Subgroups — C₃×C₅×#3076 #14276110

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#479	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#478	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#477	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#475	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#474	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#427	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#416	C₂	1	2	yes	maximal
12	C₅×#3076	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×#125	C₂²	1	2	yes	—
18	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
19	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
20	C₃×C₄×C₅×Q₈	—	2	1	no	—
21	C₃×C₄×C₅×Q₈	—	2	1	no	—
22	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
24	C₃×C₄×C₅×D₄	—	2	1	no	—
25	C₃×C₄×C₅×D₄	—	2	1	no	—
26	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
28	C₃×C₅×#117	—	2	1	no	—
29	C₃×C₅×#117	C₂²	1	1	yes	characteristic
30	C₃×C₅×#117	C₂²	1	2	yes	—
31	C₂×C₃×C₄²×C₅	—	2	1	no	—
32	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
33	C₃×C₅×#107	C₂²	1	2	yes	—
34	C₃×C₅×#107	C₂²	1	2	yes	—
35	C₃×C₅×#106	C₂²	1	2	yes	—
36	C₃×C₅×#106	C₂²	1	2	yes	—
37	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
40	C₃×C₅×#103	C₂²	1	2	yes	—
41	C₃×C₅×#103	C₂²	1	2	yes	—
42	C₃×C₅×#102	C₂²	1	2	yes	—
43	C₃×C₅×#102	C₂²	1	2	yes	—
44	C₃×#3076	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₅×#533	C₂×C₃	1	1	yes	characteristic, complemented
46	C₄×C₅×#41	C₂×C₃	1	1	yes	characteristic
47	C₅×#479	C₂×C₃	1	2	yes	complemented
48	C₅×#478	C₂×C₃	1	2	yes	complemented
49	C₅×#477	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#476	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#475	C₂×C₃	1	1	yes	characteristic, complemented
52	C₅×#474	C₂×C₃	1	1	yes	characteristic, complemented
53	C₅×#427	C₂×C₃	1	2	yes	complemented
54	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
55	C₅×#416	C₂×C₃	1	2	yes	—
56	C₃×C₅×#41	—	2	2	no	—
57	C₃×C₅×#41	Q₈	1	4	yes	complemented
58	C₂×C₃×C₅×Q₈	—	2	1	no	—
59	C₂×C₃×C₅×Q₈	—	2	1	no	—
60	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₅×D₄	—	2	1	no	—
62	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	—	2	1	no	—
64	C₂²×C₃×C₄×C₅	—	2	1	no	—
65	C₂²×C₃×C₄×C₅	—	2	1	no	—
66	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₅×C₈	—	2	4	no	—
70	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
71	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
72	C₃×C₅×C₄⋊C₄	—	2	1	no	—
73	C₃×C₅×C₄⋊C₄	—	2	1	no	—
74	C₃×C₅×C₄⋊C₄	—	2	2	no	—
75	C₃×C₅×C₄⋊C₄	—	2	2	no	—
76	C₃×C₅×C₄⋊C₄	—	2	1	no	—
77	C₃×C₅×C₄⋊C₄	—	2	1	no	—
78	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
81	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
82	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
83	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
84	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
85	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
86	C₃×C₄²×C₅	—	2	1	no	—
87	C₃×C₄²×C₅	—	2	1	no	—
88	C₃×C₄²×C₅	—	2	1	no	—
89	C₃×C₄²×C₅	—	2	2	no	—
90	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
91	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
92	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
93	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
94	C₃×#533	C₂×C₅	1	1	yes	characteristic, complemented
95	C₃×C₄×#41	C₂×C₅	1	1	yes	characteristic
96	C₃×#479	C₂×C₅	1	2	yes	complemented
97	C₃×#478	C₂×C₅	1	2	yes	complemented
98	C₃×#477	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#476	C₂×C₅	1	1	yes	characteristic, complemented
100	C₃×#475	C₂×C₅	1	1	yes	characteristic, complemented
101	C₃×#474	C₂×C₅	1	1	yes	characteristic, complemented
102	C₃×#427	C₂×C₅	1	2	yes	complemented
103	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
104	C₃×#416	C₂×C₅	1	2	yes	—
105	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
106	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
107	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
108	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
109	C₅×#125	C₂²×C₃	1	2	yes	—
110	C₅×C₂²⋊Q₈	—	2	1	no	—
