Subgroups — C₂₃×#36750 #19184376

Order 5888.

1778 conjugacy classes of subgroups.

The subgroup lattice has 894 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×#2851	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2807	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2788	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2768	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2763	C₂	1	2	yes	maximal, complemented
7	C₂₃×#2729	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2720	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2704	C₂	1	2	yes	maximal, complemented
10	C₂₃×#2704	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2659	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2646	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2549	C₂	1	2	yes	maximal, complemented
14	C₂₃×#2442	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2437	C₂	1	2	yes	maximal
16	C₂₃×#2437	C₂	1	2	yes	maximal
17	C₂₃×#2315	C₂	1	1	yes	maximal, characteristic
18	C₂₃×#2312	C₂	1	1	yes	maximal, characteristic
19	C₂×C₂₃×#388	C₂	1	1	yes	maximal, characteristic
20	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₂₃×#125	C₂²	1	2	yes	complemented
22	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
33	C₂₃×#400	C₂²	1	2	yes	complemented
34	C₂₃×#400	C₂²	1	2	yes	complemented
35	C₂₃×#400	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×#398	C₂²	1	2	yes	complemented
40	C₂₃×#398	C₂²	1	2	yes	complemented
41	C₂₃×#398	C₂²	1	2	yes	complemented
42	C₂₃×#398	C₂²	1	2	yes	complemented
43	C₂₃×#398	C₂²	1	2	yes	complemented
44	C₂₃×#398	C₂²	1	2	yes	complemented
45	C₂₃×#398	C₂²	1	2	yes	complemented
46	C₂₃×#398	C₂²	1	2	yes	complemented
47	C₂₃×#396	C₂²	1	2	yes	—
48	C₂₃×#396	C₂²	1	2	yes	—
49	C₂₃×#396	C₂²	1	2	yes	—
50	C₂₃×#396	C₂²	1	2	yes	—
51	C₂₃×#395	C₂²	1	2	yes	complemented
52	C₂₃×#395	C₂²	1	2	yes	complemented
53	C₂₃×#395	C₂²	1	2	yes	complemented
54	C₂₃×#395	C₂²	1	2	yes	complemented
55	C₂₃×#393	C₂²	1	2	yes	—
56	C₂₃×#393	C₂²	1	2	yes	—
57	C₂₃×#391	C₂²	1	2	yes	complemented
58	C₂₃×#391	C₂²	1	2	yes	complemented
59	C₂₃×#391	C₂²	1	2	yes	complemented
60	C₂₃×#389	C₂²	1	2	yes	complemented
61	C₂₃×#389	C₂²	1	2	yes	complemented
62	C₂₃×#389	C₂²	1	1	yes	characteristic, complemented
63	C₂₃×#389	C₂²	1	2	yes	complemented
64	C₂₃×#389	C₂²	1	2	yes	complemented
65	C₂₃×#389	C₂²	1	1	yes	characteristic, 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×#387	C₂²	1	2	yes	complemented
78	C₂₃×#387	C₂²	1	2	yes	complemented
79	C₂₃×#385	C₂²	1	2	yes	—
80	C₂₃×#385	C₂²	1	2	yes	—
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	—
88	C₂₃×#385	C₂²	1	2	yes	—
89	C₂₃×#385	C₂²	1	2	yes	—
90	C₂₃×#385	C₂²	1	2	yes	—
91	C₂₃×#384	C₂²	1	1	yes	characteristic, complemented
92	C₂₃×#382	C₂²	1	2	yes	complemented
93	C₂₃×#382	C₂²	1	1	yes	characteristic, complemented
94	C₂₃×#380	C₂²	1	2	yes	—
95	C₂₃×#380	C₂²	1	1	yes	characteristic
96	C₂₃×#380	C₂²	1	1	yes	characteristic
97	C₂₃×#380	C₂²	1	2	yes	—
98	C₂₃×#380	C₂²	1	2	yes	—
99	C₂₃×#380	C₂²	1	2	yes	—
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	2	yes	—
109	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
110	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
