Subgroups — C₂×C₅×#3414 #11985351

Order 1280.

2098 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#135	C₂	1	2	yes	maximal, complemented
2	C₅×#3414	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₅×#510	C₂	1	4	yes	maximal, complemented
4	C₂×C₅×#509	C₂	1	4	yes	maximal, complemented
5	C₂×C₅×#508	C₂	1	4	yes	maximal, complemented
6	C₂²×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₅×#41	—	2	2	no	—
8	C₂×C₅×#135	—	2	2	no	—
9	C₂×C₅×#135	—	2	2	no	—
10	C₂×C₅×#135	—	2	8	no	—
11	C₂×C₅×#135	C₂²	1	4	yes	—
12	C₂×C₅×#135	C₂²	1	4	yes	complemented
13	C₂×C₅×#135	C₂²	1	16	yes	complemented
14	C₂²×C₅×Q₁₆	C₂²	1	2	yes	complemented
15	C₂²×C₅×SD₁₆	—	2	2	no	—
16	C₂²×C₅×D₈	C₂²	1	2	yes	complemented
17	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₅×#510	C₂²	1	32	yes	complemented
19	C₅×#509	C₂²	1	32	yes	complemented
20	C₅×#508	C₂²	1	32	yes	complemented
21	C₂×C₅×Q₃₂	C₂²	1	4	yes	complemented
22	C₂×C₅×SD₃₂	C₂²	1	8	yes	complemented
23	C₂×C₅×D₁₆	C₂²	1	4	yes	complemented
24	C₂×C₅×M₃₂	C₂²	1	4	yes	complemented
25	C₂×C₅×M₃₂	C₂²	1	8	yes	complemented
26	C₂²×C₅×C₁₆	C₂²	1	2	yes	complemented
27	C₂×#3414	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂×C₅×#41	—	2	4	no	—
29	C₂×C₅×#41	—	2	16	no	—
30	C₂×C₅×#41	—	2	4	no	—
31	C₂×C₅×#41	—	4	2	no	—
32	C₂×C₅×#41	—	4	8	no	—
33	C₂×C₅×#41	—	4	2	no	—
34	C₂²×C₅×Q₈	—	2	2	no	—
35	C₂²×C₅×D₄	—	2	2	no	—
36	C₂²×C₅×D₄	—	4	2	no	—
37	C₂³×C₄×C₅	—	4	2	no	—
38	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
39	C₅×#135	—	2	8	no	—
40	C₅×#135	—	2	16	no	—
41	C₅×#135	—	2	8	no	—
42	C₅×#135	—	2	16	no	—
43	C₅×#135	C₂³	1	16	yes	—
44	C₅×#135	C₂³	1	16	yes	complemented
45	C₂×C₅×Q₁₆	—	2	2	no	—
46	C₂×C₅×Q₁₆	—	2	4	no	—
47	C₂×C₅×Q₁₆	C₂³	1	4	yes	—
48	C₂×C₅×Q₁₆	C₂³	1	8	yes	complemented
49	C₂×C₅×SD₁₆	—	2	4	no	—
50	C₂×C₅×SD₁₆	—	2	4	no	—
51	C₂×C₅×SD₁₆	—	2	16	no	—
52	C₂×C₅×D₈	—	2	2	no	—
53	C₂×C₅×D₈	—	2	4	no	—
54	C₂×C₅×D₈	C₂³	1	4	yes	—
55	C₂×C₅×D₈	C₂³	1	8	yes	complemented
56	C₂²×C₅×C₈	D₄	1	2	yes	—
57	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
58	C₂²×C₅×C₈	D₄	1	4	yes	—
59	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₅×C₈	C₂³	1	2	yes	—
61	C₂²×C₅×C₈	C₂³	1	4	yes	—
62	C₅×Q₃₂	C₂³	1	16	yes	complemented
63	C₅×SD₃₂	C₂³	1	32	yes	complemented
64	C₅×D₁₆	C₂³	1	16	yes	complemented
65	C₅×M₃₂	C₂³	1	16	yes	complemented
66	C₂×C₅×C₁₆	C₂³	1	4	yes	—
67	C₂×C₅×C₁₆	C₂³	1	8	yes	complemented
68	C₂²×#135	C₂×C₅	1	2	yes	complemented
69	#3414	C₂×C₅	1	16	yes	direct product factor
70	C₂×#510	C₂×C₅	1	4	yes	complemented
71	C₂×#509	C₂×C₅	1	4	yes	complemented
