Subgroups — C₂₃×#36703 #19184329

Order 5888.

4062 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₂₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#2846	C₂	1	2	yes	maximal, complemented
4	C₂₃×#2685	C₂	1	4	yes	maximal, complemented
5	C₂₃×#2678	C₂	1	4	yes	maximal, complemented
6	C₂₃×#2670	C₂	1	4	yes	maximal, complemented
7	C₂₃×#2669	C₂	1	4	yes	maximal, complemented
8	C₂₃×#2613	C₂	1	2	yes	maximal, complemented
9	C₂₃×#2561	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#2539	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#2534	C₂	1	2	yes	maximal, complemented
12	C₂₃×#2435	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#2433	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#2408	C₂	1	2	yes	maximal, complemented
15	C₂₃×#2312	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁶×C₂₃	C₂²	1	1	yes	characteristic
17	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#538	—	2	8	no	—
21	C₂×C₂₃×#127	C₂²	1	2	yes	complemented
22	C₂×C₂₃×#126	C₂²	1	2	yes	complemented
23	C₂×C₂₃×#124	C₂²	1	2	yes	complemented
24	C₂×C₂₃×#124	C₂²	1	2	yes	complemented
25	C₂×C₂₃×#123	C₂²	1	2	yes	complemented
26	C₂×C₂₃×#123	C₂²	1	2	yes	complemented
27	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
29	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
30	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₂₃×#120	—	2	8	no	—
32	C₂×C₂₃×#120	C₂²	1	4	yes	—
33	C₂×C₂₃×#120	C₂²	1	4	yes	—
34	C₂×C₂₃×#120	C₂²	1	2	yes	—
35	C₂×C₂₃×#120	C₂²	1	2	yes	—
36	C₂×C₂₃×#120	C₂²	1	2	yes	—
37	C₂×C₂₃×#120	C₂²	1	4	yes	complemented
38	C₂×C₂₃×#120	C₂²	1	4	yes	complemented
39	C₂×C₂₃×#120	C₂²	1	2	yes	complemented
40	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	complemented
41	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
43	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂₃×#399	C₂²	1	2	yes	complemented
45	C₂₃×#397	C₂²	1	2	yes	complemented
46	C₂₃×#396	C₂²	1	4	yes	complemented
47	C₂₃×#394	C₂²	1	4	yes	complemented
48	C₂₃×#394	C₂²	1	4	yes	complemented
49	C₂₃×#394	C₂²	1	4	yes	complemented
50	C₂₃×#394	C₂²	1	4	yes	complemented
51	C₂₃×#394	C₂²	1	4	yes	complemented
52	C₂₃×#393	C₂²	1	2	yes	complemented
53	C₂₃×#392	C₂²	1	4	yes	complemented
54	C₂₃×#392	C₂²	1	2	yes	complemented
55	C₂₃×#392	C₂²	1	4	yes	complemented
56	C₂₃×#392	C₂²	1	4	yes	complemented
57	C₂₃×#392	C₂²	1	4	yes	complemented
58	C₂₃×#390	C₂²	1	4	yes	complemented
59	C₂₃×#390	C₂²	1	4	yes	complemented
60	C₂₃×#390	C₂²	1	2	yes	complemented
61	C₂₃×#390	C₂²	1	2	yes	complemented
62	C₂₃×#388	C₂²	1	4	yes	complemented
63	C₂₃×#388	C₂²	1	4	yes	complemented
64	C₂₃×#388	C₂²	1	4	yes	complemented
65	C₂₃×#388	C₂²	1	4	yes	complemented
66	C₂₃×#386	C₂²	1	4	yes	complemented
67	C₂₃×#381	C₂²	1	2	yes	complemented
68	C₂₃×#380	C₂²	1	2	yes	complemented
69	C₂₃×#379	C₂²	1	2	yes	—
70	C₂₃×#379	C₂²	1	2	yes	—
71	C₂₃×#379	C₂²	1	2	yes	—
72	C₂₃×#379	C₂²	1	4	yes	complemented
73	C₂₃×#379	C₂²	1	4	yes	complemented
74	C₂₃×#379	C₂²	1	2	yes	complemented
75	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
76	C₄×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
77	C₂⁵×C₂₃	—	2	4	no	—
78	C₂⁵×C₂₃	—	4	4	no	—
79	C₂⁵×C₂₃	—	4	4	no	—
80	C₂⁵×C₂₃	—	4	4	no	—
81	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
82	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
83	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
84	C₂⁵×C₂₃	C₂³	1	4	yes	—
85	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic, complemented
87	C₂²×D₄×C₂₃	—	2	4	no	—
88	C₂²×D₄×C₂₃	—	2	4	no	—
89	C₂²×D₄×C₂₃	—	2	4	no	—
90	C₂²×D₄×C₂₃	—	4	4	no	—
91	C₂²×D₄×C₂₃	—	4	4	no	—
92	C₂²×D₄×C₂₃	—	4	4	no	—
93	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
94	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
95	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
96	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
97	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
98	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
99	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
100	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
