Subgroups — C₃×C₅×#3082 #14276116

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#544	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#519	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#479	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#479	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#477	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#475	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#428	C₂	1	1	yes	maximal, characteristic
8	C₃×C₅×#427	C₂	1	1	yes	maximal, characteristic
9	C₃×C₅×#424	C₂	1	1	yes	maximal, characteristic
10	C₃×C₅×#419	C₂	1	1	yes	maximal, characteristic
11	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic
12	C₅×#3082	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
17	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₃×C₅×#125	—	2	1	no	—
19	C₃×C₅×#125	C₂²	1	2	yes	—
20	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
21	C₃×C₄×C₅×Q₈	—	2	1	no	—
22	C₃×C₄×C₅×Q₈	—	2	1	no	—
23	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
24	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
25	C₃×C₅×#117	—	2	2	no	—
26	C₃×C₅×#117	C₂²	1	1	yes	characteristic
27	C₃×C₅×#117	C₂²	1	1	yes	characteristic
28	C₃×C₅×#117	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₃×C₅×#107	C₂²	1	1	yes	characteristic
31	C₃×C₅×#107	C₂²	1	2	yes	—
32	C₃×C₅×#107	C₂²	1	1	yes	characteristic
33	C₃×C₅×#106	C₂²	1	1	yes	characteristic
34	C₃×C₅×#106	C₂²	1	2	yes	—
35	C₃×C₅×#106	C₂²	1	1	yes	characteristic
36	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
37	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
38	C₃×C₅×#103	C₂²	1	2	yes	—
39	C₃×C₅×#103	C₂²	1	2	yes	—
40	C₃×C₅×#103	C₂²	1	2	yes	—
41	C₃×C₅×#103	C₂²	1	2	yes	—
42	C₃×#3082	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#544	C₂×C₃	1	1	yes	characteristic
44	C₅×#519	C₂×C₃	1	1	yes	characteristic
45	C₅×#479	C₂×C₃	1	2	yes	complemented
46	C₅×#479	C₂×C₃	1	2	yes	complemented
47	C₅×#477	C₂×C₃	1	2	yes	complemented
48	C₅×#475	C₂×C₃	1	2	yes	complemented
49	C₅×#428	C₂×C₃	1	1	yes	characteristic
50	C₅×#427	C₂×C₃	1	1	yes	characteristic
51	C₅×#424	C₂×C₃	1	1	yes	characteristic
52	C₅×#419	C₂×C₃	1	1	yes	characteristic
53	C₂×C₅×#103	C₂×C₃	1	1	yes	characteristic
54	C₂×C₃×C₅×Q₈	—	2	1	no	—
55	C₂×C₃×C₅×Q₈	—	2	2	no	—
56	C₂×C₃×C₅×Q₈	—	2	2	no	—
57	C₂×C₃×C₅×Q₈	Q₈	1	4	yes	complemented
58	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	—	2	1	no	—
60	C₂²×C₃×C₄×C₅	—	2	1	no	—
61	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₃×C₅×M₁₆	—	2	2	no	—
63	C₂×C₃×C₅×C₈	—	2	2	no	—
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
67	C₃×C₅×C₄⋊C₄	—	2	1	no	—
68	C₃×C₅×C₄⋊C₄	—	2	2	no	—
69	C₃×C₅×C₄⋊C₄	—	2	2	no	—
70	C₃×C₅×C₄⋊C₄	—	2	2	no	—
71	C₃×C₅×C₄⋊C₄	—	2	2	no	—
72	C₃×C₅×C₄⋊C₄	—	2	2	no	—
73	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
74	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
75	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
76	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
81	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
82	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
83	C₃×C₄²×C₅	—	2	2	no	—
84	C₃×C₄²×C₅	—	2	2	no	—
85	C₃×C₄²×C₅	—	2	1	no	—
86	C₃×C₄²×C₅	—	2	1	no	—
87	C₃×C₄²×C₅	C₂³	1	2	yes	—
88	C₃×#544	C₂×C₅	1	1	yes	characteristic
89	C₃×#519	C₂×C₅	1	1	yes	characteristic
90	C₃×#479	C₂×C₅	1	2	yes	complemented
91	C₃×#479	C₂×C₅	1	2	yes	complemented
92	C₃×#477	C₂×C₅	1	2	yes	complemented
93	C₃×#475	C₂×C₅	1	2	yes	complemented
94	C₃×#428	C₂×C₅	1	1	yes	characteristic