72	C₂×#508	C₂×C₅	1	4	yes	complemented
73	C₂²×M₃₂	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂⁴×C₅	—	4	2	no	—
75	C₂⁴×C₅	D₈	1	1	yes	characteristic
76	C₅×#41	—	2	16	no	—
77	C₅×#41	—	2	16	no	—
78	C₅×#41	—	4	16	no	—
79	C₅×#41	—	4	8	no	—
80	C₅×#41	—	4	8	no	—
81	C₅×#41	—	4	16	no	—
82	C₂×C₅×Q₈	—	2	4	no	—
83	C₂×C₅×Q₈	—	2	8	no	—
84	C₂×C₅×Q₈	—	4	2	no	—
85	C₂×C₅×Q₈	—	4	4	no	—
86	C₂×C₅×D₄	—	2	4	no	—
87	C₂×C₅×D₄	—	2	8	no	—
88	C₂×C₅×D₄	—	4	4	no	—
89	C₂×C₅×D₄	—	4	4	no	—
90	C₂×C₅×D₄	—	4	16	no	—
91	C₂×C₅×D₄	—	4	2	no	—
92	C₂×C₅×D₄	—	4	4	no	—
93	C₂²×C₄×C₅	—	4	2	no	—
94	C₂²×C₄×C₅	—	4	4	no	—
95	C₂²×C₄×C₅	—	4	16	no	—
96	C₂²×C₄×C₅	—	4	4	no	—
97	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
98	C₂²×C₄×C₅	D₈	1	4	yes	—
99	C₂²×C₄×C₅	D₈	1	2	yes	—
100	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₅×Q₁₆	—	2	4	no	—
104	C₅×Q₁₆	—	2	8	no	—
105	C₅×Q₁₆	C₂⁴	1	8	yes	—
106	C₅×SD₁₆	—	2	16	no	—
107	C₅×SD₁₆	—	2	16	no	—
108	C₅×D₈	—	2	4	no	—
109	C₅×D₈	—	2	8	no	—
110	C₅×D₈	C₂⁴	1	8	yes	—
111	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
112	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
113	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
114	C₂×C₅×C₈	C₂×D₄	1	8	yes	—
115	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
116	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
117	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
118	C₂×C₅×C₈	C₂⁴	1	4	yes	—
119	C₂×C₅×C₈	C₂⁴	1	2	yes	—
120	C₅×C₁₆	C₂⁴	1	8	yes	—
121	C₂²×#41	—	2	2	no	—
122	C₂×#135	—	2	2	no	—
123	C₂×#135	—	2	2	no	—
124	C₂×#135	—	2	8	no	—
125	C₂×#135	C₂²×C₅	1	4	yes	—
126	C₂×#135	C₂²×C₅	1	4	yes	complemented
127	C₂×#135	C₂²×C₅	1	16	yes	complemented
128	C₂²×Q₁₆	C₂²×C₅	1	2	yes	complemented
129	C₂²×SD₁₆	—	2	2	no	—
130	C₂²×D₈	C₂²×C₅	1	2	yes	complemented
131	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
132	#510	C₂²×C₅	1	32	yes	complemented
133	#509	C₂²×C₅	1	32	yes	complemented
134	#508	C₂²×C₅	1	32	yes	complemented
135	C₂×Q₃₂	C₂²×C₅	1	4	yes	complemented
136	C₂×SD₃₂	C₂²×C₅	1	8	yes	complemented
137	C₂×D₁₆	C₂²×C₅	1	4	yes	complemented
138	C₂×M₃₂	C₂²×C₅	1	4	yes	complemented
139	C₂×M₃₂	C₂²×C₅	1	8	yes	complemented
140	C₂²×C₁₆	C₂²×C₅	1	2	yes	complemented
141	C₂³×C₅	—	4	2	no	—
142	C₂³×C₅	—	4	8	no	—
143	C₂³×C₅	—	4	4	no	—
144	C₂³×C₅	—	8	8	no	—
145	C₂³×C₅	C₂×D₈	1	2	yes	—
146	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
147	C₂³×C₅	C₂×D₈	1	4	yes	—
148	C₅×Q₈	—	2	8	no	—
149	C₅×Q₈	—	4	8	no	—
150	C₅×Q₈	—	4	4	no	—
151	C₅×D₄	—	2	8	no	—
152	C₅×D₄	—	4	16	no	—
