Subgroups — C₂×C₅×#3507 #11985497

Order 1280.

7130 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3507	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₅×#559	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#557	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#556	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#556	C₂	1	4	yes	maximal, complemented
6	C₂×C₅×#554	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#552	C₂	1	4	yes	maximal, complemented
8	C₂×C₅×#539	C₂	1	4	yes	maximal, complemented
9	C₂×C₅×#536	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#532	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×#529	C₂	1	4	yes	maximal, complemented
13	C₂×C₅×#520	C₂	1	2	yes	maximal, complemented
14	C₂²×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₅×#41	C₂²	1	2	yes	—
16	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₅×#559	C₂²	1	32	yes	complemented
18	C₅×#557	C₂²	1	32	yes	complemented
19	C₅×#556	C₂²	1	32	yes	complemented
20	C₅×#556	C₂²	1	64	yes	complemented
21	C₅×#554	C₂²	1	32	yes	complemented
22	C₅×#552	C₂²	1	64	yes	complemented
23	C₅×#539	C₂²	1	64	yes	complemented
24	C₅×#536	C₂²	1	32	yes	complemented
25	C₅×#533	C₂²	1	16	yes	complemented
26	C₅×#532	C₂²	1	16	yes	—
27	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
31	C₂×C₅×#127	C₂²	1	1	yes	characteristic
32	C₅×#529	C₂²	1	64	yes	complemented
33	C₂×C₅×#126	C₂²	1	8	yes	—
34	C₂×C₅×#126	C₂²	1	8	yes	—
35	C₂×C₅×#125	C₂²	1	4	yes	—
36	C₂×C₅×#125	C₂²	1	2	yes	—
37	C₂×C₅×#125	C₂²	1	8	yes	—
38	C₂×C₅×#124	C₂²	1	4	yes	—
39	C₂×C₅×#124	C₂²	1	2	yes	—
40	C₂×C₅×#124	C₂²	1	4	yes	—
41	C₂×C₅×#123	C₂²	1	8	yes	—
42	C₂×C₅×#123	C₂²	1	8	yes	—
43	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
44	C₂×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
45	C₂×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
46	C₂×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
47	C₂×C₅×C₂²⋊Q₈	C₂²	1	8	yes	—
48	C₂×C₅×#121	C₂²	1	2	yes	—
49	C₂×C₅×#121	C₂²	1	2	yes	—
50	C₅×#520	C₂²	1	32	yes	complemented
51	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
52	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
53	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
54	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
55	C₂×C₄×C₅×Q₈	C₂²	1	4	yes	—
56	C₂×C₄×C₅×Q₈	C₂²	1	4	yes	—
57	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
58	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
59	C₂×C₄×C₅×Q₈	C₂²	1	16	yes	complemented
60	C₂×C₄×C₅×D₄	C₂²	1	8	yes	—
61	C₂×C₄×C₅×D₄	C₂²	1	4	yes	—
62	C₂×C₄×C₅×D₄	C₂²	1	4	yes	—
63	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
64	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
65	C₂×C₅×#117	C₂²	1	2	yes	—
66	C₂×C₅×#117	C₂²	1	4	yes	—
67	C₂×C₅×#117	C₂²	1	8	yes	—
68	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
69	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
70	C₂²×C₅×C₄⋊C₄	C₂²	1	4	yes	—
71	C₂²×C₄²×C₅	C₂²	1	2	yes	—
72	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
