Subgroups — C₅×#33646 #11956366

Order 1280.

628 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3050	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2236	C₂	1	2	yes	maximal, complemented
4	C₅×#2235	C₂	1	2	yes	maximal, complemented
5	C₅×#2233	C₂	1	2	yes	maximal, complemented
6	C₅×#2232	C₂	1	2	yes	maximal, complemented
7	C₅×#2159	C₂	1	2	yes	maximal, complemented
8	C₅×#2139	C₂	1	2	yes	maximal, complemented
9	C₅×#2112	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#135	C₂²	1	1	yes	characteristic
11	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₅×#525	—	2	1	no	—
13	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
14	C₂×C₅×M₃₂	C₂²	1	2	yes	—
15	C₅×#467	C₂²	1	1	yes	characteristic
16	C₅×#467	C₂²	1	1	yes	characteristic
17	C₅×#466	C₂²	1	1	yes	characteristic
18	C₅×#466	C₂²	1	1	yes	characteristic
19	C₅×#465	—	2	1	no	—
20	C₅×#465	—	2	1	no	—
21	C₅×#427	C₂²	1	1	yes	characteristic
22	C₂×C₅×#107	—	2	1	no	—
23	C₂×C₅×#107	—	2	1	no	—
24	C₂×C₅×#107	—	2	1	no	—
25	C₂×C₅×#107	C₂²	1	2	yes	—
26	C₂×C₅×#107	C₂²	1	2	yes	—
27	C₂×C₅×#107	C₂²	1	2	yes	—
28	C₅×#416	—	2	1	no	—
29	C₅×#367	C₂²	1	4	yes	complemented
30	C₅×#366	C₂²	1	4	yes	complemented
31	C₅×#358	C₂²	1	4	yes	complemented
32	C₅×#357	C₂²	1	4	yes	complemented
33	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
34	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
35	#33646	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂×C₅×#41	—	2	1	no	—
37	C₂³×C₄×C₅	—	4	1	no	—
38	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
39	C₅×#135	—	2	4	no	—
40	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
41	C₂×C₅×SD₁₆	—	2	1	no	—
42	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
43	C₂²×C₅×C₈	—	2	4	no	—
44	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
45	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
46	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
47	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₅×#123	—	4	1	no	—
51	C₅×C₂²⋊Q₈	—	2	1	no	—
52	C₅×C₂²⋊Q₈	—	2	1	no	—
53	C₅×#121	—	2	1	no	—
54	C₅×#121	—	2	1	no	—
55	C₅×#120	—	4	1	no	—
56	C₄×C₅×D₄	—	4	1	no	—
57	C₄×C₅×D₄	—	4	1	no	—
58	C₅×#117	—	2	1	no	—
59	C₂×C₅×C₄⋊C₄	—	2	2	no	—
60	C₂×C₅×C₄⋊C₄	—	2	2	no	—
61	C₂×C₅×C₄⋊C₄	—	2	2	no	—
62	C₂×C₅×C₄⋊C₄	—	4	1	no	—
63	C₂×C₅×C₄⋊C₄	—	4	1	no	—
64	C₂×C₅×C₄⋊C₄	—	4	1	no	—
65	C₅×M₃₂	—	2	4	no	—
66	C₂×C₅×C₁₆	C₂³	1	4	yes	—
67	C₅×#107	—	2	2	no	—
68	C₅×#107	—	2	2	no	—
69	C₅×#107	—	2	2	no	—
70	C₅×#107	C₂³	1	4	yes	—
71	C₅×#107	C₂³	1	1	yes	characteristic
72	C₅×#107	C₂³	1	1	yes	characteristic
73	C₅×#106	—	2	1	no	—
74	C₅×#103	—	2	1	no	—
75	C₅×#103	—	2	1	no	—
76	C₅×#102	—	2	1	no	—
77	C₅×#102	—	2	1	no	—
78	#3050	C₂×C₅	1	1	yes	characteristic
79	C₂²×#107	C₂×C₅	1	1	yes	characteristic, complemented
80	#2236	C₂×C₅	1	2	yes	complemented
81	#2235	C₂×C₅	1	2	yes	complemented
82	#2233	C₂×C₅	1	2	yes	complemented
83	#2232	C₂×C₅	1	2	yes	complemented
84	#2159	C₂×C₅	1	2	yes	complemented
85	#2139	C₂×C₅	1	2	yes	complemented
86	#2112	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂⁴×C₅	D₈	1	1	yes	characteristic