111	C₅×C₂²⋊Q₈	—	2	1	no	—
112	C₄×C₅×Q₈	—	2	1	no	—
113	C₄×C₅×Q₈	—	2	1	no	—
114	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
115	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
116	C₄×C₅×D₄	—	2	1	no	—
117	C₄×C₅×D₄	—	2	1	no	—
118	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
119	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
120	C₅×#117	—	2	1	no	—
121	C₅×#117	C₂²×C₃	1	2	yes	—
122	C₅×#117	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₄²×C₅	—	2	1	no	—
124	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
125	C₅×#107	C₂²×C₃	1	2	yes	—
126	C₅×#107	C₂²×C₃	1	2	yes	—
127	C₅×#106	C₂²×C₃	1	2	yes	—
128	C₅×#106	C₂²×C₃	1	2	yes	—
129	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
130	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
131	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
132	C₅×#103	C₂²×C₃	1	2	yes	—
133	C₅×#103	C₂²×C₃	1	2	yes	—
134	C₅×#102	C₂²×C₃	1	2	yes	—
135	C₅×#102	C₂²×C₃	1	2	yes	—
136	#3076	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
137	C₂³×C₃×C₅	—	2	1	no	—
138	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
139	C₃×C₅×Q₈	—	2	1	no	—
140	C₃×C₅×Q₈	—	4	2	no	—
141	C₃×C₅×Q₈	—	4	2	no	—
142	C₃×C₅×Q₈	C₂×Q₈	1	2	yes	—
143	C₃×C₅×D₄	—	2	4	no	—
144	C₃×C₅×D₄	—	2	1	no	—
145	C₃×C₅×D₄	C₂×Q₈	1	2	yes	—
146	C₂×C₃×C₄×C₅	—	2	1	no	—
147	C₂×C₃×C₄×C₅	—	2	4	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	—	4	1	no	—
154	C₂×C₃×C₄×C₅	—	4	2	no	—
155	C₂×C₃×C₄×C₅	—	4	2	no	—
156	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
158	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
159	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
161	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
162	C₂×C₃×C₄×C₅	#41	1	2	yes	—
163	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
164	C₃×C₅×C₈	—	2	2	no	—
165	C₃×C₅×C₈	—	2	2	no	—
166	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
167	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
168	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
169	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
170	C₃×#125	C₂²×C₅	1	2	yes	—
171	C₃×C₂²⋊Q₈	—	2	1	no	—
172	C₃×C₂²⋊Q₈	—	2	1	no	—
173	C₃×C₄×Q₈	—	2	1	no	—
174	C₃×C₄×Q₈	—	2	1	no	—
175	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
176	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
177	C₃×C₄×D₄	—	2	1	no	—
178	C₃×C₄×D₄	—	2	1	no	—
179	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
180	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
181	C₃×#117	—	2	1	no	—
182	C₃×#117	C₂²×C₅	1	2	yes	—
183	C₃×#117	C₂²×C₅	1	1	yes	characteristic
184	C₂×C₃×C₄²	—	2	1	no	—
185	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
186	C₃×#107	C₂²×C₅	1	2	yes	—
187	C₃×#107	C₂²×C₅	1	2	yes	—
188	C₃×#106	C₂²×C₅	1	2	yes	—
189	C₃×#106	C₂²×C₅	1	2	yes	—
190	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
191	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
192	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
193	C₃×#103	C₂²×C₅	1	2	yes	—
194	C₃×#103	C₂²×C₅	1	2	yes	—
195	C₃×#102	C₂²×C₅	1	2	yes	—
196	C₃×#102	C₂²×C₅	1	2	yes	—
197	C₅×#41	—	2	2	no	—
198	C₅×#41	C₃×Q₈	1	4	yes	complemented
199	C₂×C₅×Q₈	—	2	1	no	—
200	C₂×C₅×Q₈	—	2	1	no	—
201	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
202	C₂×C₅×D₄	—	2	1	no	—
203	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
204	C₂²×C₄×C₅	—	2	1	no	—
205	C₂²×C₄×C₅	—	2	1	no	—
206	C₂²×C₄×C₅	—	2	1	no	—
207	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
208	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
210	C₂×C₅×C₈	—	2	4	no	—
211	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
212	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
213	C₅×C₄⋊C₄	—	2	1	no	—
214	C₅×C₄⋊C₄	—	2	1	no	—
215	C₅×C₄⋊C₄	—	2	2	no	—
216	C₅×C₄⋊C₄	—	2	2	no	—
217	C₅×C₄⋊C₄	—	2	1	no	—
218	C₅×C₄⋊C₄	—	2	1	no	—
219	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
220	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
221	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
222	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
223	C₅×C₂²⋊C₄	—	2	1	no	—
224	C₅×C₂²⋊C₄	—	2	2	no	—
