Subgroups — C₅×#35338 #11958058

Order 1280.

2422 conjugacy classes of subgroups.

The subgroup lattice has 358 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	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#124	C₂	1	1	yes	maximal, characteristic
3	C₅×#2861	C₂	1	4	yes	maximal, complemented
4	C₅×#2640	C₂	1	4	yes	maximal, complemented
5	C₅×#2592	C₂	1	8	yes	maximal, complemented
6	C₅×#2561	C₂	1	8	yes	maximal, complemented
7	C₅×#2310	C₂	1	2	yes	maximal, complemented
8	C₅×#2309	C₂	1	2	yes	maximal
9	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₅×#533	—	2	8	no	—
13	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
14	C₂×C₅×#125	C₂²	1	2	yes	complemented
15	C₂×C₅×#124	—	2	8	no	—
16	C₂×C₅×#124	C₂²	1	4	yes	—
17	C₂×C₅×#124	C₂²	1	2	yes	—
18	C₂×C₅×#124	C₂²	1	2	yes	—
19	C₂×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
20	C₂×C₄×C₅×Q₈	C₂²	1	4	yes	complemented
21	C₂×C₅×#117	C₂²	1	2	yes	—
22	C₂×C₅×#117	C₂²	1	2	yes	—
23	C₂²×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
24	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₅×#397	C₂²	1	16	yes	complemented
26	C₅×#393	C₂²	1	16	yes	complemented
27	C₅×#391	C₂²	1	8	yes	complemented
28	C₅×#391	C₂²	1	8	yes	complemented
29	C₅×#390	C₂²	1	8	yes	—
30	C₅×#390	C₂²	1	8	yes	—
31	C₅×#388	C₂²	1	32	yes	complemented
32	C₅×#381	C₂²	1	8	yes	—
33	C₅×#379	C₂²	1	8	yes	—
34	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
35	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
36	C₅×#376	C₂²	1	2	yes	complemented
37	C₄³×C₅	C₂²	1	2	yes	complemented
38	#35338	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂⁵×C₅	C₂³	1	2	yes	—
40	C₂²×C₅×Q₈	—	2	4	no	—
41	C₂²×C₅×Q₈	—	2	8	no	—
42	C₂²×C₅×Q₈	C₂³	1	2	yes	—
43	C₂²×C₅×Q₈	C₂³	1	2	yes	—
44	C₂²×C₅×Q₈	C₂³	1	4	yes	—
45	C₂²×C₅×D₄	—	2	4	no	—
46	C₂²×C₅×D₄	—	2	8	no	—
47	C₂²×C₅×D₄	C₂³	1	2	yes	—
48	C₂²×C₅×D₄	C₂³	1	2	yes	—
49	C₂³×C₄×C₅	C₂³	1	2	yes	—
50	C₂³×C₄×C₅	C₂³	1	2	yes	—
51	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₅×C₄⋊Q₈	—	2	8	no	—
53	C₅×#125	—	2	8	no	—
54	C₅×#124	—	2	16	no	—
55	C₅×#124	—	2	8	no	—
56	C₅×#124	—	2	8	no	—
57	C₅×C₂²⋊Q₈	—	2	16	no	—
58	C₄×C₅×Q₈	—	2	16	no	—
59	C₅×#117	—	2	8	no	—
60	C₅×#117	—	2	8	no	—
61	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
62	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
63	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
64	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
65	C₂×C₅×C₂²⋊C₄	—	2	16	no	—
66	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
67	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
