Subgroups — C₂₃×#34996 #19182622

Order 5888.

2078 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2852	C₂	1	2	yes	maximal, complemented
2	C₂₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2626	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#2622	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2617	C₂	1	1	yes	maximal, characteristic
7	C₂₃×#2523	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2518	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2518	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2517	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2467	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2466	C₂	1	2	yes	maximal, complemented
13	C₂₃×#2460	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2459	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2325	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2318	C₂	1	2	yes	maximal, complemented
18	C₄×C₂₃×#120	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#126	C₂²	1	2	yes	complemented
22	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₂₃×C₂²⋊Q₈	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×D₄×C₂₃	C₂²	1	2	yes	—
28	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
34	C₂₃×#399	C₂²	1	2	yes	—
35	C₂₃×#397	C₂²	1	2	yes	—
36	C₂₃×#397	C₂²	1	2	yes	—
37	C₂₃×#397	C₂²	1	2	yes	—
38	C₂₃×#397	C₂²	1	2	yes	—
39	C₂₃×#397	C₂²	1	2	yes	—
40	C₂₃×#396	C₂²	1	2	yes	—
41	C₂₃×#396	C₂²	1	2	yes	—
42	C₂₃×#394	C₂²	1	2	yes	—
43	C₂₃×#394	C₂²	1	2	yes	—
44	C₂₃×#394	C₂²	1	2	yes	—
45	C₂₃×#394	C₂²	1	2	yes	—
46	C₂₃×#394	C₂²	1	2	yes	—
47	C₂₃×#394	C₂²	1	2	yes	—
48	C₂₃×#393	C₂²	1	2	yes	—
49	C₂₃×#392	C₂²	1	2	yes	—
50	C₂₃×#391	C₂²	1	2	yes	complemented
51	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
52	C₂₃×#390	C₂²	1	1	yes	characteristic, complemented
53	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
54	C₂₃×#389	C₂²	1	2	yes	complemented
55	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
56	C₂₃×#388	C₂²	1	2	yes	complemented
57	C₂₃×#388	C₂²	1	2	yes	complemented
58	C₂₃×#388	C₂²	1	2	yes	complemented
59	C₂₃×#388	C₂²	1	2	yes	complemented
60	C₂₃×#388	C₂²	1	2	yes	complemented
61	C₂₃×#388	C₂²	1	2	yes	complemented
62	C₂₃×#388	C₂²	1	2	yes	complemented
63	C₂₃×#388	C₂²	1	2	yes	complemented
64	C₂₃×#387	C₂²	1	2	yes	complemented
65	C₂₃×#387	C₂²	1	2	yes	complemented
66	C₂₃×#387	C₂²	1	2	yes	complemented
67	C₂₃×#387	C₂²	1	2	yes	complemented
68	C₂₃×#387	C₂²	1	2	yes	complemented
69	C₂₃×#387	C₂²	1	2	yes	complemented
70	C₂₃×#387	C₂²	1	2	yes	complemented
71	C₂₃×#387	C₂²	1	2	yes	complemented
72	C₂₃×#387	C₂²	1	2	yes	complemented
73	C₂₃×#387	C₂²	1	2	yes	complemented
74	C₂₃×#386	C₂²	1	2	yes	—
75	C₂₃×#386	C₂²	1	2	yes	—
76	C₂₃×#386	C₂²	1	2	yes	—
77	C₂₃×#386	C₂²	1	2	yes	—
78	C₂₃×#386	C₂²	1	2	yes	—
79	C₂₃×#386	C₂²	1	2	yes	—
80	C₂₃×#386	C₂²	1	2	yes	complemented
81	C₂₃×#385	C₂²	1	2	yes	—
82	C₂₃×#385	C₂²	1	2	yes	—
83	C₂₃×#385	C₂²	1	2	yes	—
84	C₂₃×#385	C₂²	1	2	yes	—
85	C₂₃×#385	C₂²	1	2	yes	—
86	C₂₃×#385	C₂²	1	2	yes	—
87	C₂₃×#385	C₂²	1	2	yes	complemented
88	C₂₃×#383	C₂²	1	2	yes	complemented
89	C₂₃×#383	C₂²	1	2	yes	complemented
90	C₂₃×#382	C₂²	1	1	yes	characteristic, complemented
91	C₂₃×#382	C₂²	1	2	yes	complemented
92	C₂₃×#382	C₂²	1	1	yes	characteristic, complemented
93	C₂₃×#381	C₂²	1	2	yes	complemented
94	C₂₃×#380	C₂²	1	1	yes	characteristic
95	C₂₃×#380	C₂²	1	1	yes	characteristic
96	C₂₃×#380	C₂²	1	2	yes	complemented
97	C₂₃×#379	C₂²	1	2	yes	—
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	—
101	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
102	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
103	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
104	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
105	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
106	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
107	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
