Subgroups — C₅×#22210 #11944930

Order 1280.

866 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	C₂×C₅×C₈×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#436	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×#124	C₂	1	1	yes	maximal, characteristic
4	C₅×#1984	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1954	C₂	1	1	yes	maximal, characteristic
6	C₅×#1923	C₂	1	4	yes	maximal, complemented
7	C₅×#1851	C₂	1	4	yes	maximal, complemented
8	C₅×#1842	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1744	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
11	C₂×C₅×#124	C₄	1	1	yes	characteristic
12	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₅×C₈×Q₈	—	2	4	no	—
15	C₅×#436	—	2	4	no	—
16	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	4	yes	—
20	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₅×C₂²⋊C₈	C₂²	1	4	yes	—
22	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
23	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₅×#391	C₄	1	1	yes	characteristic
26	C₅×#390	C₄	1	1	yes	characteristic
27	C₅×#388	C₄	1	4	yes	—
28	C₅×#382	C₄	1	1	yes	characteristic
29	C₄×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
30	C₄³×C₅	C₂²	1	1	yes	characteristic
31	C₅×#336	C₂²	1	2	yes	—
32	C₅×#336	C₂²	1	4	yes	—
33	C₅×#336	C₂²	1	2	yes	—
34	#22210	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₅	C₂³	1	2	yes	—
38	C₂×C₅×M₁₆	—	2	4	no	—
39	C₂×C₅×M₁₆	—	4	4	no	—
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	1	yes	characteristic
44	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
45	C₅×#124	—	2	4	no	—
46	C₄×C₅×Q₈	—	2	2	no	—
47	C₄×C₅×Q₈	—	2	2	no	—
48	C₄×C₅×D₄	—	2	2	no	—
49	C₄×C₅×D₄	—	2	2	no	—
50	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
51	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
52	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
54	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
55	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₅	C₂³	1	2	yes	—
60	C₂×C₄²×C₅	C₂³	1	2	yes	—
61	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₅×C₄⋊C₈	—	2	4	no	—
63	C₅×C₄⋊C₈	—	2	2	no	—
64	C₅×C₄⋊C₈	—	2	2	no	—
65	C₅×C₄⋊C₈	—	4	4	no	—
66	C₅×C₂²⋊C₈	—	2	4	no	—
67	C₅×C₂²⋊C₈	—	4	4	no	—
68	C₄×C₅×C₈	—	2	4	no	—
69	C₄×C₅×C₈	—	2	2	no	—
70	C₄×C₅×C₈	D₄	1	4	yes	—
71	C₅×#95	C₂×C₄	1	4	yes	—
72	C₅×#95	C₂×C₄	1	4	yes	—
73	C₂×C₈×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×#436	C₂×C₅	1	1	yes	characteristic
75	C₄×#124	C₂×C₅	1	1	yes	characteristic
76	#1984	C₂×C₅	1	1	yes	characteristic, complemented
77	#1954	C₂×C₅	1	1	yes	characteristic
78	#1923	C₂×C₅	1	4	yes	complemented
79	#1851	C₂×C₅	1	4	yes	complemented
80	#1842	C₂×C₅	1	1	yes	characteristic, complemented
81	#1744	C₂×C₅	1	1	yes	characteristic, complemented
82	C₂⁴×C₅	C₂²×C₄	1	2	yes	—
83	C₂×C₅×Q₈	—	2	2	no	—
84	C₂×C₅×Q₈	—	2	2	no	—
85	C₂×C₅×Q₈	M₁₆	1	4	yes	complemented
86	C₂×C₅×D₄	—	2	2	no	—
87	C₂×C₅×D₄	—	2	2	no	—
88	C₂×C₅×D₄	—	2	2	no	—
89	C₂²×C₄×C₅	—	2	2	no	—
90	C₂²×C₄×C₅	—	2	2	no	—
91	C₂²×C₄×C₅	—	2	4	no	—
92	C₂²×C₄×C₅	—	2	4	no	—
93	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
101	C₅×M₁₆	—	4	8	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	4	no	—
108	C₂×C₅×C₈	—	2	2	no	—
109	C₂×C₅×C₈	—	2	4	no	—
110	C₂×C₅×C₈	—	2	2	no	—
111	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
112	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
113	C₅×C₄⋊C₄	—	2	2	no	—
114	C₅×C₄⋊C₄	—	2	4	no	—
115	C₅×C₄⋊C₄	—	2	2	no	—
116	C₅×C₂²⋊C₄	—	2	4	no	—
117	C₅×C₂²⋊C₄	—	2	8	no	—
118	C₅×C₂²⋊C₄	—	2	8	no	—
119	C₄²×C₅	—	2	2	no	—
120	C₄²×C₅	—	2	2	no	—
121	C₄²×C₅	—	2	4	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	C₂×D₄	1	2	yes	—
127	C₄²×C₅	#41	1	2	yes	—
128	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
129	C₂×#124	C₄×C₅	1	1	yes	characteristic
130	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
132	C₈×Q₈	—	2	4	no	—
133	#436	—	2	4	no	—
134	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
