Subgroups — C₅×#33850 #11956570

Order 1280.

686 conjugacy classes of subgroups.

The subgroup lattice has 398 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	2	yes	maximal, complemented
2	C₅×#3287	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3283	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2248	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2217	C₂	1	2	yes	maximal, complemented
6	C₅×#2209	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2206	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2189	C₂	1	2	yes	maximal, complemented
9	C₅×#2186	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×SD₃₂	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	C₂×C₅×#135	C₂²	1	2	yes	—
14	C₅×#550	—	2	1	no	—
15	C₅×#547	—	2	1	no	—
16	C₅×#508	—	2	8	no	—
17	C₂×C₅×Q₃₂	C₂²	1	2	yes	—
18	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
19	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
20	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic
21	C₂×C₅×D₁₆	C₂²	1	2	yes	—
22	C₂²×C₅×C₁₆	C₂²	1	2	yes	—
23	C₅×#494	C₂²	1	1	yes	characteristic
24	C₅×#493	C₂²	1	1	yes	characteristic
25	C₅×#467	C₂²	1	2	yes	—
26	C₅×#466	C₂²	1	2	yes	—
27	C₅×#461	—	2	1	no	—
28	C₅×#460	—	2	1	no	—
29	C₅×#452	—	2	2	no	—
30	C₅×#449	—	2	2	no	—
31	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
32	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
33	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
34	C₅×#367	C₂²	1	1	yes	characteristic
35	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₅×#358	C₂²	1	1	yes	characteristic
37	C₅×#358	C₂²	1	2	yes	—
38	C₅×#357	C₂²	1	1	yes	characteristic
39	C₅×#357	C₂²	1	2	yes	—
40	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
42	#33850	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂×C₅×#41	—	2	2	no	—
44	C₂×C₅×#41	—	2	2	no	—
45	C₅×#135	—	2	4	no	—
46	C₅×#135	—	2	4	no	—
47	C₅×#135	—	4	2	no	—
48	C₅×#135	—	4	2	no	—
49	C₂×C₅×Q₁₆	—	2	1	no	—
50	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
51	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
52	C₂×C₅×SD₁₆	—	2	2	no	—
53	C₂×C₅×SD₁₆	—	2	2	no	—
54	C₂×C₅×D₈	—	2	1	no	—
55	C₂×C₅×D₈	C₂³	1	2	yes	—
56	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂³	1	2	yes	—
58	C₅×C₄⋊Q₈	—	2	1	no	—
59	C₅×#127	—	2	1	no	—
60	C₅×#127	—	4	1	no	—
61	C₅×#123	—	4	2	no	—
62	C₅×C₂²⋊Q₈	—	2	2	no	—
63	C₅×#121	—	2	2	no	—
64	C₅×#121	—	4	1	no	—
65	C₅×#121	—	4	2	no	—
66	C₄×C₅×Q₈	—	2	1	no	—
67	C₄×C₅×D₄	—	2	1	no	—
68	C₄×C₅×D₄	—	4	1	no	—
69	C₄×C₅×D₄	D₄	1	1	yes	characteristic
70	C₂×C₅×C₄⋊C₄	—	4	1	no	—
71	C₅×Q₃₂	—	2	4	no	—
72	C₅×SD₃₂	—	2	4	no	—
73	C₅×SD₃₂	—	4	2	no	—
74	C₅×SD₃₂	D₄	1	4	yes	complemented
75	C₅×D₁₆	—	2	4	no	—
76	C₂×C₅×C₁₆	—	2	4	no	—
77	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₅×C₁₆	C₂³	1	2	yes	—
79	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
80	C₅×#107	C₂³	1	1	yes	characteristic
81	C₅×#107	C₂³	1	1	yes	characteristic
82	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
83	C₅×#103	—	2	1	no	—
84	C₅×#103	—	2	2	no	—
85	C₅×#102	—	2	1	no	—
86	C₅×#102	—	2	2	no	—
87	C₅×C₂²⋊C₈	D₄	1	2	yes	—