88	C₅×#41	—	4	2	no	—
89	C₅×#41	—	4	2	no	—
90	C₂×C₅×Q₈	—	2	1	no	—
91	C₂×C₅×D₄	—	2	1	no	—
92	C₂×C₅×D₄	—	4	1	no	—
93	C₂×C₅×D₄	—	4	1	no	—
94	C₂×C₅×D₄	—	4	1	no	—
95	C₂²×C₄×C₅	—	2	2	no	—
96	C₂²×C₄×C₅	—	2	2	no	—
97	C₂²×C₄×C₅	—	4	2	no	—
98	C₂²×C₄×C₅	—	4	2	no	—
99	C₂²×C₄×C₅	—	4	2	no	—
100	C₂²×C₄×C₅	—	4	1	no	—
101	C₂²×C₄×C₅	—	8	4	no	—
102	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
103	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
104	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
105	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
108	C₅×Q₁₆	—	2	2	no	—
109	C₅×SD₁₆	—	4	2	no	—
110	C₅×D₈	—	2	2	no	—
111	C₂×C₅×C₈	—	2	2	no	—
112	C₂×C₅×C₈	—	2	2	no	—
113	C₂×C₅×C₈	—	2	2	no	—
114	C₂×C₅×C₈	—	2	2	no	—
115	C₂×C₅×C₈	—	2	2	no	—
116	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
117	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
118	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
119	C₂×C₅×C₈	#41	1	4	yes	—
120	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
121	C₅×C₄⋊C₄	—	2	4	no	—
122	C₅×C₄⋊C₄	—	2	1	no	—
123	C₅×C₄⋊C₄	—	2	1	no	—
124	C₅×C₄⋊C₄	—	4	2	no	—
125	C₅×C₄⋊C₄	—	4	2	no	—
126	C₅×C₄⋊C₄	—	4	2	no	—
127	C₅×C₄⋊C₄	—	4	1	no	—
128	C₅×C₄⋊C₄	—	4	1	no	—
129	C₅×C₂²⋊C₄	—	4	1	no	—
130	C₅×C₂²⋊C₄	—	4	1	no	—
131	C₅×C₂²⋊C₄	—	4	1	no	—
132	C₅×C₂²⋊C₄	—	4	1	no	—
133	C₅×C₂²⋊C₄	—	4	1	no	—
134	C₄²×C₅	—	4	1	no	—
135	C₅×C₁₆	—	2	4	no	—
136	C₂×#135	C₂²×C₅	1	1	yes	characteristic
137	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
138	#525	—	2	1	no	—
139	C₂²×C₄⋊C₄	—	2	1	no	—
140	C₂×M₃₂	C₂²×C₅	1	2	yes	—
141	#467	C₂²×C₅	1	1	yes	characteristic
142	#467	C₂²×C₅	1	1	yes	characteristic
143	#466	C₂²×C₅	1	1	yes	characteristic
144	#466	C₂²×C₅	1	1	yes	characteristic
145	#465	—	2	1	no	—
146	#465	—	2	1	no	—
147	#427	C₂²×C₅	1	1	yes	characteristic
148	C₂×#107	—	2	1	no	—
149	C₂×#107	—	2	1	no	—
150	C₂×#107	—	2	1	no	—
151	C₂×#107	C₂²×C₅	1	2	yes	—
152	C₂×#107	C₂²×C₅	1	2	yes	—
153	C₂×#107	C₂²×C₅	1	2	yes	—
154	#416	—	2	1	no	—
155	#367	C₂²×C₅	1	4	yes	complemented
156	#366	C₂²×C₅	1	4	yes	complemented
157	#358	C₂²×C₅	1	4	yes	complemented
158	#357	C₂²×C₅	1	4	yes	complemented
159	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
160	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
161	C₂³×C₅	—	2	2	no	—
162	C₂³×C₅	—	2	2	no	—
163	C₂³×C₅	—	2	2	no	—
164	C₂³×C₅	—	4	1	no	—
165	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
166	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
167	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
168	C₅×Q₈	—	4	1	no	—
169	C₅×Q₈	—	4	1	no	—
170	C₅×D₄	—	4	1	no	—
171	C₅×D₄	—	4	1	no	—
172	C₅×D₄	—	8	2	no	—
173	C₅×D₄	—	8	2	no	—
174	C₅×D₄	—	8	2	no	—
175	C₂×C₄×C₅	—	2	2	no	—
176	C₂×C₄×C₅	—	2	1	no	—
177	C₂×C₄×C₅	—	2	1	no	—
178	C₂×C₄×C₅	—	2	1	no	—
179	C₂×C₄×C₅	—	2	1	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	4	1	no	—
183	C₂×C₄×C₅	—	4	1	no	—
184	C₂×C₄×C₅	—	4	1	no	—
185	C₂×C₄×C₅	—	4	4	no	—
186	C₂×C₄×C₅	—	8	4	no	—
187	C₂×C₄×C₅	—	8	4	no	—
188	C₂×C₄×C₅	—	8	4	no	—