135	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
136	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
137	C₂×C₄⋊C₈	C₂²×C₅	1	4	yes	—
138	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
139	C₂×C₂²⋊C₈	C₂²×C₅	1	4	yes	—
140	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
141	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
142	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
143	#391	C₄×C₅	1	1	yes	characteristic
144	#390	C₄×C₅	1	1	yes	characteristic
145	#388	C₄×C₅	1	4	yes	—
146	#382	C₄×C₅	1	1	yes	characteristic
147	C₄×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
148	C₄³	C₂²×C₅	1	1	yes	characteristic
149	#336	C₂²×C₅	1	2	yes	—
150	#336	C₂²×C₅	1	4	yes	—
151	#336	C₂²×C₅	1	2	yes	—
152	C₂³×C₅	—	2	2	no	—
153	C₂³×C₅	—	2	4	no	—
154	C₂³×C₅	—	2	2	no	—
155	C₂³×C₅	—	2	4	no	—
156	C₂³×C₅	—	2	2	no	—
157	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
158	C₅×Q₈	—	2	8	no	—
159	C₅×D₄	—	4	4	no	—
160	C₂×C₄×C₅	—	2	2	no	—
161	C₂×C₄×C₅	—	2	2	no	—
162	C₂×C₄×C₅	—	2	2	no	—
163	C₂×C₄×C₅	—	2	2	no	—
164	C₂×C₄×C₅	—	2	2	no	—
165	C₂×C₄×C₅	—	2	2	no	—
166	C₂×C₄×C₅	—	2	2	no	—
167	C₂×C₄×C₅	—	2	2	no	—
168	C₂×C₄×C₅	—	2	4	no	—
169	C₂×C₄×C₅	—	2	2	no	—
170	C₂×C₄×C₅	—	2	2	no	—
171	C₂×C₄×C₅	—	2	4	no	—
172	C₂×C₄×C₅	—	4	2	no	—
173	C₂×C₄×C₅	—	4	2	no	—
174	C₂×C₄×C₅	—	4	4	no	—
175	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
176	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
177	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
178	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
179	C₂×C₄×C₅	#131	1	4	yes	—
180	C₂×C₄×C₅	#131	1	2	yes	—
181	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
184	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
185	C₅×C₈	—	2	2	no	—
186	C₅×C₈	—	2	2	no	—
187	C₅×C₈	—	4	2	no	—
188	C₅×C₈	—	4	2	no	—
189	C₅×C₈	—	4	2	no	—
190	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
191	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
192	C₂³×C₄	C₂³×C₅	1	2	yes	—
193	C₂×M₁₆	—	2	4	no	—
194	C₂×M₁₆	—	4	4	no	—
195	C₂²×C₈	C₂³×C₅	1	2	yes	—
196	C₂²×C₈	C₂³×C₅	1	2	yes	—
197	C₂²×C₈	C₂³×C₅	1	2	yes	—
198	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
199	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
200	#124	—	2	4	no	—
201	C₄×Q₈	—	2	2	no	—
202	C₄×Q₈	—	2	2	no	—
203	C₄×D₄	—	2	2	no	—
204	C₄×D₄	—	2	2	no	—
205	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
207	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
208	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
209	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
210	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
211	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
212	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
213	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
214	C₂×C₄²	C₂³×C₅	1	2	yes	—
215	C₂×C₄²	C₂³×C₅	1	2	yes	—
216	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
217	C₄⋊C₈	—	2	4	no	—
218	C₄⋊C₈	—	2	2	no	—
219	C₄⋊C₈	—	2	2	no	—
220	C₄⋊C₈	—	4	4	no	—
221	C₂²⋊C₈	—	2	4	no	—
222	C₂²⋊C₈	—	4	4	no	—
223	C₄×C₈	—	2	4	no	—
224	C₄×C₈	—	2	2	no	—
225	C₄×C₈	C₅×D₄	1	4	yes	—
226	#95	C₂×C₄×C₅	1	4	yes	—
227	#95	C₂×C₄×C₅	1	4	yes	—
228	C₂²×C₅	—	4	2	no	—
229	C₂²×C₅	—	4	2	no	—
230	C₂²×C₅	—	4	2	no	—
231	C₂²×C₅	—	4	4	no	—
232	C₂²×C₅	—	4	4	no	—
233	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
234	C₂²×C₅	#520	1	2	yes	—
235	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
236	C₂²×C₅	C₂×#131	1	1	yes	characteristic
237	C₂²×C₅	C₂×#131	1	2	yes	—
238	C₄×C₅	—	2	4	no	—
239	C₄×C₅	—	2	2	no	—
240	C₄×C₅	—	2	4	no	—
241	C₄×C₅	—	4	2	no	—
242	C₄×C₅	—	4	2	no	—
243	C₄×C₅	—	4	2	no	—
244	C₄×C₅	#435	1	4	yes	—
245	C₄×C₅	#535	1	1	yes	characteristic
246	C₄×C₅	#536	1	1	yes	characteristic
247	C₄×C₅	#542	1	2	yes	—
248	C₂⁴	C₂²×C₄×C₅	1	2	yes	—
249	C₂×Q₈	—	2	2	no	—
250	C₂×Q₈	—	2	2	no	—
251	C₂×Q₈	C₅×M₁₆	1	4	yes	complemented
