Subgroups — C₅×#22318 #11945038

Order 1280.

672 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2396	C₂	1	1	yes	maximal, characteristic
2	C₅×#1984	C₂	1	2	yes	maximal, complemented
3	C₅×#1923	C₂	1	2	yes	maximal
4	C₅×#1923	C₂	1	2	yes	maximal
5	C₅×#1917	C₂	1	2	yes	maximal, complemented
6	C₅×#1916	C₂	1	2	yes	maximal, complemented
7	C₅×#1818	C₂	1	1	yes	maximal, characteristic
8	C₅×C₈×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₅×#1750	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₅×#117	C₂²	1	1	yes	characteristic
12	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
13	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
14	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
15	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×#97	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
19	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
21	C₅×#400	C₄	1	1	yes	characteristic
22	C₅×#399	C₄	1	1	yes	characteristic
23	C₅×#398	C₄	1	2	yes	—
24	C₅×#396	C₄	1	2	yes	—
25	C₅×#395	C₄	1	1	yes	characteristic
26	C₅×#393	C₄	1	1	yes	characteristic
27	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
28	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₅×#336	C₂²	1	2	yes	—
31	C₅×#336	C₂²	1	2	yes	—
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	#22318	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
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	C₄×C₅×Q₈	—	4	1	no	—
45	C₄×C₅×Q₈	—	4	1	no	—
46	C₅×#117	—	4	1	no	—
47	C₅×#117	—	4	1	no	—
48	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
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	1	yes	characteristic
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×C₂²⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₅×C₂²⋊C₄	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	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
63	C₅×C₄⋊C₈	—	2	4	no	—
64	C₅×C₄⋊C₈	—	4	2	no	—
65	C₅×C₂²⋊C₈	—	2	4	no	—
66	C₅×C₂²⋊C₈	—	4	1	no	—
67	C₅×C₂²⋊C₈	—	4	1	no	—
68	C₅×#97	—	4	1	no	—
69	C₄×C₅×C₈	—	2	4	no	—
70	C₄×C₅×C₈	—	4	1	no	—
71	C₄×C₅×C₈	—	4	2	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	1	yes	characteristic
76	C₅×#95	C₂×C₄	1	1	yes	characteristic
77	C₅×#95	C₂×C₄	1	2	yes	—
78	#2396	C₂×C₅	1	1	yes	characteristic
79	#1984	C₂×C₅	1	2	yes	complemented
80	#1923	C₂×C₅	1	2	yes	—
81	#1923	C₂×C₅	1	2	yes	—
82	#1917	C₂×C₅	1	2	yes	complemented
83	#1916	C₂×C₅	1	2	yes	complemented
84	#1818	C₂×C₅	1	1	yes	characteristic
85	C₈×C₄⋊C₄	C₂×C₅	1	2	yes	complemented
86	#1750	C₂×C₅	1	1	yes	characteristic
87	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₅×Q₈	—	2	4	no	—
89	C₂×C₅×Q₈	—	4	1	no	—
90	C₂²×C₄×C₅	—	2	2	no	—
91	C₂²×C₄×C₅	—	2	1	no	—
92	C₂²×C₄×C₅	—	2	1	no	—
93	C₂²×C₄×C₅	—	2	2	no	—
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	1	yes	characteristic
97	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
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	—	2	2	no	—
110	C₂×C₅×C₈	—	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	#41	1	4	yes	—
116	C₅×C₄⋊C₄	—	2	4	no	—
117	C₅×C₄⋊C₄	—	2	4	no	—
118	C₅×C₄⋊C₄	—	2	4	no	—
119	C₅×C₄⋊C₄	—	4	1	no	—
120	C₅×C₄⋊C₄	—	4	1	no	—
121	C₅×C₄⋊C₄	—	4	2	no	—
122	C₅×C₄⋊C₄	—	4	1	no	—
123	C₅×C₂²⋊C₄	—	2	4	no	—
124	C₅×C₂²⋊C₄	—	2	4	no	—
125	C₅×C₂²⋊C₄	—	4	1	no	—
126	C₅×C₂²⋊C₄	—	4	1	no	—
127	C₄²×C₅	—	2	2	no	—
128	C₄²×C₅	—	2	2	no	—
129	C₄²×C₅	—	2	1	no	—
130	C₄²×C₅	—	2	1	no	—
131	C₄²×C₅	—	2	1	no	—
132	C₄²×C₅	—	2	1	no	—
133	C₄²×C₅	—	2	2	no	—
134	C₄²×C₅	—	2	2	no	—
135	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
