Subgroups — C₅×#82231 #14322713

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic
2	C₅×#5212	C₂	1	2	yes	maximal
3	C₅×#4980	C₂	1	4	yes	maximal, complemented
4	C₅×#4951	C₂	1	4	yes	maximal
5	C₅×#4936	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4935	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₅×C₄⋊Dic₃	C₂	1	2	yes	maximal, complemented
8	C₅×#2314	—	3	1	no	maximal, Hall
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₃×C₅×#117	C₄	1	8	yes	complemented
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×#217	C₂²	1	4	yes	—
16	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	4	yes	—
19	C₂×C₄×C₅×Dic₃	C₂²	1	4	yes	—
20	C₅×C₃⋊#95	C₂²	1	4	yes	—
21	C₅×C₃⋊#95	C₂²	1	4	yes	—
22	C₅×C₃⋊#95	C₂²	1	4	yes	—
23	#82231	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₂×C₅×#117	D₃	1	1	yes	characteristic
25	C₅×#388	—	3	4	no	—
26	C₅×#387	—	3	4	no	—
27	C₅×#384	—	3	1	no	—
28	C₅×#382	—	3	1	no	—
29	C₅×#380	—	3	2	no	—
30	C₄×C₅×C₄⋊C₄	—	3	2	no	—
31	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	—	2	2	no	—
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
35	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
40	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
41	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	—
42	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
43	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
44	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
45	C₅×#217	—	4	4	no	—
46	C₅×C₄⋊Dic₃	—	2	4	no	—
47	C₅×C₄⋊Dic₃	—	2	4	no	—
48	C₅×C₄⋊Dic₃	—	4	4	no	—
49	C₄×C₅×Dic₃	—	4	4	no	—
50	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic
51	#5212	C₂×C₅	1	2	yes	—
52	#4980	C₂×C₅	1	4	yes	complemented
53	#4951	C₂×C₅	1	4	yes	—
54	#4936	C₂×C₅	1	1	yes	characteristic, complemented
55	#4935	C₂×C₅	1	1	yes	characteristic, complemented
56	C₄×C₄⋊Dic₃	C₂×C₅	1	2	yes	complemented
57	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
58	C₅×#117	Dic₃	1	8	yes	complemented
59	C₂×C₅×C₄⋊C₄	—	3	2	no	—
60	C₂×C₅×C₄⋊C₄	—	3	2	no	—
61	C₂×C₅×C₄⋊C₄	—	3	4	no	—
62	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
63	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
64	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
65	C₂×C₄²×C₅	—	3	4	no	—
66	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
67	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
68	C₅×#95	—	3	4	no	—
69	C₅×#95	—	3	4	no	—
70	C₅×#95	—	3	4	no	—
71	#2314	—	3	1	no	Sylow
72	C₂³×C₃×C₅	—	2	1	no	—
73	C₂³×C₃×C₅	—	2	1	no	—
74	C₂³×C₃×C₅	—	2	2	no	—
75	C₂³×C₃×C₅	—	2	2	no	—
76	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
77	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
78	C₂×C₃×C₄×C₅	—	2	1	no	—
79	C₂×C₃×C₄×C₅	—	2	1	no	—
80	C₂×C₃×C₄×C₅	—	2	2	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	2	2	no	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	2	8	no	—
85	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
86	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
87	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	#41	1	2	yes	—
90	C₂×C₃×C₄×C₅	#41	1	2	yes	—
91	C₂×C₅×Dic₃	—	2	4	no	—
92	C₂×C₅×Dic₃	—	2	4	no	—
93	C₂×C₅×Dic₃	—	2	4	no	—
94	C₂×C₅×Dic₃	—	2	4	no	—
