Subgroups — C₃×C₅×#2331 #14275365

Order 1920.

920 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#391	C₂	1	4	yes	maximal
3	C₃×C₅×#389	C₂	1	2	yes	maximal
4	C₃×C₅×#387	C₂	1	4	yes	maximal
5	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic
6	C₃×C₄×C₅×C₄⋊C₄	C₂	1	2	yes	maximal
7	C₃×C₅×#376	C₂	1	1	yes	maximal, characteristic
8	C₅×#2331	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
10	C₃×C₅×C₄⋊Q₈	C₄	1	8	yes	complemented
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	C₂²	1	4	yes	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₃×C₅×#95	C₂²	1	2	yes	—
20	C₃×C₅×#95	C₂²	1	2	yes	—
21	C₃×C₅×#95	C₂²	1	4	yes	—
22	C₃×C₅×#95	C₂²	1	2	yes	—
23	C₃×C₅×#95	C₂²	1	2	yes	—
24	C₃×C₅×#95	C₂²	1	4	yes	—
25	C₃×#2331	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
26	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
27	C₅×#391	C₂×C₃	1	4	yes	—
28	C₅×#389	C₂×C₃	1	2	yes	—
29	C₅×#387	C₂×C₃	1	4	yes	—
30	C₅×#382	C₂×C₃	1	1	yes	characteristic
31	C₄×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	—
32	C₅×#376	C₂×C₃	1	1	yes	characteristic
33	C₂×C₃×C₅×Q₈	—	4	4	no	—
34	C₂×C₃×C₅×Q₈	C₂×C₄	1	8	yes	—
35	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
36	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
42	C₃×C₅×C₄⋊C₄	—	2	4	no	—
43	C₃×C₅×C₄⋊C₄	—	4	4	no	—
44	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	—
45	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	—
46	C₃×C₄²×C₅	—	2	2	no	—
47	C₃×C₄²×C₅	—	4	4	no	—
48	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
49	C₃×C₄²×C₅	Q₈	1	4	yes	complemented
50	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
51	C₃×#391	C₂×C₅	1	4	yes	—
52	C₃×#389	C₂×C₅	1	2	yes	—
53	C₃×#387	C₂×C₅	1	4	yes	—
54	C₃×#382	C₂×C₅	1	1	yes	characteristic
55	C₃×C₄×C₄⋊C₄	C₂×C₅	1	2	yes	—
56	C₃×#376	C₂×C₅	1	1	yes	characteristic
57	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
58	C₅×C₄⋊Q₈	C₃×C₄	1	8	yes	complemented
59	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
60	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
61	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
62	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
63	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
64	C₂×C₄²×C₅	C₂²×C₃	1	4	yes	—
65	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
66	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
67	C₅×#95	C₂²×C₃	1	2	yes	—
68	C₅×#95	C₂²×C₃	1	2	yes	—
69	C₅×#95	C₂²×C₃	1	4	yes	—
70	C₅×#95	C₂²×C₃	1	2	yes	—
71	C₅×#95	C₂²×C₃	1	2	yes	—
72	C₅×#95	C₂²×C₃	1	4	yes	—
73	#2331	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
74	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
75	C₃×C₅×Q₈	—	4	8	no	—
76	C₂×C₃×C₄×C₅	—	2	2	no	—
77	C₂×C₃×C₄×C₅	—	2	4	no	—
78	C₂×C₃×C₄×C₅	—	2	4	no	—
79	C₂×C₃×C₄×C₅	—	2	2	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	4	no	—
84	C₂×C₃×C₄×C₅	—	2	4	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	2	2	no	—
87	C₂×C₃×C₄×C₅	—	2	4	no	—
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂²×C₄	1	8	yes	—
91	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
93	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
94	C₂×C₃×C₄×C₅	#41	1	2	yes	—
95	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
96	C₃×C₄⋊Q₈	C₄×C₅	1	8	yes	complemented
97	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
98	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
99	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
100	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
101	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
102	C₂×C₃×C₄²	C₂²×C₅	1	4	yes	—
103	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
104	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
105	C₃×#95	C₂²×C₅	1	2	yes	—
106	C₃×#95	C₂²×C₅	1	2	yes	—
107	C₃×#95	C₂²×C₅	1	4	yes	—
108	C₃×#95	C₂²×C₅	1	2	yes	—
109	C₃×#95	C₂²×C₅	1	2	yes	—
110	C₃×#95	C₂²×C₅	1	4	yes	—
111	C₂×C₅×Q₈	—	4	4	no	—
112	C₂×C₅×Q₈	C₂×C₃×C₄	1	8	yes	—
113	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
114	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
115	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
116	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
118	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
119	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