225	C₅×C₂²⋊C₄	—	2	1	no	—
226	C₅×C₂²⋊C₄	—	2	1	no	—
227	C₄²×C₅	—	2	1	no	—
228	C₄²×C₅	—	2	1	no	—
229	C₄²×C₅	—	2	1	no	—
230	C₄²×C₅	—	2	2	no	—
231	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
232	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
233	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
234	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
235	#533	C₂×C₃×C₅	1	1	yes	characteristic, complemented
236	C₄×#41	C₂×C₃×C₅	1	1	yes	characteristic
237	#479	C₂×C₃×C₅	1	2	yes	complemented
238	#478	C₂×C₃×C₅	1	2	yes	complemented
239	#477	C₂×C₃×C₅	1	1	yes	characteristic, complemented
240	#476	C₂×C₃×C₅	1	1	yes	characteristic, complemented
241	#475	C₂×C₃×C₅	1	1	yes	characteristic, complemented
242	#474	C₂×C₃×C₅	1	1	yes	characteristic, complemented
243	#427	C₂×C₃×C₅	1	2	yes	complemented
244	C₂×C₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
245	#416	C₂×C₃×C₅	1	2	yes	—
246	C₂²×C₃×C₅	—	2	1	no	—
247	C₂²×C₃×C₅	—	2	1	no	—
248	C₂²×C₃×C₅	—	2	2	no	—
249	C₂²×C₃×C₅	—	4	1	no	—
250	C₂²×C₃×C₅	—	4	1	no	—
251	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
252	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
253	C₃×C₄×C₅	—	2	2	no	—
254	C₃×C₄×C₅	—	2	1	no	—
255	C₃×C₄×C₅	—	2	1	no	—
256	C₃×C₄×C₅	—	2	1	no	—
257	C₃×C₄×C₅	—	4	1	no	—
258	C₃×C₄×C₅	—	4	2	no	—
259	C₃×C₄×C₅	—	4	1	no	—
260	C₃×C₄×C₅	—	4	2	no	—
261	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
262	C₃×C₄×C₅	#135	1	2	yes	—
263	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
264	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
265	C₃×#41	—	2	2	no	—
266	C₃×#41	C₅×Q₈	1	4	yes	complemented
267	C₂×C₃×Q₈	—	2	1	no	—
268	C₂×C₃×Q₈	—	2	1	no	—
269	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
270	C₂×C₃×D₄	—	2	1	no	—
271	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
272	C₂²×C₃×C₄	—	2	1	no	—
273	C₂²×C₃×C₄	—	2	1	no	—
274	C₂²×C₃×C₄	—	2	1	no	—
275	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
276	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
277	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
278	C₂×C₃×C₈	—	2	4	no	—
279	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
280	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
281	C₃×C₄⋊C₄	—	2	1	no	—
282	C₃×C₄⋊C₄	—	2	1	no	—
283	C₃×C₄⋊C₄	—	2	2	no	—
284	C₃×C₄⋊C₄	—	2	2	no	—
285	C₃×C₄⋊C₄	—	2	1	no	—
286	C₃×C₄⋊C₄	—	2	1	no	—
287	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
288	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
289	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
290	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
291	C₃×C₂²⋊C₄	—	2	1	no	—
292	C₃×C₂²⋊C₄	—	2	2	no	—
293	C₃×C₂²⋊C₄	—	2	1	no	—
294	C₃×C₂²⋊C₄	—	2	1	no	—
295	C₃×C₄²	—	2	1	no	—
296	C₃×C₄²	—	2	1	no	—
297	C₃×C₄²	—	2	1	no	—
298	C₃×C₄²	—	2	2	no	—
299	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
300	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
301	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
302	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
303	C₂³×C₅	—	2	1	no	—
304	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
305	C₅×Q₈	—	2	1	no	—
306	C₅×Q₈	—	4	2	no	—
307	C₅×Q₈	—	4	2	no	—
308	C₅×Q₈	C₂×C₃×Q₈	1	2	yes	—
309	C₅×D₄	—	2	4	no	—
310	C₅×D₄	—	2	1	no	—
311	C₅×D₄	C₂×C₃×Q₈	1	2	yes	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	4	no	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	2	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	4	1	no	—
320	C₂×C₄×C₅	—	4	2	no	—
321	C₂×C₄×C₅	—	4	2	no	—
322	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
323	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
324	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
325	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
326	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
327	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
328	C₂×C₄×C₅	C₃×#41	1	2	yes	—
329	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
330	C₅×C₈	—	2	2	no	—
331	C₅×C₈	—	2	2	no	—
332	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
333	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
