Subgroups — C₂₃×#21855 #19169481

Order 5888.

1128 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#529	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₃×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#1985	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₃×#1955	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂₃×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#1870	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#1869	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#1798	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#1798	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#529	—	2	4	no	—
19	C₂₃×#529	—	2	4	no	—
20	C₂×C₂₃×#126	C₄	1	1	yes	characteristic
21	C₂×C₂₃×#126	C₄	1	1	yes	characteristic
22	C₂×C₂₃×#125	C₄	1	1	yes	characteristic
23	C₂×C₂₃×#124	C₄	1	1	yes	characteristic
24	C₂×C₂₃×#123	C₄	1	1	yes	characteristic
25	C₂×C₂₃×#123	C₄	1	1	yes	characteristic
26	C₂×C₂₃×C₂²⋊Q₈	C₄	1	1	yes	characteristic
27	C₂×C₂₃×#121	C₄	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
32	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
35	C₂₃×#433	—	2	4	no	—
36	C₂₃×#424	—	2	4	no	—
37	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
48	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
49	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
50	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
51	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
52	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
53	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
55	C₂₃×#336	C₂²	1	1	yes	characteristic
56	C₂₃×#336	C₂²	1	1	yes	characteristic
57	C₂₃×#336	C₂²	1	1	yes	characteristic
58	C₂₃×#336	C₂²	1	1	yes	characteristic
59	C₂₃×#336	C₂²	1	1	yes	characteristic
60	C₂₃×#336	C₂²	1	1	yes	characteristic
61	C₂₃×#336	C₂²	1	1	yes	characteristic
62	C₂₃×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₂₃	C₂×C₄	1	1	yes	characteristic
64	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
65	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
66	C₂²×D₄×C₂₃	C₂×C₄	1	1	yes	characteristic
67	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
69	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
72	C₂×M₁₆×C₂₃	—	2	2	no	—
73	C₂×M₁₆×C₂₃	—	4	1	no	—
74	C₂×M₁₆×C₂₃	—	4	1	no	—
75	C₂²×C₈×C₂₃	—	2	2	no	—
76	C₂²×C₈×C₂₃	—	4	1	no	—
77	C₂²×C₈×C₂₃	—	4	1	no	—
78	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
86	C₂₃×#126	—	2	4	no	—
87	C₂₃×#126	—	2	4	no	—
88	C₂₃×#125	—	2	4	no	—
89	C₂₃×#124	—	2	4	no	—
90	C₂₃×#123	—	2	4	no	—
91	C₂₃×#123	—	2	4	no	—
92	C₂₃×C₂²⋊Q₈	—	2	4	no	—
93	C₂₃×#121	—	2	4	no	—
94	C₄×Q₈×C₂₃	—	2	2	no	—
95	C₄×Q₈×C₂₃	—	2	2	no	—
96	C₄×D₄×C₂₃	—	2	2	no	—
97	C₄×D₄×C₂₃	—	2	2	no	—
98	C₄×D₄×C₂₃	—	2	2	no	—
99	C₄×D₄×C₂₃	—	2	2	no	—
100	C₄×D₄×C₂₃	—	2	2	no	—
101	C₄×D₄×C₂₃	—	2	2	no	—
102	C₂₃×#117	—	2	2	no	—
103	C₂₃×#117	—	2	2	no	—
104	C₂₃×#117	D₄	1	4	yes	—
105	C₂₃×#117	D₄	1	4	yes	—