95	C₃×#427	C₂×C₅	1	1	yes	characteristic
96	C₃×#424	C₂×C₅	1	1	yes	characteristic
97	C₃×#419	C₂×C₅	1	1	yes	characteristic
98	C₂×C₃×#103	C₂×C₅	1	1	yes	characteristic
99	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
101	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
102	C₅×C₄⋊Q₈	—	2	1	no	—
103	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
104	C₅×#125	—	2	1	no	—
105	C₅×#125	C₂²×C₃	1	2	yes	—
106	C₅×C₂²⋊Q₈	—	2	2	no	—
107	C₄×C₅×Q₈	—	2	1	no	—
108	C₄×C₅×Q₈	—	2	1	no	—
109	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
110	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
111	C₅×#117	—	2	2	no	—
112	C₅×#117	C₂²×C₃	1	1	yes	characteristic
113	C₅×#117	C₂²×C₃	1	1	yes	characteristic
114	C₅×#117	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₅×#107	C₂²×C₃	1	1	yes	characteristic
117	C₅×#107	C₂²×C₃	1	1	yes	characteristic
118	C₅×#107	C₂²×C₃	1	2	yes	—
119	C₅×#106	C₂²×C₃	1	1	yes	characteristic
120	C₅×#106	C₂²×C₃	1	1	yes	characteristic
121	C₅×#106	C₂²×C₃	1	2	yes	—
122	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
123	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
124	C₅×#103	C₂²×C₃	1	2	yes	—
125	C₅×#103	C₂²×C₃	1	2	yes	—
126	C₅×#103	C₂²×C₃	1	2	yes	—
127	C₅×#103	C₂²×C₃	1	2	yes	—
128	#3082	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
129	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
130	C₃×C₅×Q₈	—	2	4	no	—
131	C₃×C₅×Q₈	—	2	2	no	—
132	C₃×C₅×Q₈	—	8	2	no	—
133	C₃×C₅×Q₈	C₂×Q₈	1	4	yes	—
134	C₂×C₃×C₄×C₅	—	2	4	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	1	no	—
137	C₂×C₃×C₄×C₅	—	2	1	no	—
138	C₂×C₃×C₄×C₅	—	2	1	no	—
139	C₂×C₃×C₄×C₅	—	2	1	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	8	1	no	—
142	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
143	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
144	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
146	C₂×C₃×C₄×C₅	#41	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₃×C₅×C₈	—	2	1	no	—
149	C₃×C₅×C₈	—	2	1	no	—
150	C₃×C₅×C₈	—	2	2	no	—
151	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
153	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
154	C₃×C₄⋊Q₈	—	2	1	no	—
155	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
156	C₃×#125	—	2	1	no	—
157	C₃×#125	C₂²×C₅	1	2	yes	—
158	C₃×C₂²⋊Q₈	—	2	2	no	—
159	C₃×C₄×Q₈	—	2	1	no	—
160	C₃×C₄×Q₈	—	2	1	no	—
161	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
162	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
163	C₃×#117	—	2	2	no	—
164	C₃×#117	C₂²×C₅	1	1	yes	characteristic
165	C₃×#117	C₂²×C₅	1	1	yes	characteristic
166	C₃×#117	C₂²×C₅	1	1	yes	characteristic
167	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
168	C₃×#107	C₂²×C₅	1	1	yes	characteristic
169	C₃×#107	C₂²×C₅	1	1	yes	characteristic
170	C₃×#107	C₂²×C₅	1	2	yes	—
171	C₃×#106	C₂²×C₅	1	1	yes	characteristic
172	C₃×#106	C₂²×C₅	1	1	yes	characteristic
173	C₃×#106	C₂²×C₅	1	2	yes	—
174	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
175	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
176	C₃×#103	C₂²×C₅	1	2	yes	—
177	C₃×#103	C₂²×C₅	1	2	yes	—
178	C₃×#103	C₂²×C₅	1	2	yes	—
179	C₃×#103	C₂²×C₅	1	2	yes	—
180	C₂×C₅×Q₈	—	2	1	no	—
181	C₂×C₅×Q₈	—	2	2	no	—
182	C₂×C₅×Q₈	—	2	2	no	—
183	C₂×C₅×Q₈	C₃×Q₈	1	4	yes	complemented
184	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
185	C₂²×C₄×C₅	—	2	1	no	—
186	C₂²×C₄×C₅	—	2	1	no	—
187	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
188	C₅×M₁₆	—	2	2	no	—
189	C₂×C₅×C₈	—	2	2	no	—
190	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
