Subgroups — C₂×C₅×#2358 #11956850

Order 1280.

5942 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#120	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₅×D₄	C₂	1	2	yes	maximal, complemented
3	C₂³×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
4	C₅×#2358	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#388	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#386	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#386	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#385	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
11	C₂⁶×C₅	C₂²	1	1	yes	characteristic
12	C₂³×C₅×D₄	C₂²	1	2	yes	—
13	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₅	C₂²	1	2	yes	—
15	C₂⁴×C₄×C₅	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₅×#120	C₄	1	16	yes	complemented
18	C₂×C₅×#120	C₂²	1	8	yes	—
19	C₂×C₄×C₅×D₄	—	2	16	no	—
20	C₂×C₄×C₅×D₄	C₂²	1	16	yes	complemented
21	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
22	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₅×C₂²⋊C₄	—	2	16	no	—
24	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₅×C₂²⋊C₄	C₂²	1	16	yes	complemented
31	C₂²×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
32	C₂²×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₄²×C₅	C₂²	1	2	yes	complemented
34	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
35	C₅×#390	C₂²	1	8	yes	complemented
36	C₅×#388	C₂²	1	16	yes	complemented
37	C₅×#386	C₂²	1	8	yes	complemented
38	C₅×#386	C₂²	1	16	yes	complemented
39	C₅×#385	C₂²	1	16	yes	complemented
40	C₄×C₅×C₂²⋊C₄	C₂²	1	16	yes	complemented
41	C₂×C₅×#95	C₂²	1	2	yes	complemented
42	C₂×C₅×#95	C₂²	1	2	yes	complemented
43	C₂×C₅×#95	C₂²	1	2	yes	complemented
44	C₂×#2358	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂⁵×C₅	—	2	8	no	—
46	C₂⁵×C₅	—	2	8	no	—
47	C₂⁵×C₅	—	4	2	no	—
48	C₂⁵×C₅	—	4	2	no	—
49	C₂⁵×C₅	C₂×C₄	1	8	yes	complemented
50	C₂⁵×C₅	C₂³	1	1	yes	characteristic
51	C₂⁵×C₅	C₂³	1	1	yes	characteristic
52	C₂⁵×C₅	C₂³	1	4	yes	—
53	C₂⁵×C₅	C₂³	1	2	yes	—
54	C₂²×C₅×D₄	—	2	8	no	—
55	C₂²×C₅×D₄	—	2	8	no	—
56	C₂²×C₅×D₄	—	4	2	no	—
57	C₂²×C₅×D₄	—	4	2	no	—
58	C₂²×C₅×D₄	C₂×C₄	1	16	yes	complemented
59	C₂²×C₅×D₄	C₂×C₄	1	8	yes	complemented
60	C₂²×C₅×D₄	C₂³	1	8	yes	—
61	C₂²×C₅×D₄	C₂³	1	4	yes	—
62	C₂³×C₄×C₅	—	2	8	no	—
63	C₂³×C₄×C₅	—	2	8	no	—
64	C₂³×C₄×C₅	—	2	8	no	—
65	C₂³×C₄×C₅	—	2	8	no	—
66	C₂³×C₄×C₅	—	2	8	no	—
67	C₂³×C₄×C₅	—	4	4	no	—
68	C₂³×C₄×C₅	—	4	4	no	—
69	C₂³×C₄×C₅	—	4	2	no	—
70	C₂³×C₄×C₅	C₂³	1	2	yes	—
71	C₂³×C₄×C₅	C₂³	1	2	yes	—
72	C₂³×C₄×C₅	C₂³	1	8	yes	—
73	C₂³×C₄×C₅	C₂³	1	8	yes	—
74	C₂³×C₄×C₅	C₂³	1	2	yes	—
75	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₅	C₂³	1	2	yes	—
77	C₂³×C₄×C₅	C₂³	1	2	yes	—
78	C₂³×C₄×C₅	C₂³	1	4	yes	complemented
79	C₅×#120	C₂×C₄	1	64	yes	complemented
80	C₄×C₅×D₄	—	2	64	no	—
81	C₂×C₅×C₄⋊C₄	—	2	8	no	—
82	C₂×C₅×C₄⋊C₄	—	4	2	no	—
