Subgroups — C₅×#33665 #11956385

Order 1280.

616 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3168	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2236	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2233	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2228	C₂	1	2	yes	maximal, complemented
6	C₅×#2210	C₂	1	2	yes	maximal, complemented
7	C₅×#2187	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2184	C₂	1	1	yes	maximal, characteristic
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	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
13	C₅×#529	—	2	1	no	—
14	C₂×C₄×C₅×D₄	—	2	1	no	—
15	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
16	C₂×C₅×D₁₆	C₂²	1	2	yes	—
17	C₅×#499	C₂²	1	1	yes	characteristic, complemented
18	C₅×#495	C₂²	1	1	yes	characteristic, complemented
19	C₅×#488	—	2	1	no	—
20	C₅×#467	C₂²	1	1	yes	characteristic
21	C₅×#466	C₂²	1	1	yes	characteristic
22	C₅×#465	—	2	1	no	—
23	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₄×C₅×SD₁₆	—	2	1	no	—
25	C₄×C₅×D₈	—	2	1	no	—
26	C₄×C₅×D₈	—	2	1	no	—
27	C₄×C₅×D₈	C₂²	1	2	yes	—
28	C₄×C₅×D₈	C₂²	1	2	yes	—
29	C₄×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₅×#107	C₂²	1	1	yes	characteristic
31	C₂×C₅×#102	—	2	1	no	—
32	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₅×#367	C₂²	1	2	yes	complemented
34	C₅×#366	C₂²	1	2	yes	complemented
35	C₅×C₄⋊C₁₆	C₂²	1	2	yes	complemented
36	C₅×#358	C₂²	1	2	yes	complemented
37	C₅×#357	C₂²	1	2	yes	—
38	C₅×#357	C₂²	1	2	yes	—
39	C₅×#357	C₂²	1	2	yes	complemented
40	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
41	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
42	C₄×C₅×C₁₆	C₂²	1	2	yes	complemented
43	#33665	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×D₄	—	2	1	no	—
45	C₂³×C₄×C₅	—	4	1	no	—
46	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
47	C₂×C₅×SD₁₆	—	2	1	no	—
48	C₂×C₅×D₈	—	2	4	no	—
49	C₂×C₅×D₈	—	2	1	no	—
50	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
51	C₂×C₅×D₈	C₂³	1	2	yes	—
52	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
53	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
54	C₅×#126	—	4	1	no	—
55	C₅×#125	—	2	1	no	—
56	C₅×#124	—	2	1	no	—
57	C₅×#123	—	4	1	no	—
58	C₅×C₂²⋊Q₈	—	2	1	no	—
59	C₅×#121	—	2	1	no	—
60	C₄×C₅×Q₈	—	2	1	no	—
61	C₄×C₅×D₄	—	2	2	no	—
62	C₄×C₅×D₄	—	2	2	no	—
63	C₄×C₅×D₄	—	2	1	no	—
64	C₄×C₅×D₄	—	4	1	no	—
65	C₄×C₅×D₄	—	4	1	no	—
66	C₄×C₅×D₄	—	4	1	no	—
67	C₅×#117	—	4	1	no	—
68	C₂×C₅×C₄⋊C₄	—	2	1	no	—
69	C₂×C₅×C₂²⋊C₄	—	4	1	no	—
70	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
71	C₅×SD₃₂	—	2	4	no	—
72	C₅×D₁₆	—	2	4	no	—
73	C₂×C₅×C₁₆	C₂³	1	2	yes	—
74	C₂×C₅×C₁₆	C₂³	1	2	yes	—
75	C₅×#107	—	2	1	no	—
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	1	no	—
80	C₅×#103	—	2	1	no	—
81	C₅×#103	—	2	1	no	—
82	C₅×#102	—	2	2	no	—
83	C₅×#102	—	2	2	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	#3168	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×C₄×D₈	C₂×C₅	1	1	yes	characteristic, complemented
92	#2236	C₂×C₅	1	1	yes	characteristic, complemented
93	#2233	C₂×C₅	1	1	yes	characteristic, complemented
94	#2228	C₂×C₅	1	2	yes	complemented
95	#2210	C₂×C₅	1	2	yes	complemented
96	#2187	C₂×C₅	1	1	yes	characteristic, complemented
97	#2184	C₂×C₅	1	1	yes	characteristic
98	C₄×SD₃₂	C₂×C₅	1	2	yes	complemented