109	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₂₃	—	2	4	no	—
114	C₂³×C₄×C₂₃	—	4	2	no	—
115	C₂³×C₄×C₂₃	—	4	2	no	—
116	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
118	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
119	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
120	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
122	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
123	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
124	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
125	C₂₃×#126	—	4	4	no	—
126	C₂₃×#125	—	4	2	no	—
127	C₂₃×#124	—	4	2	no	—
128	C₂₃×C₂²⋊Q₈	—	2	4	no	—
129	C₂₃×#121	—	2	4	no	—
130	C₂₃×#120	—	2	8	no	—
131	C₄×D₄×C₂₃	—	2	8	no	—
132	C₄×D₄×C₂₃	—	4	4	no	—
133	C₄×D₄×C₂₃	—	4	4	no	—
134	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
136	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
138	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
145	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
151	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
152	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
163	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
164	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
165	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
166	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
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×C₄²×C₂₃	—	4	2	no	—
176	C₂×C₄²×C₂₃	—	4	2	no	—
177	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
178	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
181	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
182	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
183	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
184	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
186	C₂₃×#95	C₂³	1	2	yes	—
187	C₂₃×#95	C₂³	1	2	yes	—
188	C₂₃×#95	C₂³	1	2	yes	—
189	C₂₃×#95	C₂³	1	2	yes	—
190	C₂₃×#95	C₂³	1	2	yes	—
191	C₂₃×#95	C₂³	1	2	yes	—
192	C₂₃×#95	C₂³	1	2	yes	—
193	C₂₃×#95	C₂³	1	2	yes	—
194	C₂₃×#95	C₂³	1	2	yes	—
195	C₂₃×#95	C₂³	1	2	yes	—
196	C₂₃×#95	C₂³	1	2	yes	—
197	C₂₃×#95	C₂³	1	2	yes	—
198	C₂₃×#95	C₂³	1	2	yes	—
199	C₂₃×#95	C₂³	1	2	yes	—
200	C₂₃×#95	C₂³	1	2	yes	—
201	C₂₃×#95	C₂³	1	2	yes	—
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	C₂⁴×C₂₃	—	2	2	no	—
211	C₂⁴×C₂₃	—	2	2	no	—
212	C₂⁴×C₂₃	—	4	1	no	—
213	C₂⁴×C₂₃	—	4	1	no	—
214	C₂⁴×C₂₃	—	4	1	no	—
215	C₂⁴×C₂₃	—	4	1	no	—
216	C₂⁴×C₂₃	#41	1	4	yes	—
217	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
218	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
219	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
220	C₂×Q₈×C₂₃	—	2	2	no	—
221	C₂×Q₈×C₂₃	—	4	1	no	—
222	C₂×Q₈×C₂₃	—	4	1	no	—
223	C₂×D₄×C₂₃	—	2	4	no	—
224	C₂×D₄×C₂₃	—	2	4	no	—
225	C₂×D₄×C₂₃	—	2	4	no	—
226	C₂×D₄×C₂₃	—	2	4	no	—
227	C₂×D₄×C₂₃	—	2	4	no	—
228	C₂×D₄×C₂₃	—	2	2	no	—
229	C₂×D₄×C₂₃	—	4	2	no	—
230	C₂×D₄×C₂₃	—	4	2	no	—
231	C₂×D₄×C₂₃	—	4	2	no	—
232	C₂×D₄×C₂₃	—	4	2	no	—
233	C₂×D₄×C₂₃	—	4	1	no	—
234	C₂×D₄×C₂₃	—	4	1	no	—
235	C₂²×C₄×C₂₃	—	2	2	no	—
236	C₂²×C₄×C₂₃	—	2	2	no	—
237	C₂²×C₄×C₂₃	—	2	2	no	—
238	C₂²×C₄×C₂₃	—	2	2	no	—
239	C₂²×C₄×C₂₃	—	2	2	no	—
240	C₂²×C₄×C₂₃	—	2	2	no	—
241	C₂²×C₄×C₂₃	—	2	4	no	—
242	C₂²×C₄×C₂₃	—	2	4	no	—
243	C₂²×C₄×C₂₃	—	2	4	no	—
244	C₂²×C₄×C₂₃	—	2	4	no	—
245	C₂²×C₄×C₂₃	—	2	4	no	—
246	C₂²×C₄×C₂₃	—	4	1	no	—
247	C₂²×C₄×C₂₃	—	4	1	no	—
248	C₂²×C₄×C₂₃	—	4	1	no	—
249	C₂²×C₄×C₂₃	—	4	1	no	—
250	C₂²×C₄×C₂₃	—	4	2	no	—
251	C₂²×C₄×C₂₃	—	4	2	no	—
252	C₂²×C₄×C₂₃	—	4	1	no	—
253	C₂²×C₄×C₂₃	—	4	1	no	—
254	C₂²×C₄×C₂₃	—	4	1	no	—
255	C₂²×C₄×C₂₃	—	4	1	no	—
256	C₂²×C₄×C₂₃	—	4	1	no	—
257	C₂²×C₄×C₂₃	—	4	1	no	—
258	C₂²×C₄×C₂₃	—	4	2	no	—
259	C₂²×C₄×C₂₃	—	4	2	no	—
260	C₂²×C₄×C₂₃	—	4	16	no	—
261	C₂²×C₄×C₂₃	#41	1	4	yes	—
262	C₂²×C₄×C₂₃	#41	1	4	yes	—
263	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
267	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