120	C₅×C₄⋊C₄	—	2	4	no	—
121	C₅×C₄⋊C₄	—	4	4	no	—
122	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
123	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
124	C₄²×C₅	—	2	2	no	—
125	C₄²×C₅	—	4	4	no	—
126	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
127	C₄²×C₅	C₃×Q₈	1	4	yes	complemented
128	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
129	#391	C₂×C₃×C₅	1	4	yes	—
130	#389	C₂×C₃×C₅	1	2	yes	—
131	#387	C₂×C₃×C₅	1	4	yes	—
132	#382	C₂×C₃×C₅	1	1	yes	characteristic
133	C₄×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	—
134	#376	C₂×C₃×C₅	1	1	yes	characteristic
135	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
136	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
137	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
138	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
139	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
140	C₃×C₄×C₅	—	2	8	no	—
141	C₃×C₄×C₅	—	2	2	no	—
142	C₃×C₄×C₅	—	2	2	no	—
143	C₃×C₄×C₅	—	2	4	no	—
144	C₃×C₄×C₅	—	4	2	no	—
145	C₃×C₄×C₅	—	4	4	no	—
146	C₃×C₄×C₅	C₄×Q₈	1	4	yes	—
147	C₂×C₃×Q₈	—	4	4	no	—
148	C₂×C₃×Q₈	C₂×C₄×C₅	1	8	yes	—
149	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
150	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
151	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
153	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
154	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
155	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
156	C₃×C₄⋊C₄	—	2	4	no	—
157	C₃×C₄⋊C₄	—	4	4	no	—
158	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	—
159	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	—
160	C₃×C₄²	—	2	2	no	—
161	C₃×C₄²	—	4	4	no	—
162	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
163	C₃×C₄²	C₅×Q₈	1	4	yes	complemented
164	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
165	C₅×Q₈	—	4	8	no	—
166	C₂×C₄×C₅	—	2	2	no	—
167	C₂×C₄×C₅	—	2	4	no	—
168	C₂×C₄×C₅	—	2	4	no	—
169	C₂×C₄×C₅	—	2	2	no	—
170	C₂×C₄×C₅	—	2	2	no	—
171	C₂×C₄×C₅	—	2	2	no	—
172	C₂×C₄×C₅	—	2	2	no	—
173	C₂×C₄×C₅	—	2	4	no	—
174	C₂×C₄×C₅	—	2	4	no	—
175	C₂×C₄×C₅	—	2	2	no	—
176	C₂×C₄×C₅	—	2	2	no	—
177	C₂×C₄×C₅	—	2	4	no	—
178	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
179	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
180	C₂×C₄×C₅	C₂²×C₃×C₄	1	8	yes	—
181	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
182	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
183	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
184	C₂×C₄×C₅	C₃×#41	1	2	yes	—
185	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
186	C₄⋊Q₈	C₃×C₄×C₅	1	8	yes	complemented
187	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
188	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
189	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
190	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
191	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
192	C₂×C₄²	C₂²×C₃×C₅	1	4	yes	—
193	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
194	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
195	#95	C₂²×C₃×C₅	1	2	yes	—
196	#95	C₂²×C₃×C₅	1	2	yes	—
197	#95	C₂²×C₃×C₅	1	4	yes	—
198	#95	C₂²×C₃×C₅	1	2	yes	—
199	#95	C₂²×C₃×C₅	1	2	yes	—
200	#95	C₂²×C₃×C₅	1	4	yes	—
201	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
202	C₂×C₃×C₅	#518	1	1	yes	characteristic
203	C₂×C₃×C₅	#519	1	1	yes	characteristic
204	C₂×C₃×C₅	#542	1	2	yes	—
205	C₂×C₃×C₅	#544	1	2	yes	—
206	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
207	C₃×Q₈	—	4	8	no	—
208	C₂×C₃×C₄	—	2	2	no	—
209	C₂×C₃×C₄	—	2	4	no	—
210	C₂×C₃×C₄	—	2	4	no	—
211	C₂×C₃×C₄	—	2	2	no	—
212	C₂×C₃×C₄	—	2	2	no	—
213	C₂×C₃×C₄	—	2	2	no	—
214	C₂×C₃×C₄	—	2	2	no	—
215	C₂×C₃×C₄	—	2	4	no	—
216	C₂×C₃×C₄	—	2	4	no	—
217	C₂×C₃×C₄	—	2	2	no	—
218	C₂×C₃×C₄	—	2	2	no	—
219	C₂×C₃×C₄	—	2	4	no	—
220	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
221	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
222	C₂×C₃×C₄	C₂²×C₄×C₅	1	8	yes	—
223	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
224	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
225	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
226	C₂×C₃×C₄	C₅×#41	1	2	yes	—
227	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
