Subgroups — C₅×#21181 #11943901

Order 1280.

874 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#108	C₂	1	1	yes	maximal, characteristic
2	C₅×#2911	C₂	1	2	yes	maximal
3	C₂×C₅×#427	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic
5	C₅×#1952	C₂	1	4	yes	maximal, complemented
6	C₅×#1951	C₂	1	4	yes	maximal, complemented
7	C₅×#1742	C₂	1	2	yes	maximal
8	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
9	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
10	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₅×#117	C₂²	1	1	yes	characteristic
12	C₂×C₅×#117	C₂²	1	2	yes	—
13	C₂×C₅×#108	C₄	1	8	yes	complemented
14	C₂×C₅×#108	C₂²	1	2	yes	—
15	C₂×C₅×#108	C₂²	1	2	yes	—
16	C₅×#428	—	2	4	no	—
17	C₅×#428	C₂²	1	8	yes	—
18	C₅×#427	—	2	1	no	—
19	C₅×#427	—	2	1	no	—
20	C₅×#427	—	2	1	no	—
21	C₅×#427	—	2	1	no	—
22	C₅×#427	—	2	4	no	—
23	C₂×C₅×#107	C₂²	1	2	yes	—
24	C₂×C₅×#106	C₂²	1	2	yes	—
25	C₅×#405	—	2	1	no	—
26	C₅×#405	—	2	1	no	—
27	C₅×#405	C₂²	1	2	yes	—
28	C₅×#405	C₂²	1	2	yes	—
29	C₂×C₅×#97	—	2	1	no	—
30	C₂×C₄×C₅×C₈	—	2	1	no	—
31	C₅×#343	C₂²	1	8	yes	—
32	#21181	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
34	C₂×C₅×M₁₆	—	2	1	no	—
35	C₂×C₅×M₁₆	—	2	2	no	—
36	C₂×C₅×M₁₆	—	2	4	no	—
37	C₂×C₅×M₁₆	—	2	2	no	—
38	C₂×C₅×M₁₆	C₂×C₄	1	8	yes	—
39	C₂×C₅×M₁₆	Q₈	1	4	yes	—
40	C₂×C₅×M₁₆	C₂³	1	4	yes	—
41	C₂×C₅×M₁₆	C₂³	1	2	yes	—
42	C₂²×C₅×C₈	—	2	1	no	—
43	C₂²×C₅×C₈	—	2	2	no	—
44	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
45	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
46	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
47	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
48	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
49	C₂²×C₅×C₈	Q₈	1	4	yes	—
50	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₅×#117	—	2	1	no	—
53	C₅×#117	—	2	1	no	—
54	C₅×#117	—	2	2	no	—
55	C₅×#117	—	2	2	no	—
56	C₅×#117	—	2	2	no	—
57	C₅×#117	—	2	2	no	—
58	C₅×#117	D₄	1	2	yes	—
59	C₅×#117	C₂³	1	2	yes	—
60	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
61	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
62	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
63	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₄²×C₅	—	2	1	no	—
65	C₂×C₄²×C₅	—	2	2	no	—
66	C₅×#108	C₂×C₄	1	8	yes	complemented
67	C₅×#108	C₂×C₄	1	8	yes	complemented
68	C₅×#107	—	2	2	no	—
69	C₅×#107	—	2	2	no	—
70	C₅×#107	—	2	8	no	—
71	C₅×#106	—	2	2	no	—
72	C₅×#106	—	2	2	no	—
73	C₅×#106	—	2	8	no	—
74	C₅×#97	—	2	2	no	—
75	C₅×#97	—	2	2	no	—
76	C₄×C₅×C₈	—	2	2	no	—
77	C₄×C₅×C₈	—	2	2	no	—
78	C₂²×#108	C₂×C₅	1	1	yes	characteristic
79	#2911	C₂×C₅	1	2	yes	—
80	C₂×#427	C₂×C₅	1	1	yes	characteristic
81	C₂×#405	C₂×C₅	1	1	yes	characteristic
82	#1952	C₂×C₅	1	4	yes	complemented
83	#1951	C₂×C₅	1	4	yes	complemented
84	#1742	C₂×C₅	1	2	yes	—
85	C₂⁴×C₅	#41	1	1	yes	characteristic
86	C₂²×C₄×C₅	—	2	2	no	—
87	C₂²×C₄×C₅	—	2	4	no	—
88	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
94	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₅	#41	1	2	yes	—
96	C₂²×C₄×C₅	#41	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
98	C₅×M₁₆	—	2	8	no	—
99	C₅×M₁₆	—	2	4	no	—
100	C₅×M₁₆	—	2	4	no	—
101	C₅×M₁₆	—	2	2	no	—
102	C₅×M₁₆	C₂²×C₄	1	8	yes	—
103	C₅×M₁₆	C₂×Q₈	1	4	yes	—
104	C₂×C₅×C₈	—	2	8	no	—