83	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	complemented
84	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
85	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
86	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
87	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
88	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
89	C₂×C₅×C₂²⋊C₄	—	2	64	no	—
90	C₂×C₅×C₂²⋊C₄	—	4	2	no	—
91	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
92	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
93	C₂×C₅×C₂²⋊C₄	D₄	1	16	yes	complemented
94	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
95	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
96	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
97	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
98	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
99	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
100	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	complemented
101	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
102	C₂×C₄²×C₅	—	2	8	no	—
103	C₂×C₄²×C₅	—	4	2	no	—
104	C₂×C₄²×C₅	C₂³	1	8	yes	complemented
105	C₂×C₄²×C₅	C₂³	1	4	yes	complemented
106	C₅×#95	C₂³	1	8	yes	complemented
107	C₅×#95	C₂³	1	8	yes	complemented
108	C₅×#95	C₂³	1	8	yes	complemented
109	C₂²×#120	C₂×C₅	1	1	yes	characteristic
110	C₂²×C₄×D₄	C₂×C₅	1	2	yes	complemented
111	C₂³×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
112	#2358	C₂×C₅	1	16	yes	direct product factor
113	C₂×#390	C₂×C₅	1	1	yes	characteristic, complemented
114	C₂×#388	C₂×C₅	1	2	yes	complemented
115	C₂×#386	C₂×C₅	1	1	yes	characteristic, complemented
116	C₂×#386	C₂×C₅	1	2	yes	complemented
117	C₂×#385	C₂×C₅	1	2	yes	complemented
118	C₂×C₄×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
119	C₂⁴×C₅	—	2	4	no	—
120	C₂⁴×C₅	—	2	4	no	—
121	C₂⁴×C₅	—	2	4	no	—
122	C₂⁴×C₅	—	2	4	no	—
123	C₂⁴×C₅	—	2	64	no	—
124	C₂⁴×C₅	—	2	16	no	—
125	C₂⁴×C₅	—	2	4	no	—
126	C₂⁴×C₅	—	2	4	no	—
127	C₂⁴×C₅	—	2	4	no	—
128	C₂⁴×C₅	—	2	16	no	—
129	C₂⁴×C₅	—	2	4	no	—
130	C₂⁴×C₅	—	2	2	no	—
131	C₂⁴×C₅	—	2	2	no	—
132	C₂⁴×C₅	—	2	2	no	—
133	C₂⁴×C₅	—	2	2	no	—
134	C₂⁴×C₅	—	4	16	no	—
135	C₂⁴×C₅	—	4	4	no	—
136	C₂⁴×C₅	—	4	4	no	—
137	C₂⁴×C₅	—	4	16	no	—
138	C₂⁴×C₅	—	4	32	no	—
139	C₂⁴×C₅	—	4	16	no	—
140	C₂⁴×C₅	C₂²×C₄	1	4	yes	—
141	C₂⁴×C₅	C₂²×C₄	1	4	yes	—
142	C₂⁴×C₅	C₂²×C₄	1	8	yes	—
143	C₂⁴×C₅	C₂²×C₄	1	16	yes	complemented
144	C₂⁴×C₅	C₂×D₄	1	8	yes	—
145	C₂⁴×C₅	#41	1	8	yes	—
146	C₂⁴×C₅	C₂⁴	1	2	yes	—
147	C₂⁴×C₅	C₂⁴	1	2	yes	—
148	C₂⁴×C₅	C₂⁴	1	4	yes	—
149	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
150	C₂×C₅×D₄	—	2	64	no	—
151	C₂×C₅×D₄	—	2	16	no	—
152	C₂×C₅×D₄	—	2	16	no	—
153	C₂×C₅×D₄	—	4	16	no	—
154	C₂×C₅×D₄	—	4	4	no	—
155	C₂×C₅×D₄	—	4	4	no	—
156	C₂×C₅×D₄	C₂²×C₄	1	32	yes	complemented
157	C₂×C₅×D₄	C₂²×C₄	1	16	yes	complemented
158	C₂²×C₄×C₅	—	2	4	no	—
159	C₂²×C₄×C₅	—	2	4	no	—
160	C₂²×C₄×C₅	—	2	4	no	—