73	C₂×#3507	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₂×C₅×#41	—	2	16	no	—
75	C₂×C₅×#41	C₂³	1	16	yes	—
76	C₂²×C₅×Q₈	—	2	8	no	—
77	C₂²×C₅×Q₈	C₂³	1	2	yes	—
78	C₂²×C₅×Q₈	C₂³	1	2	yes	—
79	C₂²×C₅×Q₈	C₂³	1	2	yes	—
80	C₂²×C₅×Q₈	C₂³	1	2	yes	—
81	C₂²×C₅×Q₈	C₂³	1	8	yes	—
82	C₂²×C₅×Q₈	C₂³	1	2	yes	—
83	C₂²×C₅×D₄	C₂³	1	2	yes	—
84	C₂²×C₅×D₄	C₂³	1	4	yes	—
85	C₂²×C₅×D₄	C₂³	1	2	yes	—
86	C₂²×C₅×D₄	C₂³	1	2	yes	—
87	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₅	C₂³	1	2	yes	—
89	C₂³×C₄×C₅	C₂³	1	4	yes	—
90	C₂³×C₄×C₅	C₂³	1	2	yes	—
91	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₅	C₂³	1	8	yes	—
93	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
94	C₅×C₄⋊Q₈	C₂³	1	8	yes	—
95	C₅×C₄⋊Q₈	C₂³	1	8	yes	—
96	C₅×C₄⋊Q₈	C₂³	1	8	yes	—
97	C₅×C₄⋊Q₈	C₂³	1	32	yes	—
98	C₅×#127	C₂³	1	8	yes	—
99	C₅×#126	C₂³	1	64	yes	—
100	C₅×#126	C₂³	1	64	yes	—
101	C₅×#125	C₂³	1	32	yes	—
102	C₅×#125	C₂³	1	16	yes	—
103	C₅×#125	C₂³	1	64	yes	—
104	C₅×#124	C₂³	1	32	yes	—
105	C₅×#124	C₂³	1	16	yes	—
106	C₅×#124	C₂³	1	32	yes	—
107	C₅×#123	C₂³	1	64	yes	—
108	C₅×#123	C₂³	1	64	yes	—
109	C₅×C₂²⋊Q₈	C₂³	1	16	yes	—
110	C₅×C₂²⋊Q₈	C₂³	1	16	yes	—
111	C₅×C₂²⋊Q₈	C₂³	1	32	yes	—
112	C₅×C₂²⋊Q₈	C₂³	1	32	yes	—
113	C₅×C₂²⋊Q₈	C₂³	1	64	yes	—
114	C₅×#121	C₂³	1	16	yes	—
115	C₅×#121	C₂³	1	16	yes	—
116	C₄×C₅×Q₈	C₂³	1	16	yes	—
117	C₄×C₅×Q₈	C₂³	1	16	yes	—
118	C₄×C₅×Q₈	C₂³	1	16	yes	—
119	C₄×C₅×Q₈	C₂³	1	16	yes	—
120	C₄×C₅×Q₈	C₂³	1	32	yes	—
121	C₄×C₅×Q₈	C₂³	1	32	yes	—
122	C₄×C₅×Q₈	C₂³	1	16	yes	—
123	C₄×C₅×Q₈	C₂³	1	16	yes	—
124	C₄×C₅×D₄	C₂³	1	64	yes	—
125	C₄×C₅×D₄	C₂³	1	32	yes	—
126	C₄×C₅×D₄	C₂³	1	32	yes	—
127	C₄×C₅×D₄	C₂³	1	16	yes	—
128	C₄×C₅×D₄	C₂³	1	16	yes	—
129	C₅×#117	C₂³	1	16	yes	—
130	C₅×#117	C₂³	1	32	yes	—
131	C₅×#117	C₂³	1	64	yes	—
132	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
133	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
135	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
136	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
137	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
138	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
139	C₂×C₅×C₄⋊C₄	C₂³	1	16	yes	—
140	C₂×C₅×C₄⋊C₄	C₂³	1	32	yes	—
141	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
143	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
144	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
148	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
149	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
151	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
152	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
153	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
154	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
155	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
156	C₂×C₄²×C₅	C₂³	1	4	yes	—
157	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
158	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₅	C₂³	1	4	yes	—
160	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₅	C₂³	1	16	yes	—
163	C₂×C₄²×C₅	C₂³	1	8	yes	—
164	C₂×C₄²×C₅	C₂³	1	8	yes	—
165	C₂×C₄²×C₅	C₂³	1	4	yes	—