192	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
193	C₅×C₄⋊C₄	—	2	1	no	—
194	C₅×C₄⋊C₄	—	2	2	no	—
195	C₅×C₄⋊C₄	—	2	2	no	—
196	C₅×C₄⋊C₄	—	2	2	no	—
197	C₅×C₄⋊C₄	—	2	2	no	—
198	C₅×C₄⋊C₄	—	2	2	no	—
199	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
200	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
201	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
202	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
203	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
204	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
205	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
206	C₅×C₂²⋊C₄	—	2	1	no	—
207	C₅×C₂²⋊C₄	—	2	1	no	—
208	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
209	C₄²×C₅	—	2	2	no	—
210	C₄²×C₅	—	2	2	no	—
211	C₄²×C₅	—	2	1	no	—
212	C₄²×C₅	—	2	1	no	—
213	C₄²×C₅	C₂³×C₃	1	2	yes	—
214	#544	C₂×C₃×C₅	1	1	yes	characteristic
215	#519	C₂×C₃×C₅	1	1	yes	characteristic
216	#479	C₂×C₃×C₅	1	2	yes	complemented
217	#479	C₂×C₃×C₅	1	2	yes	complemented
218	#477	C₂×C₃×C₅	1	2	yes	complemented
219	#475	C₂×C₃×C₅	1	2	yes	complemented
220	#428	C₂×C₃×C₅	1	1	yes	characteristic
221	#427	C₂×C₃×C₅	1	1	yes	characteristic
222	#424	C₂×C₃×C₅	1	1	yes	characteristic
223	#419	C₂×C₃×C₅	1	1	yes	characteristic
224	C₂×#103	C₂×C₃×C₅	1	1	yes	characteristic
225	C₂²×C₃×C₅	—	2	1	no	—
226	C₂²×C₃×C₅	—	2	1	no	—
227	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
228	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
229	C₃×C₄×C₅	—	2	4	no	—
230	C₃×C₄×C₅	—	2	2	no	—
231	C₃×C₄×C₅	—	2	2	no	—
232	C₃×C₄×C₅	—	4	1	no	—
233	C₃×C₄×C₅	—	4	2	no	—
234	C₃×C₄×C₅	—	4	1	no	—
235	C₃×C₄×C₅	—	4	1	no	—
236	C₃×C₄×C₅	—	4	1	no	—
237	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
238	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
239	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
240	C₂×C₃×Q₈	—	2	1	no	—
241	C₂×C₃×Q₈	—	2	2	no	—
242	C₂×C₃×Q₈	—	2	2	no	—
243	C₂×C₃×Q₈	C₅×Q₈	1	4	yes	complemented
244	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
245	C₂²×C₃×C₄	—	2	1	no	—
246	C₂²×C₃×C₄	—	2	1	no	—
247	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
248	C₃×M₁₆	—	2	2	no	—
249	C₂×C₃×C₈	—	2	2	no	—
250	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
251	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
252	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
253	C₃×C₄⋊C₄	—	2	1	no	—
254	C₃×C₄⋊C₄	—	2	2	no	—
255	C₃×C₄⋊C₄	—	2	2	no	—
256	C₃×C₄⋊C₄	—	2	2	no	—
257	C₃×C₄⋊C₄	—	2	2	no	—
258	C₃×C₄⋊C₄	—	2	2	no	—
259	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
260	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
261	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
262	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
263	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
264	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
265	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
266	C₃×C₂²⋊C₄	—	2	1	no	—
267	C₃×C₂²⋊C₄	—	2	1	no	—
268	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
269	C₃×C₄²	—	2	2	no	—
270	C₃×C₄²	—	2	2	no	—
271	C₃×C₄²	—	2	1	no	—
272	C₃×C₄²	—	2	1	no	—
273	C₃×C₄²	C₂³×C₅	1	2	yes	—
274	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
275	C₅×Q₈	—	2	4	no	—
276	C₅×Q₈	—	2	2	no	—
277	C₅×Q₈	—	8	2	no	—
278	C₅×Q₈	C₂×C₃×Q₈	1	4	yes	—
279	C₂×C₄×C₅	—	2	4	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	1	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	8	1	no	—
287	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
