Subgroups — C₅×#33507 #11956227

Order 1280.

492 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2966	C₂	1	1	yes	maximal, characteristic
2	C₅×#2183	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×Q₈×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2169	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2169	C₂	1	2	yes	maximal, complemented
6	C₅×#2168	C₂	1	2	yes	maximal, complemented
7	C₅×D₄×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2164	C₂	1	2	yes	maximal, complemented
9	C₅×#2162	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2151	C₂	1	2	yes	maximal, complemented
11	C₅×#2150	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#529	C₄	1	1	yes	characteristic
13	C₂×C₅×M₃₂	C₂²	1	2	yes	—
14	C₂×C₅×M₃₂	C₂²	1	2	yes	—
15	C₂²×C₅×C₁₆	C₂²	1	2	yes	—
16	C₅×#446	C₄	1	1	yes	characteristic
17	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
18	C₅×#436	C₄	1	1	yes	characteristic
19	C₅×#435	C₄	1	2	yes	—
20	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
21	C₅×C₈×D₄	C₂²	1	2	yes	—
22	C₅×#433	C₄	1	2	yes	—
23	C₅×#432	C₄	1	1	yes	characteristic
24	C₅×#405	C₂²	1	2	yes	—
25	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₅×C₄⋊C₁₆	C₂²	1	2	yes	—
27	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
28	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
29	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
30	C₅×C₄⋊C₁₆	C₂²	1	2	yes	—
31	C₅×C₄⋊C₁₆	C₂²	1	2	yes	—
32	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
33	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
34	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
35	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
36	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
37	C₅×#346	C₂²	1	2	yes	—
38	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
39	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
40	C₄×C₅×C₁₆	C₂²	1	2	yes	—
41	#33507	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
43	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₅×C₈	C₂³	1	2	yes	—
46	C₅×#126	C₈	1	2	yes	—
47	C₅×#125	C₈	1	1	yes	characteristic
48	C₅×#124	C₈	1	1	yes	characteristic
49	C₅×#123	C₈	1	2	yes	—
50	C₅×C₂²⋊Q₈	C₈	1	1	yes	characteristic
51	C₅×#121	C₈	1	1	yes	characteristic
52	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
53	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
54	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
55	C₅×#117	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
57	C₅×M₃₂	—	4	2	no	—
58	C₅×M₃₂	—	4	2	no	—
59	C₂×C₅×C₁₆	—	4	2	no	—
60	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
62	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
63	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
64	C₂×C₅×C₁₆	C₂³	1	2	yes	—
65	C₂×C₅×C₁₆	C₂³	1	2	yes	—
66	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
67	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
68	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
69	C₅×C₄⋊C₈	C₂×C₄	1	2	yes	—
70	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
71	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
72	C₅×C₂²⋊C₈	C₂×C₄	1	2	yes	—
73	C₅×#97	C₂×C₄	1	2	yes	—
74	C₅×#97	C₂×C₄	1	2	yes	—
75	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
76	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₄×C₅×C₈	C₂³	1	2	yes	—
80	#2966	C₂×C₅	1	1	yes	characteristic
81	#2183	C₂×C₅	1	1	yes	characteristic, complemented
82	Q₈×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