106	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
114	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
124	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
125	C₂×C₂²⋊C₄×C₂₃	C₂×C₄	1	1	yes	characteristic
126	C₂×C₄²×C₂₃	—	2	2	no	—
127	C₂×C₄²×C₂₃	—	2	2	no	—
128	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
129	C₂×C₄²×C₂₃	C₂×C₄	1	1	yes	characteristic
130	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
134	C₂₃×C₄⋊C₈	—	2	2	no	—
135	C₂₃×C₄⋊C₈	—	2	2	no	—
136	C₂₃×C₄⋊C₈	—	2	2	no	—
137	C₂₃×C₄⋊C₈	—	2	2	no	—
138	C₂₃×C₄⋊C₈	—	2	2	no	—
139	C₂₃×C₄⋊C₈	—	2	2	no	—
140	C₂₃×C₂²⋊C₈	—	2	2	no	—
141	C₂₃×C₂²⋊C₈	—	2	2	no	—
142	C₂₃×C₂²⋊C₈	—	4	1	no	—
143	C₂₃×C₂²⋊C₈	—	4	1	no	—
144	C₂₃×C₂²⋊C₈	—	4	1	no	—
145	C₂₃×C₂²⋊C₈	—	4	1	no	—
146	C₂₃×C₂²⋊C₈	—	4	1	no	—
147	C₂₃×C₂²⋊C₈	—	4	1	no	—
148	C₂₃×C₂²⋊C₈	—	4	1	no	—
149	C₂₃×C₂²⋊C₈	—	4	1	no	—
150	C₂₃×#97	—	2	2	no	—
151	C₄×C₈×C₂₃	—	2	2	no	—
152	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
153	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
154	C₂⁴×C₂₃	C₂²×C₄	1	1	yes	characteristic
155	C₂×Q₈×C₂₃	—	2	2	no	—
156	C₂×Q₈×C₂₃	—	2	2	no	—
157	C₂×Q₈×C₂₃	—	4	1	no	—
158	C₂×D₄×C₂₃	—	2	2	no	—
159	C₂×D₄×C₂₃	—	2	2	no	—
160	C₂×D₄×C₂₃	—	2	2	no	—
161	C₂×D₄×C₂₃	—	2	2	no	—
162	C₂×D₄×C₂₃	—	2	2	no	—
163	C₂×D₄×C₂₃	—	2	2	no	—
164	C₂×D₄×C₂₃	—	4	1	no	—
165	C₂×D₄×C₂₃	—	4	1	no	—
166	C₂×D₄×C₂₃	—	4	1	no	—
167	C₂²×C₄×C₂₃	—	2	1	no	—
168	C₂²×C₄×C₂₃	—	2	1	no	—
169	C₂²×C₄×C₂₃	—	2	1	no	—
170	C₂²×C₄×C₂₃	—	2	1	no	—
171	C₂²×C₄×C₂₃	—	2	2	no	—
172	C₂²×C₄×C₂₃	—	2	2	no	—
173	C₂²×C₄×C₂₃	—	2	2	no	—
174	C₂²×C₄×C₂₃	—	2	2	no	—
175	C₂²×C₄×C₂₃	—	2	1	no	—
176	C₂²×C₄×C₂₃	—	2	1	no	—
177	C₂²×C₄×C₂₃	—	2	1	no	—
178	C₂²×C₄×C₂₃	—	2	1	no	—
179	C₂²×C₄×C₂₃	—	2	1	no	—
180	C₂²×C₄×C₂₃	—	2	1	no	—
181	C₂²×C₄×C₂₃	—	2	1	no	—
182	C₂²×C₄×C₂₃	—	2	1	no	—
183	C₂²×C₄×C₂₃	—	2	1	no	—
184	C₂²×C₄×C₂₃	—	2	1	no	—
185	C₂²×C₄×C₂₃	—	2	1	no	—
186	C₂²×C₄×C₂₃	—	2	1	no	—
187	C₂²×C₄×C₂₃	—	4	1	no	—
188	C₂²×C₄×C₂₃	—	4	1	no	—
189	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
195	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
196	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
197	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
198	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
199	C₂²×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
201	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
202	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
203	M₁₆×C₂₃	—	4	4	no	—
204	C₂×C₈×C₂₃	—	2	1	no	—
205	C₂×C₈×C₂₃	—	2	1	no	—
206	C₂×C₈×C₂₃	—	2	1	no	—
207	C₂×C₈×C₂₃	—	2	1	no	—
208	C₂×C₈×C₂₃	—	2	1	no	—
209	C₂×C₈×C₂₃	—	2	1	no	—
210	C₂×C₈×C₂₃	—	2	1	no	—
211	C₂×C₈×C₂₃	—	2	1	no	—
212	C₂×C₈×C₂₃	—	2	1	no	—
213	C₂×C₈×C₂₃	—	2	1	no	—
214	C₂×C₈×C₂₃	—	2	1	no	—
215	C₂×C₈×C₂₃	—	2	1	no	—
216	C₂×C₈×C₂₃	—	2	1	no	—
217	C₂×C₈×C₂₃	—	2	1	no	—
218	C₂×C₈×C₂₃	—	2	1	no	—
219	C₂×C₈×C₂₃	—	2	1	no	—
220	C₂×C₈×C₂₃	—	2	1	no	—
221	C₂×C₈×C₂₃	—	2	1	no	—