166	#3507	C₂×C₅	1	32	yes	direct product factor
167	C₂×#559	C₂×C₅	1	2	yes	complemented
168	C₂×#557	C₂×C₅	1	2	yes	complemented
169	C₂×#556	C₂×C₅	1	2	yes	complemented
170	C₂×#556	C₂×C₅	1	4	yes	complemented
171	C₂×#554	C₂×C₅	1	2	yes	complemented
172	C₂×#552	C₂×C₅	1	4	yes	complemented
173	C₂×#539	C₂×C₅	1	4	yes	complemented
174	C₂×#536	C₂×C₅	1	2	yes	complemented
175	C₂×#533	C₂×C₅	1	1	yes	characteristic, complemented
176	C₂×#532	C₂×C₅	1	1	yes	characteristic
177	C₂×#529	C₂×C₅	1	4	yes	complemented
178	C₂×#520	C₂×C₅	1	2	yes	complemented
179	C₂²×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
180	C₂⁴×C₅	C₂⁴	1	4	yes	—
181	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
182	C₅×#41	—	2	64	no	—
183	C₂×C₅×Q₈	—	2	8	no	—
184	C₂×C₅×Q₈	—	2	8	no	—
185	C₂×C₅×Q₈	—	2	32	no	—
186	C₂×C₅×Q₈	—	2	8	no	—
187	C₂×C₅×Q₈	—	2	8	no	—
188	C₂×C₅×Q₈	—	4	4	no	—
189	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
190	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
191	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
192	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
193	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
194	C₂×C₅×D₄	—	2	16	no	—
195	C₂×C₅×D₄	—	2	8	no	—
196	C₂×C₅×D₄	—	2	8	no	—
197	C₂×C₅×D₄	—	4	4	no	—
198	C₂×C₅×D₄	C₂⁴	1	8	yes	—
199	C₂×C₅×D₄	C₂⁴	1	16	yes	—
200	C₂×C₅×D₄	C₂⁴	1	8	yes	—
201	C₂×C₅×D₄	C₂⁴	1	8	yes	—
202	C₂²×C₄×C₅	—	2	8	no	—
203	C₂²×C₄×C₅	—	2	16	no	—
204	C₂²×C₄×C₅	—	2	4	no	—
205	C₂²×C₄×C₅	—	4	4	no	—
206	C₂²×C₄×C₅	—	4	16	no	—
207	C₂²×C₄×C₅	—	4	2	no	—
208	C₂²×C₄×C₅	#41	1	8	yes	—
209	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
210	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
211	C₂²×C₄×C₅	C₂⁴	1	16	yes	—
212	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
213	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
214	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
215	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
216	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
217	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
218	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
219	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
220	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
221	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
222	C₂²×C₄×C₅	C₂⁴	1	32	yes	—
223	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
224	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
227	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
228	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
229	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
230	C₅×C₄⋊C₄	C₂⁴	1	32	yes	—
231	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
232	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
233	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
234	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
235	C₅×C₄⋊C₄	C₂⁴	1	32	yes	—
236	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
237	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
