Subgroups — C₅×#33626 #11956346

Order 1280.

546 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3160	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×#135	C₂	1	1	yes	maximal, characteristic
3	C₅×#2229	C₂	1	2	yes	maximal, complemented
4	C₅×#2228	C₂	1	2	yes	maximal, complemented
5	C₅×#2227	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2226	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2225	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2224	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2158	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2138	C₂	1	2	yes	maximal
12	C₂×C₅×#135	C₂²	1	1	yes	characteristic
13	C₅×#533	—	2	1	no	—
14	C₄×C₅×#41	—	2	1	no	—
15	C₂²×C₅×C₁₆	C₂²	1	2	yes	—
16	C₅×#500	C₂²	1	1	yes	characteristic
17	C₅×#500	C₂²	1	1	yes	characteristic
18	C₅×#499	—	2	1	no	—
19	C₅×#499	C₂²	1	2	yes	—
20	C₅×#498	—	2	1	no	—
21	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
22	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
23	C₄×C₅×SD₁₆	—	2	1	no	—
24	C₄×C₅×SD₁₆	—	2	1	no	—
25	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
26	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
27	C₅×#427	—	2	1	no	—
28	C₅×#427	C₂²	1	2	yes	—
29	C₅×#427	C₂²	1	1	yes	characteristic
30	C₅×#416	—	2	1	no	—
31	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
32	C₅×#367	C₂²	1	2	yes	—
33	C₅×#367	C₂²	1	2	yes	—
34	C₅×#366	C₂²	1	2	yes	—
35	C₅×#366	C₂²	1	2	yes	—
36	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₅×C₄⋊C₁₆	C₂²	1	2	yes	—
39	C₅×#358	C₂²	1	2	yes	—
40	C₅×#358	C₂²	1	2	yes	—
41	C₅×#357	C₂²	1	2	yes	—
42	C₅×#357	C₂²	1	2	yes	—
43	#33626	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₅×#41	—	2	1	no	—
45	C₅×#135	—	2	2	no	—
46	C₅×#135	Q₈	1	4	yes	complemented
47	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
48	C₂×C₅×SD₁₆	—	2	1	no	—
49	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
50	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
51	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
52	C₅×C₄⋊Q₈	—	2	1	no	—
53	C₅×C₄⋊Q₈	—	2	1	no	—
54	C₅×#125	—	2	2	no	—
55	C₅×C₂²⋊Q₈	—	4	1	no	—
56	C₅×C₂²⋊Q₈	—	4	1	no	—
57	C₄×C₅×Q₈	—	2	1	no	—
58	C₄×C₅×Q₈	—	2	1	no	—
59	C₄×C₅×Q₈	—	4	1	no	—
60	C₄×C₅×Q₈	—	4	1	no	—
61	C₄×C₅×D₄	—	2	1	no	—
62	C₄×C₅×D₄	—	2	1	no	—
63	C₄×C₅×D₄	—	4	1	no	—
64	C₄×C₅×D₄	—	4	1	no	—
65	C₅×#117	—	2	1	no	—
66	C₅×#117	—	2	2	no	—
67	C₅×#117	—	4	1	no	—
68	C₂×C₄²×C₅	—	4	1	no	—
69	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
70	C₂×C₅×C₁₆	—	2	4	no	—
71	C₂×C₅×C₁₆	C₂³	1	2	yes	—
72	C₂×C₅×C₁₆	C₂³	1	2	yes	—
73	C₅×#107	—	2	1	no	—
74	C₅×#107	—	2	1	no	—
75	C₅×#107	C₂³	1	2	yes	—
76	C₅×#107	C₂³	1	2	yes	—
77	C₅×#107	C₂³	1	1	yes	characteristic
78	C₅×#107	C₂³	1	1	yes	characteristic
79	C₅×#106	—	2	2	no	—
80	C₅×#106	—	2	1	no	—
81	C₅×#106	—	2	2	no	—
82	C₅×#103	—	2	1	no	—
83	C₅×#103	—	2	1	no	—
84	C₅×#102	—	2	1	no	—
85	C₅×#102	—	2	1	no	—
86	C₄×C₅×C₈	D₄	1	1	yes	characteristic
87	C₄×C₅×C₈	D₄	1	1	yes	characteristic
88	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
89	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