273	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
279	C₄⋊C₄×C₂₃	—	2	4	no	—
280	C₄⋊C₄×C₂₃	—	2	2	no	—
281	C₄⋊C₄×C₂₃	—	2	2	no	—
282	C₄⋊C₄×C₂₃	—	2	4	no	—
283	C₄⋊C₄×C₂₃	—	2	4	no	—
284	C₄⋊C₄×C₂₃	—	2	4	no	—
285	C₄⋊C₄×C₂₃	—	4	1	no	—
286	C₄⋊C₄×C₂₃	—	4	1	no	—
287	C₄⋊C₄×C₂₃	—	4	2	no	—
288	C₄⋊C₄×C₂₃	—	4	2	no	—
289	C₄⋊C₄×C₂₃	—	4	2	no	—
290	C₄⋊C₄×C₂₃	—	4	1	no	—
291	C₄⋊C₄×C₂₃	—	4	1	no	—
292	C₄⋊C₄×C₂₃	—	4	2	no	—
293	C₄⋊C₄×C₂₃	—	4	2	no	—
294	C₄⋊C₄×C₂₃	—	4	2	no	—
295	C₂²⋊C₄×C₂₃	—	2	4	no	—
296	C₂²⋊C₄×C₂₃	—	2	4	no	—
297	C₂²⋊C₄×C₂₃	—	2	4	no	—
298	C₂²⋊C₄×C₂₃	—	2	4	no	—
299	C₂²⋊C₄×C₂₃	—	2	4	no	—
300	C₂²⋊C₄×C₂₃	—	2	4	no	—
301	C₂²⋊C₄×C₂₃	—	2	4	no	—
302	C₂²⋊C₄×C₂₃	—	2	4	no	—
303	C₂²⋊C₄×C₂₃	—	2	4	no	—
304	C₂²⋊C₄×C₂₃	—	2	4	no	—
305	C₂²⋊C₄×C₂₃	—	2	4	no	—
306	C₂²⋊C₄×C₂₃	—	2	4	no	—
307	C₂²⋊C₄×C₂₃	—	2	4	no	—
308	C₂²⋊C₄×C₂₃	—	4	2	no	—
309	C₂²⋊C₄×C₂₃	—	4	2	no	—
310	C₂²⋊C₄×C₂₃	—	4	2	no	—
311	C₂²⋊C₄×C₂₃	—	4	2	no	—
312	C₂²⋊C₄×C₂₃	—	4	2	no	—
313	C₂²⋊C₄×C₂₃	—	4	2	no	—
314	C₂²⋊C₄×C₂₃	—	4	2	no	—
315	C₂²⋊C₄×C₂₃	—	4	2	no	—
316	C₂²⋊C₄×C₂₃	—	4	2	no	—
317	C₂²⋊C₄×C₂₃	—	4	2	no	—
318	C₄²×C₂₃	—	2	4	no	—
319	C₄²×C₂₃	—	2	2	no	—
320	C₄²×C₂₃	—	2	2	no	—
321	C₄²×C₂₃	—	2	4	no	—
322	C₄²×C₂₃	—	4	1	no	—
323	C₄²×C₂₃	—	4	1	no	—
324	C₄²×C₂₃	—	4	2	no	—
325	C₄²×C₂₃	—	4	2	no	—
326	C₄²×C₂₃	—	4	2	no	—
327	#34996	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
328	C₂³×C₂₃	—	2	1	no	—
329	C₂³×C₂₃	—	2	1	no	—
330	C₂³×C₂₃	—	2	1	no	—
331	C₂³×C₂₃	—	2	1	no	—
332	C₂³×C₂₃	—	2	8	no	—
333	C₂³×C₂₃	—	2	2	no	—
334	C₂³×C₂₃	—	2	2	no	—
335	C₂³×C₂₃	—	2	2	no	—
336	C₂³×C₂₃	—	2	2	no	—
337	C₂³×C₂₃	—	2	2	no	—
338	C₂³×C₂₃	—	2	2	no	—
339	C₂³×C₂₃	—	2	2	no	—
340	C₂³×C₂₃	—	2	2	no	—
341	C₂³×C₂₃	—	2	2	no	—
342	C₂³×C₂₃	—	2	2	no	—
343	C₂³×C₂₃	—	2	2	no	—
344	C₂³×C₂₃	—	2	2	no	—
345	C₂³×C₂₃	—	2	2	no	—
346	C₂³×C₂₃	—	4	4	no	—
347	C₂³×C₂₃	—	4	4	no	—
348	C₂³×C₂₃	—	4	4	no	—
349	C₂³×C₂₃	—	4	4	no	—
350	C₂³×C₂₃	—	4	4	no	—
351	C₂³×C₂₃	—	4	4	no	—
352	C₂³×C₂₃	C₂×#41	1	4	yes	—
353	C₂³×C₂₃	C₂×#41	1	2	yes	—
354	C₂³×C₂₃	C₂×#41	1	2	yes	—
355	C₂³×C₂₃	C₂×#41	1	2	yes	—
356	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
357	Q₈×C₂₃	—	8	2	no	—
358	D₄×C₂₃	—	4	8	no	—
359	D₄×C₂₃	—	4	8	no	—
360	D₄×C₂₃	—	4	8	no	—
361	D₄×C₂₃	—	8	2	no	—
362	C₂×C₄×C₂₃	—	2	8	no	—
363	C₂×C₄×C₂₃	—	2	1	no	—
364	C₂×C₄×C₂₃	—	2	1	no	—
365	C₂×C₄×C₂₃	—	2	1	no	—
366	C₂×C₄×C₂₃	—	2	1	no	—
367	C₂×C₄×C₂₃	—	2	1	no	—
368	C₂×C₄×C₂₃	—	2	1	no	—
369	C₂×C₄×C₂₃	—	2	2	no	—
370	C₂×C₄×C₂₃	—	2	2	no	—
371	C₂×C₄×C₂₃	—	2	1	no	—
372	C₂×C₄×C₂₃	—	2	1	no	—
373	C₂×C₄×C₂₃	—	2	2	no	—
374	C₂×C₄×C₂₃	—	2	2	no	—
375	C₂×C₄×C₂₃	—	2	1	no	—
376	C₂×C₄×C₂₃	—	2	2	no	—
377	C₂×C₄×C₂₃	—	2	1	no	—
378	C₂×C₄×C₂₃	—	2	2	no	—
379	C₂×C₄×C₂₃	—	2	2	no	—
380	C₂×C₄×C₂₃	—	2	2	no	—
381	C₂×C₄×C₂₃	—	2	2	no	—
382	C₂×C₄×C₂₃	—	2	2	no	—
383	C₂×C₄×C₂₃	—	2	2	no	—
384	C₂×C₄×C₂₃	—	2	2	no	—
385	C₂×C₄×C₂₃	—	2	2	no	—
386	C₂×C₄×C₂₃	—	2	1	no	—
387	C₂×C₄×C₂₃	—	2	2	no	—
388	C₂×C₄×C₂₃	—	2	2	no	—
389	C₂×C₄×C₂₃	—	2	1	no	—
390	C₂×C₄×C₂₃	—	2	2	no	—
391	C₂×C₄×C₂₃	—	2	2	no	—
392	C₂×C₄×C₂₃	—	2	2	no	—
393	C₂×C₄×C₂₃	—	2	2	no	—
394	C₂×C₄×C₂₃	—	2	2	no	—
395	C₂×C₄×C₂₃	—	2	2	no	—
396	C₂×C₄×C₂₃	—	2	2	no	—
397	C₂×C₄×C₂₃	—	2	2	no	—
398	C₂×C₄×C₂₃	—	2	1	no	—
399	C₂×C₄×C₂₃	—	2	2	no	—
400	C₂×C₄×C₂₃	—	2	2	no	—
401	C₂×C₄×C₂₃	—	2	2	no	—
402	C₂×C₄×C₂₃	—	2	2	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	—	4	4	no	—
407	C₂×C₄×C₂₃	—	4	4	no	—
408	C₂×C₄×C₂₃	—	4	8	no	—
409	C₂×C₄×C₂₃	—	4	8	no	—
410	C₂×C₄×C₂₃	—	4	4	no	—
411	C₂×C₄×C₂₃	—	4	4	no	—
412	C₂×C₄×C₂₃	—	4	4	no	—
413	C₂×C₄×C₂₃	—	8	4	no	—
414	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
415	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
416	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
417	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
418	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
419	#2852	C₂×C₂₃	1	2	yes	complemented
420	#2851	C₂×C₂₃	1	1	yes	characteristic, complemented