99	C₄×D₁₆	C₂×C₅	1	2	yes	complemented
100	#2162	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂⁴×C₅	—	4	1	no	—
102	C₂×C₅×Q₈	—	2	1	no	—
103	C₂×C₅×D₄	—	2	4	no	—
104	C₂×C₅×D₄	—	2	2	no	—
105	C₂×C₅×D₄	—	2	1	no	—
106	C₂×C₅×D₄	—	4	2	no	—
107	C₂×C₅×D₄	—	4	1	no	—
108	C₂×C₅×D₄	—	4	1	no	—
109	C₂²×C₄×C₅	—	4	1	no	—
110	C₂²×C₄×C₅	—	4	2	no	—
111	C₂²×C₄×C₅	—	4	1	no	—
112	C₂²×C₄×C₅	—	4	2	no	—
113	C₂²×C₄×C₅	—	8	4	no	—
114	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
115	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₅×Q₁₆	—	2	2	no	—
118	C₅×SD₁₆	—	4	2	no	—
119	C₅×D₈	—	2	4	no	—
120	C₅×D₈	—	2	2	no	—
121	C₅×D₈	—	2	2	no	—
122	C₅×D₈	#41	1	4	yes	—
123	C₂×C₅×C₈	—	2	2	no	—
124	C₂×C₅×C₈	—	4	1	no	—
125	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
126	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
127	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
128	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
129	C₅×C₄⋊C₄	—	2	2	no	—
130	C₅×C₄⋊C₄	—	2	1	no	—
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	4	1	no	—
133	C₅×C₄⋊C₄	—	4	1	no	—
134	C₅×C₄⋊C₄	—	4	1	no	—
135	C₅×C₄⋊C₄	—	4	1	no	—
136	C₅×C₄⋊C₄	—	4	1	no	—
137	C₅×C₂²⋊C₄	—	4	1	no	—
138	C₅×C₂²⋊C₄	—	4	2	no	—
139	C₅×C₂²⋊C₄	—	4	2	no	—
140	C₅×C₂²⋊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	C₄²×C₅	—	4	1	no	—
145	C₄²×C₅	D₈	1	1	yes	characteristic
146	C₄²×C₅	D₈	1	1	yes	characteristic
147	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
149	C₅×C₁₆	—	2	2	no	—
150	C₅×C₁₆	—	2	2	no	—
151	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
152	#529	—	2	1	no	—
153	C₂×C₄×D₄	—	2	1	no	—
154	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
155	C₂×D₁₆	C₂²×C₅	1	2	yes	—
156	#499	C₂²×C₅	1	1	yes	characteristic, complemented
157	#495	C₂²×C₅	1	1	yes	characteristic, complemented
158	#488	—	2	1	no	—
159	#467	C₂²×C₅	1	1	yes	characteristic
160	#466	C₂²×C₅	1	1	yes	characteristic
161	#465	—	2	1	no	—
162	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
163	C₄×SD₁₆	—	2	1	no	—
164	C₄×D₈	—	2	1	no	—
165	C₄×D₈	—	2	1	no	—
166	C₄×D₈	C₂²×C₅	1	2	yes	—
167	C₄×D₈	C₂²×C₅	1	2	yes	—
168	C₄×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
169	C₂×#107	C₂²×C₅	1	1	yes	characteristic
170	C₂×#102	—	2	1	no	—
171	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
172	#367	C₂²×C₅	1	2	yes	complemented
173	#366	C₂²×C₅	1	2	yes	complemented
174	C₄⋊C₁₆	C₂²×C₅	1	2	yes	complemented
175	#358	C₂²×C₅	1	2	yes	complemented
176	#357	C₂²×C₅	1	2	yes	—
177	#357	C₂²×C₅	1	2	yes	—
178	#357	C₂²×C₅	1	2	yes	complemented
179	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
180	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
181	C₄×C₁₆	C₂²×C₅	1	2	yes	complemented
182	C₂³×C₅	—	4	4	no	—
183	C₂³×C₅	—	4	2	no	—
184	C₂³×C₅	—	4	1	no	—
185	C₂³×C₅	—	8	2	no	—
186	C₂³×C₅	—	8	2	no	—
187	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
188	C₅×Q₈	—	4	1	no	—
189	C₅×Q₈	—	4	1	no	—
190	C₅×D₄	—	2	4	no	—
191	C₅×D₄	—	4	4	no	—
192	C₅×D₄	—	4	1	no	—
193	C₅×D₄	—	4	2	no	—
194	C₅×D₄	—	4	1	no	—
195	C₅×D₄	—	8	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	1	no	—
198	C₂×C₄×C₅	—	2	1	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	2	no	—
206	C₂×C₄×C₅	—	8	2	no	—
207	C₂×C₄×C₅	—	8	4	no	—
208	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
209	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
