Subgroups — C₂×C₂₃×#2648 #19182192

Order 5888.

2654 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#2648	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₂₃×#400	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#396	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#392	C₂	1	1	yes	maximal, characteristic
10	C₂×C₂₃×#390	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, complemented
15	C₂×C₂₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₂²⋊C₄×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
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	C₂⁴×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×C₄⋊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×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
41	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
42	C₂₃×#400	C₂²	1	8	yes	complemented
43	C₂₃×#397	C₂²	1	8	yes	complemented
44	C₂₃×#397	C₂²	1	8	yes	complemented
45	C₂₃×#396	C₂²	1	8	yes	complemented
46	C₂₃×#394	C₂²	1	8	yes	complemented
47	C₂₃×#394	C₂²	1	8	yes	complemented
48	C₂₃×#394	C₂²	1	8	yes	complemented
49	C₂₃×#392	C₂²	1	8	yes	—
50	C₂₃×#390	C₂²	1	8	yes	complemented
51	C₂₃×#388	C₂²	1	8	yes	complemented
52	C₂₃×#388	C₂²	1	8	yes	complemented
53	C₂₃×#387	C₂²	1	8	yes	complemented
54	C₂₃×#386	C₂²	1	8	yes	complemented
55	C₂₃×#386	C₂²	1	8	yes	complemented
56	C₄×C₂²⋊C₄×C₂₃	C₂²	1	8	yes	complemented
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	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₂₃	—	2	4	no	—
71	C₂²×D₄×C₂₃	—	2	4	no	—
72	C₂²×D₄×C₂₃	—	2	4	no	—
73	C₂²×D₄×C₂₃	—	4	2	no	—
74	C₂²×D₄×C₂₃	—	4	2	no	—
75	C₂²×D₄×C₂₃	—	4	2	no	—
76	C₂²×D₄×C₂₃	—	4	2	no	—
77	C₂²×D₄×C₂₃	—	4	2	no	—
78	C₂²×D₄×C₂₃	—	4	2	no	—
79	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
80	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
81	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
82	C₂³×C₄×C₂₃	—	2	4	no	—
83	C₂³×C₄×C₂₃	—	4	2	no	—
84	C₂³×C₄×C₂₃	—	4	2	no	—
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	1	yes	characteristic
94	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
99	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
100	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
101	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
102	C₂×C₄⋊C₄×C₂₃	—	4	2	no	—
103	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
105	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
107	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
109	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
110	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
111	C₂×C₂²⋊C₄×C₂₃	—	2	4	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	—	4	2	no	—
116	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
117	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
118	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
119	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
120	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
121	C₂×C₂²⋊C₄×C₂₃	—	4	2	no	—