153	C₅×D₄	—	4	16	no	—
154	C₅×D₄	—	4	8	no	—
155	C₅×D₄	—	4	4	no	—
156	C₂×C₄×C₅	—	4	8	no	—
157	C₂×C₄×C₅	—	4	4	no	—
158	C₂×C₄×C₅	—	4	16	no	—
159	C₂×C₄×C₅	—	4	16	no	—
160	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
161	C₂×C₄×C₅	C₂×D₈	1	8	yes	—
162	C₂×C₄×C₅	C₂×D₈	1	4	yes	—
163	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
164	C₂×C₄×C₅	C₂×D₈	1	4	yes	—
165	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
168	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
169	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
170	C₅×C₈	C₂²×D₄	1	4	yes	—
171	C₅×C₈	C₂²×D₄	1	2	yes	—
172	C₅×C₈	C₂⁵	1	1	yes	characteristic
173	C₂×#41	—	2	4	no	—
174	C₂×#41	—	2	4	no	—
175	C₂×#41	—	2	16	no	—
176	C₂×#41	—	4	2	no	—
177	C₂×#41	—	4	2	no	—
178	C₂×#41	—	4	8	no	—
179	C₂²×Q₈	—	2	2	no	—
180	C₂²×D₄	—	2	2	no	—
181	C₂²×D₄	—	4	2	no	—
182	C₂³×C₄	—	4	2	no	—
183	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
184	#135	—	2	8	no	—
185	#135	—	2	16	no	—
186	#135	—	2	8	no	—
187	#135	—	2	16	no	—
188	#135	C₂³×C₅	1	16	yes	—
189	#135	C₂³×C₅	1	16	yes	complemented
190	C₂×Q₁₆	—	2	2	no	—
191	C₂×Q₁₆	—	2	4	no	—
192	C₂×Q₁₆	C₂³×C₅	1	4	yes	—
193	C₂×Q₁₆	C₂³×C₅	1	8	yes	complemented
194	C₂×SD₁₆	—	2	4	no	—
195	C₂×SD₁₆	—	2	4	no	—
196	C₂×SD₁₆	—	2	16	no	—
197	C₂×D₈	—	2	2	no	—
198	C₂×D₈	—	2	4	no	—
199	C₂×D₈	C₂³×C₅	1	4	yes	—
200	C₂×D₈	C₂³×C₅	1	8	yes	complemented
201	C₂²×C₈	C₅×D₄	1	2	yes	—
202	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
203	C₂²×C₈	C₅×D₄	1	4	yes	—
204	C₂²×C₈	C₂³×C₅	1	2	yes	—
205	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
206	C₂²×C₈	C₂³×C₅	1	4	yes	—
207	Q₃₂	C₂³×C₅	1	16	yes	complemented
208	SD₃₂	C₂³×C₅	1	32	yes	complemented
209	D₁₆	C₂³×C₅	1	16	yes	complemented
210	M₃₂	C₂³×C₅	1	16	yes	complemented
211	C₂×C₁₆	C₂³×C₅	1	4	yes	—
212	C₂×C₁₆	C₂³×C₅	1	8	yes	complemented
213	C₂²×C₅	—	2	4	no	—
214	C₂²×C₅	—	2	2	no	—
215	C₂²×C₅	—	4	4	no	—
216	C₂²×C₅	—	4	8	no	—
217	C₂²×C₅	—	8	16	no	—
218	C₂²×C₅	—	8	8	no	—
219	C₂²×C₅	C₂²×D₈	1	4	yes	—
220	C₂²×C₅	C₂²×D₈	1	2	yes	—
221	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
222	C₄×C₅	—	4	8	no	—
223	C₄×C₅	C₂²×D₈	1	2	yes	—
224	C₄×C₅	C₂²×D₈	1	4	yes	—
225	C₄×C₅	C₂²×D₈	1	1	yes	characteristic
226	C₄×C₅	C₂³×D₄	1	1	yes	characteristic
227	C₂⁴	—	4	2	no	—
228	C₂⁴	C₅×D₈	1	1	yes	characteristic
229	#41	—	2	16	no	—
230	#41	—	2	16	no	—
231	#41	—	4	16	no	—
232	#41	—	4	8	no	—
233	#41	—	4	8	no	—
234	#41	—	4	16	no	—
235	C₂×Q₈	—	2	4	no	—
236	C₂×Q₈	—	2	8	no	—
237	C₂×Q₈	—	4	2	no	—
238	C₂×Q₈	—	4	4	no	—
239	C₂×D₄	—	2	4	no	—
240	C₂×D₄	—	2	8	no	—
