Subgroups — C₂₃×#36872 #19184498

Order 5888.

1966 conjugacy classes of subgroups.

The subgroup lattice has 918 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2849	C₂	1	2	yes	maximal, complemented
2	C₂₃×#2797	C₂	1	2	yes	maximal, complemented
3	C₂₃×#2763	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#2761	C₂	1	2	yes	maximal, complemented
5	C₂₃×#2751	C₂	1	2	yes	maximal, complemented
6	C₂₃×#2736	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#2717	C₂	1	2	yes	maximal, complemented
8	C₂₃×#2703	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2693	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2678	C₂	1	2	yes	maximal, complemented
11	C₂₃×#2670	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2638	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2631	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2573	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2557	C₂	1	2	yes	maximal, complemented
16	C₂₃×#2461	C₂	1	2	yes	maximal, complemented
17	C₂₃×#2420	C₂	1	2	yes	maximal, complemented
18	C₂₃×#2335	C₂	1	2	yes	maximal, complemented
19	C₄×C₂₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
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×#123	C₂²	1	2	yes	—
25	C₂×C₂₃×#123	C₂²	1	2	yes	—
26	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₂₃×#121	C₂²	1	2	yes	—
28	C₂×C₂₃×#120	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#120	C₂²	1	2	yes	—
30	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
32	C₂₃×#400	C₂²	1	2	yes	complemented
33	C₂₃×#400	C₂²	1	2	yes	complemented
34	C₂₃×#398	C₂²	1	1	yes	characteristic, complemented
35	C₂₃×#397	C₂²	1	2	yes	—
36	C₂₃×#397	C₂²	1	2	yes	—
37	C₂₃×#397	C₂²	1	1	yes	characteristic
38	C₂₃×#397	C₂²	1	2	yes	complemented
39	C₂₃×#397	C₂²	1	2	yes	complemented
40	C₂₃×#397	C₂²	1	2	yes	complemented
41	C₂₃×#397	C₂²	1	2	yes	complemented
42	C₂₃×#397	C₂²	1	2	yes	complemented
43	C₂₃×#396	C₂²	1	2	yes	—
44	C₂₃×#396	C₂²	1	2	yes	complemented
45	C₂₃×#395	C₂²	1	2	yes	complemented
46	C₂₃×#395	C₂²	1	1	yes	characteristic, complemented
47	C₂₃×#394	C₂²	1	2	yes	—
48	C₂₃×#394	C₂²	1	2	yes	—
49	C₂₃×#394	C₂²	1	2	yes	—
50	C₂₃×#394	C₂²	1	2	yes	complemented
51	C₂₃×#393	C₂²	1	1	yes	characteristic
52	C₂₃×#393	C₂²	1	2	yes	—
53	C₂₃×#393	C₂²	1	1	yes	characteristic
54	C₂₃×#393	C₂²	1	1	yes	characteristic, complemented
55	C₂₃×#392	C₂²	1	1	yes	characteristic
56	C₂₃×#392	C₂²	1	2	yes	—
57	C₂₃×#392	C₂²	1	2	yes	—
58	C₂₃×#392	C₂²	1	2	yes	—
59	C₂₃×#392	C₂²	1	1	yes	characteristic, complemented
60	C₂₃×#391	C₂²	1	2	yes	complemented
61	C₂₃×#390	C₂²	1	2	yes	—
62	C₂₃×#390	C₂²	1	2	yes	—
63	C₂₃×#390	C₂²	1	2	yes	—
64	C₂₃×#390	C₂²	1	2	yes	complemented
65	C₂₃×#389	C₂²	1	2	yes	complemented
66	C₂₃×#388	C₂²	1	2	yes	—
67	C₂₃×#388	C₂²	1	2	yes	—
68	C₂₃×#388	C₂²	1	2	yes	—
69	C₂₃×#388	C₂²	1	2	yes	—
70	C₂₃×#388	C₂²	1	2	yes	—
71	C₂₃×#388	C₂²	1	2	yes	complemented
72	C₂₃×#388	C₂²	1	2	yes	complemented
73	C₂₃×#388	C₂²	1	2	yes	complemented
74	C₂₃×#387	C₂²	1	2	yes	complemented
75	C₂₃×#387	C₂²	1	2	yes	complemented
76	C₂₃×#387	C₂²	1	2	yes	complemented
77	C₂₃×#387	C₂²	1	2	yes	complemented
78	C₂₃×#387	C₂²	1	2	yes	complemented
79	C₂₃×#386	C₂²	1	2	yes	—
80	C₂₃×#386	C₂²	1	2	yes	—
81	C₂₃×#386	C₂²	1	2	yes	—
82	C₂₃×#386	C₂²	1	2	yes	—
83	C₂₃×#386	C₂²	1	2	yes	—
84	C₂₃×#386	C₂²	1	1	yes	characteristic
85	C₂₃×#386	C₂²	1	2	yes	—
86	C₂₃×#386	C₂²	1	2	yes	complemented
