Subgroups — C₅×#83881 #14439633

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5816	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#942	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#904	C₂	1	1	yes	maximal, characteristic
5	C₅×#5191	C₂	1	2	yes	maximal, complemented
6	C₅×#5190	C₂	1	4	yes	maximal, complemented
7	C₅×#5183	C₂	1	2	yes	maximal, complemented
8	C₅×#5101	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#3156	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
11	C₂×C₅×#235	C₂²	1	2	yes	—
12	C₂×C₃×C₅×Q₁₆	—	2	4	no	—
13	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₅×#947	C₂²	1	4	yes	—
17	C₅×#946	—	2	4	no	—
18	C₅×#944	C₂²	1	4	yes	—
19	C₂×C₅×#216	C₂²	1	4	yes	—
20	C₅×#942	—	2	8	no	—
21	C₂×C₅×#215	C₂²	1	4	yes	—
22	C₅×#929	—	2	4	no	—
23	C₅×#926	C₂²	1	1	yes	characteristic
24	C₂×C₅×#208	C₂²	1	1	yes	characteristic
25	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
26	C₅×#904	—	2	4	no	—
27	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
28	C₂×C₅×#204	C₂²	1	2	yes	—
29	C₅×#815	C₂²	1	2	yes	—
30	C₅×C₈×Dic₃	C₂²	1	2	yes	—
31	#83881	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₅×#137	—	3	2	no	—
33	C₂×C₅×#135	—	3	1	no	—
34	C₂²×C₅×Q₁₆	D₃	1	1	yes	characteristic, complemented
35	C₅×#536	—	3	2	no	—
36	C₅×#497	—	3	4	no	—
37	C₅×#495	—	3	2	no	—
38	C₅×#494	—	3	2	no	—
39	C₅×#405	—	3	1	no	—
40	C₂×C₃×C₅×Q₈	—	2	2	no	—
41	C₂×C₃×C₅×Q₈	—	2	4	no	—
42	C₂×C₃×C₅×Q₈	—	2	4	no	—
43	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
44	C₂²×C₃×C₄×C₅	—	2	2	no	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂×C₅×#67	—	2	2	no	—
47	C₅×#235	—	2	4	no	—
48	C₅×#235	—	2	4	no	—
49	C₂×C₅×D₁₂	C₂³	1	2	yes	—
50	C₂×C₄×C₅×D₃	—	2	2	no	—
51	C₂×C₅×Dic₆	C₂³	1	2	yes	—
52	C₃×C₅×Q₁₆	—	2	4	no	—
53	C₃×C₅×Q₁₆	—	2	4	no	—
54	C₂×C₃×C₅×C₈	D₄	1	4	yes	—
55	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
57	C₅×#217	D₄	1	2	yes	—
58	C₅×#216	—	2	8	no	—
59	C₅×#215	—	2	8	no	—
60	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
61	C₅×C₄⋊Dic₃	D₄	1	2	yes	—
62	C₅×Dic₃⋊C₄	—	2	8	no	—
63	C₄×C₅×Dic₃	C₂³	1	2	yes	—
64	C₅×#208	D₄	1	4	yes	—
65	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
66	C₅×Dic₁₂	—	2	2	no	—
67	C₅×D₂₄	—	2	2	no	—
68	C₅×#204	—	2	4	no	—
69	C₂²×C₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
70	#5816	C₂×C₅	1	2	yes	complemented
71	C₂×#942	C₂×C₅	1	2	yes	complemented
72	C₂×#904	C₂×C₅	1	1	yes	characteristic
73	#5191	C₂×C₅	1	2	yes	complemented
74	#5190	C₂×C₅	1	4	yes	complemented
75	#5183	C₂×C₅	1	2	yes	complemented
76	#5101	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂×C₅×#41	—	3	2	no	—
78	C₂²×C₅×Q₈	C₂×D₃	1	2	yes	—
79	C₅×#137	—	6	8	no	—
80	C₅×#135	—	6	4	no	—
81	C₂×C₅×Q₁₆	—	2	4	no	—
82	C₂×C₅×Q₁₆	—	3	4	no	—
83	C₂×C₅×Q₁₆	—	3	1	no	—
84	C₂×C₅×Q₁₆	C₂×D₃	1	2	yes	—
85	C₂×C₅×Q₁₆	C₂×D₃	1	2	yes	—
86	C₂×C₅×SD₁₆	—	3	4	no	—
87	C₂×C₅×SD₁₆	—	3	2	no	—
88	C₂×C₅×D₈	—	3	1	no	—
89	C₂×C₅×M₁₆	—	3	1	no	—
90	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
91	C₅×C₄⋊Q₈	—	3	4	no	—
92	C₅×#124	—	3	4	no	—
93	C₅×#123	—	6	4	no	—
94	C₅×C₂²⋊Q₈	—	6	4	no	—
95	C₅×#117	—	3	1	no	—
96	C₅×#97	—	3	2	no	—
97	C₄×C₅×C₈	—	3	2	no	—
98	#3156	—	3	1	no	Sylow
99	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₅×D₃	—	2	2	no	—
101	C₃×C₅×Q₈	—	2	4	no	—
102	C₃×C₅×Q₈	—	2	4	no	—
