Subgroups — C₅×#79165 #14416212

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#904	C₂	1	1	yes	maximal, characteristic
2	C₅×#5522	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#427	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5002	C₂	1	2	yes	maximal, complemented
6	C₅×#4873	C₂	1	2	yes	maximal, complemented
7	C₅×#4872	C₂	1	2	yes	maximal, complemented
8	C₅×#4852	C₂	1	4	yes	maximal, complemented
9	C₄×C₅×#135	—	3	1	no	maximal, Hall
10	C₂×C₅×#235	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₅×#117	C₂²	1	2	yes	—
13	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
14	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×Dic₁₂	C₂²	1	1	yes	characteristic
16	C₅×#904	C₄	1	8	yes	complemented
17	C₂×C₅×D₂₄	C₂²	1	1	yes	characteristic
18	C₂×C₅×#204	C₂²	1	2	yes	—
19	C₅×#893	C₂²	1	4	yes	—
20	C₅×#887	C₂²	1	4	yes	—
21	C₅×#67⋊C₄	—	2	4	no	—
22	C₅×#872	—	2	2	no	—
23	C₄²×C₅×D₃	—	2	2	no	—
24	C₃×C₅×#107	C₂²	1	2	yes	—
25	C₃×C₅×#106	C₂²	1	2	yes	—
26	C₅×C₈×Dic₃	C₂²	1	2	yes	—
27	C₅×C₈×Dic₃	C₂²	1	2	yes	—
28	C₅×#810	C₂²	1	4	yes	—
29	C₅×#809	C₂²	1	4	yes	—
30	#79165	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂×C₅×#135	—	3	1	no	—
32	C₄×C₅×#41	—	3	2	no	—
33	C₄×C₅×Q₁₆	—	3	2	no	—
34	C₄×C₅×SD₁₆	—	3	4	no	—
35	C₄×C₅×D₈	—	3	2	no	—
36	C₅×#427	D₃	1	1	yes	characteristic, complemented
37	C₅×#416	—	3	2	no	—
38	C₂×C₄×C₅×C₈	—	3	1	no	—
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂×C₅×#67	—	2	2	no	—
41	C₂²×C₅×Dic₃	D₄	1	2	yes	—
42	C₅×#235	—	2	4	no	—
43	C₅×#235	C₂×C₄	1	8	yes	complemented
44	C₂×C₅×D₁₂	C₂³	1	2	yes	—
45	C₂×C₄×C₅×D₃	—	2	2	no	—
46	C₂×C₄×C₅×D₃	—	2	4	no	—
47	C₂×C₅×Dic₆	C₂³	1	2	yes	—
48	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	complemented
49	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
52	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
53	C₃×C₄²×C₅	—	2	2	no	—
54	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
55	C₅×Dic₃⋊C₄	—	2	4	no	—
56	C₄×C₅×Dic₃	—	2	4	no	—
57	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
58	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
59	C₄×C₅×Dic₃	C₂³	1	2	yes	—
60	C₂×C₅×C₃⋊C₈	—	2	2	no	—
61	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
62	C₅×Dic₁₂	C₂×C₄	1	4	yes	complemented
63	C₅×D₂₄	C₂×C₄	1	4	yes	complemented
64	C₅×#204	C₂×C₄	1	8	yes	complemented
65	C₂×#904	C₂×C₅	1	1	yes	characteristic
66	#5522	C₂×C₅	1	2	yes	complemented
67	C₃×#427	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂×C₈×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
69	#5002	C₂×C₅	1	2	yes	complemented
70	#4873	C₂×C₅	1	2	yes	complemented
71	#4872	C₂×C₅	1	2	yes	complemented
72	#4852	C₂×C₅	1	4	yes	complemented
73	C₂×C₅×#41	—	3	2	no	—
74	C₅×#135	—	3	8	no	—
75	C₂×C₅×Q₁₆	—	3	1	no	—
76	C₂×C₅×SD₁₆	—	3	2	no	—