87	C₂₃×#386	C₂²	1	2	yes	complemented
88	C₂₃×#385	C₂²	1	1	yes	characteristic
89	C₂₃×#385	C₂²	1	2	yes	—
90	C₂₃×#385	C₂²	1	2	yes	—
91	C₂₃×#385	C₂²	1	2	yes	—
92	C₂₃×#385	C₂²	1	2	yes	—
93	C₂₃×#385	C₂²	1	2	yes	—
94	C₂₃×#383	C₂²	1	1	yes	characteristic, complemented
95	C₂₃×#382	C₂²	1	2	yes	complemented
96	C₂₃×#381	C₂²	1	2	yes	—
97	C₂₃×#381	C₂²	1	2	yes	—
98	C₂₃×#381	C₂²	1	1	yes	characteristic, complemented
99	C₂₃×#380	C₂²	1	2	yes	complemented
100	C₂₃×#380	C₂²	1	2	yes	complemented
101	C₂₃×#379	C₂²	1	1	yes	characteristic
102	C₂₃×#379	C₂²	1	2	yes	—
103	C₄×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
104	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
105	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
106	C₄×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
107	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
108	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
109	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
110	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
111	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
112	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
113	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
115	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
116	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
117	C₂³×C₄×C₂₃	—	4	2	no	—
118	C₂³×C₄×C₂₃	—	4	4	no	—
119	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
120	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
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×#124	—	4	2	no	—
126	C₂₃×#124	—	4	4	no	—
127	C₂₃×#123	—	2	8	no	—
128	C₂₃×#123	—	4	4	no	—
129	C₂₃×#123	—	4	4	no	—
130	C₂₃×C₂²⋊Q₈	—	4	2	no	—
131	C₂₃×#121	—	4	4	no	—
132	C₂₃×#120	—	2	4	no	—
133	C₂₃×#120	—	4	4	no	—
134	C₄×D₄×C₂₃	—	4	2	no	—
135	C₄×D₄×C₂₃	—	4	4	no	—
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	2	yes	—
141	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
149	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
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	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	2	yes	—
182	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
198	C₂₃×#95	C₂³	1	2	yes	—
199	C₂₃×#95	C₂³	1	2	yes	—
200	C₂₃×#95	C₂³	1	1	yes	characteristic
201	C₂₃×#95	C₂³	1	1	yes	characteristic
202	C₂₃×#95	C₂³	1	2	yes	—
203	C₂₃×#95	C₂³	1	2	yes	—
204	C₂₃×#95	C₂³	1	2	yes	—
205	C₂₃×#95	C₂³	1	2	yes	—
206	C₂₃×#95	C₂³	1	2	yes	—
207	C₂⁴×C₂₃	—	2	2	no	—
208	C₂⁴×C₂₃	—	2	4	no	—
209	C₂⁴×C₂₃	—	4	1	no	—
210	C₂⁴×C₂₃	—	4	2	no	—
211	C₂⁴×C₂₃	—	4	1	no	—
212	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
213	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
214	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
215	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
216	C₂×Q₈×C₂₃	—	4	1	no	—
217	C₂×Q₈×C₂₃	—	4	1	no	—
218	C₂×Q₈×C₂₃	—	4	2	no	—
219	C₂×Q₈×C₂₃	—	4	2	no	—
220	C₂×D₄×C₂₃	—	2	2	no	—
221	C₂×D₄×C₂₃	—	2	4	no	—
222	C₂×D₄×C₂₃	—	2	4	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	—	4	1	no	—
227	C₂×D₄×C₂₃	—	4	2	no	—
228	C₂×D₄×C₂₃	—	4	1	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	2	no	—
235	C₂×D₄×C₂₃	—	4	2	no	—
236	C₂×D₄×C₂₃	—	4	2	no	—
237	C₂×D₄×C₂₃	—	4	2	no	—
238	C₂×D₄×C₂₃	—	4	2	no	—
239	C₂×D₄×C₂₃	—	4	2	no	—
240	C₂²×C₄×C₂₃	—	2	4	no	—
241	C₂²×C₄×C₂₃	—	2	4	no	—
242	C₂²×C₄×C₂₃	—	2	2	no	—
243	C₂²×C₄×C₂₃	—	2	4	no	—
244	C₂²×C₄×C₂₃	—	2	4	no	—
