Subgroups — C₂₃×#36766 #19184392

Order 5888.

1842 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2801	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2795	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2773	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2759	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2757	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2730	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2710	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2674	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2626	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2617	C₂	1	1	yes	maximal, characteristic
13	C₂₃×#2510	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2472	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2449	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2418	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂₃×#2325	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₂₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₂₃×#124	C₂²	1	2	yes	—
22	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₂₃×#123	C₂²	1	2	yes	—
24	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#120	C₂²	1	2	yes	—
29	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
30	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
35	C₂₃×#401	C₂²	1	2	yes	complemented
36	C₂₃×#400	C₂²	1	2	yes	complemented
37	C₂₃×#399	C₂²	1	2	yes	—
38	C₂₃×#399	C₂²	1	2	yes	—
39	C₂₃×#399	C₂²	1	2	yes	complemented
40	C₂₃×#398	C₂²	1	2	yes	complemented
41	C₂₃×#397	C₂²	1	2	yes	—
42	C₂₃×#397	C₂²	1	2	yes	—
43	C₂₃×#397	C₂²	1	2	yes	—
44	C₂₃×#397	C₂²	1	2	yes	complemented
45	C₂₃×#397	C₂²	1	2	yes	complemented
46	C₂₃×#396	C₂²	1	2	yes	—
47	C₂₃×#396	C₂²	1	2	yes	—
48	C₂₃×#396	C₂²	1	2	yes	complemented
49	C₂₃×#395	C₂²	1	2	yes	complemented
50	C₂₃×#394	C₂²	1	2	yes	—
51	C₂₃×#394	C₂²	1	2	yes	—
52	C₂₃×#394	C₂²	1	2	yes	—
53	C₂₃×#394	C₂²	1	2	yes	—
54	C₂₃×#394	C₂²	1	2	yes	—
55	C₂₃×#394	C₂²	1	2	yes	—
56	C₂₃×#393	C₂²	1	2	yes	—
57	C₂₃×#393	C₂²	1	2	yes	—
58	C₂₃×#392	C₂²	1	2	yes	—
59	C₂₃×#391	C₂²	1	2	yes	complemented
60	C₂₃×#391	C₂²	1	2	yes	complemented
61	C₂₃×#391	C₂²	1	1	yes	characteristic, complemented
62	C₂₃×#390	C₂²	1	2	yes	—
63	C₂₃×#390	C₂²	1	1	yes	characteristic, complemented
64	C₂₃×#389	C₂²	1	2	yes	complemented
65	C₂₃×#389	C₂²	1	2	yes	complemented
66	C₂₃×#389	C₂²	1	2	yes	complemented
67	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
69	C₂₃×#388	C₂²	1	2	yes	—
70	C₂₃×#388	C₂²	1	2	yes	—
71	C₂₃×#388	C₂²	1	2	yes	—
72	C₂₃×#388	C₂²	1	2	yes	—
73	C₂₃×#388	C₂²	1	2	yes	—
74	C₂₃×#388	C₂²	1	2	yes	—
75	C₂₃×#388	C₂²	1	2	yes	—
76	C₂₃×#388	C₂²	1	2	yes	—
77	C₂₃×#388	C₂²	1	2	yes	complemented
78	C₂₃×#388	C₂²	1	2	yes	complemented
79	C₂₃×#388	C₂²	1	2	yes	complemented
80	C₂₃×#388	C₂²	1	2	yes	complemented
81	C₂₃×#388	C₂²	1	2	yes	complemented
82	C₂₃×#387	C₂²	1	2	yes	complemented
83	C₂₃×#387	C₂²	1	2	yes	complemented
84	C₂₃×#387	C₂²	1	2	yes	complemented
85	C₂₃×#387	C₂²	1	2	yes	complemented
86	C₂₃×#387	C₂²	1	2	yes	complemented
87	C₂₃×#386	C₂²	1	2	yes	—
88	C₂₃×#386	C₂²	1	2	yes	—
89	C₂₃×#386	C₂²	1	2	yes	—
90	C₂₃×#386	C₂²	1	2	yes	—
91	C₂₃×#386	C₂²	1	2	yes	—
92	C₂₃×#386	C₂²	1	2	yes	complemented
93	C₂₃×#385	C₂²	1	2	yes	—
94	C₂₃×#385	C₂²	1	2	yes	—
95	C₂₃×#385	C₂²	1	2	yes	complemented
