Subgroups — C₂×C₅×#3170 #11983392

Order 1280.

2006 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#533	C₂	1	2	yes	maximal
2	C₅×#3170	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₅×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#487	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#467	C₂	1	4	yes	maximal
7	C₂×C₄×C₅×Q₁₆	C₂	1	4	yes	maximal, complemented
8	C₂²×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₅×Q₁₆	C₂²	1	4	yes	—
10	C₂³×C₅×C₈	C₂²	1	2	yes	—
11	C₅×#533	—	2	8	no	—
12	C₅×#533	C₂²	1	16	yes	—
13	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₅×#125	—	2	2	no	—
16	C₂×C₅×C₂²⋊Q₈	—	2	2	no	—
17	C₂×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
18	C₂×C₄×C₅×Q₈	—	2	2	no	—
19	C₂×C₄×C₅×Q₈	C₂²	1	4	yes	—
20	C₂×C₅×#117	—	2	2	no	—
21	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₅×#500	C₂²	1	8	yes	complemented
23	C₅×#494	C₂²	1	8	yes	complemented
24	C₅×#487	C₂²	1	16	yes	complemented
25	C₅×#467	C₂²	1	32	yes	—
26	C₄×C₅×Q₁₆	C₂²	1	32	yes	complemented
27	C₂×C₅×#107	C₂²	1	4	yes	—
28	C₂×C₅×#103	C₂²	1	8	yes	—
29	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×C₈	C₂²	1	8	yes	—
32	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
33	C₂×#3170	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₂²×C₅×Q₈	—	2	2	no	—
35	C₂²×C₅×Q₈	C₂³	1	4	yes	—
36	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂×C₅×Q₁₆	—	2	16	no	—
40	C₂×C₅×Q₁₆	C₂³	1	16	yes	—
41	C₂²×C₅×C₈	—	2	8	no	—
42	C₂²×C₅×C₈	C₂³	1	2	yes	—
43	C₂²×C₅×C₈	C₂³	1	8	yes	—
44	C₂²×C₅×C₈	C₂³	1	2	yes	—
45	C₅×C₄⋊Q₈	—	2	4	no	—
46	C₅×C₄⋊Q₈	—	2	4	no	—
47	C₅×C₄⋊Q₈	C₂³	1	8	yes	—
48	C₅×C₄⋊Q₈	C₂³	1	8	yes	—
49	C₅×#125	—	2	16	no	—
50	C₅×C₂²⋊Q₈	—	2	16	no	—
51	C₅×C₂²⋊Q₈	—	2	8	no	—
52	C₅×C₂²⋊Q₈	C₂³	1	16	yes	—
53	C₄×C₅×Q₈	—	2	16	no	—
54	C₄×C₅×Q₈	—	2	8	no	—
55	C₄×C₅×Q₈	C₂³	1	16	yes	—
56	C₅×#117	—	2	16	no	—
57	C₂×C₅×C₄⋊C₄	—	2	2	no	—
58	C₂×C₅×C₄⋊C₄	—	2	2	no	—
59	C₂×C₅×C₄⋊C₄	—	2	2	no	—
60	C₂×C₅×C₄⋊C₄	—	2	4	no	—
61	C₂×C₅×C₄⋊C₄	—	2	4	no	—
62	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
63	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
64	C₂×C₄²×C₅	—	2	4	no	—
65	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₅	D₄	1	4	yes	—
67	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₅	C₂³	1	4	yes	—
70	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₅×#107	C₂³	1	16	yes	—
72	C₅×#103	C₂³	1	32	yes	—
73	C₄×C₅×C₈	C₂³	1	8	yes	—
74	C₄×C₅×C₈	C₂³	1	4	yes	—
75	C₄×C₅×C₈	C₂³	1	4	yes	—
76	C₂×#533	C₂×C₅	1	2	yes	—
77	#3170	C₂×C₅	1	16	yes	direct product factor
78	C₂×#500	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂×#494	C₂×C₅	1	1	yes	characteristic, complemented
80	C₂×#487	C₂×C₅	1	2	yes	complemented
81	C₂×#467	C₂×C₅	1	4	yes	—
82	C₂×C₄×Q₁₆	C₂×C₅	1	4	yes	complemented
83	C₂²×C₄×C₈	C₂×C₅	1	1	yes	characteristic
84	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
85	C₂×C₅×Q₈	—	2	4	no	—
86	C₂×C₅×Q₈	—	2	8	no	—
87	C₂×C₅×Q₈	—	2	16	no	—
88	C₂×C₅×Q₈	—	4	8	no	—
89	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
90	C₂²×C₄×C₅	—	2	4	no	—