90	#3160	C₂×C₅	1	1	yes	characteristic, complemented
91	C₄×#135	C₂×C₅	1	1	yes	characteristic
92	#2229	C₂×C₅	1	2	yes	complemented
93	#2228	C₂×C₅	1	2	yes	complemented
94	#2227	C₂×C₅	1	1	yes	characteristic, complemented
95	#2226	C₂×C₅	1	1	yes	characteristic, complemented
96	#2225	C₂×C₅	1	1	yes	characteristic, complemented
97	#2224	C₂×C₅	1	1	yes	characteristic, complemented
98	#2158	C₂×C₅	1	2	yes	complemented
99	C₂×C₄⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
100	#2138	C₂×C₅	1	2	yes	—
101	C₅×#41	—	2	4	no	—
102	C₅×#41	—	4	2	no	—
103	C₂×C₅×Q₈	—	2	1	no	—
104	C₂×C₅×Q₈	—	4	1	no	—
105	C₂×C₅×Q₈	—	4	1	no	—
106	C₂×C₅×D₄	—	2	1	no	—
107	C₂×C₅×D₄	—	4	1	no	—
108	C₂²×C₄×C₅	—	4	1	no	—
109	C₂²×C₄×C₅	—	4	1	no	—
110	C₂²×C₄×C₅	—	4	1	no	—
111	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
112	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₅×Q₁₆	—	2	1	no	—
115	C₅×Q₁₆	C₂×Q₈	1	2	yes	—
116	C₅×SD₁₆	—	2	4	no	—
117	C₅×D₈	—	2	1	no	—
118	C₅×D₈	C₂×Q₈	1	2	yes	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
121	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
122	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
123	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
124	C₂×C₅×C₈	#41	1	2	yes	—
125	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
126	C₅×C₄⋊C₄	—	2	1	no	—
127	C₅×C₄⋊C₄	—	2	1	no	—
128	C₅×C₄⋊C₄	—	2	2	no	—
129	C₅×C₄⋊C₄	—	2	2	no	—
130	C₅×C₄⋊C₄	—	4	1	no	—
131	C₅×C₄⋊C₄	—	4	1	no	—
132	C₅×C₄⋊C₄	—	4	2	no	—
133	C₅×C₄⋊C₄	—	4	2	no	—
134	C₅×C₄⋊C₄	—	4	1	no	—
135	C₅×C₄⋊C₄	—	4	1	no	—
136	C₅×C₂²⋊C₄	—	4	1	no	—
137	C₅×C₂²⋊C₄	—	4	2	no	—
138	C₅×C₂²⋊C₄	—	4	1	no	—
139	C₅×C₂²⋊C₄	—	4	1	no	—
140	C₄²×C₅	—	4	1	no	—
141	C₄²×C₅	—	4	1	no	—
142	C₄²×C₅	—	4	1	no	—
143	C₄²×C₅	—	4	2	no	—
144	C₄²×C₅	D₈	1	1	yes	characteristic
145	C₄²×C₅	D₈	1	1	yes	characteristic
146	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
148	C₅×C₁₆	—	2	2	no	—
149	C₅×C₁₆	—	2	2	no	—
150	C₂×#135	C₂²×C₅	1	1	yes	characteristic
151	#533	—	2	1	no	—
152	C₄×#41	—	2	1	no	—
153	C₂²×C₁₆	C₂²×C₅	1	2	yes	—
154	#500	C₂²×C₅	1	1	yes	characteristic
155	#500	C₂²×C₅	1	1	yes	characteristic
156	#499	—	2	1	no	—
157	#499	C₂²×C₅	1	2	yes	—
158	#498	—	2	1	no	—
159	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
160	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
161	C₄×SD₁₆	—	2	1	no	—
162	C₄×SD₁₆	—	2	1	no	—
163	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
164	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
165	#427	—	2	1	no	—
166	#427	C₂²×C₅	1	2	yes	—
167	#427	C₂²×C₅	1	1	yes	characteristic
168	#416	—	2	1	no	—
169	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
170	#367	C₂²×C₅	1	2	yes	—
171	#367	C₂²×C₅	1	2	yes	—
172	#366	C₂²×C₅	1	2	yes	—
173	#366	C₂²×C₅	1	2	yes	—
174	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
175	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
176	C₄⋊C₁₆	C₂²×C₅	1	2	yes	—
177	#358	C₂²×C₅	1	2	yes	—
178	#358	C₂²×C₅	1	2	yes	—
179	#357	C₂²×C₅	1	2	yes	—
180	#357	C₂²×C₅	1	2	yes	—
181	C₂³×C₅	—	4	1	no	—
182	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
183	C₅×Q₈	—	2	2	no	—
184	C₅×Q₈	—	4	1	no	—