115	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
116	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
118	C₂₃×C₄⋊Q₈	—	4	2	no	—
119	C₂₃×#125	—	4	2	no	—
120	C₂₃×#125	—	4	4	no	—
121	C₂₃×C₂²⋊Q₈	—	4	4	no	—
122	C₂₃×C₂²⋊Q₈	—	4	4	no	—
123	C₂₃×C₂²⋊Q₈	—	4	4	no	—
124	C₂₃×C₂²⋊Q₈	—	4	4	no	—
125	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
126	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
127	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
128	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
129	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
130	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
131	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
132	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	2	yes	—
140	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
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×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
151	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
152	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
157	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
158	C₂×C₂²⋊C₄×C₂₃	—	4	4	no	—
159	C₂×C₂²⋊C₄×C₂₃	Q₈	1	8	yes	complemented
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×C₄²×C₂₃	—	4	2	no	—
177	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
178	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
180	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
181	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
183	C₂₃×#95	C₂³	1	2	yes	—
184	C₂₃×#95	C₂³	1	2	yes	—
185	C₂₃×#95	C₂³	1	2	yes	—
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	C₂⁴×C₂₃	—	2	2	no	—
208	C₂⁴×C₂₃	—	2	2	no	—
209	C₂⁴×C₂₃	—	4	1	no	—
210	C₂⁴×C₂₃	—	4	1	no	—
211	C₂⁴×C₂₃	—	4	1	no	—
212	C₂⁴×C₂₃	—	4	1	no	—
213	C₂⁴×C₂₃	C₂×Q₈	1	4	yes	—
214	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
215	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
216	C₂×Q₈×C₂₃	—	2	4	no	—
217	C₂×Q₈×C₂₃	—	4	2	no	—
218	C₂×Q₈×C₂₃	—	4	2	no	—
219	C₂×Q₈×C₂₃	—	4	2	no	—
220	C₂×Q₈×C₂₃	—	4	2	no	—
221	C₂×Q₈×C₂₃	—	4	2	no	—
222	C₂²×C₄×C₂₃	—	2	2	no	—
223	C₂²×C₄×C₂₃	—	2	2	no	—
224	C₂²×C₄×C₂₃	—	2	2	no	—
225	C₂²×C₄×C₂₃	—	2	2	no	—
226	C₂²×C₄×C₂₃	—	2	2	no	—
227	C₂²×C₄×C₂₃	—	2	2	no	—
228	C₂²×C₄×C₂₃	—	4	1	no	—
229	C₂²×C₄×C₂₃	—	4	1	no	—
230	C₂²×C₄×C₂₃	—	4	1	no	—
231	C₂²×C₄×C₂₃	—	4	1	no	—
232	C₂²×C₄×C₂₃	—	4	1	no	—
233	C₂²×C₄×C₂₃	—	4	1	no	—
234	C₂²×C₄×C₂₃	—	4	1	no	—
235	C₂²×C₄×C₂₃	—	4	2	no	—
236	C₂²×C₄×C₂₃	—	4	2	no	—
237	C₂²×C₄×C₂₃	—	4	1	no	—
238	C₂²×C₄×C₂₃	—	4	1	no	—
239	C₂²×C₄×C₂₃	—	4	2	no	—
240	C₂²×C₄×C₂₃	—	4	2	no	—
241	C₂²×C₄×C₂₃	—	4	2	no	—
242	C₂²×C₄×C₂₃	—	4	2	no	—
243	C₂²×C₄×C₂₃	—	4	1	no	—
244	C₂²×C₄×C₂₃	C₂×Q₈	1	4	yes	—
245	C₂²×C₄×C₂₃	C₂×Q₈	1	4	yes	—
246	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₂₃	C₂⁴	1	2	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	1	yes	characteristic
262	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
263	C₄⋊C₄×C₂₃	—	2	4	no	—
264	C₄⋊C₄×C₂₃	—	2	4	no	—
265	C₄⋊C₄×C₂₃	—	2	4	no	—
266	C₄⋊C₄×C₂₃	—	2	4	no	—
267	C₄⋊C₄×C₂₃	—	4	2	no	—
268	C₄⋊C₄×C₂₃	—	4	2	no	—
269	C₄⋊C₄×C₂₃	—	4	1	no	—
270	C₄⋊C₄×C₂₃	—	4	1	no	—
271	C₄⋊C₄×C₂₃	—	4	1	no	—