241	C₂×D₄	—	4	4	no	—
242	C₂×D₄	—	4	4	no	—
243	C₂×D₄	—	4	16	no	—
244	C₂×D₄	—	4	2	no	—
245	C₂×D₄	—	4	4	no	—
246	C₂²×C₄	—	4	2	no	—
247	C₂²×C₄	—	4	4	no	—
248	C₂²×C₄	—	4	4	no	—
249	C₂²×C₄	—	4	16	no	—
250	C₂²×C₄	C₅×D₈	1	2	yes	—
251	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
252	C₂²×C₄	C₅×D₈	1	4	yes	—
253	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
254	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
255	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
256	Q₁₆	—	2	4	no	—
257	Q₁₆	—	2	8	no	—
258	Q₁₆	C₂⁴×C₅	1	8	yes	—
259	SD₁₆	—	2	16	no	—
260	SD₁₆	—	2	16	no	—
261	D₈	—	2	4	no	—
262	D₈	—	2	8	no	—
263	D₈	C₂⁴×C₅	1	8	yes	—
264	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
265	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
266	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
267	C₂×C₈	C₂×C₅×D₄	1	8	yes	—
268	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
269	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
270	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
271	C₂×C₈	C₂⁴×C₅	1	2	yes	—
272	C₂×C₈	C₂⁴×C₅	1	4	yes	—
273	C₁₆	C₂⁴×C₅	1	8	yes	—
274	C₂×C₅	—	2	4	no	—
275	C₂×C₅	—	2	2	no	—
276	C₂×C₅	—	8	8	no	—
277	C₂×C₅	#3414	1	2	yes	direct product factor
278	C₂×C₅	C₂³×D₈	1	1	yes	characteristic
279	C₂³	—	4	2	no	—
280	C₂³	—	4	8	no	—
281	C₂³	—	4	4	no	—
282	C₂³	—	8	8	no	—
283	C₂³	C₂×C₅×D₈	1	2	yes	—
284	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
285	C₂³	C₂×C₅×D₈	1	4	yes	—
286	Q₈	—	2	8	no	—
287	Q₈	—	4	8	no	—
288	Q₈	—	4	4	no	—
289	D₄	—	2	8	no	—
290	D₄	—	4	16	no	—
291	D₄	—	4	16	no	—
292	D₄	—	4	8	no	—
293	D₄	—	4	4	no	—
294	C₂×C₄	—	4	8	no	—
295	C₂×C₄	—	4	4	no	—
296	C₂×C₄	—	4	16	no	—
297	C₂×C₄	—	4	16	no	—
298	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
299	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
300	C₂×C₄	C₂×C₅×D₈	1	8	yes	—
301	C₂×C₄	C₂×C₅×D₈	1	4	yes	—
302	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
303	C₂×C₄	C₂×C₅×D₈	1	4	yes	—
304	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
305	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
306	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
307	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
308	C₈	C₂²×C₅×D₄	1	4	yes	—
309	C₈	C₂²×C₅×D₄	1	2	yes	—
310	C₈	C₂⁵×C₅	1	1	yes	characteristic
311	C₅	C₂×#3414	1	1	yes	characteristic, direct product factor, Sylow
312	C₂²	—	2	4	no	—
313	C₂²	—	2	2	no	—
314	C₂²	—	4	4	no	—
315	C₂²	—	4	8	no	—
316	C₂²	—	8	16	no	—
317	C₂²	—	8	8	no	—
318	C₂²	C₂²×C₅×D₈	1	4	yes	—
