Subgroups — C₅×#33666 #11956386

Order 1280.

596 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3169	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2234	C₂	1	2	yes	maximal, complemented
4	C₅×#2227	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2226	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2207	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2206	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2186	C₂	1	2	yes	maximal, complemented
9	C₄×C₅×SD₃₂	C₂	1	2	yes	maximal, complemented
10	C₄×C₅×D₁₆	C₂	1	2	yes	maximal, complemented
11	C₅×#2162	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	C₂²	1	1	yes	characteristic
13	C₅×#532	—	2	1	no	—
14	C₄×C₅×#41	—	2	1	no	—
15	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
16	C₂×C₅×D₁₆	C₂²	1	2	yes	—
17	C₅×#500	C₂²	1	1	yes	characteristic
18	C₅×#493	C₂²	1	1	yes	characteristic
19	C₅×#486	—	2	1	no	—
20	C₅×#466	—	2	1	no	—
21	C₅×#466	C₂²	1	2	yes	—
22	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
23	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
24	C₄×C₅×SD₁₆	—	2	1	no	—
25	C₄×C₅×SD₁₆	—	2	1	no	—
26	C₄×C₅×D₈	—	2	1	no	—
27	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
28	C₄×C₅×D₈	C₂²	1	2	yes	—
29	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
30	C₅×#427	C₂²	1	1	yes	characteristic
31	C₅×#416	—	2	1	no	—
32	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₅×#367	C₂²	1	2	yes	—
34	C₅×#366	C₂²	1	2	yes	—
35	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₅×#358	C₂²	1	2	yes	—
38	C₅×#357	C₂²	1	2	yes	—
39	C₅×#357	C₂²	1	2	yes	—
40	C₅×#357	C₂²	1	2	yes	—
41	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
42	C₄×C₅×C₁₆	C₂²	1	2	yes	—
43	#33666	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₅×#41	—	2	1	no	—
45	C₂×C₅×#41	—	4	1	no	—
46	C₅×#135	—	2	2	no	—
47	C₅×#135	—	2	2	no	—
48	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
49	C₂×C₅×SD₁₆	—	2	1	no	—
50	C₂×C₅×D₈	—	2	1	no	—
51	C₂×C₅×D₈	C₂³	1	2	yes	—
52	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
53	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
54	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
55	C₅×C₄⋊Q₈	—	2	1	no	—
56	C₅×#127	—	2	1	no	—
57	C₅×#124	—	4	1	no	—
58	C₅×#121	—	2	2	no	—
59	C₅×#121	—	4	1	no	—
60	C₄×C₅×Q₈	—	2	1	no	—
61	C₄×C₅×Q₈	—	2	1	no	—
62	C₄×C₅×D₄	—	2	2	no	—
63	C₄×C₅×D₄	—	2	1	no	—
64	C₄×C₅×D₄	—	2	1	no	—
65	C₄×C₅×D₄	—	4	1	no	—
66	C₄×C₅×D₄	—	4	1	no	—
67	C₄×C₅×D₄	—	4	1	no	—
68	C₅×#117	—	2	1	no	—
69	C₅×#117	—	4	1	no	—
70	C₂×C₄²×C₅	—	4	1	no	—
71	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
72	C₅×SD₃₂	—	2	4	no	—
73	C₅×D₁₆	—	2	4	no	—
74	C₂×C₅×C₁₆	C₂³	1	2	yes	—
75	C₂×C₅×C₁₆	C₂³	1	2	yes	—
76	C₅×#107	—	2	1	no	—
77	C₅×#107	C₂³	1	1	yes	characteristic
78	C₅×#107	C₂³	1	1	yes	characteristic
79	C₅×#107	C₂³	1	2	yes	—
80	C₅×#106	—	2	1	no	—
81	C₅×#103	—	2	1	no	—
82	C₅×#103	—	2	1	no	—
83	C₅×#102	—	2	1	no	—
84	C₅×#102	—	2	1	no	—
85	C₅×#102	—	2	2	no	—
86	C₅×#102	—	2	2	no	—
87	C₄×C₅×C₈	D₄	1	1	yes	characteristic
88	C₄×C₅×C₈	D₄	1	1	yes	characteristic
89	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
90	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