136	C₂×#117	C₂²×C₅	1	1	yes	characteristic
137	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
138	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
139	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
140	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
141	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
142	C₂×#97	C₂²×C₅	1	1	yes	characteristic
143	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
144	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
145	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
146	#400	C₄×C₅	1	1	yes	characteristic
147	#399	C₄×C₅	1	1	yes	characteristic
148	#398	C₄×C₅	1	2	yes	—
149	#396	C₄×C₅	1	2	yes	—
150	#395	C₄×C₅	1	1	yes	characteristic
151	#393	C₄×C₅	1	1	yes	characteristic
152	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
153	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
154	C₄×C₂²⋊C₄	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	#336	C₂²×C₅	1	2	yes	—
161	#336	C₂²×C₅	1	2	yes	—
162	C₂³×C₅	—	2	1	no	—
163	C₂³×C₅	—	2	1	no	—
164	C₂³×C₅	—	2	1	no	—
165	C₂³×C₅	—	2	2	no	—
166	C₂³×C₅	—	2	2	no	—
167	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
168	C₅×Q₈	—	4	4	no	—
169	C₂×C₄×C₅	—	2	2	no	—
170	C₂×C₄×C₅	—	2	2	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	1	no	—
175	C₂×C₄×C₅	—	2	1	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	2	no	—
180	C₂×C₄×C₅	—	2	1	no	—
181	C₂×C₄×C₅	—	2	1	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	2	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	—	2	2	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	4	2	no	—
191	C₂×C₄×C₅	—	4	2	no	—
192	C₂×C₄×C₅	#131	1	4	yes	—
193	C₂×C₄×C₅	#131	1	4	yes	—
194	C₂×C₄×C₅	C₂×#41	1	2	yes	—
195	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
196	C₂×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
197	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
198	C₅×C₈	—	2	4	no	—
199	C₅×C₈	—	4	2	no	—
200	C₅×C₈	—	4	2	no	—
201	C₅×C₈	—	4	2	no	—
202	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
203	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
204	C₂²×C₈	C₂³×C₅	1	2	yes	—
205	C₂²×C₈	C₂³×C₅	1	2	yes	—
206	C₂²×C₈	C₂³×C₅	1	2	yes	—
207	C₂²×C₈	C₂³×C₅	1	2	yes	—
208	C₄×Q₈	—	4	1	no	—
209	C₄×Q₈	—	4	1	no	—
210	#117	—	4	1	no	—
211	#117	—	4	1	no	—
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	2	yes	—
215	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
218	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
219	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
220	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	—
221	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
222	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
223	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
224	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
225	C₂×C₄²	C₂³×C₅	1	2	yes	—
226	C₂×C₄²	C₂³×C₅	1	2	yes	—
227	C₄⋊C₈	—	2	4	no	—
228	C₄⋊C₈	—	4	2	no	—
229	C₂²⋊C₈	—	2	4	no	—
230	C₂²⋊C₈	—	4	1	no	—
231	C₂²⋊C₈	—	4	1	no	—
232	#97	—	4	1	no	—
233	C₄×C₈	—	2	4	no	—
234	C₄×C₈	—	4	1	no	—
235	C₄×C₈	—	4	2	no	—
236	#95	C₂×C₄×C₅	1	2	yes	—
237	#95	C₂×C₄×C₅	1	2	yes	—
238	#95	C₂×C₄×C₅	1	2	yes	—
239	#95	C₂×C₄×C₅	1	1	yes	characteristic
240	#95	C₂×C₄×C₅	1	1	yes	characteristic
241	#95	C₂×C₄×C₅	1	2	yes	—
242	C₂²×C₅	—	4	1	no	—
243	C₂²×C₅	—	4	2	no	—
244	C₂²×C₅	—	4	1	no	—
245	C₂²×C₅	—	4	1	no	—
246	C₂²×C₅	—	4	2	no	—
247	C₂²×C₅	C₄×#41	1	1	yes	characteristic
248	C₂²×C₅	#518	1	1	yes	characteristic
249	C₂²×C₅	#519	1	1	yes	characteristic