334	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
335	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
336	#125	C₂²×C₃×C₅	1	2	yes	—
337	C₂²⋊Q₈	—	2	1	no	—
338	C₂²⋊Q₈	—	2	1	no	—
339	C₄×Q₈	—	2	1	no	—
340	C₄×Q₈	—	2	1	no	—
341	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
342	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
343	C₄×D₄	—	2	1	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
346	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
347	#117	—	2	1	no	—
348	#117	C₂²×C₃×C₅	1	1	yes	characteristic
349	#117	C₂²×C₃×C₅	1	2	yes	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
352	#107	C₂²×C₃×C₅	1	2	yes	—
353	#107	C₂²×C₃×C₅	1	2	yes	—
354	#106	C₂²×C₃×C₅	1	2	yes	—
355	#106	C₂²×C₃×C₅	1	2	yes	—
356	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
357	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
358	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
359	#103	C₂²×C₃×C₅	1	2	yes	—
360	#103	C₂²×C₃×C₅	1	2	yes	—
361	#102	C₂²×C₃×C₅	1	2	yes	—
362	#102	C₂²×C₃×C₅	1	2	yes	—
363	C₂×C₃×C₅	—	2	2	no	—
364	C₂×C₃×C₅	—	4	2	no	—
365	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
366	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
367	C₂×C₃×C₅	#575	1	1	yes	characteristic
368	C₂³×C₃	—	2	1	no	—
369	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
370	C₃×Q₈	—	2	1	no	—
371	C₃×Q₈	—	4	2	no	—
372	C₃×Q₈	—	4	2	no	—
373	C₃×Q₈	C₂×C₅×Q₈	1	2	yes	—
374	C₃×D₄	—	2	4	no	—
375	C₃×D₄	—	2	1	no	—
376	C₃×D₄	C₂×C₅×Q₈	1	2	yes	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	4	no	—
379	C₂×C₃×C₄	—	2	2	no	—
380	C₂×C₃×C₄	—	2	1	no	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	—	2	2	no	—
384	C₂×C₃×C₄	—	4	1	no	—
385	C₂×C₃×C₄	—	4	2	no	—
386	C₂×C₃×C₄	—	4	2	no	—
387	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
388	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
389	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
390	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
391	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
392	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
393	C₂×C₃×C₄	C₅×#41	1	2	yes	—
394	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
395	C₃×C₈	—	2	2	no	—
396	C₃×C₈	—	2	2	no	—
397	C₂²×C₅	—	2	1	no	—
398	C₂²×C₅	—	2	1	no	—
399	C₂²×C₅	—	2	2	no	—
400	C₂²×C₅	—	4	1	no	—
401	C₂²×C₅	—	4	1	no	—
402	C₂²×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
403	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
404	C₄×C₅	—	2	1	no	—
405	C₄×C₅	—	2	1	no	—
406	C₄×C₅	—	2	1	no	—
407	C₄×C₅	—	2	2	no	—
408	C₄×C₅	—	4	1	no	—
409	C₄×C₅	—	4	2	no	—
410	C₄×C₅	—	4	1	no	—
411	C₄×C₅	—	4	2	no	—
412	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
413	C₄×C₅	C₃×#135	1	2	yes	—
414	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
415	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
416	#41	—	2	2	no	—
417	#41	C₃×C₅×Q₈	1	4	yes	complemented
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
427	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
428	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
429	C₂×C₈	—	2	4	no	—
430	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
431	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
439	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
440	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
441	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	2	2	no	—
444	C₂²⋊C₄	—	2	1	no	—
445	C₂²⋊C₄	—	2	1	no	—
446	C₄²	—	2	1	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₄²	—	2	2	no	—
450	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
451	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
452	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
453	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
454	C₃×C₅	#3076	1	1	yes	characteristic, direct product factor, Hall
455	C₂²×C₃	—	2	1	no	—
456	C₂²×C₃	—	2	1	no	—
457	C₂²×C₃	—	2	2	no	—
458	C₂²×C₃	—	4	1	no	—
459	C₂²×C₃	—	4	1	no	—
460	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
461	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
462	C₃×C₄	—	2	2	no	—
463	C₃×C₄	—	2	1	no	—