96	C₂₃×#385	C₂²	1	2	yes	complemented
97	C₂₃×#384	C₂²	1	1	yes	characteristic, complemented
98	C₂₃×#383	C₂²	1	2	yes	complemented
99	C₂₃×#382	C₂²	1	1	yes	characteristic, complemented
100	C₂₃×#380	C₂²	1	2	yes	—
101	C₂₃×#380	C₂²	1	1	yes	characteristic
102	C₂₃×#380	C₂²	1	1	yes	characteristic
103	C₂₃×#379	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×Q₈×C₂₃	C₂³	1	2	yes	—
110	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
112	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
114	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
119	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
120	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂₃×C₄⋊Q₈	—	4	2	no	—
122	C₂₃×#124	—	4	2	no	—
123	C₂₃×#124	—	4	4	no	—
124	C₂₃×#123	—	4	4	no	—
125	C₂₃×C₂²⋊Q₈	—	2	4	no	—
126	C₂₃×C₂²⋊Q₈	—	4	4	no	—
127	C₂₃×C₂²⋊Q₈	—	4	4	no	—
128	C₂₃×#121	—	2	4	no	—
129	C₂₃×#120	—	4	4	no	—
130	C₄×D₄×C₂₃	—	4	4	no	—
131	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
132	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
133	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
134	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
135	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
139	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	2	yes	—
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
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×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
152	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
153	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
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×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×C₄²×C₂₃	—	4	2	no	—
180	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
183	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
184	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
185	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
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	C₂⁴×C₂₃	—	2	2	no	—
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	C₂⁴	1	2	yes	—
217	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
218	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
219	C₂×Q₈×C₂₃	—	2	2	no	—
220	C₂×Q₈×C₂₃	—	2	4	no	—
221	C₂×Q₈×C₂₃	—	4	2	no	—
222	C₂×Q₈×C₂₃	—	4	1	no	—
223	C₂×Q₈×C₂₃	—	4	2	no	—
224	C₂×Q₈×C₂₃	—	4	1	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	1	no	—
233	C₂×D₄×C₂₃	—	4	2	no	—
234	C₂×D₄×C₂₃	—	4	1	no	—
235	C₂×D₄×C₂₃	—	4	2	no	—
236	C₂×D₄×C₂₃	—	4	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	2	no	—
242	C₂²×C₄×C₂₃	—	2	2	no	—
243	C₂²×C₄×C₂₃	—	2	2	no	—
244	C₂²×C₄×C₂₃	—	4	1	no	—
245	C₂²×C₄×C₂₃	—	4	1	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	1	no	—
251	C₂²×C₄×C₂₃	—	4	1	no	—
252	C₂²×C₄×C₂₃	—	4	1	no	—
253	C₂²×C₄×C₂₃	—	4	2	no	—
254	C₂²×C₄×C₂₃	—	4	2	no	—
255	C₂²×C₄×C₂₃	—	4	2	no	—
256	C₂²×C₄×C₂₃	—	4	1	no	—
257	C₂²×C₄×C₂₃	#41	1	4	yes	—
258	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
259	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
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	1	yes	characteristic
271	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
272	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
274	C₄⋊C₄×C₂₃	—	2	2	no	—
275	C₄⋊C₄×C₂₃	—	2	2	no	—
276	C₄⋊C₄×C₂₃	—	2	4	no	—