77	C₂×C₅×D₈	—	3	1	no	—
78	C₂²×C₅×C₈	—	3	1	no	—
79	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
80	C₄×C₅×Q₈	—	3	4	no	—
81	C₄×C₅×D₄	—	3	4	no	—
82	C₄×C₅×D₄	—	6	4	no	—
83	C₅×#117	—	6	2	no	—
84	C₅×#117	C₂×D₃	1	2	yes	—
85	C₂×C₄²×C₅	—	3	1	no	—
86	C₂×C₄²×C₅	—	6	2	no	—
87	C₅×#107	C₂×D₃	1	2	yes	—
88	C₅×#106	C₂×D₃	1	2	yes	—
89	C₅×#103	—	3	4	no	—
90	C₅×#102	—	3	4	no	—
91	C₄×C₅×C₈	—	3	2	no	—
92	C₄×C₅×C₈	—	3	2	no	—
93	C₄×#135	—	3	1	no	Sylow
94	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₅×D₃	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	4	no	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	#41	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
101	C₅×#67	—	2	8	no	—
102	C₂×C₅×Dic₃	—	2	2	no	—
103	C₂×C₅×Dic₃	—	2	4	no	—
104	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
105	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
106	C₅×D₁₂	—	2	2	no	—
107	C₅×D₁₂	C₂²×C₄	1	4	yes	—
108	C₄×C₅×D₃	—	2	8	no	—
109	C₄×C₅×D₃	—	4	8	no	—
110	C₅×Dic₆	—	2	2	no	—
111	C₅×Dic₆	C₂²×C₄	1	4	yes	—
112	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
113	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
114	C₅×C₃⋊C₈	—	2	2	no	—
115	C₂×#235	C₂²×C₅	1	2	yes	—
116	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
117	C₃×#117	C₂²×C₅	1	2	yes	—
118	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
119	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
120	C₂×Dic₁₂	C₂²×C₅	1	1	yes	characteristic
121	#904	C₄×C₅	1	8	yes	complemented
122	C₂×D₂₄	C₂²×C₅	1	1	yes	characteristic
123	C₂×#204	C₂²×C₅	1	2	yes	—
124	#893	C₂²×C₅	1	4	yes	—
125	#887	C₂²×C₅	1	4	yes	—
126	#67⋊C₄	—	2	4	no	—
127	#872	—	2	2	no	—
128	C₄²×D₃	—	2	2	no	—
129	C₃×#107	C₂²×C₅	1	2	yes	—
130	C₃×#106	C₂²×C₅	1	2	yes	—
131	C₈×Dic₃	C₂²×C₅	1	2	yes	—
132	C₈×Dic₃	C₂²×C₅	1	2	yes	—
133	#810	C₂²×C₅	1	4	yes	—
134	#809	C₂²×C₅	1	4	yes	—
135	C₅×#41	—	3	8	no	—
136	C₅×#41	—	6	4	no	—
137	C₂×C₅×Q₈	—	3	2	no	—
138	C₂×C₅×D₄	—	3	2	no	—
139	C₂×C₅×D₄	—	6	2	no	—
140	C₂²×C₄×C₅	—	3	2	no	—
141	C₂²×C₄×C₅	—	6	4	no	—
142	C₂²×C₄×C₅	—	6	2	no	—
143	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
144	C₅×Q₁₆	—	3	4	no	—
145	C₅×SD₁₆	—	3	8	no	—
146	C₅×D₈	—	3	4	no	—
147	C₂×C₅×C₈	—	3	2	no	—
148	C₂×C₅×C₈	—	6	2	no	—
149	C₂×C₅×C₈	C₄×D₃	1	4	yes	complemented
150	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
151	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
152	C₅×C₄⋊C₄	—	6	4	no	—
153	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
154	C₅×C₂²⋊C₄	—	2	2	no	—
155	C₅×C₂²⋊C₄	—	6	4	no	—
156	C₄²×C₅	—	2	2	no	—
157	C₄²×C₅	—	3	1	no	—
158	C₄²×C₅	—	3	1	no	—
159	C₄²×C₅	—	3	2	no	—
160	C₄²×C₅	—	6	4	no	—
161	C₂×#135	—	3	1	no	—
162	C₄×#41	—	3	2	no	—
163	C₄×Q₁₆	—	3	2	no	—
164	C₄×SD₁₆	—	3	4	no	—
165	C₄×D₈	—	3	2	no	—