103	C₃×C₅×Q₈	—	4	4	no	—
104	C₂×C₃×C₄×C₅	—	2	4	no	—
105	C₂×C₃×C₄×C₅	—	4	4	no	—
106	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
109	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
110	C₅×#67	—	4	4	no	—
111	C₂×C₅×Dic₃	—	2	2	no	—
112	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
113	C₅×D₁₂	—	2	2	no	—
114	C₅×D₁₂	—	2	2	no	—
115	C₄×C₅×D₃	—	4	4	no	—
116	C₅×Dic₆	—	2	2	no	—
117	C₅×Dic₆	—	2	2	no	—
118	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
119	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
120	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
121	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
122	C₂×#235	C₂²×C₅	1	2	yes	—
123	C₂×C₃×Q₁₆	—	2	4	no	—
124	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
125	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
126	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
127	#947	C₂²×C₅	1	4	yes	—
128	#946	—	2	4	no	—
129	#944	C₂²×C₅	1	4	yes	—
130	C₂×#216	C₂²×C₅	1	4	yes	—
131	#942	—	2	8	no	—
132	C₂×#215	C₂²×C₅	1	4	yes	—
133	#929	—	2	4	no	—
134	#926	C₂²×C₅	1	1	yes	characteristic
135	C₂×#208	C₂²×C₅	1	1	yes	characteristic
136	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
137	#904	—	2	4	no	—
138	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
139	C₂×#204	C₂²×C₅	1	2	yes	—
140	#815	C₂²×C₅	1	2	yes	—
141	C₈×Dic₃	C₂²×C₅	1	2	yes	—
142	C₅×#41	—	6	4	no	—
143	C₅×#41	—	6	4	no	—
144	C₂×C₅×Q₈	—	2	2	no	—
145	C₂×C₅×Q₈	—	2	4	no	—
146	C₂×C₅×Q₈	—	2	4	no	—
147	C₂×C₅×Q₈	—	3	2	no	—
148	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
149	C₂×C₅×D₄	—	3	2	no	—
150	C₂×C₅×D₄	—	6	2	no	—
151	C₂²×C₄×C₅	—	2	2	no	—
152	C₂²×C₄×C₅	—	6	2	no	—
153	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
154	C₅×Q₁₆	—	2	4	no	—
155	C₅×Q₁₆	—	2	4	no	—
156	C₅×Q₁₆	—	6	8	no	—
157	C₅×Q₁₆	—	6	2	no	—
158	C₅×SD₁₆	—	6	8	no	—
159	C₅×SD₁₆	—	6	4	no	—
160	C₅×D₈	—	6	2	no	—
161	C₅×M₁₆	—	3	4	no	—
162	C₂×C₅×C₈	—	3	2	no	—
163	C₂×C₅×C₈	#67	1	4	yes	—
164	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
165	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
166	C₅×C₄⋊C₄	—	3	2	no	—
167	C₅×C₄⋊C₄	—	6	8	no	—
168	C₅×C₂²⋊C₄	—	3	2	no	—
169	C₅×C₂²⋊C₄	—	6	8	no	—
170	C₄²×C₅	—	3	2	no	—
171	C₂×#137	—	3	2	no	—
172	C₂×#135	—	3	1	no	—
173	C₂²×Q₁₆	C₅×D₃	1	1	yes	characteristic, complemented
174	#536	—	3	2	no	—
175	#497	—	3	4	no	—
176	#495	—	3	2	no	—
177	#494	—	3	2	no	—
178	#405	—	3	1	no	—
179	C₂²×C₃×C₅	—	2	2	no	—
180	C₂²×C₃×C₅	#127	1	2	yes	—
181	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₅×D₃	—	4	2	no	—
183	C₂×C₅×D₃	—	4	4	no	—
184	C₃×C₄×C₅	—	4	4	no	—
185	C₃×C₄×C₅	#127	1	2	yes	—
186	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
187	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
188	C₅×Dic₃	—	2	4	no	—
189	C₅×Dic₃	—	4	2	no	—
190	C₂×C₃×Q₈	—	2	2	no	—
191	C₂×C₃×Q₈	—	2	4	no	—
192	C₂×C₃×Q₈	—	2	4	no	—
193	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
194	C₂²×C₃×C₄	—	2	2	no	—
195	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
196	C₂×#67	—	2	2	no	—
197	#235	—	2	4	no	—
198	#235	—	2	4	no	—
199	C₂×D₁₂	C₂³×C₅	1	2	yes	—
200	C₂×C₄×D₃	—	2	2	no	—
201	C₂×Dic₆	C₂³×C₅	1	2	yes	—
202	C₃×Q₁₆	—	2	4	no	—
203	C₃×Q₁₆	—	2	4	no	—
204	C₂×C₃×C₈	C₅×D₄	1	4	yes	—
205	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