222	C₂×C₈×C₂₃	—	2	1	no	—
223	C₂×C₈×C₂₃	—	2	1	no	—
224	C₂×C₈×C₂₃	—	2	1	no	—
225	C₂×C₈×C₂₃	—	2	1	no	—
226	C₂×C₈×C₂₃	—	2	1	no	—
227	C₂×C₈×C₂₃	—	2	1	no	—
228	C₂×C₈×C₂₃	—	4	4	no	—
229	C₄⋊C₄×C₂₃	—	2	2	no	—
230	C₄⋊C₄×C₂₃	—	2	2	no	—
231	C₄⋊C₄×C₂₃	—	2	2	no	—
232	C₄⋊C₄×C₂₃	—	2	2	no	—
233	C₄⋊C₄×C₂₃	—	2	2	no	—
234	C₄⋊C₄×C₂₃	—	2	2	no	—
235	C₄⋊C₄×C₂₃	—	2	2	no	—
236	C₄⋊C₄×C₂₃	—	2	2	no	—
237	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	4	yes	—
238	C₄⋊C₄×C₂₃	C₂²⋊C₄	1	4	yes	—
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	—	2	2	no	—
245	C₂²⋊C₄×C₂₃	—	2	2	no	—
246	C₂²⋊C₄×C₂₃	—	2	2	no	—
247	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	4	yes	—
248	C₂²⋊C₄×C₂₃	C₂²⋊C₄	1	4	yes	—
249	C₄²×C₂₃	—	2	2	no	—
250	C₄²×C₂₃	—	2	2	no	—
251	C₄²×C₂₃	—	2	1	no	—
252	C₄²×C₂₃	—	2	1	no	—
253	C₄²×C₂₃	—	2	1	no	—
254	C₄²×C₂₃	—	2	1	no	—
255	C₄²×C₂₃	C₂×D₄	1	2	yes	—
256	C₄²×C₂₃	C₂×D₄	1	2	yes	—
257	C₄²×C₂₃	C₂×D₄	1	2	yes	—
258	C₄²×C₂₃	C₂×D₄	1	2	yes	—
259	#21855	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
260	C₂³×C₂₃	—	2	1	no	—
261	C₂³×C₂₃	—	2	1	no	—
262	C₂³×C₂₃	—	2	1	no	—
263	C₂³×C₂₃	—	2	1	no	—
264	C₂³×C₂₃	—	2	1	no	—
265	C₂³×C₂₃	—	2	1	no	—
266	C₂³×C₂₃	—	2	1	no	—
267	C₂³×C₂₃	—	2	1	no	—
268	C₂³×C₂₃	—	2	1	no	—
269	C₂³×C₂₃	—	2	1	no	—
270	C₂³×C₂₃	—	2	1	no	—
271	C₂³×C₂₃	—	2	1	no	—
272	C₂³×C₂₃	—	2	1	no	—
273	C₂³×C₂₃	—	2	1	no	—
274	C₂³×C₂₃	—	2	1	no	—
275	C₂³×C₂₃	—	2	1	no	—
276	C₂³×C₂₃	—	2	1	no	—
277	C₂³×C₂₃	—	2	1	no	—
278	C₂³×C₂₃	—	2	1	no	—
279	C₂³×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
280	C₂³×C₂₃	#131	1	2	yes	—
281	C₂³×C₂₃	C₂³×C₄	1	1	yes	characteristic
282	Q₈×C₂₃	—	4	4	no	—
283	D₄×C₂₃	—	4	4	no	—
284	D₄×C₂₃	—	4	4	no	—
285	D₄×C₂₃	—	4	4	no	—
286	C₂×C₄×C₂₃	—	2	1	no	—
287	C₂×C₄×C₂₃	—	2	1	no	—
288	C₂×C₄×C₂₃	—	2	1	no	—
289	C₂×C₄×C₂₃	—	2	1	no	—
290	C₂×C₄×C₂₃	—	2	1	no	—
291	C₂×C₄×C₂₃	—	2	1	no	—
292	C₂×C₄×C₂₃	—	2	1	no	—
293	C₂×C₄×C₂₃	—	2	1	no	—
294	C₂×C₄×C₂₃	—	2	1	no	—
295	C₂×C₄×C₂₃	—	2	1	no	—
296	C₂×C₄×C₂₃	—	2	1	no	—
297	C₂×C₄×C₂₃	—	2	1	no	—
298	C₂×C₄×C₂₃	—	2	2	no	—
299	C₂×C₄×C₂₃	—	2	2	no	—
300	C₂×C₄×C₂₃	—	2	2	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	1	no	—
303	C₂×C₄×C₂₃	—	2	1	no	—
304	C₂×C₄×C₂₃	—	2	1	no	—
305	C₂×C₄×C₂₃	—	2	1	no	—
306	C₂×C₄×C₂₃	—	2	1	no	—
307	C₂×C₄×C₂₃	—	2	1	no	—
308	C₂×C₄×C₂₃	—	2	1	no	—
309	C₂×C₄×C₂₃	—	2	1	no	—
310	C₂×C₄×C₂₃	—	2	1	no	—
311	C₂×C₄×C₂₃	—	2	1	no	—
312	C₂×C₄×C₂₃	—	2	1	no	—
313	C₂×C₄×C₂₃	—	2	1	no	—
314	C₂×C₄×C₂₃	—	2	1	no	—
315	C₂×C₄×C₂₃	—	2	1	no	—
316	C₂×C₄×C₂₃	—	2	1	no	—
317	C₂×C₄×C₂₃	—	4	4	no	—
318	C₂×C₄×C₂₃	—	4	4	no	—
319	C₂×C₄×C₂₃	—	4	1	no	—
320	C₂×C₄×C₂₃	—	4	1	no	—
321	C₂×C₄×C₂₃	—	4	1	no	—
322	C₂×C₄×C₂₃	—	4	1	no	—
323	C₂×C₄×C₂₃	—	4	1	no	—
324	C₂×C₄×C₂₃	—	4	1	no	—
325	C₂×C₄×C₂₃	—	4	1	no	—
326	C₂×C₄×C₂₃	—	4	1	no	—
327	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
328	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
329	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