91	C₂²×C₄×C₅	—	2	4	no	—
92	C₂²×C₄×C₅	—	2	4	no	—
93	C₂²×C₄×C₅	—	2	4	no	—
94	C₂²×C₄×C₅	Q₁₆	1	8	yes	complemented
95	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
104	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
105	C₅×Q₁₆	—	2	32	no	—
106	C₂×C₅×C₈	—	2	4	no	—
107	C₂×C₅×C₈	—	2	16	no	—
108	C₂×C₅×C₈	#41	1	8	yes	—
109	C₂×C₅×C₈	C₂⁴	1	4	yes	—
110	C₂×C₅×C₈	C₂⁴	1	4	yes	—
111	C₅×C₄⋊C₄	—	2	8	no	—
112	C₅×C₄⋊C₄	—	2	8	no	—
113	C₅×C₄⋊C₄	—	2	8	no	—
114	C₅×C₄⋊C₄	—	2	16	no	—
115	C₅×C₄⋊C₄	—	2	16	no	—
116	C₅×C₄⋊C₄	—	2	4	no	—
117	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
118	C₅×C₂²⋊C₄	—	2	16	no	—
119	C₄²×C₅	—	2	16	no	—
120	C₄²×C₅	C₂×D₄	1	4	yes	—
121	C₄²×C₅	C₂×D₄	1	2	yes	—
122	C₄²×C₅	C₂×D₄	1	4	yes	—
123	C₄²×C₅	C₂×D₄	1	2	yes	—
124	C₄²×C₅	C₂⁴	1	2	yes	—
125	C₄²×C₅	C₂⁴	1	2	yes	—
126	C₂²×Q₁₆	C₂²×C₅	1	4	yes	—
127	C₂³×C₈	C₂²×C₅	1	2	yes	—
128	#533	—	2	8	no	—
129	#533	C₂²×C₅	1	16	yes	—
130	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
131	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
132	C₂×#125	—	2	2	no	—
133	C₂×C₂²⋊Q₈	—	2	2	no	—
134	C₂×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
135	C₂×C₄×Q₈	—	2	2	no	—
136	C₂×C₄×Q₈	C₂²×C₅	1	4	yes	—
137	C₂×#117	—	2	2	no	—
138	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
139	#500	C₂²×C₅	1	8	yes	complemented
140	#494	C₂²×C₅	1	8	yes	complemented
141	#487	C₂²×C₅	1	16	yes	complemented
142	#467	C₂²×C₅	1	32	yes	—
143	C₄×Q₁₆	C₂²×C₅	1	32	yes	complemented
144	C₂×#107	C₂²×C₅	1	4	yes	—
145	C₂×#103	C₂²×C₅	1	8	yes	—
146	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
147	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
148	C₂×C₄×C₈	C₂²×C₅	1	8	yes	—
149	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
150	C₂³×C₅	—	2	2	no	—
151	C₂³×C₅	—	2	2	no	—
152	C₂³×C₅	C₂×Q₁₆	1	4	yes	—
153	C₂³×C₅	C₂²×D₄	1	2	yes	—
154	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
155	C₅×Q₈	—	2	16	no	—
156	C₅×Q₈	—	4	8	no	—
157	C₅×Q₈	—	4	16	no	—
158	C₂×C₄×C₅	—	2	2	no	—
159	C₂×C₄×C₅	—	2	2	no	—
160	C₂×C₄×C₅	—	2	4	no	—
161	C₂×C₄×C₅	—	2	8	no	—
162	C₂×C₄×C₅	—	2	4	no	—
163	C₂×C₄×C₅	—	2	8	no	—
164	C₂×C₄×C₅	—	2	8	no	—
165	C₂×C₄×C₅	—	4	8	no	—
166	C₂×C₄×C₅	—	4	8	no	—
167	C₂×C₄×C₅	C₂×Q₁₆	1	4	yes	—
168	C₂×C₄×C₅	C₂×Q₁₆	1	4	yes	—
169	C₂×C₄×C₅	C₂×Q₁₆	1	16	yes	complemented
170	C₂×C₄×C₅	#135	1	4	yes	—
171	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
172	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
173	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
175	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
176	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
177	C₂×C₄×C₅	C₂×#41	1	4	yes	—
178	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
179	C₅×C₈	—	2	4	no	—
180	C₅×C₈	C₂×#41	1	8	yes	—
181	C₂²×Q₈	—	2	2	no	—
182	C₂²×Q₈	C₂³×C₅	1	4	yes	—
183	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
184	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
185	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
186	C₂×Q₁₆	—	2	16	no	—
187	C₂×Q₁₆	C₂³×C₅	1	16	yes	—