83	#2169	C₂×C₅	1	1	yes	characteristic, complemented
84	#2169	C₂×C₅	1	2	yes	complemented
85	#2168	C₂×C₅	1	2	yes	complemented
86	D₄×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
87	#2164	C₂×C₅	1	2	yes	complemented
88	#2162	C₂×C₅	1	1	yes	characteristic, complemented
89	#2151	C₂×C₅	1	2	yes	complemented
90	#2150	C₂×C₅	1	1	yes	characteristic, complemented
91	C₂×C₅×Q₈	C₂×C₈	1	1	yes	characteristic
92	C₂×C₅×D₄	C₂×C₈	1	1	yes	characteristic
93	C₂×C₅×D₄	C₂×C₈	1	2	yes	—
94	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₅	C₂×C₈	1	1	yes	characteristic
96	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
98	C₅×M₁₆	—	4	2	no	—
99	C₂×C₅×C₈	—	2	2	no	—
100	C₂×C₅×C₈	—	2	1	no	—
101	C₂×C₅×C₈	—	2	1	no	—
102	C₂×C₅×C₈	—	2	2	no	—
103	C₂×C₅×C₈	—	4	1	no	—
104	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
108	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
109	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
110	C₅×C₄⋊C₄	C₂×C₈	1	2	yes	—
111	C₅×C₄⋊C₄	C₂×C₈	1	2	yes	—
112	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
113	C₅×C₄⋊C₄	C₂×C₈	1	2	yes	—
114	C₅×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
115	C₅×C₄⋊C₄	C₂×C₈	1	2	yes	—
116	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
117	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
118	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
119	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
120	C₅×C₂²⋊C₄	C₂×C₈	1	2	yes	—
121	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
122	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
123	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₅	C₂²×C₄	1	2	yes	—
126	C₅×C₁₆	—	2	1	no	—
127	C₅×C₁₆	—	2	2	no	—
128	C₅×C₁₆	—	2	1	no	—
129	C₅×C₁₆	—	2	2	no	—
130	C₅×C₁₆	—	2	1	no	—
131	C₅×C₁₆	—	2	1	no	—
132	#529	C₄×C₅	1	1	yes	characteristic
133	C₂×M₃₂	C₂²×C₅	1	2	yes	—
134	C₂×M₃₂	C₂²×C₅	1	2	yes	—
135	C₂²×C₁₆	C₂²×C₅	1	2	yes	—
136	#446	C₄×C₅	1	1	yes	characteristic
137	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
138	#436	C₄×C₅	1	1	yes	characteristic
139	#435	C₄×C₅	1	2	yes	—
140	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
141	C₈×D₄	C₂²×C₅	1	2	yes	—
142	#433	C₄×C₅	1	2	yes	—
143	#432	C₄×C₅	1	1	yes	characteristic
144	#405	C₂²×C₅	1	2	yes	—
145	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
146	C₄⋊C₁₆	C₂²×C₅	1	2	yes	—
147	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
148	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
149	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
150	C₄⋊C₁₆	C₂²×C₅	1	2	yes	—
151	C₄⋊C₁₆	C₂²×C₅	1	2	yes	—
152	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
153	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
154	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
155	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
156	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
157	#346	C₂²×C₅	1	2	yes	—
158	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic
159	C₄×C₁₆	C₂²×C₅	1	1	yes	characteristic
160	C₄×C₁₆	C₂²×C₅	1	2	yes	—
161	C₂³×C₅	C₂²×C₈	1	2	yes	—
162	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
163	C₅×Q₈	—	2	2	no	—
164	C₅×D₄	—	2	2	no	—
165	C₅×D₄	—	4	2	no	—
166	C₂×C₄×C₅	—	2	2	no	—
167	C₂×C₄×C₅	—	2	1	no	—
168	C₂×C₄×C₅	—	2	1	no	—
169	C₂×C₄×C₅	—	2	2	no	—
170	C₂×C₄×C₅	—	2	2	no	—
171	C₂×C₄×C₅	—	4	1	no	—
172	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
173	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
