Subgroups — C₃×C₅×#2295 #14275329

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#391	C₂	1	2	yes	maximal
3	C₃×C₅×#389	C₂	1	2	yes	maximal
4	C₃×C₅×#387	C₂	1	4	yes	maximal
5	C₃×C₄×C₅×C₄⋊C₄	C₂	1	2	yes	maximal
6	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#376	C₂	1	2	yes	maximal
8	C₃×C₄³×C₅	C₂	1	1	yes	maximal, characteristic
9	C₅×#2295	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₃×C₄×C₅×Q₈	C₄	1	8	yes	complemented
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×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
17	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₃×C₅×#95	C₂²	1	4	yes	—
24	C₃×C₅×#95	C₂²	1	4	yes	—
25	C₃×C₅×#95	C₂²	1	2	yes	—
26	C₃×C₅×#95	C₂²	1	4	yes	—
27	C₃×#2295	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic
29	C₅×#391	C₂×C₃	1	2	yes	—
30	C₅×#389	C₂×C₃	1	2	yes	—
31	C₅×#387	C₂×C₃	1	4	yes	—
32	C₄×C₅×C₄⋊C₄	C₂×C₃	1	2	yes	—
33	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
34	C₅×#376	C₂×C₃	1	2	yes	—
35	C₄³×C₅	C₂×C₃	1	1	yes	characteristic
36	C₂×C₃×C₅×Q₈	—	2	4	no	—
37	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	—
38	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
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	2	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₃×C₅×C₄⋊C₄	—	2	8	no	—
47	C₃×C₅×C₄⋊C₄	—	2	4	no	—
48	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	—
49	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
50	C₃×C₄²×C₅	—	2	4	no	—
51	C₃×C₄²×C₅	—	2	4	no	—
52	C₃×C₄²×C₅	—	2	2	no	—
53	C₃×C₄²×C₅	—	2	4	no	—
54	C₃×C₄²×C₅	C₂×C₄	1	8	yes	—
55	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
56	C₃×C₄²×C₅	Q₈	1	4	yes	complemented
57	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic
58	C₃×#391	C₂×C₅	1	2	yes	—
59	C₃×#389	C₂×C₅	1	2	yes	—
60	C₃×#387	C₂×C₅	1	4	yes	—
61	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
62	C₃×C₄×C₄⋊C₄	C₂×C₅	1	2	yes	—
63	C₃×#376	C₂×C₅	1	2	yes	—
64	C₃×C₄³	C₂×C₅	1	1	yes	characteristic
65	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
66	C₄×C₅×Q₈	C₃×C₄	1	8	yes	complemented
67	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
68	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
69	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
70	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
72	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
73	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
74	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
75	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
77	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
78	C₅×#95	C₂²×C₃	1	4	yes	—
79	C₅×#95	C₂²×C₃	1	4	yes	—
80	C₅×#95	C₂²×C₃	1	2	yes	—
81	C₅×#95	C₂²×C₃	1	4	yes	—
82	#2295	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
83	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
84	C₃×C₅×Q₈	—	2	8	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	2	2	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	—	2	2	no	—
89	C₂×C₃×C₄×C₅	—	2	2	no	—
90	C₂×C₃×C₄×C₅	—	2	4	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	—	2	4	no	—
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
97	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
101	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
102	C₂×C₃×C₄×C₅	#41	1	4	yes	—
103	C₂×C₃×C₄×C₅	#41	1	4	yes	—
104	C₂×C₃×C₄×C₅	#41	1	2	yes	—
105	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
106	C₃×C₄×Q₈	C₄×C₅	1	8	yes	complemented
107	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	4	yes	—
108	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
109	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
110	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
111	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
112	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
113	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
114	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
115	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
116	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
117	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
118	C₃×#95	C₂²×C₅	1	4	yes	—
119	C₃×#95	C₂²×C₅	1	4	yes	—
120	C₃×#95	C₂²×C₅	1	2	yes	—
121	C₃×#95	C₂²×C₅	1	4	yes	—
122	C₂×C₅×Q₈	—	2	4	no	—
123	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	—
124	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
125	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
127	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
128	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
129	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
130	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