245	C₂²×C₄×C₂₃	—	2	2	no	—
246	C₂²×C₄×C₂₃	—	4	2	no	—
247	C₂²×C₄×C₂₃	—	4	2	no	—
248	C₂²×C₄×C₂₃	—	4	2	no	—
249	C₂²×C₄×C₂₃	—	4	2	no	—
250	C₂²×C₄×C₂₃	—	4	1	no	—
251	C₂²×C₄×C₂₃	—	4	2	no	—
252	C₂²×C₄×C₂₃	—	4	2	no	—
253	C₂²×C₄×C₂₃	—	4	2	no	—
254	C₂²×C₄×C₂₃	—	4	2	no	—
255	C₂²×C₄×C₂₃	—	4	16	no	—
256	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
265	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
266	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
269	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
271	C₄⋊C₄×C₂₃	—	2	4	no	—
272	C₄⋊C₄×C₂₃	—	2	4	no	—
273	C₄⋊C₄×C₂₃	—	2	4	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	1	no	—
279	C₄⋊C₄×C₂₃	—	4	2	no	—
280	C₄⋊C₄×C₂₃	—	4	1	no	—
281	C₄⋊C₄×C₂₃	—	4	2	no	—
282	C₄⋊C₄×C₂₃	—	4	2	no	—
283	C₄⋊C₄×C₂₃	—	4	2	no	—
284	C₂²⋊C₄×C₂₃	—	2	4	no	—
285	C₂²⋊C₄×C₂₃	—	2	4	no	—
286	C₂²⋊C₄×C₂₃	—	2	4	no	—
287	C₂²⋊C₄×C₂₃	—	2	4	no	—
288	C₂²⋊C₄×C₂₃	—	2	4	no	—
289	C₂²⋊C₄×C₂₃	—	2	4	no	—
290	C₂²⋊C₄×C₂₃	—	2	4	no	—
291	C₂²⋊C₄×C₂₃	—	4	1	no	—
292	C₂²⋊C₄×C₂₃	—	4	2	no	—
293	C₂²⋊C₄×C₂₃	—	4	2	no	—
294	C₂²⋊C₄×C₂₃	—	4	2	no	—
295	C₂²⋊C₄×C₂₃	—	4	2	no	—
296	C₂²⋊C₄×C₂₃	—	4	2	no	—
297	C₂²⋊C₄×C₂₃	—	4	2	no	—
298	C₂²⋊C₄×C₂₃	—	4	1	no	—
299	C₂²⋊C₄×C₂₃	—	4	1	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	—	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	#41	1	4	yes	—
313	C₄²×C₂₃	—	2	2	no	—
314	C₄²×C₂₃	—	4	2	no	—
315	C₄²×C₂₃	—	4	2	no	—
316	C₄²×C₂₃	—	4	2	no	—
317	C₄²×C₂₃	—	4	2	no	—
318	#36872	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
319	C₂³×C₂₃	—	2	2	no	—
320	C₂³×C₂₃	—	2	1	no	—
321	C₂³×C₂₃	—	2	2	no	—
322	C₂³×C₂₃	—	2	2	no	—
323	C₂³×C₂₃	—	2	2	no	—
324	C₂³×C₂₃	—	2	1	no	—
325	C₂³×C₂₃	—	2	2	no	—
326	C₂³×C₂₃	—	2	2	no	—
327	C₂³×C₂₃	—	2	2	no	—
328	C₂³×C₂₃	—	2	2	no	—
329	C₂³×C₂₃	—	2	2	no	—
330	C₂³×C₂₃	—	2	1	no	—
331	C₂³×C₂₃	—	2	2	no	—
332	C₂³×C₂₃	—	2	2	no	—
333	C₂³×C₂₃	—	2	1	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	1	no	—
340	C₂³×C₂₃	—	2	2	no	—
341	C₂³×C₂₃	—	4	4	no	—
342	C₂³×C₂₃	—	4	8	no	—
343	C₂³×C₂₃	—	4	4	no	—
344	C₂³×C₂₃	—	4	8	no	—
345	C₂³×C₂₃	—	4	4	no	—
346	C₂³×C₂₃	C₂×#41	1	2	yes	—
347	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
348	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
349	Q₈×C₂₃	—	8	2	no	—
350	Q₈×C₂₃	—	8	2	no	—
351	D₄×C₂₃	—	4	8	no	—
352	D₄×C₂₃	—	4	4	no	—
353	D₄×C₂₃	—	8	4	no	—
354	D₄×C₂₃	—	8	4	no	—
355	D₄×C₂₃	—	8	4	no	—
356	D₄×C₂₃	—	8	4	no	—
357	D₄×C₂₃	—	8	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	1	no	—
366	C₂×C₄×C₂₃	—	2	1	no	—
367	C₂×C₄×C₂₃	—	2	2	no	—
368	C₂×C₄×C₂₃	—	2	2	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	2	no	—
374	C₂×C₄×C₂₃	—	2	2	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	1	no	—
379	C₂×C₄×C₂₃	—	2	1	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	2	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	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	1	no	—
397	C₂×C₄×C₂₃	—	4	8	no	—
398	C₂×C₄×C₂₃	—	4	4	no	—
399	C₂×C₄×C₂₃	—	4	8	no	—
400	C₂×C₄×C₂₃	—	4	4	no	—
401	C₂×C₄×C₂₃	—	8	4	no	—
402	C₂×C₄×C₂₃	—	8	2	no	—
403	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
404	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
405	#2849	C₂×C₂₃	1	2	yes	complemented
406	#2797	C₂×C₂₃	1	2	yes	complemented
407	#2763	C₂×C₂₃	1	1	yes	characteristic, complemented
408	#2761	C₂×C₂₃	1	2	yes	complemented
409	#2751	C₂×C₂₃	1	2	yes	complemented
