Subgroups — C₃×C₅×#1972 #14275006

Order 1920.

752 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#102	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#390	C₂	1	2	yes	maximal, complemented
6	C₅×#1972	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
8	C₂×C₃×C₅×D₈	—	2	2	no	—
9	C₂×C₃×C₅×D₈	—	2	2	no	—
10	C₂×C₃×C₅×D₈	C₄	1	4	yes	complemented
11	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×C₂²⋊C₄	—	2	4	no	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₃×C₅×#106	—	2	2	no	—
17	C₃×C₅×#102	—	2	4	no	—
18	C₃×C₅×#97	—	2	2	no	—
19	C₃×#1972	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂²×C₅×D₈	C₂×C₃	1	1	yes	characteristic
21	C₂×C₅×#106	C₂×C₃	1	1	yes	characteristic, complemented
22	C₂×C₅×#102	C₂×C₃	1	2	yes	complemented
23	C₂×C₅×#97	C₂×C₃	1	1	yes	characteristic, complemented
24	C₅×#390	C₂×C₃	1	2	yes	complemented
25	C₂⁴×C₃×C₅	—	2	2	no	—
26	C₂×C₃×C₅×D₄	—	2	2	no	—
27	C₂×C₃×C₅×D₄	—	2	2	no	—
28	C₂×C₃×C₅×D₄	—	2	2	no	—
29	C₂×C₃×C₅×D₄	—	2	2	no	—
30	C₂×C₃×C₅×D₄	—	2	2	no	—
31	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
32	C₂²×C₃×C₄×C₅	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₃×C₅×D₈	—	2	8	no	—
36	C₂×C₃×C₅×C₈	—	2	1	no	—
37	C₂×C₃×C₅×C₈	—	2	1	no	—
38	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
39	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
40	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
41	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
42	C₃×C₅×C₄⋊C₄	—	2	2	no	—
43	C₃×C₅×C₄⋊C₄	—	2	2	no	—
44	C₃×C₅×C₂²⋊C₄	—	4	8	no	—
45	C₃×C₄²×C₅	—	2	1	no	—
46	C₃×C₄²×C₅	—	2	1	no	—
47	C₂²×C₃×D₈	C₂×C₅	1	1	yes	characteristic
48	C₂×C₃×#106	C₂×C₅	1	1	yes	characteristic, complemented
49	C₂×C₃×#102	C₂×C₅	1	2	yes	complemented
50	C₂×C₃×#97	C₂×C₅	1	1	yes	characteristic, complemented
51	C₃×#390	C₂×C₅	1	2	yes	complemented
52	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
53	C₂×C₅×D₈	—	2	2	no	—
54	C₂×C₅×D₈	—	2	2	no	—
55	C₂×C₅×D₈	C₃×C₄	1	4	yes	complemented
56	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
57	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
58	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
59	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
60	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
61	C₅×#106	—	2	2	no	—
62	C₅×#102	—	2	4	no	—
63	C₅×#97	—	2	2	no	—
64	#1972	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
65	C₂³×C₃×C₅	—	2	4	no	—
66	C₂³×C₃×C₅	—	4	2	no	—
67	C₂³×C₃×C₅	—	4	2	no	—
68	C₂³×C₃×C₅	—	4	4	no	—
69	C₂³×C₃×C₅	—	4	4	no	—
70	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
71	C₃×C₅×D₄	—	2	4	no	—
72	C₃×C₅×D₄	—	2	4	no	—
73	C₃×C₅×D₄	—	4	2	no	—
74	C₃×C₅×D₄	—	4	2	no	—
75	C₂×C₃×C₄×C₅	—	2	2	no	—
76	C₂×C₃×C₄×C₅	—	2	4	no	—
77	C₂×C₃×C₄×C₅	—	4	2	no	—
78	C₂×C₃×C₄×C₅	—	4	4	no	—
79	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
80	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
81	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
82	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
83	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
84	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
85	C₃×C₅×C₈	—	2	2	no	—
86	C₃×C₅×C₈	C₂²⋊C₄	1	4	yes	complemented
87	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
88	C₂×C₃×D₈	—	2	2	no	—
89	C₂×C₃×D₈	—	2	2	no	—