206	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
207	#217	C₅×D₄	1	2	yes	—
208	#216	—	2	8	no	—
209	#215	—	2	8	no	—
210	(C₂×D₃)⋊C₄	—	2	8	no	—
211	C₄⋊Dic₃	C₅×D₄	1	2	yes	—
212	Dic₃⋊C₄	—	2	8	no	—
213	C₄×Dic₃	C₂³×C₅	1	2	yes	—
214	#208	C₅×D₄	1	4	yes	—
215	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
216	Dic₁₂	—	2	2	no	—
217	D₂₄	—	2	2	no	—
218	#204	—	2	4	no	—
219	C₂³×C₅	—	6	2	no	—
220	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
221	C₅×Q₈	—	2	4	no	—
222	C₅×Q₈	—	2	4	no	—
223	C₅×Q₈	—	4	4	no	—
224	C₅×Q₈	—	6	2	no	—
225	C₅×Q₈	—	6	2	no	—
226	C₅×D₄	—	6	2	no	—
227	C₅×D₄	—	6	2	no	—
228	C₅×D₄	—	12	4	no	—
229	C₂×C₄×C₅	—	2	4	no	—
230	C₂×C₄×C₅	—	3	4	no	—
231	C₂×C₄×C₅	—	4	4	no	—
232	C₂×C₄×C₅	—	6	2	no	—
233	C₂×C₄×C₅	—	12	4	no	—
234	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
235	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
236	C₂×C₄×C₅	C₂×#67	1	2	yes	—
237	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
238	C₅×C₈	—	3	4	no	—
239	C₅×C₈	C₂×#67	1	2	yes	—
240	C₅×C₈	C₂×#67	1	2	yes	—
241	C₂×#41	—	3	2	no	—
242	C₂²×Q₈	C₂×C₅×D₃	1	2	yes	—
243	#137	—	6	8	no	—
244	#135	—	6	4	no	—
245	C₂×Q₁₆	—	2	4	no	—
246	C₂×Q₁₆	—	3	4	no	—
247	C₂×Q₁₆	—	3	1	no	—
248	C₂×Q₁₆	C₂×C₅×D₃	1	2	yes	—
249	C₂×Q₁₆	C₂×C₅×D₃	1	2	yes	—
250	C₂×SD₁₆	—	3	4	no	—
251	C₂×SD₁₆	—	3	2	no	—
252	C₂×D₈	—	3	1	no	—
253	C₂×M₁₆	—	3	1	no	—
254	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
255	C₄⋊Q₈	—	3	4	no	—
256	#124	—	3	4	no	—
257	#123	—	6	4	no	—
258	C₂²⋊Q₈	—	6	4	no	—
259	#117	—	3	1	no	—
260	#97	—	3	2	no	—
261	C₄×C₈	—	3	2	no	—
262	C₂×C₃×C₅	—	2	2	no	—
263	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
264	C₂×C₃×C₅	#578	1	2	yes	—
265	C₅×D₃	—	8	2	no	—
266	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
267	C₂²×D₃	—	2	2	no	—
268	C₃×Q₈	—	2	4	no	—
269	C₃×Q₈	—	2	4	no	—
270	C₃×Q₈	—	4	4	no	—
271	C₂×C₃×C₄	—	2	4	no	—
272	C₂×C₃×C₄	—	4	4	no	—
273	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
275	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
276	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
277	#67	—	4	4	no	—
278	C₂×Dic₃	—	2	2	no	—
279	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
280	D₁₂	—	2	2	no	—
281	D₁₂	—	2	2	no	—
282	C₄×D₃	—	4	4	no	—
283	Dic₆	—	2	2	no	—
284	Dic₆	—	2	2	no	—
285	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
286	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
287	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	—
288	C₂²×C₅	—	2	2	no	—
289	C₂²×C₅	—	12	4	no	—
290	C₂²×C₅	—	12	2	no	—
291	C₂²×C₅	#940	1	2	yes	—
292	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
293	C₄×C₅	—	4	4	no	—
294	C₄×C₅	—	6	4	no	—
295	C₄×C₅	—	12	2	no	—
296	C₄×C₅	#940	1	2	yes	—
297	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
298	C₄×C₅	C₂²×#67	1	1	yes	characteristic
299	#41	—	6	4	no	—
300	#41	—	6	4	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	—	3	2	no	—
305	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
306	C₂×D₄	—	3	2	no	—
307	C₂×D₄	—	6	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	6	2	no	—
310	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
311	Q₁₆	—	2	4	no	—
312	Q₁₆	—	2	4	no	—
313	Q₁₆	—	6	8	no	—
314	Q₁₆	—	6	2	no	—
315	SD₁₆	—	6	8	no	—
316	SD₁₆	—	6	4	no	—
317	D₈	—	6	2	no	—