105	C₂×C₅×C₈	—	2	4	no	—
106	C₂×C₅×C₈	—	2	2	no	—
107	C₂×C₅×C₈	—	2	4	no	—
108	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
109	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
110	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
111	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
112	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
113	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
114	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
115	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
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×Q₈	1	2	yes	—
119	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
120	C₅×C₄⋊C₄	—	2	2	no	—
121	C₅×C₄⋊C₄	—	2	4	no	—
122	C₅×C₄⋊C₄	—	2	4	no	—
123	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
124	C₅×C₂²⋊C₄	—	2	2	no	—
125	C₅×C₂²⋊C₄	—	2	2	no	—
126	C₅×C₂²⋊C₄	—	4	2	no	—
127	C₅×C₂²⋊C₄	—	4	2	no	—
128	C₄²×C₅	—	2	2	no	—
129	C₄²×C₅	—	2	2	no	—
130	C₄²×C₅	—	4	2	no	—
131	C₄²×C₅	—	4	2	no	—
132	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
133	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
134	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
135	C₂×#117	C₂²×C₅	1	1	yes	characteristic
136	C₂×#117	C₂²×C₅	1	2	yes	—
137	C₂×#108	C₄×C₅	1	8	yes	complemented
138	C₂×#108	C₂²×C₅	1	2	yes	—
139	C₂×#108	C₂²×C₅	1	2	yes	—
140	#428	—	2	4	no	—
141	#428	C₂²×C₅	1	8	yes	—
142	#427	—	2	1	no	—
143	#427	—	2	1	no	—
144	#427	—	2	1	no	—
145	#427	—	2	1	no	—
146	#427	—	2	4	no	—
147	C₂×#107	C₂²×C₅	1	2	yes	—
148	C₂×#106	C₂²×C₅	1	2	yes	—
149	#405	—	2	1	no	—
150	#405	—	2	1	no	—
151	#405	C₂²×C₅	1	2	yes	—
152	#405	C₂²×C₅	1	2	yes	—
153	C₂×#97	—	2	1	no	—
154	C₂×C₄×C₈	—	2	1	no	—
155	#343	C₂²×C₅	1	8	yes	—
156	C₂³×C₅	—	4	2	no	—
157	C₂³×C₅	C₄×Q₈	1	2	yes	—
158	C₂³×C₅	#121	1	1	yes	characteristic
159	C₂³×C₅	#121	1	1	yes	characteristic
160	C₂³×C₅	#125	1	2	yes	—
161	C₂³×C₅	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₅	—	2	4	no	—
163	C₂×C₄×C₅	—	4	4	no	—
164	C₂×C₄×C₅	—	4	4	no	—
165	C₂×C₄×C₅	—	8	4	no	—
166	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
167	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
168	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
169	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
171	C₂×C₄×C₅	#121	1	1	yes	characteristic
172	C₂×C₄×C₅	#121	1	1	yes	characteristic
173	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
174	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
175	C₂×C₄×C₅	#125	1	2	yes	—
176	C₂×C₄×C₅	C₄⋊Q₈	1	2	yes	—
177	C₂×C₄×C₅	C₄⋊Q₈	1	2	yes	—
178	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
184	C₅×C₈	—	2	8	no	—
185	C₅×C₈	—	2	4	no	—
186	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
187	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
188	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
189	C₅×C₈	C₂×C₄⋊C₄	1	2	yes	—
190	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
191	C₂×M₁₆	—	2	1	no	—
192	C₂×M₁₆	—	2	2	no	—
193	C₂×M₁₆	—	2	4	no	—
194	C₂×M₁₆	—	2	2	no	—
195	C₂×M₁₆	C₂×C₄×C₅	1	8	yes	—
196	C₂×M₁₆	C₅×Q₈	1	4	yes	—
197	C₂×M₁₆	C₂³×C₅	1	4	yes	—
198	C₂×M₁₆	C₂³×C₅	1	2	yes	—
199	C₂²×C₈	—	2	1	no	—
200	C₂²×C₈	—	2	2	no	—
201	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
