Subgroups — C₃×C₅×#3156 #14276190

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#137	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#536	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#497	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#495	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#494	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#3156	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
12	C₃×C₅×#137	—	2	8	no	—
13	C₃×C₅×#135	—	2	4	no	—
14	C₂×C₃×C₅×Q₁₆	—	2	4	no	—
15	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×Q₁₆	C₂²	1	4	yes	—
18	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
19	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	—
20	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
21	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
25	C₃×C₅×#124	C₂²	1	4	yes	—
26	C₃×C₅×#123	—	2	4	no	—
27	C₃×C₅×C₂²⋊Q₈	—	2	4	no	—
28	C₃×C₅×#117	C₂²	1	1	yes	characteristic
29	C₃×C₅×#97	C₂²	1	2	yes	—
30	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
31	C₃×#3156	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₅×#137	C₂×C₃	1	2	yes	complemented
33	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic
34	C₂²×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
35	C₅×#536	C₂×C₃	1	2	yes	complemented
36	C₅×#497	C₂×C₃	1	4	yes	complemented
37	C₅×#495	C₂×C₃	1	2	yes	complemented
38	C₅×#494	C₂×C₃	1	2	yes	complemented
39	C₅×#405	C₂×C₃	1	1	yes	characteristic, complemented
40	C₃×C₅×#41	—	2	4	no	—
41	C₃×C₅×#41	—	2	4	no	—
42	C₂×C₃×C₅×Q₈	—	2	2	no	—
43	C₂×C₃×C₅×Q₈	—	2	4	no	—
44	C₂×C₃×C₅×Q₈	—	2	4	no	—
45	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
46	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
47	C₂×C₃×C₅×D₄	—	2	2	no	—
48	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	—	2	2	no	—
50	C₂²×C₃×C₄×C₅	—	2	2	no	—
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₃×C₅×Q₁₆	—	2	4	no	—
53	C₃×C₅×Q₁₆	—	2	4	no	—
54	C₃×C₅×Q₁₆	—	2	2	no	—
55	C₃×C₅×Q₁₆	—	2	8	no	—
56	C₃×C₅×SD₁₆	—	2	4	no	—
57	C₃×C₅×SD₁₆	—	2	8	no	—
58	C₃×C₅×D₈	—	2	2	no	—
59	C₃×C₅×M₁₆	D₄	1	4	yes	—
60	C₂×C₃×C₅×C₈	D₄	1	4	yes	—
61	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
64	C₃×C₅×C₄⋊C₄	—	2	8	no	—
65	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
66	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
67	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
68	C₃×C₄²×C₅	C₂³	1	2	yes	—
69	C₂×C₃×#137	C₂×C₅	1	2	yes	complemented
70	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic
71	C₂²×C₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
72	C₃×#536	C₂×C₅	1	2	yes	complemented
73	C₃×#497	C₂×C₅	1	4	yes	complemented
74	C₃×#495	C₂×C₅	1	2	yes	complemented
75	C₃×#494	C₂×C₅	1	2	yes	complemented
76	C₃×#405	C₂×C₅	1	1	yes	characteristic, complemented
77	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
78	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
79	C₅×#137	—	2	8	no	—
80	C₅×#135	—	2	4	no	—
81	C₂×C₅×Q₁₆	—	2	4	no	—
82	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
84	C₂×C₅×Q₁₆	C₂²×C₃	1	4	yes	—
85	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
86	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	—
87	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
88	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
90	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
91	C₅×C₄⋊Q₈	C₂²×C₃	1	4	yes	—
92	C₅×#124	C₂²×C₃	1	4	yes	—
93	C₅×#123	—	2	4	no	—
94	C₅×C₂²⋊Q₈	—	2	4	no	—
95	C₅×#117	C₂²×C₃	1	1	yes	characteristic
96	C₅×#97	C₂²×C₃	1	2	yes	—
97	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
98	#3156	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
99	C₂³×C₃×C₅	—	2	2	no	—
100	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
101	C₃×C₅×Q₈	—	2	4	no	—