101	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
102	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic, complemented
103	C₂²×D₄×C₂₃	C₂³	1	4	yes	complemented
104	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₂₃	C₂³	1	2	yes	complemented
108	C₂₃×#127	—	4	4	no	—
109	C₂₃×#126	—	2	8	no	—
110	C₂₃×#124	—	2	8	no	—
111	C₂₃×#124	—	4	4	no	—
112	C₂₃×#123	—	2	8	no	—
113	C₂₃×#123	—	4	4	no	—
114	C₂₃×C₂²⋊Q₈	—	2	4	no	—
115	C₂₃×#121	—	2	4	no	—
116	C₂₃×#121	—	2	8	no	—
117	C₂₃×#121	—	4	8	no	—
118	C₂₃×#120	—	2	8	no	—
119	C₂₃×#120	—	2	16	no	—
120	C₂₃×#120	—	2	16	no	—
121	C₂₃×#120	—	4	4	no	—
122	C₂₃×#120	—	4	4	no	—
123	C₂₃×#120	—	4	4	no	—
124	C₂₃×#120	—	4	8	no	—
125	C₂₃×#120	—	4	8	no	—
126	C₄×D₄×C₂₃	—	2	8	no	—
127	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	complemented
128	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic, complemented
129	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic, complemented
130	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	complemented
131	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
132	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
133	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
134	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
135	C₂×C₂²⋊C₄×C₂₃	D₄	1	8	yes	complemented
136	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
144	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
146	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	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	complemented
155	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	complemented
156	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
157	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
158	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
159	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
160	C₂×C₄²×C₂₃	C₂³	1	2	yes	complemented
161	C₂×C₄²×C₂₃	C₂³	1	2	yes	complemented
162	C₂×C₄²×C₂₃	C₂³	1	2	yes	complemented
163	C₂₃×#95	C₂³	1	2	yes	complemented
164	C₂₃×#95	C₂³	1	2	yes	complemented
165	C₂₃×#95	C₂³	1	4	yes	complemented
166	C₂₃×#95	C₂³	1	4	yes	complemented
167	C₂₃×#95	C₂³	1	4	yes	complemented
168	C₂⁴×C₂₃	—	2	2	no	—
169	C₂⁴×C₂₃	—	2	2	no	—
170	C₂⁴×C₂₃	—	2	4	no	—
171	C₂⁴×C₂₃	—	2	4	no	—
172	C₂⁴×C₂₃	—	2	4	no	—
173	C₂⁴×C₂₃	—	2	8	no	—
174	C₂⁴×C₂₃	—	2	2	no	—
175	C₂⁴×C₂₃	—	2	8	no	—
176	C₂⁴×C₂₃	—	2	8	no	—
177	C₂⁴×C₂₃	—	2	4	no	—
178	C₂⁴×C₂₃	—	2	4	no	—
179	C₂⁴×C₂₃	—	2	4	no	—
180	C₂⁴×C₂₃	—	4	2	no	—
181	C₂⁴×C₂₃	—	4	2	no	—
182	C₂⁴×C₂₃	—	4	2	no	—
183	C₂⁴×C₂₃	—	4	2	no	—
184	C₂⁴×C₂₃	—	4	4	no	—
185	C₂⁴×C₂₃	—	4	4	no	—
186	C₂⁴×C₂₃	—	4	4	no	—
187	C₂⁴×C₂₃	—	4	4	no	—
188	C₂⁴×C₂₃	—	4	2	no	—
189	C₂⁴×C₂₃	—	4	2	no	—
190	C₂⁴×C₂₃	—	4	16	no	—
191	C₂⁴×C₂₃	—	4	16	no	—
192	C₂⁴×C₂₃	—	4	16	no	—
193	C₂⁴×C₂₃	—	4	64	no	—
194	C₂⁴×C₂₃	C₂×D₄	1	4	yes	—
195	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
196	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
197	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
198	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
199	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
200	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
201	C₂×Q₈×C₂₃	—	2	2	no	—
202	C₂×Q₈×C₂₃	—	4	2	no	—
203	C₂×D₄×C₂₃	—	2	4	no	—
204	C₂×D₄×C₂₃	—	2	8	no	—
205	C₂×D₄×C₂₃	—	2	4	no	—
206	C₂×D₄×C₂₃	—	2	4	no	—
207	C₂×D₄×C₂₃	—	2	8	no	—
208	C₂×D₄×C₂₃	—	2	4	no	—
209	C₂×D₄×C₂₃	—	2	4	no	—
210	C₂×D₄×C₂₃	—	2	4	no	—
211	C₂×D₄×C₂₃	—	2	4	no	—
212	C₂×D₄×C₂₃	—	2	8	no	—
213	C₂×D₄×C₂₃	—	2	8	no	—
214	C₂×D₄×C₂₃	—	2	8	no	—
215	C₂×D₄×C₂₃	—	2	4	no	—
216	C₂×D₄×C₂₃	—	2	4	no	—
217	C₂×D₄×C₂₃	—	2	2	no	—
218	C₂×D₄×C₂₃	—	4	2	no	—
219	C₂×D₄×C₂₃	—	4	2	no	—
220	C₂×D₄×C₂₃	—	4	4	no	—
221	C₂×D₄×C₂₃	—	4	4	no	—
222	C₂×D₄×C₂₃	—	4	4	no	—
223	C₂×D₄×C₂₃	—	4	4	no	—
224	C₂×D₄×C₂₃	—	4	4	no	—
225	C₂×D₄×C₂₃	—	4	4	no	—
226	C₂×D₄×C₂₃	—	4	4	no	—
227	C₂×D₄×C₂₃	—	4	4	no	—
228	C₂×D₄×C₂₃	—	4	4	no	—
229	C₂×D₄×C₂₃	—	4	4	no	—
230	C₂×D₄×C₂₃	—	4	4	no	—
231	C₂×D₄×C₂₃	—	4	2	no	—
232	C₂×D₄×C₂₃	—	4	4	no	—
233	C₂×D₄×C₂₃	—	4	16	no	—
234	C₂×D₄×C₂₃	—	4	16	no	—
235	C₂×D₄×C₂₃	—	4	16	no	—
236	C₂²×C₄×C₂₃	—	2	2	no	—