277	C₄⋊C₄×C₂₃	—	2	4	no	—
278	C₄⋊C₄×C₂₃	—	2	4	no	—
279	C₄⋊C₄×C₂₃	—	4	2	no	—
280	C₄⋊C₄×C₂₃	—	4	1	no	—
281	C₄⋊C₄×C₂₃	—	4	1	no	—
282	C₄⋊C₄×C₂₃	—	4	2	no	—
283	C₄⋊C₄×C₂₃	—	4	2	no	—
284	C₄⋊C₄×C₂₃	—	4	2	no	—
285	C₄⋊C₄×C₂₃	—	4	2	no	—
286	C₄⋊C₄×C₂₃	—	4	2	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	2	no	—
291	C₄⋊C₄×C₂₃	—	4	1	no	—
292	C₄⋊C₄×C₂₃	—	4	1	no	—
293	C₂²⋊C₄×C₂₃	—	2	4	no	—
294	C₂²⋊C₄×C₂₃	—	2	4	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	—	4	2	no	—
304	C₂²⋊C₄×C₂₃	—	4	2	no	—
305	C₂²⋊C₄×C₂₃	—	4	2	no	—
306	C₂²⋊C₄×C₂₃	—	4	2	no	—
307	C₂²⋊C₄×C₂₃	—	4	2	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	2	no	—
319	C₄²×C₂₃	—	2	2	no	—
320	C₄²×C₂₃	—	4	1	no	—
321	C₄²×C₂₃	—	4	1	no	—
322	C₄²×C₂₃	—	4	2	no	—
323	C₄²×C₂₃	—	4	2	no	—
324	C₄²×C₂₃	—	4	2	no	—
325	#36766	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
326	C₂³×C₂₃	—	2	1	no	—
327	C₂³×C₂₃	—	2	1	no	—
328	C₂³×C₂₃	—	2	1	no	—
329	C₂³×C₂₃	—	2	1	no	—
330	C₂³×C₂₃	—	2	2	no	—
331	C₂³×C₂₃	—	2	2	no	—
332	C₂³×C₂₃	—	2	2	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	—	4	4	no	—
345	C₂³×C₂₃	—	4	4	no	—
346	C₂³×C₂₃	—	4	4	no	—
347	C₂³×C₂₃	—	8	2	no	—
348	C₂³×C₂₃	—	8	2	no	—
349	C₂³×C₂₃	—	8	2	no	—
350	C₂³×C₂₃	—	8	2	no	—
351	C₂³×C₂₃	C₂×#41	1	2	yes	—
352	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
353	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
354	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
355	Q₈×C₂₃	—	8	2	no	—
356	Q₈×C₂₃	—	8	4	no	—
357	D₄×C₂₃	—	4	8	no	—
358	D₄×C₂₃	—	8	2	no	—
359	D₄×C₂₃	—	8	4	no	—
360	D₄×C₂₃	—	8	4	no	—
361	C₂×C₄×C₂₃	—	2	1	no	—
362	C₂×C₄×C₂₃	—	2	1	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	2	no	—
372	C₂×C₄×C₂₃	—	2	2	no	—
373	C₂×C₄×C₂₃	—	2	1	no	—
374	C₂×C₄×C₂₃	—	2	1	no	—
375	C₂×C₄×C₂₃	—	2	2	no	—
376	C₂×C₄×C₂₃	—	2	2	no	—
377	C₂×C₄×C₂₃	—	2	2	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	2	no	—
390	C₂×C₄×C₂₃	—	2	2	no	—
391	C₂×C₄×C₂₃	—	2	2	no	—
392	C₂×C₄×C₂₃	—	2	1	no	—
393	C₂×C₄×C₂₃	—	2	1	no	—
394	C₂×C₄×C₂₃	—	2	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	2	no	—
399	C₂×C₄×C₂₃	—	2	2	no	—
400	C₂×C₄×C₂₃	—	2	2	no	—
401	C₂×C₄×C₂₃	—	2	1	no	—
402	C₂×C₄×C₂₃	—	2	2	no	—
403	C₂×C₄×C₂₃	—	2	2	no	—
404	C₂×C₄×C₂₃	—	2	2	no	—
405	C₂×C₄×C₂₃	—	4	4	no	—
406	C₂×C₄×C₂₃	—	4	4	no	—
407	C₂×C₄×C₂₃	—	4	4	no	—
408	C₂×C₄×C₂₃	—	4	4	no	—
409	C₂×C₄×C₂₃	—	8	2	no	—
410	C₂×C₄×C₂₃	—	8	2	no	—
411	C₂×C₄×C₂₃	—	8	4	no	—
412	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
413	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
414	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
415	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
416	#2857	C₂×C₂₃	1	1	yes	characteristic, complemented
417	#2850	C₂×C₂₃	1	1	yes	characteristic, complemented
418	#2801	C₂×C₂₃	1	2	yes	complemented
419	#2795	C₂×C₂₃	1	2	yes	complemented
420	#2773	C₂×C₂₃	1	2	yes	complemented
421	#2759	C₂×C₂₃	1	2	yes	complemented
422	#2757	C₂×C₂₃	1	2	yes	complemented
423	#2730	C₂×C₂₃	1	2	yes	complemented
424	#2710	C₂×C₂₃	1	2	yes	complemented
425	#2674	C₂×C₂₃	1	2	yes	complemented
426	#2626	C₂×C₂₃	1	1	yes	characteristic, complemented
427	#2617	C₂×C₂₃	1	1	yes	characteristic
428	#2510	C₂×C₂₃	1	2	yes	complemented
429	#2472	C₂×C₂₃	1	2	yes	complemented
430	#2449	C₂×C₂₃	1	2	yes	complemented
431	#2418	C₂×C₂₃	1	2	yes	complemented