421	#2850	C₂×C₂₃	1	1	yes	characteristic, complemented
422	#2626	C₂×C₂₃	1	1	yes	characteristic, complemented
423	#2622	C₂×C₂₃	1	2	yes	complemented
424	#2617	C₂×C₂₃	1	1	yes	characteristic
425	#2523	C₂×C₂₃	1	2	yes	complemented
426	#2518	C₂×C₂₃	1	2	yes	complemented
427	#2518	C₂×C₂₃	1	2	yes	complemented
428	#2517	C₂×C₂₃	1	2	yes	complemented
429	#2467	C₂×C₂₃	1	2	yes	complemented
430	#2466	C₂×C₂₃	1	2	yes	complemented
431	#2460	C₂×C₂₃	1	2	yes	complemented
432	#2459	C₂×C₂₃	1	2	yes	complemented
433	#2329	C₂×C₂₃	1	1	yes	characteristic, complemented
434	#2325	C₂×C₂₃	1	1	yes	characteristic, complemented
435	#2318	C₂×C₂₃	1	2	yes	complemented
436	C₄×#120	C₂×C₂₃	1	2	yes	complemented
437	C₂×C₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
438	C₂²×C₂₃	—	2	2	no	—
439	C₂²×C₂₃	—	2	2	no	—
440	C₂²×C₂₃	—	2	2	no	—
441	C₂²×C₂₃	—	2	2	no	—
442	C₂²×C₂₃	—	2	2	no	—
443	C₂²×C₂₃	—	2	2	no	—
444	C₂²×C₂₃	—	2	4	no	—
445	C₂²×C₂₃	—	2	4	no	—
446	C₂²×C₂₃	—	2	4	no	—
447	C₂²×C₂₃	—	4	16	no	—
448	C₂²×C₂₃	—	4	2	no	—
449	C₂²×C₂₃	—	4	2	no	—
450	C₂²×C₂₃	—	4	2	no	—
451	C₂²×C₂₃	—	4	2	no	—
452	C₂²×C₂₃	—	4	2	no	—
453	C₂²×C₂₃	—	4	2	no	—
454	C₂²×C₂₃	—	4	2	no	—
455	C₂²×C₂₃	—	4	2	no	—
456	C₂²×C₂₃	—	4	2	no	—
457	C₂²×C₂₃	—	4	2	no	—
458	C₂²×C₂₃	—	4	2	no	—
459	C₂²×C₂₃	#529	1	4	yes	—
460	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
461	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
462	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
463	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
464	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
465	C₂²×C₂₃	#585	1	1	yes	characteristic
466	C₂²×C₂₃	#585	1	1	yes	characteristic
467	C₄×C₂₃	—	2	2	no	—
468	C₄×C₂₃	—	2	2	no	—
469	C₄×C₂₃	—	2	4	no	—
470	C₄×C₂₃	—	2	2	no	—
471	C₄×C₂₃	—	2	2	no	—
472	C₄×C₂₃	—	4	2	no	—
473	C₄×C₂₃	—	4	1	no	—
474	C₄×C₂₃	—	4	2	no	—
475	C₄×C₂₃	—	4	1	no	—
476	C₄×C₂₃	—	4	2	no	—
477	C₄×C₂₃	—	4	2	no	—
478	C₄×C₂₃	—	4	2	no	—
479	C₄×C₂₃	—	4	2	no	—
480	C₄×C₂₃	—	4	2	no	—
481	C₄×C₂₃	—	4	2	no	—
482	C₄×C₂₃	—	4	2	no	—
483	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
484	C₂×#126	C₂²×C₂₃	1	2	yes	complemented
485	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic, complemented
486	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic, complemented
487	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
488	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
489	C₂×#120	C₂²×C₂₃	1	2	yes	—
490	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
491	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
492	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
493	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
494	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
495	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
496	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
497	#399	C₂²×C₂₃	1	2	yes	—
498	#397	C₂²×C₂₃	1	2	yes	—
499	#397	C₂²×C₂₃	1	2	yes	—
500	#397	C₂²×C₂₃	1	2	yes	—
501	#397	C₂²×C₂₃	1	2	yes	—
502	#397	C₂²×C₂₃	1	2	yes	—
503	#396	C₂²×C₂₃	1	2	yes	—
504	#396	C₂²×C₂₃	1	2	yes	—
505	#394	C₂²×C₂₃	1	2	yes	—
506	#394	C₂²×C₂₃	1	2	yes	—
507	#394	C₂²×C₂₃	1	2	yes	—
508	#394	C₂²×C₂₃	1	2	yes	—
509	#394	C₂²×C₂₃	1	2	yes	—
510	#394	C₂²×C₂₃	1	2	yes	—
511	#393	C₂²×C₂₃	1	2	yes	—
512	#392	C₂²×C₂₃	1	2	yes	—
513	#391	C₂²×C₂₃	1	2	yes	complemented
514	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
515	#390	C₂²×C₂₃	1	1	yes	characteristic, complemented
516	#389	C₂²×C₂₃	1	2	yes	complemented
517	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
518	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
519	#388	C₂²×C₂₃	1	2	yes	complemented
520	#388	C₂²×C₂₃	1	2	yes	complemented
521	#388	C₂²×C₂₃	1	2	yes	complemented
522	#388	C₂²×C₂₃	1	2	yes	complemented
523	#388	C₂²×C₂₃	1	2	yes	complemented
524	#388	C₂²×C₂₃	1	2	yes	complemented
525	#388	C₂²×C₂₃	1	2	yes	complemented
526	#388	C₂²×C₂₃	1	2	yes	complemented