237	C₂²×C₄×C₂₃	—	2	4	no	—
238	C₂²×C₄×C₂₃	—	2	4	no	—
239	C₂²×C₄×C₂₃	—	4	2	no	—
240	C₂²×C₄×C₂₃	—	4	2	no	—
241	C₂²×C₄×C₂₃	—	4	4	no	—
242	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
243	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
244	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
246	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
248	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
252	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₂₃	—	2	4	no	—
254	C₄⋊C₄×C₂₃	—	2	4	no	—
255	C₄⋊C₄×C₂₃	—	2	2	no	—
256	C₄⋊C₄×C₂₃	—	2	2	no	—
257	C₄⋊C₄×C₂₃	—	4	4	no	—
258	C₄⋊C₄×C₂₃	—	4	4	no	—
259	C₂²⋊C₄×C₂₃	—	2	4	no	—
260	C₂²⋊C₄×C₂₃	—	2	4	no	—
261	C₂²⋊C₄×C₂₃	—	2	4	no	—
262	C₂²⋊C₄×C₂₃	—	2	4	no	—
263	C₂²⋊C₄×C₂₃	—	2	8	no	—
264	C₂²⋊C₄×C₂₃	—	2	4	no	—
265	C₂²⋊C₄×C₂₃	—	2	8	no	—
266	C₂²⋊C₄×C₂₃	—	2	8	no	—
267	C₂²⋊C₄×C₂₃	—	2	4	no	—
268	C₂²⋊C₄×C₂₃	—	2	4	no	—
269	C₂²⋊C₄×C₂₃	—	2	4	no	—
270	C₂²⋊C₄×C₂₃	—	2	4	no	—
271	C₂²⋊C₄×C₂₃	—	4	4	no	—
272	C₂²⋊C₄×C₂₃	—	4	4	no	—
273	C₂²⋊C₄×C₂₃	—	4	4	no	—
274	C₂²⋊C₄×C₂₃	—	4	4	no	—
275	C₂²⋊C₄×C₂₃	—	4	4	no	—
276	C₂²⋊C₄×C₂₃	—	4	4	no	—
277	C₂²⋊C₄×C₂₃	—	4	4	no	—
278	C₂²⋊C₄×C₂₃	—	4	4	no	—
279	C₂²⋊C₄×C₂₃	—	4	4	no	—
280	C₂²⋊C₄×C₂₃	—	4	4	no	—
281	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
282	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
283	C₄²×C₂₃	—	2	4	no	—
284	C₄²×C₂₃	—	4	2	no	—
285	C₄²×C₂₃	—	4	2	no	—
286	#36703	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂³×C₂₃	—	2	2	no	—
288	C₂³×C₂₃	—	2	2	no	—
289	C₂³×C₂₃	—	2	8	no	—
290	C₂³×C₂₃	—	2	8	no	—
291	C₂³×C₂₃	—	2	8	no	—
292	C₂³×C₂₃	—	2	2	no	—
293	C₂³×C₂₃	—	2	2	no	—
294	C₂³×C₂₃	—	2	4	no	—
295	C₂³×C₂₃	—	2	4	no	—
296	C₂³×C₂₃	—	2	4	no	—
297	C₂³×C₂₃	—	2	4	no	—
298	C₂³×C₂₃	—	2	4	no	—
299	C₂³×C₂₃	—	2	4	no	—
300	C₂³×C₂₃	—	2	2	no	—
301	C₂³×C₂₃	—	2	2	no	—
302	C₂³×C₂₃	—	2	2	no	—
303	C₂³×C₂₃	—	2	2	no	—
304	C₂³×C₂₃	—	2	2	no	—
305	C₂³×C₂₃	—	2	2	no	—
306	C₂³×C₂₃	—	2	2	no	—
307	C₂³×C₂₃	—	2	2	no	—
308	C₂³×C₂₃	—	2	4	no	—
309	C₂³×C₂₃	—	2	4	no	—
310	C₂³×C₂₃	—	2	4	no	—
311	C₂³×C₂₃	—	2	2	no	—
312	C₂³×C₂₃	—	2	4	no	—
313	C₂³×C₂₃	—	2	2	no	—
314	C₂³×C₂₃	—	4	4	no	—
315	C₂³×C₂₃	—	4	4	no	—
316	C₂³×C₂₃	—	4	16	no	—
317	C₂³×C₂₃	—	4	16	no	—
318	C₂³×C₂₃	—	4	16	no	—
319	C₂³×C₂₃	—	4	16	no	—
320	C₂³×C₂₃	—	4	16	no	—
321	C₂³×C₂₃	—	4	4	no	—
322	C₂³×C₂₃	—	4	4	no	—
323	C₂³×C₂₃	—	4	16	no	—
324	C₂³×C₂₃	—	4	16	no	—
325	C₂³×C₂₃	—	4	16	no	—
326	C₂³×C₂₃	—	4	16	no	—
327	C₂³×C₂₃	—	4	4	no	—
328	C₂³×C₂₃	—	4	4	no	—
329	C₂³×C₂₃	—	4	128	no	—
330	C₂³×C₂₃	—	4	16	no	—
331	C₂³×C₂₃	—	4	4	no	—
332	C₂³×C₂₃	—	4	4	no	—
333	C₂³×C₂₃	—	4	4	no	—
334	C₂³×C₂₃	—	8	8	no	—
335	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
336	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
337	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
338	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
339	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
340	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
341	Q₈×C₂₃	—	8	2	no	—
342	D₄×C₂₃	—	4	16	no	—
343	D₄×C₂₃	—	4	8	no	—
344	D₄×C₂₃	—	4	8	no	—
345	D₄×C₂₃	—	4	16	no	—
346	D₄×C₂₃	—	4	8	no	—
347	D₄×C₂₃	—	8	2	no	—
348	D₄×C₂₃	—	8	4	no	—
349	D₄×C₂₃	—	8	4	no	—
350	D₄×C₂₃	—	8	8	no	—
351	D₄×C₂₃	—	8	8	no	—
352	D₄×C₂₃	—	8	8	no	—
353	C₂×C₄×C₂₃	—	2	2	no	—
354	C₂×C₄×C₂₃	—	2	2	no	—
355	C₂×C₄×C₂₃	—	2	4	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	4	no	—
361	C₂×C₄×C₂₃	—	2	4	no	—
362	C₂×C₄×C₂₃	—	2	4	no	—
363	C₂×C₄×C₂₃	—	2	4	no	—
364	C₂×C₄×C₂₃	—	2	4	no	—
365	C₂×C₄×C₂₃	—	2	4	no	—
366	C₂×C₄×C₂₃	—	2	4	no	—
367	C₂×C₄×C₂₃	—	2	2	no	—
368	C₂×C₄×C₂₃	—	2	4	no	—
369	C₂×C₄×C₂₃	—	2	2	no	—
370	C₂×C₄×C₂₃	—	2	4	no	—
371	C₂×C₄×C₂₃	—	4	4	no	—
372	C₂×C₄×C₂₃	—	4	4	no	—
373	C₂×C₄×C₂₃	—	4	4	no	—
374	C₂×C₄×C₂₃	—	8	4	no	—
375	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
376	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
378	C₂×#538	C₂×C₂₃	1	1	yes	characteristic, complemented
379	C₂²×#120	C₂×C₂₃	1	1	yes	characteristic, complemented
380	#2846	C₂×C₂₃	1	2	yes	complemented
381	#2685	C₂×C₂₃	1	4	yes	complemented
382	#2678	C₂×C₂₃	1	4	yes	complemented
383	#2670	C₂×C₂₃	1	4	yes	complemented