188	C₂²×C₈	—	2	8	no	—
189	C₂²×C₈	C₂³×C₅	1	2	yes	—
190	C₂²×C₈	C₂³×C₅	1	8	yes	—
191	C₂²×C₈	C₂³×C₅	1	2	yes	—
192	C₄⋊Q₈	—	2	4	no	—
193	C₄⋊Q₈	—	2	4	no	—
194	C₄⋊Q₈	C₂³×C₅	1	8	yes	—
195	C₄⋊Q₈	C₂³×C₅	1	8	yes	—
196	#125	—	2	16	no	—
197	C₂²⋊Q₈	—	2	16	no	—
198	C₂²⋊Q₈	—	2	8	no	—
199	C₂²⋊Q₈	C₂³×C₅	1	16	yes	—
200	C₄×Q₈	—	2	16	no	—
201	C₄×Q₈	—	2	8	no	—
202	C₄×Q₈	C₂³×C₅	1	16	yes	—
203	#117	—	2	16	no	—
204	C₂×C₄⋊C₄	—	2	2	no	—
205	C₂×C₄⋊C₄	—	2	2	no	—
206	C₂×C₄⋊C₄	—	2	2	no	—
207	C₂×C₄⋊C₄	—	2	4	no	—
208	C₂×C₄⋊C₄	—	2	4	no	—
209	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
210	C₂×C₂²⋊C₄	—	2	4	no	—
211	C₂×C₄²	—	2	4	no	—
212	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
213	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
214	C₂×C₄²	C₅×D₄	1	4	yes	—
215	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
216	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
217	C₂×C₄²	C₂³×C₅	1	4	yes	—
218	#107	C₂³×C₅	1	16	yes	—
219	#103	C₂³×C₅	1	32	yes	—
220	C₄×C₈	C₂³×C₅	1	8	yes	—
221	C₄×C₈	C₂³×C₅	1	4	yes	—
222	C₄×C₈	C₂³×C₅	1	4	yes	—
223	C₂²×C₅	—	2	8	no	—
224	C₂²×C₅	—	2	2	no	—
225	C₂²×C₅	—	2	2	no	—
226	C₂²×C₅	#532	1	2	yes	—
227	C₂²×C₅	C₂²×Q₁₆	1	4	yes	—
228	C₂²×C₅	C₂²×Q₁₆	1	2	yes	—
229	C₂²×C₅	C₂×#135	1	2	yes	—
230	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
231	C₄×C₅	—	2	2	no	—
232	C₄×C₅	—	2	2	no	—
233	C₄×C₅	—	4	8	no	—
234	C₄×C₅	—	4	8	no	—
235	C₄×C₅	#532	1	2	yes	—
236	C₄×C₅	C₂²×Q₁₆	1	4	yes	—
237	C₄×C₅	C₂²×Q₁₆	1	4	yes	—
238	C₄×C₅	C₂×#135	1	4	yes	—
239	C₄×C₅	C₂²×#41	1	2	yes	—
240	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
241	C₂×Q₈	—	2	4	no	—
242	C₂×Q₈	—	2	8	no	—
243	C₂×Q₈	—	2	16	no	—
244	C₂×Q₈	—	4	8	no	—
245	C₂×Q₈	C₂⁴×C₅	1	8	yes	—
246	C₂²×C₄	—	2	4	no	—
247	C₂²×C₄	—	2	4	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	2	4	no	—
250	C₂²×C₄	C₅×Q₁₆	1	8	yes	complemented
251	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
252	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
253	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
254	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
255	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
256	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
257	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
258	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
259	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
260	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
261	Q₁₆	—	2	32	no	—
262	C₂×C₈	—	2	4	no	—
263	C₂×C₈	—	2	16	no	—
264	C₂×C₈	C₅×#41	1	8	yes	—
265	C₂×C₈	C₂⁴×C₅	1	4	yes	—
266	C₂×C₈	C₂⁴×C₅	1	4	yes	—
267	C₄⋊C₄	—	2	8	no	—
268	C₄⋊C₄	—	2	8	no	—
269	C₄⋊C₄	—	2	8	no	—
270	C₄⋊C₄	—	2	16	no	—
271	C₄⋊C₄	—	2	16	no	—
272	C₄⋊C₄	—	2	4	no	—
273	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
274	C₂²⋊C₄	—	2	16	no	—
275	C₄²	—	2	16	no	—
276	C₄²	C₂×C₅×D₄	1	4	yes	—
277	C₄²	C₂×C₅×D₄	1	2	yes	—
278	C₄²	C₂×C₅×D₄	1	4	yes	—
279	C₄²	C₂×C₅×D₄	1	2	yes	—
280	C₄²	C₂⁴×C₅	1	2	yes	—
281	C₄²	C₂⁴×C₅	1	2	yes	—
282	C₂×C₅	—	2	4	no	—
283	C₂×C₅	#3170	1	4	yes	direct product factor