95	C₂×C₅×Dic₃	—	2	4	no	—
96	C₂×C₅×Dic₃	—	2	4	no	—
97	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
98	C₃×#117	C₄×C₅	1	8	yes	complemented
99	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
100	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
101	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
102	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
103	C₂×#217	C₂²×C₅	1	4	yes	—
104	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
105	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
106	C₂×C₄⋊Dic₃	C₂²×C₅	1	4	yes	—
107	C₂×C₄×Dic₃	C₂²×C₅	1	4	yes	—
108	C₃⋊#95	C₂²×C₅	1	4	yes	—
109	C₃⋊#95	C₂²×C₅	1	4	yes	—
110	C₃⋊#95	C₂²×C₅	1	4	yes	—
111	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
112	C₂²×C₄×C₅	—	2	2	no	—
113	C₂²×C₄×C₅	—	2	2	no	—
114	C₂²×C₄×C₅	—	3	4	no	—
115	C₂²×C₄×C₅	—	3	4	no	—
116	C₂²×C₄×C₅	C₂×Dic₃	1	4	yes	—
117	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
118	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
119	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
121	C₅×C₄⋊C₄	—	6	4	no	—
122	C₅×C₄⋊C₄	—	6	4	no	—
123	C₅×C₄⋊C₄	—	12	4	no	—
124	C₅×C₄⋊C₄	C₂×Dic₃	1	8	yes	—
125	C₅×C₂²⋊C₄	—	12	4	no	—
126	C₅×C₂²⋊C₄	C₂×Dic₃	1	8	yes	—
127	C₄²×C₅	—	12	4	no	—
128	C₄²×C₅	C₂×Dic₃	1	4	yes	—
129	C₄²×C₅	C₂×Dic₃	1	4	yes	—
130	C₂×#117	C₅×D₃	1	1	yes	characteristic
131	#388	—	3	4	no	—
132	#387	—	3	4	no	—
133	#384	—	3	1	no	—
134	#382	—	3	1	no	—
135	#380	—	3	2	no	—
136	C₄×C₄⋊C₄	—	3	2	no	—
137	C₂²×C₃×C₅	—	2	2	no	—
138	C₂²×C₃×C₅	—	2	4	no	—
139	C₂²×C₃×C₅	—	4	1	no	—
140	C₂²×C₃×C₅	—	4	1	no	—
141	C₂²×C₃×C₅	—	4	2	no	—
142	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
143	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
144	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
145	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
146	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
147	C₃×C₄×C₅	—	2	2	no	—
148	C₃×C₄×C₅	—	2	4	no	—
149	C₃×C₄×C₅	—	2	4	no	—
150	C₃×C₄×C₅	#117	1	4	yes	—
151	C₅×Dic₃	—	4	4	no	—
152	C₅×Dic₃	—	4	4	no	—
153	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
154	C₂²×C₃×C₄	—	2	2	no	—
155	C₂²×C₃×C₄	—	2	2	no	—
156	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
157	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
158	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
159	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
160	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
161	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
162	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
163	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	—
164	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	—
165	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
166	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
167	#217	—	4	4	no	—
168	C₄⋊Dic₃	—	2	4	no	—
169	C₄⋊Dic₃	—	2	4	no	—
170	C₄⋊Dic₃	—	4	4	no	—
171	C₄×Dic₃	—	4	4	no	—
172	C₂³×C₅	—	2	1	no	—
173	C₂³×C₅	—	2	1	no	—
174	C₂³×C₅	—	2	2	no	—
175	C₂³×C₅	—	2	2	no	—
176	C₂³×C₅	C₂²×Dic₃	1	2	yes	—
177	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
178	C₂×C₄×C₅	—	2	1	no	—
179	C₂×C₄×C₅	—	2	1	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	8	no	—
