Subgroups — C₃×C₅×#3141 #14276175

Order 1920.

848 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#489	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#487	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#486	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#417	C₂	1	4	yes	maximal, complemented
7	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#3141	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
10	C₂²×C₃×C₅×Q₈	—	2	1	no	—
11	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
12	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
13	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
16	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₃×C₅×#127	C₂²	1	1	yes	characteristic
18	C₃×C₅×#124	C₂²	1	2	yes	—
19	C₃×C₅×#121	—	2	1	no	—
20	C₃×C₅×#121	—	2	1	no	—
21	C₃×C₄×C₅×D₄	—	2	1	no	—
22	C₃×C₄×C₅×D₄	—	2	1	no	—
23	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₃×C₅×#103	C₂²	1	8	yes	—
27	C₃×C₅×#102	C₂²	1	8	yes	—
28	C₃×C₅×#97	C₂²	1	2	yes	—
29	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
30	C₃×#3141	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₅×#532	C₂×C₃	1	1	yes	characteristic
32	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
33	C₅×#489	C₂×C₃	1	4	yes	complemented
34	C₅×#487	C₂×C₃	1	2	yes	complemented
35	C₅×#486	C₂×C₃	1	2	yes	complemented
36	C₅×#417	C₂×C₃	1	4	yes	complemented
37	C₄×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
38	C₃×C₅×#41	—	2	8	no	—
39	C₂×C₃×C₅×Q₈	—	2	2	no	—
40	C₂×C₃×C₅×Q₈	—	2	2	no	—
41	C₂×C₃×C₅×Q₈	—	4	4	no	—
42	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	—	2	1	no	—
45	C₂×C₃×C₅×D₄	—	2	1	no	—
46	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	—	2	2	no	—
48	C₂²×C₃×C₄×C₅	—	2	2	no	—
49	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₃×C₅×M₁₆	—	2	4	no	—
53	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
54	C₃×C₅×C₄⋊C₄	—	2	2	no	—
55	C₃×C₅×C₄⋊C₄	—	2	2	no	—
56	C₃×C₅×C₄⋊C₄	—	2	2	no	—
57	C₃×C₅×C₄⋊C₄	—	2	1	no	—
58	C₃×C₅×C₄⋊C₄	—	2	1	no	—
59	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
60	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
61	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
62	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
63	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
64	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
65	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₃×#532	C₂×C₅	1	1	yes	characteristic
67	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
68	C₃×#489	C₂×C₅	1	4	yes	complemented
69	C₃×#487	C₂×C₅	1	2	yes	complemented
70	C₃×#486	C₂×C₅	1	2	yes	complemented
71	C₃×#417	C₂×C₅	1	4	yes	complemented
72	C₃×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
73	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
74	C₂²×C₅×Q₈	—	2	1	no	—
75	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
76	C₅×C₄⋊Q₈	—	2	1	no	—
77	C₅×C₄⋊Q₈	—	2	1	no	—
78	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
79	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
80	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
81	C₅×#127	C₂²×C₃	1	1	yes	characteristic
82	C₅×#124	C₂²×C₃	1	2	yes	—
83	C₅×#121	—	2	1	no	—
84	C₅×#121	—	2	1	no	—
85	C₄×C₅×D₄	—	2	1	no	—
86	C₄×C₅×D₄	—	2	1	no	—
87	C₂×C₅×C₄⋊C₄	—	2	1	no	—
88	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
89	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
90	C₅×#103	C₂²×C₃	1	8	yes	—
91	C₅×#102	C₂²×C₃	1	8	yes	—
92	C₅×#97	C₂²×C₃	1	2	yes	—
93	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
94	#3141	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