174	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
175	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
176	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
177	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
178	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
179	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
181	C₅×C₈	—	2	2	no	—
182	C₅×C₈	—	2	1	no	—
183	C₅×C₈	—	2	1	no	—
184	C₅×C₈	—	2	1	no	—
185	C₅×C₈	—	2	2	no	—
186	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
187	C₅×C₈	2₋¹⁺⁴	1	1	yes	characteristic
188	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
189	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
190	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
191	C₂²×C₈	C₂³×C₅	1	2	yes	—
192	#126	C₅×C₈	1	2	yes	—
193	#125	C₅×C₈	1	1	yes	characteristic
194	#124	C₅×C₈	1	1	yes	characteristic
195	#123	C₅×C₈	1	2	yes	—
196	C₂²⋊Q₈	C₅×C₈	1	1	yes	characteristic
197	#121	C₅×C₈	1	1	yes	characteristic
198	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
199	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
200	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
201	#117	C₂×C₄×C₅	1	2	yes	—
202	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
203	M₃₂	—	4	2	no	—
204	M₃₂	—	4	2	no	—
205	C₂×C₁₆	—	4	2	no	—
206	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
207	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
208	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
209	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
210	C₂×C₁₆	C₂³×C₅	1	2	yes	—
211	C₂×C₁₆	C₂³×C₅	1	2	yes	—
212	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
213	C₄⋊C₈	C₂×C₄×C₅	1	1	yes	characteristic
214	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
215	C₄⋊C₈	C₂×C₄×C₅	1	2	yes	—
216	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
217	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
218	C₂²⋊C₈	C₂×C₄×C₅	1	2	yes	—
219	#97	C₂×C₄×C₅	1	2	yes	—
220	#97	C₂×C₄×C₅	1	2	yes	—
221	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
222	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
223	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
224	C₄×C₈	C₂³×C₅	1	2	yes	—
225	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
226	C₂²×C₅	—	2	1	no	—
227	C₂²×C₅	—	2	2	no	—
228	C₂²×C₅	—	2	1	no	—
229	C₂²×C₅	—	2	2	no	—
230	C₂²×C₅	—	2	1	no	—
231	C₂²×C₅	—	2	2	no	—
232	C₂²×C₅	C₂³×C₈	1	1	yes	characteristic
233	C₄×C₅	—	2	1	no	—
234	C₄×C₅	—	2	2	no	—
235	C₄×C₅	—	2	1	no	—
236	C₄×C₅	—	2	1	no	—
237	C₄×C₅	—	2	2	no	—
238	C₄×C₅	—	2	1	no	—
239	C₄×C₅	—	2	2	no	—
240	C₄×C₅	#504	1	2	yes	—
241	C₄×C₅	#520	1	1	yes	characteristic
242	C₄×C₅	#568	1	1	yes	characteristic
243	C₂×Q₈	C₂×C₅×C₈	1	1	yes	characteristic
244	C₂×D₄	C₂×C₅×C₈	1	1	yes	characteristic
245	C₂×D₄	C₂×C₅×C₈	1	2	yes	—
246	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
247	C₂²×C₄	C₂×C₅×C₈	1	1	yes	characteristic
248	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
249	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
250	M₁₆	—	4	2	no	—
251	C₂×C₈	—	2	2	no	—
252	C₂×C₈	—	2	1	no	—
253	C₂×C₈	—	2	1	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	4	1	no	—
256	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
257	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
258	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
259	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
260	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
