Subgroups — C₅×#22221 #11944941

Order 1280.

822 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#487	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₅×#1990	C₂	1	1	yes	maximal, characteristic
5	C₅×#1956	C₂	1	1	yes	maximal, characteristic
6	C₅×#1928	C₂	1	4	yes	maximal
7	C₅×#1863	C₂	1	4	yes	maximal
8	C₅×#1845	C₂	1	1	yes	maximal, characteristic
9	C₅×#1744	C₂	1	1	yes	maximal, characteristic
10	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₅×Q₈	—	2	1	no	—
13	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
14	C₅×#487	C₄	1	8	yes	complemented
15	C₂×C₅×#107	C₂²	1	4	yes	—
16	C₂×C₅×#103	C₂²	1	4	yes	—
17	C₂×C₅×#103	C₂²	1	4	yes	—
18	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₅×#391	—	2	1	no	—
21	C₅×#391	C₂²	1	2	yes	—
22	C₅×#389	—	2	1	no	—
23	C₅×#389	—	2	1	no	—
24	C₅×#389	—	2	1	no	—
25	C₅×#389	C₂²	1	2	yes	—
26	C₅×#384	C₂²	1	1	yes	characteristic
27	C₅×#384	C₂²	1	1	yes	characteristic
28	C₄×C₅×C₄⋊C₄	—	2	1	no	—
29	C₄×C₅×C₄⋊C₄	—	2	1	no	—
30	C₄×C₅×C₄⋊C₄	—	2	1	no	—
31	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
32	C₄³×C₅	C₂²	1	1	yes	characteristic
33	C₅×#340	C₂²	1	4	yes	—
34	C₅×#336	C₂²	1	2	yes	—
35	C₅×#336	C₂²	1	2	yes	—
36	#22221	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂²×C₅×Q₈	—	2	1	no	—
38	C₂²×C₅×Q₈	C₂³	1	2	yes	—
39	C₂²×C₅×C₈	C₂³	1	2	yes	—
40	C₂²×C₅×C₈	C₂³	1	2	yes	—
41	C₅×C₄⋊Q₈	—	2	2	no	—
42	C₅×C₄⋊Q₈	—	2	2	no	—
43	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	—
44	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	—
45	C₄×C₅×Q₈	—	4	4	no	—
46	C₄×C₅×Q₈	—	4	4	no	—
47	C₂×C₅×C₄⋊C₄	—	2	1	no	—
48	C₂×C₅×C₄⋊C₄	—	2	1	no	—
49	C₂×C₅×C₄⋊C₄	—	2	1	no	—
50	C₂×C₅×C₄⋊C₄	—	2	1	no	—
51	C₂×C₅×C₄⋊C₄	—	2	1	no	—
52	C₂×C₅×C₄⋊C₄	—	2	1	no	—
53	C₂×C₅×C₄⋊C₄	—	2	1	no	—
54	C₂×C₅×C₄⋊C₄	—	2	2	no	—
55	C₂×C₅×C₄⋊C₄	—	2	2	no	—
56	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
57	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
58	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
59	C₂×C₄²×C₅	—	2	2	no	—
60	C₂×C₄²×C₅	—	2	2	no	—
61	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
68	C₅×#107	—	4	4	no	—
69	C₅×#103	—	4	4	no	—
70	C₅×#103	C₂×C₄	1	16	yes	—
71	C₄×C₅×C₈	—	2	2	no	—
72	C₄×C₅×C₈	C₂×C₄	1	4	yes	—
73	C₅×#95	—	2	2	no	—
74	C₅×#95	—	2	2	no	—
75	C₅×#95	—	2	2	no	—
76	C₅×#95	—	2	2	no	—
77	C₂×#487	C₂×C₅	1	1	yes	characteristic
78	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
79	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
80	#1990	C₂×C₅	1	1	yes	characteristic
81	#1956	C₂×C₅	1	1	yes	characteristic
82	#1928	C₂×C₅	1	4	yes	—
83	#1863	C₂×C₅	1	4	yes	—
84	#1845	C₂×C₅	1	1	yes	characteristic
85	#1744	C₂×C₅	1	1	yes	characteristic
86	C₂×C₅×Q₈	—	2	4	no	—
87	C₂×C₅×Q₈	—	2	2	no	—
88	C₂×C₅×Q₈	—	2	4	no	—
89	C₂×C₅×Q₈	—	2	4	no	—
90	C₂×C₅×Q₈	—	4	2	no	—
91	C₂×C₅×Q₈	—	4	2	no	—
92	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₅	—	2	2	no	—
94	C₂²×C₄×C₅	—	2	2	no	—
95	C₂²×C₄×C₅	—	2	2	no	—
96	C₂²×C₄×C₅	—	2	2	no	—
97	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
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	C₂²×C₄	1	4	yes	—
110	C₅×C₄⋊C₄	—	2	4	no	—
111	C₅×C₄⋊C₄	—	2	4	no	—
112	C₅×C₄⋊C₄	—	2	4	no	—
113	C₅×C₄⋊C₄	—	2	2	no	—
114	C₅×C₄⋊C₄	—	2	4	no	—
115	C₅×C₄⋊C₄	—	2	4	no	—
116	C₅×C₄⋊C₄	—	4	4	no	—
117	C₅×C₄⋊C₄	—	4	4	no	—
118	C₅×C₄⋊C₄	—	4	2	no	—
119	C₅×C₄⋊C₄	—	4	2	no	—
120	C₅×C₄⋊C₄	—	4	2	no	—
121	C₅×C₄⋊C₄	—	4	2	no	—
122	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
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	4	no	—
129	C₄²×C₅	—	4	4	no	—
130	C₄²×C₅	Q₁₆	1	4	yes	—
131	C₄²×C₅	C₂²×C₄	1	2	yes	—