410	#2736	C₂×C₂₃	1	1	yes	characteristic, complemented
411	#2717	C₂×C₂₃	1	2	yes	complemented
412	#2703	C₂×C₂₃	1	2	yes	complemented
413	#2693	C₂×C₂₃	1	1	yes	characteristic, complemented
414	#2678	C₂×C₂₃	1	2	yes	complemented
415	#2670	C₂×C₂₃	1	1	yes	characteristic, complemented
416	#2638	C₂×C₂₃	1	1	yes	characteristic, complemented
417	#2631	C₂×C₂₃	1	1	yes	characteristic, complemented
418	#2573	C₂×C₂₃	1	2	yes	complemented
419	#2557	C₂×C₂₃	1	2	yes	complemented
420	#2461	C₂×C₂₃	1	2	yes	complemented
421	#2420	C₂×C₂₃	1	2	yes	complemented
422	#2335	C₂×C₂₃	1	2	yes	complemented
423	C₄×#120	C₂×C₂₃	1	1	yes	characteristic, complemented
424	C₂²×C₂₃	—	2	2	no	—
425	C₂²×C₂₃	—	2	4	no	—
426	C₂²×C₂₃	—	2	4	no	—
427	C₂²×C₂₃	—	2	4	no	—
428	C₂²×C₂₃	—	2	4	no	—
429	C₂²×C₂₃	—	4	16	no	—
430	C₂²×C₂₃	—	4	2	no	—
431	C₂²×C₂₃	—	4	2	no	—
432	C₂²×C₂₃	—	4	1	no	—
433	C₂²×C₂₃	—	4	2	no	—
434	C₂²×C₂₃	—	4	2	no	—
435	C₂²×C₂₃	—	4	1	no	—
436	C₂²×C₂₃	—	4	2	no	—
437	C₂²×C₂₃	—	4	1	no	—
438	C₂²×C₂₃	—	4	2	no	—
439	C₂²×C₂₃	—	4	2	no	—
440	C₂²×C₂₃	—	4	2	no	—
441	C₂²×C₂₃	—	4	2	no	—
442	C₂²×C₂₃	—	4	1	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	1	no	—
449	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
450	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
451	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
452	C₂²×C₂₃	#585	1	1	yes	characteristic
453	C₂²×C₂₃	#585	1	2	yes	—
454	C₄×C₂₃	—	2	4	no	—
455	C₄×C₂₃	—	2	2	no	—
456	C₄×C₂₃	—	4	2	no	—
457	C₄×C₂₃	—	4	1	no	—
458	C₄×C₂₃	—	4	2	no	—
459	C₄×C₂₃	—	4	2	no	—
460	C₄×C₂₃	—	4	2	no	—
461	C₄×C₂₃	—	4	1	no	—
462	C₄×C₂₃	—	4	1	no	—
463	C₄×C₂₃	—	4	2	no	—
464	C₄×C₂₃	—	4	2	no	—
465	C₄×C₂₃	—	4	2	no	—
466	C₄×C₂₃	—	4	2	no	—
467	C₄×C₂₃	—	4	1	no	—
468	C₄×C₂₃	—	4	2	no	—
469	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
470	C₂×#124	C₂²×C₂₃	1	2	yes	—
471	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic, complemented
472	C₂×#123	C₂²×C₂₃	1	2	yes	—
473	C₂×#123	C₂²×C₂₃	1	2	yes	—
474	C₂×#123	C₂²×C₂₃	1	2	yes	—
475	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
476	C₂×#121	C₂²×C₂₃	1	2	yes	—
477	C₂×#120	C₂²×C₂₃	1	1	yes	characteristic
478	C₂×#120	C₂²×C₂₃	1	2	yes	—
479	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
480	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
481	#400	C₂²×C₂₃	1	2	yes	complemented
482	#400	C₂²×C₂₃	1	2	yes	complemented
483	#398	C₂²×C₂₃	1	1	yes	characteristic, complemented
484	#397	C₂²×C₂₃	1	2	yes	—
485	#397	C₂²×C₂₃	1	1	yes	characteristic
486	#397	C₂²×C₂₃	1	2	yes	—
487	#397	C₂²×C₂₃	1	2	yes	complemented
488	#397	C₂²×C₂₃	1	2	yes	complemented
489	#397	C₂²×C₂₃	1	2	yes	complemented
490	#397	C₂²×C₂₃	1	2	yes	complemented
491	#397	C₂²×C₂₃	1	2	yes	complemented
492	#396	C₂²×C₂₃	1	2	yes	—
493	#396	C₂²×C₂₃	1	2	yes	complemented
494	#395	C₂²×C₂₃	1	1	yes	characteristic, complemented
495	#395	C₂²×C₂₃	1	2	yes	complemented
496	#394	C₂²×C₂₃	1	2	yes	—
497	#394	C₂²×C₂₃	1	2	yes	—
498	#394	C₂²×C₂₃	1	2	yes	—
499	#394	C₂²×C₂₃	1	2	yes	complemented
500	#393	C₂²×C₂₃	1	1	yes	characteristic
501	#393	C₂²×C₂₃	1	1	yes	characteristic
502	#393	C₂²×C₂₃	1	2	yes	—
503	#393	C₂²×C₂₃	1	1	yes	characteristic, complemented
504	#392	C₂²×C₂₃	1	1	yes	characteristic
505	#392	C₂²×C₂₃	1	2	yes	—
506	#392	C₂²×C₂₃	1	2	yes	—
507	#392	C₂²×C₂₃	1	2	yes	—
508	#392	C₂²×C₂₃	1	1	yes	characteristic, complemented
509	#391	C₂²×C₂₃	1	2	yes	complemented
510	#390	C₂²×C₂₃	1	2	yes	—
511	#390	C₂²×C₂₃	1	2	yes	—