238	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
239	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
240	C₅×C₄⋊C₄	C₂⁴	1	32	yes	—
241	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
242	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
243	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
244	C₅×C₂²⋊C₄	C₂⁴	1	32	yes	—
245	C₅×C₂²⋊C₄	C₂⁴	1	32	yes	—
246	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
247	C₅×C₂²⋊C₄	C₂⁴	1	32	yes	—
248	C₄²×C₅	C₂⁴	1	16	yes	—
249	C₄²×C₅	C₂⁴	1	4	yes	—
250	C₄²×C₅	C₂⁴	1	4	yes	—
251	C₄²×C₅	C₂⁴	1	16	yes	—
252	C₄²×C₅	C₂⁴	1	4	yes	—
253	C₄²×C₅	C₂⁴	1	4	yes	—
254	C₄²×C₅	C₂⁴	1	32	yes	—
255	C₄²×C₅	C₂⁴	1	16	yes	—
256	C₂²×#41	C₂²×C₅	1	2	yes	—
257	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic
258	#559	C₂²×C₅	1	32	yes	complemented
259	#557	C₂²×C₅	1	32	yes	complemented
260	#556	C₂²×C₅	1	32	yes	complemented
261	#556	C₂²×C₅	1	64	yes	complemented
262	#554	C₂²×C₅	1	32	yes	complemented
263	#552	C₂²×C₅	1	64	yes	complemented
264	#539	C₂²×C₅	1	64	yes	complemented
265	#536	C₂²×C₅	1	32	yes	complemented
266	#533	C₂²×C₅	1	16	yes	complemented
267	#532	C₂²×C₅	1	16	yes	—
268	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
269	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
270	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
271	C₂×C₄⋊Q₈	C₂²×C₅	1	4	yes	—
272	C₂×#127	C₂²×C₅	1	1	yes	characteristic
273	#529	C₂²×C₅	1	64	yes	complemented
274	C₂×#126	C₂²×C₅	1	8	yes	—
275	C₂×#126	C₂²×C₅	1	8	yes	—
276	C₂×#125	C₂²×C₅	1	4	yes	—
277	C₂×#125	C₂²×C₅	1	2	yes	—
278	C₂×#125	C₂²×C₅	1	8	yes	—
279	C₂×#124	C₂²×C₅	1	4	yes	—
280	C₂×#124	C₂²×C₅	1	2	yes	—
281	C₂×#124	C₂²×C₅	1	4	yes	—
282	C₂×#123	C₂²×C₅	1	8	yes	—
283	C₂×#123	C₂²×C₅	1	8	yes	—
284	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
285	C₂×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
286	C₂×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
287	C₂×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
288	C₂×C₂²⋊Q₈	C₂²×C₅	1	8	yes	—
289	C₂×#121	C₂²×C₅	1	2	yes	—
290	C₂×#121	C₂²×C₅	1	2	yes	—
291	#520	C₂²×C₅	1	32	yes	complemented
292	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
293	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
294	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
295	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
296	C₂×C₄×Q₈	C₂²×C₅	1	4	yes	—
297	C₂×C₄×Q₈	C₂²×C₅	1	4	yes	—
298	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
299	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
300	C₂×C₄×Q₈	C₂²×C₅	1	16	yes	complemented
301	C₂×C₄×D₄	C₂²×C₅	1	8	yes	—
302	C₂×C₄×D₄	C₂²×C₅	1	4	yes	—
303	C₂×C₄×D₄	C₂²×C₅	1	4	yes	—
304	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
305	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
306	C₂×#117	C₂²×C₅	1	2	yes	—
307	C₂×#117	C₂²×C₅	1	4	yes	—
308	C₂×#117	C₂²×C₅	1	8	yes	—
309	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
310	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
311	C₂²×C₄⋊C₄	C₂²×C₅	1	4	yes	—
312	C₂²×C₄²	C₂²×C₅	1	2	yes	—
