Subgroups — C₅×#22244 #11944964

Order 1280.

722 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#446	C₂	1	2	yes	maximal
2	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₅×#1985	C₂	1	2	yes	maximal
4	C₅×#1917	C₂	1	2	yes	maximal
5	C₅×#1917	C₂	1	2	yes	maximal
6	C₅×#1916	C₂	1	2	yes	maximal
7	C₅×#1916	C₂	1	2	yes	maximal
8	C₅×#1831	C₂	1	1	yes	maximal, characteristic
9	C₅×#1745	C₂	1	1	yes	maximal, characteristic
10	C₂×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic
11	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
12	C₅×#446	—	2	8	no	—
13	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
15	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
16	C₂×C₅×#97	C₂²	1	2	yes	—
17	C₂×C₅×#97	C₂²	1	1	yes	characteristic
18	C₂×C₅×#97	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
20	C₅×#391	C₄	1	2	yes	—
21	C₅×#389	C₄	1	2	yes	—
22	C₅×#389	C₄	1	1	yes	characteristic
23	C₅×#389	C₄	1	1	yes	characteristic
24	C₅×#384	C₄	1	1	yes	characteristic
25	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
27	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₄³×C₅	C₂²	1	1	yes	characteristic
29	C₅×#336	C₂²	1	1	yes	characteristic
30	C₅×#336	C₂²	1	2	yes	—
31	C₅×#336	C₂²	1	1	yes	characteristic
32	C₅×#336	C₂²	1	2	yes	—
33	C₅×#336	C₂²	1	2	yes	—
34	C₅×#336	C₂²	1	2	yes	—
35	C₅×#336	C₂²	1	2	yes	—
36	C₅×#336	C₂²	1	2	yes	—
37	C₅×#336	C₂²	1	2	yes	—
38	#22244	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
40	C₂²×C₅×C₈	C₂³	1	2	yes	—
41	C₂²×C₅×C₈	C₂³	1	2	yes	—
42	C₂²×C₅×C₈	C₂³	1	2	yes	—
43	C₂²×C₅×C₈	C₂³	1	2	yes	—
44	C₅×C₄⋊Q₈	—	2	4	no	—
45	C₄×C₅×Q₈	—	2	4	no	—
46	C₄×C₅×Q₈	—	2	4	no	—
47	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
48	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
50	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
61	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₅	C₂³	1	2	yes	—
63	C₂×C₄²×C₅	C₂³	1	2	yes	—
64	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
65	C₅×C₄⋊C₈	—	2	4	no	—
66	C₅×C₄⋊C₈	—	2	4	no	—
67	C₅×C₄⋊C₈	—	2	4	no	—
68	C₅×#97	—	2	4	no	—
69	C₅×#97	—	2	2	no	—
70	C₅×#97	D₄	1	4	yes	—
71	C₄×C₅×C₈	—	2	4	no	—
72	C₅×#95	C₂×C₄	1	2	yes	—
73	C₅×#95	C₂×C₄	1	2	yes	—
74	C₅×#95	C₂×C₄	1	2	yes	—
75	C₅×#95	C₂×C₄	1	2	yes	—
76	C₂×#446	C₂×C₅	1	2	yes	—
77	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
78	#1985	C₂×C₅	1	2	yes	—
79	#1917	C₂×C₅	1	2	yes	—
80	#1917	C₂×C₅	1	2	yes	—
81	#1916	C₂×C₅	1	2	yes	—
82	#1916	C₂×C₅	1	2	yes	—
83	#1831	C₂×C₅	1	1	yes	characteristic
84	#1745	C₂×C₅	1	1	yes	characteristic
85	C₂×C₅×Q₈	—	2	4	no	—
86	C₂×C₅×Q₈	—	2	4	no	—
87	C₂×C₅×Q₈	—	4	2	no	—
88	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
99	C₂×C₅×C₈	—	2	2	no	—
100	C₂×C₅×C₈	—	2	2	no	—
101	C₂×C₅×C₈	—	2	2	no	—
102	C₂×C₅×C₈	—	2	2	no	—
103	C₂×C₅×C₈	—	2	2	no	—
104	C₂×C₅×C₈	—	2	2	no	—
105	C₂×C₅×C₈	—	2	2	no	—
106	C₂×C₅×C₈	—	2	2	no	—
107	C₂×C₅×C₈	—	2	2	no	—
108	C₂×C₅×C₈	—	2	2	no	—
109	C₂×C₅×C₈	—	2	2	no	—
110	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
111	C₅×C₄⋊C₄	—	2	4	no	—
112	C₅×C₄⋊C₄	—	2	4	no	—
113	C₅×C₄⋊C₄	—	2	4	no	—
114	C₅×C₄⋊C₄	—	2	4	no	—
115	C₅×C₄⋊C₄	—	2	2	no	—
116	C₅×C₄⋊C₄	—	2	4	no	—
117	C₅×C₄⋊C₄	—	4	1	no	—
118	C₅×C₄⋊C₄	—	4	1	no	—
119	C₅×C₄⋊C₄	M₁₆	1	4	yes	—
120	C₄²×C₅	—	2	2	no	—
121	C₄²×C₅	—	2	2	no	—
122	C₄²×C₅	—	2	2	no	—
123	C₄²×C₅	—	2	2	no	—
124	C₄²×C₅	—	2	2	no	—
125	C₄²×C₅	—	2	2	no	—
126	C₄²×C₅	—	2	2	no	—
127	C₄²×C₅	—	2	2	no	—
128	C₄²×C₅	—	4	1	no	—
129	C₄²×C₅	—	4	1	no	—
130	C₄²×C₅	C₂×D₄	1	2	yes	—
131	C₄²×C₅	#41	1	2	yes	—
132	C₂×C₄⋊Q₈	C₄×C₅	1	1	yes	characteristic
133	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
134	#446	—	2	8	no	—
135	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