330	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
331	C₂×C₄×C₂₃	C₂×C₂²⋊C₄	1	2	yes	—
332	C₂×C₄×C₂₃	#131	1	2	yes	—
333	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
336	C₂×C₄×C₂₃	H(5,𝔽₂)	1	1	yes	characteristic
337	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
338	C₂×C₄×C₂₃	2₋¹⁺⁴	1	1	yes	characteristic
339	C₈×C₂₃	—	4	1	no	—
340	C₈×C₂₃	—	4	1	no	—
341	C₈×C₂₃	—	4	1	no	—
342	C₈×C₂₃	—	4	1	no	—
343	C₈×C₂₃	—	4	1	no	—
344	C₈×C₂₃	—	4	1	no	—
345	C₈×C₂₃	—	4	1	no	—
346	C₈×C₂₃	—	4	1	no	—
347	C₂×#529	C₂×C₂₃	1	1	yes	characteristic
348	C₂×#433	C₂×C₂₃	1	1	yes	characteristic, complemented
349	C₂×#424	C₂×C₂₃	1	1	yes	characteristic, complemented
350	#1985	C₂×C₂₃	1	1	yes	characteristic, complemented
351	#1984	C₂×C₂₃	1	1	yes	characteristic, complemented
352	#1955	C₂×C₂₃	1	1	yes	characteristic, complemented
353	#1954	C₂×C₂₃	1	1	yes	characteristic, complemented
354	#1870	C₂×C₂₃	1	1	yes	characteristic, complemented
355	#1870	C₂×C₂₃	1	1	yes	characteristic, complemented
356	#1869	C₂×C₂₃	1	1	yes	characteristic, complemented
357	#1869	C₂×C₂₃	1	1	yes	characteristic, complemented
358	#1798	C₂×C₂₃	1	1	yes	characteristic, complemented
359	#1798	C₂×C₂₃	1	1	yes	characteristic, complemented
360	#1797	C₂×C₂₃	1	1	yes	characteristic, complemented
361	#1797	C₂×C₂₃	1	1	yes	characteristic, complemented
362	C₂²×C₂₃	—	2	2	no	—
363	C₂²×C₂₃	—	2	2	no	—
364	C₂²×C₂₃	—	2	2	no	—
365	C₂²×C₂₃	—	2	2	no	—
366	C₂²×C₂₃	—	2	2	no	—
367	C₂²×C₂₃	—	2	2	no	—
368	C₂²×C₂₃	—	4	1	no	—
369	C₂²×C₂₃	—	4	1	no	—
370	C₂²×C₂₃	—	4	1	no	—
371	C₂²×C₂₃	—	4	1	no	—
372	C₂²×C₂₃	—	4	1	no	—
373	C₂²×C₂₃	—	4	1	no	—
374	C₂²×C₂₃	—	4	1	no	—
375	C₂²×C₂₃	—	4	1	no	—
376	C₂²×C₂₃	—	4	1	no	—
377	C₂²×C₂₃	—	4	1	no	—
378	C₂²×C₂₃	—	4	1	no	—
379	C₂²×C₂₃	—	4	1	no	—
380	C₂²×C₂₃	—	4	1	no	—
381	C₂²×C₂₃	—	4	1	no	—
382	C₂²×C₂₃	—	4	1	no	—
383	C₂²×C₂₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
384	C₂²×C₂₃	#520	1	1	yes	characteristic
385	C₂²×C₂₃	#520	1	1	yes	characteristic
386	C₂²×C₂₃	C₂×#131	1	1	yes	characteristic
387	C₂²×C₂₃	C₂×#131	1	1	yes	characteristic
388	C₂²×C₂₃	#568	1	1	yes	characteristic
389	C₂²×C₂₃	#568	1	1	yes	characteristic
390	C₄×C₂₃	—	2	2	no	—
391	C₄×C₂₃	—	2	2	no	—
392	C₄×C₂₃	—	2	2	no	—
393	C₄×C₂₃	—	2	2	no	—
394	C₄×C₂₃	—	2	2	no	—
395	C₄×C₂₃	—	2	2	no	—
396	C₄×C₂₃	—	4	1	no	—
397	C₄×C₂₃	—	4	1	no	—
398	C₄×C₂₃	—	4	1	no	—
399	C₄×C₂₃	—	4	1	no	—
400	C₄×C₂₃	—	4	1	no	—
401	C₄×C₂₃	#535	1	1	yes	characteristic
402	C₄×C₂₃	#536	1	1	yes	characteristic
403	C₄×C₂₃	#537	1	1	yes	characteristic
404	C₄×C₂₃	#537	1	1	yes	characteristic
405	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
406	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
407	#529	—	2	4	no	—
408	#529	—	2	4	no	—
409	C₂×#126	C₄×C₂₃	1	1	yes	characteristic
410	C₂×#126	C₄×C₂₃	1	1	yes	characteristic
411	C₂×#125	C₄×C₂₃	1	1	yes	characteristic
412	C₂×#124	C₄×C₂₃	1	1	yes	characteristic