512	#390	C₂²×C₂₃	1	2	yes	—
513	#390	C₂²×C₂₃	1	2	yes	complemented
514	#389	C₂²×C₂₃	1	2	yes	complemented
515	#388	C₂²×C₂₃	1	2	yes	—
516	#388	C₂²×C₂₃	1	2	yes	—
517	#388	C₂²×C₂₃	1	2	yes	—
518	#388	C₂²×C₂₃	1	2	yes	—
519	#388	C₂²×C₂₃	1	2	yes	—
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	#387	C₂²×C₂₃	1	2	yes	complemented
524	#387	C₂²×C₂₃	1	2	yes	complemented
525	#387	C₂²×C₂₃	1	2	yes	complemented
526	#387	C₂²×C₂₃	1	2	yes	complemented
527	#387	C₂²×C₂₃	1	2	yes	complemented
528	#386	C₂²×C₂₃	1	2	yes	—
529	#386	C₂²×C₂₃	1	2	yes	—
530	#386	C₂²×C₂₃	1	2	yes	—
531	#386	C₂²×C₂₃	1	2	yes	—
532	#386	C₂²×C₂₃	1	2	yes	—
533	#386	C₂²×C₂₃	1	2	yes	—
534	#386	C₂²×C₂₃	1	1	yes	characteristic
535	#386	C₂²×C₂₃	1	2	yes	complemented
536	#386	C₂²×C₂₃	1	2	yes	complemented
537	#385	C₂²×C₂₃	1	2	yes	—
538	#385	C₂²×C₂₃	1	2	yes	—
539	#385	C₂²×C₂₃	1	2	yes	—
540	#385	C₂²×C₂₃	1	2	yes	—
541	#385	C₂²×C₂₃	1	1	yes	characteristic
542	#385	C₂²×C₂₃	1	2	yes	—
543	#383	C₂²×C₂₃	1	1	yes	characteristic, complemented
544	#382	C₂²×C₂₃	1	2	yes	complemented
545	#381	C₂²×C₂₃	1	2	yes	—
546	#381	C₂²×C₂₃	1	2	yes	—
547	#381	C₂²×C₂₃	1	1	yes	characteristic, complemented
548	#380	C₂²×C₂₃	1	2	yes	complemented
549	#380	C₂²×C₂₃	1	2	yes	complemented
550	#379	C₂²×C₂₃	1	2	yes	—
551	#379	C₂²×C₂₃	1	1	yes	characteristic
552	C₄×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
553	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
554	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
555	C₄×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
556	C₂×C₂₃	—	4	2	no	—
557	C₂×C₂₃	—	4	4	no	—
558	C₂×C₂₃	—	8	1	no	—
559	C₂×C₂₃	—	8	2	no	—
560	C₂×C₂₃	#3460	1	1	yes	characteristic
561	C₂×C₂₃	#3513	1	2	yes	—
562	C₂×C₂₃	#3532	1	1	yes	characteristic
563	C₂×C₂₃	#3533	1	2	yes	—
564	C₂×C₂₃	#3540	1	1	yes	characteristic
565	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
566	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
567	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
568	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
569	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
570	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
571	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
572	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
573	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
574	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
575	C₂³×C₄	—	4	2	no	—
576	C₂³×C₄	—	4	4	no	—
577	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
578	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
580	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
581	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
582	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
583	#124	—	4	2	no	—
584	#124	—	4	4	no	—
585	#123	—	2	8	no	—
586	#123	—	4	4	no	—
587	#123	—	4	4	no	—
588	C₂²⋊Q₈	—	4	2	no	—
589	#121	—	4	4	no	—
590	#120	—	2	4	no	—
591	#120	—	4	4	no	—
592	C₄×D₄	—	4	2	no	—
593	C₄×D₄	—	4	4	no	—
594	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
597	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
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	1	yes	characteristic
601	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
604	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
605	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
606	C₂×C₄⋊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	1	yes	characteristic