91	#3169	C₂×C₅	1	1	yes	characteristic, complemented
92	C₄×#135	C₂×C₅	1	1	yes	characteristic, complemented
93	#2234	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	#2207	C₂×C₅	1	1	yes	characteristic, complemented
97	#2206	C₂×C₅	1	1	yes	characteristic, complemented
98	#2186	C₂×C₅	1	2	yes	complemented
99	C₄×SD₃₂	C₂×C₅	1	2	yes	complemented
100	C₄×D₁₆	C₂×C₅	1	2	yes	complemented
101	#2162	C₂×C₅	1	1	yes	characteristic, complemented
102	C₅×#41	—	2	4	no	—
103	C₅×#41	—	4	2	no	—
104	C₅×#41	—	8	4	no	—
105	C₂×C₅×Q₈	—	2	1	no	—
106	C₂×C₅×Q₈	—	4	1	no	—
107	C₂×C₅×D₄	—	2	1	no	—
108	C₂×C₅×D₄	—	2	2	no	—
109	C₂×C₅×D₄	—	4	1	no	—
110	C₂×C₅×D₄	—	4	2	no	—
111	C₂×C₅×D₄	—	4	1	no	—
112	C₂×C₅×D₄	—	4	1	no	—
113	C₂²×C₄×C₅	—	4	1	no	—
114	C₂²×C₄×C₅	—	4	1	no	—
115	C₂²×C₄×C₅	—	4	1	no	—
116	C₂²×C₄×C₅	—	4	2	no	—
117	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
118	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₅×Q₁₆	—	2	1	no	—
121	C₅×Q₁₆	#41	1	2	yes	complemented
122	C₅×SD₁₆	—	2	4	no	—
123	C₅×D₈	—	2	1	no	—
124	C₅×D₈	—	2	2	no	—
125	C₅×D₈	—	2	2	no	—
126	C₅×D₈	—	4	2	no	—
127	C₅×D₈	#41	1	2	yes	complemented
128	C₂×C₅×C₈	—	2	1	no	—
129	C₂×C₅×C₈	—	2	1	no	—
130	C₂×C₅×C₈	—	4	1	no	—
131	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
132	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
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	—	2	2	no	—
138	C₅×C₄⋊C₄	—	4	1	no	—
139	C₅×C₄⋊C₄	—	4	1	no	—
140	C₅×C₄⋊C₄	—	4	1	no	—
141	C₅×C₂²⋊C₄	—	4	1	no	—
142	C₅×C₂²⋊C₄	—	4	1	no	—
143	C₅×C₂²⋊C₄	—	4	1	no	—
144	C₅×C₂²⋊C₄	—	4	2	no	—
145	C₅×C₂²⋊C₄	—	4	2	no	—
146	C₄²×C₅	—	4	1	no	—
147	C₄²×C₅	—	4	1	no	—
148	C₄²×C₅	—	4	1	no	—
149	C₄²×C₅	D₈	1	1	yes	characteristic
150	C₄²×C₅	D₈	1	1	yes	characteristic
151	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
153	C₅×C₁₆	—	2	2	no	—
154	C₅×C₁₆	—	2	2	no	—
155	C₂×#135	C₂²×C₅	1	1	yes	characteristic
156	#532	—	2	1	no	—
157	C₄×#41	—	2	1	no	—
158	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
159	C₂×D₁₆	C₂²×C₅	1	2	yes	—
160	#500	C₂²×C₅	1	1	yes	characteristic
161	#493	C₂²×C₅	1	1	yes	characteristic
162	#486	—	2	1	no	—
163	#466	—	2	1	no	—
164	#466	C₂²×C₅	1	2	yes	—
165	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
166	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
167	C₄×SD₁₆	—	2	1	no	—
168	C₄×SD₁₆	—	2	1	no	—
169	C₄×D₈	—	2	1	no	—
170	C₄×D₈	C₂²×C₅	1	2	yes	—
171	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
172	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
173	#427	C₂²×C₅	1	1	yes	characteristic
174	#416	—	2	1	no	—
175	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
176	#367	C₂²×C₅	1	2	yes	—
177	#366	C₂²×C₅	1	2	yes	—
178	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
179	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
180	#358	C₂²×C₅	1	2	yes	—
181	#357	C₂²×C₅	1	2	yes	—
182	#357	C₂²×C₅	1	2	yes	—
183	#357	C₂²×C₅	1	2	yes	—
184	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
185	C₄×C₁₆	C₂²×C₅	1	2	yes	—
186	C₂³×C₅	—	4	1	no	—
187	C₂³×C₅	—	4	2	no	—
188	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
189	C₅×Q₈	—	2	2	no	—
190	C₅×Q₈	—	4	1	no	—
191	C₅×Q₈	—	8	2	no	—
192	C₅×D₄	—	2	2	no	—
193	C₅×D₄	—	4	4	no	—