210	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
212	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
213	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₅×C₈	—	2	1	no	—
215	C₅×C₈	—	2	1	no	—
216	C₅×C₈	—	2	1	no	—
217	C₅×C₈	C₂×#41	1	2	yes	—
218	C₂²×D₄	—	2	1	no	—
219	C₂³×C₄	—	4	1	no	—
220	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
221	C₂×SD₁₆	—	2	1	no	—
222	C₂×D₈	—	2	4	no	—
223	C₂×D₈	—	2	1	no	—
224	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
225	C₂×D₈	C₂³×C₅	1	2	yes	—
226	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
227	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
228	#126	—	4	1	no	—
229	#125	—	2	1	no	—
230	#124	—	2	1	no	—
231	#123	—	4	1	no	—
232	C₂²⋊Q₈	—	2	1	no	—
233	#121	—	2	1	no	—
234	C₄×Q₈	—	2	1	no	—
235	C₄×D₄	—	2	2	no	—
236	C₄×D₄	—	2	2	no	—
237	C₄×D₄	—	2	1	no	—
238	C₄×D₄	—	4	1	no	—
239	C₄×D₄	—	4	1	no	—
240	C₄×D₄	—	4	1	no	—
241	#117	—	4	1	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₂²⋊C₄	—	4	1	no	—
244	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
245	SD₃₂	—	2	4	no	—
246	D₁₆	—	2	4	no	—
247	C₂×C₁₆	C₂³×C₅	1	2	yes	—
248	C₂×C₁₆	C₂³×C₅	1	2	yes	—
249	#107	—	2	1	no	—
250	#107	C₂³×C₅	1	1	yes	characteristic
251	#107	C₂³×C₅	1	1	yes	characteristic
252	#107	C₂³×C₅	1	2	yes	—
253	#106	—	2	1	no	—
254	#103	—	2	1	no	—
255	#103	—	2	1	no	—
256	#102	—	2	2	no	—
257	#102	—	2	2	no	—
258	#102	—	2	1	no	—
259	#102	—	2	1	no	—
260	C₄×C₈	C₅×D₄	1	1	yes	characteristic
261	C₄×C₈	C₅×D₄	1	1	yes	characteristic
262	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
263	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
264	C₂²×C₅	—	2	1	no	—
265	C₂²×C₅	—	2	1	no	—
266	C₂²×C₅	—	4	4	no	—
267	C₂²×C₅	—	8	8	no	—
268	C₂²×C₅	—	8	2	no	—
269	C₂²×C₅	—	8	2	no	—
270	C₂²×C₅	—	8	1	no	—
271	C₂²×C₅	—	8	1	no	—
272	C₂²×C₅	—	8	1	no	—
273	C₂²×C₅	#508	1	2	yes	—
274	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
275	C₄×C₅	—	2	1	no	—
276	C₄×C₅	—	2	1	no	—
277	C₄×C₅	—	2	1	no	—
278	C₄×C₅	—	2	1	no	—
279	C₄×C₅	—	8	1	no	—
280	C₄×C₅	—	8	1	no	—
281	C₄×C₅	—	8	1	no	—
282	C₄×C₅	—	8	2	no	—
283	C₄×C₅	#509	1	2	yes	—
284	C₄×C₅	#525	1	1	yes	characteristic
285	C₄×C₅	#575	1	1	yes	characteristic
286	C₂⁴	—	4	1	no	—
287	C₂×Q₈	—	2	1	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	4	1	no	—
294	C₂²×C₄	—	4	1	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	2	no	—
298	C₂²×C₄	—	8	4	no	—
299	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
300	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
302	Q₁₆	—	2	2	no	—
303	SD₁₆	—	4	2	no	—
304	D₈	—	2	4	no	—
305	D₈	—	2	2	no	—
306	D₈	—	2	2	no	—
307	D₈	C₅×#41	1	4	yes	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	4	1	no	—
310	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
311	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
312	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
313	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	2	1	no	—
317	C₄⋊C₄	—	4	1	no	—
318	C₄⋊C₄	—	4	1	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	4	1	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₂²⋊C₄	—	4	1	no	—
326	C₂²⋊C₄	—	4	1	no	—
327	C₂²⋊C₄	—	4	1	no	—
328	C₂²⋊C₄	—	4	1	no	—
329	C₄²	—	4	1	no	—
330	C₄²	C₅×D₈	1	1	yes	characteristic
331	C₄²	C₅×D₈	1	1	yes	characteristic
332	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