615	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
636	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
638	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
639	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
640	C₂×C₄²	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	1	yes	characteristic
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	#95	C₂³×C₂₃	1	2	yes	—
654	#95	C₂³×C₂₃	1	2	yes	—
655	#95	C₂³×C₂₃	1	1	yes	characteristic
656	#95	C₂³×C₂₃	1	2	yes	—
657	#95	C₂³×C₂₃	1	2	yes	—
658	#95	C₂³×C₂₃	1	1	yes	characteristic
659	#95	C₂³×C₂₃	1	1	yes	characteristic
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	C₂₃	#36872	1	1	yes	characteristic, direct product factor, Sylow
666	C₂⁴	—	2	2	no	—
667	C₂⁴	—	2	4	no	—
668	C₂⁴	—	4	1	no	—
669	C₂⁴	—	4	2	no	—
670	C₂⁴	—	4	1	no	—
671	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
672	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
673	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
674	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
675	C₂×Q₈	—	4	1	no	—
676	C₂×Q₈	—	4	1	no	—
677	C₂×Q₈	—	4	2	no	—
678	C₂×Q₈	—	4	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	—	2	4	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	4	no	—
685	C₂×D₄	—	4	1	no	—
686	C₂×D₄	—	4	2	no	—
687	C₂×D₄	—	4	1	no	—
688	C₂×D₄	—	4	2	no	—
689	C₂×D₄	—	4	2	no	—
690	C₂×D₄	—	4	2	no	—
691	C₂×D₄	—	4	2	no	—
692	C₂×D₄	—	4	1	no	—
693	C₂×D₄	—	4	2	no	—
694	C₂×D₄	—	4	2	no	—
695	C₂×D₄	—	4	2	no	—
696	C₂×D₄	—	4	2	no	—
697	C₂×D₄	—	4	2	no	—
698	C₂×D₄	—	4	2	no	—
699	C₂²×C₄	—	2	4	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	4	no	—
703	C₂²×C₄	—	2	4	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	4	2	no	—
706	C₂²×C₄	—	4	2	no	—
707	C₂²×C₄	—	4	2	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	1	no	—
710	C₂²×C₄	—	4	2	no	—
711	C₂²×C₄	—	4	2	no	—
712	C₂²×C₄	—	4	2	no	—
713	C₂²×C₄	—	4	2	no	—
714	C₂²×C₄	—	4	16	no	—
715	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
716	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
719	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
720	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
721	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
723	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
725	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
726	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
727	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
729	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	4	2	no	—
734	C₄⋊C₄	—	4	1	no	—
735	C₄⋊C₄	—	4	2	no	—
736	C₄⋊C₄	—	4	1	no	—
737	C₄⋊C₄	—	4	2	no	—
738	C₄⋊C₄	—	4	2	no	—
739	C₄⋊C₄	—	4	2	no	—
740	C₄⋊C₄	—	4	2	no	—
741	C₄⋊C₄	—	4	2	no	—
742	C₄⋊C₄	—	4	2	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	4	no	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	4	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	4	1	no	—
751	C₂²⋊C₄	—	4	1	no	—
752	C₂²⋊C₄	—	4	2	no	—
753	C₂²⋊C₄	—	4	2	no	—
754	C₂²⋊C₄	—	4	2	no	—
755	C₂²⋊C₄	—	4	2	no	—
756	C₂²⋊C₄	—	4	2	no	—
757	C₂²⋊C₄	—	4	2	no	—
758	C₂²⋊C₄	—	4	2	no	—
759	C₂²⋊C₄	—	4	2	no	—
760	C₂²⋊C₄	—	4	2	no	—
761	C₂²⋊C₄	—	4	2	no	—
762	C₂²⋊C₄	—	4	2	no	—
763	C₂²⋊C₄	—	4	2	no	—
764	C₂²⋊C₄	—	4	1	no	—
765	C₂²⋊C₄	—	4	2	no	—
766	C₂²⋊C₄	—	4	2	no	—
767	C₂²⋊C₄	—	4	2	no	—
768	C₂²⋊C₄	—	4	2	no	—
769	C₂²⋊C₄	—	4	2	no	—
770	C₂²⋊C₄	—	4	2	no	—