189	C₂×C₄×C₅	—	8	2	no	—
190	C₂×C₄×C₅	#123	1	2	yes	—
191	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
192	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
194	C₂×C₄×C₅	#137	1	2	yes	—
195	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
196	C₅×C₈	—	2	1	no	—
197	C₅×C₈	—	2	1	no	—
198	C₅×C₈	#123	1	2	yes	—
199	C₅×C₈	C₂×#41	1	2	yes	—
200	C₂×#41	—	2	1	no	—
201	C₂³×C₄	—	4	1	no	—
202	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
203	#135	—	2	4	no	—
204	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
205	C₂×SD₁₆	—	2	1	no	—
206	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
207	C₂²×C₈	—	2	4	no	—
208	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
209	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
210	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
211	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
212	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
213	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
214	#123	—	4	1	no	—
215	C₂²⋊Q₈	—	2	1	no	—
216	C₂²⋊Q₈	—	2	1	no	—
217	#121	—	2	1	no	—
218	#121	—	2	1	no	—
219	#120	—	4	1	no	—
220	C₄×D₄	—	4	1	no	—
221	C₄×D₄	—	4	1	no	—
222	#117	—	2	1	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	—	2	2	no	—
226	C₂×C₄⋊C₄	—	4	1	no	—
227	C₂×C₄⋊C₄	—	4	1	no	—
228	C₂×C₄⋊C₄	—	4	1	no	—
229	M₃₂	—	2	4	no	—
230	C₂×C₁₆	C₂³×C₅	1	4	yes	—
231	#107	—	2	2	no	—
232	#107	—	2	2	no	—
233	#107	—	2	2	no	—
234	#107	C₂³×C₅	1	4	yes	—
235	#107	C₂³×C₅	1	1	yes	characteristic
236	#107	C₂³×C₅	1	1	yes	characteristic
237	#106	—	2	1	no	—
238	#103	—	2	1	no	—
239	#103	—	2	1	no	—
240	#102	—	2	1	no	—
241	#102	—	2	1	no	—
242	C₂²×C₅	—	2	8	no	—
243	C₂²×C₅	—	2	1	no	—
244	C₂²×C₅	—	2	1	no	—
245	C₂²×C₅	—	2	1	no	—
246	C₂²×C₅	—	2	1	no	—
247	C₂²×C₅	—	2	1	no	—
248	C₂²×C₅	—	2	1	no	—
249	C₂²×C₅	—	8	1	no	—
250	C₂²×C₅	—	8	1	no	—
251	C₂²×C₅	—	8	1	no	—
252	C₂²×C₅	#480	1	2	yes	—
253	C₂²×C₅	#509	1	2	yes	—
254	C₂²×C₅	#510	1	2	yes	—
255	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
256	C₄×C₅	—	2	1	no	—
257	C₄×C₅	—	2	1	no	—
258	C₄×C₅	—	8	1	no	—
259	C₄×C₅	—	8	4	no	—
260	C₄×C₅	—	8	1	no	—
261	C₄×C₅	—	8	1	no	—
262	C₄×C₅	#480	1	2	yes	—
263	C₄×C₅	C₂×#123	1	1	yes	characteristic
264	C₄×C₅	C₂×#137	1	1	yes	characteristic
265	C₂⁴	C₅×D₈	1	1	yes	characteristic
266	#41	—	4	2	no	—
267	#41	—	4	2	no	—
268	C₂×Q₈	—	2	1	no	—
269	C₂×D₄	—	2	1	no	—
270	C₂×D₄	—	4	1	no	—
271	C₂×D₄	—	4	1	no	—
272	C₂×D₄	—	4	1	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	—	8	4	no	—
280	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
281	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
282	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
286	Q₁₆	—	2	2	no	—
287	SD₁₆	—	4	2	no	—
288	D₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
295	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
296	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
297	C₂×C₈	C₅×#41	1	4	yes	—
298	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	4	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₂²⋊C₄	—	4	1	no	—