272	C₄⋊C₄×C₂₃	—	4	1	no	—
273	C₄⋊C₄×C₂₃	—	4	2	no	—
274	C₄⋊C₄×C₂₃	—	4	2	no	—
275	C₄⋊C₄×C₂₃	—	4	2	no	—
276	C₄⋊C₄×C₂₃	—	4	2	no	—
277	C₄⋊C₄×C₂₃	—	4	2	no	—
278	C₄⋊C₄×C₂₃	—	4	2	no	—
279	C₄⋊C₄×C₂₃	—	4	2	no	—
280	C₄⋊C₄×C₂₃	—	4	2	no	—
281	C₄⋊C₄×C₂₃	—	4	2	no	—
282	C₄⋊C₄×C₂₃	—	4	2	no	—
283	C₄⋊C₄×C₂₃	—	4	2	no	—
284	C₄⋊C₄×C₂₃	—	4	1	no	—
285	C₄⋊C₄×C₂₃	—	4	1	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	1	no	—
291	C₄⋊C₄×C₂₃	—	4	2	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	—	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	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	C₂×Q₈	1	8	yes	—
308	C₂²⋊C₄×C₂₃	C₂×Q₈	1	8	yes	—
309	C₄²×C₂₃	—	2	2	no	—
310	C₄²×C₂₃	—	2	2	no	—
311	C₄²×C₂₃	—	4	1	no	—
312	C₄²×C₂₃	—	4	1	no	—
313	C₄²×C₂₃	—	4	2	no	—
314	C₄²×C₂₃	—	4	2	no	—
315	#36750	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
316	C₂³×C₂₃	—	2	1	no	—
317	C₂³×C₂₃	—	2	1	no	—
318	C₂³×C₂₃	—	2	1	no	—
319	C₂³×C₂₃	—	2	1	no	—
320	C₂³×C₂₃	—	2	2	no	—
321	C₂³×C₂₃	—	2	2	no	—
322	C₂³×C₂₃	—	2	2	no	—
323	C₂³×C₂₃	—	2	2	no	—
324	C₂³×C₂₃	—	2	2	no	—
325	C₂³×C₂₃	—	2	2	no	—
326	C₂³×C₂₃	—	2	8	no	—
327	C₂³×C₂₃	—	4	4	no	—
328	C₂³×C₂₃	—	4	4	no	—
329	C₂³×C₂₃	—	8	2	no	—
330	C₂³×C₂₃	—	8	2	no	—
331	C₂³×C₂₃	—	8	2	no	—
332	C₂³×C₂₃	—	8	2	no	—
333	C₂³×C₂₃	C₂²×Q₈	1	4	yes	—
334	C₂³×C₂₃	C₂²×Q₈	1	2	yes	—
335	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
336	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
337	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
338	Q₈×C₂₃	—	8	4	no	—
339	Q₈×C₂₃	—	8	4	no	—
340	C₂×C₄×C₂₃	—	2	1	no	—
341	C₂×C₄×C₂₃	—	2	1	no	—
342	C₂×C₄×C₂₃	—	2	1	no	—
343	C₂×C₄×C₂₃	—	2	2	no	—
344	C₂×C₄×C₂₃	—	2	1	no	—
345	C₂×C₄×C₂₃	—	2	1	no	—
346	C₂×C₄×C₂₃	—	2	2	no	—
347	C₂×C₄×C₂₃	—	2	1	no	—
348	C₂×C₄×C₂₃	—	2	1	no	—
349	C₂×C₄×C₂₃	—	2	1	no	—
350	C₂×C₄×C₂₃	—	2	1	no	—
351	C₂×C₄×C₂₃	—	2	1	no	—
352	C₂×C₄×C₂₃	—	2	2	no	—
353	C₂×C₄×C₂₃	—	2	2	no	—
354	C₂×C₄×C₂₃	—	2	2	no	—
355	C₂×C₄×C₂₃	—	2	2	no	—
356	C₂×C₄×C₂₃	—	2	2	no	—
357	C₂×C₄×C₂₃	—	2	2	no	—
358	C₂×C₄×C₂₃	—	2	2	no	—
359	C₂×C₄×C₂₃	—	2	2	no	—
360	C₂×C₄×C₂₃	—	2	2	no	—
361	C₂×C₄×C₂₃	—	2	2	no	—
362	C₂×C₄×C₂₃	—	2	1	no	—
363	C₂×C₄×C₂₃	—	2	2	no	—
364	C₂×C₄×C₂₃	—	2	2	no	—
365	C₂×C₄×C₂₃	—	2	2	no	—
366	C₂×C₄×C₂₃	—	2	2	no	—
367	C₂×C₄×C₂₃	—	2	2	no	—
368	C₂×C₄×C₂₃	—	2	2	no	—
369	C₂×C₄×C₂₃	—	2	1	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	2	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	1	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	—	4	4	no	—
387	C₂×C₄×C₂₃	—	4	4	no	—
388	C₂×C₄×C₂₃	—	4	4	no	—
389	C₂×C₄×C₂₃	—	4	4	no	—
390	C₂×C₄×C₂₃	—	8	2	no	—
391	C₂×C₄×C₂₃	—	8	2	no	—
392	C₂×C₄×C₂₃	—	8	4	no	—
393	C₂×C₄×C₂₃	—	8	4	no	—
394	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
395	C₂×C₄×C₂₃	C₂²×Q₈	1	2	yes	—
396	C₂×C₄×C₂₃	C₂²×Q₈	1	4	yes	—
397	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
398	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
399	#2857	C₂×C₂₃	1	1	yes	characteristic, complemented
400	#2851	C₂×C₂₃	1	1	yes	characteristic, complemented
401	#2807	C₂×C₂₃	1	2	yes	complemented
402	#2788	C₂×C₂₃	1	2	yes	complemented
403	#2768	C₂×C₂₃	1	2	yes	complemented
404	#2763	C₂×C₂₃	1	2	yes	complemented
405	#2729	C₂×C₂₃	1	2	yes	complemented