432	#2329	C₂×C₂₃	1	1	yes	characteristic, complemented
433	#2325	C₂×C₂₃	1	1	yes	characteristic, complemented
434	C₂×#388	C₂×C₂₃	1	1	yes	characteristic, complemented
435	C₂²×C₂₃	—	2	2	no	—
436	C₂²×C₂₃	—	2	2	no	—
437	C₂²×C₂₃	—	2	2	no	—
438	C₂²×C₂₃	—	2	2	no	—
439	C₂²×C₂₃	—	2	2	no	—
440	C₂²×C₂₃	—	2	2	no	—
441	C₂²×C₂₃	—	4	2	no	—
442	C₂²×C₂₃	—	4	2	no	—
443	C₂²×C₂₃	—	4	2	no	—
444	C₂²×C₂₃	—	4	2	no	—
445	C₂²×C₂₃	—	4	2	no	—
446	C₂²×C₂₃	—	4	2	no	—
447	C₂²×C₂₃	—	4	2	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	—	8	8	no	—
456	C₂²×C₂₃	#542	1	4	yes	—
457	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
458	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
460	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
461	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
462	C₂²×C₂₃	#585	1	1	yes	characteristic
463	C₂²×C₂₃	#585	1	1	yes	characteristic
464	C₄×C₂₃	—	2	2	no	—
465	C₄×C₂₃	—	2	2	no	—
466	C₄×C₂₃	—	2	2	no	—
467	C₄×C₂₃	—	2	2	no	—
468	C₄×C₂₃	—	4	2	no	—
469	C₄×C₂₃	—	4	2	no	—
470	C₄×C₂₃	—	4	2	no	—
471	C₄×C₂₃	—	4	2	no	—
472	C₄×C₂₃	—	4	1	no	—
473	C₄×C₂₃	—	4	1	no	—
474	C₄×C₂₃	—	4	2	no	—
475	C₄×C₂₃	—	4	2	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	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
481	C₂×#124	C₂²×C₂₃	1	2	yes	—
482	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic, complemented
483	C₂×#123	C₂²×C₂₃	1	2	yes	—
484	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
485	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
486	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
487	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
488	C₂×#120	C₂²×C₂₃	1	2	yes	—
489	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
490	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
491	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
492	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
493	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
494	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
495	#401	C₂²×C₂₃	1	2	yes	complemented
496	#400	C₂²×C₂₃	1	2	yes	complemented
497	#399	C₂²×C₂₃	1	2	yes	—
498	#399	C₂²×C₂₃	1	2	yes	—
499	#399	C₂²×C₂₃	1	2	yes	complemented
500	#398	C₂²×C₂₃	1	2	yes	complemented
501	#397	C₂²×C₂₃	1	2	yes	—
502	#397	C₂²×C₂₃	1	2	yes	—
503	#397	C₂²×C₂₃	1	2	yes	—
504	#397	C₂²×C₂₃	1	2	yes	complemented
505	#397	C₂²×C₂₃	1	2	yes	complemented
506	#396	C₂²×C₂₃	1	2	yes	—
507	#396	C₂²×C₂₃	1	2	yes	—
508	#396	C₂²×C₂₃	1	2	yes	complemented
509	#395	C₂²×C₂₃	1	2	yes	complemented
510	#394	C₂²×C₂₃	1	2	yes	—
511	#394	C₂²×C₂₃	1	2	yes	—
512	#394	C₂²×C₂₃	1	2	yes	—
513	#394	C₂²×C₂₃	1	2	yes	—
514	#394	C₂²×C₂₃	1	2	yes	—
515	#394	C₂²×C₂₃	1	2	yes	—
516	#393	C₂²×C₂₃	1	2	yes	—
517	#393	C₂²×C₂₃	1	2	yes	—
518	#392	C₂²×C₂₃	1	2	yes	—
519	#391	C₂²×C₂₃	1	2	yes	complemented
520	#391	C₂²×C₂₃	1	1	yes	characteristic, complemented
521	#391	C₂²×C₂₃	1	2	yes	complemented
522	#390	C₂²×C₂₃	1	2	yes	—
523	#390	C₂²×C₂₃	1	1	yes	characteristic, complemented
524	#389	C₂²×C₂₃	1	2	yes	complemented
525	#389	C₂²×C₂₃	1	2	yes	complemented
526	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
527	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
528	#389	C₂²×C₂₃	1	2	yes	complemented
529	#388	C₂²×C₂₃	1	2	yes	—
530	#388	C₂²×C₂₃	1	2	yes	—
531	#388	C₂²×C₂₃	1	2	yes	—
532	#388	C₂²×C₂₃	1	2	yes	—
