Subgroups — C₂×C₂₃×#2653 #19182194

Order 5888.

2394 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2653	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₂₃×#401	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#394	C₂	1	1	yes	maximal, characteristic
7	C₂×C₂₃×#394	C₂	1	1	yes	maximal, characteristic
8	C₂×C₂₃×#393	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#393	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#391	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#386	C₂	1	1	yes	maximal, characteristic
15	C₂×C₂₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊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	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
38	C₂₃×#401	C₂²	1	8	yes	complemented
39	C₂₃×#398	C₂²	1	8	yes	complemented
40	C₂₃×#397	C₂²	1	8	yes	complemented
41	C₂₃×#397	C₂²	1	8	yes	complemented
42	C₂₃×#394	C₂²	1	8	yes	—
43	C₂₃×#394	C₂²	1	8	yes	—
44	C₂₃×#393	C₂²	1	8	yes	complemented
45	C₂₃×#393	C₂²	1	8	yes	complemented
46	C₂₃×#391	C₂²	1	8	yes	complemented
47	C₂₃×#388	C₂²	1	8	yes	complemented
48	C₂₃×#388	C₂²	1	8	yes	complemented
49	C₂₃×#387	C₂²	1	8	yes	complemented
50	C₂₃×#386	C₂²	1	8	yes	—
51	C₂₃×#385	C₂²	1	8	yes	complemented
52	C₄×C₂²⋊C₄×C₂₃	C₂²	1	8	yes	complemented
53	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
54	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
55	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
56	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
57	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
58	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
59	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
60	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
61	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
62	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
63	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
64	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
65	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
66	C₂×C₂₃×#95	C₂²	1	1	yes	characteristic
67	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
68	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
69	C₂²×Q₈×C₂₃	—	2	4	no	—
70	C₂²×Q₈×C₂₃	—	4	2	no	—
71	C₂²×Q₈×C₂₃	—	4	2	no	—
72	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
73	C₂²×D₄×C₂₃	—	2	4	no	—
74	C₂²×D₄×C₂₃	—	4	2	no	—
75	C₂²×D₄×C₂₃	—	4	2	no	—
76	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
77	C₂³×C₄×C₂₃	—	2	4	no	—
78	C₂³×C₄×C₂₃	—	4	2	no	—
79	C₂³×C₄×C₂₃	—	4	2	no	—
80	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
95	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
96	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
97	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
98	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
99	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
105	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
106	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
107	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