313	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
314	C₂³×C₅	—	2	2	no	—
315	C₂³×C₅	—	2	2	no	—
316	C₂³×C₅	—	2	8	no	—
317	C₂³×C₅	—	2	8	no	—
318	C₂³×C₅	—	2	8	no	—
319	C₂³×C₅	C₂×#41	1	4	yes	—
320	C₂³×C₅	C₂⁵	1	8	yes	—
321	C₂³×C₅	C₂⁵	1	2	yes	—
322	C₂³×C₅	C₂⁵	1	1	yes	characteristic
323	C₅×Q₈	—	2	16	no	—
324	C₅×Q₈	—	2	16	no	—
325	C₅×Q₈	—	2	16	no	—
326	C₅×Q₈	—	2	16	no	—
327	C₅×Q₈	—	4	8	no	—
328	C₅×D₄	—	2	32	no	—
329	C₅×D₄	—	2	16	no	—
330	C₅×D₄	—	2	16	no	—
331	C₅×D₄	—	4	8	no	—
332	C₂×C₄×C₅	—	2	8	no	—
333	C₂×C₄×C₅	—	2	16	no	—
334	C₂×C₄×C₅	—	2	8	no	—
335	C₂×C₄×C₅	—	2	2	no	—
336	C₂×C₄×C₅	—	2	8	no	—
337	C₂×C₄×C₅	—	2	8	no	—
338	C₂×C₄×C₅	—	2	8	no	—
339	C₂×C₄×C₅	—	2	2	no	—
340	C₂×C₄×C₅	—	2	2	no	—
341	C₂×C₄×C₅	—	2	32	no	—
342	C₂×C₄×C₅	—	2	8	no	—
343	C₂×C₄×C₅	—	4	8	no	—
344	C₂×C₄×C₅	—	4	32	no	—
345	C₂×C₄×C₅	—	4	4	no	—
346	C₂×C₄×C₅	C₂×#41	1	4	yes	—
347	C₂×C₄×C₅	C₂×#41	1	4	yes	—
348	C₂×C₄×C₅	C₂×#41	1	16	yes	—
349	C₂×C₄×C₅	2₋¹⁺⁴	1	4	yes	—
350	C₂×C₄×C₅	C₂⁵	1	2	yes	—
351	C₂×C₄×C₅	C₂⁵	1	8	yes	—
352	C₂×C₄×C₅	C₂⁵	1	8	yes	—
353	C₂×C₄×C₅	C₂⁵	1	8	yes	—
354	C₂×C₄×C₅	C₂⁵	1	2	yes	—
355	C₂×C₄×C₅	C₂⁵	1	8	yes	—
356	C₂×C₄×C₅	C₂⁵	1	2	yes	—
357	C₂×C₄×C₅	C₂⁵	1	8	yes	—
358	C₂×C₄×C₅	C₂⁵	1	2	yes	—
359	C₂×C₄×C₅	C₂⁵	1	2	yes	—
360	C₂×C₄×C₅	C₂⁵	1	2	yes	—
361	C₂×#41	—	2	16	no	—
362	C₂×#41	C₂³×C₅	1	16	yes	—
363	C₂²×Q₈	—	2	8	no	—
364	C₂²×Q₈	C₂³×C₅	1	2	yes	—
365	C₂²×Q₈	C₂³×C₅	1	2	yes	—
366	C₂²×Q₈	C₂³×C₅	1	2	yes	—
367	C₂²×Q₈	C₂³×C₅	1	2	yes	—
368	C₂²×Q₈	C₂³×C₅	1	8	yes	—
369	C₂²×Q₈	C₂³×C₅	1	2	yes	—
370	C₂²×D₄	C₂³×C₅	1	2	yes	—
371	C₂²×D₄	C₂³×C₅	1	4	yes	—
372	C₂²×D₄	C₂³×C₅	1	2	yes	—
373	C₂²×D₄	C₂³×C₅	1	2	yes	—
374	C₂³×C₄	C₂³×C₅	1	4	yes	—
375	C₂³×C₄	C₂³×C₅	1	2	yes	—
376	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
377	C₂³×C₄	C₂³×C₅	1	2	yes	—
378	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
379	C₂³×C₄	C₂³×C₅	1	8	yes	—
380	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
381	C₄⋊Q₈	C₂³×C₅	1	8	yes	—
382	C₄⋊Q₈	C₂³×C₅	1	8	yes	—
383	C₄⋊Q₈	C₂³×C₅	1	8	yes	—
384	C₄⋊Q₈	C₂³×C₅	1	32	yes	—
385	#127	C₂³×C₅	1	8	yes	—
386	#126	C₂³×C₅	1	64	yes	—
387	#126	C₂³×C₅	1	64	yes	—
388	#125	C₂³×C₅	1	32	yes	—
389	#125	C₂³×C₅	1	16	yes	—
390	#125	C₂³×C₅	1	64	yes	—
391	#124	C₂³×C₅	1	32	yes	—
392	#124	C₂³×C₅	1	16	yes	—
393	#124	C₂³×C₅	1	32	yes	—
394	#123	C₂³×C₅	1	64	yes	—
395	#123	C₂³×C₅	1	64	yes	—
396	C₂²⋊Q₈	C₂³×C₅	1	16	yes	—
397	C₂²⋊Q₈	C₂³×C₅	1	16	yes	—
398	C₂²⋊Q₈	C₂³×C₅	1	32	yes	—
399	C₂²⋊Q₈	C₂³×C₅	1	32	yes	—
400	C₂²⋊Q₈	C₂³×C₅	1	64	yes	—
401	#121	C₂³×C₅	1	16	yes	—
402	#121	C₂³×C₅	1	16	yes	—
403	C₄×Q₈	C₂³×C₅	1	16	yes	—
404	C₄×Q₈	C₂³×C₅	1	16	yes	—
405	C₄×Q₈	C₂³×C₅	1	16	yes	—
406	C₄×Q₈	C₂³×C₅	1	16	yes	—
407	C₄×Q₈	C₂³×C₅	1	32	yes	—
408	C₄×Q₈	C₂³×C₅	1	32	yes	—
409	C₄×Q₈	C₂³×C₅	1	16	yes	—
410	C₄×Q₈	C₂³×C₅	1	16	yes	—
411	C₄×D₄	C₂³×C₅	1	64	yes	—
412	C₄×D₄	C₂³×C₅	1	32	yes	—
413	C₄×D₄	C₂³×C₅	1	32	yes	—
414	C₄×D₄	C₂³×C₅	1	16	yes	—
415	C₄×D₄	C₂³×C₅	1	16	yes	—
416	#117	C₂³×C₅	1	16	yes	—
417	#117	C₂³×C₅	1	32	yes	—
418	#117	C₂³×C₅	1	64	yes	—
419	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