90	C₂×C₃×D₈	C₄×C₅	1	4	yes	complemented
91	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
92	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
93	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
94	C₂×C₃×C₂²⋊C₄	—	2	4	no	—
95	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
96	C₃×#106	—	2	2	no	—
97	C₃×#102	—	2	4	no	—
98	C₃×#97	—	2	2	no	—
99	C₂⁴×C₅	—	2	2	no	—
100	C₂×C₅×D₄	—	2	2	no	—
101	C₂×C₅×D₄	—	2	2	no	—
102	C₂×C₅×D₄	—	2	2	no	—
103	C₂×C₅×D₄	—	2	2	no	—
104	C₂×C₅×D₄	—	2	2	no	—
105	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
106	C₂²×C₄×C₅	—	2	2	no	—
107	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
108	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
109	C₅×D₈	—	2	8	no	—
110	C₂×C₅×C₈	—	2	1	no	—
111	C₂×C₅×C₈	—	2	1	no	—
112	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
113	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
114	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
115	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
116	C₅×C₄⋊C₄	—	2	2	no	—
117	C₅×C₄⋊C₄	—	2	2	no	—
118	C₅×C₂²⋊C₄	—	4	8	no	—
119	C₄²×C₅	—	2	1	no	—
120	C₄²×C₅	—	2	1	no	—
121	C₂²×D₈	C₂×C₃×C₅	1	1	yes	characteristic
122	C₂×#106	C₂×C₃×C₅	1	1	yes	characteristic, complemented
123	C₂×#102	C₂×C₃×C₅	1	2	yes	complemented
124	C₂×#97	C₂×C₃×C₅	1	1	yes	characteristic, complemented
125	#390	C₂×C₃×C₅	1	2	yes	complemented
126	C₂²×C₃×C₅	—	4	4	no	—
127	C₂²×C₃×C₅	—	4	8	no	—
128	C₂²×C₃×C₅	—	8	4	no	—
129	C₂²×C₃×C₅	—	8	2	no	—
130	C₂²×C₃×C₅	—	8	2	no	—
131	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
132	C₂²×C₃×C₅	#121	1	1	yes	characteristic
133	C₂²×C₃×C₅	#127	1	1	yes	characteristic
134	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	4	yes	—
135	C₃×C₄×C₅	—	4	2	no	—
136	C₃×C₄×C₅	—	8	2	no	—
137	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
139	C₃×C₄×C₅	#121	1	1	yes	characteristic
140	C₃×C₄×C₅	#124	1	1	yes	characteristic
141	C₂⁴×C₃	—	2	2	no	—
142	C₂×C₃×D₄	—	2	2	no	—
143	C₂×C₃×D₄	—	2	2	no	—
144	C₂×C₃×D₄	—	2	2	no	—
145	C₂×C₃×D₄	—	2	2	no	—
146	C₂×C₃×D₄	—	2	2	no	—
147	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
148	C₂²×C₃×C₄	—	2	2	no	—
149	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
150	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
151	C₃×D₈	—	2	8	no	—
152	C₂×C₃×C₈	—	2	1	no	—
153	C₂×C₃×C₈	—	2	1	no	—
154	C₂×C₃×C₈	C₂×C₄×C₅	1	2	yes	—
155	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
156	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
157	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
158	C₃×C₄⋊C₄	—	2	2	no	—
159	C₃×C₄⋊C₄	—	2	2	no	—
160	C₃×C₂²⋊C₄	—	4	8	no	—
161	C₃×C₄²	—	2	1	no	—
162	C₃×C₄²	—	2	1	no	—
163	C₂³×C₅	—	2	4	no	—
164	C₂³×C₅	—	4	2	no	—
165	C₂³×C₅	—	4	2	no	—
166	C₂³×C₅	—	4	4	no	—
167	C₂³×C₅	—	4	4	no	—
168	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
169	C₅×D₄	—	2	4	no	—
170	C₅×D₄	—	2	4	no	—
171	C₅×D₄	—	4	2	no	—
172	C₅×D₄	—	4	2	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	4	no	—
175	C₂×C₄×C₅	—	4	2	no	—
176	C₂×C₄×C₅	—	4	4	no	—
177	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
178	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
179	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
181	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