166	#427	C₅×D₃	1	1	yes	characteristic, complemented
167	#416	—	3	2	no	—
168	C₂×C₄×C₈	—	3	1	no	—
169	C₂²×C₃×C₅	—	2	2	no	—
170	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
171	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₅×D₃	—	2	4	no	—
173	C₂×C₅×D₃	—	4	4	no	—
174	C₃×C₄×C₅	—	4	4	no	—
175	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
176	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
177	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
178	C₅×Dic₃	—	2	4	no	—
179	C₅×Dic₃	—	2	2	no	—
180	C₅×Dic₃	#135	1	4	yes	complemented
181	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
182	C₂×#67	—	2	2	no	—
183	C₂²×Dic₃	C₅×D₄	1	2	yes	—
184	#235	—	2	4	no	—
185	#235	C₂×C₄×C₅	1	8	yes	complemented
186	C₂×D₁₂	C₂³×C₅	1	2	yes	—
187	C₂×C₄×D₃	—	2	2	no	—
188	C₂×C₄×D₃	—	2	4	no	—
189	C₂×Dic₆	C₂³×C₅	1	2	yes	—
190	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	complemented
191	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
192	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
193	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
194	C₃×C₂²⋊C₄	—	2	2	no	—
195	C₃×C₄²	—	2	2	no	—
196	(C₂×D₃)⋊C₄	—	2	4	no	—
197	Dic₃⋊C₄	—	2	4	no	—
198	C₄×Dic₃	—	2	4	no	—
199	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
200	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
201	C₄×Dic₃	C₂³×C₅	1	2	yes	—
202	C₂×C₃⋊C₈	—	2	2	no	—
203	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
204	Dic₁₂	C₂×C₄×C₅	1	4	yes	complemented
205	D₂₄	C₂×C₄×C₅	1	4	yes	complemented
206	#204	C₂×C₄×C₅	1	8	yes	complemented
207	C₂³×C₅	—	6	2	no	—
208	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
209	C₅×Q₈	—	3	4	no	—
210	C₅×Q₈	—	6	2	no	—
211	C₅×D₄	—	3	4	no	—
212	C₅×D₄	—	6	8	no	—
213	C₅×D₄	—	6	2	no	—
214	C₂×C₄×C₅	—	2	4	no	—
215	C₂×C₄×C₅	—	3	2	no	—
216	C₂×C₄×C₅	—	3	2	no	—
217	C₂×C₄×C₅	—	6	4	no	—
218	C₂×C₄×C₅	—	6	2	no	—
219	C₂×C₄×C₅	—	6	8	no	—
220	C₂×C₄×C₅	—	12	8	no	—
221	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
222	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
223	C₂×C₄×C₅	#239	1	2	yes	—
224	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
225	C₅×C₈	—	6	2	no	—
226	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
227	C₅×C₈	C₂×C₄×D₃	1	2	yes	—
228	C₂×#41	—	3	2	no	—
229	#135	—	3	8	no	—
230	C₂×Q₁₆	—	3	1	no	—
231	C₂×SD₁₆	—	3	2	no	—
232	C₂×D₈	—	3	1	no	—
233	C₂²×C₈	—	3	1	no	—
234	C₂²×C₈	C₂×C₅×D₃	1	1	yes	characteristic
235	C₄×Q₈	—	3	4	no	—
236	C₄×D₄	—	3	4	no	—
237	C₄×D₄	—	6	4	no	—
238	#117	—	6	2	no	—
239	#117	C₂×C₅×D₃	1	2	yes	—
240	C₂×C₄²	—	3	1	no	—
241	C₂×C₄²	—	6	2	no	—
242	#107	C₂×C₅×D₃	1	2	yes	—
243	#106	C₂×C₅×D₃	1	2	yes	—
244	#103	—	3	4	no	—
245	#102	—	3	4	no	—
246	C₄×C₈	—	3	2	no	—
247	C₄×C₈	—	3	2	no	—
248	C₂×C₃×C₅	—	2	2	no	—