108	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
109	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
110	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
111	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
112	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
113	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
114	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
115	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
116	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
123	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
124	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
126	C₂×C₄²×C₂₃	—	4	2	no	—
127	C₂×C₄²×C₂₃	—	4	2	no	—
128	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
129	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
130	C₂₃×#95	C₂³	1	4	yes	—
131	C₂₃×#95	C₂³	1	4	yes	—
132	C₂₃×#95	C₂³	1	4	yes	—
133	C₂₃×#95	C₂³	1	4	yes	—
134	C₂₃×#95	C₂³	1	4	yes	—
135	C₂₃×#95	C₂³	1	4	yes	—
136	C₂₃×#95	C₂³	1	4	yes	—
137	C₂₃×#95	C₂³	1	4	yes	—
138	C₂₃×#95	C₂³	1	4	yes	—
139	C₂₃×#95	C₂³	1	4	yes	—
140	C₂₃×#95	C₂³	1	4	yes	—
141	C₂₃×#95	C₂³	1	4	yes	—
142	C₂₃×#95	C₂³	1	4	yes	—
143	C₂₃×#95	C₂³	1	4	yes	—
144	C₂⁴×C₂₃	—	2	2	no	—
145	C₂⁴×C₂₃	—	2	2	no	—
146	C₂⁴×C₂₃	—	2	2	no	—
147	C₂⁴×C₂₃	—	2	2	no	—
148	C₂⁴×C₂₃	—	2	2	no	—
149	C₂⁴×C₂₃	—	2	2	no	—
150	C₂⁴×C₂₃	—	2	2	no	—
151	C₂⁴×C₂₃	—	2	2	no	—
152	C₂⁴×C₂₃	—	2	2	no	—
153	C₂⁴×C₂₃	—	2	2	no	—
154	C₂⁴×C₂₃	—	2	2	no	—
155	C₂⁴×C₂₃	—	2	2	no	—
156	C₂⁴×C₂₃	—	2	2	no	—
157	C₂⁴×C₂₃	#41	1	4	yes	—
158	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
159	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
160	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
161	C₂×Q₈×C₂₃	—	2	8	no	—
162	C₂×Q₈×C₂₃	—	4	4	no	—
163	C₂×Q₈×C₂₃	—	4	4	no	—
164	C₂×Q₈×C₂₃	—	4	16	no	—
165	C₂×D₄×C₂₃	—	2	8	no	—
166	C₂×D₄×C₂₃	—	4	4	no	—
167	C₂×D₄×C₂₃	—	4	4	no	—
168	C₂×D₄×C₂₃	—	4	16	no	—
169	C₂²×C₄×C₂₃	—	2	2	no	—
170	C₂²×C₄×C₂₃	—	2	2	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	2	no	—
176	C₂²×C₄×C₂₃	—	2	2	no	—
177	C₂²×C₄×C₂₃	—	2	2	no	—
178	C₂²×C₄×C₂₃	—	2	2	no	—
179	C₂²×C₄×C₂₃	—	2	2	no	—
180	C₂²×C₄×C₂₃	—	2	2	no	—
181	C₂²×C₄×C₂₃	—	2	2	no	—
182	C₂²×C₄×C₂₃	—	2	2	no	—
183	C₂²×C₄×C₂₃	—	2	2	no	—
184	C₂²×C₄×C₂₃	—	2	2	no	—
185	C₂²×C₄×C₂₃	—	2	2	no	—
186	C₂²×C₄×C₂₃	—	2	2	no	—
187	C₂²×C₄×C₂₃	—	2	2	no	—
188	C₂²×C₄×C₂₃	—	2	2	no	—
189	C₂²×C₄×C₂₃	—	2	2	no	—
190	C₂²×C₄×C₂₃	—	2	2	no	—
191	C₂²×C₄×C₂₃	—	2	2	no	—
192	C₂²×C₄×C₂₃	—	2	2	no	—
193	C₂²×C₄×C₂₃	—	2	2	no	—
194	C₂²×C₄×C₂₃	—	2	2	no	—
195	C₂²×C₄×C₂₃	—	2	2	no	—
196	C₂²×C₄×C₂₃	—	2	2	no	—
197	C₂²×C₄×C₂₃	—	2	2	no	—
198	C₂²×C₄×C₂₃	—	2	2	no	—
199	C₂²×C₄×C₂₃	—	2	2	no	—
200	C₂²×C₄×C₂₃	—	2	2	no	—
201	C₂²×C₄×C₂₃	—	2	2	no	—
202	C₂²×C₄×C₂₃	—	2	2	no	—
203	C₂²×C₄×C₂₃	—	2	2	no	—
204	C₂²×C₄×C₂₃	—	2	2	no	—
205	C₂²×C₄×C₂₃	—	2	2	no	—
206	C₂²×C₄×C₂₃	—	2	8	no	—
207	C₂²×C₄×C₂₃	—	4	4	no	—
208	C₂²×C₄×C₂₃	—	4	4	no	—
209	C₂²×C₄×C₂₃	—	4	16	no	—
210	C₂²×C₄×C₂₃	#41	1	4	yes	—
211	C₂²×C₄×C₂₃	#41	1	4	yes	—
212	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
213	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