161	C₂²×C₄×C₅	—	2	4	no	—
162	C₂²×C₄×C₅	—	2	4	no	—
163	C₂²×C₄×C₅	—	2	2	no	—
164	C₂²×C₄×C₅	—	2	2	no	—
165	C₂²×C₄×C₅	—	2	4	no	—
166	C₂²×C₄×C₅	—	2	4	no	—
167	C₂²×C₄×C₅	—	2	4	no	—
168	C₂²×C₄×C₅	—	2	4	no	—
169	C₂²×C₄×C₅	—	2	16	no	—
170	C₂²×C₄×C₅	—	2	16	no	—
171	C₂²×C₄×C₅	—	2	4	no	—
172	C₂²×C₄×C₅	—	2	4	no	—
173	C₂²×C₄×C₅	—	2	4	no	—
174	C₂²×C₄×C₅	—	2	16	no	—
175	C₂²×C₄×C₅	—	2	16	no	—
176	C₂²×C₄×C₅	—	2	16	no	—
177	C₂²×C₄×C₅	—	4	8	no	—
178	C₂²×C₄×C₅	—	4	8	no	—
179	C₂²×C₄×C₅	—	4	4	no	—
180	C₂²×C₄×C₅	—	4	16	no	—
181	C₂²×C₄×C₅	—	4	32	no	—
182	C₂²×C₄×C₅	—	4	32	no	—
183	C₂²×C₄×C₅	C₂²×C₄	1	8	yes	—
184	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
185	C₂²×C₄×C₅	C₂×D₄	1	8	yes	—
186	C₂²×C₄×C₅	C₂×D₄	1	8	yes	—
187	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
192	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
193	C₅×C₄⋊C₄	—	2	16	no	—
194	C₅×C₄⋊C₄	—	4	4	no	—
195	C₅×C₂²⋊C₄	—	2	16	no	—
196	C₅×C₂²⋊C₄	—	2	16	no	—
197	C₅×C₂²⋊C₄	—	2	16	no	—
198	C₅×C₂²⋊C₄	—	2	16	no	—
199	C₅×C₂²⋊C₄	—	4	4	no	—
200	C₅×C₂²⋊C₄	C₂²×C₄	1	16	yes	complemented
201	C₅×C₂²⋊C₄	C₂²×C₄	1	32	yes	complemented
202	C₅×C₂²⋊C₄	C₂×D₄	1	32	yes	complemented
203	C₄²×C₅	—	2	16	no	—
204	C₄²×C₅	—	4	4	no	—
205	C₂⁶	C₂²×C₅	1	1	yes	characteristic
206	C₂³×D₄	C₂²×C₅	1	2	yes	—
207	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
208	C₂⁴×C₄	C₂²×C₅	1	2	yes	—
209	C₂⁴×C₄	C₂²×C₅	1	2	yes	—
210	C₂⁴×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
211	C₂×#120	C₄×C₅	1	16	yes	complemented
212	C₂×#120	C₂²×C₅	1	8	yes	—
213	C₂×C₄×D₄	—	2	16	no	—
214	C₂×C₄×D₄	C₂²×C₅	1	16	yes	complemented
215	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
216	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
217	C₂²×C₂²⋊C₄	—	2	16	no	—
218	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
219	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
220	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
221	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
222	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
223	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
224	C₂²×C₂²⋊C₄	C₂²×C₅	1	16	yes	complemented
225	C₂²×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
226	C₂²×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
227	C₂²×C₄²	C₂²×C₅	1	2	yes	complemented
228	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
229	#390	C₂²×C₅	1	8	yes	complemented
230	#388	C₂²×C₅	1	16	yes	complemented
231	#386	C₂²×C₅	1	8	yes	complemented
232	#386	C₂²×C₅	1	16	yes	complemented
233	#385	C₂²×C₅	1	16	yes	complemented
234	C₄×C₂²⋊C₄	C₂²×C₅	1	16	yes	complemented
235	C₂×#95	C₂²×C₅	1	2	yes	complemented
236	C₂×#95	C₂²×C₅	1	2	yes	complemented
237	C₂×#95	C₂²×C₅	1	2	yes	complemented
238	C₂³×C₅	—	2	16	no	—
239	C₂³×C₅	—	2	16	no	—
240	C₂³×C₅	—	2	16	no	—
241	C₂³×C₅	—	2	16	no	—
242	C₂³×C₅	—	2	16	no	—
243	C₂³×C₅	—	2	16	no	—