261	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
262	C₄⋊C₄	C₂×C₅×C₈	1	2	yes	—
263	C₄⋊C₄	C₂×C₅×C₈	1	2	yes	—
264	C₄⋊C₄	C₂×C₅×C₈	1	1	yes	characteristic
265	C₄⋊C₄	C₂×C₅×C₈	1	2	yes	—
266	C₄⋊C₄	C₂×C₅×C₈	1	1	yes	characteristic
267	C₄⋊C₄	C₂×C₅×C₈	1	2	yes	—
268	C₂²⋊C₄	C₂×C₅×C₈	1	2	yes	—
269	C₂²⋊C₄	C₂×C₅×C₈	1	2	yes	—
270	C₂²⋊C₄	C₂×C₅×C₈	1	2	yes	—
271	C₂²⋊C₄	C₂×C₅×C₈	1	2	yes	—
272	C₂²⋊C₄	C₂×C₅×C₈	1	2	yes	—
273	C₄²	C₂×C₅×C₈	1	1	yes	characteristic
274	C₄²	C₂×C₅×C₈	1	1	yes	characteristic
275	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
276	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
277	C₄²	C₂²×C₄×C₅	1	2	yes	—
278	C₁₆	—	2	1	no	—
279	C₁₆	—	2	2	no	—
280	C₁₆	—	2	1	no	—
281	C₁₆	—	2	2	no	—
282	C₁₆	—	2	1	no	—
283	C₁₆	—	2	1	no	—
284	C₂×C₅	—	4	1	no	—
285	C₂×C₅	—	4	2	no	—
286	C₂×C₅	#2988	1	1	yes	characteristic
287	C₂×C₅	C₂×#504	1	1	yes	characteristic
288	C₂×C₅	#3407	1	1	yes	characteristic
289	C₂³	C₂²×C₅×C₈	1	2	yes	—
290	C₂³	C₂²×C₅×C₈	1	1	yes	characteristic
291	Q₈	—	2	2	no	—
292	D₄	—	2	2	no	—
293	D₄	—	4	2	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	4	1	no	—
300	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
301	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
302	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
303	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
304	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
305	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
306	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
307	C₂×C₄	C₂²×C₅×C₈	1	1	yes	characteristic
308	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
309	C₈	—	2	2	no	—
310	C₈	—	2	1	no	—
311	C₈	—	2	1	no	—
312	C₈	—	2	1	no	—
313	C₈	—	2	2	no	—
314	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
315	C₈	C₅×2₋¹⁺⁴	1	1	yes	characteristic
316	C₅	#33507	1	1	yes	characteristic, direct product factor, Sylow
317	C₂²	—	2	1	no	—
318	C₂²	—	2	2	no	—
319	C₂²	—	2	1	no	—
320	C₂²	—	2	2	no	—
321	C₂²	—	2	1	no	—
322	C₂²	—	2	2	no	—
323	C₂²	C₂³×C₅×C₈	1	1	yes	characteristic
324	C₄	—	2	1	no	—
325	C₄	—	2	2	no	—
326	C₄	—	2	1	no	—
327	C₄	—	2	2	no	—
328	C₄	—	2	1	no	—
329	C₄	—	2	1	no	—
330	C₄	—	2	2	no	—
331	C₄	C₅×#504	1	2	yes	—
332	C₄	C₅×#520	1	1	yes	characteristic
333	C₄	C₅×#568	1	1	yes	characteristic
334	C₂	—	4	1	no	—
335	C₂	—	4	2	no	—
336	C₂	C₅×#2988	1	1	yes	characteristic
337	C₂	C₂×C₅×#504	1	1	yes	characteristic
338	C₂	C₅×#3407	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅×C₈	C₂⁴
commutator	C₂²	C₂³×C₅×C₈
Frattini, cosocle	C₂×C₈	C₂⁴×C₅
socle	C₂²×C₅	C₂³×C₈
prime radical	C₅×#121	C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2183	C₂	semidirect
3. C₅×Q₈×C₁₆	C₂	semidirect
4. C₅×#2169	C₂	semidirect
5. C₅×#2169	C₂	semidirect
6. C₅×#2168	C₂	semidirect
7. C₅×D₄×C₁₆	C₂	semidirect
8. C₅×#2164	C₂	semidirect
9. C₅×#2162	C₂	semidirect
10. C₅×#2151	C₂	semidirect
11. C₅×#2150	C₂	semidirect
41. #33507	C₅	direct (N × H)
81. #2183	C₂×C₅	semidirect
82. Q₈×C₁₆	C₂×C₅	semidirect
83. #2169	C₂×C₅	semidirect
84. #2169	C₂×C₅	semidirect
85. #2168	C₂×C₅	semidirect
86. D₄×C₁₆	C₂×C₅	semidirect
87. #2164	C₂×C₅	semidirect
88. #2162	C₂×C₅	semidirect
89. #2151	C₂×C₅	semidirect
90. #2150	C₂×C₅	semidirect
316. C₅	#33507	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×#2966	2
C₅×#2183	2
C₅×Q₈×C₁₆	2
C₅×#2169	2
C₅×#2168	2
C₅×D₄×C₁₆	2
C₅×#2164	2
C₅×#2162	2
C₅×#2151	2
C₅×#2150	2
#33507	5

Subgroups — C5×#33507 #11956227

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33507 #11956227