413	C₂×#123	C₄×C₂₃	1	1	yes	characteristic
414	C₂×#123	C₄×C₂₃	1	1	yes	characteristic
415	C₂×C₂²⋊Q₈	C₄×C₂₃	1	1	yes	characteristic
416	C₂×#121	C₄×C₂₃	1	1	yes	characteristic
417	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
418	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
419	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
420	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
421	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
422	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
423	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
424	#433	—	2	4	no	—
425	#424	—	2	4	no	—
426	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
428	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
429	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
430	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
432	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
433	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
434	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
435	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
436	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
437	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
438	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
439	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
440	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
441	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
442	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
443	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
444	#336	C₂²×C₂₃	1	1	yes	characteristic
445	#336	C₂²×C₂₃	1	1	yes	characteristic
446	#336	C₂²×C₂₃	1	1	yes	characteristic
447	#336	C₂²×C₂₃	1	1	yes	characteristic
448	#336	C₂²×C₂₃	1	1	yes	characteristic
449	#336	C₂²×C₂₃	1	1	yes	characteristic
450	#336	C₂²×C₂₃	1	1	yes	characteristic
451	#336	C₂²×C₂₃	1	1	yes	characteristic
452	C₂×C₂₃	—	4	2	no	—
453	C₂×C₂₃	—	4	2	no	—
454	C₂×C₂₃	—	8	1	no	—
455	C₂×C₂₃	#2311	1	1	yes	characteristic
456	C₂×C₂₃	#2880	1	1	yes	characteristic
457	C₂×C₂₃	#2880	1	1	yes	characteristic
458	C₂×C₂₃	#2992	1	1	yes	characteristic
459	C₂×C₂₃	#2993	1	1	yes	characteristic
460	C₂×C₂₃	#2994	1	1	yes	characteristic
461	C₂×C₂₃	#2995	1	1	yes	characteristic
462	C₂²×Q₈	C₂×C₄×C₂₃	1	1	yes	characteristic
463	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
464	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
465	C₂²×D₄	C₂×C₄×C₂₃	1	1	yes	characteristic
466	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
467	C₂³×C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
468	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
469	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
471	C₂×M₁₆	—	2	2	no	—
472	C₂×M₁₆	—	4	1	no	—
473	C₂×M₁₆	—	4	1	no	—
474	C₂²×C₈	—	2	2	no	—
475	C₂²×C₈	—	4	1	no	—
476	C₂²×C₈	—	4	1	no	—
477	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