216	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
219	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
220	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
221	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
223	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
225	C₄⋊C₄×C₂₃	—	2	8	no	—
226	C₄⋊C₄×C₂₃	—	4	4	no	—
227	C₄⋊C₄×C₂₃	—	4	4	no	—
228	C₄⋊C₄×C₂₃	—	4	4	no	—
229	C₄⋊C₄×C₂₃	—	4	4	no	—
230	C₂²⋊C₄×C₂₃	—	2	8	no	—
231	C₂²⋊C₄×C₂₃	—	2	8	no	—
232	C₂²⋊C₄×C₂₃	—	2	8	no	—
233	C₂²⋊C₄×C₂₃	—	2	8	no	—
234	C₂²⋊C₄×C₂₃	—	2	8	no	—
235	C₂²⋊C₄×C₂₃	—	4	4	no	—
236	C₂²⋊C₄×C₂₃	—	4	4	no	—
237	C₂²⋊C₄×C₂₃	—	4	4	no	—
238	C₂²⋊C₄×C₂₃	—	4	4	no	—
239	C₂²⋊C₄×C₂₃	—	4	4	no	—
240	C₂²⋊C₄×C₂₃	—	4	4	no	—
241	C₄²×C₂₃	—	4	4	no	—
242	C₄²×C₂₃	—	4	4	no	—
243	C₂×#2653	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
244	C₂³×C₂₃	—	2	8	no	—
245	C₂³×C₂₃	—	2	8	no	—
246	C₂³×C₂₃	—	2	8	no	—
247	C₂³×C₂₃	—	2	2	no	—
248	C₂³×C₂₃	—	2	2	no	—
249	C₂³×C₂₃	—	2	2	no	—
250	C₂³×C₂₃	—	2	2	no	—
251	C₂³×C₂₃	—	2	2	no	—
252	C₂³×C₂₃	—	2	2	no	—
253	C₂³×C₂₃	—	2	2	no	—
254	C₂³×C₂₃	—	2	2	no	—
255	C₂³×C₂₃	—	2	2	no	—
256	C₂³×C₂₃	—	2	2	no	—
257	C₂³×C₂₃	—	2	2	no	—
258	C₂³×C₂₃	—	2	2	no	—
259	C₂³×C₂₃	—	2	2	no	—
260	C₂³×C₂₃	—	4	4	no	—
261	C₂³×C₂₃	—	4	4	no	—
262	C₂³×C₂₃	—	4	4	no	—
263	C₂³×C₂₃	—	4	4	no	—
264	C₂³×C₂₃	—	4	4	no	—
265	C₂³×C₂₃	—	4	4	no	—
266	C₂³×C₂₃	—	4	4	no	—
267	C₂³×C₂₃	—	4	4	no	—
268	C₂³×C₂₃	—	4	4	no	—
269	C₂³×C₂₃	—	4	4	no	—
270	C₂³×C₂₃	—	4	4	no	—
271	C₂³×C₂₃	C₂×#41	1	4	yes	—
272	C₂³×C₂₃	C₂×#41	1	2	yes	—
273	C₂³×C₂₃	C₂×#41	1	2	yes	—
274	C₂³×C₂₃	C₂×#41	1	2	yes	—
275	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
276	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
277	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
278	C₂³×C₂₃	2₋¹⁺⁴	1	2	yes	—
279	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
280	Q₈×C₂₃	—	4	16	no	—
281	D₄×C₂₃	—	4	16	no	—
282	C₂×C₄×C₂₃	—	2	8	no	—
283	C₂×C₄×C₂₃	—	2	8	no	—
284	C₂×C₄×C₂₃	—	2	2	no	—
285	C₂×C₄×C₂₃	—	2	2	no	—
286	C₂×C₄×C₂₃	—	2	2	no	—
287	C₂×C₄×C₂₃	—	2	2	no	—
288	C₂×C₄×C₂₃	—	2	2	no	—
289	C₂×C₄×C₂₃	—	2	2	no	—
290	C₂×C₄×C₂₃	—	2	2	no	—
291	C₂×C₄×C₂₃	—	2	2	no	—
292	C₂×C₄×C₂₃	—	2	2	no	—
293	C₂×C₄×C₂₃	—	2	2	no	—
294	C₂×C₄×C₂₃	—	2	2	no	—
295	C₂×C₄×C₂₃	—	2	2	no	—
296	C₂×C₄×C₂₃	—	2	2	no	—
297	C₂×C₄×C₂₃	—	2	2	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	2	no	—
303	C₂×C₄×C₂₃	—	2	2	no	—
304	C₂×C₄×C₂₃	—	2	2	no	—
305	C₂×C₄×C₂₃	—	2	2	no	—
306	C₂×C₄×C₂₃	—	2	2	no	—
307	C₂×C₄×C₂₃	—	2	2	no	—
308	C₂×C₄×C₂₃	—	2	2	no	—
309	C₂×C₄×C₂₃	—	2	2	no	—
310	C₂×C₄×C₂₃	—	2	2	no	—
311	C₂×C₄×C₂₃	—	2	2	no	—
312	C₂×C₄×C₂₃	—	2	2	no	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	2	no	—
315	C₂×C₄×C₂₃	—	2	2	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	2	no	—
318	C₂×C₄×C₂₃	—	2	2	no	—
319	C₂×C₄×C₂₃	—	2	2	no	—
320	C₂×C₄×C₂₃	—	2	2	no	—
321	C₂×C₄×C₂₃	—	4	16	no	—
322	C₂×C₄×C₂₃	—	4	4	no	—
323	C₂×C₄×C₂₃	—	4	4	no	—
324	C₂×C₄×C₂₃	—	4	4	no	—
325	C₂×C₄×C₂₃	—	4	4	no	—
326	C₂×C₄×C₂₃	—	4	4	no	—
327	C₂×C₄×C₂₃	—	4	4	no	—
328	C₂×C₄×C₂₃	—	4	4	no	—
329	C₂×C₄×C₂₃	—	4	4	no	—