95	C₂³×C₃×C₅	—	2	2	no	—
96	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
97	C₃×C₅×Q₈	—	2	4	no	—
98	C₃×C₅×Q₈	—	4	4	no	—
99	C₃×C₅×Q₈	—	4	4	no	—
100	C₃×C₅×D₄	—	2	4	no	—
101	C₃×C₅×D₄	—	4	4	no	—
102	C₃×C₅×D₄	—	4	2	no	—
103	C₃×C₅×D₄	—	4	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	4	no	—
108	C₂×C₃×C₄×C₅	—	4	4	no	—
109	C₂×C₃×C₄×C₅	—	4	4	no	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	#41	1	4	yes	—
116	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
117	C₃×C₅×C₈	—	2	4	no	—
118	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
119	C₂²×C₃×Q₈	—	2	1	no	—
120	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
121	C₃×C₄⋊Q₈	—	2	1	no	—
122	C₃×C₄⋊Q₈	—	2	1	no	—
123	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
124	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
125	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
126	C₃×#127	C₂²×C₅	1	1	yes	characteristic
127	C₃×#124	C₂²×C₅	1	2	yes	—
128	C₃×#121	—	2	1	no	—
129	C₃×#121	—	2	1	no	—
130	C₃×C₄×D₄	—	2	1	no	—
131	C₃×C₄×D₄	—	2	1	no	—
132	C₂×C₃×C₄⋊C₄	—	2	1	no	—
133	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
134	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
135	C₃×#103	C₂²×C₅	1	8	yes	—
136	C₃×#102	C₂²×C₅	1	8	yes	—
137	C₃×#97	C₂²×C₅	1	2	yes	—
138	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
139	C₅×#41	—	2	8	no	—
140	C₂×C₅×Q₈	—	2	2	no	—
141	C₂×C₅×Q₈	—	2	2	no	—
142	C₂×C₅×Q₈	—	4	4	no	—
143	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
144	C₂×C₅×D₄	—	2	2	no	—
145	C₂×C₅×D₄	—	2	1	no	—
146	C₂×C₅×D₄	—	2	1	no	—
147	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
148	C₂²×C₄×C₅	—	2	2	no	—
149	C₂²×C₄×C₅	—	2	2	no	—
150	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
153	C₅×M₁₆	—	2	4	no	—
154	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
155	C₅×C₄⋊C₄	—	2	2	no	—
156	C₅×C₄⋊C₄	—	2	2	no	—
157	C₅×C₄⋊C₄	—	2	2	no	—
158	C₅×C₄⋊C₄	—	2	1	no	—
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
161	C₅×C₂²⋊C₄	—	2	2	no	—
162	C₅×C₂²⋊C₄	—	2	2	no	—
163	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
164	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
165	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
166	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
167	#532	C₂×C₃×C₅	1	1	yes	characteristic
168	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
169	#489	C₂×C₃×C₅	1	4	yes	complemented
170	#487	C₂×C₃×C₅	1	2	yes	complemented
171	#486	C₂×C₃×C₅	1	2	yes	complemented
172	#417	C₂×C₃×C₅	1	4	yes	complemented
173	C₄×M₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
174	C₂²×C₃×C₅	—	2	1	no	—
175	C₂²×C₃×C₅	—	2	1	no	—
176	C₂²×C₃×C₅	—	4	2	no	—
177	C₂²×C₃×C₅	—	4	2	no	—
178	C₂²×C₃×C₅	—	4	2	no	—
179	C₂²×C₃×C₅	#124	1	2	yes	—
180	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
181	C₃×C₄×C₅	—	2	1	no	—
182	C₃×C₄×C₅	—	2	1	no	—
183	C₃×C₄×C₅	—	4	2	no	—
184	C₃×C₄×C₅	—	4	4	no	—
185	C₃×C₄×C₅	#124	1	2	yes	—
186	C₃×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
187	C₃×C₄×C₅	#137	1	2	yes	—
188	C₃×C₄×C₅	C₂×#41	1	2	yes	—
189	C₃×#41	—	2	8	no	—
190	C₂×C₃×Q₈	—	2	2	no	—
191	C₂×C₃×Q₈	—	2	2	no	—
192	C₂×C₃×Q₈	—	4	4	no	—
193	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
194	C₂×C₃×D₄	—	2	2	no	—
195	C₂×C₃×D₄	—	2	1	no	—
196	C₂×C₃×D₄	—	2	1	no	—
197	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
198	C₂²×C₃×C₄	—	2	2	no	—
199	C₂²×C₃×C₄	—	2	2	no	—
200	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
201	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
202	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