185	C₅×Q₈	—	8	2	no	—
186	C₅×Q₈	—	8	2	no	—
187	C₅×D₄	—	2	2	no	—
188	C₅×D₄	—	4	4	no	—
189	C₅×D₄	—	4	1	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	4	1	no	—
192	C₂×C₄×C₅	—	4	1	no	—
193	C₂×C₄×C₅	—	4	4	no	—
194	C₂×C₄×C₅	—	4	1	no	—
195	C₂×C₄×C₅	—	4	1	no	—
196	C₂×C₄×C₅	—	4	2	no	—
197	C₂×C₄×C₅	—	4	2	no	—
198	C₂×C₄×C₅	—	8	2	no	—
199	C₂×C₄×C₅	—	8	2	no	—
200	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
201	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
206	C₂×C₄×C₅	#137	1	2	yes	—
207	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
208	C₅×C₈	—	2	1	no	—
209	C₅×C₈	—	2	1	no	—
210	C₅×C₈	C₂²⋊Q₈	1	2	yes	—
211	C₅×C₈	C₂²×Q₈	1	1	yes	characteristic
212	C₅×C₈	C₂×#41	1	1	yes	characteristic
213	C₂×#41	—	2	1	no	—
214	#135	—	2	2	no	—
215	#135	C₅×Q₈	1	4	yes	complemented
216	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
217	C₂×SD₁₆	—	2	1	no	—
218	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
219	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
220	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
221	C₄⋊Q₈	—	2	1	no	—
222	C₄⋊Q₈	—	2	1	no	—
223	#125	—	2	2	no	—
224	C₂²⋊Q₈	—	4	1	no	—
225	C₂²⋊Q₈	—	4	1	no	—
226	C₄×Q₈	—	2	1	no	—
227	C₄×Q₈	—	2	1	no	—
228	C₄×Q₈	—	4	1	no	—
229	C₄×Q₈	—	4	1	no	—
230	C₄×D₄	—	2	1	no	—
231	C₄×D₄	—	2	1	no	—
232	C₄×D₄	—	4	1	no	—
233	C₄×D₄	—	4	1	no	—
234	#117	—	2	1	no	—
235	#117	—	2	2	no	—
236	#117	—	4	1	no	—
237	C₂×C₄²	—	4	1	no	—
238	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
239	C₂×C₁₆	—	2	4	no	—
240	C₂×C₁₆	C₂³×C₅	1	2	yes	—
241	C₂×C₁₆	C₂³×C₅	1	2	yes	—
242	#107	—	2	1	no	—
243	#107	—	2	1	no	—
244	#107	C₂³×C₅	1	2	yes	—
245	#107	C₂³×C₅	1	2	yes	—
246	#107	C₂³×C₅	1	1	yes	characteristic
247	#107	C₂³×C₅	1	1	yes	characteristic
248	#106	—	2	2	no	—
249	#106	—	2	1	no	—
250	#106	—	2	2	no	—
251	#103	—	2	1	no	—
252	#103	—	2	1	no	—
253	#102	—	2	1	no	—
254	#102	—	2	1	no	—
255	C₄×C₈	C₅×D₄	1	1	yes	characteristic
256	C₄×C₈	C₅×D₄	1	1	yes	characteristic
257	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
258	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
259	C₂²×C₅	—	2	1	no	—
260	C₂²×C₅	—	2	1	no	—
261	C₂²×C₅	—	4	2	no	—
262	C₂²×C₅	—	8	1	no	—
263	C₂²×C₅	—	8	1	no	—
264	C₂²×C₅	#474	1	2	yes	—
265	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
266	C₄×C₅	—	2	1	no	—
267	C₄×C₅	—	2	1	no	—
268	C₄×C₅	—	2	1	no	—
269	C₄×C₅	—	4	2	no	—
270	C₄×C₅	—	8	1	no	—
271	C₄×C₅	—	8	2	no	—
272	C₄×C₅	—	8	1	no	—
273	C₄×C₅	—	8	2	no	—
274	C₄×C₅	#474	1	2	yes	—
275	C₄×C₅	#508	1	2	yes	—
276	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
277	C₄×C₅	C₂×#137	1	1	yes	characteristic
278	#41	—	2	4	no	—
279	#41	—	4	2	no	—
280	C₂×Q₈	—	2	1	no	—
281	C₂×Q₈	—	4	1	no	—
282	C₂×Q₈	—	4	1	no	—
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
289	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
291	Q₁₆	—	2	1	no	—
292	Q₁₆	C₂×C₅×Q₈	1	2	yes	—
293	SD₁₆	—	2	4	no	—
294	D₈	—	2	1	no	—
295	D₈	C₂×C₅×Q₈	1	2	yes	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
298	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
299	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