182	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
183	C₅×C₈	—	2	2	no	—
184	C₅×C₈	C₃×C₂²⋊C₄	1	4	yes	complemented
185	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
186	C₂×D₈	—	2	2	no	—
187	C₂×D₈	—	2	2	no	—
188	C₂×D₈	C₃×C₄×C₅	1	4	yes	complemented
189	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
190	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
191	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
192	C₂×C₂²⋊C₄	—	2	4	no	—
193	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
194	#106	—	2	2	no	—
195	#102	—	2	4	no	—
196	#97	—	2	2	no	—
197	C₂×C₃×C₅	—	8	4	no	—
198	C₂×C₃×C₅	#390	1	1	yes	characteristic
199	C₂×C₃×C₅	#442	1	2	yes	—
200	C₂×C₃×C₅	#469	1	2	yes	—
201	C₂×C₃×C₅	#496	1	2	yes	—
202	C₂³×C₃	—	2	4	no	—
203	C₂³×C₃	—	4	2	no	—
204	C₂³×C₃	—	4	2	no	—
205	C₂³×C₃	—	4	4	no	—
206	C₂³×C₃	—	4	4	no	—
207	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
208	C₃×D₄	—	2	4	no	—
209	C₃×D₄	—	2	4	no	—
210	C₃×D₄	—	4	2	no	—
211	C₃×D₄	—	4	2	no	—
212	C₂×C₃×C₄	—	2	2	no	—
213	C₂×C₃×C₄	—	2	4	no	—
214	C₂×C₃×C₄	—	4	2	no	—
215	C₂×C₃×C₄	—	4	4	no	—
216	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
217	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
218	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
219	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
220	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
221	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
222	C₃×C₈	—	2	2	no	—
223	C₃×C₈	C₅×C₂²⋊C₄	1	4	yes	complemented
224	C₂²×C₅	—	4	4	no	—
225	C₂²×C₅	—	4	8	no	—
226	C₂²×C₅	—	8	4	no	—
227	C₂²×C₅	—	8	2	no	—
228	C₂²×C₅	—	8	2	no	—
229	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
230	C₂²×C₅	C₃×#121	1	1	yes	characteristic
231	C₂²×C₅	C₃×#127	1	1	yes	characteristic
232	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	4	yes	—
233	C₄×C₅	—	4	2	no	—
234	C₄×C₅	—	8	2	no	—
235	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
236	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
237	C₄×C₅	C₃×#121	1	1	yes	characteristic
238	C₄×C₅	C₃×#124	1	1	yes	characteristic
239	C₂⁴	—	2	2	no	—
240	C₂×D₄	—	2	2	no	—
241	C₂×D₄	—	2	2	no	—
242	C₂×D₄	—	2	2	no	—
243	C₂×D₄	—	2	2	no	—
244	C₂×D₄	—	2	2	no	—
245	C₂×D₄	C₂×C₃×C₄×C₅	1	4	yes	—
246	C₂²×C₄	—	2	2	no	—
247	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
248	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
249	D₈	—	2	8	no	—
250	C₂×C₈	—	2	1	no	—
251	C₂×C₈	—	2	1	no	—
252	C₂×C₈	C₂×C₃×C₄×C₅	1	2	yes	—
253	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
254	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
255	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
256	C₄⋊C₄	—	2	2	no	—
257	C₄⋊C₄	—	2	2	no	—
258	C₂²⋊C₄	—	4	8	no	—
259	C₄²	—	2	1	no	—
260	C₄²	—	2	1	no	—
261	C₃×C₅	#1972	1	1	yes	characteristic, direct product factor, Hall
262	C₂²×C₃	—	4	4	no	—
263	C₂²×C₃	—	4	8	no	—
264	C₂²×C₃	—	8	4	no	—
265	C₂²×C₃	—	8	2	no	—
266	C₂²×C₃	—	8	2	no	—
267	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
268	C₂²×C₃	C₅×#121	1	1	yes	characteristic
269	C₂²×C₃	C₅×#127	1	1	yes	characteristic
270	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	4	yes	—
271	C₃×C₄	—	4	2	no	—
272	C₃×C₄	—	8	2	no	—
273	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
274	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