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×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
136	C₂×C₄²×C₂₃	—	4	2	no	—
137	C₂×C₄²×C₂₃	—	4	2	no	—
138	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
139	C₂×C₄²×C₂₃	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	C₂₃×#95	C₂³	1	4	yes	—
145	C₂₃×#95	C₂³	1	4	yes	—
146	C₂₃×#95	C₂³	1	4	yes	—
147	C₂₃×#95	C₂³	1	4	yes	—
148	C₂₃×#95	C₂³	1	4	yes	—
149	C₂₃×#95	C₂³	1	4	yes	—
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	—	2	2	no	—
158	C₂⁴×C₂₃	—	2	2	no	—
159	C₂⁴×C₂₃	—	2	2	no	—
160	C₂⁴×C₂₃	—	2	2	no	—
161	C₂⁴×C₂₃	—	2	2	no	—
162	C₂⁴×C₂₃	—	2	2	no	—
163	C₂⁴×C₂₃	—	2	2	no	—
164	C₂⁴×C₂₃	—	2	2	no	—
165	C₂⁴×C₂₃	—	2	2	no	—
166	C₂⁴×C₂₃	—	2	2	no	—
167	C₂⁴×C₂₃	—	2	2	no	—
168	C₂⁴×C₂₃	—	2	2	no	—
169	C₂⁴×C₂₃	—	2	2	no	—
170	C₂⁴×C₂₃	#41	1	4	yes	—
171	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
172	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
173	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
174	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
175	C₂×D₄×C₂₃	—	2	8	no	—
176	C₂×D₄×C₂₃	—	2	8	no	—
177	C₂×D₄×C₂₃	—	2	8	no	—
178	C₂×D₄×C₂₃	—	4	4	no	—
179	C₂×D₄×C₂₃	—	4	4	no	—
180	C₂×D₄×C₂₃	—	4	4	no	—
181	C₂×D₄×C₂₃	—	4	4	no	—
182	C₂×D₄×C₂₃	—	4	4	no	—
183	C₂×D₄×C₂₃	—	4	4	no	—
184	C₂×D₄×C₂₃	—	4	16	no	—
185	C₂×D₄×C₂₃	—	4	16	no	—
186	C₂×D₄×C₂₃	—	4	16	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	2	no	—
207	C₂²×C₄×C₂₃	—	2	2	no	—
208	C₂²×C₄×C₂₃	—	2	2	no	—
209	C₂²×C₄×C₂₃	—	2	2	no	—
210	C₂²×C₄×C₂₃	—	2	2	no	—
211	C₂²×C₄×C₂₃	—	2	2	no	—
212	C₂²×C₄×C₂₃	—	2	2	no	—
213	C₂²×C₄×C₂₃	—	2	2	no	—
214	C₂²×C₄×C₂₃	—	2	2	no	—
215	C₂²×C₄×C₂₃	—	2	2	no	—
216	C₂²×C₄×C₂₃	—	2	2	no	—
217	C₂²×C₄×C₂₃	—	2	2	no	—
218	C₂²×C₄×C₂₃	—	2	2	no	—
219	C₂²×C₄×C₂₃	—	2	2	no	—
220	C₂²×C₄×C₂₃	—	2	2	no	—
221	C₂²×C₄×C₂₃	—	2	8	no	—
222	C₂²×C₄×C₂₃	—	4	4	no	—
223	C₂²×C₄×C₂₃	—	4	4	no	—
224	C₂²×C₄×C₂₃	—	4	16	no	—
225	C₂²×C₄×C₂₃	#41	1	4	yes	—
226	C₂²×C₄×C₂₃	#41	1	4	yes	—
227	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
229	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
230	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
231	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
232	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
233	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
235	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
236	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
237	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
238	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
239	C₄⋊C₄×C₂₃	—	2	8	no	—
240	C₄⋊C₄×C₂₃	—	4	4	no	—
241	C₄⋊C₄×C₂₃	—	4	4	no	—
242	C₄⋊C₄×C₂₃	—	4	4	no	—
243	C₄⋊C₄×C₂₃	—	4	4	no	—
244	C₂²⋊C₄×C₂₃	—	2	8	no	—
245	C₂²⋊C₄×C₂₃	—	2	8	no	—
246	C₂²⋊C₄×C₂₃	—	2	8	no	—
247	C₂²⋊C₄×C₂₃	—	2	8	no	—
248	C₂²⋊C₄×C₂₃	—	4	4	no	—
249	C₂²⋊C₄×C₂₃	—	4	4	no	—
250	C₂²⋊C₄×C₂₃	—	4	4	no	—
251	C₂²⋊C₄×C₂₃	—	4	4	no	—
252	C₂²⋊C₄×C₂₃	—	4	4	no	—
253	C₂²⋊C₄×C₂₃	—	4	4	no	—
254	C₂²⋊C₄×C₂₃	—	4	4	no	—
255	C₂²⋊C₄×C₂₃	—	4	4	no	—
256	C₂²⋊C₄×C₂₃	—	4	4	no	—
257	C₂²⋊C₄×C₂₃	—	4	4	no	—