249	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
250	C₂×C₃×C₅	C₂×#135	1	2	yes	—
251	C₅×D₃	—	4	4	no	—
252	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
253	C₂²×D₃	—	2	2	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
256	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
257	C₂×C₃×C₄	C₅×#41	1	2	yes	—
258	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
259	#67	—	2	8	no	—
260	C₂×Dic₃	—	2	2	no	—
261	C₂×Dic₃	—	2	4	no	—
262	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
263	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
264	D₁₂	—	2	2	no	—
265	D₁₂	C₂²×C₄×C₅	1	4	yes	—
266	C₄×D₃	—	2	8	no	—
267	C₄×D₃	—	4	8	no	—
268	Dic₆	—	2	2	no	—
269	Dic₆	C₂²×C₄×C₅	1	4	yes	—
270	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
271	C₃×C₈	C₂²×C₄×C₅	1	2	yes	—
272	C₃⋊C₈	—	2	2	no	—
273	C₂²×C₅	—	2	2	no	—
274	C₂²×C₅	—	6	4	no	—
275	C₂²×C₅	—	12	4	no	—
276	C₂²×C₅	#893	1	2	yes	—
277	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
278	C₄×C₅	—	3	4	no	—
279	C₄×C₅	—	4	4	no	—
280	C₄×C₅	—	6	4	no	—
281	C₄×C₅	—	6	2	no	—
282	C₄×C₅	#893	1	2	yes	—
283	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
284	C₄×C₅	C₂×#239	1	1	yes	characteristic
285	#41	—	3	8	no	—
286	#41	—	6	4	no	—
287	C₂×Q₈	—	3	2	no	—
288	C₂×D₄	—	3	2	no	—
289	C₂×D₄	—	6	2	no	—
290	C₂²×C₄	—	3	2	no	—
291	C₂²×C₄	—	6	4	no	—
292	C₂²×C₄	—	6	2	no	—
293	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
294	Q₁₆	—	3	4	no	—
295	SD₁₆	—	3	8	no	—
296	D₈	—	3	4	no	—
297	C₂×C₈	—	3	2	no	—
298	C₂×C₈	—	6	2	no	—
299	C₂×C₈	C₄×C₅×D₃	1	4	yes	complemented
300	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
301	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
302	C₄⋊C₄	—	6	4	no	—
303	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	6	4	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	3	1	no	—
308	C₄²	—	3	1	no	—
309	C₄²	—	3	2	no	—
310	C₄²	—	6	4	no	—
311	C₃×C₅	C₄×#135	1	1	yes	characteristic, complemented, Hall
312	C₂²×C₃	—	2	2	no	—
313	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
314	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
315	C₂×D₃	—	2	4	no	—
316	C₂×D₃	—	4	4	no	—
317	C₃×C₄	—	4	4	no	—
318	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
319	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
320	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
321	Dic₃	—	2	4	no	—
322	Dic₃	—	2	2	no	—
323	Dic₃	C₅×#135	1	4	yes	complemented
324	C₂×C₅	—	2	2	no	—
325	C₂×C₅	—	12	4	no	—
326	C₂×C₅	C₂×#893	1	1	yes	characteristic
327	C₂×C₅	D₃×#135	1	2	yes	—
328	C₂³	—	6	2	no	—
329	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
330	Q₈	—	3	4	no	—
331	Q₈	—	6	2	no	—
332	D₄	—	3	4	no	—
333	D₄	—	6	8	no	—
334	D₄	—	6	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	3	2	no	—
337	C₂×C₄	—	3	2	no	—
