Subgroups — C₅×#68420 #14284802

Order 1920.

480 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×#4837	C₂	1	1	yes	maximal, characteristic
3	C₅×#4833	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#332	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4547	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4486	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4482	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1546	—	3	1	no	maximal, Hall
9	C₂×C₅×D₃×Q₈	—	2	1	no	—
10	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₅×#944	—	2	1	no	—
12	C₂×C₅×ΓL(1,𝔽₂₅)	—	2	1	no	—
13	C₅×D₃×C₄⋊C₄	—	2	1	no	—
14	C₅×D₃×C₄⋊C₄	C₄	1	2	yes	—
15	C₅×#888	—	2	1	no	—
16	C₅×#888	C₄	1	2	yes	—
17	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
18	C₅×#869	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₅×(C₂×D₃)⋊C₈	—	2	1	no	—
22	C₅×Dic₃⋊C₈	—	2	1	no	—
23	C₅×C₈×Dic₃	—	2	1	no	—
24	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
25	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
26	#68420	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
28	C₅×#431	—	3	1	no	—
29	C₅×#423	—	3	1	no	—
30	C₅×#332	—	3	1	no	—
31	C₅×#332	—	3	1	no	—
32	C₅×#332	—	3	1	no	—
33	C₅×#332	D₃	1	1	yes	characteristic, complemented
34	C₂×C₃×C₅×Q₈	—	2	1	no	—
35	C₅×D₃×Q₈	—	4	2	no	—
36	C₅×D₃×Q₈	—	4	2	no	—
37	C₂×C₄×C₅×D₃	—	2	2	no	—
38	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
40	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
41	C₂×C₅×Dic₆	—	2	1	no	—
42	C₂×C₅×Dic₆	—	2	2	no	—
43	C₂×C₃×C₅×C₈	—	2	1	no	—
44	C₂×C₃×C₅×C₈	—	2	1	no	—
45	C₃×C₅×C₄⋊C₄	—	2	1	no	—
46	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
47	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
48	C₅×C₄⋊Dic₃	—	2	1	no	—
49	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
50	C₅×Dic₃⋊C₄	—	2	2	no	—
51	C₅×Dic₃⋊C₄	—	2	2	no	—
52	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
53	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
54	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
55	C₂×C₅×C₃⋊C₈	—	2	1	no	—
56	C₂×C₅×C₃⋊C₈	—	2	1	no	—
57	C₅×ΓL(1,𝔽₂₅)	—	4	2	no	—
58	D₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
59	#4837	C₂×C₅	1	1	yes	characteristic
60	#4833	C₂×C₅	1	1	yes	characteristic
61	C₃×#332	C₂×C₅	1	1	yes	characteristic, complemented
62	#4547	C₂×C₅	1	1	yes	characteristic, complemented
63	#4486	C₂×C₅	1	1	yes	characteristic, complemented
64	#4482	C₂×C₅	1	1	yes	characteristic, complemented
65	C₂²×C₅×Q₈	—	6	1	no	—
66	C₂×C₅×M₁₆	—	6	1	no	—
67	C₅×C₄⋊Q₈	—	3	2	no	—
68	C₅×C₄⋊Q₈	—	3	1	no	—
69	C₅×C₄⋊Q₈	—	6	1	no	—
70	C₅×C₄⋊Q₈	—	6	1	no	—
71	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
72	C₂×C₅×C₄⋊C₄	—	3	2	no	—
73	C₂×C₅×C₄⋊C₄	—	6	1	no	—
74	C₂×C₄²×C₅	—	3	1	no	—
75	C₅×C₄⋊C₈	—	3	1	no	—
76	C₅×C₄⋊C₈	—	3	1	no	—
77	C₅×C₄⋊C₈	—	6	1	no	—
78	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
79	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
80	C₅×C₂²⋊C₈	—	6	1	no	—
81	C₄×C₅×C₈	—	6	1	no	—
82	#1546	—	3	1	no	Sylow
83	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
84	C₃×C₅×Q₈	—	4	1	no	—
85	C₃×C₅×Q₈	—	4	1	no	—
86	C₂×C₃×C₄×C₅	—	2	2	no	—