406	#2720	C₂×C₂₃	1	2	yes	complemented
407	#2704	C₂×C₂₃	1	2	yes	complemented
408	#2704	C₂×C₂₃	1	2	yes	complemented
409	#2659	C₂×C₂₃	1	1	yes	characteristic, complemented
410	#2646	C₂×C₂₃	1	1	yes	characteristic, complemented
411	#2549	C₂×C₂₃	1	2	yes	complemented
412	#2442	C₂×C₂₃	1	2	yes	complemented
413	#2437	C₂×C₂₃	1	2	yes	—
414	#2437	C₂×C₂₃	1	2	yes	—
415	#2315	C₂×C₂₃	1	1	yes	characteristic
416	#2312	C₂×C₂₃	1	1	yes	characteristic
417	C₂×#388	C₂×C₂₃	1	1	yes	characteristic
418	C₂²×C₂₃	—	2	2	no	—
419	C₂²×C₂₃	—	2	2	no	—
420	C₂²×C₂₃	—	2	2	no	—
421	C₂²×C₂₃	—	2	2	no	—
422	C₂²×C₂₃	—	2	2	no	—
423	C₂²×C₂₃	—	2	2	no	—
424	C₂²×C₂₃	—	2	4	no	—
425	C₂²×C₂₃	—	2	4	no	—
426	C₂²×C₂₃	—	2	4	no	—
427	C₂²×C₂₃	—	4	2	no	—
428	C₂²×C₂₃	—	4	2	no	—
429	C₂²×C₂₃	—	4	2	no	—
430	C₂²×C₂₃	—	4	2	no	—
431	C₂²×C₂₃	—	8	8	no	—
432	C₂²×C₂₃	#544	1	4	yes	—
433	C₂²×C₂₃	C₂³×Q₈	1	1	yes	characteristic
434	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
435	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
436	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
437	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
438	C₂²×C₂₃	#585	1	1	yes	characteristic
439	C₂²×C₂₃	#585	1	1	yes	characteristic
440	C₄×C₂₃	—	2	2	no	—
441	C₄×C₂₃	—	2	2	no	—
442	C₄×C₂₃	—	2	4	no	—
443	C₄×C₂₃	—	2	2	no	—
444	C₄×C₂₃	—	2	2	no	—
445	C₄×C₂₃	—	4	1	no	—
446	C₄×C₂₃	—	4	2	no	—
447	C₄×C₂₃	—	4	2	no	—
448	C₄×C₂₃	—	4	2	no	—
449	C₄×C₂₃	—	4	2	no	—
450	C₄×C₂₃	—	4	1	no	—
451	C₄×C₂₃	—	4	2	no	—
452	C₄×C₂₃	—	4	2	no	—
453	C₄×C₂₃	—	4	2	no	—
454	C₄×C₂₃	—	4	2	no	—
455	C₄×C₂₃	—	4	2	no	—
456	C₄×C₂₃	—	4	2	no	—
457	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
458	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic, complemented
459	C₂×#125	C₂²×C₂₃	1	2	yes	complemented
460	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
461	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
462	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
463	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
464	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
465	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
466	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
467	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
468	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
469	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
470	#400	C₂²×C₂₃	1	2	yes	complemented
471	#400	C₂²×C₂₃	1	2	yes	complemented
472	#400	C₂²×C₂₃	1	2	yes	complemented
473	#400	C₂²×C₂₃	1	2	yes	complemented
474	#399	C₂²×C₂₃	1	2	yes	—
475	#399	C₂²×C₂₃	1	2	yes	—
476	#398	C₂²×C₂₃	1	2	yes	complemented
477	#398	C₂²×C₂₃	1	2	yes	complemented
478	#398	C₂²×C₂₃	1	2	yes	complemented
479	#398	C₂²×C₂₃	1	2	yes	complemented
480	#398	C₂²×C₂₃	1	2	yes	complemented
481	#398	C₂²×C₂₃	1	2	yes	complemented
482	#398	C₂²×C₂₃	1	2	yes	complemented
483	#398	C₂²×C₂₃	1	2	yes	complemented
484	#396	C₂²×C₂₃	1	2	yes	—
485	#396	C₂²×C₂₃	1	2	yes	—
486	#396	C₂²×C₂₃	1	2	yes	—
487	#396	C₂²×C₂₃	1	2	yes	—
488	#395	C₂²×C₂₃	1	2	yes	complemented
489	#395	C₂²×C₂₃	1	2	yes	complemented
490	#395	C₂²×C₂₃	1	2	yes	complemented
491	#395	C₂²×C₂₃	1	2	yes	complemented
492	#393	C₂²×C₂₃	1	2	yes	—