258	C₄²×C₂₃	—	4	4	no	—
259	C₄²×C₂₃	—	4	4	no	—
260	C₂×#2648	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₂³×C₂₃	—	2	8	no	—
262	C₂³×C₂₃	—	2	8	no	—
263	C₂³×C₂₃	—	2	8	no	—
264	C₂³×C₂₃	—	2	2	no	—
265	C₂³×C₂₃	—	2	2	no	—
266	C₂³×C₂₃	—	2	2	no	—
267	C₂³×C₂₃	—	2	2	no	—
268	C₂³×C₂₃	—	2	2	no	—
269	C₂³×C₂₃	—	2	2	no	—
270	C₂³×C₂₃	—	2	2	no	—
271	C₂³×C₂₃	—	2	2	no	—
272	C₂³×C₂₃	—	2	2	no	—
273	C₂³×C₂₃	—	2	2	no	—
274	C₂³×C₂₃	—	2	2	no	—
275	C₂³×C₂₃	—	2	2	no	—
276	C₂³×C₂₃	—	2	2	no	—
277	C₂³×C₂₃	—	2	2	no	—
278	C₂³×C₂₃	—	2	2	no	—
279	C₂³×C₂₃	—	2	2	no	—
280	C₂³×C₂₃	—	2	2	no	—
281	C₂³×C₂₃	—	2	2	no	—
282	C₂³×C₂₃	—	2	2	no	—
283	C₂³×C₂₃	—	2	2	no	—
284	C₂³×C₂₃	—	4	4	no	—
285	C₂³×C₂₃	—	4	4	no	—
286	C₂³×C₂₃	—	4	4	no	—
287	C₂³×C₂₃	—	4	4	no	—
288	C₂³×C₂₃	—	4	4	no	—
289	C₂³×C₂₃	—	4	4	no	—
290	C₂³×C₂₃	—	4	4	no	—
291	C₂³×C₂₃	—	4	4	no	—
292	C₂³×C₂₃	—	4	4	no	—
293	C₂³×C₂₃	—	4	4	no	—
294	C₂³×C₂₃	—	4	4	no	—
295	C₂³×C₂₃	—	4	4	no	—
296	C₂³×C₂₃	—	4	4	no	—
297	C₂³×C₂₃	—	4	4	no	—
298	C₂³×C₂₃	—	4	4	no	—
299	C₂³×C₂₃	—	4	4	no	—
300	C₂³×C₂₃	—	4	4	no	—
301	C₂³×C₂₃	—	4	4	no	—
302	C₂³×C₂₃	C₂×#41	1	4	yes	—
303	C₂³×C₂₃	C₂×#41	1	2	yes	—
304	C₂³×C₂₃	C₂×#41	1	2	yes	—
305	C₂³×C₂₃	C₂×#41	1	2	yes	—
306	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
307	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
308	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
309	C₂³×C₂₃	H(5,𝔽₂)	1	2	yes	—
310	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
311	D₄×C₂₃	—	4	16	no	—
312	D₄×C₂₃	—	4	16	no	—
313	D₄×C₂₃	—	4	16	no	—
314	C₂×C₄×C₂₃	—	2	8	no	—
315	C₂×C₄×C₂₃	—	2	8	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	—	2	2	no	—
322	C₂×C₄×C₂₃	—	2	2	no	—
323	C₂×C₄×C₂₃	—	2	2	no	—
324	C₂×C₄×C₂₃	—	2	2	no	—
325	C₂×C₄×C₂₃	—	2	2	no	—
326	C₂×C₄×C₂₃	—	2	2	no	—
327	C₂×C₄×C₂₃	—	2	2	no	—
328	C₂×C₄×C₂₃	—	2	2	no	—
329	C₂×C₄×C₂₃	—	2	2	no	—
330	C₂×C₄×C₂₃	—	2	2	no	—
331	C₂×C₄×C₂₃	—	2	2	no	—
332	C₂×C₄×C₂₃	—	2	2	no	—
333	C₂×C₄×C₂₃	—	2	2	no	—
334	C₂×C₄×C₂₃	—	2	2	no	—
335	C₂×C₄×C₂₃	—	2	2	no	—
336	C₂×C₄×C₂₃	—	2	2	no	—
337	C₂×C₄×C₂₃	—	2	2	no	—
338	C₂×C₄×C₂₃	—	2	2	no	—
339	C₂×C₄×C₂₃	—	2	2	no	—
340	C₂×C₄×C₂₃	—	2	2	no	—
341	C₂×C₄×C₂₃	—	2	2	no	—
342	C₂×C₄×C₂₃	—	2	2	no	—
343	C₂×C₄×C₂₃	—	2	2	no	—
344	C₂×C₄×C₂₃	—	2	2	no	—
345	C₂×C₄×C₂₃	—	2	2	no	—
346	C₂×C₄×C₂₃	—	2	2	no	—
347	C₂×C₄×C₂₃	—	2	2	no	—
348	C₂×C₄×C₂₃	—	2	2	no	—
349	C₂×C₄×C₂₃	—	2	2	no	—
350	C₂×C₄×C₂₃	—	4	16	no	—
351	C₂×C₄×C₂₃	—	4	4	no	—
352	C₂×C₄×C₂₃	—	4	4	no	—
353	C₂×C₄×C₂₃	—	4	4	no	—
354	C₂×C₄×C₂₃	—	4	4	no	—
355	C₂×C₄×C₂₃	—	4	4	no	—
356	C₂×C₄×C₂₃	—	4	4	no	—
357	C₂×C₄×C₂₃	—	4	4	no	—
358	C₂×C₄×C₂₃	—	4	4	no	—
359	C₂×C₄×C₂₃	—	4	4	no	—
360	C₂×C₄×C₂₃	—	4	4	no	—
361	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
362	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
363	#2648	C₂×C₂₃	1	16	yes	direct product factor
364	C₂×#400	C₂×C₂₃	1	1	yes	characteristic, complemented
365	C₂×#397	C₂×C₂₃	1	1	yes	characteristic, complemented
366	C₂×#397	C₂×C₂₃	1	1	yes	characteristic, complemented
367	C₂×#396	C₂×C₂₃	1	1	yes	characteristic, complemented