132	C₄²×C₅	#41	1	2	yes	—
133	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
135	C₂×C₄×Q₈	—	2	1	no	—
136	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
137	#487	C₄×C₅	1	8	yes	complemented
138	C₂×#107	C₂²×C₅	1	4	yes	—
139	C₂×#103	C₂²×C₅	1	4	yes	—
140	C₂×#103	C₂²×C₅	1	4	yes	—
141	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
142	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
143	#391	—	2	1	no	—
144	#391	C₂²×C₅	1	2	yes	—
145	#389	—	2	1	no	—
146	#389	—	2	1	no	—
147	#389	—	2	1	no	—
148	#389	C₂²×C₅	1	2	yes	—
149	#384	C₂²×C₅	1	1	yes	characteristic
150	#384	C₂²×C₅	1	1	yes	characteristic
151	C₄×C₄⋊C₄	—	2	1	no	—
152	C₄×C₄⋊C₄	—	2	1	no	—
153	C₄×C₄⋊C₄	—	2	1	no	—
154	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
155	C₄³	C₂²×C₅	1	1	yes	characteristic
156	#340	C₂²×C₅	1	4	yes	—
157	#336	C₂²×C₅	1	2	yes	—
158	#336	C₂²×C₅	1	2	yes	—
159	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
160	C₅×Q₈	—	2	8	no	—
161	C₅×Q₈	—	4	4	no	—
162	C₅×Q₈	—	4	8	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	4	no	—
168	C₂×C₄×C₅	—	2	4	no	—
169	C₂×C₄×C₅	—	2	1	no	—
170	C₂×C₄×C₅	—	2	1	no	—
171	C₂×C₄×C₅	—	2	1	no	—
172	C₂×C₄×C₅	—	2	1	no	—
173	C₂×C₄×C₅	—	2	1	no	—
174	C₂×C₄×C₅	—	2	1	no	—
175	C₂×C₄×C₅	—	4	2	no	—
176	C₂×C₄×C₅	—	4	2	no	—
177	C₂×C₄×C₅	—	4	2	no	—
178	C₂×C₄×C₅	—	4	2	no	—
179	C₂×C₄×C₅	—	4	2	no	—
180	C₂×C₄×C₅	—	4	2	no	—
181	C₂×C₄×C₅	—	4	2	no	—
182	C₂×C₄×C₅	—	4	2	no	—
183	C₂×C₄×C₅	—	4	2	no	—
184	C₂×C₄×C₅	—	4	2	no	—
185	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
187	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
188	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
189	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
190	C₂×C₄×C₅	#135	1	2	yes	—
191	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
192	C₂×C₄×C₅	#137	1	2	yes	—
193	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
196	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
197	C₅×C₈	—	2	4	no	—
198	C₅×C₈	—	4	2	no	—
199	C₂²×Q₈	—	2	1	no	—
200	C₂²×Q₈	C₂³×C₅	1	2	yes	—
201	C₂²×C₈	C₂³×C₅	1	2	yes	—
202	C₂²×C₈	C₂³×C₅	1	2	yes	—
203	C₄⋊Q₈	—	2	2	no	—
204	C₄⋊Q₈	—	2	2	no	—
205	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	—
206	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	—
207	C₄×Q₈	—	4	4	no	—
208	C₄×Q₈	—	4	4	no	—
209	C₂×C₄⋊C₄	—	2	1	no	—
210	C₂×C₄⋊C₄	—	2	1	no	—
211	C₂×C₄⋊C₄	—	2	1	no	—
212	C₂×C₄⋊C₄	—	2	1	no	—
213	C₂×C₄⋊C₄	—	2	2	no	—
214	C₂×C₄⋊C₄	—	2	2	no	—
215	C₂×C₄⋊C₄	—	2	1	no	—
216	C₂×C₄⋊C₄	—	2	1	no	—
217	C₂×C₄⋊C₄	—	2	1	no	—
218	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
219	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
220	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
221	C₂×C₄²	—	2	2	no	—
222	C₂×C₄²	—	2	2	no	—
223	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
224	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
225	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
226	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
227	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
228	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
230	#107	—	4	4	no	—
231	#103	—	4	4	no	—
232	#103	C₂×C₄×C₅	1	16	yes	—
233	C₄×C₈	—	2	2	no	—
234	C₄×C₈	C₂×C₄×C₅	1	4	yes	—
235	#95	—	2	2	no	—
236	#95	—	2	2	no	—
237	#95	—	2	2	no	—
238	#95	—	2	2	no	—
239	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
240	C₂²×C₅	#535	1	1	yes	characteristic
241	C₂²×C₅	#536	1	1	yes	characteristic
242	C₂²×C₅	C₂²×Q₁₆	1	1	yes	characteristic
243	C₂²×C₅	C₂×#135	1	1	yes	characteristic