68	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
69	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
70	C₂×C₅×C₂²⋊C₄	C₂³	1	32	yes	—
71	C₂×C₄²×C₅	D₄	1	8	yes	—
72	C₂×C₄²×C₅	C₂³	1	4	yes	—
73	C₂×C₄²×C₅	C₂³	1	4	yes	—
74	C₂×C₄²×C₅	C₂³	1	8	yes	—
75	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₅	C₂³	1	2	yes	—
78	C₅×#95	C₂³	1	8	yes	—
79	C₅×#95	C₂³	1	32	yes	—
80	C₂×#533	C₂×C₅	1	1	yes	characteristic, complemented
81	C₂²×#124	C₂×C₅	1	1	yes	characteristic
82	#2861	C₂×C₅	1	4	yes	complemented
83	#2640	C₂×C₅	1	4	yes	complemented
84	#2592	C₂×C₅	1	8	yes	complemented
85	#2561	C₂×C₅	1	8	yes	complemented
86	#2310	C₂×C₅	1	2	yes	complemented
87	#2309	C₂×C₅	1	2	yes	—
88	C₄×#117	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂⁴×C₅	—	2	4	no	—
90	C₂⁴×C₅	—	2	8	no	—
91	C₂⁴×C₅	—	4	8	no	—
92	C₂⁴×C₅	C₂⁴	1	4	yes	—
93	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
94	C₂×C₅×Q₈	—	2	8	no	—
95	C₂×C₅×Q₈	—	2	4	no	—
96	C₂×C₅×Q₈	—	2	4	no	—
97	C₂×C₅×Q₈	—	2	8	no	—
98	C₂×C₅×Q₈	—	2	8	no	—
99	C₂×C₅×Q₈	—	4	8	no	—
100	C₂×C₅×Q₈	—	4	16	no	—
101	C₂×C₅×D₄	—	2	4	no	—
102	C₂×C₅×D₄	—	2	4	no	—
103	C₂×C₅×D₄	—	2	8	no	—
104	C₂×C₅×D₄	—	2	8	no	—
105	C₂×C₅×D₄	—	4	16	no	—
106	C₂²×C₄×C₅	—	2	4	no	—
107	C₂²×C₄×C₅	—	2	8	no	—
108	C₂²×C₄×C₅	—	4	4	no	—
109	C₂²×C₄×C₅	C₂×D₄	1	8	yes	—
110	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
111	C₂²×C₄×C₅	#41	1	8	yes	—
112	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
113	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
114	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
115	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
116	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
119	C₅×C₄⋊C₄	—	2	8	no	—
120	C₅×C₄⋊C₄	—	2	16	no	—
121	C₅×C₄⋊C₄	—	2	8	no	—
122	C₅×C₄⋊C₄	—	2	8	no	—
123	C₅×C₂²⋊C₄	—	2	8	no	—
124	C₅×C₂²⋊C₄	—	2	8	no	—
125	C₅×C₂²⋊C₄	—	2	16	no	—
126	C₅×C₂²⋊C₄	—	2	16	no	—
127	C₅×C₂²⋊C₄	—	4	32	no	—
128	C₄²×C₅	—	2	8	no	—
129	C₄²×C₅	—	2	8	no	—
130	C₄²×C₅	—	4	8	no	—
131	C₄²×C₅	C₂×D₄	1	8	yes	—
132	C₄²×C₅	C₂×D₄	1	4	yes	—
133	C₄²×C₅	C₂×D₄	1	4	yes	—
134	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic
135	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
136	#533	—	2	8	no	—
137	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
138	C₂×#125	C₂²×C₅	1	2	yes	complemented
139	C₂×#124	—	2	8	no	—
140	C₂×#124	C₂²×C₅	1	4	yes	—
141	C₂×#124	C₂²×C₅	1	2	yes	—
142	C₂×#124	C₂²×C₅	1	2	yes	—
143	C₂×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
144	C₂×C₄×Q₈	C₂²×C₅	1	4	yes	complemented
145	C₂×#117	C₂²×C₅	1	2	yes	—
146	C₂×#117	C₂²×C₅	1	2	yes	—