330	C₂×C₄×C₂₃	—	4	4	no	—
331	C₂×C₄×C₂₃	—	4	4	no	—
332	C₂×C₄×C₂₃	—	4	4	no	—
333	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
334	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
335	#2653	C₂×C₂₃	1	16	yes	direct product factor
336	C₂×#401	C₂×C₂₃	1	1	yes	characteristic, complemented
337	C₂×#398	C₂×C₂₃	1	1	yes	characteristic, complemented
338	C₂×#397	C₂×C₂₃	1	1	yes	characteristic, complemented
339	C₂×#397	C₂×C₂₃	1	1	yes	characteristic, complemented
340	C₂×#394	C₂×C₂₃	1	1	yes	characteristic
341	C₂×#394	C₂×C₂₃	1	1	yes	characteristic
342	C₂×#393	C₂×C₂₃	1	1	yes	characteristic, complemented
343	C₂×#393	C₂×C₂₃	1	1	yes	characteristic, complemented
344	C₂×#391	C₂×C₂₃	1	1	yes	characteristic, complemented
345	C₂×#388	C₂×C₂₃	1	1	yes	characteristic, complemented
346	C₂×#388	C₂×C₂₃	1	1	yes	characteristic, complemented
347	C₂×#387	C₂×C₂₃	1	1	yes	characteristic, complemented
348	C₂×#386	C₂×C₂₃	1	1	yes	characteristic
349	C₂×#385	C₂×C₂₃	1	1	yes	characteristic, complemented
350	C₂×C₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
351	C₂²×C₂₃	—	2	4	no	—
352	C₂²×C₂₃	—	2	4	no	—
353	C₂²×C₂₃	—	2	4	no	—
354	C₂²×C₂₃	—	4	16	no	—
355	C₂²×C₂₃	—	4	2	no	—
356	C₂²×C₂₃	—	4	2	no	—
357	C₂²×C₂₃	—	4	2	no	—
358	C₂²×C₂₃	—	4	2	no	—
359	C₂²×C₂₃	—	4	2	no	—
360	C₂²×C₂₃	—	4	2	no	—
361	C₂²×C₂₃	—	4	2	no	—
362	C₂²×C₂₃	—	4	2	no	—
363	C₂²×C₂₃	—	4	2	no	—
364	C₂²×C₂₃	—	4	2	no	—
365	C₂²×C₂₃	—	4	2	no	—
366	C₂²×C₂₃	—	8	8	no	—
367	C₂²×C₂₃	#529	1	4	yes	—
368	C₂²×C₂₃	#538	1	4	yes	—
369	C₂²×C₂₃	#538	1	4	yes	—
370	C₂²×C₂₃	#538	1	4	yes	—
371	C₂²×C₂₃	#539	1	4	yes	—
372	C₂²×C₂₃	#542	1	4	yes	—
373	C₂²×C₂₃	#542	1	4	yes	—
374	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
375	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
376	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
377	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
379	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
380	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
381	C₄×C₂₃	—	2	4	no	—
382	C₄×C₂₃	—	2	4	no	—
383	C₄×C₂₃	—	4	2	no	—
384	C₄×C₂₃	—	4	2	no	—
385	C₄×C₂₃	—	4	2	no	—
386	C₄×C₂₃	—	4	2	no	—
387	C₄×C₂₃	—	4	2	no	—
388	C₄×C₂₃	—	4	2	no	—
389	C₄×C₂₃	—	4	2	no	—
390	C₄×C₂₃	—	4	2	no	—
391	C₄×C₂₃	—	4	2	no	—
392	C₄×C₂₃	—	4	2	no	—
393	C₄×C₂₃	—	4	2	no	—
394	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
395	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
396	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
397	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
398	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
399	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
400	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
401	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
402	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
403	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
404	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
405	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
406	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
407	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