244	C₂³×C₅	—	2	4	no	—
245	C₂³×C₅	—	2	4	no	—
246	C₂³×C₅	—	2	4	no	—
247	C₂³×C₅	—	2	4	no	—
248	C₂³×C₅	—	2	16	no	—
249	C₂³×C₅	—	2	16	no	—
250	C₂³×C₅	—	2	64	no	—
251	C₂³×C₅	—	2	8	no	—
252	C₂³×C₅	—	2	8	no	—
253	C₂³×C₅	—	2	4	no	—
254	C₂³×C₅	—	2	4	no	—
255	C₂³×C₅	—	2	4	no	—
256	C₂³×C₅	—	2	4	no	—
257	C₂³×C₅	—	2	2	no	—
258	C₂³×C₅	—	2	2	no	—
259	C₂³×C₅	—	2	2	no	—
260	C₂³×C₅	—	2	2	no	—
261	C₂³×C₅	—	4	16	no	—
262	C₂³×C₅	—	4	128	no	—
263	C₂³×C₅	—	4	16	no	—
264	C₂³×C₅	—	4	32	no	—
265	C₂³×C₅	—	4	16	no	—
266	C₂³×C₅	—	4	4	no	—
267	C₂³×C₅	—	4	4	no	—
268	C₂³×C₅	—	4	8	no	—
269	C₂³×C₅	—	4	8	no	—
270	C₂³×C₅	—	4	4	no	—
271	C₂³×C₅	—	4	4	no	—
272	C₂³×C₅	C₄×D₄	1	32	yes	complemented
273	C₂³×C₅	C₂³×C₄	1	4	yes	—
274	C₂³×C₅	C₂³×C₄	1	4	yes	—
275	C₂³×C₅	C₂³×C₄	1	8	yes	—
276	C₂³×C₅	C₂³×C₄	1	2	yes	—
277	C₂³×C₅	C₂²×D₄	1	8	yes	—
278	C₂³×C₅	C₂²×D₄	1	4	yes	—
279	C₂³×C₅	C₂×#41	1	8	yes	—
280	C₂³×C₅	C₂×#41	1	4	yes	—
281	C₂³×C₅	H(5,𝔽₂)	1	2	yes	—
282	C₂³×C₅	H(5,𝔽₂)	1	2	yes	—
283	C₂³×C₅	C₂⁵	1	1	yes	characteristic
284	C₅×D₄	—	2	64	no	—
285	C₅×D₄	—	4	16	no	—
286	C₂×C₄×C₅	—	2	16	no	—
287	C₂×C₄×C₅	—	2	8	no	—
288	C₂×C₄×C₅	—	2	16	no	—
289	C₂×C₄×C₅	—	2	16	no	—
290	C₂×C₄×C₅	—	2	4	no	—
291	C₂×C₄×C₅	—	2	4	no	—
292	C₂×C₄×C₅	—	2	4	no	—
293	C₂×C₄×C₅	—	2	4	no	—
294	C₂×C₄×C₅	—	2	4	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	—	2	4	no	—
298	C₂×C₄×C₅	—	2	4	no	—
299	C₂×C₄×C₅	—	2	4	no	—
300	C₂×C₄×C₅	—	2	4	no	—
301	C₂×C₄×C₅	—	2	4	no	—
302	C₂×C₄×C₅	—	2	4	no	—
303	C₂×C₄×C₅	—	2	4	no	—
304	C₂×C₄×C₅	—	4	16	no	—
305	C₂×C₄×C₅	—	4	32	no	—
306	C₂×C₄×C₅	—	4	32	no	—
307	C₂×C₄×C₅	—	4	8	no	—
308	C₂×C₄×C₅	—	4	8	no	—
309	C₂×C₄×C₅	C₂³×C₄	1	8	yes	—
310	C₂×C₄×C₅	C₂³×C₄	1	4	yes	—
311	C₂×C₄×C₅	C₂²×D₄	1	8	yes	—
312	C₂×C₄×C₅	C₂²×D₄	1	8	yes	—
313	C₂⁵	—	2	8	no	—
314	C₂⁵	—	2	8	no	—
315	C₂⁵	—	4	2	no	—
316	C₂⁵	—	4	2	no	—
317	C₂⁵	C₂×C₄×C₅	1	8	yes	complemented
318	C₂⁵	C₂³×C₅	1	1	yes	characteristic
319	C₂⁵	C₂³×C₅	1	1	yes	characteristic
320	C₂⁵	C₂³×C₅	1	4	yes	—
321	C₂⁵	C₂³×C₅	1	2	yes	—
322	C₂²×D₄	—	2	8	no	—
323	C₂²×D₄	—	2	8	no	—
324	C₂²×D₄	—	4	2	no	—
325	C₂²×D₄	—	4	2	no	—
326	C₂²×D₄	C₂×C₄×C₅	1	16	yes	complemented
327	C₂²×D₄	C₂×C₄×C₅	1	8	yes	complemented
328	C₂²×D₄	C₂³×C₅	1	8	yes	—
329	C₂²×D₄	C₂³×C₅	1	4	yes	—
330	C₂³×C₄	—	2	8	no	—
331	C₂³×C₄	—	2	8	no	—
332	C₂³×C₄	—	2	8	no	—
333	C₂³×C₄	—	2	8	no	—
334	C₂³×C₄	—	2	8	no	—
335	C₂³×C₄	—	4	4	no	—
336	C₂³×C₄	—	4	4	no	—
337	C₂³×C₄	—	4	2	no	—
338	C₂³×C₄	C₂³×C₅	1	2	yes	—
339	C₂³×C₄	C₂³×C₅	1	2	yes	—
340	C₂³×C₄	C₂³×C₅	1	8	yes	—
341	C₂³×C₄	C₂³×C₅	1	8	yes	—
342	C₂³×C₄	C₂³×C₅	1	2	yes	—
343	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
344	C₂³×C₄	C₂³×C₅	1	2	yes	—
345	C₂³×C₄	C₂³×C₅	1	2	yes	—
346	C₂³×C₄	C₂³×C₅	1	4	yes	complemented
347	#120	C₂×C₄×C₅	1	64	yes	complemented
348	C₄×D₄	—	2	64	no	—
349	C₂×C₄⋊C₄	—	2	8	no	—
350	C₂×C₄⋊C₄	—	4	2	no	—
351	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	complemented