533	#388	C₂²×C₂₃	1	2	yes	—
534	#388	C₂²×C₂₃	1	2	yes	—
535	#388	C₂²×C₂₃	1	2	yes	—
536	#388	C₂²×C₂₃	1	2	yes	—
537	#388	C₂²×C₂₃	1	2	yes	complemented
538	#388	C₂²×C₂₃	1	2	yes	complemented
539	#388	C₂²×C₂₃	1	2	yes	complemented
540	#388	C₂²×C₂₃	1	2	yes	complemented
541	#388	C₂²×C₂₃	1	2	yes	complemented
542	#387	C₂²×C₂₃	1	2	yes	complemented
543	#387	C₂²×C₂₃	1	2	yes	complemented
544	#387	C₂²×C₂₃	1	2	yes	complemented
545	#387	C₂²×C₂₃	1	2	yes	complemented
546	#387	C₂²×C₂₃	1	2	yes	complemented
547	#386	C₂²×C₂₃	1	2	yes	—
548	#386	C₂²×C₂₃	1	2	yes	—
549	#386	C₂²×C₂₃	1	2	yes	—
550	#386	C₂²×C₂₃	1	2	yes	—
551	#386	C₂²×C₂₃	1	2	yes	—
552	#386	C₂²×C₂₃	1	2	yes	complemented
553	#385	C₂²×C₂₃	1	2	yes	—
554	#385	C₂²×C₂₃	1	2	yes	—
555	#385	C₂²×C₂₃	1	2	yes	complemented
556	#385	C₂²×C₂₃	1	2	yes	complemented
557	#384	C₂²×C₂₃	1	1	yes	characteristic, complemented
558	#383	C₂²×C₂₃	1	2	yes	complemented
559	#382	C₂²×C₂₃	1	1	yes	characteristic, complemented
560	#380	C₂²×C₂₃	1	1	yes	characteristic
561	#380	C₂²×C₂₃	1	1	yes	characteristic
562	#380	C₂²×C₂₃	1	2	yes	—
563	#379	C₂²×C₂₃	1	2	yes	—
564	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
565	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
566	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
567	C₂×C₂₃	—	2	4	no	—
568	C₂×C₂₃	—	8	2	no	—
569	C₂×C₂₃	—	8	2	no	—
570	C₂×C₂₃	C₂×#542	1	1	yes	characteristic
571	C₂×C₂₃	#3505	1	1	yes	characteristic
572	C₂×C₂₃	#3506	1	1	yes	characteristic
573	C₂×C₂₃	#3535	1	1	yes	characteristic
574	C₂×C₂₃	#3537	1	1	yes	characteristic
575	C₂×C₂₃	#3560	1	1	yes	characteristic
576	C₂×C₂₃	#3561	1	1	yes	characteristic
577	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
578	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
579	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
580	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
581	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
582	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
583	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
584	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
585	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
586	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
587	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
588	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
589	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
590	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
591	C₄⋊Q₈	—	4	2	no	—
592	#124	—	4	2	no	—
593	#124	—	4	4	no	—
594	#123	—	4	4	no	—
595	C₂²⋊Q₈	—	2	4	no	—
596	C₂²⋊Q₈	—	4	4	no	—
597	C₂²⋊Q₈	—	4	4	no	—
598	#121	—	2	4	no	—
599	#120	—	4	4	no	—
600	C₄×D₄	—	4	4	no	—
601	C₂×C₄⋊C₄	—	4	2	no	—
602	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
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	2	yes	—
611	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
615	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
616	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
617	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
618	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
619	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
621	C₂×C₂²⋊C₄	—	2	4	no	—
622	C₂×C₂²⋊C₄	—	4	2	no	—
623	C₂×C₂²⋊C₄	—	4	2	no	—
624	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