132	C₅×C₄⋊C₄	—	2	8	no	—
133	C₅×C₄⋊C₄	—	2	4	no	—
134	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	—
135	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
136	C₄²×C₅	—	2	4	no	—
137	C₄²×C₅	—	2	4	no	—
138	C₄²×C₅	—	2	2	no	—
139	C₄²×C₅	—	2	4	no	—
140	C₄²×C₅	C₂×C₃×C₄	1	8	yes	—
141	C₄²×C₅	C₂×C₃×C₄	1	4	yes	—
142	C₄²×C₅	C₃×Q₈	1	4	yes	complemented
143	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
144	#391	C₂×C₃×C₅	1	2	yes	—
145	#389	C₂×C₃×C₅	1	2	yes	—
146	#387	C₂×C₃×C₅	1	4	yes	—
147	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
148	C₄×C₄⋊C₄	C₂×C₃×C₅	1	2	yes	—
149	#376	C₂×C₃×C₅	1	2	yes	—
150	C₄³	C₂×C₃×C₅	1	1	yes	characteristic
151	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
152	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
153	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
154	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
155	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
156	C₃×C₄×C₅	—	2	4	no	—
157	C₃×C₄×C₅	—	2	2	no	—
158	C₃×C₄×C₅	—	2	4	no	—
159	C₃×C₄×C₅	—	2	4	no	—
160	C₃×C₄×C₅	—	2	4	no	—
161	C₃×C₄×C₅	—	4	4	no	—
162	C₃×C₄×C₅	#117	1	4	yes	—
163	C₃×C₄×C₅	C₄×Q₈	1	4	yes	—
164	C₂×C₃×Q₈	—	2	4	no	—
165	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	—
166	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
167	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
168	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
169	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
170	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
171	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
172	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
174	C₃×C₄⋊C₄	—	2	8	no	—
175	C₃×C₄⋊C₄	—	2	4	no	—
176	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	—
177	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
178	C₃×C₄²	—	2	4	no	—
179	C₃×C₄²	—	2	4	no	—
180	C₃×C₄²	—	2	2	no	—
181	C₃×C₄²	—	2	4	no	—
182	C₃×C₄²	C₂×C₄×C₅	1	8	yes	—
183	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
184	C₃×C₄²	C₅×Q₈	1	4	yes	complemented
185	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
186	C₅×Q₈	—	2	8	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	2	2	no	—
190	C₂×C₄×C₅	—	2	2	no	—
191	C₂×C₄×C₅	—	2	2	no	—
192	C₂×C₄×C₅	—	2	4	no	—
193	C₂×C₄×C₅	—	2	4	no	—
194	C₂×C₄×C₅	—	2	4	no	—
195	C₂×C₄×C₅	—	2	4	no	—
196	C₂×C₄×C₅	—	2	4	no	—
197	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
198	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
199	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
200	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
201	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
202	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
203	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
204	C₂×C₄×C₅	C₃×#41	1	4	yes	—
205	C₂×C₄×C₅	C₃×#41	1	4	yes	—
206	C₂×C₄×C₅	C₃×#41	1	2	yes	—
207	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
208	C₄×Q₈	C₃×C₄×C₅	1	8	yes	complemented
209	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	4	yes	—
210	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
211	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
212	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
213	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
214	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
215	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
216	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
217	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
218	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
219	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
220	#95	C₂²×C₃×C₅	1	4	yes	—
221	#95	C₂²×C₃×C₅	1	4	yes	—
222	#95	C₂²×C₃×C₅	1	2	yes	—
223	#95	C₂²×C₃×C₅	1	4	yes	—
224	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
225	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
226	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
227	C₂×C₃×C₅	#529	1	2	yes	—
228	C₂×C₃×C₅	#533	1	2	yes	—
229	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
230	C₃×Q₈	—	2	8	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	2	4	no	—
237	C₂×C₃×C₄	—	2	4	no	—
238	C₂×C₃×C₄	—	2	4	no	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	—	2	4	no	—
241	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
242	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
243	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
244	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
245	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
246	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