308	C₂²⋊C₄	—	4	1	no	—
309	C₂²⋊C₄	—	4	1	no	—
310	C₂²⋊C₄	—	4	1	no	—
311	C₂²⋊C₄	—	4	1	no	—
312	C₄²	—	4	1	no	—
313	C₁₆	—	2	4	no	—
314	C₂×C₅	—	2	2	no	—
315	C₂×C₅	—	2	2	no	—
316	C₂×C₅	—	2	2	no	—
317	C₂×C₅	—	16	1	no	—
318	C₂×C₅	C₂×#480	1	1	yes	characteristic
319	C₂×C₅	C₂×#509	1	1	yes	characteristic
320	C₂×C₅	C₂×#510	1	1	yes	characteristic
321	C₂³	—	2	2	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	2	2	no	—
324	C₂³	—	4	1	no	—
325	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
326	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
327	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
328	Q₈	—	4	1	no	—
329	Q₈	—	4	1	no	—
330	D₄	—	4	1	no	—
331	D₄	—	4	1	no	—
332	D₄	—	8	2	no	—
333	D₄	—	8	2	no	—
334	D₄	—	8	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	8	4	no	—
347	C₂×C₄	—	8	4	no	—
348	C₂×C₄	—	8	4	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	C₅×#123	1	2	yes	—
351	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
352	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
353	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
354	C₂×C₄	C₅×#137	1	2	yes	—
355	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
356	C₈	—	2	1	no	—
357	C₈	—	2	1	no	—
358	C₈	C₅×#123	1	2	yes	—
359	C₈	C₂×C₅×#41	1	2	yes	—
360	C₅	#33646	1	1	yes	characteristic, direct product factor, Sylow
361	C₂²	—	2	8	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	8	1	no	—
369	C₂²	—	8	1	no	—
370	C₂²	—	8	1	no	—
371	C₂²	C₅×#480	1	2	yes	—
372	C₂²	C₅×#509	1	2	yes	—
373	C₂²	C₅×#510	1	2	yes	—
374	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	8	1	no	—
378	C₄	—	8	4	no	—
379	C₄	—	8	1	no	—
380	C₄	—	8	1	no	—
381	C₄	C₅×#480	1	2	yes	—
382	C₄	C₂×C₅×#123	1	1	yes	characteristic
383	C₄	C₂×C₅×#137	1	1	yes	characteristic
384	C₂	—	2	2	no	—
385	C₂	—	2	2	no	—
386	C₂	—	2	2	no	—
387	C₂	—	16	1	no	—
388	C₂	C₂×C₅×#480	1	1	yes	characteristic
389	C₂	C₂×C₅×#509	1	1	yes	characteristic
390	C₂	C₂×C₅×#510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
prime radical	C₅×#3050	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×#107	C₂	semidirect
3. C₅×#2236	C₂	semidirect
4. C₅×#2235	C₂	semidirect
5. C₅×#2233	C₂	semidirect
6. C₅×#2232	C₂	semidirect
7. C₅×#2159	C₂	semidirect
8. C₅×#2139	C₂	semidirect
9. C₅×#2112	C₂	semidirect
29. C₅×#367	C₂²	semidirect
30. C₅×#366	C₂²	semidirect
31. C₅×#358	C₂²	semidirect
32. C₅×#357	C₂²	semidirect
35. #33646	C₅	direct (N × H)
79. C₂²×#107	C₂×C₅	semidirect
80. #2236	C₂×C₅	semidirect
81. #2235	C₂×C₅	semidirect
82. #2233	C₂×C₅	semidirect
83. #2232	C₂×C₅	semidirect
84. #2159	C₂×C₅	semidirect
85. #2139	C₂×C₅	semidirect
86. #2112	C₂×C₅	semidirect
155. #367	C₂²×C₅	semidirect
156. #366	C₂²×C₅	semidirect
157. #358	C₂²×C₅	semidirect
158. #357	C₂²×C₅	semidirect
360. C₅	#33646	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×#3050	2
C₂²×C₅×#107	2
C₅×#2236	2
C₅×#2235	2
C₅×#2233	2
C₅×#2232	2
C₅×#2159	2
C₅×#2139	2
C₅×#2112	2
#33646	5

Subgroups — C5×#33646 #11956366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33646 #11956366