185	C₂×C₄×C₅	—	6	4	no	—
186	C₂×C₄×C₅	—	6	4	no	—
187	C₂×C₄×C₅	—	6	4	no	—
188	C₂×C₄×C₅	—	6	4	no	—
189	C₂×C₄×C₅	—	6	4	no	—
190	C₂×C₄×C₅	—	6	4	no	—
191	C₂×C₄×C₅	#235	1	2	yes	—
192	C₂×C₄×C₅	#235	1	2	yes	—
193	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
194	C₂×C₄×C₅	C₂²×Dic₃	1	4	yes	—
195	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
196	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
197	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
198	#117	C₅×Dic₃	1	8	yes	complemented
199	C₂×C₄⋊C₄	—	3	2	no	—
200	C₂×C₄⋊C₄	—	3	2	no	—
201	C₂×C₄⋊C₄	—	3	4	no	—
202	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
203	C₂×C₂²⋊C₄	—	3	4	no	—
204	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
205	C₂×C₄²	—	3	4	no	—
206	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
207	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
208	#95	—	3	4	no	—
209	#95	—	3	4	no	—
210	#95	—	3	4	no	—
211	C₂×C₃×C₅	—	4	2	no	—
212	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
213	C₂×C₃×C₅	#520	1	2	yes	—
214	C₂×C₃×C₅	#540	1	1	yes	characteristic
215	C₂×C₃×C₅	#541	1	1	yes	characteristic
216	C₂×C₃×C₅	#542	1	2	yes	—
217	C₂³×C₃	—	2	1	no	—
218	C₂³×C₃	—	2	1	no	—
219	C₂³×C₃	—	2	2	no	—
220	C₂³×C₃	—	2	2	no	—
221	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
222	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
223	C₂×C₃×C₄	—	2	1	no	—
224	C₂×C₃×C₄	—	2	1	no	—
225	C₂×C₃×C₄	—	2	2	no	—
226	C₂×C₃×C₄	—	2	2	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	2	2	no	—
229	C₂×C₃×C₄	—	2	8	no	—
230	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
231	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
232	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
233	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
234	C₂×C₃×C₄	C₅×#41	1	2	yes	—
235	C₂×C₃×C₄	C₅×#41	1	2	yes	—
236	C₂×Dic₃	—	2	4	no	—
237	C₂×Dic₃	—	2	4	no	—
238	C₂×Dic₃	—	2	4	no	—
239	C₂×Dic₃	—	2	4	no	—
240	C₂×Dic₃	—	2	4	no	—
241	C₂×Dic₃	—	2	4	no	—
242	C₂²×C₅	—	2	2	no	—
243	C₂²×C₅	—	2	4	no	—
244	C₂²×C₅	—	4	1	no	—
245	C₂²×C₅	—	4	2	no	—
246	C₂²×C₅	—	4	1	no	—
247	C₂²×C₅	C₂×#235	1	1	yes	characteristic
248	C₂²×C₅	C₂×#235	1	1	yes	characteristic
249	C₂²×C₅	#1009	1	2	yes	—
250	C₂²×C₅	#1010	1	2	yes	—
251	C₂²×C₅	C₂³×Dic₃	1	1	yes	characteristic
252	C₄×C₅	—	2	2	no	—
253	C₄×C₅	—	2	4	no	—
254	C₄×C₅	—	2	4	no	—
255	C₄×C₅	—	12	4	no	—
256	C₄×C₅	—	12	4	no	—
257	C₄×C₅	#926	1	4	yes	—
258	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	3	4	no	—
262	C₂²×C₄	—	3	4	no	—
263	C₂²×C₄	C₂×C₅×Dic₃	1	4	yes	—
264	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
265	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
266	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
267	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
268	C₄⋊C₄	—	6	4	no	—
269	C₄⋊C₄	—	6	4	no	—
270	C₄⋊C₄	—	12	4	no	—
271	C₄⋊C₄	C₂×C₅×Dic₃	1	8	yes	—
272	C₂²⋊C₄	—	12	4	no	—
273	C₂²⋊C₄	C₂×C₅×Dic₃	1	8	yes	—
274	C₄²	—	12	4	no	—
275	C₄²	C₂×C₅×Dic₃	1	4	yes	—
276	C₄²	C₂×C₅×Dic₃	1	4	yes	—
277	C₃×C₅	#2314	1	1	yes	characteristic, complemented, Hall
278	C₂²×C₃	—	2	2	no	—
279	C₂²×C₃	—	2	4	no	—
280	C₂²×C₃	—	4	1	no	—
281	C₂²×C₃	—	4	1	no	—