275	C₃×C₄	C₅×#121	1	1	yes	characteristic
276	C₃×C₄	C₅×#124	1	1	yes	characteristic
277	C₂×C₅	—	8	4	no	—
278	C₂×C₅	C₃×#390	1	1	yes	characteristic
279	C₂×C₅	C₃×#442	1	2	yes	—
280	C₂×C₅	C₃×#469	1	2	yes	—
281	C₂×C₅	C₃×#496	1	2	yes	—
282	C₂³	—	2	4	no	—
283	C₂³	—	4	2	no	—
284	C₂³	—	4	2	no	—
285	C₂³	—	4	4	no	—
286	C₂³	—	4	4	no	—
287	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
288	D₄	—	2	4	no	—
289	D₄	—	2	4	no	—
290	D₄	—	4	2	no	—
291	D₄	—	4	2	no	—
292	C₂×C₄	—	2	2	no	—
293	C₂×C₄	—	2	4	no	—
294	C₂×C₄	—	4	2	no	—
295	C₂×C₄	—	4	4	no	—
296	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
297	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
298	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
299	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
300	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
301	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
302	C₈	—	2	2	no	—
303	C₈	C₃×C₅×C₂²⋊C₄	1	4	yes	complemented
304	C₂×C₃	—	8	4	no	—
305	C₂×C₃	C₅×#390	1	1	yes	characteristic
306	C₂×C₃	C₅×#442	1	2	yes	—
307	C₂×C₃	C₅×#469	1	2	yes	—
308	C₂×C₃	C₅×#496	1	2	yes	—
309	C₅	C₃×#1972	1	1	yes	characteristic, direct product factor, Sylow
310	C₂²	—	4	4	no	—
311	C₂²	—	4	8	no	—
312	C₂²	—	8	4	no	—
313	C₂²	—	8	2	no	—
314	C₂²	—	8	2	no	—
315	C₂²	C₃×C₄×C₅×D₄	1	1	yes	characteristic
316	C₂²	C₃×C₅×#121	1	1	yes	characteristic
317	C₂²	C₃×C₅×#127	1	1	yes	characteristic
318	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	4	yes	—
319	C₄	—	4	2	no	—
320	C₄	—	8	2	no	—
321	C₄	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
322	C₄	C₃×C₄×C₅×D₄	1	1	yes	characteristic
323	C₄	C₃×C₅×#121	1	1	yes	characteristic
324	C₄	C₃×C₅×#124	1	1	yes	characteristic
325	C₃	C₅×#1972	1	1	yes	characteristic, direct product factor, Sylow
326	C₂	—	8	4	no	—
327	C₂	C₃×C₅×#390	1	1	yes	characteristic
328	C₂	C₃×C₅×#442	1	2	yes	—
329	C₂	C₃×C₅×#469	1	2	yes	—
330	C₂	C₃×C₅×#496	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂×D₄
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
prime radical	C₂²×C₃×C₅×D₈	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#106	C₂	semidirect
3. C₂×C₃×C₅×#102	C₂	semidirect
4. C₂×C₃×C₅×#97	C₂	semidirect
5. C₃×C₅×#390	C₂	semidirect
6. C₅×#1972	C₃	direct (N × H)
10. C₂×C₃×C₅×D₈	C₄	semidirect
19. C₃×#1972	C₅	direct (N × H)
21. C₂×C₅×#106	C₂×C₃	semidirect
22. C₂×C₅×#102	C₂×C₃	semidirect
23. C₂×C₅×#97	C₂×C₃	semidirect
24. C₅×#390	C₂×C₃	semidirect
48. C₂×C₃×#106	C₂×C₅	semidirect
49. C₂×C₃×#102	C₂×C₅	semidirect
50. C₂×C₃×#97	C₂×C₅	semidirect
51. C₃×#390	C₂×C₅	semidirect
55. C₂×C₅×D₈	C₃×C₄	semidirect
64. #1972	C₃×C₅	direct (N × H)
86. C₃×C₅×C₈	C₂²⋊C₄	semidirect
90. C₂×C₃×D₈	C₄×C₅	semidirect
122. C₂×#106	C₂×C₃×C₅	semidirect
123. C₂×#102	C₂×C₃×C₅	semidirect
124. C₂×#97	C₂×C₃×C₅	semidirect
125. #390	C₂×C₃×C₅	semidirect
184. C₅×C₈	C₃×C₂²⋊C₄	semidirect
188. C₂×D₈	C₃×C₄×C₅	semidirect
223. C₃×C₈	C₅×C₂²⋊C₄	semidirect
261. C₃×C₅	#1972	direct (N × H)
303. C₈	C₃×C₅×C₂²⋊C₄	semidirect
309. C₅	C₃×#1972	direct (N × H)
325. C₃	C₅×#1972	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×D₈	2
C₂×C₃×C₅×#106	2
C₂×C₃×C₅×#102	2
C₂×C₃×C₅×#97	2
C₃×C₅×#390	2
C₅×#1972	3
C₃×#1972	5

Subgroups — C3×C5×#1972 #14275006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1972 #14275006