479	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
480	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
481	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
482	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
483	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
484	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
485	#126	—	2	4	no	—
486	#126	—	2	4	no	—
487	#125	—	2	4	no	—
488	#124	—	2	4	no	—
489	#123	—	2	4	no	—
490	#123	—	2	4	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	#121	—	2	4	no	—
493	C₄×Q₈	—	2	2	no	—
494	C₄×Q₈	—	2	2	no	—
495	C₄×D₄	—	2	2	no	—
496	C₄×D₄	—	2	2	no	—
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	—	2	2	no	—
501	#117	—	2	2	no	—
502	#117	—	2	2	no	—
503	#117	D₄×C₂₃	1	4	yes	—
504	#117	D₄×C₂₃	1	4	yes	—
505	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
510	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
511	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
513	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
515	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
516	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
517	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
518	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
519	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
520	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
521	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
522	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
523	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
524	C₂×C₂²⋊C₄	C₂×C₄×C₂₃	1	1	yes	characteristic
525	C₂×C₄²	—	2	2	no	—
526	C₂×C₄²	—	2	2	no	—
527	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
528	C₂×C₄²	C₂×C₄×C₂₃	1	1	yes	characteristic
529	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
530	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
532	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
533	C₄⋊C₈	—	2	2	no	—
534	C₄⋊C₈	—	2	2	no	—
535	C₄⋊C₈	—	2	2	no	—
536	C₄⋊C₈	—	2	2	no	—
537	C₄⋊C₈	—	2	2	no	—
538	C₄⋊C₈	—	2	2	no	—
539	C₂²⋊C₈	—	2	2	no	—
540	C₂²⋊C₈	—	2	2	no	—
541	C₂²⋊C₈	—	4	1	no	—
542	C₂²⋊C₈	—	4	1	no	—
543	C₂²⋊C₈	—	4	1	no	—
544	C₂²⋊C₈	—	4	1	no	—
545	C₂²⋊C₈	—	4	1	no	—
546	C₂²⋊C₈	—	4	1	no	—
547	C₂²⋊C₈	—	4	1	no	—
548	C₂²⋊C₈	—	4	1	no	—
549	#97	—	2	2	no	—
550	C₄×C₈	—	2	2	no	—
551	C₂₃	#21855	1	1	yes	characteristic, direct product factor, Sylow
552	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
553	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
554	C₂⁴	C₂²×C₄×C₂₃	1	1	yes	characteristic
555	C₂×Q₈	—	2	2	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	4	1	no	—
558	C₂×D₄	—	2	2	no	—
559	C₂×D₄	—	2	2	no	—
560	C₂×D₄	—	2	2	no	—
561	C₂×D₄	—	2	2	no	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	4	1	no	—
565	C₂×D₄	—	4	1	no	—
566	C₂×D₄	—	4	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	1	no	—
581	C₂²×C₄	—	2	1	no	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	4	1	no	—