771	C₂²⋊C₄	#41×C₂₃	1	4	yes	—
772	C₄²	—	2	2	no	—
773	C₄²	—	4	2	no	—
774	C₄²	—	4	2	no	—
775	C₄²	—	4	2	no	—
776	C₄²	—	4	2	no	—
777	C₂³	—	2	2	no	—
778	C₂³	—	2	1	no	—
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	2	1	no	—
783	C₂³	—	2	2	no	—
784	C₂³	—	2	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	1	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	2	no	—
791	C₂³	—	2	1	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	2	no	—
795	C₂³	—	2	2	no	—
796	C₂³	—	2	2	no	—
797	C₂³	—	2	1	no	—
798	C₂³	—	2	2	no	—
799	C₂³	—	4	4	no	—
800	C₂³	—	4	8	no	—
801	C₂³	—	4	4	no	—
802	C₂³	—	4	8	no	—
803	C₂³	—	4	4	no	—
804	C₂³	C₂×#41×C₂₃	1	2	yes	—
805	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
806	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
807	Q₈	—	8	2	no	—
808	Q₈	—	8	2	no	—
809	D₄	—	4	8	no	—
810	D₄	—	4	4	no	—
811	D₄	—	8	4	no	—
812	D₄	—	8	4	no	—
813	D₄	—	8	4	no	—
814	D₄	—	8	4	no	—
815	D₄	—	8	2	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	1	no	—
824	C₂×C₄	—	2	1	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	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	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	1	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	2	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	2	no	—
844	C₂×C₄	—	2	2	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	1	no	—
855	C₂×C₄	—	4	8	no	—
856	C₂×C₄	—	4	4	no	—
857	C₂×C₄	—	4	8	no	—
858	C₂×C₄	—	4	4	no	—
859	C₂×C₄	—	8	4	no	—
860	C₂×C₄	—	8	2	no	—
861	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
862	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
863	C₂²	—	2	2	no	—
864	C₂²	—	2	4	no	—
865	C₂²	—	2	4	no	—
866	C₂²	—	2	4	no	—
867	C₂²	—	2	4	no	—
868	C₂²	—	4	16	no	—
869	C₂²	—	4	2	no	—
870	C₂²	—	4	2	no	—
871	C₂²	—	4	1	no	—
872	C₂²	—	4	2	no	—
873	C₂²	—	4	2	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	4	2	no	—
876	C₂²	—	4	1	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	2	no	—
879	C₂²	—	4	2	no	—
880	C₂²	—	4	2	no	—
881	C₂²	—	4	1	no	—
882	C₂²	—	4	2	no	—
883	C₂²	—	4	2	no	—
884	C₂²	—	4	2	no	—
885	C₂²	—	4	2	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	1	no	—
888	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
889	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
890	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
891	C₂²	C₂₃×#585	1	1	yes	characteristic
892	C₂²	C₂₃×#585	1	2	yes	—
893	C₄	—	2	4	no	—
894	C₄	—	2	2	no	—
895	C₄	—	4	1	no	—
896	C₄	—	4	2	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	1	no	—
901	C₄	—	4	1	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	—	4	2	no	—
905	C₄	—	4	2	no	—
906	C₄	—	4	1	no	—
907	C₄	—	4	2	no	—
908	C₂	—	4	2	no	—
909	C₂	—	4	4	no	—
910	C₂	—	8	1	no	—
911	C₂	—	8	2	no	—
912	C₂	C₂₃×#3460	1	1	yes	characteristic
913	C₂	C₂₃×#3513	1	2	yes	—
914	C₂	C₂₃×#3532	1	1	yes	characteristic
915	C₂	C₂₃×#3533	1	2	yes	—
916	C₂	C₂₃×#3540	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×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×#2849	C₂	semidirect
2. C₂₃×#2797	C₂	semidirect
3. C₂₃×#2763	C₂	semidirect
4. C₂₃×#2761	C₂	semidirect
5. C₂₃×#2751	C₂	semidirect
6. C₂₃×#2736	C₂	semidirect
7. C₂₃×#2717	C₂	semidirect
8. C₂₃×#2703	C₂	semidirect
9. C₂₃×#2693	C₂	semidirect
10. C₂₃×#2678	C₂	semidirect
11. C₂₃×#2670	C₂	semidirect
12. C₂₃×#2638	C₂	semidirect
13. C₂₃×#2631	C₂	semidirect
14. C₂₃×#2573	C₂	semidirect