136	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
137	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
138	C₂×#97	C₂²×C₅	1	2	yes	—
139	C₂×#97	C₂²×C₅	1	1	yes	characteristic
140	C₂×#97	C₂²×C₅	1	1	yes	characteristic
141	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
142	#391	C₄×C₅	1	2	yes	—
143	#389	C₄×C₅	1	2	yes	—
144	#389	C₄×C₅	1	1	yes	characteristic
145	#389	C₄×C₅	1	1	yes	characteristic
146	#384	C₄×C₅	1	1	yes	characteristic
147	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
148	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
149	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
150	C₄³	C₂²×C₅	1	1	yes	characteristic
151	#336	C₂²×C₅	1	1	yes	characteristic
152	#336	C₂²×C₅	1	2	yes	—
153	#336	C₂²×C₅	1	1	yes	characteristic
154	#336	C₂²×C₅	1	2	yes	—
155	#336	C₂²×C₅	1	2	yes	—
156	#336	C₂²×C₅	1	2	yes	—
157	#336	C₂²×C₅	1	2	yes	—
158	#336	C₂²×C₅	1	2	yes	—
159	#336	C₂²×C₅	1	2	yes	—
160	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
161	C₅×Q₈	—	4	8	no	—
162	C₂×C₄×C₅	—	2	2	no	—
163	C₂×C₄×C₅	—	2	1	no	—
164	C₂×C₄×C₅	—	2	1	no	—
165	C₂×C₄×C₅	—	2	1	no	—
166	C₂×C₄×C₅	—	2	1	no	—
167	C₂×C₄×C₅	—	2	1	no	—
168	C₂×C₄×C₅	—	2	1	no	—
169	C₂×C₄×C₅	—	2	1	no	—
170	C₂×C₄×C₅	—	2	1	no	—
171	C₂×C₄×C₅	—	2	2	no	—
172	C₂×C₄×C₅	—	2	2	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	2	1	no	—
176	C₂×C₄×C₅	—	2	1	no	—
177	C₂×C₄×C₅	—	2	2	no	—
178	C₂×C₄×C₅	—	2	1	no	—
179	C₂×C₄×C₅	—	2	2	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	1	no	—
182	C₂×C₄×C₅	—	2	1	no	—
183	C₂×C₄×C₅	—	2	1	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
188	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
189	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
190	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
191	C₂×C₄×C₅	#131	1	2	yes	—
192	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
195	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
196	C₅×C₈	—	2	4	no	—
197	C₅×C₈	—	4	2	no	—
198	C₅×C₈	—	4	2	no	—
199	C₅×C₈	—	4	2	no	—
200	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
201	C₂²×C₈	C₂³×C₅	1	2	yes	—
202	C₂²×C₈	C₂³×C₅	1	2	yes	—
203	C₂²×C₈	C₂³×C₅	1	2	yes	—
204	C₂²×C₈	C₂³×C₅	1	2	yes	—
205	C₄⋊Q₈	—	2	4	no	—
206	C₄×Q₈	—	2	4	no	—
207	C₄×Q₈	—	2	4	no	—
208	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
209	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
210	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
211	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
212	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
213	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
214	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
215	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
217	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
218	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
219	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
220	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
221	C₂×C₄²	C₂³×C₅	1	2	yes	—
222	C₂×C₄²	C₂³×C₅	1	2	yes	—
223	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
224	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
225	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
226	C₄⋊C₈	—	2	4	no	—
227	C₄⋊C₈	—	2	4	no	—
228	C₄⋊C₈	—	2	4	no	—
229	#97	—	2	4	no	—
230	#97	—	2	2	no	—
231	#97	C₅×D₄	1	4	yes	—
232	C₄×C₈	—	2	4	no	—
233	#95	C₂×C₄×C₅	1	2	yes	—
234	#95	C₂×C₄×C₅	1	2	yes	—
235	#95	C₂×C₄×C₅	1	2	yes	—
236	#95	C₂×C₄×C₅	1	2	yes	—
237	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
238	C₂²×C₅	#519	1	1	yes	characteristic
239	C₂²×C₅	#519	1	1	yes	characteristic
240	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
241	C₂²×C₅	C₂×#131	1	1	yes	characteristic