250	C₂²×C₅	C₂×#131	1	2	yes	—
251	C₂²×C₅	C₂×#131	1	2	yes	—
252	C₄×C₅	—	2	4	no	—
253	C₄×C₅	—	2	4	no	—
254	C₄×C₅	—	4	1	no	—
255	C₄×C₅	—	4	2	no	—
256	C₄×C₅	—	4	1	no	—
257	C₄×C₅	—	4	1	no	—
258	C₄×C₅	—	4	1	no	—
259	C₄×C₅	—	4	1	no	—
260	C₄×C₅	—	4	2	no	—
261	C₄×C₅	#539	1	2	yes	—
262	C₄×C₅	#542	1	2	yes	—
263	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
264	C₂×Q₈	—	2	4	no	—
265	C₂×Q₈	—	4	1	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
271	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
272	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
273	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
275	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
276	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
277	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
278	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
279	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	C₅×#41	1	4	yes	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	4	1	no	—
296	C₄⋊C₄	—	4	1	no	—
297	C₄⋊C₄	—	4	2	no	—
298	C₄⋊C₄	—	4	1	no	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	2	4	no	—
301	C₂²⋊C₄	—	4	1	no	—
302	C₂²⋊C₄	—	4	1	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	1	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	2	1	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	1	no	—
310	C₄²	—	2	1	no	—
311	C₂×C₅	—	8	1	no	—
312	C₂×C₅	#2332	1	1	yes	characteristic
313	C₂×C₅	#2966	1	2	yes	—
314	C₂×C₅	#2977	1	1	yes	characteristic
315	C₂×C₅	#2979	1	1	yes	characteristic
316	C₂×C₅	#2986	1	2	yes	—
317	C₂³	—	2	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
323	Q₈	—	4	4	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	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	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	C₅×#131	1	4	yes	—
348	C₂×C₄	C₅×#131	1	4	yes	—
349	C₂×C₄	C₂×C₅×#41	1	2	yes	—
350	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
351	C₂×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
352	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
353	C₈	—	2	4	no	—
354	C₈	—	4	2	no	—
355	C₈	—	4	2	no	—
356	C₈	—	4	2	no	—
357	C₅	#22318	1	1	yes	characteristic, direct product factor, Sylow
358	C₂²	—	4	2	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	C₄×C₅×#41	1	1	yes	characteristic
364	C₂²	C₅×#518	1	1	yes	characteristic
365	C₂²	C₅×#519	1	1	yes	characteristic
366	C₂²	C₂×C₅×#131	1	2	yes	—
367	C₂²	C₂×C₅×#131	1	2	yes	—
368	C₄	—	2	4	no	—
369	C₄	—	2	4	no	—
370	C₄	—	4	1	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	1	no	—
373	C₄	—	4	1	no	—
374	C₄	—	4	1	no	—
375	C₄	—	4	1	no	—
376	C₄	—	4	2	no	—
377	C₄	C₅×#539	1	2	yes	—
378	C₄	C₅×#542	1	2	yes	—
379	C₂	—	8	1	no	—
380	C₂	C₅×#2332	1	1	yes	characteristic
381	C₂	C₅×#2966	1	2	yes	—
382	C₂	C₅×#2977	1	1	yes	characteristic
383	C₂	C₅×#2979	1	1	yes	characteristic
384	C₂	C₅×#2986	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	C₂⁴×C₅	C₂²×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
2. C₅×#1984	C₂	semidirect
5. C₅×#1917	C₂	semidirect
6. C₅×#1916	C₂	semidirect
8. C₅×C₈×C₄⋊C₄	C₂	semidirect
37. #22318	C₅	direct (N × H)
79. #1984	C₂×C₅	semidirect
82. #1917	C₂×C₅	semidirect
83. #1916	C₂×C₅	semidirect
85. C₈×C₄⋊C₄	C₂×C₅	semidirect
357. C₅	#22318	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×#2396	2
C₅×#1984	2
C₅×#1923	2
C₅×#1917	2
C₅×#1916	2
C₅×#1818	2
C₅×C₈×C₄⋊C₄	2
C₅×#1750	2
#22318	5

Subgroups — C5×#22318 #11945038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22318 #11945038