423	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
424	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
425	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
426	C₂×C₄⋊C₄	C₂³×C₅	1	16	yes	—
427	C₂×C₄⋊C₄	C₂³×C₅	1	32	yes	—
428	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
429	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
430	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
431	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
432	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
433	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
434	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
435	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
436	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
438	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
439	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
440	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
441	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
442	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
443	C₂×C₄²	C₂³×C₅	1	8	yes	—
444	C₂×C₄²	C₂³×C₅	1	4	yes	—
445	C₂×C₄²	C₂³×C₅	1	4	yes	—
446	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
447	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
448	C₂×C₄²	C₂³×C₅	1	4	yes	—
449	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
450	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
451	C₂×C₄²	C₂³×C₅	1	16	yes	—
452	C₂×C₄²	C₂³×C₅	1	8	yes	—
453	C₂²×C₅	—	2	2	no	—
454	C₂²×C₅	—	2	2	no	—
455	C₂²×C₅	—	2	8	no	—
456	C₂²×C₅	—	2	8	no	—
457	C₂²×C₅	—	2	8	no	—
458	C₂²×C₅	—	2	8	no	—
459	C₂²×C₅	—	4	16	no	—
460	C₂²×C₅	C₂²×#41	1	4	yes	—
461	C₂²×C₅	C₂²×#41	1	2	yes	—
462	C₂²×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
463	C₂²×C₅	#585	1	2	yes	—
464	C₂²×C₅	C₂⁶	1	1	yes	characteristic
465	C₄×C₅	—	2	8	no	—
466	C₄×C₅	—	2	8	no	—
467	C₄×C₅	—	2	2	no	—
468	C₄×C₅	—	2	8	no	—
469	C₄×C₅	—	2	8	no	—
470	C₄×C₅	—	2	8	no	—
471	C₄×C₅	—	2	2	no	—
472	C₄×C₅	—	2	2	no	—
473	C₄×C₅	C₂²×#41	1	4	yes	—
474	C₄×C₅	C₂²×#41	1	4	yes	—
475	C₄×C₅	C₂×2₋¹⁺⁴	1	4	yes	—
476	C₂⁴	C₂⁴×C₅	1	4	yes	—
477	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
478	#41	—	2	64	no	—
479	C₂×Q₈	—	2	8	no	—
480	C₂×Q₈	—	2	8	no	—
481	C₂×Q₈	—	2	32	no	—
482	C₂×Q₈	—	2	8	no	—
483	C₂×Q₈	—	2	8	no	—
484	C₂×Q₈	—	4	4	no	—
485	C₂×Q₈	C₂⁴×C₅	1	8	yes	—
486	C₂×Q₈	C₂⁴×C₅	1	8	yes	—
487	C₂×Q₈	C₂⁴×C₅	1	8	yes	—
488	C₂×Q₈	C₂⁴×C₅	1	8	yes	—
489	C₂×Q₈	C₂⁴×C₅	1	8	yes	—
490	C₂×D₄	—	2	16	no	—
491	C₂×D₄	—	2	8	no	—
492	C₂×D₄	—	2	8	no	—
493	C₂×D₄	—	4	4	no	—
494	C₂×D₄	C₂⁴×C₅	1	8	yes	—
495	C₂×D₄	C₂⁴×C₅	1	16	yes	—
496	C₂×D₄	C₂⁴×C₅	1	8	yes	—
497	C₂×D₄	C₂⁴×C₅	1	8	yes	—
498	C₂²×C₄	—	2	8	no	—
499	C₂²×C₄	—	2	16	no	—
500	C₂²×C₄	—	2	4	no	—
501	C₂²×C₄	—	4	4	no	—
502	C₂²×C₄	—	4	16	no	—
503	C₂²×C₄	—	4	2	no	—
504	C₂²×C₄	C₅×#41	1	8	yes	—
505	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
506	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
507	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
508	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