408	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
409	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
410	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
411	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
412	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
413	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
414	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
415	#401	C₂²×C₂₃	1	8	yes	complemented
416	#398	C₂²×C₂₃	1	8	yes	complemented
417	#397	C₂²×C₂₃	1	8	yes	complemented
418	#397	C₂²×C₂₃	1	8	yes	complemented
419	#394	C₂²×C₂₃	1	8	yes	—
420	#394	C₂²×C₂₃	1	8	yes	—
421	#393	C₂²×C₂₃	1	8	yes	complemented
422	#393	C₂²×C₂₃	1	8	yes	complemented
423	#391	C₂²×C₂₃	1	8	yes	complemented
424	#388	C₂²×C₂₃	1	8	yes	complemented
425	#388	C₂²×C₂₃	1	8	yes	complemented
426	#387	C₂²×C₂₃	1	8	yes	complemented
427	#386	C₂²×C₂₃	1	8	yes	—
428	#385	C₂²×C₂₃	1	8	yes	complemented
429	C₄×C₂²⋊C₄	C₂²×C₂₃	1	8	yes	complemented
430	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
432	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
433	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
434	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
435	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
436	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
437	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
438	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
439	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
440	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
441	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
442	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
443	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
444	C₂×C₂₃	—	4	4	no	—
445	C₂×C₂₃	—	8	2	no	—
446	C₂×C₂₃	#2653	1	8	yes	direct product factor
447	C₂×C₂₃	C₂×#529	1	1	yes	characteristic
448	C₂×C₂₃	C₂×#538	1	1	yes	characteristic
449	C₂×C₂₃	C₂×#538	1	1	yes	characteristic
450	C₂×C₂₃	C₂×#538	1	1	yes	characteristic
451	C₂×C₂₃	C₂×#539	1	1	yes	characteristic
452	C₂×C₂₃	C₂×#542	1	1	yes	characteristic
453	C₂×C₂₃	C₂×#542	1	1	yes	characteristic
454	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
455	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
456	C₂²×Q₈	—	2	4	no	—
457	C₂²×Q₈	—	4	2	no	—
458	C₂²×Q₈	—	4	2	no	—
459	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
460	C₂²×D₄	—	2	4	no	—
461	C₂²×D₄	—	4	2	no	—
462	C₂²×D₄	—	4	2	no	—
463	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
464	C₂³×C₄	—	2	4	no	—
465	C₂³×C₄	—	4	2	no	—
466	C₂³×C₄	—	4	2	no	—
467	C₂³×C₄	C₂³×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	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
472	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
475	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
476	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
477	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
478	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
479	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