87	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
89	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂×C₅×Dic₃	—	2	2	no	—
91	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
94	C₄×C₅×D₃	—	2	1	no	—
95	C₄×C₅×D₃	—	2	1	no	—
96	C₄×C₅×D₃	—	2	2	no	—
97	C₄×C₅×D₃	—	4	4	no	—
98	C₄×C₅×D₃	D₈	1	2	yes	—
99	C₄×C₅×D₃	SD₁₆	1	2	yes	—
100	C₅×Dic₆	—	4	1	no	—
101	C₅×Dic₆	—	4	1	no	—
102	C₅×Dic₆	—	4	4	no	—
103	C₃×C₅×C₈	—	4	1	no	—
104	C₃×C₅×C₈	—	4	1	no	—
105	C₅×C₃⋊C₈	—	4	1	no	—
106	C₅×C₃⋊C₈	—	4	1	no	—
107	C₂×D₃×Q₈	—	2	1	no	—
108	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
109	#944	—	2	1	no	—
110	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
111	D₃×C₄⋊C₄	—	2	1	no	—
112	D₃×C₄⋊C₄	C₄×C₅	1	2	yes	—
113	#888	—	2	1	no	—
114	#888	C₄×C₅	1	2	yes	—
115	C₄²×D₃	C₂²×C₅	1	1	yes	characteristic
116	#869	C₂²×C₅	1	1	yes	characteristic
117	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
118	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
119	(C₂×D₃)⋊C₈	—	2	1	no	—
120	Dic₃⋊C₈	—	2	1	no	—
121	C₈×Dic₃	—	2	1	no	—
122	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
123	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
124	C₂×C₅×Q₈	—	2	1	no	—
125	C₂×C₅×Q₈	—	6	2	no	—
126	C₂×C₅×Q₈	—	6	1	no	—
127	C₂×C₅×Q₈	—	12	2	no	—
128	C₂×C₅×Q₈	—	12	2	no	—
129	C₂²×C₄×C₅	—	3	1	no	—
130	C₂²×C₄×C₅	—	3	1	no	—
131	C₂²×C₄×C₅	—	3	1	no	—
132	C₂²×C₄×C₅	—	6	2	no	—
133	C₅×M₁₆	—	12	2	no	—
134	C₂×C₅×C₈	—	2	1	no	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	—	6	1	no	—
137	C₂×C₅×C₈	—	6	1	no	—
138	C₅×C₄⋊C₄	—	2	1	no	—
139	C₅×C₄⋊C₄	—	3	2	no	—
140	C₅×C₄⋊C₄	—	6	2	no	—
141	C₅×C₄⋊C₄	—	6	2	no	—
142	C₅×C₄⋊C₄	—	6	1	no	—
143	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
144	C₄²×C₅	—	3	1	no	—
145	C₄²×C₅	—	3	1	no	—
146	C₄²×C₅	—	3	1	no	—
147	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
148	C₂×C₄⋊Q₈	—	3	1	no	—
149	#431	—	3	1	no	—
150	#423	—	3	1	no	—
151	#332	—	3	1	no	—
152	#332	—	3	1	no	—
153	#332	—	3	1	no	—
154	#332	C₅×D₃	1	1	yes	characteristic, complemented
155	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₅×D₃	—	2	1	no	—
157	C₂×C₅×D₃	—	2	1	no	—
158	C₂×C₅×D₃	#102	1	2	yes	—
159	C₃×C₄×C₅	—	2	1	no	—
160	C₃×C₄×C₅	—	4	2	no	—
161	C₃×C₄×C₅	C₂×D₈	1	1	yes	characteristic
162	C₃×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
163	C₃×C₄×C₅	#137	1	1	yes	characteristic
164	C₃×C₄×C₅	#137	1	1	yes	characteristic
165	C₅×Dic₃	—	2	1	no	—
166	C₅×Dic₃	—	4	2	no	—
167	C₅×Dic₃	#101	1	2	yes	—
168	C₅×Dic₃	#102	1	2	yes	—
169	C₂×C₃×Q₈	—	2	1	no	—
170	D₃×Q₈	—	4	2	no	—
171	D₃×Q₈	—	4	2	no	—
172	C₂×C₄×D₃	—	2	2	no	—
173	C₂×C₄×D₃	C₂×C₄×C₅	1	1	yes	characteristic
174	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
175	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
176	C₂×Dic₆	—	2	1	no	—
177	C₂×Dic₆	—	2	2	no	—
178	C₂×C₃×C₈	—	2	1	no	—
179	C₂×C₃×C₈	—	2	1	no	—
180	C₃×C₄⋊C₄	—	2	1	no	—
181	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
182	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
183	C₄⋊Dic₃	—	2	1	no	—
184	C₄⋊Dic₃	C₂×C₄×C₅	1	2	yes	—
185	Dic₃⋊C₄	—	2	2	no	—
186	Dic₃⋊C₄	—	2	2	no	—