588	C₂²×C₄	—	4	1	no	—
589	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
590	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
591	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
592	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
593	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
594	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
595	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
596	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
597	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
598	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
599	C₂²×C₄	C₂²×C₄×C₂₃	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
601	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
603	M₁₆	—	4	4	no	—
604	C₂×C₈	—	2	1	no	—
605	C₂×C₈	—	2	1	no	—
606	C₂×C₈	—	2	1	no	—
607	C₂×C₈	—	2	1	no	—
608	C₂×C₈	—	2	1	no	—
609	C₂×C₈	—	2	1	no	—
610	C₂×C₈	—	2	1	no	—
611	C₂×C₈	—	2	1	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	2	1	no	—
628	C₂×C₈	—	4	4	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	—	2	2	no	—
632	C₄⋊C₄	—	2	2	no	—
633	C₄⋊C₄	—	2	2	no	—
634	C₄⋊C₄	—	2	2	no	—
635	C₄⋊C₄	—	2	2	no	—
636	C₄⋊C₄	—	2	2	no	—
637	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	4	yes	—
638	C₄⋊C₄	C₂²⋊C₄×C₂₃	1	4	yes	—
639	C₂²⋊C₄	—	2	2	no	—
640	C₂²⋊C₄	—	2	2	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	2	no	—
643	C₂²⋊C₄	—	2	2	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	4	yes	—
648	C₂²⋊C₄	C₂²⋊C₄×C₂₃	1	4	yes	—
649	C₄²	—	2	2	no	—
650	C₄²	—	2	2	no	—
651	C₄²	—	2	1	no	—
652	C₄²	—	2	1	no	—
653	C₄²	—	2	1	no	—
654	C₄²	—	2	1	no	—
655	C₄²	C₂×D₄×C₂₃	1	2	yes	—
656	C₄²	C₂×D₄×C₂₃	1	2	yes	—
657	C₄²	C₂×D₄×C₂₃	1	2	yes	—
658	C₄²	C₂×D₄×C₂₃	1	2	yes	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	1	no	—
663	C₂³	—	2	1	no	—
664	C₂³	—	2	1	no	—
665	C₂³	—	2	1	no	—
666	C₂³	—	2	1	no	—
667	C₂³	—	2	1	no	—
668	C₂³	—	2	1	no	—
669	C₂³	—	2	1	no	—
670	C₂³	—	2	1	no	—
671	C₂³	—	2	1	no	—
672	C₂³	—	2	1	no	—
673	C₂³	—	2	1	no	—
674	C₂³	—	2	1	no	—
675	C₂³	—	2	1	no	—
676	C₂³	—	2	1	no	—
677	C₂³	—	2	1	no	—
678	C₂³	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
679	C₂³	C₂₃×#131	1	2	yes	—
680	C₂³	C₂³×C₄×C₂₃	1	1	yes	characteristic
681	Q₈	—	4	4	no	—
682	D₄	—	4	4	no	—
683	D₄	—	4	4	no	—
684	D₄	—	4	4	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	2	2	no	—
700	C₂×C₄	—	2	2	no	—
701	C₂×C₄	—	2	1	no	—
702	C₂×C₄	—	2	1	no	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
727	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
728	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
729	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
730	C₂×C₄	C₂×C₂²⋊C₄×C₂₃	1	2	yes	—
731	C₂×C₄	C₂₃×#131	1	2	yes	—
732	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
733	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
734	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
