Subgroups — C₅×#33851 #11956571

Order 1280.

674 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×#508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3285	C₂	1	2	yes	maximal, complemented
4	C₅×#2249	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2216	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2215	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2211	C₂	1	2	yes	maximal, complemented
8	C₅×#2189	C₂	1	2	yes	maximal, complemented
9	C₅×#2185	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₄×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	C₂²	1	2	yes	—
13	C₂²×C₅×Q₁₆	C₂²	1	2	yes	—
14	C₅×#548	—	2	2	no	—
15	C₅×#508	—	2	4	no	—
16	C₂×C₅×Q₃₂	—	2	4	no	—
17	C₂×C₅×Q₃₂	C₂²	1	2	yes	—
18	C₂×C₅×Q₃₂	C₂²	1	1	yes	characteristic
19	C₂×C₅×Q₃₂	C₂²	1	1	yes	characteristic
20	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
21	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
22	C₂×C₅×D₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
25	C₅×#495	C₂²	1	2	yes	—
26	C₅×#467	C₂²	1	2	yes	—
27	C₅×#466	C₂²	1	2	yes	—
28	C₅×#464	—	2	2	no	—
29	C₅×#452	—	2	2	no	—
30	C₅×#448	—	2	2	no	—
31	C₄×C₅×Q₁₆	C₂²	1	2	yes	—
32	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
33	C₅×#366	C₂²	1	1	yes	characteristic
34	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
35	C₅×#358	C₂²	1	2	yes	—
36	C₅×#358	C₂²	1	2	yes	—
37	C₅×#357	C₂²	1	2	yes	—
38	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
40	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
41	#33851	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₅×#41	—	2	2	no	—
43	C₂²×C₅×Q₈	—	2	2	no	—
44	C₅×#135	—	2	4	no	—
45	C₅×#135	—	4	2	no	—
46	C₂×C₅×Q₁₆	—	2	4	no	—
47	C₂×C₅×Q₁₆	—	2	2	no	—
48	C₂×C₅×Q₁₆	—	4	2	no	—
49	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
50	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
51	C₂×C₅×SD₁₆	—	2	2	no	—
52	C₂×C₅×SD₁₆	—	2	2	no	—
53	C₂×C₅×D₈	C₂³	1	2	yes	—
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₅×#124	—	2	2	no	—
57	C₅×#124	—	4	2	no	—
58	C₅×C₂²⋊Q₈	—	2	2	no	—
59	C₅×C₂²⋊Q₈	—	4	2	no	—
60	C₅×#121	—	2	2	no	—
61	C₅×#121	—	4	2	no	—
62	C₄×C₅×Q₈	—	2	2	no	—
63	C₄×C₅×D₄	—	4	2	no	—
64	C₄×C₅×D₄	D₄	1	1	yes	characteristic
65	C₅×Q₃₂	—	2	4	no	—
66	C₅×Q₃₂	—	2	2	no	—
67	C₅×Q₃₂	D₄	1	4	yes	complemented
68	C₅×SD₃₂	—	2	4	no	—
69	C₅×SD₃₂	—	4	2	no	—
70	C₅×D₁₆	—	2	2	no	—
71	C₂×C₅×C₁₆	—	2	2	no	—
72	C₂×C₅×C₁₆	—	2	2	no	—
73	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
74	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
75	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
76	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
77	C₅×#107	C₂³	1	2	yes	—
78	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
79	C₅×#103	—	2	2	no	—
80	C₅×#103	—	2	2	no	—
81	C₅×#102	—	2	2	no	—
82	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
83	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
84	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₂×#508	C₂×C₅	1	1	yes	characteristic, complemented
86	C₂²×Q₃₂	C₂×C₅	1	1	yes	characteristic, complemented
87	#3285	C₂×C₅	1	2	yes	complemented
88	#2249	C₂×C₅	1	1	yes	characteristic, complemented
89	#2216	C₂×C₅	1	1	yes	characteristic, complemented