368	C₂×#394	C₂×C₂₃	1	1	yes	characteristic, complemented
369	C₂×#394	C₂×C₂₃	1	1	yes	characteristic, complemented
370	C₂×#394	C₂×C₂₃	1	1	yes	characteristic, complemented
371	C₂×#392	C₂×C₂₃	1	1	yes	characteristic
372	C₂×#390	C₂×C₂₃	1	1	yes	characteristic, complemented
373	C₂×#388	C₂×C₂₃	1	1	yes	characteristic, complemented
374	C₂×#388	C₂×C₂₃	1	1	yes	characteristic, complemented
375	C₂×#387	C₂×C₂₃	1	1	yes	characteristic, complemented
376	C₂×#386	C₂×C₂₃	1	1	yes	characteristic, complemented
377	C₂×#386	C₂×C₂₃	1	1	yes	characteristic, complemented
378	C₂×C₄×C₂²⋊C₄	C₂×C₂₃	1	1	yes	characteristic, complemented
379	C₂²×C₂₃	—	2	4	no	—
380	C₂²×C₂₃	—	2	4	no	—
381	C₂²×C₂₃	—	2	4	no	—
382	C₂²×C₂₃	—	4	16	no	—
383	C₂²×C₂₃	—	4	2	no	—
384	C₂²×C₂₃	—	4	2	no	—
385	C₂²×C₂₃	—	4	2	no	—
386	C₂²×C₂₃	—	4	2	no	—
387	C₂²×C₂₃	—	4	2	no	—
388	C₂²×C₂₃	—	4	2	no	—
389	C₂²×C₂₃	—	4	2	no	—
390	C₂²×C₂₃	—	4	2	no	—
391	C₂²×C₂₃	—	4	2	no	—
392	C₂²×C₂₃	—	4	2	no	—
393	C₂²×C₂₃	—	4	2	no	—
394	C₂²×C₂₃	—	4	2	no	—
395	C₂²×C₂₃	—	4	2	no	—
396	C₂²×C₂₃	—	4	2	no	—
397	C₂²×C₂₃	—	4	2	no	—
398	C₂²×C₂₃	—	4	2	no	—
399	C₂²×C₂₃	—	4	2	no	—
400	C₂²×C₂₃	—	4	2	no	—
401	C₂²×C₂₃	—	8	8	no	—
402	C₂²×C₂₃	—	8	8	no	—
403	C₂²×C₂₃	#529	1	4	yes	—
404	C₂²×C₂₃	#538	1	4	yes	—
405	C₂²×C₂₃	#538	1	4	yes	—
406	C₂²×C₂₃	#538	1	4	yes	—
407	C₂²×C₂₃	#538	1	4	yes	—
408	C₂²×C₂₃	#540	1	4	yes	—
409	C₂²×C₂₃	#540	1	4	yes	—
410	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
411	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
412	C₂²×C₂₃	C₂²×#41	1	1	yes	characteristic
413	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
415	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
416	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
417	C₄×C₂₃	—	2	4	no	—
418	C₄×C₂₃	—	2	4	no	—
419	C₄×C₂₃	—	4	2	no	—
420	C₄×C₂₃	—	4	2	no	—
421	C₄×C₂₃	—	4	2	no	—
422	C₄×C₂₃	—	4	2	no	—
423	C₄×C₂₃	—	4	2	no	—
424	C₄×C₂₃	—	4	2	no	—
425	C₄×C₂₃	—	4	2	no	—
426	C₄×C₂₃	—	4	2	no	—
427	C₄×C₂₃	—	4	2	no	—
428	C₄×C₂₃	—	4	2	no	—
429	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
430	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
431	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
432	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
433	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
434	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
435	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
436	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
437	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
438	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
439	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
440	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
441	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
442	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
443	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
444	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
445	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