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×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
649	C₂×C₄²	—	4	2	no	—
650	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
653	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
654	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
655	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
657	#95	C₂³×C₂₃	1	2	yes	—
658	#95	C₂³×C₂₃	1	2	yes	—
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	C₂₃	#36766	1	1	yes	characteristic, direct product factor, Sylow
680	C₂⁴	—	2	2	no	—
681	C₂⁴	—	2	2	no	—
682	C₂⁴	—	2	2	no	—
683	C₂⁴	—	4	1	no	—
684	C₂⁴	—	4	1	no	—
685	C₂⁴	—	4	1	no	—
686	C₂⁴	—	4	1	no	—
687	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
688	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
689	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
690	C₂×Q₈	—	2	2	no	—
691	C₂×Q₈	—	2	4	no	—
692	C₂×Q₈	—	4	2	no	—
693	C₂×Q₈	—	4	1	no	—
694	C₂×Q₈	—	4	2	no	—
695	C₂×Q₈	—	4	1	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	4	no	—
698	C₂×D₄	—	2	4	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	4	2	no	—
701	C₂×D₄	—	4	2	no	—
702	C₂×D₄	—	4	2	no	—
703	C₂×D₄	—	4	1	no	—
704	C₂×D₄	—	4	2	no	—
705	C₂×D₄	—	4	1	no	—
706	C₂×D₄	—	4	2	no	—
707	C₂×D₄	—	4	2	no	—
708	C₂²×C₄	—	2	2	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	—	4	1	no	—
716	C₂²×C₄	—	4	1	no	—
717	C₂²×C₄	—	4	1	no	—
718	C₂²×C₄	—	4	1	no	—
719	C₂²×C₄	—	4	1	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	2	no	—
727	C₂²×C₄	—	4	1	no	—
728	C₂²×C₄	#41×C₂₃	1	4	yes	—
729	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
730	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
732	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
733	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
734	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
735	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
736	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
737	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
738	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
740	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
743	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
744	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	4	no	—
748	C₄⋊C₄	—	2	4	no	—
749	C₄⋊C₄	—	2	4	no	—
750	C₄⋊C₄	—	4	2	no	—
751	C₄⋊C₄	—	4	2	no	—
752	C₄⋊C₄	—	4	2	no	—
753	C₄⋊C₄	—	4	2	no	—
754	C₄⋊C₄	—	4	2	no	—
755	C₄⋊C₄	—	4	2	no	—
756	C₄⋊C₄	—	4	2	no	—
757	C₄⋊C₄	—	4	2	no	—
758	C₄⋊C₄	—	4	1	no	—
759	C₄⋊C₄	—	4	1	no	—
760	C₄⋊C₄	—	4	1	no	—
761	C₄⋊C₄	—	4	1	no	—
762	C₄⋊C₄	—	4	2	no	—
763	C₄⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	2	4	no	—
765	C₂²⋊C₄	—	2	4	no	—
766	C₂²⋊C₄	—	2	4	no	—
767	C₂²⋊C₄	—	2	4	no	—
768	C₂²⋊C₄	—	2	4	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	—	4	2	no	—
775	C₂²⋊C₄	—	4	2	no	—
776	C₂²⋊C₄	—	4	2	no	—
777	C₂²⋊C₄	—	4	2	no	—
778	C₂²⋊C₄	—	4	2	no	—
779	C₂²⋊C₄	—	4	2	no	—
780	C₂²⋊C₄	—	4	2	no	—
781	C₂²⋊C₄	—	4	2	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	C₄²	—	2	2	no	—
790	C₄²	—	2	2	no	—
791	C₄²	—	4	1	no	—
792	C₄²	—	4	1	no	—
793	C₄²	—	4	2	no	—
794	C₄²	—	4	2	no	—
795	C₄²	—	4	2	no	—
796	C₂³	—	2	1	no	—
797	C₂³	—	2	1	no	—
798	C₂³	—	2	1	no	—
799	C₂³	—	2	1	no	—