90	#2215	C₂×C₅	1	1	yes	characteristic, complemented
91	#2211	C₂×C₅	1	2	yes	complemented
92	#2189	C₂×C₅	1	2	yes	complemented
93	#2185	C₂×C₅	1	2	yes	complemented
94	C₄×Q₃₂	C₂×C₅	1	1	yes	characteristic, complemented
95	D₄×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
96	C₅×#41	—	4	4	no	—
97	C₅×#41	—	8	2	no	—
98	C₂×C₅×Q₈	—	2	2	no	—
99	C₂×C₅×Q₈	—	2	2	no	—
100	C₂×C₅×Q₈	—	4	4	no	—
101	C₂×C₅×Q₈	—	4	2	no	—
102	C₂×C₅×Q₈	—	8	2	no	—
103	C₂×C₅×D₄	—	2	2	no	—
104	C₂×C₅×D₄	—	4	2	no	—
105	C₂×C₅×D₄	—	4	2	no	—
106	C₂×C₅×D₄	D₈	1	1	yes	characteristic
107	C₂²×C₄×C₅	—	4	2	no	—
108	C₂²×C₄×C₅	—	4	2	no	—
109	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₅×Q₁₆	—	2	2	no	—
112	C₅×Q₁₆	—	2	2	no	—
113	C₅×Q₁₆	—	2	2	no	—
114	C₅×Q₁₆	—	4	4	no	—
115	C₅×Q₁₆	C₂×D₄	1	4	yes	—
116	C₅×SD₁₆	—	4	4	no	—
117	C₅×SD₁₆	—	8	2	no	—
118	C₅×D₈	—	2	2	no	—
119	C₅×D₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	1	no	—
121	C₂×C₅×C₈	—	2	1	no	—
122	C₂×C₅×C₈	—	2	1	no	—
123	C₂×C₅×C₈	—	2	1	no	—
124	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
125	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
126	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
127	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
128	C₅×C₄⋊C₄	—	2	2	no	—
129	C₅×C₄⋊C₄	—	4	2	no	—
130	C₅×C₄⋊C₄	—	4	2	no	—
131	C₅×C₄⋊C₄	D₈	1	1	yes	characteristic
132	C₅×C₂²⋊C₄	—	4	2	no	—
133	C₅×C₂²⋊C₄	—	4	2	no	—
134	C₅×C₂²⋊C₄	—	4	2	no	—
135	C₅×C₂²⋊C₄	—	4	2	no	—
136	C₅×C₂²⋊C₄	D₈	1	1	yes	characteristic
137	C₅×C₂²⋊C₄	D₈	1	1	yes	characteristic
138	C₄²×C₅	—	4	2	no	—
139	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
140	C₅×C₁₆	—	2	1	no	—
141	C₅×C₁₆	—	2	1	no	—
142	C₅×C₁₆	—	2	1	no	—
143	C₅×C₁₆	C₂×D₄	1	2	yes	—
144	C₂×#135	C₂²×C₅	1	2	yes	—
145	C₂²×Q₁₆	C₂²×C₅	1	2	yes	—
146	#548	—	2	2	no	—
147	#508	—	2	4	no	—
148	C₂×Q₃₂	—	2	4	no	—
149	C₂×Q₃₂	C₂²×C₅	1	2	yes	—
150	C₂×Q₃₂	C₂²×C₅	1	1	yes	characteristic
151	C₂×Q₃₂	C₂²×C₅	1	1	yes	characteristic
152	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
153	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
154	C₂×D₁₆	C₂²×C₅	1	1	yes	characteristic
155	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
156	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
157	#495	C₂²×C₅	1	2	yes	—
158	#467	C₂²×C₅	1	2	yes	—
159	#466	C₂²×C₅	1	2	yes	—
160	#464	—	2	2	no	—
161	#452	—	2	2	no	—
162	#448	—	2	2	no	—
163	C₄×Q₁₆	C₂²×C₅	1	2	yes	—
164	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
165	#366	C₂²×C₅	1	1	yes	characteristic
166	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
167	#358	C₂²×C₅	1	2	yes	—
168	#358	C₂²×C₅	1	2	yes	—
169	#357	C₂²×C₅	1	2	yes	—
170	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
171	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
172	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic
173	C₂³×C₅	—	4	2	no	—
174	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
175	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
176	C₅×Q₈	—	2	4	no	—
177	C₅×Q₈	—	4	2	no	—
178	C₅×Q₈	—	4	2	no	—
179	C₅×Q₈	—	4	2	no	—
180	C₅×Q₈	—	8	4	no	—
181	C₅×D₄	—	2	2	no	—
182	C₅×D₄	—	4	2	no	—
183	C₅×D₄	—	4	2	no	—
184	C₅×D₄	—	8	4	no	—
185	C₅×D₄	—	8	4	no	—
186	C₂×C₄×C₅	—	2	1	no	—
187	C₂×C₄×C₅	—	2	1	no	—
188	C₂×C₄×C₅	—	2	1	no	—