509	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
510	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
511	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
512	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
513	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
514	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
515	C₂²×C₄	C₂⁴×C₅	1	16	yes	—
516	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
517	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
518	C₂²×C₄	C₂⁴×C₅	1	32	yes	—
519	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
520	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
521	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
522	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
523	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
524	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
525	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
526	C₄⋊C₄	C₂⁴×C₅	1	32	yes	—
527	C₄⋊C₄	C₂⁴×C₅	1	16	yes	—
528	C₄⋊C₄	C₂⁴×C₅	1	16	yes	—
529	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
530	C₄⋊C₄	C₂⁴×C₅	1	16	yes	—
531	C₄⋊C₄	C₂⁴×C₅	1	32	yes	—
532	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
533	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
534	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
535	C₄⋊C₄	C₂⁴×C₅	1	16	yes	—
536	C₄⋊C₄	C₂⁴×C₅	1	32	yes	—
537	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
538	C₂²⋊C₄	C₂⁴×C₅	1	16	yes	—
539	C₂²⋊C₄	C₂⁴×C₅	1	16	yes	—
540	C₂²⋊C₄	C₂⁴×C₅	1	32	yes	—
541	C₂²⋊C₄	C₂⁴×C₅	1	32	yes	—
542	C₂²⋊C₄	C₂⁴×C₅	1	16	yes	—
543	C₂²⋊C₄	C₂⁴×C₅	1	32	yes	—
544	C₄²	C₂⁴×C₅	1	16	yes	—
545	C₄²	C₂⁴×C₅	1	4	yes	—
546	C₄²	C₂⁴×C₅	1	4	yes	—
547	C₄²	C₂⁴×C₅	1	16	yes	—
548	C₄²	C₂⁴×C₅	1	4	yes	—
549	C₄²	C₂⁴×C₅	1	4	yes	—
550	C₄²	C₂⁴×C₅	1	32	yes	—
551	C₄²	C₂⁴×C₅	1	16	yes	—
552	C₂×C₅	—	2	4	no	—
553	C₂×C₅	—	4	8	no	—
554	C₂×C₅	#3507	1	4	yes	direct product factor
555	C₂×C₅	C₂³×#41	1	1	yes	characteristic
556	C₂×C₅	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
557	C₂×C₅	C₂×#585	1	1	yes	characteristic
558	C₂³	—	2	2	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	8	no	—
561	C₂³	—	2	8	no	—
562	C₂³	—	2	8	no	—
563	C₂³	C₂×C₅×#41	1	4	yes	—
564	C₂³	C₂⁵×C₅	1	8	yes	—
565	C₂³	C₂⁵×C₅	1	2	yes	—
566	C₂³	C₂⁵×C₅	1	1	yes	characteristic
567	Q₈	—	2	16	no	—
568	Q₈	—	2	16	no	—
569	Q₈	—	2	16	no	—
570	Q₈	—	2	16	no	—
571	Q₈	—	4	8	no	—
572	D₄	—	2	32	no	—
573	D₄	—	2	16	no	—
574	D₄	—	2	16	no	—
575	D₄	—	4	8	no	—
576	C₂×C₄	—	2	8	no	—
577	C₂×C₄	—	2	16	no	—
578	C₂×C₄	—	2	8	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	8	no	—
581	C₂×C₄	—	2	8	no	—
582	C₂×C₄	—	2	8	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	32	no	—
586	C₂×C₄	—	2	8	no	—
587	C₂×C₄	—	4	8	no	—
588	C₂×C₄	—	4	32	no	—
589	C₂×C₄	—	4	4	no	—
590	C₂×C₄	C₂×C₅×#41	1	4	yes	—
591	C₂×C₄	C₂×C₅×#41	1	4	yes	—
592	C₂×C₄	C₂×C₅×#41	1	16	yes	—
593	C₂×C₄	C₅×2₋¹⁺⁴	1	4	yes	—
594	C₂×C₄	C₂⁵×C₅	1	2	yes	—
595	C₂×C₄	C₂⁵×C₅	1	8	yes	—
596	C₂×C₄	C₂⁵×C₅	1	8	yes	—
597	C₂×C₄	C₂⁵×C₅	1	8	yes	—
598	C₂×C₄	C₂⁵×C₅	1	2	yes	—