252	C₂×D₄	—	2	2	no	—
253	C₂×D₄	—	2	2	no	—
254	C₂×D₄	—	2	2	no	—
255	C₂²×C₄	—	2	2	no	—
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
260	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
261	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
262	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
263	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
264	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
265	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
266	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
267	M₁₆	—	4	8	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
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	4	no	—
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
278	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
279	C₄⋊C₄	—	2	2	no	—
280	C₄⋊C₄	—	2	4	no	—
281	C₄⋊C₄	—	2	2	no	—
282	C₂²⋊C₄	—	2	4	no	—
283	C₂²⋊C₄	—	2	8	no	—
284	C₂²⋊C₄	—	2	8	no	—
285	C₄²	—	2	2	no	—
286	C₄²	—	2	2	no	—
287	C₄²	—	2	4	no	—
288	C₄²	—	2	2	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	2	2	no	—
292	C₄²	C₂×C₅×D₄	1	2	yes	—
293	C₄²	C₅×#41	1	2	yes	—
294	C₂×C₅	—	8	2	no	—
295	C₂×C₅	#2326	1	1	yes	characteristic
296	C₂×C₅	C₂×#435	1	1	yes	characteristic
297	C₂×C₅	#2931	1	1	yes	characteristic
298	C₂×C₅	#2991	1	2	yes	—
299	C₂×C₅	#2994	1	2	yes	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	4	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	2	2	no	—
305	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
306	Q₈	—	2	8	no	—
307	D₄	—	4	4	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	4	2	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
324	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
325	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	—
326	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
327	C₂×C₄	C₅×#131	1	4	yes	—
328	C₂×C₄	C₅×#131	1	2	yes	—
329	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
330	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
331	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
332	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
333	C₈	—	2	2	no	—
334	C₈	—	2	2	no	—
335	C₈	—	4	2	no	—
336	C₈	—	4	2	no	—
337	C₈	—	4	2	no	—
338	C₅	#22210	1	1	yes	characteristic, direct product factor, Sylow
339	C₂²	—	4	4	no	—
340	C₂²	—	4	4	no	—
341	C₂²	—	4	2	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	2	no	—
344	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
345	C₂²	C₅×#520	1	2	yes	—
346	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
347	C₂²	C₂×C₅×#131	1	2	yes	—
348	C₂²	C₂×C₅×#131	1	1	yes	characteristic
349	C₄	—	2	4	no	—
350	C₄	—	2	4	no	—
351	C₄	—	2	2	no	—
352	C₄	—	4	2	no	—
353	C₄	—	4	2	no	—
354	C₄	—	4	2	no	—
355	C₄	C₅×#435	1	4	yes	—
356	C₄	C₅×#535	1	1	yes	characteristic
357	C₄	C₅×#536	1	1	yes	characteristic
358	C₄	C₅×#542	1	2	yes	—
359	C₂	—	8	2	no	—
360	C₂	C₅×#2326	1	1	yes	characteristic
361	C₂	C₂×C₅×#435	1	1	yes	characteristic
362	C₂	C₅×#2931	1	1	yes	characteristic
363	C₂	C₅×#2991	1	2	yes	—
364	C₂	C₅×#2994	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂³	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂²×C₅×D₄	C₂×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
1. C₂×C₅×C₈×Q₈	C₂	semidirect
4. C₅×#1984	C₂	semidirect
6. C₅×#1923	C₂	semidirect
7. C₅×#1851	C₂	semidirect
8. C₅×#1842	C₂	semidirect
9. C₅×#1744	C₂	semidirect
34. #22210	C₅	direct (N × H)
73. C₂×C₈×Q₈	C₂×C₅	semidirect
76. #1984	C₂×C₅	semidirect
78. #1923	C₂×C₅	semidirect
79. #1851	C₂×C₅	semidirect
80. #1842	C₂×C₅	semidirect
81. #1744	C₂×C₅	semidirect
85. C₂×C₅×Q₈	M₁₆	semidirect
251. C₂×Q₈	C₅×M₁₆	semidirect
338. C₅	#22210	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×C₈×Q₈	2
C₂×C₅×#436	2
C₄×C₅×#124	2
C₅×#1984	2
C₅×#1954	2
C₅×#1923	2
C₅×#1851	2
C₅×#1842	2
C₅×#1744	2
#22210	5

Subgroups — C5×#22210 #11944930

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22210 #11944930