102	C₃×C₅×Q₈	—	2	2	no	—
103	C₃×C₅×Q₈	—	2	4	no	—
104	C₃×C₅×Q₈	—	2	2	no	—
105	C₃×C₅×Q₈	—	4	4	no	—
106	C₃×C₅×D₄	—	2	2	no	—
107	C₃×C₅×D₄	—	2	2	no	—
108	C₃×C₅×D₄	—	4	4	no	—
109	C₂×C₃×C₄×C₅	—	2	4	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	4	4	no	—
112	C₂×C₃×C₄×C₅	—	4	4	no	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
118	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
119	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
120	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
121	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
122	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
123	C₃×#137	—	2	8	no	—
124	C₃×#135	—	2	4	no	—
125	C₂×C₃×Q₁₆	—	2	4	no	—
126	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
127	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
128	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₃×Q₁₆	C₂²×C₅	1	4	yes	—
130	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
131	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	—
132	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
133	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
134	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
135	C₃×C₄⋊Q₈	C₂²×C₅	1	4	yes	—
136	C₃×#124	C₂²×C₅	1	4	yes	—
137	C₃×#123	—	2	4	no	—
138	C₃×C₂²⋊Q₈	—	2	4	no	—
139	C₃×#117	C₂²×C₅	1	1	yes	characteristic
140	C₃×#97	C₂²×C₅	1	2	yes	—
141	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
142	C₅×#41	—	2	4	no	—
143	C₅×#41	—	2	4	no	—
144	C₂×C₅×Q₈	—	2	2	no	—
145	C₂×C₅×Q₈	—	2	4	no	—
146	C₂×C₅×Q₈	—	2	4	no	—
147	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
148	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
149	C₂×C₅×D₄	—	2	2	no	—
150	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
151	C₂²×C₄×C₅	—	2	2	no	—
152	C₂²×C₄×C₅	—	2	2	no	—
153	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
154	C₅×Q₁₆	—	2	4	no	—
155	C₅×Q₁₆	—	2	4	no	—
156	C₅×Q₁₆	—	2	2	no	—
157	C₅×Q₁₆	—	2	8	no	—
158	C₅×SD₁₆	—	2	4	no	—
159	C₅×SD₁₆	—	2	8	no	—
160	C₅×D₈	—	2	2	no	—
161	C₅×M₁₆	C₃×D₄	1	4	yes	—
162	C₂×C₅×C₈	C₃×D₄	1	4	yes	—
163	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
164	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
165	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
166	C₅×C₄⋊C₄	—	2	8	no	—
167	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
168	C₅×C₂²⋊C₄	—	2	8	no	—
169	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
170	C₄²×C₅	C₂³×C₃	1	2	yes	—
171	C₂×#137	C₂×C₃×C₅	1	2	yes	complemented
172	C₂×#135	C₂×C₃×C₅	1	1	yes	characteristic
173	C₂²×Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
174	#536	C₂×C₃×C₅	1	2	yes	complemented
175	#497	C₂×C₃×C₅	1	4	yes	complemented
176	#495	C₂×C₃×C₅	1	2	yes	complemented
177	#494	C₂×C₃×C₅	1	2	yes	complemented
178	#405	C₂×C₃×C₅	1	1	yes	characteristic, complemented
179	C₂²×C₃×C₅	—	2	2	no	—
180	C₂²×C₃×C₅	—	4	2	no	—
181	C₂²×C₃×C₅	—	4	4	no	—
182	C₂²×C₃×C₅	#127	1	2	yes	—
183	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
184	C₃×C₄×C₅	—	2	4	no	—
185	C₃×C₄×C₅	—	4	2	no	—
186	C₃×C₄×C₅	—	4	4	no	—
187	C₃×C₄×C₅	#127	1	2	yes	—
188	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
189	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
190	C₃×#41	—	2	4	no	—
191	C₃×#41	—	2	4	no	—
192	C₂×C₃×Q₈	—	2	2	no	—
193	C₂×C₃×Q₈	—	2	4	no	—
194	C₂×C₃×Q₈	—	2	4	no	—
195	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
196	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
197	C₂×C₃×D₄	—	2	2	no	—
198	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
199	C₂²×C₃×C₄	—	2	2	no	—
200	C₂²×C₃×C₄	—	2	2	no	—
201	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
202	C₃×Q₁₆	—	2	4	no	—
203	C₃×Q₁₆	—	2	4	no	—
204	C₃×Q₁₆	—	2	2	no	—
205	C₃×Q₁₆	—	2	8	no	—
206	C₃×SD₁₆	—	2	4	no	—