480	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
481	C₂×C₄⋊C₄	—	2	4	no	—
482	C₂×C₄⋊C₄	—	4	2	no	—
483	C₂×C₄⋊C₄	—	4	2	no	—
484	C₂×C₄⋊C₄	—	4	2	no	—
485	C₂×C₄⋊C₄	—	4	2	no	—
486	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
487	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
488	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
489	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
490	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
491	C₂×C₂²⋊C₄	—	2	4	no	—
492	C₂×C₂²⋊C₄	—	2	4	no	—
493	C₂×C₂²⋊C₄	—	2	4	no	—
494	C₂×C₂²⋊C₄	—	2	4	no	—
495	C₂×C₂²⋊C₄	—	2	4	no	—
496	C₂×C₂²⋊C₄	—	4	2	no	—
497	C₂×C₂²⋊C₄	—	4	2	no	—
498	C₂×C₂²⋊C₄	—	4	2	no	—
499	C₂×C₂²⋊C₄	—	4	2	no	—
500	C₂×C₂²⋊C₄	—	4	2	no	—
501	C₂×C₂²⋊C₄	—	4	2	no	—
502	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
503	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
504	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
505	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
506	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
507	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
508	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
509	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
510	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
511	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
513	C₂×C₄²	—	4	2	no	—
514	C₂×C₄²	—	4	2	no	—
515	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
516	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
517	#95	C₂³×C₂₃	1	4	yes	—
518	#95	C₂³×C₂₃	1	4	yes	—
519	#95	C₂³×C₂₃	1	4	yes	—
520	#95	C₂³×C₂₃	1	4	yes	—
521	#95	C₂³×C₂₃	1	4	yes	—
522	#95	C₂³×C₂₃	1	4	yes	—
523	#95	C₂³×C₂₃	1	4	yes	—
524	#95	C₂³×C₂₃	1	4	yes	—
525	#95	C₂³×C₂₃	1	4	yes	—
526	#95	C₂³×C₂₃	1	4	yes	—
527	#95	C₂³×C₂₃	1	4	yes	—
528	#95	C₂³×C₂₃	1	4	yes	—
529	#95	C₂³×C₂₃	1	4	yes	—
530	#95	C₂³×C₂₃	1	4	yes	—
531	C₂₃	C₂×#2653	1	1	yes	characteristic, direct product factor, Sylow
532	C₂⁴	—	2	2	no	—
533	C₂⁴	—	2	2	no	—
534	C₂⁴	—	2	2	no	—
535	C₂⁴	—	2	2	no	—
536	C₂⁴	—	2	2	no	—
537	C₂⁴	—	2	2	no	—
538	C₂⁴	—	2	2	no	—
539	C₂⁴	—	2	2	no	—
540	C₂⁴	—	2	2	no	—
541	C₂⁴	—	2	2	no	—
542	C₂⁴	—	2	2	no	—
543	C₂⁴	—	2	2	no	—
544	C₂⁴	—	2	2	no	—
545	C₂⁴	#41×C₂₃	1	4	yes	—
546	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
547	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
548	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
549	C₂×Q₈	—	2	8	no	—
550	C₂×Q₈	—	4	4	no	—
551	C₂×Q₈	—	4	4	no	—
552	C₂×Q₈	—	4	16	no	—
553	C₂×D₄	—	2	8	no	—
554	C₂×D₄	—	4	4	no	—
555	C₂×D₄	—	4	4	no	—
556	C₂×D₄	—	4	16	no	—
557	C₂²×C₄	—	2	2	no	—
558	C₂²×C₄	—	2	2	no	—
559	C₂²×C₄	—	2	2	no	—
560	C₂²×C₄	—	2	2	no	—
561	C₂²×C₄	—	2	2	no	—
562	C₂²×C₄	—	2	2	no	—
563	C₂²×C₄	—	2	2	no	—
564	C₂²×C₄	—	2	2	no	—
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	2	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	2	no	—
570	C₂²×C₄	—	2	2	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	2	no	—
576	C₂²×C₄	—	2	2	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	2	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	2	no	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	8	no	—