735	C₂×C₄	C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
736	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
737	C₂×C₄	C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
738	C₈	—	4	1	no	—
739	C₈	—	4	1	no	—
740	C₈	—	4	1	no	—
741	C₈	—	4	1	no	—
742	C₈	—	4	1	no	—
743	C₈	—	4	1	no	—
744	C₈	—	4	1	no	—
745	C₈	—	4	1	no	—
746	C₂²	—	2	2	no	—
747	C₂²	—	2	2	no	—
748	C₂²	—	2	2	no	—
749	C₂²	—	2	2	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	4	1	no	—
753	C₂²	—	4	1	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	4	1	no	—
766	C₂²	—	4	1	no	—
767	C₂²	C₂²×C₂²⋊C₄×C₂₃	1	1	yes	characteristic
768	C₂²	C₂₃×#520	1	1	yes	characteristic
769	C₂²	C₂₃×#520	1	1	yes	characteristic
770	C₂²	C₂×C₂₃×#131	1	1	yes	characteristic
771	C₂²	C₂×C₂₃×#131	1	1	yes	characteristic
772	C₂²	C₂₃×#568	1	1	yes	characteristic
773	C₂²	C₂₃×#568	1	1	yes	characteristic
774	C₄	—	2	2	no	—
775	C₄	—	2	2	no	—
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	2	2	no	—
779	C₄	—	2	2	no	—
780	C₄	—	4	1	no	—
781	C₄	—	4	1	no	—
782	C₄	—	4	1	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	1	no	—
785	C₄	C₂₃×#535	1	1	yes	characteristic
786	C₄	C₂₃×#536	1	1	yes	characteristic
787	C₄	C₂₃×#537	1	1	yes	characteristic
788	C₄	C₂₃×#537	1	1	yes	characteristic
789	C₂	—	4	2	no	—
790	C₂	—	4	2	no	—
791	C₂	—	8	1	no	—
792	C₂	C₂₃×#2311	1	1	yes	characteristic
793	C₂	C₂₃×#2880	1	1	yes	characteristic
794	C₂	C₂₃×#2880	1	1	yes	characteristic
795	C₂	C₂₃×#2992	1	1	yes	characteristic
796	C₂	C₂₃×#2993	1	1	yes	characteristic
797	C₂	C₂₃×#2994	1	1	yes	characteristic
798	C₂	C₂₃×#2995	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₂₃
socle	C₂³×C₂₃	C₂³×C₄
prime radical	C₂×C₂₃×#121	C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₂₃×#433	C₂	semidirect
3. C₂×C₂₃×#424	C₂	semidirect
4. C₂₃×#1985	C₂	semidirect
5. C₂₃×#1984	C₂	semidirect
6. C₂₃×#1955	C₂	semidirect
7. C₂₃×#1954	C₂	semidirect
8. C₂₃×#1870	C₂	semidirect
9. C₂₃×#1870	C₂	semidirect
10. C₂₃×#1869	C₂	semidirect
11. C₂₃×#1869	C₂	semidirect
12. C₂₃×#1798	C₂	semidirect
13. C₂₃×#1798	C₂	semidirect
14. C₂₃×#1797	C₂	semidirect
15. C₂₃×#1797	C₂	semidirect
259. #21855	C₂₃	direct (N × H)
348. C₂×#433	C₂×C₂₃	semidirect
349. C₂×#424	C₂×C₂₃	semidirect
350. #1985	C₂×C₂₃	semidirect
351. #1984	C₂×C₂₃	semidirect
352. #1955	C₂×C₂₃	semidirect
353. #1954	C₂×C₂₃	semidirect
354. #1870	C₂×C₂₃	semidirect
355. #1870	C₂×C₂₃	semidirect
356. #1869	C₂×C₂₃	semidirect
357. #1869	C₂×C₂₃	semidirect
358. #1798	C₂×C₂₃	semidirect
359. #1798	C₂×C₂₃	semidirect
360. #1797	C₂×C₂₃	semidirect
361. #1797	C₂×C₂₃	semidirect
551. C₂₃	#21855	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×#529	2
C₂×C₂₃×#433	2
C₂×C₂₃×#424	2
C₂₃×#1985	2
C₂₃×#1984	2
C₂₃×#1955	2
C₂₃×#1954	2
C₂₃×#1870	2
C₂₃×#1869	2
C₂₃×#1798	2
C₂₃×#1797	2
#21855	23

Subgroups — C23×#21855 #19169481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#21855 #19169481