384	#2669	C₂×C₂₃	1	4	yes	complemented
385	#2613	C₂×C₂₃	1	2	yes	complemented
386	#2561	C₂×C₂₃	1	1	yes	characteristic, complemented
387	#2539	C₂×C₂₃	1	1	yes	characteristic, complemented
388	#2534	C₂×C₂₃	1	2	yes	complemented
389	#2435	C₂×C₂₃	1	1	yes	characteristic, complemented
390	#2433	C₂×C₂₃	1	1	yes	characteristic, complemented
391	#2408	C₂×C₂₃	1	2	yes	complemented
392	#2312	C₂×C₂₃	1	1	yes	characteristic, complemented
393	C₂²×C₂₃	—	2	2	no	—
394	C₂²×C₂₃	—	2	2	no	—
395	C₂²×C₂₃	—	2	8	no	—
396	C₂²×C₂₃	—	2	4	no	—
397	C₂²×C₂₃	—	2	4	no	—
398	C₂²×C₂₃	—	2	4	no	—
399	C₂²×C₂₃	—	2	4	no	—
400	C₂²×C₂₃	—	2	4	no	—
401	C₂²×C₂₃	—	2	8	no	—
402	C₂²×C₂₃	—	2	8	no	—
403	C₂²×C₂₃	—	4	16	no	—
404	C₂²×C₂₃	—	4	16	no	—
405	C₂²×C₂₃	—	4	16	no	—
406	C₂²×C₂₃	—	4	64	no	—
407	C₂²×C₂₃	—	4	2	no	—
408	C₂²×C₂₃	—	4	2	no	—
409	C₂²×C₂₃	—	4	2	no	—
410	C₂²×C₂₃	—	4	2	no	—
411	C₂²×C₂₃	—	4	4	no	—
412	C₂²×C₂₃	—	4	4	no	—
413	C₂²×C₂₃	—	4	4	no	—
414	C₂²×C₂₃	—	4	4	no	—
415	C₂²×C₂₃	—	4	2	no	—
416	C₂²×C₂₃	—	4	2	no	—
417	C₂²×C₂₃	—	4	2	no	—
418	C₂²×C₂₃	—	4	2	no	—
419	C₂²×C₂₃	—	4	2	no	—
420	C₂²×C₂₃	—	4	2	no	—
421	C₂²×C₂₃	—	4	4	no	—
422	C₂²×C₂₃	—	4	4	no	—
423	C₂²×C₂₃	—	4	4	no	—
424	C₂²×C₂₃	—	4	4	no	—
425	C₂²×C₂₃	—	8	8	no	—
426	C₂²×C₂₃	#535	1	4	yes	—
427	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
428	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
429	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
430	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
431	C₄×C₂₃	—	2	4	no	—
432	C₄×C₂₃	—	2	2	no	—
433	C₄×C₂₃	—	2	2	no	—
434	C₄×C₂₃	—	4	2	no	—
435	C₄×C₂₃	—	4	2	no	—
436	C₄×C₂₃	—	4	2	no	—
437	C₄×C₂₃	—	4	2	no	—
438	C₄×C₂₃	—	4	4	no	—
439	C₄×C₂₃	—	4	4	no	—
440	C₂⁶	C₂²×C₂₃	1	1	yes	characteristic
441	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
442	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
443	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
444	#538	—	2	8	no	—
445	C₂×#127	C₂²×C₂₃	1	2	yes	complemented
446	C₂×#126	C₂²×C₂₃	1	2	yes	complemented
447	C₂×#124	C₂²×C₂₃	1	2	yes	complemented
448	C₂×#124	C₂²×C₂₃	1	2	yes	complemented
449	C₂×#123	C₂²×C₂₃	1	2	yes	complemented
450	C₂×#123	C₂²×C₂₃	1	2	yes	complemented
451	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
452	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
453	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
454	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic, complemented
455	C₂×#120	—	2	8	no	—
456	C₂×#120	C₂²×C₂₃	1	2	yes	—
457	C₂×#120	C₂²×C₂₃	1	4	yes	—
458	C₂×#120	C₂²×C₂₃	1	4	yes	—
459	C₂×#120	C₂²×C₂₃	1	2	yes	—
460	C₂×#120	C₂²×C₂₃	1	2	yes	—
461	C₂×#120	C₂²×C₂₃	1	4	yes	complemented
462	C₂×#120	C₂²×C₂₃	1	4	yes	complemented
463	C₂×#120	C₂²×C₂₃	1	2	yes	complemented
464	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	complemented
465	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
466	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
467	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
468	#399	C₂²×C₂₃	1	2	yes	complemented
469	#397	C₂²×C₂₃	1	2	yes	complemented
470	#396	C₂²×C₂₃	1	4	yes	complemented
471	#394	C₂²×C₂₃	1	4	yes	complemented
472	#394	C₂²×C₂₃	1	4	yes	complemented
473	#394	C₂²×C₂₃	1	4	yes	complemented
474	#394	C₂²×C₂₃	1	4	yes	complemented
475	#394	C₂²×C₂₃	1	4	yes	complemented
476	#393	C₂²×C₂₃	1	2	yes	complemented
477	#392	C₂²×C₂₃	1	4	yes	complemented
478	#392	C₂²×C₂₃	1	4	yes	complemented
479	#392	C₂²×C₂₃	1	4	yes	complemented
480	#392	C₂²×C₂₃	1	2	yes	complemented
481	#392	C₂²×C₂₃	1	4	yes	complemented
482	#390	C₂²×C₂₃	1	4	yes	complemented
483	#390	C₂²×C₂₃	1	4	yes	complemented
484	#390	C₂²×C₂₃	1	2	yes	complemented
485	#390	C₂²×C₂₃	1	2	yes	complemented
486	#388	C₂²×C₂₃	1	4	yes	complemented
487	#388	C₂²×C₂₃	1	4	yes	complemented
488	#388	C₂²×C₂₃	1	4	yes	complemented
489	#388	C₂²×C₂₃	1	4	yes	complemented
490	#386	C₂²×C₂₃	1	4	yes	complemented
491	#381	C₂²×C₂₃	1	2	yes	complemented
492	#380	C₂²×C₂₃	1	2	yes	complemented
493	#379	C₂²×C₂₃	1	2	yes	—
494	#379	C₂²×C₂₃	1	2	yes	—
495	#379	C₂²×C₂₃	1	2	yes	—
496	#379	C₂²×C₂₃	1	4	yes	complemented