595	C₂²×C₄	—	4	4	no	—
596	C₂²×C₄	—	4	4	no	—
597	C₂²×C₄	—	4	16	no	—
598	C₂²×C₄	#41×C₂₃	1	4	yes	—
599	C₂²×C₄	#41×C₂₃	1	4	yes	—
600	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
601	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
602	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
603	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
604	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
608	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
609	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
612	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
613	C₄⋊C₄	—	2	8	no	—
614	C₄⋊C₄	—	4	4	no	—
615	C₄⋊C₄	—	4	4	no	—
616	C₄⋊C₄	—	4	4	no	—
617	C₄⋊C₄	—	4	4	no	—
618	C₂²⋊C₄	—	2	8	no	—
619	C₂²⋊C₄	—	2	8	no	—
620	C₂²⋊C₄	—	2	8	no	—
621	C₂²⋊C₄	—	2	8	no	—
622	C₂²⋊C₄	—	2	8	no	—
623	C₂²⋊C₄	—	4	4	no	—
624	C₂²⋊C₄	—	4	4	no	—
625	C₂²⋊C₄	—	4	4	no	—
626	C₂²⋊C₄	—	4	4	no	—
627	C₂²⋊C₄	—	4	4	no	—
628	C₂²⋊C₄	—	4	4	no	—
629	C₄²	—	4	4	no	—
630	C₄²	—	4	4	no	—
631	C₂³	—	2	2	no	—
632	C₂³	—	2	2	no	—
633	C₂³	—	2	2	no	—
634	C₂³	—	2	2	no	—
635	C₂³	—	2	2	no	—
636	C₂³	—	2	2	no	—
637	C₂³	—	2	8	no	—
638	C₂³	—	2	8	no	—
639	C₂³	—	2	8	no	—
640	C₂³	—	2	2	no	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	2	2	no	—
646	C₂³	—	2	2	no	—
647	C₂³	—	4	4	no	—
648	C₂³	—	4	4	no	—
649	C₂³	—	4	4	no	—
650	C₂³	—	4	4	no	—
651	C₂³	—	4	4	no	—
652	C₂³	—	4	4	no	—
653	C₂³	—	4	4	no	—
654	C₂³	—	4	4	no	—
655	C₂³	—	4	4	no	—
656	C₂³	—	4	4	no	—
657	C₂³	—	4	4	no	—
658	C₂³	C₂×#41×C₂₃	1	4	yes	—
659	C₂³	C₂×#41×C₂₃	1	2	yes	—
660	C₂³	C₂×#41×C₂₃	1	2	yes	—
661	C₂³	C₂×#41×C₂₃	1	2	yes	—
662	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
663	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
664	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
665	C₂³	C₂₃×2₋¹⁺⁴	1	2	yes	—
666	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
667	Q₈	—	4	16	no	—
668	D₄	—	4	16	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	8	no	—
674	C₂×C₄	—	2	8	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	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	2	no	—
702	C₂×C₄	—	2	2	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	4	16	no	—
709	C₂×C₄	—	4	4	no	—
710	C₂×C₄	—	4	4	no	—
711	C₂×C₄	—	4	4	no	—
712	C₂×C₄	—	4	4	no	—
713	C₂×C₄	—	4	4	no	—
714	C₂×C₄	—	4	4	no	—
715	C₂×C₄	—	4	4	no	—
716	C₂×C₄	—	4	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
721	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
722	C₂²	—	2	4	no	—
723	C₂²	—	2	4	no	—
724	C₂²	—	2	4	no	—
725	C₂²	—	4	16	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	4	2	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	4	2	no	—
735	C₂²	—	4	2	no	—
736	C₂²	—	4	2	no	—
737	C₂²	—	8	8	no	—
738	C₂²	C₂₃×#529	1	4	yes	—
739	C₂²	C₂₃×#538	1	4	yes	—
740	C₂²	C₂₃×#538	1	4	yes	—
741	C₂²	C₂₃×#538	1	4	yes	—
742	C₂²	C₂₃×#539	1	4	yes	—
743	C₂²	C₂₃×#542	1	4	yes	—
744	C₂²	C₂₃×#542	1	4	yes	—
745	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