202	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
203	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
204	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
205	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
206	C₂²×C₈	C₅×Q₈	1	4	yes	—
207	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
208	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
209	#117	—	2	1	no	—
210	#117	—	2	1	no	—
211	#117	—	2	2	no	—
212	#117	—	2	2	no	—
213	#117	—	2	2	no	—
214	#117	—	2	2	no	—
215	#117	C₅×D₄	1	2	yes	—
216	#117	C₂³×C₅	1	2	yes	—
217	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
218	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
219	C₂×C₂²⋊C₄	—	2	1	no	—
220	C₂×C₂²⋊C₄	—	2	2	no	—
221	C₂×C₄²	—	2	1	no	—
222	C₂×C₄²	—	2	2	no	—
223	#108	C₂×C₄×C₅	1	8	yes	complemented
224	#108	C₂×C₄×C₅	1	8	yes	complemented
225	#107	—	2	2	no	—
226	#107	—	2	2	no	—
227	#107	—	2	8	no	—
228	#106	—	2	2	no	—
229	#106	—	2	2	no	—
230	#106	—	2	8	no	—
231	#97	—	2	2	no	—
232	#97	—	2	2	no	—
233	C₄×C₈	—	2	2	no	—
234	C₄×C₈	—	2	2	no	—
235	C₂²×C₅	—	2	2	no	—
236	C₂²×C₅	—	2	2	no	—
237	C₂²×C₅	—	2	2	no	—
238	C₂²×C₅	—	4	2	no	—
239	C₂²×C₅	—	4	2	no	—
240	C₂²×C₅	#389	1	2	yes	—
241	C₂²×C₅	#389	1	2	yes	—
242	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
243	C₂²×C₅	C₂×#121	1	1	yes	characteristic
244	C₂²×C₅	C₂×#125	1	1	yes	characteristic
245	C₄×C₅	—	4	4	no	—
246	C₄×C₅	—	8	4	no	—
247	C₄×C₅	#389	1	2	yes	—
248	C₄×C₅	#389	1	2	yes	—
249	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
250	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
251	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
252	C₄×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
253	C₂⁴	C₅×#41	1	1	yes	characteristic
254	C₂²×C₄	—	2	2	no	—
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
257	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
258	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
259	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
260	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
261	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
262	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
263	C₂²×C₄	C₅×#41	1	2	yes	—
264	C₂²×C₄	C₅×#41	1	1	yes	characteristic
265	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
266	M₁₆	—	2	8	no	—
267	M₁₆	—	2	4	no	—
268	M₁₆	—	2	4	no	—
269	M₁₆	—	2	2	no	—
270	M₁₆	C₂²×C₄×C₅	1	8	yes	—
271	M₁₆	C₂×C₅×Q₈	1	4	yes	—
272	C₂×C₈	—	2	8	no	—
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
277	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
278	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
279	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
280	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
281	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
282	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
283	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
284	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
285	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
286	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
287	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
292	C₂²⋊C₄	—	2	2	no	—
293	C₂²⋊C₄	—	2	2	no	—
294	C₂²⋊C₄	—	4	2	no	—