464	C₃×C₄	—	2	1	no	—
465	C₃×C₄	—	2	1	no	—
466	C₃×C₄	—	4	1	no	—
467	C₃×C₄	—	4	2	no	—
468	C₃×C₄	—	4	1	no	—
469	C₃×C₄	—	4	2	no	—
470	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
471	C₃×C₄	C₅×#135	1	2	yes	—
472	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
473	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
474	C₂×C₅	—	2	2	no	—
475	C₂×C₅	—	4	2	no	—
476	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
477	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
478	C₂×C₅	C₃×#575	1	1	yes	characteristic
479	C₂³	—	2	1	no	—
480	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
481	Q₈	—	2	1	no	—
482	Q₈	—	4	2	no	—
483	Q₈	—	4	2	no	—
484	Q₈	C₂×C₃×C₅×Q₈	1	2	yes	—
485	D₄	—	2	4	no	—
486	D₄	—	2	1	no	—
487	D₄	C₂×C₃×C₅×Q₈	1	2	yes	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
499	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
500	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
501	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
502	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
503	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
504	C₂×C₄	C₃×C₅×#41	1	2	yes	—
505	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
506	C₈	—	2	2	no	—
507	C₈	—	2	2	no	—
508	C₂×C₃	—	2	2	no	—
509	C₂×C₃	—	4	2	no	—
510	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
511	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
512	C₂×C₃	C₅×#575	1	1	yes	characteristic
513	C₅	C₃×#3076	1	1	yes	characteristic, direct product factor, Sylow
514	C₂²	—	2	1	no	—
515	C₂²	—	2	1	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	1	no	—
519	C₂²	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
520	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
521	C₄	—	2	2	no	—
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	4	1	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	2	no	—
529	C₄	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
530	C₄	C₃×C₅×#135	1	2	yes	—
531	C₄	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
532	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
533	C₃	C₅×#3076	1	1	yes	characteristic, direct product factor, Sylow
534	C₂	—	2	2	no	—
535	C₂	—	4	2	no	—
536	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
537	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
538	C₂	C₃×C₅×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#533	C₂	semidirect
3. C₃×C₅×#479	C₂	semidirect
4. C₃×C₅×#478	C₂	semidirect
5. C₃×C₅×#477	C₂	semidirect
6. C₃×C₅×#476	C₂	semidirect
7. C₃×C₅×#475	C₂	semidirect
8. C₃×C₅×#474	C₂	semidirect
9. C₃×C₅×#427	C₂	semidirect
10. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
12. C₅×#3076	C₃	direct (N × H)
44. C₃×#3076	C₅	direct (N × H)
45. C₅×#533	C₂×C₃	semidirect
47. C₅×#479	C₂×C₃	semidirect
48. C₅×#478	C₂×C₃	semidirect
49. C₅×#477	C₂×C₃	semidirect
50. C₅×#476	C₂×C₃	semidirect
51. C₅×#475	C₂×C₃	semidirect
52. C₅×#474	C₂×C₃	semidirect
53. C₅×#427	C₂×C₃	semidirect
54. C₂×C₅×C₄⋊C₈	C₂×C₃	semidirect
57. C₃×C₅×#41	Q₈	semidirect
94. C₃×#533	C₂×C₅	semidirect
96. C₃×#479	C₂×C₅	semidirect
97. C₃×#478	C₂×C₅	semidirect
98. C₃×#477	C₂×C₅	semidirect
99. C₃×#476	C₂×C₅	semidirect
100. C₃×#475	C₂×C₅	semidirect
101. C₃×#474	C₂×C₅	semidirect
102. C₃×#427	C₂×C₅	semidirect
103. C₂×C₃×C₄⋊C₈	C₂×C₅	semidirect
136. #3076	C₃×C₅	direct (N × H)
198. C₅×#41	C₃×Q₈	semidirect
235. #533	C₂×C₃×C₅	semidirect
237. #479	C₂×C₃×C₅	semidirect
238. #478	C₂×C₃×C₅	semidirect
239. #477	C₂×C₃×C₅	semidirect
240. #476	C₂×C₃×C₅	semidirect
241. #475	C₂×C₃×C₅	semidirect
242. #474	C₂×C₃×C₅	semidirect
243. #427	C₂×C₃×C₅	semidirect
244. C₂×C₄⋊C₈	C₂×C₃×C₅	semidirect
266. C₃×#41	C₅×Q₈	semidirect
417. #41	C₃×C₅×Q₈	semidirect
454. C₃×C₅	#3076	direct (N × H)
513. C₅	C₃×#3076	direct (N × H)
533. C₃	C₅×#3076	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×#533	2
C₃×C₄×C₅×#41	2
C₃×C₅×#479	2
C₃×C₅×#478	2
C₃×C₅×#477	2
C₃×C₅×#476	2
C₃×C₅×#475	2
C₃×C₅×#474	2
C₃×C₅×#427	2
C₂×C₃×C₅×C₄⋊C₈	2
C₃×C₅×#416	2
C₅×#3076	3
C₃×#3076	5

Subgroups — C3×C5×#3076 #14276110

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3076 #14276110