746	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
747	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
748	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
749	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
750	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
751	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
752	C₄	—	2	4	no	—
753	C₄	—	2	4	no	—
754	C₄	—	4	2	no	—
755	C₄	—	4	2	no	—
756	C₄	—	4	2	no	—
757	C₄	—	4	2	no	—
758	C₄	—	4	2	no	—
759	C₄	—	4	2	no	—
760	C₄	—	4	2	no	—
761	C₄	—	4	2	no	—
762	C₄	—	4	2	no	—
763	C₄	—	4	2	no	—
764	C₄	—	4	2	no	—
765	C₂	—	4	4	no	—
766	C₂	—	8	2	no	—
767	C₂	C₂₃×#2653	1	8	yes	direct product factor
768	C₂	C₂×C₂₃×#529	1	1	yes	characteristic
769	C₂	C₂×C₂₃×#538	1	1	yes	characteristic
770	C₂	C₂×C₂₃×#538	1	1	yes	characteristic
771	C₂	C₂×C₂₃×#538	1	1	yes	characteristic
772	C₂	C₂×C₂₃×#539	1	1	yes	characteristic
773	C₂	C₂×C₂₃×#542	1	1	yes	characteristic
774	C₂	C₂×C₂₃×#542	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂³×D₄×C₂₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#2653	C₂	direct (N × H)
2. C₂×C₂₃×#401	C₂	semidirect
3. C₂×C₂₃×#398	C₂	semidirect
4. C₂×C₂₃×#397	C₂	semidirect
5. C₂×C₂₃×#397	C₂	semidirect
8. C₂×C₂₃×#393	C₂	semidirect
9. C₂×C₂₃×#393	C₂	semidirect
10. C₂×C₂₃×#391	C₂	semidirect
11. C₂×C₂₃×#388	C₂	semidirect
12. C₂×C₂₃×#388	C₂	semidirect
13. C₂×C₂₃×#387	C₂	semidirect
15. C₂×C₂₃×#385	C₂	semidirect
16. C₂×C₄×C₂²⋊C₄×C₂₃	C₂	semidirect
38. C₂₃×#401	C₂²	semidirect
39. C₂₃×#398	C₂²	semidirect
40. C₂₃×#397	C₂²	semidirect
41. C₂₃×#397	C₂²	semidirect
44. C₂₃×#393	C₂²	semidirect
45. C₂₃×#393	C₂²	semidirect
46. C₂₃×#391	C₂²	semidirect
47. C₂₃×#388	C₂²	semidirect
48. C₂₃×#388	C₂²	semidirect
49. C₂₃×#387	C₂²	semidirect
51. C₂₃×#385	C₂²	semidirect
52. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
243. C₂×#2653	C₂₃	direct (N × H)
335. #2653	C₂×C₂₃	direct (N × H)
336. C₂×#401	C₂×C₂₃	semidirect
337. C₂×#398	C₂×C₂₃	semidirect
338. C₂×#397	C₂×C₂₃	semidirect
339. C₂×#397	C₂×C₂₃	semidirect
342. C₂×#393	C₂×C₂₃	semidirect
343. C₂×#393	C₂×C₂₃	semidirect
344. C₂×#391	C₂×C₂₃	semidirect
345. C₂×#388	C₂×C₂₃	semidirect
346. C₂×#388	C₂×C₂₃	semidirect
347. C₂×#387	C₂×C₂₃	semidirect
349. C₂×#385	C₂×C₂₃	semidirect
350. C₂×C₄×C₂²⋊C₄	C₂×C₂₃	semidirect
415. #401	C₂²×C₂₃	semidirect
416. #398	C₂²×C₂₃	semidirect
417. #397	C₂²×C₂₃	semidirect
418. #397	C₂²×C₂₃	semidirect
421. #393	C₂²×C₂₃	semidirect
422. #393	C₂²×C₂₃	semidirect
423. #391	C₂²×C₂₃	semidirect
424. #388	C₂²×C₂₃	semidirect
425. #388	C₂²×C₂₃	semidirect
426. #387	C₂²×C₂₃	semidirect
428. #385	C₂²×C₂₃	semidirect
429. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
446. C₂×C₂₃	#2653	direct (N × H)
531. C₂₃	C₂×#2653	direct (N × H)
767. C₂	C₂₃×#2653	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×#2653	2
C₂×C₂₃×#401	2
C₂×C₂₃×#398	2
C₂×C₂₃×#397	2
C₂×C₂₃×#394	2
C₂×C₂₃×#393	2
C₂×C₂₃×#391	2
C₂×C₂₃×#388	2
C₂×C₂₃×#387	2
C₂×C₂₃×#386	2
C₂×C₂₃×#385	2
C₂×C₄×C₂²⋊C₄×C₂₃	2
C₂×#2653	23

Subgroups — C2×C23×#2653 #19182194

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2653 #19182194