189	C₂×C₄×C₅	—	2	1	no	—
190	C₂×C₄×C₅	—	4	2	no	—
191	C₂×C₄×C₅	—	4	2	no	—
192	C₂×C₄×C₅	—	4	2	no	—
193	C₂×C₄×C₅	—	8	4	no	—
194	C₂×C₄×C₅	—	8	4	no	—
195	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
196	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
197	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
198	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
199	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
200	C₅×C₈	—	2	1	no	—
201	C₅×C₈	—	2	1	no	—
202	C₅×C₈	—	2	1	no	—
203	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
204	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
205	C₂×#41	—	2	2	no	—
206	C₂²×Q₈	—	2	2	no	—
207	#135	—	2	4	no	—
208	#135	—	4	2	no	—
209	C₂×Q₁₆	—	2	4	no	—
210	C₂×Q₁₆	—	2	2	no	—
211	C₂×Q₁₆	—	4	2	no	—
212	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
213	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
214	C₂×SD₁₆	—	2	2	no	—
215	C₂×SD₁₆	—	2	2	no	—
216	C₂×D₈	C₂³×C₅	1	2	yes	—
217	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
218	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
219	#124	—	2	2	no	—
220	#124	—	4	2	no	—
221	C₂²⋊Q₈	—	2	2	no	—
222	C₂²⋊Q₈	—	4	2	no	—
223	#121	—	2	2	no	—
224	#121	—	4	2	no	—
225	C₄×Q₈	—	2	2	no	—
226	C₄×D₄	—	4	2	no	—
227	C₄×D₄	C₅×D₄	1	1	yes	characteristic
228	Q₃₂	—	2	4	no	—
229	Q₃₂	—	2	2	no	—
230	Q₃₂	C₅×D₄	1	4	yes	complemented
231	SD₃₂	—	2	4	no	—
232	SD₃₂	—	4	2	no	—
233	D₁₆	—	2	2	no	—
234	C₂×C₁₆	—	2	2	no	—
235	C₂×C₁₆	—	2	2	no	—
236	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
237	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
238	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
239	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
240	#107	C₂³×C₅	1	2	yes	—
241	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
242	#103	—	2	2	no	—
243	#103	—	2	2	no	—
244	#102	—	2	2	no	—
245	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
246	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
247	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
248	C₂²×C₅	—	2	1	no	—
249	C₂²×C₅	—	2	1	no	—
250	C₂²×C₅	—	2	1	no	—
251	C₂²×C₅	—	2	1	no	—
252	C₂²×C₅	—	2	1	no	—
253	C₂²×C₅	—	8	2	no	—
254	C₂²×C₅	—	8	2	no	—
255	C₂²×C₅	—	8	2	no	—
256	C₂²×C₅	#508	1	2	yes	complemented
257	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
258	C₄×C₅	—	2	1	no	—
259	C₄×C₅	—	2	1	no	—
260	C₄×C₅	—	2	1	no	—
261	C₄×C₅	—	2	1	no	—
262	C₄×C₅	—	4	4	no	—
263	C₄×C₅	—	8	2	no	—
264	C₄×C₅	—	8	2	no	—
265	C₄×C₅	D₄²	1	1	yes	characteristic
266	C₄×C₅	#576	1	1	yes	characteristic
267	#41	—	4	4	no	—
268	#41	—	8	2	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	4	4	no	—
272	C₂×Q₈	—	4	2	no	—
273	C₂×Q₈	—	8	2	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	4	2	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	C₅×D₈	1	1	yes	characteristic
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
282	Q₁₆	—	2	2	no	—
283	Q₁₆	—	2	2	no	—
284	Q₁₆	—	2	2	no	—
285	Q₁₆	—	4	4	no	—
286	Q₁₆	C₂×C₅×D₄	1	4	yes	—
287	SD₁₆	—	4	4	no	—
288	SD₁₆	—	8	2	no	—
289	D₈	—	2	2	no	—
290	D₈	—	2	2	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
296	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
297	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