493	#393	C₂²×C₂₃	1	2	yes	—
494	#391	C₂²×C₂₃	1	2	yes	complemented
495	#391	C₂²×C₂₃	1	2	yes	complemented
496	#391	C₂²×C₂₃	1	2	yes	complemented
497	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
498	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
499	#389	C₂²×C₂₃	1	2	yes	complemented
500	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
501	#389	C₂²×C₂₃	1	1	yes	characteristic, complemented
502	#389	C₂²×C₂₃	1	2	yes	complemented
503	#389	C₂²×C₂₃	1	2	yes	complemented
504	#389	C₂²×C₂₃	1	2	yes	complemented
505	#389	C₂²×C₂₃	1	2	yes	complemented
506	#388	C₂²×C₂₃	1	2	yes	—
507	#388	C₂²×C₂₃	1	2	yes	—
508	#388	C₂²×C₂₃	1	2	yes	—
509	#388	C₂²×C₂₃	1	2	yes	—
510	#388	C₂²×C₂₃	1	2	yes	—
511	#388	C₂²×C₂₃	1	2	yes	—
512	#388	C₂²×C₂₃	1	2	yes	—
513	#388	C₂²×C₂₃	1	2	yes	—
514	#387	C₂²×C₂₃	1	2	yes	complemented
515	#387	C₂²×C₂₃	1	2	yes	complemented
516	#385	C₂²×C₂₃	1	2	yes	—
517	#385	C₂²×C₂₃	1	2	yes	—
518	#385	C₂²×C₂₃	1	2	yes	—
519	#385	C₂²×C₂₃	1	2	yes	—
520	#385	C₂²×C₂₃	1	2	yes	—
521	#385	C₂²×C₂₃	1	2	yes	—
522	#385	C₂²×C₂₃	1	2	yes	—
523	#385	C₂²×C₂₃	1	2	yes	—
524	#385	C₂²×C₂₃	1	2	yes	—
525	#385	C₂²×C₂₃	1	2	yes	—
526	#385	C₂²×C₂₃	1	2	yes	—
527	#385	C₂²×C₂₃	1	2	yes	—
528	#384	C₂²×C₂₃	1	1	yes	characteristic, complemented
529	#382	C₂²×C₂₃	1	1	yes	characteristic, complemented
530	#382	C₂²×C₂₃	1	2	yes	complemented
531	#380	C₂²×C₂₃	1	1	yes	characteristic
532	#380	C₂²×C₂₃	1	1	yes	characteristic
533	#380	C₂²×C₂₃	1	1	yes	characteristic
534	#380	C₂²×C₂₃	1	1	yes	characteristic
535	#380	C₂²×C₂₃	1	2	yes	—
536	#380	C₂²×C₂₃	1	2	yes	—
537	#380	C₂²×C₂₃	1	2	yes	—
538	#380	C₂²×C₂₃	1	2	yes	—
539	#380	C₂²×C₂₃	1	2	yes	—
540	#379	C₂²×C₂₃	1	2	yes	—
541	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
542	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
543	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
544	C₂×C₂₃	—	2	4	no	—
545	C₂×C₂₃	—	4	4	no	—
546	C₂×C₂₃	C₂×#544	1	1	yes	characteristic
547	C₂×C₂₃	#3501	1	1	yes	characteristic
548	C₂×C₂₃	#3501	1	1	yes	characteristic
549	C₂×C₂₃	#3534	1	1	yes	characteristic
550	C₂×C₂₃	#3536	1	1	yes	characteristic
551	C₂×C₂₃	#3558	1	1	yes	characteristic
552	C₂×C₂₃	#3564	1	1	yes	characteristic
553	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
554	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
555	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
556	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
557	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
558	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
559	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
560	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
561	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
562	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
563	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
564	C₄⋊Q₈	—	4	2	no	—
565	#125	—	4	2	no	—
566	#125	—	4	4	no	—
567	C₂²⋊Q₈	—	4	4	no	—
568	C₂²⋊Q₈	—	4	4	no	—
569	C₂²⋊Q₈	—	4	4	no	—
570	C₂²⋊Q₈	—	4	4	no	—
571	C₂×C₄⋊C₄	—	4	2	no	—
572	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
573	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
576	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