284	C₂×C₅	C₂×#532	1	1	yes	characteristic
285	C₂×C₅	C₂³×Q₁₆	1	1	yes	characteristic
286	C₂×C₅	C₂²×#135	1	1	yes	characteristic
287	C₂³	—	2	2	no	—
288	C₂³	—	2	2	no	—
289	C₂³	C₂×C₅×Q₁₆	1	4	yes	—
290	C₂³	C₂²×C₅×D₄	1	2	yes	—
291	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
292	Q₈	—	2	16	no	—
293	Q₈	—	4	8	no	—
294	Q₈	—	4	16	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	4	no	—
298	C₂×C₄	—	2	8	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	8	no	—
301	C₂×C₄	—	2	8	no	—
302	C₂×C₄	—	4	8	no	—
303	C₂×C₄	—	4	8	no	—
304	C₂×C₄	C₂×C₅×Q₁₆	1	4	yes	—
305	C₂×C₄	C₂×C₅×Q₁₆	1	4	yes	—
306	C₂×C₄	C₂×C₅×Q₁₆	1	16	yes	complemented
307	C₂×C₄	C₅×#135	1	4	yes	—
308	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
309	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
310	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
311	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
312	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
313	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
314	C₂×C₄	C₂×C₅×#41	1	4	yes	—
315	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
316	C₈	—	2	4	no	—
317	C₈	C₂×C₅×#41	1	8	yes	—
318	C₅	C₂×#3170	1	1	yes	characteristic, direct product factor, Sylow
319	C₂²	—	2	2	no	—
320	C₂²	—	2	8	no	—
321	C₂²	—	2	2	no	—
322	C₂²	C₅×#532	1	2	yes	—
323	C₂²	C₂²×C₅×Q₁₆	1	4	yes	—
324	C₂²	C₂²×C₅×Q₁₆	1	2	yes	—
325	C₂²	C₂×C₅×#135	1	2	yes	—
326	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
327	C₄	—	2	2	no	—
328	C₄	—	2	2	no	—
329	C₄	—	4	8	no	—
330	C₄	—	4	8	no	—
331	C₄	C₅×#532	1	2	yes	—
332	C₄	C₂²×C₅×Q₁₆	1	4	yes	—
333	C₄	C₂²×C₅×Q₁₆	1	4	yes	—
334	C₄	C₂×C₅×#135	1	4	yes	—
335	C₄	C₂²×C₅×#41	1	2	yes	—
336	C₂	—	2	4	no	—
337	C₂	C₅×#3170	1	4	yes	direct product factor
338	C₂	C₂×C₅×#532	1	1	yes	characteristic
339	C₂	C₂³×C₅×Q₁₆	1	1	yes	characteristic
340	C₂	C₂²×C₅×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
socle	C₂³×C₅	C₂²×D₄
prime radical	C₂⁴×C₅	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#3170	C₂	direct (N × H)
3. C₂×C₅×#500	C₂	semidirect
4. C₂×C₅×#494	C₂	semidirect
5. C₂×C₅×#487	C₂	semidirect
7. C₂×C₄×C₅×Q₁₆	C₂	semidirect
22. C₅×#500	C₂²	semidirect
23. C₅×#494	C₂²	semidirect
24. C₅×#487	C₂²	semidirect
26. C₄×C₅×Q₁₆	C₂²	semidirect
33. C₂×#3170	C₅	direct (N × H)
77. #3170	C₂×C₅	direct (N × H)
78. C₂×#500	C₂×C₅	semidirect
79. C₂×#494	C₂×C₅	semidirect
80. C₂×#487	C₂×C₅	semidirect
82. C₂×C₄×Q₁₆	C₂×C₅	semidirect
94. C₂²×C₄×C₅	Q₁₆	semidirect
139. #500	C₂²×C₅	semidirect
140. #494	C₂²×C₅	semidirect
141. #487	C₂²×C₅	semidirect
143. C₄×Q₁₆	C₂²×C₅	semidirect
169. C₂×C₄×C₅	C₂×Q₁₆	semidirect
250. C₂²×C₄	C₅×Q₁₆	semidirect
283. C₂×C₅	#3170	direct (N × H)
306. C₂×C₄	C₂×C₅×Q₁₆	semidirect
318. C₅	C₂×#3170	direct (N × H)
337. C₂	C₅×#3170	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#533	2
C₅×#3170	2
C₂×C₅×#500	2
C₂×C₅×#494	2
C₂×C₅×#487	2
C₂×C₅×#467	2
C₂×C₄×C₅×Q₁₆	2
C₂²×C₄×C₅×C₈	2
C₂×#3170	5

Subgroups — C2×C5×#3170 #11983392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3170 #11983392