352	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	complemented
353	C₂×C₂²⋊C₄	—	2	8	no	—
354	C₂×C₂²⋊C₄	—	2	8	no	—
355	C₂×C₂²⋊C₄	—	2	8	no	—
356	C₂×C₂²⋊C₄	—	2	8	no	—
357	C₂×C₂²⋊C₄	—	2	64	no	—
358	C₂×C₂²⋊C₄	—	4	2	no	—
359	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
360	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
361	C₂×C₂²⋊C₄	C₅×D₄	1	16	yes	complemented
362	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
363	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
364	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
365	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
366	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
367	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
368	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	complemented
369	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	complemented
370	C₂×C₄²	—	2	8	no	—
371	C₂×C₄²	—	4	2	no	—
372	C₂×C₄²	C₂³×C₅	1	8	yes	complemented
373	C₂×C₄²	C₂³×C₅	1	4	yes	complemented
374	#95	C₂³×C₅	1	8	yes	complemented
375	#95	C₂³×C₅	1	8	yes	complemented
376	#95	C₂³×C₅	1	8	yes	complemented
377	C₂²×C₅	—	2	64	no	—
378	C₂²×C₅	—	2	8	no	—
379	C₂²×C₅	—	2	8	no	—
380	C₂²×C₅	—	2	8	no	—
381	C₂²×C₅	—	2	8	no	—
382	C₂²×C₅	—	2	8	no	—
383	C₂²×C₅	—	2	8	no	—
384	C₂²×C₅	—	2	8	no	—
385	C₂²×C₅	—	2	8	no	—
386	C₂²×C₅	—	2	4	no	—
387	C₂²×C₅	—	2	4	no	—
388	C₂²×C₅	—	4	64	no	—
389	C₂²×C₅	—	4	16	no	—
390	C₂²×C₅	—	4	16	no	—
391	C₂²×C₅	—	4	2	no	—
392	C₂²×C₅	—	4	2	no	—
393	C₂²×C₅	—	4	4	no	—
394	C₂²×C₅	—	4	4	no	—
395	C₂²×C₅	—	4	2	no	—
396	C₂²×C₅	—	4	2	no	—
397	C₂²×C₅	C₂×C₄×D₄	1	8	yes	—
398	C₂²×C₅	C₂×C₄×D₄	1	16	yes	complemented
399	C₂²×C₅	#518	1	4	yes	—
400	C₂²×C₅	D₄²	1	4	yes	—
401	C₂²×C₅	#546	1	8	yes	—
402	C₂²×C₅	#551	1	4	yes	—
403	C₂²×C₅	C₂⁴×C₄	1	1	yes	characteristic
404	C₂²×C₅	C₂³×D₄	1	2	yes	—
405	C₂²×C₅	C₂²×#41	1	2	yes	—
406	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
407	C₂²×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
408	C₄×C₅	—	2	8	no	—
409	C₄×C₅	—	2	4	no	—
410	C₄×C₅	—	2	8	no	—
411	C₄×C₅	—	2	8	no	—
412	C₄×C₅	—	4	4	no	—
413	C₄×C₅	—	4	4	no	—
414	C₂⁴	—	2	4	no	—
415	C₂⁴	—	2	4	no	—
416	C₂⁴	—	2	4	no	—
417	C₂⁴	—	2	4	no	—
418	C₂⁴	—	2	64	no	—
419	C₂⁴	—	2	16	no	—
420	C₂⁴	—	2	4	no	—
421	C₂⁴	—	2	4	no	—
422	C₂⁴	—	2	4	no	—
423	C₂⁴	—	2	16	no	—
424	C₂⁴	—	2	4	no	—
425	C₂⁴	—	2	2	no	—
426	C₂⁴	—	2	2	no	—
427	C₂⁴	—	2	2	no	—
428	C₂⁴	—	2	2	no	—
429	C₂⁴	—	4	16	no	—
430	C₂⁴	—	4	4	no	—
431	C₂⁴	—	4	4	no	—
432	C₂⁴	—	4	16	no	—
433	C₂⁴	—	4	32	no	—
434	C₂⁴	—	4	16	no	—
435	C₂⁴	C₂²×C₄×C₅	1	4	yes	—
436	C₂⁴	C₂²×C₄×C₅	1	4	yes	—
437	C₂⁴	C₂²×C₄×C₅	1	8	yes	—
438	C₂⁴	C₂²×C₄×C₅	1	16	yes	complemented
439	C₂⁴	C₂×C₅×D₄	1	8	yes	—
440	C₂⁴	C₅×#41	1	8	yes	—
441	C₂⁴	C₂⁴×C₅	1	2	yes	—
442	C₂⁴	C₂⁴×C₅	1	2	yes	—
443	C₂⁴	C₂⁴×C₅	1	4	yes	—
444	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
445	C₂×D₄	—	2	64	no	—