527	#387	C₂²×C₂₃	1	2	yes	complemented
528	#387	C₂²×C₂₃	1	2	yes	complemented
529	#387	C₂²×C₂₃	1	2	yes	complemented
530	#387	C₂²×C₂₃	1	2	yes	complemented
531	#387	C₂²×C₂₃	1	2	yes	complemented
532	#387	C₂²×C₂₃	1	2	yes	complemented
533	#387	C₂²×C₂₃	1	2	yes	complemented
534	#387	C₂²×C₂₃	1	2	yes	complemented
535	#387	C₂²×C₂₃	1	2	yes	complemented
536	#387	C₂²×C₂₃	1	2	yes	complemented
537	#386	C₂²×C₂₃	1	2	yes	—
538	#386	C₂²×C₂₃	1	2	yes	—
539	#386	C₂²×C₂₃	1	2	yes	—
540	#386	C₂²×C₂₃	1	2	yes	—
541	#386	C₂²×C₂₃	1	2	yes	—
542	#386	C₂²×C₂₃	1	2	yes	—
543	#386	C₂²×C₂₃	1	2	yes	complemented
544	#385	C₂²×C₂₃	1	2	yes	—
545	#385	C₂²×C₂₃	1	2	yes	—
546	#385	C₂²×C₂₃	1	2	yes	—
547	#385	C₂²×C₂₃	1	2	yes	—
548	#385	C₂²×C₂₃	1	2	yes	—
549	#385	C₂²×C₂₃	1	2	yes	—
550	#385	C₂²×C₂₃	1	2	yes	complemented
551	#383	C₂²×C₂₃	1	2	yes	complemented
552	#383	C₂²×C₂₃	1	2	yes	complemented
553	#382	C₂²×C₂₃	1	2	yes	complemented
554	#382	C₂²×C₂₃	1	1	yes	characteristic, complemented
555	#382	C₂²×C₂₃	1	1	yes	characteristic, complemented
556	#381	C₂²×C₂₃	1	2	yes	complemented
557	#380	C₂²×C₂₃	1	1	yes	characteristic
558	#380	C₂²×C₂₃	1	1	yes	characteristic
559	#380	C₂²×C₂₃	1	2	yes	complemented
560	#379	C₂²×C₂₃	1	2	yes	—
561	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
562	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
563	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
564	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
565	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
566	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
567	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
568	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
569	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
570	C₂×C₂₃	—	2	4	no	—
571	C₂×C₂₃	—	4	4	no	—
572	C₂×C₂₃	—	8	2	no	—
573	C₂×C₂₃	C₂×#529	1	1	yes	characteristic
574	C₂×C₂₃	#3459	1	1	yes	characteristic
575	C₂×C₂₃	#3459	1	1	yes	characteristic
576	C₂×C₂₃	#3490	1	1	yes	characteristic
577	C₂×C₂₃	#3493	1	1	yes	characteristic
578	C₂×C₂₃	#3505	1	1	yes	characteristic
579	C₂×C₂₃	#3506	1	1	yes	characteristic
580	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
581	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
582	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
583	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
584	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
585	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
586	C₂³×C₄	—	2	4	no	—
587	C₂³×C₄	—	4	2	no	—
588	C₂³×C₄	—	4	2	no	—
589	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
590	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
591	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
592	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
593	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
594	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
595	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
596	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
597	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
598	#126	—	4	4	no	—
599	#125	—	4	2	no	—
600	#124	—	4	2	no	—
601	C₂²⋊Q₈	—	2	4	no	—
602	#121	—	2	4	no	—
603	#120	—	2	8	no	—
604	C₄×D₄	—	2	8	no	—
605	C₄×D₄	—	4	4	no	—
606	C₄×D₄	—	4	4	no	—
607	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
610	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
612	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
614	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
615	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
616	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
617	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
618	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
623	C₂×C₂²⋊C₄	—	2	4	no	—
624	C₂×C₂²⋊C₄	—	2	4	no	—
625	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
626	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