244	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₂²×C₅	C₂×#137	1	1	yes	characteristic
246	C₄×C₅	—	2	2	no	—
247	C₄×C₅	—	2	2	no	—
248	C₄×C₅	—	4	4	no	—
249	C₄×C₅	—	4	4	no	—
250	C₄×C₅	—	4	1	no	—
251	C₄×C₅	—	4	1	no	—
252	C₄×C₅	—	8	2	no	—
253	C₄×C₅	—	8	2	no	—
254	C₄×C₅	C₄×Q₁₆	1	4	yes	—
255	C₄×C₅	#440	1	4	yes	—
256	C₄×C₅	#520	1	2	yes	—
257	C₄×C₅	#542	1	2	yes	—
258	C₂×Q₈	—	2	4	no	—
259	C₂×Q₈	—	2	2	no	—
260	C₂×Q₈	—	2	4	no	—
261	C₂×Q₈	—	2	4	no	—
262	C₂×Q₈	—	4	2	no	—
263	C₂×Q₈	—	4	2	no	—
264	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
270	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
275	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
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	C₂²×C₄×C₅	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	2	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	4	4	no	—
289	C₄⋊C₄	—	4	4	no	—
290	C₄⋊C₄	—	4	2	no	—
291	C₄⋊C₄	—	4	2	no	—
292	C₄⋊C₄	—	4	2	no	—
293	C₄⋊C₄	—	4	2	no	—
294	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	4	4	no	—
301	C₄²	—	4	4	no	—
302	C₄²	C₅×Q₁₆	1	4	yes	—
303	C₄²	C₂²×C₄×C₅	1	2	yes	—
304	C₄²	C₅×#41	1	2	yes	—
305	C₂×C₅	#2326	1	1	yes	characteristic
306	C₂×C₅	C₂×C₄×Q₁₆	1	1	yes	characteristic
307	C₂×C₅	C₂×#440	1	1	yes	characteristic
308	C₂×C₅	#3207	1	1	yes	characteristic
309	C₂×C₅	#3209	1	1	yes	characteristic
310	C₂×C₅	#3230	1	1	yes	characteristic
311	C₂×C₅	#3231	1	1	yes	characteristic
312	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
313	Q₈	—	2	8	no	—
314	Q₈	—	4	8	no	—
315	Q₈	—	4	4	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	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
339	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
340	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
341	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
342	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
343	C₂×C₄	C₅×#135	1	2	yes	—
344	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
345	C₂×C₄	C₅×#137	1	2	yes	—
346	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
347	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
348	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
349	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
350	C₈	—	2	4	no	—
351	C₈	—	4	2	no	—
352	C₅	#22221	1	1	yes	characteristic, direct product factor, Sylow
353	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
354	C₂²	C₅×#535	1	1	yes	characteristic
355	C₂²	C₅×#536	1	1	yes	characteristic
356	C₂²	C₂²×C₅×Q₁₆	1	1	yes	characteristic
357	C₂²	C₂×C₅×#135	1	1	yes	characteristic
358	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
359	C₂²	C₂×C₅×#137	1	1	yes	characteristic
360	C₄	—	2	2	no	—
361	C₄	—	2	2	no	—
362	C₄	—	4	4	no	—
363	C₄	—	4	4	no	—
364	C₄	—	4	1	no	—
365	C₄	—	4	1	no	—
366	C₄	—	8	2	no	—
367	C₄	—	8	2	no	—
368	C₄	C₄×C₅×Q₁₆	1	4	yes	—
369	C₄	C₅×#440	1	4	yes	—
370	C₄	C₅×#520	1	2	yes	—
371	C₄	C₅×#542	1	2	yes	—
372	C₂	C₅×#2326	1	1	yes	characteristic
373	C₂	C₂×C₄×C₅×Q₁₆	1	1	yes	characteristic
374	C₂	C₂×C₅×#440	1	1	yes	characteristic
375	C₂	C₅×#3207	1	1	yes	characteristic
376	C₂	C₅×#3209	1	1	yes	characteristic
377	C₂	C₅×#3230	1	1	yes	characteristic
378	C₂	C₅×#3231	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
14. C₅×#487	C₄	semidirect
36. #22221	C₅	direct (N × H)
137. #487	C₄×C₅	semidirect
352. C₅	#22221	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×#487	2
C₄×C₅×C₄⋊Q₈	2
C₅×#1990	2
C₅×#1956	2
C₅×#1928	2
C₅×#1863	2
C₅×#1845	2
C₅×#1744	2
#22221	5

Subgroups — C5×#22221 #11944941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22221 #11944941