446	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
447	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
448	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
449	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
450	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
451	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
452	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
453	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
454	#400	C₂²×C₂₃	1	8	yes	complemented
455	#397	C₂²×C₂₃	1	8	yes	complemented
456	#397	C₂²×C₂₃	1	8	yes	complemented
457	#396	C₂²×C₂₃	1	8	yes	complemented
458	#394	C₂²×C₂₃	1	8	yes	complemented
459	#394	C₂²×C₂₃	1	8	yes	complemented
460	#394	C₂²×C₂₃	1	8	yes	complemented
461	#392	C₂²×C₂₃	1	8	yes	—
462	#390	C₂²×C₂₃	1	8	yes	complemented
463	#388	C₂²×C₂₃	1	8	yes	complemented
464	#388	C₂²×C₂₃	1	8	yes	complemented
465	#387	C₂²×C₂₃	1	8	yes	complemented
466	#386	C₂²×C₂₃	1	8	yes	complemented
467	#386	C₂²×C₂₃	1	8	yes	complemented
468	C₄×C₂²⋊C₄	C₂²×C₂₃	1	8	yes	complemented
469	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
470	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
471	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
472	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
473	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
474	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
475	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
476	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
477	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
478	C₂×#95	C₂²×C₂₃	1	1	yes	characteristic
479	C₂×C₂₃	—	4	4	no	—
480	C₂×C₂₃	—	8	2	no	—
481	C₂×C₂₃	—	8	2	no	—
482	C₂×C₂₃	#2648	1	8	yes	direct product factor
483	C₂×C₂₃	C₂×#529	1	1	yes	characteristic
484	C₂×C₂₃	C₂×#538	1	1	yes	characteristic
485	C₂×C₂₃	C₂×#538	1	1	yes	characteristic
486	C₂×C₂₃	C₂×#538	1	1	yes	characteristic
487	C₂×C₂₃	C₂×#538	1	1	yes	characteristic
488	C₂×C₂₃	C₂×#540	1	1	yes	characteristic
489	C₂×C₂₃	C₂×#540	1	1	yes	characteristic
490	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
491	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
492	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
493	C₂²×D₄	—	2	4	no	—
494	C₂²×D₄	—	2	4	no	—
495	C₂²×D₄	—	2	4	no	—
496	C₂²×D₄	—	4	2	no	—
497	C₂²×D₄	—	4	2	no	—
498	C₂²×D₄	—	4	2	no	—
499	C₂²×D₄	—	4	2	no	—
500	C₂²×D₄	—	4	2	no	—
501	C₂²×D₄	—	4	2	no	—
502	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
503	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
504	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
505	C₂³×C₄	—	2	4	no	—
506	C₂³×C₄	—	4	2	no	—
507	C₂³×C₄	—	4	2	no	—
508	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
513	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
514	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
516	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
517	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
518	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
519	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