207	C₃×SD₁₆	—	2	8	no	—
208	C₃×D₈	—	2	2	no	—
209	C₃×M₁₆	C₅×D₄	1	4	yes	—
210	C₂×C₃×C₈	C₅×D₄	1	4	yes	—
211	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
212	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
213	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
214	C₃×C₄⋊C₄	—	2	8	no	—
215	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
216	C₃×C₂²⋊C₄	—	2	8	no	—
217	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
218	C₃×C₄²	C₂³×C₅	1	2	yes	—
219	C₂³×C₅	—	2	2	no	—
220	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
221	C₅×Q₈	—	2	4	no	—
222	C₅×Q₈	—	2	2	no	—
223	C₅×Q₈	—	2	4	no	—
224	C₅×Q₈	—	2	2	no	—
225	C₅×Q₈	—	4	4	no	—
226	C₅×D₄	—	2	2	no	—
227	C₅×D₄	—	2	2	no	—
228	C₅×D₄	—	4	4	no	—
229	C₂×C₄×C₅	—	2	4	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	4	4	no	—
232	C₂×C₄×C₅	—	4	4	no	—
233	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
234	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
236	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
237	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
238	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
239	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
240	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
241	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
242	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
243	#137	—	2	8	no	—
244	#135	—	2	4	no	—
245	C₂×Q₁₆	—	2	4	no	—
246	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
247	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
248	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
249	C₂×Q₁₆	C₂²×C₃×C₅	1	4	yes	—
250	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
251	C₂×SD₁₆	C₂²×C₃×C₅	1	4	yes	—
252	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
253	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
254	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
255	C₄⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
256	#124	C₂²×C₃×C₅	1	4	yes	—
257	#123	—	2	4	no	—
258	C₂²⋊Q₈	—	2	4	no	—
259	#117	C₂²×C₃×C₅	1	1	yes	characteristic
260	#97	C₂²×C₃×C₅	1	2	yes	—
261	C₄×C₈	C₂²×C₃×C₅	1	2	yes	—
262	C₂×C₃×C₅	—	2	2	no	—
263	C₂×C₃×C₅	—	8	2	no	—
264	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
265	C₂×C₃×C₅	#578	1	2	yes	—
266	C₂³×C₃	—	2	2	no	—
267	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
268	C₃×Q₈	—	2	4	no	—
269	C₃×Q₈	—	2	2	no	—
270	C₃×Q₈	—	2	4	no	—
271	C₃×Q₈	—	2	2	no	—
272	C₃×Q₈	—	4	4	no	—
273	C₃×D₄	—	2	2	no	—
274	C₃×D₄	—	2	2	no	—
275	C₃×D₄	—	4	4	no	—
276	C₂×C₃×C₄	—	2	4	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	4	4	no	—
279	C₂×C₃×C₄	—	4	4	no	—
280	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
281	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
283	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
284	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
285	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
286	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
287	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
288	C₂²×C₅	—	2	2	no	—
289	C₂²×C₅	—	4	4	no	—
290	C₂²×C₅	—	4	2	no	—
291	C₂²×C₅	C₃×#127	1	2	yes	—
292	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
293	C₄×C₅	—	2	4	no	—
294	C₄×C₅	—	4	2	no	—
295	C₄×C₅	—	4	4	no	—
296	C₄×C₅	C₃×#127	1	2	yes	—
297	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
298	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
299	#41	—	2	4	no	—
300	#41	—	2	4	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
305	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
311	Q₁₆	—	2	4	no	—
312	Q₁₆	—	2	4	no	—
313	Q₁₆	—	2	2	no	—
314	Q₁₆	—	2	8	no	—
315	SD₁₆	—	2	4	no	—
316	SD₁₆	—	2	8	no	—
317	D₈	—	2	2	no	—
318	M₁₆	C₃×C₅×D₄	1	4	yes	—
319	C₂×C₈	C₃×C₅×D₄	1	4	yes	—