446	C₂×D₄	—	2	16	no	—
447	C₂×D₄	—	2	16	no	—
448	C₂×D₄	—	4	16	no	—
449	C₂×D₄	—	4	4	no	—
450	C₂×D₄	—	4	4	no	—
451	C₂×D₄	C₂²×C₄×C₅	1	32	yes	complemented
452	C₂×D₄	C₂²×C₄×C₅	1	16	yes	complemented
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	2	4	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	2	16	no	—
465	C₂²×C₄	—	2	16	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	2	16	no	—
470	C₂²×C₄	—	2	16	no	—
471	C₂²×C₄	—	2	16	no	—
472	C₂²×C₄	—	4	8	no	—
473	C₂²×C₄	—	4	8	no	—
474	C₂²×C₄	—	4	4	no	—
475	C₂²×C₄	—	4	16	no	—
476	C₂²×C₄	—	4	32	no	—
477	C₂²×C₄	—	4	32	no	—
478	C₂²×C₄	C₂²×C₄×C₅	1	8	yes	—
479	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
480	C₂²×C₄	C₂×C₅×D₄	1	8	yes	—
481	C₂²×C₄	C₂×C₅×D₄	1	8	yes	—
482	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
483	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
484	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
485	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
486	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
487	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
488	C₄⋊C₄	—	2	16	no	—
489	C₄⋊C₄	—	4	4	no	—
490	C₂²⋊C₄	—	2	16	no	—
491	C₂²⋊C₄	—	2	16	no	—
492	C₂²⋊C₄	—	2	16	no	—
493	C₂²⋊C₄	—	2	16	no	—
494	C₂²⋊C₄	—	4	4	no	—
495	C₂²⋊C₄	C₂²×C₄×C₅	1	16	yes	complemented
496	C₂²⋊C₄	C₂²×C₄×C₅	1	32	yes	complemented
497	C₂²⋊C₄	C₂×C₅×D₄	1	32	yes	complemented
498	C₄²	—	2	16	no	—
499	C₄²	—	4	4	no	—
500	C₂×C₅	—	2	16	no	—
501	C₂×C₅	—	4	4	no	—
502	C₂×C₅	—	4	4	no	—
503	C₂×C₅	#2358	1	8	yes	direct product factor
504	C₂×C₅	C₂²×C₄×D₄	1	2	yes	—
505	C₂×C₅	C₂×#518	1	1	yes	characteristic
506	C₂×C₅	C₂×D₄²	1	1	yes	characteristic
507	C₂×C₅	C₂×#546	1	2	yes	—
508	C₂×C₅	C₂×#551	1	1	yes	characteristic
509	C₂³	—	2	16	no	—
510	C₂³	—	2	16	no	—
511	C₂³	—	2	16	no	—
512	C₂³	—	2	16	no	—
513	C₂³	—	2	16	no	—
514	C₂³	—	2	16	no	—
515	C₂³	—	2	4	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	4	no	—
518	C₂³	—	2	4	no	—
519	C₂³	—	2	16	no	—
520	C₂³	—	2	16	no	—
521	C₂³	—	2	64	no	—
522	C₂³	—	2	8	no	—
523	C₂³	—	2	8	no	—
524	C₂³	—	2	4	no	—
525	C₂³	—	2	4	no	—
526	C₂³	—	2	4	no	—
527	C₂³	—	2	4	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	2	2	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	4	16	no	—
533	C₂³	—	4	16	no	—
534	C₂³	—	4	32	no	—
535	C₂³	—	4	16	no	—
536	C₂³	—	4	128	no	—
537	C₂³	—	4	4	no	—
538	C₂³	—	4	4	no	—
539	C₂³	—	4	8	no	—
540	C₂³	—	4	8	no	—
541	C₂³	—	4	4	no	—
542	C₂³	—	4	4	no	—
543	C₂³	C₄×C₅×D₄	1	32	yes	complemented
544	C₂³	C₂³×C₄×C₅	1	4	yes	—
545	C₂³	C₂³×C₄×C₅	1	4	yes	—
546	C₂³	C₂³×C₄×C₅	1	8	yes	—
547	C₂³	C₂³×C₄×C₅	1	2	yes	—
548	C₂³	C₂²×C₅×D₄	1	8	yes	—
549	C₂³	C₂²×C₅×D₄	1	4	yes	—
550	C₂³	C₂×C₅×#41	1	8	yes	—
551	C₂³	C₂×C₅×#41	1	4	yes	—
552	C₂³	C₅×H(5,𝔽₂)	1	2	yes	—
553	C₂³	C₅×H(5,𝔽₂)	1	2	yes	—
554	C₂³	C₂⁵×C₅	1	1	yes	characteristic
555	D₄	—	2	64	no	—
556	D₄	—	4	16	no	—