300	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
301	C₂×C₈	C₅×#41	1	2	yes	—
302	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₂²⋊C₄	—	4	1	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₂²⋊C₄	—	4	1	no	—
316	C₂²⋊C₄	—	4	1	no	—
317	C₄²	—	4	1	no	—
318	C₄²	—	4	1	no	—
319	C₄²	—	4	1	no	—
320	C₄²	—	4	2	no	—
321	C₄²	C₅×D₈	1	1	yes	characteristic
322	C₄²	C₅×D₈	1	1	yes	characteristic
323	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
324	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
325	C₁₆	—	2	2	no	—
326	C₁₆	—	2	2	no	—
327	C₂×C₅	—	2	2	no	—
328	C₂×C₅	—	8	2	no	—
329	C₂×C₅	C₂×#474	1	1	yes	characteristic
330	C₂×C₅	C₂×#508	1	1	yes	characteristic
331	C₂×C₅	#3414	1	1	yes	characteristic
332	C₂³	—	4	1	no	—
333	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
334	Q₈	—	2	2	no	—
335	Q₈	—	4	1	no	—
336	Q₈	—	8	2	no	—
337	Q₈	—	8	2	no	—
338	D₄	—	2	2	no	—
339	D₄	—	4	4	no	—
340	D₄	—	4	1	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
352	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
353	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
354	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
355	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
356	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
357	C₂×C₄	C₅×#137	1	2	yes	—
358	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	C₅×C₂²⋊Q₈	1	2	yes	—
362	C₈	C₂²×C₅×Q₈	1	1	yes	characteristic
363	C₈	C₂×C₅×#41	1	1	yes	characteristic
364	C₅	#33626	1	1	yes	characteristic, direct product factor, Sylow
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	8	1	no	—
369	C₂²	—	8	1	no	—
370	C₂²	C₅×#474	1	2	yes	—
371	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	4	2	no	—
376	C₄	—	8	1	no	—
377	C₄	—	8	2	no	—
378	C₄	—	8	1	no	—
379	C₄	—	8	2	no	—
380	C₄	C₅×#474	1	2	yes	—
381	C₄	C₅×#508	1	2	yes	—
382	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
383	C₄	C₂×C₅×#137	1	1	yes	characteristic
384	C₂	—	2	2	no	—
385	C₂	—	8	2	no	—
386	C₂	C₂×C₅×#474	1	1	yes	characteristic
387	C₂	C₂×C₅×#508	1	1	yes	characteristic
388	C₂	C₅×#3414	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
socle	C₂²×C₅	C₂²×D₈
prime radical	C₂×C₅×#135	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3160	C₂	semidirect
3. C₅×#2229	C₂	semidirect
4. C₅×#2228	C₂	semidirect
5. C₅×#2227	C₂	semidirect
6. C₅×#2226	C₂	semidirect
7. C₅×#2225	C₂	semidirect
8. C₅×#2224	C₂	semidirect
9. C₅×#2158	C₂	semidirect
10. C₂×C₅×C₄⋊C₁₆	C₂	semidirect
43. #33626	C₅	direct (N × H)
46. C₅×#135	Q₈	semidirect
90. #3160	C₂×C₅	semidirect
92. #2229	C₂×C₅	semidirect
93. #2228	C₂×C₅	semidirect
94. #2227	C₂×C₅	semidirect
95. #2226	C₂×C₅	semidirect
96. #2225	C₂×C₅	semidirect
97. #2224	C₂×C₅	semidirect
98. #2158	C₂×C₅	semidirect
99. C₂×C₄⋊C₁₆	C₂×C₅	semidirect
215. #135	C₅×Q₈	semidirect
364. C₅	#33626	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×#3160	2
C₄×C₅×#135	2
C₅×#2229	2
C₅×#2228	2
C₅×#2227	2
C₅×#2226	2
C₅×#2225	2
C₅×#2224	2
C₅×#2158	2
C₂×C₅×C₄⋊C₁₆	2
C₅×#2138	2
#33626	5

Subgroups — C5×#33626 #11956346

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33626 #11956346