247	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
248	C₂×C₃×C₄	C₅×#41	1	4	yes	—
249	C₂×C₃×C₄	C₅×#41	1	4	yes	—
250	C₂×C₃×C₄	C₅×#41	1	2	yes	—
251	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
252	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
253	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
254	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
255	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
256	C₄×C₅	—	2	4	no	—
257	C₄×C₅	—	2	2	no	—
258	C₄×C₅	—	2	4	no	—
259	C₄×C₅	—	2	4	no	—
260	C₄×C₅	—	2	4	no	—
261	C₄×C₅	—	4	4	no	—
262	C₄×C₅	C₃×#117	1	4	yes	—
263	C₄×C₅	C₃×C₄×Q₈	1	4	yes	—
264	C₂×Q₈	—	2	4	no	—
265	C₂×Q₈	C₂×C₃×C₄×C₅	1	4	yes	—
266	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
267	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
268	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
269	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
270	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
271	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
272	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
273	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
274	C₄⋊C₄	—	2	8	no	—
275	C₄⋊C₄	—	2	4	no	—
276	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
277	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	—
278	C₄²	—	2	4	no	—
279	C₄²	—	2	4	no	—
280	C₄²	—	2	2	no	—
281	C₄²	—	2	4	no	—
282	C₄²	C₂×C₃×C₄×C₅	1	8	yes	—
283	C₄²	C₂×C₃×C₄×C₅	1	4	yes	—
284	C₄²	C₃×C₅×Q₈	1	4	yes	complemented
285	C₃×C₅	#2295	1	1	yes	characteristic, direct product factor, Hall
286	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
287	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
288	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
289	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
290	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
291	C₃×C₄	—	2	4	no	—
292	C₃×C₄	—	2	2	no	—
293	C₃×C₄	—	2	4	no	—
294	C₃×C₄	—	2	4	no	—
295	C₃×C₄	—	2	4	no	—
296	C₃×C₄	—	4	4	no	—
297	C₃×C₄	C₅×#117	1	4	yes	—
298	C₃×C₄	C₄×C₅×Q₈	1	4	yes	—
299	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
300	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
301	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
302	C₂×C₅	C₃×#529	1	2	yes	—
303	C₂×C₅	C₃×#533	1	2	yes	—
304	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
305	Q₈	—	2	8	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
317	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
318	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
319	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
320	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
321	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
322	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
323	C₂×C₄	C₃×C₅×#41	1	4	yes	—
324	C₂×C₄	C₃×C₅×#41	1	4	yes	—
325	C₂×C₄	C₃×C₅×#41	1	2	yes	—
326	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
327	C₂×C₃	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
328	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
329	C₂×C₃	C₅×#529	1	2	yes	—
330	C₂×C₃	C₅×#533	1	2	yes	—
331	C₅	C₃×#2295	1	1	yes	characteristic, direct product factor, Sylow
332	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
333	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
334	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
335	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
336	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
337	C₄	—	2	4	no	—
338	C₄	—	2	2	no	—
339	C₄	—	2	4	no	—
340	C₄	—	2	4	no	—
341	C₄	—	2	4	no	—
342	C₄	—	4	4	no	—
343	C₄	C₃×C₅×#117	1	4	yes	—
344	C₄	C₃×C₄×C₅×Q₈	1	4	yes	—
345	C₃	C₅×#2295	1	1	yes	characteristic, direct product factor, Sylow
346	C₂	C₂×C₃×C₅×#117	1	1	yes	characteristic
347	C₂	C₂×C₃×C₄×C₅×Q₈	1	1	yes	characteristic
348	C₂	C₃×C₄×C₅×#41	1	1	yes	characteristic
349	C₂	C₃×C₅×#529	1	2	yes	—
350	C₂	C₃×C₅×#533	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
9. C₅×#2295	C₃	direct (N × H)
11. C₃×C₄×C₅×Q₈	C₄	semidirect
27. C₃×#2295	C₅	direct (N × H)
56. C₃×C₄²×C₅	Q₈	semidirect
66. C₄×C₅×Q₈	C₃×C₄	semidirect
82. #2295	C₃×C₅	direct (N × H)
106. C₃×C₄×Q₈	C₄×C₅	semidirect
142. C₄²×C₅	C₃×Q₈	semidirect
184. C₃×C₄²	C₅×Q₈	semidirect
208. C₄×Q₈	C₃×C₄×C₅	semidirect
284. C₄²	C₃×C₅×Q₈	semidirect
285. C₃×C₅	#2295	direct (N × H)
331. C₅	C₃×#2295	direct (N × H)
345. C₃	C₅×#2295	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×C₄×C₅×Q₈	2
C₃×C₅×#391	2
C₃×C₅×#389	2
C₃×C₅×#387	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₅×#376	2
C₃×C₄³×C₅	2
C₅×#2295	3
C₃×#2295	5

Subgroups — C3×C5×#2295 #14275329

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2295 #14275329