187	C₄×Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
188	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
189	C₄×Dic₃	C₅×D₄	1	1	yes	characteristic
190	C₂×C₃⋊C₈	—	2	1	no	—
191	C₂×C₃⋊C₈	—	2	1	no	—
192	ΓL(1,𝔽₂₅)	—	4	2	no	—
193	C₂³×C₅	—	3	1	no	—
194	C₅×Q₈	—	4	1	no	—
195	C₅×Q₈	—	4	1	no	—
196	C₅×Q₈	—	12	4	no	—
197	C₅×Q₈	—	12	1	no	—
198	C₅×Q₈	—	12	1	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	3	1	no	—
201	C₂×C₄×C₅	—	3	1	no	—
202	C₂×C₄×C₅	—	3	2	no	—
203	C₂×C₄×C₅	—	3	2	no	—
204	C₂×C₄×C₅	—	3	1	no	—
205	C₂×C₄×C₅	—	6	2	no	—
206	C₂×C₄×C₅	—	6	1	no	—
207	C₂×C₄×C₅	—	6	1	no	—
208	C₂×C₄×C₅	—	6	2	no	—
209	C₂×C₄×C₅	—	12	4	no	—
210	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
211	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
212	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
213	C₅×C₈	—	4	1	no	—
214	C₅×C₈	—	4	1	no	—
215	C₅×C₈	—	12	1	no	—
216	C₅×C₈	—	12	1	no	—
217	C₂²×Q₈	—	6	1	no	—
218	C₂×M₁₆	—	6	1	no	—
219	C₄⋊Q₈	—	3	2	no	—
220	C₄⋊Q₈	—	3	1	no	—
221	C₄⋊Q₈	—	6	1	no	—
222	C₄⋊Q₈	—	6	1	no	—
223	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
224	C₂×C₄⋊C₄	—	3	2	no	—
225	C₂×C₄⋊C₄	—	6	1	no	—
226	C₂×C₄²	—	3	1	no	—
227	C₄⋊C₈	—	3	1	no	—
228	C₄⋊C₈	—	3	1	no	—
229	C₄⋊C₈	—	6	1	no	—
230	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
231	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
232	C₂²⋊C₈	—	6	1	no	—
233	C₄×C₈	—	6	1	no	—
234	C₂×C₃×C₅	C₂×#101	1	1	yes	characteristic
235	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
236	C₂×C₃×C₅	#419	1	1	yes	characteristic
237	C₅×D₃	—	2	2	no	—
238	C₂²×D₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
239	C₃×Q₈	—	4	1	no	—
240	C₃×Q₈	—	4	1	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
245	C₂×Dic₃	—	2	2	no	—
246	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
248	C₂×Dic₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
249	C₄×D₃	—	2	1	no	—
250	C₄×D₃	—	2	1	no	—
251	C₄×D₃	—	2	2	no	—
252	C₄×D₃	—	4	4	no	—
253	C₄×D₃	C₅×D₈	1	2	yes	—
254	C₄×D₃	C₅×SD₁₆	1	2	yes	—
255	Dic₆	—	4	1	no	—
256	Dic₆	—	4	1	no	—
257	Dic₆	—	4	4	no	—
258	C₃×C₈	—	4	1	no	—
259	C₃×C₈	—	4	1	no	—
260	C₃⋊C₈	—	4	1	no	—
261	C₃⋊C₈	—	4	1	no	—
262	C₂²×C₅	—	3	2	no	—
263	C₂²×C₅	—	6	1	no	—
264	C₂²×C₅	—	6	1	no	—
265	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
266	C₄×C₅	—	2	1	no	—
267	C₄×C₅	—	3	2	no	—
268	C₄×C₅	—	3	2	no	—
269	C₄×C₅	—	4	2	no	—
270	C₄×C₅	—	6	1	no	—
271	C₄×C₅	—	12	2	no	—
272	C₄×C₅	D₃×D₈	1	1	yes	characteristic
273	C₄×C₅	D₃×SD₁₆	1	1	yes	characteristic
274	C₄×C₅	#915	1	1	yes	characteristic
275	C₄×C₅	#918	1	1	yes	characteristic
276	C₂×Q₈	—	2	1	no	—
277	C₂×Q₈	—	6	2	no	—
278	C₂×Q₈	—	6	1	no	—
279	C₂×Q₈	—	12	2	no	—
280	C₂×Q₈	—	12	2	no	—
281	C₂²×C₄	—	3	1	no	—
282	C₂²×C₄	—	3	1	no	—
283	C₂²×C₄	—	3	1	no	—
284	C₂²×C₄	—	6	2	no	—
285	M₁₆	—	12	2	no	—
286	C₂×C₈	—	2	1	no	—
287	C₂×C₈	—	2	1	no	—
288	C₂×C₈	—	6	1	no	—
289	C₂×C₈	—	6	1	no	—
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	3	2	no	—
292	C₄⋊C₄	—	6	2	no	—
293	C₄⋊C₄	—	6	2	no	—
294	C₄⋊C₄	—	6	1	no	—
295	C₄⋊C₄	C₄×C₅×D₃	1	2	yes	—
296	C₄²	—	3	1	no	—
297	C₄²	—	3	1	no	—
298	C₄²	—	3	1	no	—
299	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