288	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
289	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
290	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
291	C₂×C₄×C₅	C₃×#41	1	2	yes	—
292	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
293	C₅×C₈	—	2	1	no	—
294	C₅×C₈	—	2	1	no	—
295	C₅×C₈	—	2	2	no	—
296	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
297	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
298	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
299	C₄⋊Q₈	—	2	1	no	—
300	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
301	#125	—	2	1	no	—
302	#125	C₂²×C₃×C₅	1	2	yes	—
303	C₂²⋊Q₈	—	2	2	no	—
304	C₄×Q₈	—	2	1	no	—
305	C₄×Q₈	—	2	1	no	—
306	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
307	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
308	#117	—	2	2	no	—
309	#117	C₂²×C₃×C₅	1	1	yes	characteristic
310	#117	C₂²×C₃×C₅	1	1	yes	characteristic
311	#117	C₂²×C₃×C₅	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
313	#107	C₂²×C₃×C₅	1	1	yes	characteristic
314	#107	C₂²×C₃×C₅	1	1	yes	characteristic
315	#107	C₂²×C₃×C₅	1	2	yes	—
316	#106	C₂²×C₃×C₅	1	1	yes	characteristic
317	#106	C₂²×C₃×C₅	1	1	yes	characteristic
318	#106	C₂²×C₃×C₅	1	2	yes	—
319	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
320	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
321	#103	C₂²×C₃×C₅	1	2	yes	—
322	#103	C₂²×C₃×C₅	1	2	yes	—
323	#103	C₂²×C₃×C₅	1	2	yes	—
324	#103	C₂²×C₃×C₅	1	2	yes	—
325	C₂×C₃×C₅	—	2	2	no	—
326	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
327	C₂×C₃×C₅	#577	1	1	yes	characteristic
328	C₂×C₃×C₅	#578	1	1	yes	characteristic
329	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
330	C₃×Q₈	—	2	4	no	—
331	C₃×Q₈	—	2	2	no	—
332	C₃×Q₈	—	8	2	no	—
333	C₃×Q₈	C₂×C₅×Q₈	1	4	yes	—
334	C₂×C₃×C₄	—	2	4	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	2	1	no	—
337	C₂×C₃×C₄	—	2	1	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	1	no	—
340	C₂×C₃×C₄	—	2	2	no	—
341	C₂×C₃×C₄	—	8	1	no	—
342	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
343	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
344	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
346	C₂×C₃×C₄	C₅×#41	1	2	yes	—
347	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
348	C₃×C₈	—	2	1	no	—
349	C₃×C₈	—	2	1	no	—
350	C₃×C₈	—	2	2	no	—
351	C₂²×C₅	—	2	1	no	—
352	C₂²×C₅	—	2	1	no	—
353	C₂²×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
354	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
355	C₄×C₅	—	2	2	no	—
356	C₄×C₅	—	2	2	no	—
357	C₄×C₅	—	2	4	no	—
358	C₄×C₅	—	4	1	no	—
359	C₄×C₅	—	4	2	no	—
360	C₄×C₅	—	4	1	no	—
361	C₄×C₅	—	4	1	no	—
362	C₄×C₅	—	4	1	no	—
363	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
364	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
365	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	C₃×C₅×Q₈	1	4	yes	complemented
370	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
374	M₁₆	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
377	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
378	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
386	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
387	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
388	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
389	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
390	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
391	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	2	1	no	—