203	C₃×M₁₆	—	2	4	no	—
204	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
205	C₃×C₄⋊C₄	—	2	2	no	—
206	C₃×C₄⋊C₄	—	2	2	no	—
207	C₃×C₄⋊C₄	—	2	2	no	—
208	C₃×C₄⋊C₄	—	2	1	no	—
209	C₃×C₄⋊C₄	—	2	1	no	—
210	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
211	C₃×C₂²⋊C₄	—	2	2	no	—
212	C₃×C₂²⋊C₄	—	2	2	no	—
213	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
214	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
215	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
216	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
217	C₂³×C₅	—	2	2	no	—
218	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
219	C₅×Q₈	—	2	4	no	—
220	C₅×Q₈	—	4	4	no	—
221	C₅×Q₈	—	4	4	no	—
222	C₅×D₄	—	2	4	no	—
223	C₅×D₄	—	4	4	no	—
224	C₅×D₄	—	4	2	no	—
225	C₅×D₄	—	4	2	no	—
226	C₂×C₄×C₅	—	2	2	no	—
227	C₂×C₄×C₅	—	2	2	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	4	no	—
230	C₂×C₄×C₅	—	4	4	no	—
231	C₂×C₄×C₅	—	4	4	no	—
232	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
237	C₂×C₄×C₅	C₃×#41	1	4	yes	—
238	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
239	C₅×C₈	—	2	4	no	—
240	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
241	C₂²×Q₈	—	2	1	no	—
242	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
243	C₄⋊Q₈	—	2	1	no	—
244	C₄⋊Q₈	—	2	1	no	—
245	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
246	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
247	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
248	#127	C₂²×C₃×C₅	1	1	yes	characteristic
249	#124	C₂²×C₃×C₅	1	2	yes	—
250	#121	—	2	1	no	—
251	#121	—	2	1	no	—
252	C₄×D₄	—	2	1	no	—
253	C₄×D₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
256	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
257	#103	C₂²×C₃×C₅	1	8	yes	—
258	#102	C₂²×C₃×C₅	1	8	yes	—
259	#97	C₂²×C₃×C₅	1	2	yes	—
260	C₄×C₈	C₂²×C₃×C₅	1	2	yes	—
261	C₂×C₃×C₅	—	2	2	no	—
262	C₂×C₃×C₅	—	8	2	no	—
263	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
264	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
265	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
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	—	4	4	no	—
270	C₃×Q₈	—	4	4	no	—
271	C₃×D₄	—	2	4	no	—
272	C₃×D₄	—	4	4	no	—
273	C₃×D₄	—	4	2	no	—
274	C₃×D₄	—	4	2	no	—
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	2	no	—
278	C₂×C₃×C₄	—	2	4	no	—
279	C₂×C₃×C₄	—	4	4	no	—
280	C₂×C₃×C₄	—	4	4	no	—
281	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
286	C₂×C₃×C₄	C₅×#41	1	4	yes	—
287	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
288	C₃×C₈	—	2	4	no	—
289	C₂²×C₅	—	2	1	no	—
290	C₂²×C₅	—	2	1	no	—
291	C₂²×C₅	—	4	2	no	—
292	C₂²×C₅	—	4	2	no	—
293	C₂²×C₅	—	4	2	no	—
294	C₂²×C₅	C₃×#124	1	2	yes	—
295	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
296	C₄×C₅	—	2	1	no	—
297	C₄×C₅	—	2	1	no	—
298	C₄×C₅	—	4	4	no	—
299	C₄×C₅	—	4	2	no	—
300	C₄×C₅	C₃×#124	1	2	yes	—
301	C₄×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	—
302	C₄×C₅	C₃×#137	1	2	yes	—
303	C₄×C₅	C₂×C₃×#41	1	2	yes	—
304	#41	—	2	8	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	4	4	no	—
308	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
316	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
317	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
318	M₁₆	—	2	4	no	—
319	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	2	1	no	—
325	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
329	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
330	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