320	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
321	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
322	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
323	C₄⋊C₄	—	2	8	no	—
324	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
325	C₂²⋊C₄	—	2	8	no	—
326	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
327	C₄²	C₂³×C₃×C₅	1	2	yes	—
328	C₃×C₅	#3156	1	1	yes	characteristic, direct product factor, Hall
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	4	2	no	—
331	C₂²×C₃	—	4	4	no	—
332	C₂²×C₃	C₅×#127	1	2	yes	—
333	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
334	C₃×C₄	—	2	4	no	—
335	C₃×C₄	—	4	2	no	—
336	C₃×C₄	—	4	4	no	—
337	C₃×C₄	C₅×#127	1	2	yes	—
338	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
339	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
340	C₂×C₅	—	2	2	no	—
341	C₂×C₅	—	8	2	no	—
342	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
343	C₂×C₅	C₃×#578	1	2	yes	—
344	C₂³	—	2	2	no	—
345	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
346	Q₈	—	2	4	no	—
347	Q₈	—	2	2	no	—
348	Q₈	—	2	4	no	—
349	Q₈	—	2	2	no	—
350	Q₈	—	4	4	no	—
351	D₄	—	2	2	no	—
352	D₄	—	2	2	no	—
353	D₄	—	4	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
359	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
360	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
361	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
362	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
363	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
364	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
365	C₈	C₂×C₃×C₅×D₄	1	4	yes	—
366	C₂×C₃	—	2	2	no	—
367	C₂×C₃	—	8	2	no	—
368	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
369	C₂×C₃	C₅×#578	1	2	yes	—
370	C₅	C₃×#3156	1	1	yes	characteristic, direct product factor, Sylow
371	C₂²	—	2	2	no	—
372	C₂²	—	4	2	no	—
373	C₂²	—	4	4	no	—
374	C₂²	C₃×C₅×#127	1	2	yes	—
375	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
376	C₄	—	2	4	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	4	no	—
379	C₄	C₃×C₅×#127	1	2	yes	—
380	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
381	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
382	C₃	C₅×#3156	1	1	yes	characteristic, direct product factor, Sylow
383	C₂	—	2	2	no	—
384	C₂	—	8	2	no	—
385	C₂	C₂×C₃×C₅×#127	1	1	yes	characteristic
386	C₂	C₃×C₅×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#135	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#137	C₂	semidirect
3. C₂²×C₃×C₅×Q₁₆	C₂	semidirect
4. C₃×C₅×#536	C₂	semidirect
5. C₃×C₅×#497	C₂	semidirect
6. C₃×C₅×#495	C₂	semidirect
7. C₃×C₅×#494	C₂	semidirect
8. C₃×C₅×#405	C₂	semidirect
9. C₅×#3156	C₃	direct (N × H)
31. C₃×#3156	C₅	direct (N × H)
32. C₂×C₅×#137	C₂×C₃	semidirect
34. C₂²×C₅×Q₁₆	C₂×C₃	semidirect
35. C₅×#536	C₂×C₃	semidirect
36. C₅×#497	C₂×C₃	semidirect
37. C₅×#495	C₂×C₃	semidirect
38. C₅×#494	C₂×C₃	semidirect
39. C₅×#405	C₂×C₃	semidirect
69. C₂×C₃×#137	C₂×C₅	semidirect
71. C₂²×C₃×Q₁₆	C₂×C₅	semidirect
72. C₃×#536	C₂×C₅	semidirect
73. C₃×#497	C₂×C₅	semidirect
74. C₃×#495	C₂×C₅	semidirect
75. C₃×#494	C₂×C₅	semidirect
76. C₃×#405	C₂×C₅	semidirect
98. #3156	C₃×C₅	direct (N × H)
171. C₂×#137	C₂×C₃×C₅	semidirect
173. C₂²×Q₁₆	C₂×C₃×C₅	semidirect
174. #536	C₂×C₃×C₅	semidirect
175. #497	C₂×C₃×C₅	semidirect
176. #495	C₂×C₃×C₅	semidirect
177. #494	C₂×C₃×C₅	semidirect
178. #405	C₂×C₃×C₅	semidirect
328. C₃×C₅	#3156	direct (N × H)
370. C₅	C₃×#3156	direct (N × H)
382. C₃	C₅×#3156	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×#137	2
C₂×C₃×C₅×#135	2
C₂²×C₃×C₅×Q₁₆	2
C₃×C₅×#536	2
C₃×C₅×#497	2
C₃×C₅×#495	2
C₃×C₅×#494	2
C₃×C₅×#405	2
C₅×#3156	3
C₃×#3156	5

Subgroups — C3×C5×#3156 #14276190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3156 #14276190