194	C₅×D₄	—	4	2	no	—
195	C₅×D₄	—	4	1	no	—
196	C₅×D₄	—	4	2	no	—
197	C₅×D₄	—	8	2	no	—
198	C₅×D₄	—	8	4	no	—
199	C₅×D₄	—	8	2	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	4	4	no	—
205	C₂×C₄×C₅	—	4	1	no	—
206	C₂×C₄×C₅	—	4	1	no	—
207	C₂×C₄×C₅	—	4	1	no	—
208	C₂×C₄×C₅	—	4	2	no	—
209	C₂×C₄×C₅	—	8	2	no	—
210	C₂×C₄×C₅	—	8	2	no	—
211	C₂×C₄×C₅	—	8	4	no	—
212	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
217	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
218	C₅×C₈	—	2	1	no	—
219	C₅×C₈	—	2	1	no	—
220	C₅×C₈	—	2	1	no	—
221	C₅×C₈	C₂×#41	1	1	yes	characteristic
222	C₅×C₈	C₂×#41	1	1	yes	characteristic
223	C₂×#41	—	2	1	no	—
224	C₂×#41	—	4	1	no	—
225	#135	—	2	2	no	—
226	#135	—	2	2	no	—
227	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
228	C₂×SD₁₆	—	2	1	no	—
229	C₂×D₈	—	2	1	no	—
230	C₂×D₈	C₂³×C₅	1	2	yes	—
231	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
232	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
234	C₄⋊Q₈	—	2	1	no	—
235	#127	—	2	1	no	—
236	#124	—	4	1	no	—
237	#121	—	2	2	no	—
238	#121	—	4	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	—	2	1	no	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	2	no	—
244	C₄×D₄	—	4	1	no	—
245	C₄×D₄	—	4	1	no	—
246	C₄×D₄	—	4	1	no	—
247	#117	—	2	1	no	—
248	#117	—	4	1	no	—
249	C₂×C₄²	—	4	1	no	—
250	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
251	SD₃₂	—	2	4	no	—
252	D₁₆	—	2	4	no	—
253	C₂×C₁₆	C₂³×C₅	1	2	yes	—
254	C₂×C₁₆	C₂³×C₅	1	2	yes	—
255	#107	—	2	1	no	—
256	#107	C₂³×C₅	1	1	yes	characteristic
257	#107	C₂³×C₅	1	1	yes	characteristic
258	#107	C₂³×C₅	1	2	yes	—
259	#106	—	2	1	no	—
260	#103	—	2	1	no	—
261	#103	—	2	1	no	—
262	#102	—	2	1	no	—
263	#102	—	2	1	no	—
264	#102	—	2	2	no	—
265	#102	—	2	2	no	—
266	C₄×C₈	C₅×D₄	1	1	yes	characteristic
267	C₄×C₈	C₅×D₄	1	1	yes	characteristic
268	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
269	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
270	C₂²×C₅	—	2	1	no	—
271	C₂²×C₅	—	2	1	no	—
272	C₂²×C₅	—	2	1	no	—
273	C₂²×C₅	—	4	2	no	—
274	C₂²×C₅	—	8	1	no	—
275	C₂²×C₅	—	8	1	no	—
276	C₂²×C₅	—	8	2	no	—
277	C₂²×C₅	—	8	2	no	—
278	C₂²×C₅	—	8	2	no	—
279	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
280	C₄×C₅	—	2	1	no	—
281	C₄×C₅	—	2	1	no	—
282	C₄×C₅	—	2	1	no	—
283	C₄×C₅	—	4	2	no	—
284	C₄×C₅	—	8	1	no	—
285	C₄×C₅	—	8	1	no	—
286	C₄×C₅	—	8	2	no	—
287	C₄×C₅	#508	1	2	yes	—
288	C₄×C₅	#509	1	2	yes	—
289	C₄×C₅	#525	1	1	yes	characteristic
290	C₄×C₅	#575	1	1	yes	characteristic
291	#41	—	2	4	no	—
292	#41	—	4	2	no	—
293	#41	—	8	4	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
307	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
309	Q₁₆	—	2	1	no	—
310	Q₁₆	C₅×#41	1	2	yes	complemented
311	SD₁₆	—	2	4	no	—
312	D₈	—	2	1	no	—
313	D₈	—	2	2	no	—
314	D₈	—	2	2	no	—
315	D₈	—	4	2	no	—
316	D₈	C₅×#41	1	2	yes	complemented
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	4	1	no	—
320	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
321	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
322	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
323	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₂²⋊C₄	—	4	1	no	—
331	C₂²⋊C₄	—	4	1	no	—