300	C₃×C₅	#1546	1	1	yes	characteristic, complemented, Hall
301	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
302	C₂×D₃	—	2	1	no	—
303	C₂×D₃	—	2	1	no	—
304	C₂×D₃	C₅×#102	1	2	yes	—
305	C₃×C₄	—	2	1	no	—
306	C₃×C₄	—	4	2	no	—
307	C₃×C₄	C₂×C₅×D₈	1	1	yes	characteristic
308	C₃×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
309	C₃×C₄	C₅×#137	1	1	yes	characteristic
310	C₃×C₄	C₅×#137	1	1	yes	characteristic
311	Dic₃	—	2	1	no	—
312	Dic₃	—	4	2	no	—
313	Dic₃	C₅×#101	1	2	yes	—
314	Dic₃	C₅×#102	1	2	yes	—
315	C₂×C₅	—	6	2	no	—
316	C₂×C₅	D₃×#101	1	1	yes	characteristic
317	C₂×C₅	D₃×#102	1	1	yes	characteristic
318	C₂×C₅	#4802	1	1	yes	characteristic
319	C₂³	—	3	1	no	—
320	Q₈	—	4	1	no	—
321	Q₈	—	4	1	no	—
322	Q₈	—	12	4	no	—
323	Q₈	—	12	1	no	—
324	Q₈	—	12	1	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	3	1	no	—
327	C₂×C₄	—	3	1	no	—
328	C₂×C₄	—	3	2	no	—
329	C₂×C₄	—	3	2	no	—
330	C₂×C₄	—	3	1	no	—
331	C₂×C₄	—	6	2	no	—
332	C₂×C₄	—	6	1	no	—
333	C₂×C₄	—	6	1	no	—
334	C₂×C₄	—	6	2	no	—
335	C₂×C₄	—	12	4	no	—
336	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
337	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
338	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
339	C₈	—	4	1	no	—
340	C₈	—	4	1	no	—
341	C₈	—	12	1	no	—
342	C₈	—	12	1	no	—
343	C₂×C₃	C₂×C₅×#101	1	1	yes	characteristic
344	C₂×C₃	C₂×C₅×#102	1	1	yes	characteristic
345	C₂×C₃	C₅×#419	1	1	yes	characteristic
346	D₃	—	2	2	no	—
347	C₅	#68420	1	1	yes	characteristic, direct product factor, Sylow
348	C₂²	—	3	2	no	—
349	C₂²	—	6	1	no	—
350	C₂²	—	6	1	no	—
351	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
352	C₄	—	2	1	no	—
353	C₄	—	3	2	no	—
354	C₄	—	3	2	no	—
355	C₄	—	4	2	no	—
356	C₄	—	6	1	no	—
357	C₄	—	12	2	no	—
358	C₄	C₅×D₃×D₈	1	1	yes	characteristic
359	C₄	C₅×D₃×SD₁₆	1	1	yes	characteristic
360	C₄	C₅×#915	1	1	yes	characteristic
361	C₄	C₅×#918	1	1	yes	characteristic
362	C₃	C₅×#1546	1	1	yes	characteristic, complemented, Sylow
363	C₂	—	6	2	no	—
364	C₂	C₅×D₃×#101	1	1	yes	characteristic
365	C₂	C₅×D₃×#102	1	1	yes	characteristic
366	C₂	C₅×#4802	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	D₃×C₂²⋊C₄
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₄²	C₂²×C₅×D₃
Fitting	C₃×C₅×#332	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂²×C₅×D₃	C₂²⋊C₄
cosocle	C₃×C₄²	C₂³×C₅
hypercenter	C₅×#332	D₃
hypocenter	C₃	C₅×#1546
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₅×#332

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#332	C₂	semidirect
5. C₅×#4547	C₂	semidirect
6. C₅×#4486	C₂	semidirect
7. C₅×#4482	C₂	semidirect
26. #68420	C₅	direct (N × H)
33. C₅×#332	D₃	semidirect
61. C₃×#332	C₂×C₅	semidirect
62. #4547	C₂×C₅	semidirect
63. #4486	C₂×C₅	semidirect
64. #4482	C₂×C₅	semidirect
154. #332	C₅×D₃	semidirect
300. C₃×C₅	#1546	semidirect
347. C₅	#68420	direct (N × H)
362. C₃	C₅×#1546	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×C₄⋊Q₈	2
C₅×#4837	2
C₅×#4833	2
C₃×C₅×#332	2
C₅×#4547	2
C₅×#4486	2
C₅×#4482	2
C₅×#1546	3
#68420	5

Subgroups — C5×#68420 #14284802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#68420 #14284802