282	C₂²×C₃	—	4	2	no	—
283	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
284	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
285	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
286	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
287	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
288	C₃×C₄	—	2	2	no	—
289	C₃×C₄	—	2	4	no	—
290	C₃×C₄	—	2	4	no	—
291	C₃×C₄	C₅×#117	1	4	yes	—
292	Dic₃	—	4	4	no	—
293	Dic₃	—	4	4	no	—
294	C₂×C₅	—	4	2	no	—
295	C₂×C₅	#5518	1	1	yes	characteristic
296	C₂×C₅	#5534	1	2	yes	—
297	C₂×C₅	#5535	1	1	yes	characteristic
298	C₂×C₅	C₂×#926	1	1	yes	characteristic
299	C₂×C₅	#5827	1	2	yes	—
300	C₂³	—	2	1	no	—
301	C₂³	—	2	1	no	—
302	C₂³	—	2	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	C₂²×C₅×Dic₃	1	2	yes	—
305	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
306	C₂×C₄	—	2	1	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	8	no	—
313	C₂×C₄	—	6	4	no	—
314	C₂×C₄	—	6	4	no	—
315	C₂×C₄	—	6	4	no	—
316	C₂×C₄	—	6	4	no	—
317	C₂×C₄	—	6	4	no	—
318	C₂×C₄	—	6	4	no	—
319	C₂×C₄	C₅×#235	1	2	yes	—
320	C₂×C₄	C₅×#235	1	2	yes	—
321	C₂×C₄	C₂²×C₅×Dic₃	1	4	yes	—
322	C₂×C₄	C₂²×C₅×Dic₃	1	4	yes	—
323	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
324	C₂×C₄	C₂²×C₅×Dic₃	1	2	yes	—
325	C₂×C₃	—	4	2	no	—
326	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
327	C₂×C₃	C₅×#520	1	2	yes	—
328	C₂×C₃	C₅×#540	1	1	yes	characteristic
329	C₂×C₃	C₅×#541	1	1	yes	characteristic
330	C₂×C₃	C₅×#542	1	2	yes	—
331	C₅	#82231	1	1	yes	characteristic, direct product factor, Sylow
332	C₂²	—	2	2	no	—
333	C₂²	—	2	4	no	—
334	C₂²	—	4	1	no	—
335	C₂²	—	4	2	no	—
336	C₂²	—	4	1	no	—
337	C₂²	C₂×C₅×#235	1	1	yes	characteristic
338	C₂²	C₂×C₅×#235	1	1	yes	characteristic
339	C₂²	C₅×#1009	1	2	yes	—
340	C₂²	C₅×#1010	1	2	yes	—
341	C₂²	C₂³×C₅×Dic₃	1	1	yes	characteristic
342	C₄	—	2	2	no	—
343	C₄	—	2	4	no	—
344	C₄	—	2	4	no	—
345	C₄	—	12	4	no	—
346	C₄	—	12	4	no	—
347	C₄	C₅×#926	1	4	yes	—
348	C₃	C₅×#2314	1	1	yes	characteristic, complemented, Sylow
349	C₂	—	4	2	no	—
350	C₂	C₅×#5518	1	1	yes	characteristic
351	C₂	C₅×#5534	1	2	yes	—
352	C₂	C₅×#5535	1	1	yes	characteristic
353	C₂	C₂×C₅×#926	1	1	yes	characteristic
354	C₂	C₅×#5827	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×C₅	C₂³
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₂×C₅×#117	D₃
hypocenter	C₃	C₅×#2314
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117

Complements

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

N	H ≅ G/N	type
3. C₅×#4980	C₂	semidirect
5. C₅×#4936	C₂	semidirect
6. C₅×#4935	C₂	semidirect
7. C₄×C₅×C₄⋊Dic₃	C₂	semidirect
10. C₃×C₅×#117	C₄	semidirect
23. #82231	C₅	direct (N × H)
52. #4980	C₂×C₅	semidirect
54. #4936	C₂×C₅	semidirect
55. #4935	C₂×C₅	semidirect
56. C₄×C₄⋊Dic₃	C₂×C₅	semidirect
58. C₅×#117	Dic₃	semidirect
98. C₃×#117	C₄×C₅	semidirect
198. #117	C₅×Dic₃	semidirect
277. C₃×C₅	#2314	semidirect
331. C₅	#82231	direct (N × H)
348. C₃	C₅×#2314	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#117	2
C₅×#5212	2
C₅×#4980	2
C₅×#4951	2
C₅×#4936	2
C₅×#4935	2
C₄×C₅×C₄⋊Dic₃	2
C₅×#2314	3
#82231	5

Subgroups — C5×#82231 #14322713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#82231 #14322713