331	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
332	C₃×C₅	#3141	1	1	yes	characteristic, direct product factor, Hall
333	C₂²×C₃	—	2	1	no	—
334	C₂²×C₃	—	2	1	no	—
335	C₂²×C₃	—	4	2	no	—
336	C₂²×C₃	—	4	2	no	—
337	C₂²×C₃	—	4	2	no	—
338	C₂²×C₃	C₅×#124	1	2	yes	—
339	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
340	C₃×C₄	—	2	1	no	—
341	C₃×C₄	—	2	1	no	—
342	C₃×C₄	—	4	2	no	—
343	C₃×C₄	—	4	4	no	—
344	C₃×C₄	C₅×#124	1	2	yes	—
345	C₃×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
346	C₃×C₄	C₅×#137	1	2	yes	—
347	C₃×C₄	C₂×C₅×#41	1	2	yes	—
348	C₂×C₅	—	2	2	no	—
349	C₂×C₅	—	8	2	no	—
350	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
351	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
352	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
353	C₂³	—	2	2	no	—
354	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
355	Q₈	—	2	4	no	—
356	Q₈	—	4	4	no	—
357	Q₈	—	4	4	no	—
358	D₄	—	2	4	no	—
359	D₄	—	4	4	no	—
360	D₄	—	4	2	no	—
361	D₄	—	4	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
369	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
370	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
371	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
372	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
373	C₂×C₄	C₃×C₅×#41	1	4	yes	—
374	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
375	C₈	—	2	4	no	—
376	C₂×C₃	—	2	2	no	—
377	C₂×C₃	—	8	2	no	—
378	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
379	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
380	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
381	C₅	C₃×#3141	1	1	yes	characteristic, direct product factor, Sylow
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	C₃×C₅×#124	1	2	yes	—
388	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	4	no	—
393	C₄	C₃×C₅×#124	1	2	yes	—
394	C₄	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	—
395	C₄	C₃×C₅×#137	1	2	yes	—
396	C₄	C₂×C₃×C₅×#41	1	2	yes	—
397	C₃	C₅×#3141	1	1	yes	characteristic, direct product factor, Sylow
398	C₂	—	2	2	no	—
399	C₂	—	8	2	no	—
400	C₂	C₂×C₃×C₅×#124	1	1	yes	characteristic
401	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
402	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₃×C₅×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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×C₄⋊Q₈	C₂	semidirect
3. C₃×C₅×#489	C₂	semidirect
4. C₃×C₅×#487	C₂	semidirect
5. C₃×C₅×#486	C₂	semidirect
6. C₃×C₅×#417	C₂	semidirect
7. C₃×C₄×C₅×M₁₆	C₂	semidirect
8. C₅×#3141	C₃	direct (N × H)
30. C₃×#3141	C₅	direct (N × H)
32. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
33. C₅×#489	C₂×C₃	semidirect
34. C₅×#487	C₂×C₃	semidirect
35. C₅×#486	C₂×C₃	semidirect
36. C₅×#417	C₂×C₃	semidirect
37. C₄×C₅×M₁₆	C₂×C₃	semidirect
67. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
68. C₃×#489	C₂×C₅	semidirect
69. C₃×#487	C₂×C₅	semidirect
70. C₃×#486	C₂×C₅	semidirect
71. C₃×#417	C₂×C₅	semidirect
72. C₃×C₄×M₁₆	C₂×C₅	semidirect
94. #3141	C₃×C₅	direct (N × H)
168. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
169. #489	C₂×C₃×C₅	semidirect
170. #487	C₂×C₃×C₅	semidirect
171. #486	C₂×C₃×C₅	semidirect
172. #417	C₂×C₃×C₅	semidirect
173. C₄×M₁₆	C₂×C₃×C₅	semidirect
332. C₃×C₅	#3141	direct (N × H)
381. C₅	C₃×#3141	direct (N × H)
397. C₃	C₅×#3141	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#532	2
C₂×C₃×C₅×C₄⋊Q₈	2
C₃×C₅×#489	2
C₃×C₅×#487	2
C₃×C₅×#486	2
C₃×C₅×#417	2
C₃×C₄×C₅×M₁₆	2
C₅×#3141	3
C₃×#3141	5

Subgroups — C3×C5×#3141 #14276175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3141 #14276175