332	C₂²⋊C₄	—	4	1	no	—
333	C₂²⋊C₄	—	4	2	no	—
334	C₂²⋊C₄	—	4	2	no	—
335	C₄²	—	4	1	no	—
336	C₄²	—	4	1	no	—
337	C₄²	—	4	1	no	—
338	C₄²	C₅×D₈	1	1	yes	characteristic
339	C₄²	C₅×D₈	1	1	yes	characteristic
340	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
341	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
342	C₁₆	—	2	2	no	—
343	C₁₆	—	2	2	no	—
344	C₂×C₅	—	4	1	no	—
345	C₂×C₅	—	8	2	no	—
346	C₂×C₅	—	16	2	no	—
347	C₂×C₅	#3100	1	1	yes	characteristic
348	C₂×C₅	C₂×#508	1	1	yes	characteristic
349	C₂×C₅	C₂×#509	1	1	yes	characteristic
350	C₂³	—	4	1	no	—
351	C₂³	—	4	2	no	—
352	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
353	Q₈	—	2	2	no	—
354	Q₈	—	4	1	no	—
355	Q₈	—	8	2	no	—
356	D₄	—	2	2	no	—
357	D₄	—	4	4	no	—
358	D₄	—	4	2	no	—
359	D₄	—	4	1	no	—
360	D₄	—	4	2	no	—
361	D₄	—	8	2	no	—
362	D₄	—	8	4	no	—
363	D₄	—	8	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	8	2	no	—
374	C₂×C₄	—	8	4	no	—
375	C₂×C₄	—	8	2	no	—
376	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
377	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
378	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
379	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
380	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
381	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
382	C₈	—	2	1	no	—
383	C₈	—	2	1	no	—
384	C₈	—	2	1	no	—
385	C₈	C₂×C₅×#41	1	1	yes	characteristic
386	C₈	C₂×C₅×#41	1	1	yes	characteristic
387	C₅	#33666	1	1	yes	characteristic, direct product factor, Sylow
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	8	1	no	—
393	C₂²	—	8	1	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	4	2	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	2	no	—
404	C₄	—	8	1	no	—
405	C₄	C₅×#508	1	2	yes	—
406	C₄	C₅×#509	1	2	yes	—
407	C₄	C₅×#525	1	1	yes	characteristic
408	C₄	C₅×#575	1	1	yes	characteristic
409	C₂	—	4	1	no	—
410	C₂	—	8	2	no	—
411	C₂	—	16	2	no	—
412	C₂	C₅×#3100	1	1	yes	characteristic
413	C₂	C₂×C₅×#508	1	1	yes	characteristic
414	C₂	C₂×C₅×#509	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
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×#3169	C₂	semidirect
2. C₄×C₅×#135	C₂	semidirect
3. C₅×#2234	C₂	semidirect
4. C₅×#2227	C₂	semidirect
5. C₅×#2226	C₂	semidirect
6. C₅×#2207	C₂	semidirect
7. C₅×#2206	C₂	semidirect
8. C₅×#2186	C₂	semidirect
9. C₄×C₅×SD₃₂	C₂	semidirect
10. C₄×C₅×D₁₆	C₂	semidirect
11. C₅×#2162	C₂	semidirect
43. #33666	C₅	direct (N × H)
91. #3169	C₂×C₅	semidirect
92. C₄×#135	C₂×C₅	semidirect
93. #2234	C₂×C₅	semidirect
94. #2227	C₂×C₅	semidirect
95. #2226	C₂×C₅	semidirect
96. #2207	C₂×C₅	semidirect
97. #2206	C₂×C₅	semidirect
98. #2186	C₂×C₅	semidirect
99. C₄×SD₃₂	C₂×C₅	semidirect
100. C₄×D₁₆	C₂×C₅	semidirect
101. #2162	C₂×C₅	semidirect
121. C₅×Q₁₆	#41	semidirect
127. C₅×D₈	#41	semidirect
310. Q₁₆	C₅×#41	semidirect
316. D₈	C₅×#41	semidirect
387. C₅	#33666	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×#3169	2
C₄×C₅×#135	2
C₅×#2234	2
C₅×#2227	2
C₅×#2226	2
C₅×#2207	2
C₅×#2206	2
C₅×#2186	2
C₄×C₅×SD₃₂	2
C₄×C₅×D₁₆	2
C₅×#2162	2
#33666	5

Subgroups — C5×#33666 #11956386

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33666 #11956386