800	C₂³	—	2	2	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	2	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	2	no	—
812	C₂³	—	2	2	no	—
813	C₂³	—	2	2	no	—
814	C₂³	—	4	4	no	—
815	C₂³	—	4	4	no	—
816	C₂³	—	4	4	no	—
817	C₂³	—	8	2	no	—
818	C₂³	—	8	2	no	—
819	C₂³	—	8	2	no	—
820	C₂³	—	8	2	no	—
821	C₂³	C₂×#41×C₂₃	1	2	yes	—
822	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
823	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
824	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
825	Q₈	—	8	2	no	—
826	Q₈	—	8	4	no	—
827	D₄	—	4	8	no	—
828	D₄	—	8	2	no	—
829	D₄	—	8	4	no	—
830	D₄	—	8	4	no	—
831	C₂×C₄	—	2	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	1	no	—
835	C₂×C₄	—	2	1	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	2	no	—
841	C₂×C₄	—	2	2	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	2	no	—
846	C₂×C₄	—	2	2	no	—
847	C₂×C₄	—	2	2	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	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	1	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	2	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	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	—	4	4	no	—
876	C₂×C₄	—	4	4	no	—
877	C₂×C₄	—	4	4	no	—
878	C₂×C₄	—	4	4	no	—
879	C₂×C₄	—	8	2	no	—
880	C₂×C₄	—	8	2	no	—
881	C₂×C₄	—	8	4	no	—
882	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
883	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
884	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
885	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	4	2	no	—
893	C₂²	—	4	2	no	—
894	C₂²	—	4	2	no	—
895	C₂²	—	4	2	no	—
896	C₂²	—	4	2	no	—
897	C₂²	—	4	2	no	—
898	C₂²	—	4	2	no	—
899	C₂²	—	4	2	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	2	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	2	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	8	8	no	—
907	C₂²	C₂₃×#542	1	4	yes	—
908	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
909	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
910	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
911	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
912	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
913	C₂²	C₂₃×#585	1	1	yes	characteristic
914	C₂²	C₂₃×#585	1	1	yes	characteristic
915	C₄	—	2	2	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	4	2	no	—
920	C₄	—	4	2	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	2	no	—
923	C₄	—	4	1	no	—
924	C₄	—	4	1	no	—
925	C₄	—	4	2	no	—
926	C₄	—	4	2	no	—
927	C₄	—	4	2	no	—
928	C₄	—	4	2	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	2	no	—
931	C₂	—	2	4	no	—
932	C₂	—	8	2	no	—
933	C₂	—	8	2	no	—
934	C₂	C₂×C₂₃×#542	1	1	yes	characteristic
935	C₂	C₂₃×#3505	1	1	yes	characteristic
936	C₂	C₂₃×#3506	1	1	yes	characteristic
937	C₂	C₂₃×#3535	1	1	yes	characteristic
938	C₂	C₂₃×#3537	1	1	yes	characteristic
939	C₂	C₂₃×#3560	1	1	yes	characteristic
940	C₂	C₂₃×#3561	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×#2857	C₂	semidirect
2. C₂₃×#2850	C₂	semidirect
3. C₂₃×#2801	C₂	semidirect
4. C₂₃×#2795	C₂	semidirect
5. C₂₃×#2773	C₂	semidirect
6. C₂₃×#2759	C₂	semidirect
7. C₂₃×#2757	C₂	semidirect
8. C₂₃×#2730	C₂	semidirect
9. C₂₃×#2710	C₂	semidirect
10. C₂₃×#2674	C₂	semidirect
11. C₂₃×#2626	C₂	semidirect
13. C₂₃×#2510	C₂	semidirect
14. C₂₃×#2472	C₂	semidirect
15. C₂₃×#2449	C₂	semidirect