88	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₂×#508	C₂×C₅	1	2	yes	complemented
90	#3287	C₂×C₅	1	1	yes	characteristic, complemented
91	#3283	C₂×C₅	1	1	yes	characteristic, complemented
92	#2248	C₂×C₅	1	1	yes	characteristic, complemented
93	#2217	C₂×C₅	1	2	yes	complemented
94	#2209	C₂×C₅	1	1	yes	characteristic, complemented
95	#2206	C₂×C₅	1	1	yes	characteristic, complemented
96	#2189	C₂×C₅	1	2	yes	complemented
97	#2186	C₂×C₅	1	2	yes	complemented
98	C₄×SD₃₂	C₂×C₅	1	1	yes	characteristic, complemented
99	D₄×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
100	C₅×#41	—	4	4	no	—
101	C₅×#41	—	4	4	no	—
102	C₅×#41	—	8	2	no	—
103	C₅×#41	—	8	2	no	—
104	C₂×C₅×Q₈	—	2	1	no	—
105	C₂×C₅×Q₈	—	2	2	no	—
106	C₂×C₅×D₄	—	2	1	no	—
107	C₂×C₅×D₄	—	2	2	no	—
108	C₂×C₅×D₄	—	4	2	no	—
109	C₂×C₅×D₄	—	4	2	no	—
110	C₂×C₅×D₄	—	4	2	no	—
111	C₂×C₅×D₄	—	4	1	no	—
112	C₂×C₅×D₄	—	4	1	no	—
113	C₂×C₅×D₄	D₈	1	1	yes	characteristic
114	C₂²×C₄×C₅	—	4	1	no	—
115	C₂²×C₄×C₅	—	4	2	no	—
116	C₂²×C₄×C₅	—	4	2	no	—
117	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₅×Q₁₆	—	2	2	no	—
119	C₅×Q₁₆	—	2	1	no	—
120	C₅×Q₁₆	—	2	2	no	—
121	C₅×Q₁₆	—	8	1	no	—
122	C₅×Q₁₆	C₂×D₄	1	2	yes	—
123	C₅×SD₁₆	—	4	4	no	—
124	C₅×SD₁₆	—	4	4	no	—
125	C₅×D₈	—	2	2	no	—
126	C₅×D₈	—	2	1	no	—
127	C₅×D₈	—	2	2	no	—
128	C₅×D₈	—	8	1	no	—
129	C₅×D₈	C₂×D₄	1	2	yes	—
130	C₂×C₅×C₈	—	2	2	no	—
131	C₂×C₅×C₈	—	2	2	no	—
132	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
133	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
134	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
135	C₅×C₄⋊C₄	—	2	1	no	—
136	C₅×C₄⋊C₄	—	2	1	no	—
137	C₅×C₄⋊C₄	—	4	1	no	—
138	C₅×C₄⋊C₄	—	4	2	no	—
139	C₅×C₄⋊C₄	—	4	1	no	—
140	C₅×C₄⋊C₄	—	4	1	no	—
141	C₅×C₄⋊C₄	D₈	1	1	yes	characteristic
142	C₅×C₂²⋊C₄	—	4	2	no	—
143	C₅×C₂²⋊C₄	—	4	1	no	—
144	C₅×C₂²⋊C₄	—	4	2	no	—
145	C₅×C₂²⋊C₄	D₈	1	2	yes	—
146	C₄²×C₅	—	4	1	no	—
147	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
148	C₅×C₁₆	—	2	2	no	—
149	C₅×C₁₆	—	2	1	no	—
150	C₅×C₁₆	C₂×D₄	1	2	yes	—
151	C₂×#135	C₂²×C₅	1	2	yes	—
152	C₂×#135	C₂²×C₅	1	2	yes	—
153	#550	—	2	1	no	—
154	#547	—	2	1	no	—
155	#508	—	2	8	no	—
156	C₂×Q₃₂	C₂²×C₅	1	2	yes	—
157	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
158	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
159	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic
160	C₂×D₁₆	C₂²×C₅	1	2	yes	—
161	C₂²×C₁₆	C₂²×C₅	1	2	yes	—
162	#494	C₂²×C₅	1	1	yes	characteristic
163	#493	C₂²×C₅	1	1	yes	characteristic
164	#467	C₂²×C₅	1	2	yes	—
165	#466	C₂²×C₅	1	2	yes	—
166	#461	—	2	1	no	—
167	#460	—	2	1	no	—
168	#452	—	2	2	no	—
169	#449	—	2	2	no	—
170	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
171	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
172	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
173	#367	C₂²×C₅	1	1	yes	characteristic
174	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
175	#358	C₂²×C₅	1	1	yes	characteristic
176	#358	C₂²×C₅	1	2	yes	—
177	#357	C₂²×C₅	1	1	yes	characteristic
178	#357	C₂²×C₅	1	2	yes	—
179	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
180	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic
181	C₂³×C₅	—	4	1	no	—