298	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	4	2	no	—
301	C₄⋊C₄	—	4	2	no	—
302	C₄⋊C₄	C₅×D₈	1	1	yes	characteristic
303	C₂²⋊C₄	—	4	2	no	—
304	C₂²⋊C₄	—	4	2	no	—
305	C₂²⋊C₄	—	4	2	no	—
306	C₂²⋊C₄	—	4	2	no	—
307	C₂²⋊C₄	C₅×D₈	1	1	yes	characteristic
308	C₂²⋊C₄	C₅×D₈	1	1	yes	characteristic
309	C₄²	—	4	2	no	—
310	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
311	C₁₆	—	2	1	no	—
312	C₁₆	—	2	1	no	—
313	C₁₆	—	2	1	no	—
314	C₁₆	C₂×C₅×D₄	1	2	yes	—
315	C₂×C₅	—	2	2	no	—
316	C₂×C₅	—	4	1	no	—
317	C₂×C₅	—	16	2	no	—
318	C₂×C₅	D₄×D₈	1	1	yes	characteristic
319	C₂×C₅	C₂×#508	1	1	yes	characteristic
320	C₂×C₅	#3417	1	1	yes	characteristic
321	C₂³	—	4	2	no	—
322	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
323	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
324	Q₈	—	2	4	no	—
325	Q₈	—	4	2	no	—
326	Q₈	—	4	2	no	—
327	Q₈	—	4	2	no	—
328	Q₈	—	8	4	no	—
329	D₄	—	2	2	no	—
330	D₄	—	4	2	no	—
331	D₄	—	4	2	no	—
332	D₄	—	8	4	no	—
333	D₄	—	8	4	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	8	4	no	—
342	C₂×C₄	—	8	4	no	—
343	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
344	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
345	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
346	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
347	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
348	C₈	—	2	1	no	—
349	C₈	—	2	1	no	—
350	C₈	—	2	1	no	—
351	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
352	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
353	C₅	#33851	1	1	yes	characteristic, direct product factor, Sylow
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	8	2	no	—
360	C₂²	—	8	2	no	—
361	C₂²	—	8	2	no	—
362	C₂²	C₅×#508	1	2	yes	complemented
363	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	4	4	no	—
369	C₄	—	8	2	no	—
370	C₄	—	8	2	no	—
371	C₄	C₅×D₄²	1	1	yes	characteristic
372	C₄	C₅×#576	1	1	yes	characteristic
373	C₂	—	2	2	no	—
374	C₂	—	4	1	no	—
375	C₂	—	16	2	no	—
376	C₂	C₅×D₄×D₈	1	1	yes	characteristic
377	C₂	C₂×C₅×#508	1	1	yes	characteristic
378	C₂	C₅×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×D₄ ◁ C₅×C₈×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#508	C₂	semidirect
2. C₂²×C₅×Q₃₂	C₂	semidirect
3. C₅×#3285	C₂	semidirect
4. C₅×#2249	C₂	semidirect
5. C₅×#2216	C₂	semidirect
6. C₅×#2215	C₂	semidirect
7. C₅×#2211	C₂	semidirect
8. C₅×#2189	C₂	semidirect
9. C₅×#2185	C₂	semidirect
10. C₄×C₅×Q₃₂	C₂	semidirect
11. C₅×D₄×C₁₆	C₂	semidirect
41. #33851	C₅	direct (N × H)
67. C₅×Q₃₂	D₄	semidirect
85. C₂×#508	C₂×C₅	semidirect
86. C₂²×Q₃₂	C₂×C₅	semidirect
87. #3285	C₂×C₅	semidirect
88. #2249	C₂×C₅	semidirect
89. #2216	C₂×C₅	semidirect
90. #2215	C₂×C₅	semidirect
91. #2211	C₂×C₅	semidirect
92. #2189	C₂×C₅	semidirect
93. #2185	C₂×C₅	semidirect
94. C₄×Q₃₂	C₂×C₅	semidirect
95. D₄×C₁₆	C₂×C₅	semidirect
230. Q₃₂	C₅×D₄	semidirect
256. C₂²×C₅	#508	semidirect
353. C₅	#33851	direct (N × H)
362. C₂²	C₅×#508	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×#508	2
C₂²×C₅×Q₃₂	2
C₅×#3285	2
C₅×#2249	2
C₅×#2216	2
C₅×#2215	2
C₅×#2211	2
C₅×#2189	2
C₅×#2185	2
C₄×C₅×Q₃₂	2
C₅×D₄×C₁₆	2
#33851	5

Subgroups — C5×#33851 #11956571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33851 #11956571