318	M₁₆	—	3	4	no	—
319	C₂×C₈	—	3	2	no	—
320	C₂×C₈	C₅×#67	1	4	yes	—
321	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
322	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
323	C₄⋊C₄	—	3	2	no	—
324	C₄⋊C₄	—	6	8	no	—
325	C₂²⋊C₄	—	3	2	no	—
326	C₂²⋊C₄	—	6	8	no	—
327	C₄²	—	3	2	no	—
328	C₃×C₅	#3156	1	1	yes	characteristic, complemented, Hall
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	C₅×#127	1	2	yes	—
331	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
332	C₂×D₃	—	4	2	no	—
333	C₂×D₃	—	4	4	no	—
334	C₃×C₄	—	4	4	no	—
335	C₃×C₄	C₅×#127	1	2	yes	—
336	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
337	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
338	Dic₃	—	2	4	no	—
339	Dic₃	—	4	2	no	—
340	C₂×C₅	—	2	2	no	—
341	C₂×C₅	—	24	2	no	—
342	C₂×C₅	#5766	1	2	yes	—
343	C₂×C₅	C₂×#940	1	1	yes	characteristic
344	C₂³	—	6	2	no	—
345	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
346	Q₈	—	2	4	no	—
347	Q₈	—	2	4	no	—
348	Q₈	—	4	4	no	—
349	Q₈	—	6	2	no	—
350	Q₈	—	6	2	no	—
351	D₄	—	6	2	no	—
352	D₄	—	6	2	no	—
353	D₄	—	12	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	3	4	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	6	2	no	—
358	C₂×C₄	—	12	4	no	—
359	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
360	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
361	C₂×C₄	C₂×C₅×#67	1	2	yes	—
362	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
363	C₈	—	3	4	no	—
364	C₈	C₂×C₅×#67	1	2	yes	—
365	C₈	C₂×C₅×#67	1	2	yes	—
366	C₂×C₃	—	2	2	no	—
367	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
368	C₂×C₃	C₅×#578	1	2	yes	—
369	D₃	—	8	2	no	—
370	C₅	#83881	1	1	yes	characteristic, direct product factor, Sylow
371	C₂²	—	2	2	no	—
372	C₂²	—	12	4	no	—
373	C₂²	—	12	2	no	—
374	C₂²	C₅×#940	1	2	yes	—
375	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
376	C₄	—	4	4	no	—
377	C₄	—	6	4	no	—
378	C₄	—	12	2	no	—
379	C₄	C₅×#940	1	2	yes	—
380	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
381	C₄	C₂²×C₅×#67	1	1	yes	characteristic
382	C₃	C₅×#3156	1	1	yes	characteristic, complemented, Sylow
383	C₂	—	2	2	no	—
384	C₂	—	24	2	no	—
385	C₂	C₅×#5766	1	2	yes	—
386	C₂	C₂×C₅×#940	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₅×Q₁₆	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#904	C₂
hypercenter	C₂²×C₅×Q₁₆	D₃
hypocenter	C₃	C₅×#3156
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂²×C₅×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×Q₁₆	C₂	semidirect
2. C₅×#5816	C₂	semidirect
3. C₂×C₅×#942	C₂	semidirect
5. C₅×#5191	C₂	semidirect
6. C₅×#5190	C₂	semidirect
7. C₅×#5183	C₂	semidirect
8. C₅×#5101	C₂	semidirect
31. #83881	C₅	direct (N × H)
34. C₂²×C₅×Q₁₆	D₃	semidirect
69. C₂²×C₃×Q₁₆	C₂×C₅	semidirect
70. #5816	C₂×C₅	semidirect
71. C₂×#942	C₂×C₅	semidirect
73. #5191	C₂×C₅	semidirect
74. #5190	C₂×C₅	semidirect
75. #5183	C₂×C₅	semidirect
76. #5101	C₂×C₅	semidirect
173. C₂²×Q₁₆	C₅×D₃	semidirect
328. C₃×C₅	#3156	semidirect
370. C₅	#83881	direct (N × H)
382. C₃	C₅×#3156	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₅×Q₁₆	2
C₅×#5816	2
C₂×C₅×#942	2
C₂×C₅×#904	2
C₅×#5191	2
C₅×#5190	2
C₅×#5183	2
C₅×#5101	2
C₅×#3156	3
#83881	5

Subgroups — C5×#83881 #14439633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83881 #14439633