582	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
584	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
588	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
589	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
596	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
598	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
600	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
602	C₂×C₂²⋊C₄	—	4	2	no	—
603	C₂×C₂²⋊C₄	—	4	2	no	—
604	C₂×C₂²⋊C₄	—	4	4	no	—
605	C₂×C₂²⋊C₄	Q₈×C₂₃	1	8	yes	complemented
606	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
622	C₂×C₄²	—	4	2	no	—
623	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
626	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
627	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
628	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
629	#95	C₂³×C₂₃	1	2	yes	—
630	#95	C₂³×C₂₃	1	2	yes	—
631	#95	C₂³×C₂₃	1	2	yes	—
632	#95	C₂³×C₂₃	1	2	yes	—
633	#95	C₂³×C₂₃	1	2	yes	—
634	#95	C₂³×C₂₃	1	2	yes	—
635	#95	C₂³×C₂₃	1	2	yes	—
636	#95	C₂³×C₂₃	1	2	yes	—
637	#95	C₂³×C₂₃	1	2	yes	—
638	#95	C₂³×C₂₃	1	2	yes	—
639	#95	C₂³×C₂₃	1	2	yes	—
640	#95	C₂³×C₂₃	1	2	yes	—
641	#95	C₂³×C₂₃	1	2	yes	—
642	#95	C₂³×C₂₃	1	2	yes	—
643	#95	C₂³×C₂₃	1	2	yes	—
644	#95	C₂³×C₂₃	1	2	yes	—
645	#95	C₂³×C₂₃	1	2	yes	—
646	#95	C₂³×C₂₃	1	2	yes	—
647	#95	C₂³×C₂₃	1	2	yes	—
648	#95	C₂³×C₂₃	1	2	yes	—
649	#95	C₂³×C₂₃	1	2	yes	—
650	#95	C₂³×C₂₃	1	2	yes	—
651	#95	C₂³×C₂₃	1	2	yes	—
652	#95	C₂³×C₂₃	1	2	yes	—
653	C₂₃	#36750	1	1	yes	characteristic, direct product factor, Sylow
654	C₂⁴	—	2	2	no	—
655	C₂⁴	—	2	2	no	—
656	C₂⁴	—	4	1	no	—
657	C₂⁴	—	4	1	no	—
658	C₂⁴	—	4	1	no	—
659	C₂⁴	—	4	1	no	—
660	C₂⁴	C₂×Q₈×C₂₃	1	4	yes	—
661	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
662	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
663	C₂×Q₈	—	2	4	no	—
664	C₂×Q₈	—	4	2	no	—
665	C₂×Q₈	—	4	2	no	—
666	C₂×Q₈	—	4	2	no	—
667	C₂×Q₈	—	4	2	no	—
668	C₂×Q₈	—	4	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	4	1	no	—
676	C₂²×C₄	—	4	1	no	—
677	C₂²×C₄	—	4	1	no	—
678	C₂²×C₄	—	4	1	no	—
679	C₂²×C₄	—	4	1	no	—
680	C₂²×C₄	—	4	1	no	—
681	C₂²×C₄	—	4	1	no	—
682	C₂²×C₄	—	4	2	no	—
683	C₂²×C₄	—	4	2	no	—
684	C₂²×C₄	—	4	1	no	—
685	C₂²×C₄	—	4	1	no	—
686	C₂²×C₄	—	4	2	no	—
687	C₂²×C₄	—	4	2	no	—
688	C₂²×C₄	—	4	2	no	—
689	C₂²×C₄	—	4	2	no	—
690	C₂²×C₄	—	4	1	no	—
691	C₂²×C₄	C₂×Q₈×C₂₃	1	4	yes	—
692	C₂²×C₄	C₂×Q₈×C₂₃	1	4	yes	—
693	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
700	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
701	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
702	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
703	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
706	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
707	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	4	no	—
714	C₄⋊C₄	—	4	2	no	—
715	C₄⋊C₄	—	4	2	no	—
716	C₄⋊C₄	—	4	2	no	—
717	C₄⋊C₄	—	4	2	no	—
718	C₄⋊C₄	—	4	2	no	—
719	C₄⋊C₄	—	4	2	no	—
720	C₄⋊C₄	—	4	2	no	—
721	C₄⋊C₄	—	4	2	no	—
722	C₄⋊C₄	—	4	2	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	—	4	1	no	—
725	C₄⋊C₄	—	4	1	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	2	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	2	no	—