627	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
628	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
629	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
630	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
631	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
632	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
633	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
634	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
635	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
636	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
637	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
638	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
639	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
640	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
641	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
642	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
643	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
644	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
645	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
646	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
648	C₂×C₄²	—	4	2	no	—
649	C₂×C₄²	—	4	2	no	—
650	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
651	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
654	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
655	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
656	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
657	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
659	#95	C₂³×C₂₃	1	2	yes	—
660	#95	C₂³×C₂₃	1	2	yes	—
661	#95	C₂³×C₂₃	1	2	yes	—
662	#95	C₂³×C₂₃	1	2	yes	—
663	#95	C₂³×C₂₃	1	2	yes	—
664	#95	C₂³×C₂₃	1	2	yes	—
665	#95	C₂³×C₂₃	1	2	yes	—
666	#95	C₂³×C₂₃	1	2	yes	—
667	#95	C₂³×C₂₃	1	2	yes	—
668	#95	C₂³×C₂₃	1	2	yes	—
669	#95	C₂³×C₂₃	1	2	yes	—
670	#95	C₂³×C₂₃	1	2	yes	—
671	#95	C₂³×C₂₃	1	2	yes	—
672	#95	C₂³×C₂₃	1	2	yes	—
673	#95	C₂³×C₂₃	1	2	yes	—
674	#95	C₂³×C₂₃	1	2	yes	—
675	#95	C₂³×C₂₃	1	2	yes	—
676	#95	C₂³×C₂₃	1	2	yes	—
677	#95	C₂³×C₂₃	1	2	yes	—
678	#95	C₂³×C₂₃	1	2	yes	—
679	#95	C₂³×C₂₃	1	2	yes	—
680	#95	C₂³×C₂₃	1	2	yes	—
681	#95	C₂³×C₂₃	1	2	yes	—
682	#95	C₂³×C₂₃	1	2	yes	—
683	C₂₃	#34996	1	1	yes	characteristic, direct product factor, Sylow
684	C₂⁴	—	2	2	no	—
685	C₂⁴	—	2	2	no	—
686	C₂⁴	—	4	1	no	—
687	C₂⁴	—	4	1	no	—
688	C₂⁴	—	4	1	no	—
689	C₂⁴	—	4	1	no	—
690	C₂⁴	#41×C₂₃	1	4	yes	—
691	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
692	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
693	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
694	C₂×Q₈	—	2	2	no	—
695	C₂×Q₈	—	4	1	no	—
696	C₂×Q₈	—	4	1	no	—
697	C₂×D₄	—	2	4	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	4	no	—
700	C₂×D₄	—	2	4	no	—
701	C₂×D₄	—	2	4	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	4	2	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	4	2	no	—
706	C₂×D₄	—	4	2	no	—
707	C₂×D₄	—	4	1	no	—
708	C₂×D₄	—	4	1	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	2	no	—
714	C₂²×C₄	—	2	2	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	4	no	—
717	C₂²×C₄	—	2	4	no	—
718	C₂²×C₄	—	2	4	no	—
719	C₂²×C₄	—	2	4	no	—
720	C₂²×C₄	—	4	1	no	—
721	C₂²×C₄	—	4	1	no	—
722	C₂²×C₄	—	4	1	no	—
723	C₂²×C₄	—	4	1	no	—
724	C₂²×C₄	—	4	2	no	—
725	C₂²×C₄	—	4	2	no	—
726	C₂²×C₄	—	4	1	no	—
727	C₂²×C₄	—	4	1	no	—
728	C₂²×C₄	—	4	1	no	—
729	C₂²×C₄	—	4	1	no	—
730	C₂²×C₄	—	4	1	no	—
731	C₂²×C₄	—	4	1	no	—
732	C₂²×C₄	—	4	2	no	—
733	C₂²×C₄	—	4	2	no	—
734	C₂²×C₄	—	4	16	no	—
735	C₂²×C₄	#41×C₂₃	1	4	yes	—
736	C₂²×C₄	#41×C₂₃	1	4	yes	—
737	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
741	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
746	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
747	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
750	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
751	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