394	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	2	1	no	—
399	C₄²	C₂³×C₃×C₅	1	2	yes	—
400	C₃×C₅	#3082	1	1	yes	characteristic, direct product factor, Hall
401	C₂²×C₃	—	2	1	no	—
402	C₂²×C₃	—	2	1	no	—
403	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
404	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
405	C₃×C₄	—	2	4	no	—
406	C₃×C₄	—	2	2	no	—
407	C₃×C₄	—	2	2	no	—
408	C₃×C₄	—	4	1	no	—
409	C₃×C₄	—	4	2	no	—
410	C₃×C₄	—	4	1	no	—
411	C₃×C₄	—	4	1	no	—
412	C₃×C₄	—	4	1	no	—
413	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
414	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
415	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
416	C₂×C₅	—	2	2	no	—
417	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
418	C₂×C₅	C₃×#577	1	1	yes	characteristic
419	C₂×C₅	C₃×#578	1	1	yes	characteristic
420	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
421	Q₈	—	2	4	no	—
422	Q₈	—	2	2	no	—
423	Q₈	—	8	2	no	—
424	Q₈	C₂×C₃×C₅×Q₈	1	4	yes	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	8	1	no	—
433	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
434	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
435	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
436	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
437	C₂×C₄	C₃×C₅×#41	1	2	yes	—
438	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
439	C₈	—	2	1	no	—
440	C₈	—	2	1	no	—
441	C₈	—	2	2	no	—
442	C₂×C₃	—	2	2	no	—
443	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
444	C₂×C₃	C₅×#577	1	1	yes	characteristic
445	C₂×C₃	C₅×#578	1	1	yes	characteristic
446	C₅	C₃×#3082	1	1	yes	characteristic, direct product factor, Sylow
447	C₂²	—	2	1	no	—
448	C₂²	—	2	1	no	—
449	C₂²	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
450	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
451	C₄	—	2	4	no	—
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	1	no	—
458	C₄	—	4	1	no	—
459	C₄	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
460	C₄	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
461	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
462	C₃	C₅×#3082	1	1	yes	characteristic, direct product factor, Sylow
463	C₂	—	2	2	no	—
464	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
465	C₂	C₃×C₅×#577	1	1	yes	characteristic
466	C₂	C₃×C₅×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂³×C₃×C₅	C₂×D₄
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
3. C₃×C₅×#479	C₂	semidirect
4. C₃×C₅×#479	C₂	semidirect
5. C₃×C₅×#477	C₂	semidirect
6. C₃×C₅×#475	C₂	semidirect
12. C₅×#3082	C₃	direct (N × H)
42. C₃×#3082	C₅	direct (N × H)
45. C₅×#479	C₂×C₃	semidirect
46. C₅×#479	C₂×C₃	semidirect
47. C₅×#477	C₂×C₃	semidirect
48. C₅×#475	C₂×C₃	semidirect
57. C₂×C₃×C₅×Q₈	Q₈	semidirect
90. C₃×#479	C₂×C₅	semidirect
91. C₃×#479	C₂×C₅	semidirect
92. C₃×#477	C₂×C₅	semidirect
93. C₃×#475	C₂×C₅	semidirect
128. #3082	C₃×C₅	direct (N × H)
183. C₂×C₅×Q₈	C₃×Q₈	semidirect
216. #479	C₂×C₃×C₅	semidirect
217. #479	C₂×C₃×C₅	semidirect
218. #477	C₂×C₃×C₅	semidirect
219. #475	C₂×C₃×C₅	semidirect
243. C₂×C₃×Q₈	C₅×Q₈	semidirect
369. C₂×Q₈	C₃×C₅×Q₈	semidirect
400. C₃×C₅	#3082	direct (N × H)
446. C₅	C₃×#3082	direct (N × H)
462. C₃	C₅×#3082	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×#544	2
C₃×C₅×#519	2
C₃×C₅×#479	2
C₃×C₅×#477	2
C₃×C₅×#475	2
C₃×C₅×#428	2
C₃×C₅×#427	2
C₃×C₅×#424	2
C₃×C₅×#419	2
C₂×C₃×C₅×#103	2
C₅×#3082	3
C₃×#3082	5

Subgroups — C3×C5×#3082 #14276116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3082 #14276116