730	C₄⋊C₄	—	4	1	no	—
731	C₄⋊C₄	—	4	2	no	—
732	C₄⋊C₄	—	4	1	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	1	no	—
735	C₄⋊C₄	—	4	1	no	—
736	C₄⋊C₄	—	4	1	no	—
737	C₄⋊C₄	—	4	1	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	4	2	no	—
747	C₂²⋊C₄	—	4	2	no	—
748	C₂²⋊C₄	—	4	2	no	—
749	C₂²⋊C₄	—	4	2	no	—
750	C₂²⋊C₄	—	4	2	no	—
751	C₂²⋊C₄	—	4	2	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	C₂×Q₈×C₂₃	1	8	yes	—
755	C₂²⋊C₄	C₂×Q₈×C₂₃	1	8	yes	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	4	1	no	—
759	C₄²	—	4	1	no	—
760	C₄²	—	4	2	no	—
761	C₄²	—	4	2	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	1	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	2	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	2	no	—
772	C₂³	—	2	8	no	—
773	C₂³	—	4	4	no	—
774	C₂³	—	4	4	no	—
775	C₂³	—	8	2	no	—
776	C₂³	—	8	2	no	—
777	C₂³	—	8	2	no	—
778	C₂³	—	8	2	no	—
779	C₂³	C₂²×Q₈×C₂₃	1	4	yes	—
780	C₂³	C₂²×Q₈×C₂₃	1	2	yes	—
781	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
782	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
783	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
784	Q₈	—	8	4	no	—
785	Q₈	—	8	4	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	1	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	1	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	1	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	4	4	no	—
836	C₂×C₄	—	8	2	no	—
837	C₂×C₄	—	8	2	no	—
838	C₂×C₄	—	8	4	no	—
839	C₂×C₄	—	8	4	no	—
840	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
841	C₂×C₄	C₂²×Q₈×C₂₃	1	2	yes	—
842	C₂×C₄	C₂²×Q₈×C₂₃	1	4	yes	—
843	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
844	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
845	C₂²	—	2	2	no	—
846	C₂²	—	2	2	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	4	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	2	4	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	8	8	no	—
859	C₂²	C₂₃×#544	1	4	yes	—
860	C₂²	C₂³×Q₈×C₂₃	1	1	yes	characteristic
861	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
862	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
863	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
864	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
865	C₂²	C₂₃×#585	1	1	yes	characteristic
866	C₂²	C₂₃×#585	1	1	yes	characteristic
867	C₄	—	2	2	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	4	no	—
870	C₄	—	2	2	no	—
871	C₄	—	2	2	no	—
872	C₄	—	4	1	no	—
873	C₄	—	4	2	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	1	no	—
877	C₄	—	4	2	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	2	no	—
884	C₂	—	2	4	no	—
885	C₂	—	4	4	no	—
886	C₂	C₂×C₂₃×#544	1	1	yes	characteristic
887	C₂	C₂₃×#3501	1	1	yes	characteristic
888	C₂	C₂₃×#3501	1	1	yes	characteristic
889	C₂	C₂₃×#3534	1	1	yes	characteristic
890	C₂	C₂₃×#3536	1	1	yes	characteristic
891	C₂	C₂₃×#3558	1	1	yes	characteristic
892	C₂	C₂₃×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂⁵×C₂₃	C₂³
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×#2851	C₂	semidirect
3. C₂₃×#2807	C₂	semidirect
4. C₂₃×#2788	C₂	semidirect
5. C₂₃×#2768	C₂	semidirect