242	C₂²×C₅	#568	1	1	yes	characteristic
243	C₂²×C₅	#568	1	1	yes	characteristic
244	C₄×C₅	—	2	2	no	—
245	C₄×C₅	—	2	4	no	—
246	C₄×C₅	—	2	2	no	—
247	C₄×C₅	—	2	2	no	—
248	C₄×C₅	—	2	2	no	—
249	C₄×C₅	—	4	2	no	—
250	C₄×C₅	—	4	2	no	—
251	C₄×C₅	—	4	2	no	—
252	C₄×C₅	—	4	1	no	—
253	C₄×C₅	—	4	1	no	—
254	C₄×C₅	#536	1	2	yes	—
255	C₄×C₅	#541	1	2	yes	—
256	C₂×Q₈	—	2	4	no	—
257	C₂×Q₈	—	2	4	no	—
258	C₂×Q₈	—	4	2	no	—
259	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
260	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
261	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
262	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
263	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
264	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
265	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
266	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
267	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
268	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
269	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	2	2	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
282	C₄⋊C₄	—	2	4	no	—
283	C₄⋊C₄	—	2	4	no	—
284	C₄⋊C₄	—	2	4	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	4	1	no	—
289	C₄⋊C₄	—	4	1	no	—
290	C₄⋊C₄	C₅×M₁₆	1	4	yes	—
291	C₄²	—	2	2	no	—
292	C₄²	—	2	2	no	—
293	C₄²	—	2	2	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	4	1	no	—
300	C₄²	—	4	1	no	—
301	C₄²	C₂×C₅×D₄	1	2	yes	—
302	C₄²	C₅×#41	1	2	yes	—
303	C₂×C₅	#2327	1	1	yes	characteristic
304	C₂×C₅	D₄×M₁₆	1	1	yes	characteristic
305	C₂×C₅	#2935	1	1	yes	characteristic
306	C₂×C₅	#2983	1	1	yes	characteristic
307	C₂×C₅	#2984	1	1	yes	characteristic
308	C₂×C₅	#2985	1	1	yes	characteristic
309	C₂×C₅	#2987	1	1	yes	characteristic
310	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
311	Q₈	—	4	8	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	1	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
338	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
339	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
340	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	—
341	C₂×C₄	C₅×#131	1	2	yes	—
342	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
343	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
344	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
345	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
346	C₈	—	2	4	no	—
347	C₈	—	4	2	no	—
348	C₈	—	4	2	no	—
349	C₈	—	4	2	no	—
350	C₅	#22244	1	1	yes	characteristic, direct product factor, Sylow
351	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
352	C₂²	C₅×#519	1	1	yes	characteristic
353	C₂²	C₅×#519	1	1	yes	characteristic
354	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
355	C₂²	C₂×C₅×#131	1	1	yes	characteristic
356	C₂²	C₅×#568	1	1	yes	characteristic
357	C₂²	C₅×#568	1	1	yes	characteristic
358	C₄	—	2	2	no	—
359	C₄	—	2	2	no	—
360	C₄	—	2	2	no	—
361	C₄	—	2	4	no	—
362	C₄	—	2	2	no	—
363	C₄	—	4	1	no	—
364	C₄	—	4	1	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	C₅×#536	1	2	yes	—
369	C₄	C₅×#541	1	2	yes	—
370	C₂	C₅×#2327	1	1	yes	characteristic
371	C₂	C₅×D₄×M₁₆	1	1	yes	characteristic
372	C₂	C₅×#2935	1	1	yes	characteristic
373	C₂	C₅×#2983	1	1	yes	characteristic
374	C₂	C₅×#2984	1	1	yes	characteristic
375	C₂	C₅×#2985	1	1	yes	characteristic
376	C₂	C₅×#2987	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
38. #22244	C₅	direct (N × H)
350. C₅	#22244	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×#446	2
C₄×C₅×C₄⋊Q₈	2
C₅×#1985	2
C₅×#1917	2
C₅×#1916	2
C₅×#1831	2
C₅×#1745	2
#22244	5

Subgroups — C5×#22244 #11944964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22244 #11944964