319	C₂²	C₂²×C₅×D₈	1	2	yes	—
320	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
321	C₄	—	4	8	no	—
322	C₄	C₂²×C₅×D₈	1	2	yes	—
323	C₄	C₂²×C₅×D₈	1	4	yes	—
324	C₄	C₂²×C₅×D₈	1	1	yes	characteristic
325	C₄	C₂³×C₅×D₄	1	1	yes	characteristic
326	C₂	—	2	4	no	—
327	C₂	—	2	2	no	—
328	C₂	—	8	8	no	—
329	C₂	C₅×#3414	1	2	yes	direct product factor
330	C₂	C₂³×C₅×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₈
commutator, Frattini, cosocle	C₈	C₂⁵×C₅
socle	C₂²×C₅	C₂²×D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂³×C₄×C₅ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#135	C₂	semidirect
2. C₅×#3414	C₂	direct (N × H)
3. C₂×C₅×#510	C₂	semidirect
4. C₂×C₅×#509	C₂	semidirect
5. C₂×C₅×#508	C₂	semidirect
6. C₂²×C₅×M₃₂	C₂	semidirect
12. C₂×C₅×#135	C₂²	semidirect
13. C₂×C₅×#135	C₂²	semidirect
14. C₂²×C₅×Q₁₆	C₂²	semidirect
16. C₂²×C₅×D₈	C₂²	semidirect
18. C₅×#510	C₂²	semidirect
19. C₅×#509	C₂²	semidirect
20. C₅×#508	C₂²	semidirect
21. C₂×C₅×Q₃₂	C₂²	semidirect
22. C₂×C₅×SD₃₂	C₂²	semidirect
23. C₂×C₅×D₁₆	C₂²	semidirect
24. C₂×C₅×M₃₂	C₂²	semidirect
25. C₂×C₅×M₃₂	C₂²	semidirect
26. C₂²×C₅×C₁₆	C₂²	semidirect
27. C₂×#3414	C₅	direct (N × H)
44. C₅×#135	C₂³	semidirect
48. C₂×C₅×Q₁₆	C₂³	semidirect
55. C₂×C₅×D₈	C₂³	semidirect
62. C₅×Q₃₂	C₂³	semidirect
63. C₅×SD₃₂	C₂³	semidirect
64. C₅×D₁₆	C₂³	semidirect
65. C₅×M₃₂	C₂³	semidirect
67. C₂×C₅×C₁₆	C₂³	semidirect
68. C₂²×#135	C₂×C₅	semidirect
69. #3414	C₂×C₅	direct (N × H)
70. C₂×#510	C₂×C₅	semidirect
71. C₂×#509	C₂×C₅	semidirect
72. C₂×#508	C₂×C₅	semidirect
73. C₂²×M₃₂	C₂×C₅	semidirect
126. C₂×#135	C₂²×C₅	semidirect
127. C₂×#135	C₂²×C₅	semidirect
128. C₂²×Q₁₆	C₂²×C₅	semidirect
130. C₂²×D₈	C₂²×C₅	semidirect
132. #510	C₂²×C₅	semidirect
133. #509	C₂²×C₅	semidirect
134. #508	C₂²×C₅	semidirect
135. C₂×Q₃₂	C₂²×C₅	semidirect
136. C₂×SD₃₂	C₂²×C₅	semidirect
137. C₂×D₁₆	C₂²×C₅	semidirect
138. C₂×M₃₂	C₂²×C₅	semidirect
139. C₂×M₃₂	C₂²×C₅	semidirect
140. C₂²×C₁₆	C₂²×C₅	semidirect
189. #135	C₂³×C₅	semidirect
193. C₂×Q₁₆	C₂³×C₅	semidirect
200. C₂×D₈	C₂³×C₅	semidirect
207. Q₃₂	C₂³×C₅	semidirect
208. SD₃₂	C₂³×C₅	semidirect
209. D₁₆	C₂³×C₅	semidirect
210. M₃₂	C₂³×C₅	semidirect
212. C₂×C₁₆	C₂³×C₅	semidirect
277. C₂×C₅	#3414	direct (N × H)
311. C₅	C₂×#3414	direct (N × H)
329. C₂	C₅×#3414	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×#135	2
C₅×#3414	2
C₂×C₅×#510	2
C₂×C₅×#509	2
C₂×C₅×#508	2
C₂²×C₅×M₃₂	2
C₂×#3414	5

Subgroups — C2×C5×#3414 #11985351

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3414 #11985351