497	#379	C₂²×C₂₃	1	4	yes	complemented
498	#379	C₂²×C₂₃	1	2	yes	complemented
499	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
500	C₄×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
501	C₂×C₂₃	—	2	4	no	—
502	C₂×C₂₃	—	4	4	no	—
503	C₂×C₂₃	—	4	4	no	—
504	C₂×C₂₃	—	4	4	no	—
505	C₂×C₂₃	—	8	2	no	—
506	C₂×C₂₃	—	8	2	no	—
507	C₂×C₂₃	C₂×#535	1	1	yes	characteristic
508	C₂×C₂₃	#3484	1	1	yes	characteristic
509	C₂×C₂₃	#3484	1	1	yes	characteristic
510	C₂×C₂₃	#3532	1	4	yes	—
511	C₂⁵	—	2	4	no	—
512	C₂⁵	—	4	4	no	—
513	C₂⁵	—	4	4	no	—
514	C₂⁵	—	4	4	no	—
515	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
516	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
517	C₂⁵	C₂³×C₂₃	1	4	yes	—
518	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
519	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
520	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic, complemented
521	C₂²×D₄	—	2	4	no	—
522	C₂²×D₄	—	2	4	no	—
523	C₂²×D₄	—	2	4	no	—
524	C₂²×D₄	—	4	4	no	—
525	C₂²×D₄	—	4	4	no	—
526	C₂²×D₄	—	4	4	no	—
527	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
528	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
529	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
530	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
531	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
532	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
533	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
534	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
535	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
536	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic, complemented
537	C₂²×D₄	C₂³×C₂₃	1	4	yes	complemented
538	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
540	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
541	C₂³×C₄	C₂³×C₂₃	1	2	yes	complemented
542	#127	—	4	4	no	—
543	#126	—	2	8	no	—
544	#124	—	2	8	no	—
545	#124	—	4	4	no	—
546	#123	—	2	8	no	—
547	#123	—	4	4	no	—
548	C₂²⋊Q₈	—	2	4	no	—
549	#121	—	2	4	no	—
550	#121	—	2	8	no	—
551	#121	—	4	8	no	—
552	#120	—	2	8	no	—
553	#120	—	2	16	no	—
554	#120	—	2	16	no	—
555	#120	—	4	4	no	—
556	#120	—	4	4	no	—
557	#120	—	4	4	no	—
558	#120	—	4	8	no	—
559	#120	—	4	8	no	—
560	C₄×D₄	—	2	8	no	—
561	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	complemented
562	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	complemented
563	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic, complemented
564	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic, complemented
565	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	complemented
566	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	complemented
567	C₂×C₂²⋊C₄	—	2	4	no	—
568	C₂×C₂²⋊C₄	—	2	4	no	—
569	C₂×C₂²⋊C₄	D₄×C₂₃	1	8	yes	complemented
570	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
582	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
583	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
584	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
585	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
586	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	complemented
589	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	complemented
590	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	complemented
591	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	complemented
592	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	complemented
593	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	complemented
594	C₂×C₄²	C₂³×C₂₃	1	2	yes	complemented
595	C₂×C₄²	C₂³×C₂₃	1	2	yes	complemented
596	C₂×C₄²	C₂³×C₂₃	1	2	yes	complemented
597	#95	C₂³×C₂₃	1	2	yes	complemented
598	#95	C₂³×C₂₃	1	2	yes	complemented
599	#95	C₂³×C₂₃	1	4	yes	complemented
600	#95	C₂³×C₂₃	1	4	yes	complemented
601	#95	C₂³×C₂₃	1	4	yes	complemented
602	C₂₃	#36703	1	1	yes	characteristic, direct product factor, Sylow
603	C₂⁴	—	2	2	no	—
604	C₂⁴	—	2	2	no	—
605	C₂⁴	—	2	4	no	—
606	C₂⁴	—	2	4	no	—
607	C₂⁴	—	2	4	no	—
608	C₂⁴	—	2	8	no	—
609	C₂⁴	—	2	2	no	—
610	C₂⁴	—	2	8	no	—
611	C₂⁴	—	2	8	no	—
612	C₂⁴	—	2	4	no	—
613	C₂⁴	—	2	4	no	—