182	C₂³×C₅	—	4	2	no	—
183	C₂³×C₅	C₂×D₈	1	2	yes	—
184	C₅×Q₈	—	2	2	no	—
185	C₅×Q₈	—	4	1	no	—
186	C₅×Q₈	—	4	2	no	—
187	C₅×Q₈	—	4	2	no	—
188	C₅×D₄	—	2	2	no	—
189	C₅×D₄	—	2	2	no	—
190	C₅×D₄	—	4	2	no	—
191	C₅×D₄	—	4	1	no	—
192	C₅×D₄	—	4	2	no	—
193	C₅×D₄	—	8	4	no	—
194	C₅×D₄	—	8	4	no	—
195	C₅×D₄	—	8	2	no	—
196	C₅×D₄	—	16	1	no	—
197	C₅×D₄	—	16	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	4	1	no	—
201	C₂×C₄×C₅	—	4	1	no	—
202	C₂×C₄×C₅	—	4	1	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	—	8	4	no	—
205	C₂×C₄×C₅	—	8	4	no	—
206	C₂×C₄×C₅	—	8	2	no	—
207	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
209	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
211	C₅×C₈	—	2	2	no	—
212	C₅×C₈	—	2	1	no	—
213	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
214	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×#41	—	2	2	no	—
216	C₂×#41	—	2	2	no	—
217	#135	—	2	4	no	—
218	#135	—	2	4	no	—
219	#135	—	4	2	no	—
220	#135	—	4	2	no	—
221	C₂×Q₁₆	—	2	1	no	—
222	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
223	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
224	C₂×SD₁₆	—	2	2	no	—
225	C₂×SD₁₆	—	2	2	no	—
226	C₂×D₈	—	2	1	no	—
227	C₂×D₈	C₂³×C₅	1	2	yes	—
228	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
229	C₂²×C₈	C₂³×C₅	1	2	yes	—
230	C₄⋊Q₈	—	2	1	no	—
231	#127	—	2	1	no	—
232	#127	—	4	1	no	—
233	#123	—	4	2	no	—
234	C₂²⋊Q₈	—	2	2	no	—
235	#121	—	2	2	no	—
236	#121	—	4	1	no	—
237	#121	—	4	2	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	—	4	1	no	—
241	C₄×D₄	C₅×D₄	1	1	yes	characteristic
242	C₂×C₄⋊C₄	—	4	1	no	—
243	Q₃₂	—	2	4	no	—
244	SD₃₂	—	2	4	no	—
245	SD₃₂	—	4	2	no	—
246	SD₃₂	C₅×D₄	1	4	yes	complemented
247	D₁₆	—	2	4	no	—
248	C₂×C₁₆	—	2	4	no	—
249	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
250	C₂×C₁₆	C₂³×C₅	1	2	yes	—
251	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
252	#107	C₂³×C₅	1	1	yes	characteristic
253	#107	C₂³×C₅	1	1	yes	characteristic
254	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
255	#103	—	2	1	no	—
256	#103	—	2	2	no	—
257	#102	—	2	1	no	—
258	#102	—	2	2	no	—
259	C₂²⋊C₈	C₅×D₄	1	2	yes	—
260	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
261	C₂²×C₅	—	2	2	no	—
262	C₂²×C₅	—	2	2	no	—
263	C₂²×C₅	—	2	2	no	—
264	C₂²×C₅	—	4	2	no	—
265	C₂²×C₅	—	8	1	no	—
266	C₂²×C₅	—	8	1	no	—
267	C₂²×C₅	—	8	2	no	—
268	C₂²×C₅	—	8	2	no	—
269	C₂²×C₅	—	8	2	no	—
270	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
271	C₄×C₅	—	2	1	no	—
272	C₄×C₅	—	2	2	no	—
273	C₄×C₅	—	4	2	no	—
274	C₄×C₅	—	8	1	no	—
275	C₄×C₅	—	8	1	no	—
276	C₄×C₅	—	8	2	no	—
277	C₄×C₅	#508	1	2	yes	complemented
278	C₄×C₅	D₄²	1	1	yes	characteristic
279	C₄×C₅	#576	1	1	yes	characteristic
280	#41	—	4	4	no	—
281	#41	—	4	4	no	—
282	#41	—	8	2	no	—
283	#41	—	8	2	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	C₅×D₈	1	1	yes	characteristic
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
298	Q₁₆	—	2	2	no	—
299	Q₁₆	—	2	1	no	—
300	Q₁₆	—	2	2	no	—
301	Q₁₆	—	8	1	no	—
302	Q₁₆	C₂×C₅×D₄	1	2	yes	—
303	SD₁₆	—	4	4	no	—
304	SD₁₆	—	4	4	no	—
305	D₈	—	2	2	no	—
306	D₈	—	2	1	no	—
307	D₈	—	2	2	no	—
308	D₈	—	8	1	no	—