338	C₂×C₄	—	6	4	no	—
339	C₂×C₄	—	6	2	no	—
340	C₂×C₄	—	6	8	no	—
341	C₂×C₄	—	12	8	no	—
342	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
343	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
344	C₂×C₄	C₅×#239	1	2	yes	—
345	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
346	C₈	—	6	2	no	—
347	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
348	C₈	C₂×C₄×C₅×D₃	1	2	yes	—
349	C₂×C₃	—	2	2	no	—
350	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
351	C₂×C₃	C₂×C₅×#135	1	2	yes	—
352	D₃	—	4	4	no	—
353	C₅	#79165	1	1	yes	characteristic, direct product factor, Sylow
354	C₂²	—	2	2	no	—
355	C₂²	—	6	4	no	—
356	C₂²	—	12	4	no	—
357	C₂²	C₅×#893	1	2	yes	—
358	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
359	C₄	—	3	4	no	—
360	C₄	—	4	4	no	—
361	C₄	—	6	4	no	—
362	C₄	—	6	2	no	—
363	C₄	C₅×#893	1	2	yes	—
364	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
365	C₄	C₂×C₅×#239	1	1	yes	characteristic
366	C₃	C₄×C₅×#135	1	1	yes	characteristic, complemented, Sylow
367	C₂	—	2	2	no	—
368	C₂	—	12	4	no	—
369	C₂	C₂×C₅×#893	1	1	yes	characteristic
370	C₂	C₅×D₃×#135	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#427	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#904	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#427	D₃
hypocenter	C₃	C₄×C₅×#135
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#427

Complements

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

N	H ≅ G/N	type
2. C₅×#5522	C₂	semidirect
3. C₃×C₅×#427	C₂	semidirect
4. C₂×C₅×C₈×Dic₃	C₂	semidirect
5. C₅×#5002	C₂	semidirect
6. C₅×#4873	C₂	semidirect
7. C₅×#4872	C₂	semidirect
8. C₅×#4852	C₂	semidirect
16. C₅×#904	C₄	semidirect
30. #79165	C₅	direct (N × H)
36. C₅×#427	D₃	semidirect
43. C₅×#235	C₂×C₄	semidirect
48. C₂×C₃×C₅×C₈	C₂×C₄	semidirect
62. C₅×Dic₁₂	C₂×C₄	semidirect
63. C₅×D₂₄	C₂×C₄	semidirect
64. C₅×#204	C₂×C₄	semidirect
66. #5522	C₂×C₅	semidirect
67. C₃×#427	C₂×C₅	semidirect
68. C₂×C₈×Dic₃	C₂×C₅	semidirect
69. #5002	C₂×C₅	semidirect
70. #4873	C₂×C₅	semidirect
71. #4872	C₂×C₅	semidirect
72. #4852	C₂×C₅	semidirect
121. #904	C₄×C₅	semidirect
149. C₂×C₅×C₈	C₄×D₃	semidirect
166. #427	C₅×D₃	semidirect
180. C₅×Dic₃	#135	semidirect
185. #235	C₂×C₄×C₅	semidirect
190. C₂×C₃×C₈	C₂×C₄×C₅	semidirect
204. Dic₁₂	C₂×C₄×C₅	semidirect
205. D₂₄	C₂×C₄×C₅	semidirect
206. #204	C₂×C₄×C₅	semidirect
299. C₂×C₈	C₄×C₅×D₃	semidirect
311. C₃×C₅	C₄×#135	semidirect
323. Dic₃	C₅×#135	semidirect
353. C₅	#79165	direct (N × H)
366. C₃	C₄×C₅×#135	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#904	2
C₅×#5522	2
C₃×C₅×#427	2
C₂×C₅×C₈×Dic₃	2
C₅×#5002	2
C₅×#4873	2
C₅×#4872	2
C₅×#4852	2
C₄×C₅×#135	3
#79165	5

Subgroups — C5×#79165 #14416212

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79165 #14416212