753	C₄⋊C₄	—	2	4	no	—
754	C₄⋊C₄	—	2	2	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	4	no	—
757	C₄⋊C₄	—	2	4	no	—
758	C₄⋊C₄	—	2	4	no	—
759	C₄⋊C₄	—	4	1	no	—
760	C₄⋊C₄	—	4	1	no	—
761	C₄⋊C₄	—	4	2	no	—
762	C₄⋊C₄	—	4	2	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₄⋊C₄	—	4	1	no	—
765	C₄⋊C₄	—	4	1	no	—
766	C₄⋊C₄	—	4	2	no	—
767	C₄⋊C₄	—	4	2	no	—
768	C₄⋊C₄	—	4	2	no	—
769	C₂²⋊C₄	—	2	4	no	—
770	C₂²⋊C₄	—	2	4	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	4	no	—
774	C₂²⋊C₄	—	2	4	no	—
775	C₂²⋊C₄	—	2	4	no	—
776	C₂²⋊C₄	—	2	4	no	—
777	C₂²⋊C₄	—	2	4	no	—
778	C₂²⋊C₄	—	2	4	no	—
779	C₂²⋊C₄	—	2	4	no	—
780	C₂²⋊C₄	—	2	4	no	—
781	C₂²⋊C₄	—	2	4	no	—
782	C₂²⋊C₄	—	4	2	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	2	no	—
788	C₂²⋊C₄	—	4	2	no	—
789	C₂²⋊C₄	—	4	2	no	—
790	C₂²⋊C₄	—	4	2	no	—
791	C₂²⋊C₄	—	4	2	no	—
792	C₄²	—	2	4	no	—
793	C₄²	—	2	2	no	—
794	C₄²	—	2	2	no	—
795	C₄²	—	2	4	no	—
796	C₄²	—	4	1	no	—
797	C₄²	—	4	1	no	—
798	C₄²	—	4	2	no	—
799	C₄²	—	4	2	no	—
800	C₄²	—	4	2	no	—
801	C₂³	—	2	1	no	—
802	C₂³	—	2	1	no	—
803	C₂³	—	2	1	no	—
804	C₂³	—	2	1	no	—
805	C₂³	—	2	2	no	—
806	C₂³	—	2	2	no	—
807	C₂³	—	2	2	no	—
808	C₂³	—	2	2	no	—
809	C₂³	—	2	2	no	—
810	C₂³	—	2	2	no	—
811	C₂³	—	2	8	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	2	2	no	—
815	C₂³	—	2	2	no	—
816	C₂³	—	2	2	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	4	4	no	—
820	C₂³	—	4	4	no	—
821	C₂³	—	4	4	no	—
822	C₂³	—	4	4	no	—
823	C₂³	—	4	4	no	—
824	C₂³	—	4	4	no	—
825	C₂³	C₂×#41×C₂₃	1	4	yes	—
826	C₂³	C₂×#41×C₂₃	1	2	yes	—
827	C₂³	C₂×#41×C₂₃	1	2	yes	—
828	C₂³	C₂×#41×C₂₃	1	2	yes	—
829	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
830	Q₈	—	8	2	no	—
831	D₄	—	4	8	no	—
832	D₄	—	4	8	no	—
833	D₄	—	4	8	no	—
834	D₄	—	8	2	no	—
835	C₂×C₄	—	2	8	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	1	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	2	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	1	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	2	no	—
864	C₂×C₄	—	2	2	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	2	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	2	2	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	1	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	4	4	no	—
880	C₂×C₄	—	4	4	no	—
881	C₂×C₄	—	4	8	no	—
882	C₂×C₄	—	4	8	no	—
883	C₂×C₄	—	4	4	no	—
884	C₂×C₄	—	4	4	no	—
885	C₂×C₄	—	4	4	no	—
886	C₂×C₄	—	8	4	no	—
887	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
888	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
889	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
890	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
891	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	2	2	no	—
897	C₂²	—	2	2	no	—
898	C₂²	—	2	4	no	—
899	C₂²	—	2	4	no	—
900	C₂²	—	2	4	no	—
901	C₂²	—	4	16	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	2	no	—
908	C₂²	—	4	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	2	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	4	2	no	—
913	C₂²	C₂₃×#529	1	4	yes	—
914	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
915	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
916	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
917	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
918	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
919	C₂²	C₂₃×#585	1	1	yes	characteristic
920	C₂²	C₂₃×#585	1	1	yes	characteristic
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	4	no	—
924	C₄	—	2	2	no	—
925	C₄	—	2	2	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	1	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	1	no	—
930	C₄	—	4	2	no	—
931	C₄	—	4	2	no	—
932	C₄	—	4	2	no	—
933	C₄	—	4	2	no	—
934	C₄	—	4	2	no	—
935	C₄	—	4	2	no	—
936	C₄	—	4	2	no	—
937	C₂	—	2	4	no	—
938	C₂	—	4	4	no	—
939	C₂	—	8	2	no	—
940	C₂	C₂×C₂₃×#529	1	1	yes	characteristic
941	C₂	C₂₃×#3459	1	1	yes	characteristic