15. C₂₃×#2557	C₂	semidirect
16. C₂₃×#2461	C₂	semidirect
17. C₂₃×#2420	C₂	semidirect
18. C₂₃×#2335	C₂	semidirect
19. C₄×C₂₃×#120	C₂	semidirect
22. C₂×C₂₃×#124	C₂²	semidirect
26. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
32. C₂₃×#400	C₂²	semidirect
33. C₂₃×#400	C₂²	semidirect
34. C₂₃×#398	C₂²	semidirect
38. C₂₃×#397	C₂²	semidirect
39. C₂₃×#397	C₂²	semidirect
40. C₂₃×#397	C₂²	semidirect
41. C₂₃×#397	C₂²	semidirect
42. C₂₃×#397	C₂²	semidirect
44. C₂₃×#396	C₂²	semidirect
45. C₂₃×#395	C₂²	semidirect
46. C₂₃×#395	C₂²	semidirect
50. C₂₃×#394	C₂²	semidirect
54. C₂₃×#393	C₂²	semidirect
59. C₂₃×#392	C₂²	semidirect
60. C₂₃×#391	C₂²	semidirect
64. C₂₃×#390	C₂²	semidirect
65. C₂₃×#389	C₂²	semidirect
71. C₂₃×#388	C₂²	semidirect
72. C₂₃×#388	C₂²	semidirect
73. C₂₃×#388	C₂²	semidirect
74. C₂₃×#387	C₂²	semidirect
75. C₂₃×#387	C₂²	semidirect
76. C₂₃×#387	C₂²	semidirect
77. C₂₃×#387	C₂²	semidirect
78. C₂₃×#387	C₂²	semidirect
86. C₂₃×#386	C₂²	semidirect
87. C₂₃×#386	C₂²	semidirect
94. C₂₃×#383	C₂²	semidirect
95. C₂₃×#382	C₂²	semidirect
98. C₂₃×#381	C₂²	semidirect
99. C₂₃×#380	C₂²	semidirect
100. C₂₃×#380	C₂²	semidirect
103. C₄×C₄⋊C₄×C₂₃	C₂²	semidirect
106. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
318. #36872	C₂₃	direct (N × H)
405. #2849	C₂×C₂₃	semidirect
406. #2797	C₂×C₂₃	semidirect
407. #2763	C₂×C₂₃	semidirect
408. #2761	C₂×C₂₃	semidirect
409. #2751	C₂×C₂₃	semidirect
410. #2736	C₂×C₂₃	semidirect
411. #2717	C₂×C₂₃	semidirect
412. #2703	C₂×C₂₃	semidirect
413. #2693	C₂×C₂₃	semidirect
414. #2678	C₂×C₂₃	semidirect
415. #2670	C₂×C₂₃	semidirect
416. #2638	C₂×C₂₃	semidirect
417. #2631	C₂×C₂₃	semidirect
418. #2573	C₂×C₂₃	semidirect
419. #2557	C₂×C₂₃	semidirect
420. #2461	C₂×C₂₃	semidirect
421. #2420	C₂×C₂₃	semidirect
422. #2335	C₂×C₂₃	semidirect
423. C₄×#120	C₂×C₂₃	semidirect
471. C₂×#124	C₂²×C₂₃	semidirect
475. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
481. #400	C₂²×C₂₃	semidirect
482. #400	C₂²×C₂₃	semidirect
483. #398	C₂²×C₂₃	semidirect
487. #397	C₂²×C₂₃	semidirect
488. #397	C₂²×C₂₃	semidirect
489. #397	C₂²×C₂₃	semidirect
490. #397	C₂²×C₂₃	semidirect
491. #397	C₂²×C₂₃	semidirect
493. #396	C₂²×C₂₃	semidirect
494. #395	C₂²×C₂₃	semidirect
495. #395	C₂²×C₂₃	semidirect
499. #394	C₂²×C₂₃	semidirect
503. #393	C₂²×C₂₃	semidirect
508. #392	C₂²×C₂₃	semidirect
509. #391	C₂²×C₂₃	semidirect
513. #390	C₂²×C₂₃	semidirect
514. #389	C₂²×C₂₃	semidirect
520. #388	C₂²×C₂₃	semidirect
521. #388	C₂²×C₂₃	semidirect
522. #388	C₂²×C₂₃	semidirect
523. #387	C₂²×C₂₃	semidirect
524. #387	C₂²×C₂₃	semidirect
525. #387	C₂²×C₂₃	semidirect
526. #387	C₂²×C₂₃	semidirect
527. #387	C₂²×C₂₃	semidirect
535. #386	C₂²×C₂₃	semidirect
536. #386	C₂²×C₂₃	semidirect
543. #383	C₂²×C₂₃	semidirect
544. #382	C₂²×C₂₃	semidirect
547. #381	C₂²×C₂₃	semidirect
548. #380	C₂²×C₂₃	semidirect
549. #380	C₂²×C₂₃	semidirect
552. C₄×C₄⋊C₄	C₂²×C₂₃	semidirect
555. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
665. C₂₃	#36872	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×#2849	2
C₂₃×#2797	2
C₂₃×#2763	2
C₂₃×#2761	2
C₂₃×#2751	2
C₂₃×#2736	2
C₂₃×#2717	2
C₂₃×#2703	2
C₂₃×#2693	2
C₂₃×#2678	2
C₂₃×#2670	2
C₂₃×#2638	2
C₂₃×#2631	2
C₂₃×#2573	2
C₂₃×#2557	2
C₂₃×#2461	2
C₂₃×#2420	2
C₂₃×#2335	2
C₄×C₂₃×#120	2
#36872	23

Subgroups — C23×#36872 #19184498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36872 #19184498