147	C₂²×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
148	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
149	#397	C₂²×C₅	1	16	yes	complemented
150	#393	C₂²×C₅	1	16	yes	complemented
151	#391	C₂²×C₅	1	8	yes	complemented
152	#391	C₂²×C₅	1	8	yes	complemented
153	#390	C₂²×C₅	1	8	yes	—
154	#390	C₂²×C₅	1	8	yes	—
155	#388	C₂²×C₅	1	32	yes	complemented
156	#381	C₂²×C₅	1	8	yes	—
157	#379	C₂²×C₅	1	8	yes	—
158	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	complemented
159	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
160	#376	C₂²×C₅	1	2	yes	complemented
161	C₄³	C₂²×C₅	1	2	yes	complemented
162	C₂³×C₅	—	2	4	no	—
163	C₂³×C₅	—	2	4	no	—
164	C₂³×C₅	—	2	8	no	—
165	C₂³×C₅	—	2	16	no	—
166	C₂³×C₅	—	4	16	no	—
167	C₂³×C₅	—	4	8	no	—
168	C₂³×C₅	—	8	16	no	—
169	C₂³×C₅	C₂²×D₄	1	2	yes	—
170	C₂³×C₅	C₂×#41	1	4	yes	—
171	C₂³×C₅	C₂⁵	1	1	yes	characteristic
172	C₅×Q₈	—	4	16	no	—
173	C₅×Q₈	—	4	8	no	—
174	C₅×Q₈	—	4	8	no	—
175	C₅×D₄	—	4	8	no	—
176	C₅×D₄	—	4	8	no	—
177	C₂×C₄×C₅	—	2	4	no	—
178	C₂×C₄×C₅	—	2	4	no	—
179	C₂×C₄×C₅	—	2	8	no	—
180	C₂×C₄×C₅	—	2	4	no	—
181	C₂×C₄×C₅	—	2	8	no	—
182	C₂×C₄×C₅	—	2	8	no	—
183	C₂×C₄×C₅	—	2	16	no	—
184	C₂×C₄×C₅	—	2	16	no	—
185	C₂×C₄×C₅	—	4	8	no	—
186	C₂×C₄×C₅	—	4	8	no	—
187	C₂×C₄×C₅	#124	1	16	yes	—
188	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
189	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
190	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
191	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
192	C₂×C₄×C₅	C₂×#41	1	4	yes	—
193	C₂×C₄×C₅	C₂×#41	1	4	yes	—
194	C₂⁵	C₂³×C₅	1	2	yes	—
195	C₂²×Q₈	—	2	4	no	—
196	C₂²×Q₈	—	2	8	no	—
197	C₂²×Q₈	C₂³×C₅	1	2	yes	—
198	C₂²×Q₈	C₂³×C₅	1	2	yes	—
199	C₂²×Q₈	C₂³×C₅	1	4	yes	—
200	C₂²×D₄	—	2	4	no	—
201	C₂²×D₄	—	2	8	no	—
202	C₂²×D₄	C₂³×C₅	1	2	yes	—
203	C₂²×D₄	C₂³×C₅	1	2	yes	—
204	C₂³×C₄	C₂³×C₅	1	2	yes	—
205	C₂³×C₄	C₂³×C₅	1	2	yes	—
206	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
207	C₄⋊Q₈	—	2	8	no	—
208	#125	—	2	8	no	—
209	#124	—	2	16	no	—
210	#124	—	2	8	no	—
211	#124	—	2	8	no	—
212	C₂²⋊Q₈	—	2	16	no	—
213	C₄×Q₈	—	2	16	no	—
214	#117	—	2	8	no	—
215	#117	—	2	8	no	—
216	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
217	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
218	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
219	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
220	C₂×C₂²⋊C₄	—	2	16	no	—
221	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
222	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
223	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