228	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
229	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
230	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
231	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
232	C₄×C₅	—	2	8	no	—
233	C₄×C₅	—	2	2	no	—
234	C₄×C₅	—	2	2	no	—
235	C₄×C₅	—	2	4	no	—
236	C₄×C₅	—	4	2	no	—
237	C₄×C₅	—	4	4	no	—
238	C₄×C₅	C₃×C₄×Q₈	1	4	yes	—
239	C₂×Q₈	—	4	4	no	—
240	C₂×Q₈	C₂×C₃×C₄×C₅	1	8	yes	—
241	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
242	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
243	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
244	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
245	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
246	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
247	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
248	C₄⋊C₄	—	2	4	no	—
249	C₄⋊C₄	—	4	4	no	—
250	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
251	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
252	C₄²	—	2	2	no	—
253	C₄²	—	4	4	no	—
254	C₄²	C₂×C₃×C₄×C₅	1	4	yes	—
255	C₄²	C₃×C₅×Q₈	1	4	yes	complemented
256	C₃×C₅	#2331	1	1	yes	characteristic, direct product factor, Hall
257	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
258	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
259	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
260	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
261	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
262	C₃×C₄	—	2	8	no	—
263	C₃×C₄	—	2	2	no	—
264	C₃×C₄	—	2	2	no	—
265	C₃×C₄	—	2	4	no	—
266	C₃×C₄	—	4	2	no	—
267	C₃×C₄	—	4	4	no	—
268	C₃×C₄	C₄×C₅×Q₈	1	4	yes	—
269	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
270	C₂×C₅	C₃×#518	1	1	yes	characteristic
271	C₂×C₅	C₃×#519	1	1	yes	characteristic
272	C₂×C₅	C₃×#542	1	2	yes	—
273	C₂×C₅	C₃×#544	1	2	yes	—
274	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
275	Q₈	—	4	8	no	—
276	C₂×C₄	—	2	2	no	—
277	C₂×C₄	—	2	4	no	—
278	C₂×C₄	—	2	4	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	2	2	no	—
283	C₂×C₄	—	2	4	no	—
284	C₂×C₄	—	2	4	no	—
285	C₂×C₄	—	2	2	no	—
286	C₂×C₄	—	2	2	no	—
287	C₂×C₄	—	2	4	no	—
288	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
289	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
290	C₂×C₄	C₂²×C₃×C₄×C₅	1	8	yes	—
291	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
292	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
293	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
294	C₂×C₄	C₃×C₅×#41	1	2	yes	—
295	C₂×C₃	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
296	C₂×C₃	C₅×#518	1	1	yes	characteristic
297	C₂×C₃	C₅×#519	1	1	yes	characteristic
298	C₂×C₃	C₅×#542	1	2	yes	—
299	C₂×C₃	C₅×#544	1	2	yes	—
300	C₅	C₃×#2331	1	1	yes	characteristic, direct product factor, Sylow
301	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
302	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
303	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
304	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
305	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
306	C₄	—	2	2	no	—
307	C₄	—	2	8	no	—
308	C₄	—	2	2	no	—
309	C₄	—	2	4	no	—
310	C₄	—	4	2	no	—
311	C₄	—	4	4	no	—
312	C₄	C₃×C₄×C₅×Q₈	1	4	yes	—
313	C₃	C₅×#2331	1	1	yes	characteristic, direct product factor, Sylow
314	C₂	C₂×C₃×C₄×C₅×Q₈	1	1	yes	characteristic
315	C₂	C₃×C₅×#518	1	1	yes	characteristic
316	C₂	C₃×C₅×#519	1	1	yes	characteristic
317	C₂	C₃×C₅×#542	1	2	yes	—
318	C₂	C₃×C₅×#544	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂⁴
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₅×#2331	C₃	direct (N × H)
10. C₃×C₅×C₄⋊Q₈	C₄	semidirect
25. C₃×#2331	C₅	direct (N × H)
49. C₃×C₄²×C₅	Q₈	semidirect
58. C₅×C₄⋊Q₈	C₃×C₄	semidirect
73. #2331	C₃×C₅	direct (N × H)
96. C₃×C₄⋊Q₈	C₄×C₅	semidirect
127. C₄²×C₅	C₃×Q₈	semidirect
163. C₃×C₄²	C₅×Q₈	semidirect
186. C₄⋊Q₈	C₃×C₄×C₅	semidirect
255. C₄²	C₃×C₅×Q₈	semidirect
256. C₃×C₅	#2331	direct (N × H)
300. C₅	C₃×#2331	direct (N × H)
313. C₃	C₅×#2331	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₄⋊Q₈	2
C₃×C₅×#391	2
C₃×C₅×#389	2
C₃×C₅×#387	2
C₃×C₅×#382	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₅×#376	2
C₅×#2331	3
C₃×#2331	5

Subgroups — C3×C5×#2331 #14275365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2331 #14275365