520	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
521	C₂×C₄⋊C₄	—	2	4	no	—
522	C₂×C₄⋊C₄	—	4	2	no	—
523	C₂×C₄⋊C₄	—	4	2	no	—
524	C₂×C₄⋊C₄	—	4	2	no	—
525	C₂×C₄⋊C₄	—	4	2	no	—
526	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
527	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
528	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
529	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
530	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
531	C₂×C₂²⋊C₄	—	2	4	no	—
532	C₂×C₂²⋊C₄	—	2	4	no	—
533	C₂×C₂²⋊C₄	—	2	4	no	—
534	C₂×C₂²⋊C₄	—	2	4	no	—
535	C₂×C₂²⋊C₄	—	4	2	no	—
536	C₂×C₂²⋊C₄	—	4	2	no	—
537	C₂×C₂²⋊C₄	—	4	2	no	—
538	C₂×C₂²⋊C₄	—	4	2	no	—
539	C₂×C₂²⋊C₄	—	4	2	no	—
540	C₂×C₂²⋊C₄	—	4	2	no	—
541	C₂×C₂²⋊C₄	—	4	2	no	—
542	C₂×C₂²⋊C₄	—	4	2	no	—
543	C₂×C₂²⋊C₄	—	4	2	no	—
544	C₂×C₂²⋊C₄	—	4	2	no	—
545	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
559	C₂×C₄²	—	4	2	no	—
560	C₂×C₄²	—	4	2	no	—
561	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
562	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
563	#95	C₂³×C₂₃	1	4	yes	—
564	#95	C₂³×C₂₃	1	4	yes	—
565	#95	C₂³×C₂₃	1	4	yes	—
566	#95	C₂³×C₂₃	1	4	yes	—
567	#95	C₂³×C₂₃	1	4	yes	—
568	#95	C₂³×C₂₃	1	4	yes	—
569	#95	C₂³×C₂₃	1	4	yes	—
570	#95	C₂³×C₂₃	1	4	yes	—
571	#95	C₂³×C₂₃	1	4	yes	—
572	#95	C₂³×C₂₃	1	4	yes	—
573	C₂₃	C₂×#2648	1	1	yes	characteristic, direct product factor, Sylow
574	C₂⁴	—	2	2	no	—
575	C₂⁴	—	2	2	no	—
576	C₂⁴	—	2	2	no	—
577	C₂⁴	—	2	2	no	—
578	C₂⁴	—	2	2	no	—
579	C₂⁴	—	2	2	no	—
580	C₂⁴	—	2	2	no	—
581	C₂⁴	—	2	2	no	—
582	C₂⁴	—	2	2	no	—
583	C₂⁴	—	2	2	no	—
584	C₂⁴	—	2	2	no	—
585	C₂⁴	—	2	2	no	—
586	C₂⁴	—	2	2	no	—
587	C₂⁴	—	2	2	no	—
588	C₂⁴	—	2	2	no	—
589	C₂⁴	—	2	2	no	—
590	C₂⁴	—	2	2	no	—
591	C₂⁴	—	2	2	no	—
592	C₂⁴	—	2	2	no	—
593	C₂⁴	—	2	2	no	—
594	C₂⁴	#41×C₂₃	1	4	yes	—
595	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
596	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
597	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
598	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
599	C₂×D₄	—	2	8	no	—
600	C₂×D₄	—	2	8	no	—
601	C₂×D₄	—	2	8	no	—
602	C₂×D₄	—	4	4	no	—
603	C₂×D₄	—	4	4	no	—
604	C₂×D₄	—	4	4	no	—
605	C₂×D₄	—	4	4	no	—
606	C₂×D₄	—	4	4	no	—
607	C₂×D₄	—	4	4	no	—
608	C₂×D₄	—	4	16	no	—
609	C₂×D₄	—	4	16	no	—
610	C₂×D₄	—	4	16	no	—
611	C₂²×C₄	—	2	2	no	—
612	C₂²×C₄	—	2	2	no	—
613	C₂²×C₄	—	2	2	no	—
614	C₂²×C₄	—	2	2	no	—
615	C₂²×C₄	—	2	2	no	—
616	C₂²×C₄	—	2	2	no	—
617	C₂²×C₄	—	2	2	no	—
618	C₂²×C₄	—	2	2	no	—
619	C₂²×C₄	—	2	2	no	—
620	C₂²×C₄	—	2	2	no	—
621	C₂²×C₄	—	2	2	no	—
622	C₂²×C₄	—	2	2	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	2	no	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
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	8	no	—
646	C₂²×C₄	—	4	4	no	—
647	C₂²×C₄	—	4	4	no	—
648	C₂²×C₄	—	4	16	no	—
649	C₂²×C₄	#41×C₂₃	1	4	yes	—
650	C₂²×C₄	#41×C₂₃	1	4	yes	—
651	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
661	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
663	C₄⋊C₄	—	2	8	no	—