224	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
225	C₂×C₂²⋊C₄	C₂³×C₅	1	32	yes	—
226	C₂×C₄²	C₅×D₄	1	8	yes	—
227	C₂×C₄²	C₂³×C₅	1	4	yes	—
228	C₂×C₄²	C₂³×C₅	1	4	yes	—
229	C₂×C₄²	C₂³×C₅	1	8	yes	—
230	C₂×C₄²	C₂³×C₅	1	2	yes	—
231	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
232	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
233	#95	C₂³×C₅	1	8	yes	—
234	#95	C₂³×C₅	1	32	yes	—
235	C₂²×C₅	—	2	4	no	—
236	C₂²×C₅	—	2	8	no	—
237	C₂²×C₅	—	4	4	no	—
238	C₂²×C₅	—	4	8	no	—
239	C₂²×C₅	—	4	16	no	—
240	C₂²×C₅	—	8	16	no	—
241	C₂²×C₅	C₂×#124	1	4	yes	—
242	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
243	C₂²×C₅	C₂²×#41	1	2	yes	—
244	C₂²×C₅	#585	1	4	yes	—
245	C₄×C₅	—	2	4	no	—
246	C₄×C₅	—	2	4	no	—
247	C₄×C₅	—	4	4	no	—
248	C₄×C₅	—	4	8	no	—
249	C₄×C₅	—	4	8	no	—
250	C₄×C₅	C₂×#124	1	4	yes	—
251	C₄×C₅	C₂×#124	1	4	yes	—
252	C₂⁴	—	2	4	no	—
253	C₂⁴	—	2	8	no	—
254	C₂⁴	—	4	8	no	—
255	C₂⁴	C₂⁴×C₅	1	4	yes	—
256	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
257	C₂×Q₈	—	2	8	no	—
258	C₂×Q₈	—	2	4	no	—
259	C₂×Q₈	—	2	4	no	—
260	C₂×Q₈	—	2	8	no	—
261	C₂×Q₈	—	2	8	no	—
262	C₂×Q₈	—	4	8	no	—
263	C₂×Q₈	—	4	16	no	—
264	C₂×D₄	—	2	4	no	—
265	C₂×D₄	—	2	4	no	—
266	C₂×D₄	—	2	8	no	—
267	C₂×D₄	—	2	8	no	—
268	C₂×D₄	—	4	16	no	—
269	C₂²×C₄	—	2	4	no	—
270	C₂²×C₄	—	2	8	no	—
271	C₂²×C₄	—	4	4	no	—
272	C₂²×C₄	C₂×C₅×D₄	1	8	yes	—
273	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
274	C₂²×C₄	C₅×#41	1	8	yes	—
275	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
276	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
277	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
278	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
279	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
280	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
281	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
282	C₄⋊C₄	—	2	8	no	—
283	C₄⋊C₄	—	2	16	no	—
284	C₄⋊C₄	—	2	8	no	—
285	C₄⋊C₄	—	2	8	no	—
286	C₂²⋊C₄	—	2	8	no	—
287	C₂²⋊C₄	—	2	8	no	—
288	C₂²⋊C₄	—	2	16	no	—
289	C₂²⋊C₄	—	2	16	no	—
290	C₂²⋊C₄	—	4	32	no	—
291	C₄²	—	2	8	no	—
292	C₄²	—	2	8	no	—
293	C₄²	—	4	8	no	—
294	C₄²	C₂×C₅×D₄	1	8	yes	—
295	C₄²	C₂×C₅×D₄	1	4	yes	—
296	C₄²	C₂×C₅×D₄	1	4	yes	—
297	C₂×C₅	—	2	4	no	—
298	C₂×C₅	—	8	4	no	—
299	C₂×C₅	C₂²×#124	1	1	yes	characteristic
300	C₂×C₅	#3449	1	2	yes	—
301	C₂×C₅	#3510	1	4	yes	—
302	C₂³	—	2	4	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	2	8	no	—
305	C₂³	—	2	16	no	—
306	C₂³	—	4	16	no	—
307	C₂³	—	4	8	no	—
308	C₂³	—	8	16	no	—
309	C₂³	C₂²×C₅×D₄	1	2	yes	—
310	C₂³	C₂×C₅×#41	1	4	yes	—
311	C₂³	C₂⁵×C₅	1	1	yes	characteristic