942	C₂	C₂₃×#3459	1	1	yes	characteristic
943	C₂	C₂₃×#3490	1	1	yes	characteristic
944	C₂	C₂₃×#3493	1	1	yes	characteristic
945	C₂	C₂₃×#3505	1	1	yes	characteristic
946	C₂	C₂₃×#3506	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂₃×#2617	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#2852	C₂	semidirect
2. C₂₃×#2851	C₂	semidirect
3. C₂₃×#2850	C₂	semidirect
4. C₂₃×#2626	C₂	semidirect
5. C₂₃×#2622	C₂	semidirect
7. C₂₃×#2523	C₂	semidirect
8. C₂₃×#2518	C₂	semidirect
9. C₂₃×#2518	C₂	semidirect
10. C₂₃×#2517	C₂	semidirect
11. C₂₃×#2467	C₂	semidirect
12. C₂₃×#2466	C₂	semidirect
13. C₂₃×#2460	C₂	semidirect
14. C₂₃×#2459	C₂	semidirect
15. C₂₃×#2329	C₂	semidirect
16. C₂₃×#2325	C₂	semidirect
17. C₂₃×#2318	C₂	semidirect
18. C₄×C₂₃×#120	C₂	semidirect
19. C₂×C₄×C₂²⋊C₄×C₂₃	C₂	semidirect
21. C₂×C₂₃×#126	C₂²	semidirect
22. C₂×C₂₃×#125	C₂²	semidirect
23. C₂×C₂₃×#124	C₂²	semidirect
50. C₂₃×#391	C₂²	semidirect
51. C₂₃×#391	C₂²	semidirect
52. C₂₃×#390	C₂²	semidirect
53. C₂₃×#389	C₂²	semidirect
54. C₂₃×#389	C₂²	semidirect
55. C₂₃×#389	C₂²	semidirect
56. C₂₃×#388	C₂²	semidirect
57. C₂₃×#388	C₂²	semidirect
58. C₂₃×#388	C₂²	semidirect
59. C₂₃×#388	C₂²	semidirect
60. C₂₃×#388	C₂²	semidirect
61. C₂₃×#388	C₂²	semidirect
62. C₂₃×#388	C₂²	semidirect
63. C₂₃×#388	C₂²	semidirect
64. C₂₃×#387	C₂²	semidirect
65. C₂₃×#387	C₂²	semidirect
66. C₂₃×#387	C₂²	semidirect
67. C₂₃×#387	C₂²	semidirect
68. C₂₃×#387	C₂²	semidirect
69. C₂₃×#387	C₂²	semidirect
70. C₂₃×#387	C₂²	semidirect
71. C₂₃×#387	C₂²	semidirect
72. C₂₃×#387	C₂²	semidirect
73. C₂₃×#387	C₂²	semidirect
80. C₂₃×#386	C₂²	semidirect
87. C₂₃×#385	C₂²	semidirect
88. C₂₃×#383	C₂²	semidirect
89. C₂₃×#383	C₂²	semidirect
90. C₂₃×#382	C₂²	semidirect
91. C₂₃×#382	C₂²	semidirect
92. C₂₃×#382	C₂²	semidirect
93. C₂₃×#381	C₂²	semidirect
96. C₂₃×#380	C₂²	semidirect
327. #34996	C₂₃	direct (N × H)
419. #2852	C₂×C₂₃	semidirect
420. #2851	C₂×C₂₃	semidirect
421. #2850	C₂×C₂₃	semidirect
422. #2626	C₂×C₂₃	semidirect
423. #2622	C₂×C₂₃	semidirect
425. #2523	C₂×C₂₃	semidirect
426. #2518	C₂×C₂₃	semidirect
427. #2518	C₂×C₂₃	semidirect
428. #2517	C₂×C₂₃	semidirect
429. #2467	C₂×C₂₃	semidirect
430. #2466	C₂×C₂₃	semidirect
431. #2460	C₂×C₂₃	semidirect
432. #2459	C₂×C₂₃	semidirect
433. #2329	C₂×C₂₃	semidirect
434. #2325	C₂×C₂₃	semidirect
435. #2318	C₂×C₂₃	semidirect
436. C₄×#120	C₂×C₂₃	semidirect
437. C₂×C₄×C₂²⋊C₄	C₂×C₂₃	semidirect
484. C₂×#126	C₂²×C₂₃	semidirect
485. C₂×#125	C₂²×C₂₃	semidirect
486. C₂×#124	C₂²×C₂₃	semidirect
513. #391	C₂²×C₂₃	semidirect
514. #391	C₂²×C₂₃	semidirect
515. #390	C₂²×C₂₃	semidirect
516. #389	C₂²×C₂₃	semidirect
517. #389	C₂²×C₂₃	semidirect
518. #389	C₂²×C₂₃	semidirect
519. #388	C₂²×C₂₃	semidirect
520. #388	C₂²×C₂₃	semidirect
521. #388	C₂²×C₂₃	semidirect
522. #388	C₂²×C₂₃	semidirect
523. #388	C₂²×C₂₃	semidirect
524. #388	C₂²×C₂₃	semidirect
525. #388	C₂²×C₂₃	semidirect
526. #388	C₂²×C₂₃	semidirect
527. #387	C₂²×C₂₃	semidirect
528. #387	C₂²×C₂₃	semidirect
529. #387	C₂²×C₂₃	semidirect
530. #387	C₂²×C₂₃	semidirect
531. #387	C₂²×C₂₃	semidirect
532. #387	C₂²×C₂₃	semidirect
533. #387	C₂²×C₂₃	semidirect
534. #387	C₂²×C₂₃	semidirect
535. #387	C₂²×C₂₃	semidirect
536. #387	C₂²×C₂₃	semidirect
543. #386	C₂²×C₂₃	semidirect
550. #385	C₂²×C₂₃	semidirect
551. #383	C₂²×C₂₃	semidirect
552. #383	C₂²×C₂₃	semidirect
553. #382	C₂²×C₂₃	semidirect
554. #382	C₂²×C₂₃	semidirect
555. #382	C₂²×C₂₃	semidirect
556. #381	C₂²×C₂₃	semidirect
559. #380	C₂²×C₂₃	semidirect
683. C₂₃	#34996	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#2852	2
C₂₃×#2851	2
C₂₃×#2850	2
C₂₃×#2626	2
C₂₃×#2622	2
C₂₃×#2617	2
C₂₃×#2523	2
C₂₃×#2518	2
C₂₃×#2517	2
C₂₃×#2467	2
C₂₃×#2466	2
C₂₃×#2460	2
C₂₃×#2459	2
C₂₃×#2329	2
C₂₃×#2325	2
C₂₃×#2318	2
C₄×C₂₃×#120	2
C₂×C₄×C₂²⋊C₄×C₂₃	2
#34996	23

Subgroups — C23×#34996 #19182622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#34996 #19182622