295	C₂²⋊C₄	—	4	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	4	2	no	—
299	C₄²	—	4	2	no	—
300	C₂×C₅	—	2	1	no	—
301	C₂×C₅	—	2	1	no	—
302	C₂×C₅	—	2	2	no	—
303	C₂×C₅	—	2	2	no	—
304	C₂×C₅	C₂×#389	1	1	yes	characteristic
305	C₂×C₅	#3067	1	2	yes	—
306	C₂³	—	4	2	no	—
307	C₂³	C₄×C₅×Q₈	1	2	yes	—
308	C₂³	C₅×#121	1	1	yes	characteristic
309	C₂³	C₅×#121	1	1	yes	characteristic
310	C₂³	C₅×#125	1	2	yes	—
311	C₂³	C₂×C₅×#41	1	1	yes	characteristic
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	4	4	no	—
314	C₂×C₄	—	4	4	no	—
315	C₂×C₄	—	8	4	no	—
316	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
317	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
318	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
319	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
320	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
321	C₂×C₄	C₅×#121	1	1	yes	characteristic
322	C₂×C₄	C₅×#121	1	1	yes	characteristic
323	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
324	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
325	C₂×C₄	C₅×#125	1	2	yes	—
326	C₂×C₄	C₅×C₄⋊Q₈	1	2	yes	—
327	C₂×C₄	C₅×C₄⋊Q₈	1	2	yes	—
328	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
329	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
330	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
331	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
332	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
333	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
334	C₈	—	2	8	no	—
335	C₈	—	2	4	no	—
336	C₈	C₂×C₅×C₄⋊C₄	1	2	yes	—
337	C₈	C₂×C₅×C₄⋊C₄	1	2	yes	—
338	C₈	C₂×C₅×C₄⋊C₄	1	2	yes	—
339	C₈	C₂×C₅×C₄⋊C₄	1	2	yes	—
340	C₅	#21181	1	1	yes	characteristic, direct product factor, Sylow
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	2	no	—
346	C₂²	C₅×#389	1	2	yes	—
347	C₂²	C₅×#389	1	2	yes	—
348	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
349	C₂²	C₂×C₅×#121	1	1	yes	characteristic
350	C₂²	C₂×C₅×#125	1	1	yes	characteristic
351	C₄	—	4	4	no	—
352	C₄	—	8	4	no	—
353	C₄	C₅×#389	1	2	yes	—
354	C₄	C₅×#389	1	2	yes	—
355	C₄	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
356	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
357	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
358	C₄	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
359	C₂	—	2	2	no	—
360	C₂	—	2	2	no	—
361	C₂	—	2	1	no	—
362	C₂	—	2	1	no	—
363	C₂	C₂×C₅×#389	1	1	yes	characteristic
364	C₂	C₅×#3067	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	#121
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×#121
prime radical	C₂⁴×C₅	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂³×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₅×#1952	C₂	semidirect
6. C₅×#1951	C₂	semidirect
13. C₂×C₅×#108	C₄	semidirect
32. #21181	C₅	direct (N × H)
66. C₅×#108	C₂×C₄	semidirect
67. C₅×#108	C₂×C₄	semidirect
82. #1952	C₂×C₅	semidirect
83. #1951	C₂×C₅	semidirect
137. C₂×#108	C₄×C₅	semidirect
223. #108	C₂×C₄×C₅	semidirect
224. #108	C₂×C₄×C₅	semidirect
340. C₅	#21181	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×#108	2
C₅×#2911	2
C₂×C₅×#427	2
C₂×C₅×#405	2
C₅×#1952	2
C₅×#1951	2
C₅×#1742	2
#21181	5

Subgroups — C5×#21181 #11943901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21181 #11943901