333	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
334	C₁₆	—	2	2	no	—
335	C₁₆	—	2	2	no	—
336	C₂×C₅	—	2	2	no	—
337	C₂×C₅	—	8	4	no	—
338	C₂×C₅	—	16	1	no	—
339	C₂×C₅	#3100	1	1	yes	characteristic
340	C₂×C₅	C₂×#508	1	1	yes	characteristic
341	C₂×C₅	C₂×#509	1	1	yes	characteristic
342	C₂³	—	4	4	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	1	no	—
345	C₂³	—	8	2	no	—
346	C₂³	—	8	2	no	—
347	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
348	Q₈	—	4	1	no	—
349	Q₈	—	4	1	no	—
350	D₄	—	2	4	no	—
351	D₄	—	4	4	no	—
352	D₄	—	4	1	no	—
353	D₄	—	4	2	no	—
354	D₄	—	4	1	no	—
355	D₄	—	8	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	8	4	no	—
365	C₂×C₄	—	8	2	no	—
366	C₂×C₄	—	8	4	no	—
367	C₂×C₄	—	8	2	no	—
368	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
369	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
370	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
371	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
372	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	C₂×C₅×#41	1	2	yes	—
378	C₅	#33665	1	1	yes	characteristic, direct product factor, Sylow
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	8	8	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	1	no	—
386	C₂²	—	8	1	no	—
387	C₂²	—	8	1	no	—
388	C₂²	C₅×#508	1	2	yes	—
389	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	8	1	no	—
395	C₄	—	8	1	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	1	no	—
398	C₄	C₅×#509	1	2	yes	—
399	C₄	C₅×#525	1	1	yes	characteristic
400	C₄	C₅×#575	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	8	4	no	—
403	C₂	—	16	1	no	—
404	C₂	C₅×#3100	1	1	yes	characteristic
405	C₂	C₂×C₅×#508	1	1	yes	characteristic
406	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
prime radical	C₅×#2184	C₂
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×#3168	C₂	semidirect
2. C₂×C₄×C₅×D₈	C₂	semidirect
3. C₅×#2236	C₂	semidirect
4. C₅×#2233	C₂	semidirect
5. C₅×#2228	C₂	semidirect
6. C₅×#2210	C₂	semidirect
7. C₅×#2187	C₂	semidirect
9. C₄×C₅×SD₃₂	C₂	semidirect
10. C₄×C₅×D₁₆	C₂	semidirect
11. C₅×#2162	C₂	semidirect
17. C₅×#499	C₂²	semidirect
18. C₅×#495	C₂²	semidirect
23. C₄×C₅×Q₁₆	C₂²	semidirect
29. C₄×C₅×D₈	C₂²	semidirect
33. C₅×#367	C₂²	semidirect
34. C₅×#366	C₂²	semidirect
35. C₅×C₄⋊C₁₆	C₂²	semidirect
36. C₅×#358	C₂²	semidirect
39. C₅×#357	C₂²	semidirect
42. C₄×C₅×C₁₆	C₂²	semidirect
43. #33665	C₅	direct (N × H)
90. #3168	C₂×C₅	semidirect
91. C₂×C₄×D₈	C₂×C₅	semidirect
92. #2236	C₂×C₅	semidirect
93. #2233	C₂×C₅	semidirect
94. #2228	C₂×C₅	semidirect
95. #2210	C₂×C₅	semidirect
96. #2187	C₂×C₅	semidirect
98. C₄×SD₃₂	C₂×C₅	semidirect
99. C₄×D₁₆	C₂×C₅	semidirect
100. #2162	C₂×C₅	semidirect
156. #499	C₂²×C₅	semidirect
157. #495	C₂²×C₅	semidirect
162. C₄×Q₁₆	C₂²×C₅	semidirect
168. C₄×D₈	C₂²×C₅	semidirect
172. #367	C₂²×C₅	semidirect
173. #366	C₂²×C₅	semidirect
174. C₄⋊C₁₆	C₂²×C₅	semidirect
175. #358	C₂²×C₅	semidirect
178. #357	C₂²×C₅	semidirect
181. C₄×C₁₆	C₂²×C₅	semidirect
378. C₅	#33665	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×#3168	2
C₂×C₄×C₅×D₈	2
C₅×#2236	2
C₅×#2233	2
C₅×#2228	2
C₅×#2210	2
C₅×#2187	2
C₅×#2184	2
C₄×C₅×SD₃₂	2
C₄×C₅×D₁₆	2
C₅×#2162	2
#33665	5

Subgroups — C5×#33665 #11956385

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33665 #11956385