664	C₄⋊C₄	—	4	4	no	—
665	C₄⋊C₄	—	4	4	no	—
666	C₄⋊C₄	—	4	4	no	—
667	C₄⋊C₄	—	4	4	no	—
668	C₂²⋊C₄	—	2	8	no	—
669	C₂²⋊C₄	—	2	8	no	—
670	C₂²⋊C₄	—	2	8	no	—
671	C₂²⋊C₄	—	2	8	no	—
672	C₂²⋊C₄	—	4	4	no	—
673	C₂²⋊C₄	—	4	4	no	—
674	C₂²⋊C₄	—	4	4	no	—
675	C₂²⋊C₄	—	4	4	no	—
676	C₂²⋊C₄	—	4	4	no	—
677	C₂²⋊C₄	—	4	4	no	—
678	C₂²⋊C₄	—	4	4	no	—
679	C₂²⋊C₄	—	4	4	no	—
680	C₂²⋊C₄	—	4	4	no	—
681	C₂²⋊C₄	—	4	4	no	—
682	C₄²	—	4	4	no	—
683	C₄²	—	4	4	no	—
684	C₂³	—	2	2	no	—
685	C₂³	—	2	2	no	—
686	C₂³	—	2	2	no	—
687	C₂³	—	2	2	no	—
688	C₂³	—	2	2	no	—
689	C₂³	—	2	2	no	—
690	C₂³	—	2	8	no	—
691	C₂³	—	2	8	no	—
692	C₂³	—	2	8	no	—
693	C₂³	—	2	2	no	—
694	C₂³	—	2	2	no	—
695	C₂³	—	2	2	no	—
696	C₂³	—	2	2	no	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	2	no	—
706	C₂³	—	2	2	no	—
707	C₂³	—	4	4	no	—
708	C₂³	—	4	4	no	—
709	C₂³	—	4	4	no	—
710	C₂³	—	4	4	no	—
711	C₂³	—	4	4	no	—
712	C₂³	—	4	4	no	—
713	C₂³	—	4	4	no	—
714	C₂³	—	4	4	no	—
715	C₂³	—	4	4	no	—
716	C₂³	—	4	4	no	—
717	C₂³	—	4	4	no	—
718	C₂³	—	4	4	no	—
719	C₂³	—	4	4	no	—
720	C₂³	—	4	4	no	—
721	C₂³	—	4	4	no	—
722	C₂³	—	4	4	no	—
723	C₂³	—	4	4	no	—
724	C₂³	—	4	4	no	—
725	C₂³	C₂×#41×C₂₃	1	4	yes	—
726	C₂³	C₂×#41×C₂₃	1	2	yes	—
727	C₂³	C₂×#41×C₂₃	1	2	yes	—
728	C₂³	C₂×#41×C₂₃	1	2	yes	—
729	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
730	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
731	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
732	C₂³	C₂₃×H(5,𝔽₂)	1	2	yes	—
733	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
734	D₄	—	4	16	no	—
735	D₄	—	4	16	no	—
736	D₄	—	4	16	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	8	no	—
742	C₂×C₄	—	2	8	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	2	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	4	16	no	—
774	C₂×C₄	—	4	4	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	—	4	4	no	—
778	C₂×C₄	—	4	4	no	—
779	C₂×C₄	—	4	4	no	—
780	C₂×C₄	—	4	4	no	—
781	C₂×C₄	—	4	4	no	—
782	C₂×C₄	—	4	4	no	—
783	C₂×C₄	—	4	4	no	—
784	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
785	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
786	C₂²	—	2	4	no	—
787	C₂²	—	2	4	no	—
788	C₂²	—	2	4	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	2	no	—
791	C₂²	—	4	2	no	—
792	C₂²	—	4	2	no	—
793	C₂²	—	4	16	no	—
794	C₂²	—	4	2	no	—
795	C₂²	—	4	2	no	—
796	C₂²	—	4	2	no	—
797	C₂²	—	4	2	no	—
798	C₂²	—	4	2	no	—
799	C₂²	—	4	2	no	—
800	C₂²	—	4	2	no	—
801	C₂²	—	4	2	no	—
802	C₂²	—	4	2	no	—
803	C₂²	—	4	2	no	—
804	C₂²	—	4	2	no	—
805	C₂²	—	4	2	no	—
806	C₂²	—	4	2	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	8	8	no	—
809	C₂²	—	8	8	no	—
810	C₂²	C₂₃×#529	1	4	yes	—
811	C₂²	C₂₃×#538	1	4	yes	—
812	C₂²	C₂₃×#538	1	4	yes	—
813	C₂²	C₂₃×#538	1	4	yes	—
814	C₂²	C₂₃×#538	1	4	yes	—
815	C₂²	C₂₃×#540	1	4	yes	—
816	C₂²	C₂₃×#540	1	4	yes	—
817	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
818	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
819	C₂²	C₂²×#41×C₂₃	1	1	yes	characteristic
820	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
