	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
709	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
710	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
711	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
712	C₂×C₄	C₂³×C₄×C₂₃	1	4	yes	—
713	C₂×C₄	C₂³×C₄×C₂₃	1	2	yes	—
714	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
715	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
716	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
717	C₂²	—	2	2	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	4	no	—
720	C₂²	—	2	4	no	—
721	C₂²	—	2	4	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	2	2	no	—
725	C₂²	—	2	2	no	—
726	C₂²	—	2	4	no	—
727	C₂²	—	2	2	no	—
728	C₂²	—	2	4	no	—
729	C₂²	—	2	2	no	—
730	C₂²	—	4	16	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	4	no	—
737	C₂²	C₄×#41×C₂₃	1	4	yes	—
738	C₂²	C₂⁴×C₄×C₂₃	1	1	yes	characteristic
739	C₂²	C₂²×#41×C₂₃	1	2	yes	—
740	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
741	C₂²	C₂₃×#585	1	1	yes	characteristic
742	C₂²	C₂₃×#585	1	1	yes	characteristic
743	C₄	—	2	4	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	2	no	—
746	C₄	—	2	2	no	—
747	C₄	—	2	4	no	—
748	C₄	—	2	4	no	—
749	C₄	—	2	4	no	—
750	C₄	—	2	4	no	—
751	C₄	—	4	4	no	—
752	C₄	—	4	2	no	—
753	C₄	—	4	2	no	—
754	C₄	—	4	4	no	—
755	C₄	C₂₃×#518	1	4	yes	—
756	C₂	—	2	4	no	—
757	C₂	—	4	2	no	—
758	C₂	—	4	2	no	—
759	C₂	—	4	4	no	—
760	C₂	C₂×C₄×#41×C₂₃	1	1	yes	characteristic
761	C₂	C₂×C₂₃×#518	1	1	yes	characteristic
762	C₂	C₂₃×#3428	1	1	yes	characteristic
763	C₂	C₂₃×#3505	1	2	yes	—
764	C₂	C₂₃×#3506	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×#525	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×#2374	C₂	semidirect
3. C₂₃×#2363	C₂	semidirect
4. C₂₃×#2362	C₂	semidirect
5. C₂₃×#2357	C₂	semidirect
6. C₂₃×#2353	C₂	semidirect
7. C₂₃×#2347	C₂	semidirect
8. C₂₃×#2346	C₂	semidirect
9. C₂₃×#2341	C₂	semidirect
10. C₂₃×#2339	C₂	semidirect
11. C₂₃×#2321	C₂	semidirect
12. C₂₃×#2318	C₂	semidirect
13. C₄×C₂₃×C₂²⋊Q₈	C₂	semidirect
14. C₄×C₂₃×#121	C₂	semidirect
15. C₂₃×#2280	C₂	semidirect
16. C₂₃×#2275	C₂	semidirect
17. C₂×C₄×C₂²⋊C₄×C₂₃	C₂	semidirect
20. C₂₃×#525	C₄	semidirect
27. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
31. C₂×C₄×D₄×C₂₃	C₂²	semidirect
36. C₂₃×#391	C₂²	semidirect
39. C₂₃×#390	C₂²	semidirect
40. C₂₃×#389	C₂²	semidirect
41. C₂₃×#389	C₂²	semidirect
46. C₂₃×#388	C₂²	semidirect
47. C₂₃×#388	C₂²	semidirect
48. C₂₃×#387	C₂²	semidirect
49. C₂₃×#387	C₂²	semidirect
54. C₂₃×#383	C₂²	semidirect
55. C₂₃×#382	C₂²	semidirect
57. C₂₃×#381	C₂²	semidirect
61. C₂₃×#380	C₂²	semidirect
63. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
64. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
65. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
66. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
67. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
77. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
78. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
79. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
80. C₂₃×#376	C₂²	semidirect
83. C₂×C₂₃×#95	C₂²	semidirect
86. C₂×#41×C₂₃	C₂×C₄	semidirect
93. C₂³×C₄×C₂₃	C₂×C₄	semidirect
104. C₂₃×#123	C₂×C₄	semidirect
105. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
106. C₂₃×C₂²⋊Q₈	C₂×C₄	semidirect
108. C₂₃×#121	C₂×C₄	semidirect
109. C₂₃×#120	C₂×C₄	semidirect
113. C₄×D₄×C₂₃	C₂×C₄	semidirect
114. C₄×D₄×C₂₃	C₂×C₄	semidirect
116. C₂₃×#117	C₂×C₄	semidirect
212. C₂²×C₄×C₂₃	#41	semidirect
260. #34223	C₂₃	direct (N × H)
336. #2374	C₂×C₂₃	semidirect
337. #2363	C₂×C₂₃	semidirect
338. #2362	C₂×C₂₃	semidirect
339. #2357	C₂×C₂₃	semidirect
340. #2353	C₂×C₂₃	semidirect
341. #2347	C₂×C₂₃	semidirect
342. #2346	C₂×C₂₃	semidirect
343. #2341	C₂×C₂₃	semidirect
344. #2339	C₂×C₂₃	semidirect
345. #2321	C₂×C₂₃	semidirect
346. #2318	C₂×C₂₃	semidirect
347. C₄×C₂²⋊Q₈	C₂×C₂₃	semidirect
348. C₄×#121	C₂×C₂₃	semidirect
349. #2280	C₂×C₂₃	semidirect
350. #2275	C₂×C₂₃	semidirect
351. C₂×C₄×C₂²⋊C₄	C₂×C₂₃	semidirect
393. #525	C₄×C₂₃	semidirect
400. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
404. C₂×C₄×D₄	C₂²×C₂₃	semidirect
409. #391	C₂²×C₂₃	semidirect
412. #390	C₂²×C₂₃	semidirect
413. #389	C₂²×C₂₃	semidirect
414. #389	C₂²×C₂₃	semidirect
419. #388	C₂²×C₂₃	semidirect
420. #388	C₂²×C₂₃	semidirect
421. #387	C₂²×C₂₃	semidirect
422. #387	C₂²×C₂₃	semidirect
427. #383	C₂²×C₂₃	semidirect
428. #382	C₂²×C₂₃	semidirect
430. #381	C₂²×C₂₃	semidirect
434. #380	C₂²×C₂₃	semidirect
436. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
437. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
438. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
439. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
440. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
450. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
451. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
452. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
453. #376	C₂²×C₂₃	semidirect
456. C₂×#95	C₂²×C₂₃	semidirect
468. C₂×#41	C₂×C₄×C₂₃	semidirect
475. C₂³×C₄	C₂×C₄×C₂₃	semidirect
486. #123	C₂×C₄×C₂₃	semidirect
487. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
488. C₂²⋊Q₈	C₂×C₄×C₂₃	semidirect
490. #121	C₂×C₄×C₂₃	semidirect
491. #120	C₂×C₄×C₂₃	semidirect
495. C₄×D₄	C₂×C₄×C₂₃	semidirect
496. C₄×D₄	C₂×C₄×C₂₃	semidirect
498. #117	C₂×C₄×C₂₃	semidirect
550. C₂₃	#34223	direct (N × H)
595. C₂²×C₄	#41×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×#525	2
C₂₃×#2374	2
C₂₃×#2363	2
C₂₃×#2362	2
C₂₃×#2357	2
C₂₃×#2353	2
C₂₃×#2347	2
C₂₃×#2346	2
C₂₃×#2341	2
C₂₃×#2339	2
C₂₃×#2321	2
C₂₃×#2318	2
C₄×C₂₃×C₂²⋊Q₈	2
C₄×C₂₃×#121	2
C₂₃×#2280	2
C₂₃×#2275	2
C₂×C₄×C₂²⋊C₄×C₂₃	2
#34223	23

Subgroups — C23×#34223 #19181849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34223 #19181849