309	D₈	C₂×C₅×D₄	1	2	yes	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
313	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
314	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	C₅×D₈	1	1	yes	characteristic
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	4	1	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	C₅×D₈	1	2	yes	—
326	C₄²	—	4	1	no	—
327	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
328	C₁₆	—	2	2	no	—
329	C₁₆	—	2	1	no	—
330	C₁₆	C₂×C₅×D₄	1	2	yes	—
331	C₂×C₅	—	4	2	no	—
332	C₂×C₅	—	8	2	no	—
333	C₂×C₅	—	16	2	no	—
334	C₂×C₅	D₄×D₈	1	1	yes	characteristic
335	C₂×C₅	C₂×#508	1	1	yes	characteristic
336	C₂×C₅	#3416	1	1	yes	characteristic
337	C₂³	—	4	1	no	—
338	C₂³	—	4	2	no	—
339	C₂³	C₂×C₅×D₈	1	2	yes	—
340	Q₈	—	2	2	no	—
341	Q₈	—	4	1	no	—
342	Q₈	—	4	2	no	—
343	Q₈	—	4	2	no	—
344	D₄	—	2	2	no	—
345	D₄	—	2	2	no	—
346	D₄	—	4	2	no	—
347	D₄	—	4	1	no	—
348	D₄	—	4	2	no	—
349	D₄	—	8	4	no	—
350	D₄	—	8	4	no	—
351	D₄	—	8	2	no	—
352	D₄	—	16	1	no	—
353	D₄	—	16	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	8	4	no	—
361	C₂×C₄	—	8	4	no	—
362	C₂×C₄	—	8	2	no	—
363	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
364	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
365	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
366	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
367	C₈	—	2	2	no	—
368	C₈	—	2	1	no	—
369	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
370	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
371	C₅	#33850	1	1	yes	characteristic, direct product factor, Sylow
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	—	8	1	no	—
377	C₂²	—	8	1	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
382	C₄	—	2	2	no	—
383	C₄	—	2	1	no	—
384	C₄	—	4	2	no	—
385	C₄	—	8	2	no	—
386	C₄	—	8	1	no	—
387	C₄	—	8	1	no	—
388	C₄	C₅×#508	1	2	yes	complemented
389	C₄	C₅×D₄²	1	1	yes	characteristic
390	C₄	C₅×#576	1	1	yes	characteristic
391	C₂	—	4	2	no	—
392	C₂	—	8	2	no	—
393	C₂	—	16	2	no	—
394	C₂	C₅×D₄×D₈	1	1	yes	characteristic
395	C₂	C₂×C₅×#508	1	1	yes	characteristic
396	C₂	C₅×#3416	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. C₅×#3287	C₂	semidirect
3. C₅×#3283	C₂	semidirect
4. C₅×#2248	C₂	semidirect
5. C₅×#2217	C₂	semidirect
6. C₅×#2209	C₂	semidirect
7. C₅×#2206	C₂	semidirect
8. C₅×#2189	C₂	semidirect
9. C₅×#2186	C₂	semidirect
10. C₄×C₅×SD₃₂	C₂	semidirect
11. C₅×D₄×C₁₆	C₂	semidirect
42. #33850	C₅	direct (N × H)
74. C₅×SD₃₂	D₄	semidirect
89. C₂×#508	C₂×C₅	semidirect
90. #3287	C₂×C₅	semidirect
91. #3283	C₂×C₅	semidirect
92. #2248	C₂×C₅	semidirect
93. #2217	C₂×C₅	semidirect
94. #2209	C₂×C₅	semidirect
95. #2206	C₂×C₅	semidirect
96. #2189	C₂×C₅	semidirect
97. #2186	C₂×C₅	semidirect
98. C₄×SD₃₂	C₂×C₅	semidirect
99. D₄×C₁₆	C₂×C₅	semidirect
246. SD₃₂	C₅×D₄	semidirect
277. C₄×C₅	#508	semidirect
371. C₅	#33850	direct (N × H)
388. C₄	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
C₅×#3287	2
C₅×#3283	2
C₅×#2248	2
C₅×#2217	2
C₅×#2209	2
C₅×#2206	2
C₅×#2189	2
C₅×#2186	2
C₄×C₅×SD₃₂	2
C₅×D₄×C₁₆	2
#33850	5

Subgroups — C5×#33850 #11956570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33850 #11956570