312	Q₈	—	4	16	no	—
313	Q₈	—	4	8	no	—
314	Q₈	—	4	8	no	—
315	D₄	—	4	8	no	—
316	D₄	—	4	8	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	16	no	—
324	C₂×C₄	—	2	16	no	—
325	C₂×C₄	—	4	8	no	—
326	C₂×C₄	—	4	8	no	—
327	C₂×C₄	C₅×#124	1	16	yes	—
328	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
329	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
330	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
331	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
332	C₂×C₄	C₂×C₅×#41	1	4	yes	—
333	C₂×C₄	C₂×C₅×#41	1	4	yes	—
334	C₅	#35338	1	1	yes	characteristic, direct product factor, Sylow
335	C₂²	—	2	4	no	—
336	C₂²	—	2	8	no	—
337	C₂²	—	4	4	no	—
338	C₂²	—	4	8	no	—
339	C₂²	—	4	16	no	—
340	C₂²	—	8	16	no	—
341	C₂²	C₂×C₅×#124	1	4	yes	—
342	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
343	C₂²	C₂²×C₅×#41	1	2	yes	—
344	C₂²	C₅×#585	1	4	yes	—
345	C₄	—	2	4	no	—
346	C₄	—	2	4	no	—
347	C₄	—	4	4	no	—
348	C₄	—	4	8	no	—
349	C₄	—	4	8	no	—
350	C₄	C₂×C₅×#124	1	4	yes	—
351	C₄	C₂×C₅×#124	1	4	yes	—
352	C₂	—	2	4	no	—
353	C₂	—	8	4	no	—
354	C₂	C₂²×C₅×#124	1	1	yes	characteristic
355	C₂	C₅×#3449	1	2	yes	—
356	C₂	C₅×#3510	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#533	C₂	semidirect
3. C₅×#2861	C₂	semidirect
4. C₅×#2640	C₂	semidirect
5. C₅×#2592	C₂	semidirect
6. C₅×#2561	C₂	semidirect
7. C₅×#2310	C₂	semidirect
9. C₄×C₅×#117	C₂	semidirect
13. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
14. C₂×C₅×#125	C₂²	semidirect
20. C₂×C₄×C₅×Q₈	C₂²	semidirect
25. C₅×#397	C₂²	semidirect
26. C₅×#393	C₂²	semidirect
27. C₅×#391	C₂²	semidirect
28. C₅×#391	C₂²	semidirect
31. C₅×#388	C₂²	semidirect
34. C₄×C₅×C₄⋊C₄	C₂²	semidirect
36. C₅×#376	C₂²	semidirect
37. C₄³×C₅	C₂²	semidirect
38. #35338	C₅	direct (N × H)
80. C₂×#533	C₂×C₅	semidirect
82. #2861	C₂×C₅	semidirect
83. #2640	C₂×C₅	semidirect
84. #2592	C₂×C₅	semidirect
85. #2561	C₂×C₅	semidirect
86. #2310	C₂×C₅	semidirect
88. C₄×#117	C₂×C₅	semidirect
137. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
138. C₂×#125	C₂²×C₅	semidirect
144. C₂×C₄×Q₈	C₂²×C₅	semidirect
149. #397	C₂²×C₅	semidirect
150. #393	C₂²×C₅	semidirect
151. #391	C₂²×C₅	semidirect
152. #391	C₂²×C₅	semidirect
155. #388	C₂²×C₅	semidirect
158. C₄×C₄⋊C₄	C₂²×C₅	semidirect
160. #376	C₂²×C₅	semidirect
161. C₄³	C₂²×C₅	semidirect
334. C₅	#35338	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
C₂²×C₅×#124	2
C₅×#2861	2
C₅×#2640	2
C₅×#2592	2
C₅×#2561	2
C₅×#2310	2
C₅×#2309	2
C₄×C₅×#117	2
#35338	5

Subgroups — C5×#35338 #11958058

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#35338 #11958058