614	C₂⁴	—	2	4	no	—
615	C₂⁴	—	4	2	no	—
616	C₂⁴	—	4	2	no	—
617	C₂⁴	—	4	2	no	—
618	C₂⁴	—	4	2	no	—
619	C₂⁴	—	4	4	no	—
620	C₂⁴	—	4	4	no	—
621	C₂⁴	—	4	4	no	—
622	C₂⁴	—	4	4	no	—
623	C₂⁴	—	4	2	no	—
624	C₂⁴	—	4	2	no	—
625	C₂⁴	—	4	16	no	—
626	C₂⁴	—	4	16	no	—
627	C₂⁴	—	4	16	no	—
628	C₂⁴	—	4	64	no	—
629	C₂⁴	C₂×D₄×C₂₃	1	4	yes	—
630	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
631	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
632	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
633	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
634	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
635	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
636	C₂×Q₈	—	2	2	no	—
637	C₂×Q₈	—	4	2	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	8	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	8	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	4	no	—
646	C₂×D₄	—	2	4	no	—
647	C₂×D₄	—	2	8	no	—
648	C₂×D₄	—	2	8	no	—
649	C₂×D₄	—	2	8	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	4	no	—
652	C₂×D₄	—	2	2	no	—
653	C₂×D₄	—	4	2	no	—
654	C₂×D₄	—	4	2	no	—
655	C₂×D₄	—	4	4	no	—
656	C₂×D₄	—	4	4	no	—
657	C₂×D₄	—	4	4	no	—
658	C₂×D₄	—	4	4	no	—
659	C₂×D₄	—	4	4	no	—
660	C₂×D₄	—	4	4	no	—
661	C₂×D₄	—	4	4	no	—
662	C₂×D₄	—	4	4	no	—
663	C₂×D₄	—	4	4	no	—
664	C₂×D₄	—	4	4	no	—
665	C₂×D₄	—	4	4	no	—
666	C₂×D₄	—	4	2	no	—
667	C₂×D₄	—	4	4	no	—
668	C₂×D₄	—	4	16	no	—
669	C₂×D₄	—	4	16	no	—
670	C₂×D₄	—	4	16	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	4	no	—
673	C₂²×C₄	—	2	4	no	—
674	C₂²×C₄	—	4	2	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	4	no	—
677	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
678	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
679	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
680	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
682	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
686	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
687	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	4	4	no	—
693	C₄⋊C₄	—	4	4	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	4	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	8	no	—
699	C₂²⋊C₄	—	2	4	no	—
700	C₂²⋊C₄	—	2	8	no	—
701	C₂²⋊C₄	—	2	8	no	—
702	C₂²⋊C₄	—	2	4	no	—
703	C₂²⋊C₄	—	2	4	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	4	4	no	—
707	C₂²⋊C₄	—	4	4	no	—
708	C₂²⋊C₄	—	4	4	no	—
709	C₂²⋊C₄	—	4	4	no	—
710	C₂²⋊C₄	—	4	4	no	—
711	C₂²⋊C₄	—	4	4	no	—
712	C₂²⋊C₄	—	4	4	no	—
713	C₂²⋊C₄	—	4	4	no	—
714	C₂²⋊C₄	—	4	4	no	—
715	C₂²⋊C₄	—	4	4	no	—
716	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
717	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
718	C₄²	—	2	4	no	—
719	C₄²	—	4	2	no	—
720	C₄²	—	4	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	8	no	—
724	C₂³	—	2	8	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	4	no	—
728	C₂³	—	2	4	no	—
729	C₂³	—	2	4	no	—
730	C₂³	—	2	4	no	—
731	C₂³	—	2	4	no	—
732	C₂³	—	2	4	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	2	no	—
737	C₂³	—	2	8	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	2	2	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	4	no	—
743	C₂³	—	2	4	no	—
744	C₂³	—	2	4	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	4	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	4	4	no	—
749	C₂³	—	4	4	no	—
750	C₂³	—	4	16	no	—
751	C₂³	—	4	16	no	—
752	C₂³	—	4	16	no	—
753	C₂³	—	4	16	no	—
754	C₂³	—	4	16	no	—
755	C₂³	—	4	4	no	—
756	C₂³	—	4	4	no	—
757	C₂³	—	4	16	no	—
758	C₂³	—	4	16	no	—
759	C₂³	—	4	16	no	—
760	C₂³	—	4	16	no	—
761	C₂³	—	4	4	no	—
762	C₂³	—	4	4	no	—
763	C₂³	—	4	128	no	—
764	C₂³	—	4	16	no	—
765	C₂³	—	4	4	no	—
766	C₂³	—	4	4	no	—
767	C₂³	—	4	4	no	—
768	C₂³	—	8	8	no	—
769	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
770	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
771	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
772	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
773	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
774	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
775	Q₈	—	8	2	no	—
776	D₄	—	4	16	no	—