557	C₂×C₄	—	2	16	no	—
558	C₂×C₄	—	2	8	no	—
559	C₂×C₄	—	2	16	no	—
560	C₂×C₄	—	2	16	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	4	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	4	16	no	—
576	C₂×C₄	—	4	32	no	—
577	C₂×C₄	—	4	32	no	—
578	C₂×C₄	—	4	8	no	—
579	C₂×C₄	—	4	8	no	—
580	C₂×C₄	C₂³×C₄×C₅	1	8	yes	—
581	C₂×C₄	C₂³×C₄×C₅	1	4	yes	—
582	C₂×C₄	C₂²×C₅×D₄	1	8	yes	—
583	C₂×C₄	C₂²×C₅×D₄	1	8	yes	—
584	C₅	C₂×#2358	1	1	yes	characteristic, direct product factor, Sylow
585	C₂²	—	2	8	no	—
586	C₂²	—	2	8	no	—
587	C₂²	—	2	8	no	—
588	C₂²	—	2	8	no	—
589	C₂²	—	2	8	no	—
590	C₂²	—	2	8	no	—
591	C₂²	—	2	64	no	—
592	C₂²	—	2	8	no	—
593	C₂²	—	2	8	no	—
594	C₂²	—	2	4	no	—
595	C₂²	—	2	4	no	—
596	C₂²	—	4	64	no	—
597	C₂²	—	4	2	no	—
598	C₂²	—	4	2	no	—
599	C₂²	—	4	4	no	—
600	C₂²	—	4	4	no	—
601	C₂²	—	4	2	no	—
602	C₂²	—	4	2	no	—
603	C₂²	—	4	16	no	—
604	C₂²	—	4	16	no	—
605	C₂²	C₂×C₄×C₅×D₄	1	8	yes	—
606	C₂²	C₂×C₄×C₅×D₄	1	16	yes	complemented
607	C₂²	C₅×#518	1	4	yes	—
608	C₂²	C₅×D₄²	1	4	yes	—
609	C₂²	C₅×#546	1	8	yes	—
610	C₂²	C₅×#551	1	4	yes	—
611	C₂²	C₂⁴×C₄×C₅	1	1	yes	characteristic
612	C₂²	C₂³×C₅×D₄	1	2	yes	—
613	C₂²	C₂²×C₅×#41	1	2	yes	—
614	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
615	C₂²	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
616	C₄	—	2	8	no	—
617	C₄	—	2	4	no	—
618	C₄	—	2	8	no	—
619	C₄	—	2	8	no	—
620	C₄	—	4	4	no	—
621	C₄	—	4	4	no	—
622	C₂	—	2	16	no	—
623	C₂	—	4	4	no	—
624	C₂	—	4	4	no	—
625	C₂	C₅×#2358	1	8	yes	direct product factor
626	C₂	C₂²×C₄×C₅×D₄	1	2	yes	—
627	C₂	C₂×C₅×#518	1	1	yes	characteristic
628	C₂	C₂×C₅×D₄²	1	1	yes	characteristic
629	C₂	C₂×C₅×#546	1	2	yes	—
630	C₂	C₂×C₅×#551	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₅	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₅
Frattini, cosocle	C₂³	C₂⁵×C₅
prime radical	C₂²×C₅×#120	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₅×D₄	C₂	semidirect
3. C₂³×C₅×C₂²⋊C₄	C₂	semidirect
4. C₅×#2358	C₂	direct (N × H)
5. C₂×C₅×#390	C₂	semidirect
6. C₂×C₅×#388	C₂	semidirect
7. C₂×C₅×#386	C₂	semidirect
8. C₂×C₅×#386	C₂	semidirect
9. C₂×C₅×#385	C₂	semidirect
10. C₂×C₄×C₅×C₂²⋊C₄	C₂	semidirect
16. C₂⁴×C₄×C₅	C₂²	semidirect
17. C₂×C₅×#120	C₄	semidirect
20. C₂×C₄×C₅×D₄	C₂²	semidirect
21. C₂²×C₅×C₄⋊C₄	C₂²	semidirect
22. C₂²×C₅×C₄⋊C₄	C₂²	semidirect
30. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
31. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
32. C₂²×C₅×C₂²⋊C₄	C₂²	semidirect
33. C₂²×C₄²×C₅	C₂²	semidirect
34. C₂²×C₄²×C₅	C₂²	semidirect
35. C₅×#390	C₂²	semidirect
36. C₅×#388	C₂²	semidirect
37. C₅×#386	C₂²	semidirect
38. C₅×#386	C₂²	semidirect
39. C₅×#385	C₂²	semidirect
40. C₄×C₅×C₂²⋊C₄	C₂²	semidirect
41. C₂×C₅×#95	C₂²	semidirect
42. C₂×C₅×#95	C₂²	semidirect
43. C₂×C₅×#95	C₂²	semidirect
44. C₂×#2358	C₅	direct (N × H)
49. C₂⁵×C₅	C₂×C₄	semidirect
58. C₂²×C₅×D₄	C₂×C₄	semidirect
59. C₂²×C₅×D₄	C₂×C₄	semidirect