6. C₂₃×#2763	C₂	semidirect
7. C₂₃×#2729	C₂	semidirect
8. C₂₃×#2720	C₂	semidirect
9. C₂₃×#2704	C₂	semidirect
10. C₂₃×#2704	C₂	semidirect
11. C₂₃×#2659	C₂	semidirect
12. C₂₃×#2646	C₂	semidirect
13. C₂₃×#2549	C₂	semidirect
14. C₂₃×#2442	C₂	semidirect
20. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₂₃×#125	C₂²	semidirect
22. C₂×C₂₃×#125	C₂²	semidirect
33. C₂₃×#400	C₂²	semidirect
34. C₂₃×#400	C₂²	semidirect
35. C₂₃×#400	C₂²	semidirect
36. C₂₃×#400	C₂²	semidirect
39. C₂₃×#398	C₂²	semidirect
40. C₂₃×#398	C₂²	semidirect
41. C₂₃×#398	C₂²	semidirect
42. C₂₃×#398	C₂²	semidirect
43. C₂₃×#398	C₂²	semidirect
44. C₂₃×#398	C₂²	semidirect
45. C₂₃×#398	C₂²	semidirect
46. C₂₃×#398	C₂²	semidirect
51. C₂₃×#395	C₂²	semidirect
52. C₂₃×#395	C₂²	semidirect
53. C₂₃×#395	C₂²	semidirect
54. C₂₃×#395	C₂²	semidirect
57. C₂₃×#391	C₂²	semidirect
58. C₂₃×#391	C₂²	semidirect
59. C₂₃×#391	C₂²	semidirect
60. C₂₃×#389	C₂²	semidirect
61. C₂₃×#389	C₂²	semidirect
62. C₂₃×#389	C₂²	semidirect
63. C₂₃×#389	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×#387	C₂²	semidirect
78. C₂₃×#387	C₂²	semidirect
91. C₂₃×#384	C₂²	semidirect
92. C₂₃×#382	C₂²	semidirect
93. C₂₃×#382	C₂²	semidirect
159. C₂×C₂²⋊C₄×C₂₃	Q₈	semidirect
315. #36750	C₂₃	direct (N × H)
399. #2857	C₂×C₂₃	semidirect
400. #2851	C₂×C₂₃	semidirect
401. #2807	C₂×C₂₃	semidirect
402. #2788	C₂×C₂₃	semidirect
403. #2768	C₂×C₂₃	semidirect
404. #2763	C₂×C₂₃	semidirect
405. #2729	C₂×C₂₃	semidirect
406. #2720	C₂×C₂₃	semidirect
407. #2704	C₂×C₂₃	semidirect
408. #2704	C₂×C₂₃	semidirect
409. #2659	C₂×C₂₃	semidirect
410. #2646	C₂×C₂₃	semidirect
411. #2549	C₂×C₂₃	semidirect
412. #2442	C₂×C₂₃	semidirect
457. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
458. C₂×#125	C₂²×C₂₃	semidirect
459. C₂×#125	C₂²×C₂₃	semidirect
470. #400	C₂²×C₂₃	semidirect
471. #400	C₂²×C₂₃	semidirect
472. #400	C₂²×C₂₃	semidirect
473. #400	C₂²×C₂₃	semidirect
476. #398	C₂²×C₂₃	semidirect
477. #398	C₂²×C₂₃	semidirect
478. #398	C₂²×C₂₃	semidirect
479. #398	C₂²×C₂₃	semidirect
480. #398	C₂²×C₂₃	semidirect
481. #398	C₂²×C₂₃	semidirect
482. #398	C₂²×C₂₃	semidirect
483. #398	C₂²×C₂₃	semidirect
488. #395	C₂²×C₂₃	semidirect
489. #395	C₂²×C₂₃	semidirect
490. #395	C₂²×C₂₃	semidirect
491. #395	C₂²×C₂₃	semidirect
494. #391	C₂²×C₂₃	semidirect
495. #391	C₂²×C₂₃	semidirect
496. #391	C₂²×C₂₃	semidirect
497. #389	C₂²×C₂₃	semidirect
498. #389	C₂²×C₂₃	semidirect
499. #389	C₂²×C₂₃	semidirect
500. #389	C₂²×C₂₃	semidirect
501. #389	C₂²×C₂₃	semidirect
502. #389	C₂²×C₂₃	semidirect
503. #389	C₂²×C₂₃	semidirect
504. #389	C₂²×C₂₃	semidirect
505. #389	C₂²×C₂₃	semidirect
514. #387	C₂²×C₂₃	semidirect
515. #387	C₂²×C₂₃	semidirect
528. #384	C₂²×C₂₃	semidirect
529. #382	C₂²×C₂₃	semidirect
530. #382	C₂²×C₂₃	semidirect
605. C₂×C₂²⋊C₄	Q₈×C₂₃	semidirect
653. C₂₃	#36750	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×#2851	2
C₂₃×#2807	2
C₂₃×#2788	2
C₂₃×#2768	2
C₂₃×#2763	2
C₂₃×#2729	2
C₂₃×#2720	2
C₂₃×#2704	2
C₂₃×#2659	2
C₂₃×#2646	2
C₂₃×#2549	2
C₂₃×#2442	2
C₂₃×#2437	2
C₂₃×#2315	2
C₂₃×#2312	2
C₂×C₂₃×#388	2
#36750	23

Subgroups — C23×#36750 #19184376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36750 #19184376