777	D₄	—	4	8	no	—
778	D₄	—	4	8	no	—
779	D₄	—	4	16	no	—
780	D₄	—	4	8	no	—
781	D₄	—	8	2	no	—
782	D₄	—	8	4	no	—
783	D₄	—	8	4	no	—
784	D₄	—	8	8	no	—
785	D₄	—	8	8	no	—
786	D₄	—	8	8	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	4	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	4	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	2	4	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	4	no	—
805	C₂×C₄	—	4	4	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	8	4	no	—
809	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
810	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
811	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
812	C₂²	—	2	2	no	—
813	C₂²	—	2	2	no	—
814	C₂²	—	2	8	no	—
815	C₂²	—	2	4	no	—
816	C₂²	—	2	4	no	—
817	C₂²	—	2	4	no	—
818	C₂²	—	2	4	no	—
819	C₂²	—	2	4	no	—
820	C₂²	—	2	8	no	—
821	C₂²	—	2	8	no	—
822	C₂²	—	4	16	no	—
823	C₂²	—	4	16	no	—
824	C₂²	—	4	16	no	—
825	C₂²	—	4	64	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	4	no	—
831	C₂²	—	4	4	no	—
832	C₂²	—	4	4	no	—
833	C₂²	—	4	4	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	4	no	—
841	C₂²	—	4	4	no	—
842	C₂²	—	4	4	no	—
843	C₂²	—	4	4	no	—
844	C₂²	—	8	8	no	—
845	C₂²	C₂₃×#535	1	4	yes	—
846	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
847	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
848	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
849	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
850	C₄	—	2	4	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	4	no	—
858	C₄	—	4	4	no	—
859	C₂	—	2	4	no	—
860	C₂	—	4	4	no	—
861	C₂	—	4	4	no	—
862	C₂	—	4	4	no	—
863	C₂	—	8	2	no	—
864	C₂	—	8	2	no	—
865	C₂	C₂×C₂₃×#535	1	1	yes	characteristic
866	C₂	C₂₃×#3484	1	1	yes	characteristic
867	C₂	C₂₃×#3484	1	1	yes	characteristic
868	C₂	C₂₃×#3532	1	4	yes	—

	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. C₂×C₂₃×#538	C₂	semidirect
2. C₂²×C₂₃×#120	C₂	semidirect
3. C₂₃×#2846	C₂	semidirect
4. C₂₃×#2685	C₂	semidirect
5. C₂₃×#2678	C₂	semidirect
6. C₂₃×#2670	C₂	semidirect
7. C₂₃×#2669	C₂	semidirect
8. C₂₃×#2613	C₂	semidirect
9. C₂₃×#2561	C₂	semidirect
10. C₂₃×#2539	C₂	semidirect
11. C₂₃×#2534	C₂	semidirect
12. C₂₃×#2435	C₂	semidirect
13. C₂₃×#2433	C₂	semidirect
14. C₂₃×#2408	C₂	semidirect
15. C₂₃×#2312	C₂	semidirect
21. C₂×C₂₃×#127	C₂²	semidirect
22. C₂×C₂₃×#126	C₂²	semidirect
23. C₂×C₂₃×#124	C₂²	semidirect
24. C₂×C₂₃×#124	C₂²	semidirect
25. C₂×C₂₃×#123	C₂²	semidirect
26. C₂×C₂₃×#123	C₂²	semidirect
27. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
28. C₂×C₂₃×#121	C₂²	semidirect
29. C₂×C₂₃×#121	C₂²	semidirect
30. C₂×C₂₃×#121	C₂²	semidirect
37. C₂×C₂₃×#120	C₂²	semidirect
38. C₂×C₂₃×#120	C₂²	semidirect
39. C₂×C₂₃×#120	C₂²	semidirect
40. C₂×C₄×D₄×C₂₃	C₂²	semidirect
44. C₂₃×#399	C₂²	semidirect
45. C₂₃×#397	C₂²	semidirect
46. C₂₃×#396	C₂²	semidirect
47. C₂₃×#394	C₂²	semidirect
48. C₂₃×#394	C₂²	semidirect
49. C₂₃×#394	C₂²	semidirect
50. C₂₃×#394	C₂²	semidirect
51. C₂₃×#394	C₂²	semidirect
52. C₂₃×#393	C₂²	semidirect
53. C₂₃×#392	C₂²	semidirect
54. C₂₃×#392	C₂²	semidirect
55. C₂₃×#392	C₂²	semidirect
56. C₂₃×#392	C₂²	semidirect
57. C₂₃×#392	C₂²	semidirect
58. C₂₃×#390	C₂²	semidirect
59. C₂₃×#390	C₂²	semidirect
60. C₂₃×#390	C₂²	semidirect
61. C₂₃×#390	C₂²	semidirect
62. C₂₃×#388	C₂²	semidirect
63. C₂₃×#388	C₂²	semidirect
64. C₂₃×#388	C₂²	semidirect
65. C₂₃×#388	C₂²	semidirect
66. C₂₃×#386	C₂²	semidirect
67. C₂₃×#381	C₂²	semidirect
68. C₂₃×#380	C₂²	semidirect
72. C₂₃×#379	C₂²	semidirect
73. C₂₃×#379	C₂²	semidirect
74. C₂₃×#379	C₂²	semidirect
75. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
76. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
86. C₂²×Q₈×C₂₃	C₂³	semidirect
102. C₂²×D₄×C₂₃	C₂³	semidirect
103. C₂²×D₄×C₂₃	C₂³	semidirect
107. C₂³×C₄×C₂₃	C₂³	semidirect
127. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
128. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
129. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
130. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
131. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
132. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
135. C₂×C₂²⋊C₄×C₂₃	D₄	semidirect
154. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
155. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
156. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
157. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
158. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
159. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
160. C₂×C₄²×C₂₃	C₂³	semidirect
161. C₂×C₄²×C₂₃	C₂³	semidirect
162. C₂×C₄²×C₂₃	C₂³	semidirect
163. C₂₃×#95	C₂³	semidirect
164. C₂₃×#95	C₂³	semidirect
165. C₂₃×#95	C₂³	semidirect
166. C₂₃×#95	C₂³	semidirect
167. C₂₃×#95	C₂³	semidirect
286. #36703	C₂₃	direct (N × H)
378. C₂×#538	C₂×C₂₃	semidirect
379. C₂²×#120	C₂×C₂₃	semidirect
380. #2846	C₂×C₂₃	semidirect
381. #2685	C₂×C₂₃	semidirect
382. #2678	C₂×C₂₃	semidirect
383. #2670	C₂×C₂₃	semidirect
384. #2669	C₂×C₂₃	semidirect
385. #2613	C₂×C₂₃	semidirect
386. #2561	C₂×C₂₃	semidirect
387. #2539	C₂×C₂₃	semidirect
388. #2534	C₂×C₂₃	semidirect
389. #2435	C₂×C₂₃	semidirect
390. #2433	C₂×C₂₃	semidirect
391. #2408	C₂×C₂₃	semidirect
392. #2312	C₂×C₂₃	semidirect
445. C₂×#127	C₂²×C₂₃	semidirect
446. C₂×#126	C₂²×C₂₃	semidirect
447. C₂×#124	C₂²×C₂₃	semidirect
448. C₂×#124	C₂²×C₂₃	semidirect
449. C₂×#123	C₂²×C₂₃	semidirect
450. C₂×#123	C₂²×C₂₃	semidirect
451. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
452. C₂×#121	C₂²×C₂₃	semidirect
453. C₂×#121	C₂²×C₂₃	semidirect
454. C₂×#121	C₂²×C₂₃	semidirect
461. C₂×#120	C₂²×C₂₃	semidirect
462. C₂×#120	C₂²×C₂₃	semidirect
463. C₂×#120	C₂²×C₂₃	semidirect
464. C₂×C₄×D₄	C₂²×C₂₃	semidirect
468. #399	C₂²×C₂₃	semidirect
469. #397	C₂²×C₂₃	semidirect
470. #396	C₂²×C₂₃	semidirect
471. #394	C₂²×C₂₃	semidirect
472. #394	C₂²×C₂₃	semidirect
473. #394	C₂²×C₂₃	semidirect
474. #394	C₂²×C₂₃	semidirect
475. #394	C₂²×C₂₃	semidirect
476. #393	C₂²×C₂₃	semidirect
477. #392	C₂²×C₂₃	semidirect
478. #392	C₂²×C₂₃	semidirect
479. #392	C₂²×C₂₃	semidirect
480. #392	C₂²×C₂₃	semidirect
481. #392	C₂²×C₂₃	semidirect
482. #390	C₂²×C₂₃	semidirect
483. #390	C₂²×C₂₃	semidirect
484. #390	C₂²×C₂₃	semidirect
485. #390	C₂²×C₂₃	semidirect
486. #388	C₂²×C₂₃	semidirect
487. #388	C₂²×C₂₃	semidirect
488. #388	C₂²×C₂₃	semidirect
489. #388	C₂²×C₂₃	semidirect
490. #386	C₂²×C₂₃	semidirect
491. #381	C₂²×C₂₃	semidirect
492. #380	C₂²×C₂₃	semidirect
496. #379	C₂²×C₂₃	semidirect
497. #379	C₂²×C₂₃	semidirect
498. #379	C₂²×C₂₃	semidirect
499. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
500. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
520. C₂²×Q₈	C₂³×C₂₃	semidirect
536. C₂²×D₄	C₂³×C₂₃	semidirect
537. C₂²×D₄	C₂³×C₂₃	semidirect
541. C₂³×C₄	C₂³×C₂₃	semidirect
561. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
562. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
563. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
564. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
565. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
566. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
569. C₂×C₂²⋊C₄	D₄×C₂₃	semidirect
588. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
589. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
590. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
591. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
592. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
593. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
594. C₂×C₄²	C₂³×C₂₃	semidirect
595. C₂×C₄²	C₂³×C₂₃	semidirect
596. C₂×C₄²	C₂³×C₂₃	semidirect
597. #95	C₂³×C₂₃	semidirect
598. #95	C₂³×C₂₃	semidirect
599. #95	C₂³×C₂₃	semidirect
600. #95	C₂³×C₂₃	semidirect
601. #95	C₂³×C₂₃	semidirect
602. C₂₃	#36703	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#538	2
C₂²×C₂₃×#120	2
C₂₃×#2846	2
C₂₃×#2685	2
C₂₃×#2678	2
C₂₃×#2670	2
C₂₃×#2669	2
C₂₃×#2613	2
C₂₃×#2561	2
C₂₃×#2539	2
C₂₃×#2534	2
C₂₃×#2435	2
C₂₃×#2433	2
C₂₃×#2408	2
C₂₃×#2312	2
#36703	23

Subgroups — C23×#36703 #19184329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#36703 #19184329