821	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
822	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
823	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
824	C₄	—	2	4	no	—
825	C₄	—	2	4	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	2	no	—
832	C₄	—	4	2	no	—
833	C₄	—	4	2	no	—
834	C₄	—	4	2	no	—
835	C₄	—	4	2	no	—
836	C₂	—	4	4	no	—
837	C₂	—	8	2	no	—
838	C₂	—	8	2	no	—
839	C₂	C₂₃×#2648	1	8	yes	direct product factor
840	C₂	C₂×C₂₃×#529	1	1	yes	characteristic
841	C₂	C₂×C₂₃×#538	1	1	yes	characteristic
842	C₂	C₂×C₂₃×#538	1	1	yes	characteristic
843	C₂	C₂×C₂₃×#538	1	1	yes	characteristic
844	C₂	C₂×C₂₃×#538	1	1	yes	characteristic
845	C₂	C₂×C₂₃×#540	1	1	yes	characteristic
846	C₂	C₂×C₂₃×#540	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#392	C₂
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×#2648	C₂	direct (N × H)
2. C₂×C₂₃×#400	C₂	semidirect
3. C₂×C₂₃×#397	C₂	semidirect
4. C₂×C₂₃×#397	C₂	semidirect
5. C₂×C₂₃×#396	C₂	semidirect
6. C₂×C₂₃×#394	C₂	semidirect
7. C₂×C₂₃×#394	C₂	semidirect
8. C₂×C₂₃×#394	C₂	semidirect
10. C₂×C₂₃×#390	C₂	semidirect
11. C₂×C₂₃×#388	C₂	semidirect
12. C₂×C₂₃×#388	C₂	semidirect
13. C₂×C₂₃×#387	C₂	semidirect
14. C₂×C₂₃×#386	C₂	semidirect
15. C₂×C₂₃×#386	C₂	semidirect
16. C₂×C₄×C₂²⋊C₄×C₂₃	C₂	semidirect
42. C₂₃×#400	C₂²	semidirect
43. C₂₃×#397	C₂²	semidirect
44. C₂₃×#397	C₂²	semidirect
45. C₂₃×#396	C₂²	semidirect
46. C₂₃×#394	C₂²	semidirect
47. C₂₃×#394	C₂²	semidirect
48. C₂₃×#394	C₂²	semidirect
50. C₂₃×#390	C₂²	semidirect
51. C₂₃×#388	C₂²	semidirect
52. C₂₃×#388	C₂²	semidirect
53. C₂₃×#387	C₂²	semidirect
54. C₂₃×#386	C₂²	semidirect
55. C₂₃×#386	C₂²	semidirect
56. C₄×C₂²⋊C₄×C₂₃	C₂²	semidirect
260. C₂×#2648	C₂₃	direct (N × H)
363. #2648	C₂×C₂₃	direct (N × H)
364. C₂×#400	C₂×C₂₃	semidirect
365. C₂×#397	C₂×C₂₃	semidirect
366. C₂×#397	C₂×C₂₃	semidirect
367. C₂×#396	C₂×C₂₃	semidirect
368. C₂×#394	C₂×C₂₃	semidirect
369. C₂×#394	C₂×C₂₃	semidirect
370. C₂×#394	C₂×C₂₃	semidirect
372. C₂×#390	C₂×C₂₃	semidirect
373. C₂×#388	C₂×C₂₃	semidirect
374. C₂×#388	C₂×C₂₃	semidirect
375. C₂×#387	C₂×C₂₃	semidirect
376. C₂×#386	C₂×C₂₃	semidirect
377. C₂×#386	C₂×C₂₃	semidirect
378. C₂×C₄×C₂²⋊C₄	C₂×C₂₃	semidirect
454. #400	C₂²×C₂₃	semidirect
455. #397	C₂²×C₂₃	semidirect
456. #397	C₂²×C₂₃	semidirect
457. #396	C₂²×C₂₃	semidirect
458. #394	C₂²×C₂₃	semidirect
459. #394	C₂²×C₂₃	semidirect
460. #394	C₂²×C₂₃	semidirect
462. #390	C₂²×C₂₃	semidirect
463. #388	C₂²×C₂₃	semidirect
464. #388	C₂²×C₂₃	semidirect
465. #387	C₂²×C₂₃	semidirect
466. #386	C₂²×C₂₃	semidirect
467. #386	C₂²×C₂₃	semidirect
468. C₄×C₂²⋊C₄	C₂²×C₂₃	semidirect
482. C₂×C₂₃	#2648	direct (N × H)
573. C₂₃	C₂×#2648	direct (N × H)
839. C₂	C₂₃×#2648	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×#2648	2
C₂×C₂₃×#400	2
C₂×C₂₃×#397	2
C₂×C₂₃×#396	2
C₂×C₂₃×#394	2
C₂×C₂₃×#392	2
C₂×C₂₃×#390	2
C₂×C₂₃×#388	2
C₂×C₂₃×#387	2
C₂×C₂₃×#386	2
C₂×C₄×C₂²⋊C₄×C₂₃	2
C₂×#2648	23

Subgroups — C2×C23×#2648 #19182192

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#2648 #19182192