599	C₂×C₄	C₂⁵×C₅	1	8	yes	—
600	C₂×C₄	C₂⁵×C₅	1	2	yes	—
601	C₂×C₄	C₂⁵×C₅	1	8	yes	—
602	C₂×C₄	C₂⁵×C₅	1	2	yes	—
603	C₂×C₄	C₂⁵×C₅	1	2	yes	—
604	C₂×C₄	C₂⁵×C₅	1	2	yes	—
605	C₅	C₂×#3507	1	1	yes	characteristic, direct product factor, Sylow
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	8	no	—
609	C₂²	—	2	8	no	—
610	C₂²	—	2	8	no	—
611	C₂²	—	2	8	no	—
612	C₂²	—	4	16	no	—
613	C₂²	C₂²×C₅×#41	1	4	yes	—
614	C₂²	C₂²×C₅×#41	1	2	yes	—
615	C₂²	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
616	C₂²	C₅×#585	1	2	yes	—
617	C₂²	C₂⁶×C₅	1	1	yes	characteristic
618	C₄	—	2	8	no	—
619	C₄	—	2	8	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	8	no	—
622	C₄	—	2	8	no	—
623	C₄	—	2	8	no	—
624	C₄	—	2	2	no	—
625	C₄	—	2	2	no	—
626	C₄	C₂²×C₅×#41	1	4	yes	—
627	C₄	C₂²×C₅×#41	1	4	yes	—
628	C₄	C₂×C₅×2₋¹⁺⁴	1	4	yes	—
629	C₂	—	2	4	no	—
630	C₂	—	4	8	no	—
631	C₂	C₅×#3507	1	4	yes	direct product factor
632	C₂	C₂³×C₅×#41	1	1	yes	characteristic
633	C₂	C₂²×C₅×2₋¹⁺⁴	1	1	yes	characteristic
634	C₂	C₂×C₅×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₅
prime radical	C₂×C₅×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3507	C₂	direct (N × H)
2. C₂×C₅×#559	C₂	semidirect
3. C₂×C₅×#557	C₂	semidirect
4. C₂×C₅×#556	C₂	semidirect
5. C₂×C₅×#556	C₂	semidirect
6. C₂×C₅×#554	C₂	semidirect
7. C₂×C₅×#552	C₂	semidirect
8. C₂×C₅×#539	C₂	semidirect
9. C₂×C₅×#536	C₂	semidirect
10. C₂×C₅×#533	C₂	semidirect
12. C₂×C₅×#529	C₂	semidirect
13. C₂×C₅×#520	C₂	semidirect
14. C₂²×C₄×C₅×Q₈	C₂	semidirect
17. C₅×#559	C₂²	semidirect
18. C₅×#557	C₂²	semidirect
19. C₅×#556	C₂²	semidirect
20. C₅×#556	C₂²	semidirect
21. C₅×#554	C₂²	semidirect
22. C₅×#552	C₂²	semidirect
23. C₅×#539	C₂²	semidirect
24. C₅×#536	C₂²	semidirect
25. C₅×#533	C₂²	semidirect
32. C₅×#529	C₂²	semidirect
50. C₅×#520	C₂²	semidirect
59. C₂×C₄×C₅×Q₈	C₂²	semidirect
73. C₂×#3507	C₅	direct (N × H)
166. #3507	C₂×C₅	direct (N × H)
167. C₂×#559	C₂×C₅	semidirect
168. C₂×#557	C₂×C₅	semidirect
169. C₂×#556	C₂×C₅	semidirect
170. C₂×#556	C₂×C₅	semidirect
171. C₂×#554	C₂×C₅	semidirect
172. C₂×#552	C₂×C₅	semidirect
173. C₂×#539	C₂×C₅	semidirect
174. C₂×#536	C₂×C₅	semidirect
175. C₂×#533	C₂×C₅	semidirect
177. C₂×#529	C₂×C₅	semidirect
178. C₂×#520	C₂×C₅	semidirect
179. C₂²×C₄×Q₈	C₂×C₅	semidirect
258. #559	C₂²×C₅	semidirect
259. #557	C₂²×C₅	semidirect
260. #556	C₂²×C₅	semidirect
261. #556	C₂²×C₅	semidirect
262. #554	C₂²×C₅	semidirect
263. #552	C₂²×C₅	semidirect
264. #539	C₂²×C₅	semidirect
265. #536	C₂²×C₅	semidirect
266. #533	C₂²×C₅	semidirect
273. #529	C₂²×C₅	semidirect
291. #520	C₂²×C₅	semidirect
300. C₂×C₄×Q₈	C₂²×C₅	semidirect
554. C₂×C₅	#3507	direct (N × H)
605. C₅	C₂×#3507	direct (N × H)
631. C₂	C₅×#3507	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3507	2
C₂×C₅×#559	2
C₂×C₅×#557	2
C₂×C₅×#556	2
C₂×C₅×#554	2
C₂×C₅×#552	2
C₂×C₅×#539	2
C₂×C₅×#536	2
C₂×C₅×#533	2
C₂×C₅×#532	2
C₂×C₅×#529	2
C₂×C₅×#520	2
C₂²×C₄×C₅×Q₈	2
C₂×#3507	5

Subgroups — C2×C5×#3507 #11985497

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3507 #11985497