16. C₂₃×#2418	C₂	semidirect
17. C₂₃×#2329	C₂	semidirect
18. C₂₃×#2325	C₂	semidirect
19. C₂×C₂₃×#388	C₂	semidirect
20. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
22. C₂×C₂₃×#124	C₂²	semidirect
26. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
35. C₂₃×#401	C₂²	semidirect
36. C₂₃×#400	C₂²	semidirect
39. C₂₃×#399	C₂²	semidirect
40. C₂₃×#398	C₂²	semidirect
44. C₂₃×#397	C₂²	semidirect
45. C₂₃×#397	C₂²	semidirect
48. C₂₃×#396	C₂²	semidirect
49. C₂₃×#395	C₂²	semidirect
59. C₂₃×#391	C₂²	semidirect
60. C₂₃×#391	C₂²	semidirect
61. C₂₃×#391	C₂²	semidirect
63. C₂₃×#390	C₂²	semidirect
64. C₂₃×#389	C₂²	semidirect
65. C₂₃×#389	C₂²	semidirect
66. C₂₃×#389	C₂²	semidirect
67. C₂₃×#389	C₂²	semidirect
68. C₂₃×#389	C₂²	semidirect
77. C₂₃×#388	C₂²	semidirect
78. C₂₃×#388	C₂²	semidirect
79. C₂₃×#388	C₂²	semidirect
80. C₂₃×#388	C₂²	semidirect
81. C₂₃×#388	C₂²	semidirect
82. C₂₃×#387	C₂²	semidirect
83. C₂₃×#387	C₂²	semidirect
84. C₂₃×#387	C₂²	semidirect
85. C₂₃×#387	C₂²	semidirect
86. C₂₃×#387	C₂²	semidirect
92. C₂₃×#386	C₂²	semidirect
95. C₂₃×#385	C₂²	semidirect
96. C₂₃×#385	C₂²	semidirect
97. C₂₃×#384	C₂²	semidirect
98. C₂₃×#383	C₂²	semidirect
99. C₂₃×#382	C₂²	semidirect
325. #36766	C₂₃	direct (N × H)
416. #2857	C₂×C₂₃	semidirect
417. #2850	C₂×C₂₃	semidirect
418. #2801	C₂×C₂₃	semidirect
419. #2795	C₂×C₂₃	semidirect
420. #2773	C₂×C₂₃	semidirect
421. #2759	C₂×C₂₃	semidirect
422. #2757	C₂×C₂₃	semidirect
423. #2730	C₂×C₂₃	semidirect
424. #2710	C₂×C₂₃	semidirect
425. #2674	C₂×C₂₃	semidirect
426. #2626	C₂×C₂₃	semidirect
428. #2510	C₂×C₂₃	semidirect
429. #2472	C₂×C₂₃	semidirect
430. #2449	C₂×C₂₃	semidirect
431. #2418	C₂×C₂₃	semidirect
432. #2329	C₂×C₂₃	semidirect
433. #2325	C₂×C₂₃	semidirect
434. C₂×#388	C₂×C₂₃	semidirect
480. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
482. C₂×#124	C₂²×C₂₃	semidirect
486. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
495. #401	C₂²×C₂₃	semidirect
496. #400	C₂²×C₂₃	semidirect
499. #399	C₂²×C₂₃	semidirect
500. #398	C₂²×C₂₃	semidirect
504. #397	C₂²×C₂₃	semidirect
505. #397	C₂²×C₂₃	semidirect
508. #396	C₂²×C₂₃	semidirect
509. #395	C₂²×C₂₃	semidirect
519. #391	C₂²×C₂₃	semidirect
520. #391	C₂²×C₂₃	semidirect
521. #391	C₂²×C₂₃	semidirect
523. #390	C₂²×C₂₃	semidirect
524. #389	C₂²×C₂₃	semidirect
525. #389	C₂²×C₂₃	semidirect
526. #389	C₂²×C₂₃	semidirect
527. #389	C₂²×C₂₃	semidirect
528. #389	C₂²×C₂₃	semidirect
537. #388	C₂²×C₂₃	semidirect
538. #388	C₂²×C₂₃	semidirect
539. #388	C₂²×C₂₃	semidirect
540. #388	C₂²×C₂₃	semidirect
541. #388	C₂²×C₂₃	semidirect
542. #387	C₂²×C₂₃	semidirect
543. #387	C₂²×C₂₃	semidirect
544. #387	C₂²×C₂₃	semidirect
545. #387	C₂²×C₂₃	semidirect
546. #387	C₂²×C₂₃	semidirect
552. #386	C₂²×C₂₃	semidirect
555. #385	C₂²×C₂₃	semidirect
556. #385	C₂²×C₂₃	semidirect
557. #384	C₂²×C₂₃	semidirect
558. #383	C₂²×C₂₃	semidirect
559. #382	C₂²×C₂₃	semidirect
679. C₂₃	#36766	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×#2857	2
C₂₃×#2850	2
C₂₃×#2801	2
C₂₃×#2795	2
C₂₃×#2773	2
C₂₃×#2759	2
C₂₃×#2757	2
C₂₃×#2730	2
C₂₃×#2710	2
C₂₃×#2674	2
C₂₃×#2626	2
C₂₃×#2617	2
C₂₃×#2510	2
C₂₃×#2472	2
C₂₃×#2449	2
C₂₃×#2418	2
C₂₃×#2329	2
C₂₃×#2325	2
C₂×C₂₃×#388	2
#36766	23

Subgroups — C23×#36766 #19184392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36766 #19184392