78. C₂³×C₄×C₅	C₂³	semidirect
79. C₅×#120	C₂×C₄	semidirect
83. C₂×C₅×C₄⋊C₄	C₂³	semidirect
84. C₂×C₅×C₄⋊C₄	C₂³	semidirect
91. C₂×C₅×C₂²⋊C₄	C₂×C₄	semidirect
92. C₂×C₅×C₂²⋊C₄	C₂×C₄	semidirect
93. C₂×C₅×C₂²⋊C₄	D₄	semidirect
100. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
101. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
104. C₂×C₄²×C₅	C₂³	semidirect
105. C₂×C₄²×C₅	C₂³	semidirect
106. C₅×#95	C₂³	semidirect
107. C₅×#95	C₂³	semidirect
108. C₅×#95	C₂³	semidirect
110. C₂²×C₄×D₄	C₂×C₅	semidirect
111. C₂³×C₂²⋊C₄	C₂×C₅	semidirect
112. #2358	C₂×C₅	direct (N × H)
113. C₂×#390	C₂×C₅	semidirect
114. C₂×#388	C₂×C₅	semidirect
115. C₂×#386	C₂×C₅	semidirect
116. C₂×#386	C₂×C₅	semidirect
117. C₂×#385	C₂×C₅	semidirect
118. C₂×C₄×C₂²⋊C₄	C₂×C₅	semidirect
143. C₂⁴×C₅	C₂²×C₄	semidirect
156. C₂×C₅×D₄	C₂²×C₄	semidirect
157. C₂×C₅×D₄	C₂²×C₄	semidirect
200. C₅×C₂²⋊C₄	C₂²×C₄	semidirect
201. C₅×C₂²⋊C₄	C₂²×C₄	semidirect
202. C₅×C₂²⋊C₄	C₂×D₄	semidirect
210. C₂⁴×C₄	C₂²×C₅	semidirect
211. C₂×#120	C₄×C₅	semidirect
214. C₂×C₄×D₄	C₂²×C₅	semidirect
215. C₂²×C₄⋊C₄	C₂²×C₅	semidirect
216. C₂²×C₄⋊C₄	C₂²×C₅	semidirect
224. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
225. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
226. C₂²×C₂²⋊C₄	C₂²×C₅	semidirect
227. C₂²×C₄²	C₂²×C₅	semidirect
228. C₂²×C₄²	C₂²×C₅	semidirect
229. #390	C₂²×C₅	semidirect
230. #388	C₂²×C₅	semidirect
231. #386	C₂²×C₅	semidirect
232. #386	C₂²×C₅	semidirect
233. #385	C₂²×C₅	semidirect
234. C₄×C₂²⋊C₄	C₂²×C₅	semidirect
235. C₂×#95	C₂²×C₅	semidirect
236. C₂×#95	C₂²×C₅	semidirect
237. C₂×#95	C₂²×C₅	semidirect
272. C₂³×C₅	C₄×D₄	semidirect
317. C₂⁵	C₂×C₄×C₅	semidirect
326. C₂²×D₄	C₂×C₄×C₅	semidirect
327. C₂²×D₄	C₂×C₄×C₅	semidirect
346. C₂³×C₄	C₂³×C₅	semidirect
347. #120	C₂×C₄×C₅	semidirect
351. C₂×C₄⋊C₄	C₂³×C₅	semidirect
352. C₂×C₄⋊C₄	C₂³×C₅	semidirect
359. C₂×C₂²⋊C₄	C₂×C₄×C₅	semidirect
360. C₂×C₂²⋊C₄	C₂×C₄×C₅	semidirect
361. C₂×C₂²⋊C₄	C₅×D₄	semidirect
368. C₂×C₂²⋊C₄	C₂³×C₅	semidirect
369. C₂×C₂²⋊C₄	C₂³×C₅	semidirect
372. C₂×C₄²	C₂³×C₅	semidirect
373. C₂×C₄²	C₂³×C₅	semidirect
374. #95	C₂³×C₅	semidirect
375. #95	C₂³×C₅	semidirect
376. #95	C₂³×C₅	semidirect
398. C₂²×C₅	C₂×C₄×D₄	semidirect
438. C₂⁴	C₂²×C₄×C₅	semidirect
451. C₂×D₄	C₂²×C₄×C₅	semidirect
452. C₂×D₄	C₂²×C₄×C₅	semidirect
495. C₂²⋊C₄	C₂²×C₄×C₅	semidirect
496. C₂²⋊C₄	C₂²×C₄×C₅	semidirect
497. C₂²⋊C₄	C₂×C₅×D₄	semidirect
503. C₂×C₅	#2358	direct (N × H)
543. C₂³	C₄×C₅×D₄	semidirect
584. C₅	C₂×#2358	direct (N × H)
606. C₂²	C₂×C₄×C₅×D₄	semidirect
625. C₂	C₅×#2358	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#120	2
C₂²×C₄×C₅×D₄	2
C₂³×C₅×C₂²⋊C₄	2
C₅×#2358	2
C₂×C₅×#390	2
C₂×C₅×#388	2
C₂×C₅×#386	2
C₂×C₅×#385	2
C₂×C₄×C₅×C₂²⋊C₄	2
C₂×#2358	5

Subgroups — C2×C5×#2358 #11956850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#2358 #11956850