Subgroups — C₃×C₅×#3078 #14276112

Order 1920.

752 conjugacy classes of subgroups.

The subgroup lattice has 428 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
2	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#479	C₂	1	4	yes	maximal, complemented
4	C₃×C₅×#477	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#475	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#428	C₂	1	2	yes	maximal
7	C₃×C₅×#423	C₂	1	1	yes	maximal, characteristic
8	C₃×C₅×#419	C₂	1	2	yes	maximal
9	C₅×#3078	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
12	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×#125	C₂²	1	2	yes	—
15	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
16	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
17	C₃×C₄×C₅×Q₈	—	2	1	no	—
18	C₃×C₄×C₅×Q₈	—	2	1	no	—
19	C₃×C₄×C₅×Q₈	—	2	1	no	—
20	C₃×C₄×C₅×Q₈	—	2	1	no	—
21	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
22	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
23	C₃×C₅×#117	C₂²	1	2	yes	—
24	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄²×C₅	—	2	1	no	—
27	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₃×C₅×#107	C₂²	1	4	yes	—
29	C₃×C₅×#106	C₂²	1	4	yes	—
30	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
31	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
32	C₃×C₅×#103	C₂²	1	4	yes	—
33	C₃×C₅×#103	C₂²	1	4	yes	—
34	C₃×#3078	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
35	C₅×#533	C₂×C₃	1	1	yes	characteristic
36	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic
37	C₅×#479	C₂×C₃	1	4	yes	complemented
38	C₅×#477	C₂×C₃	1	2	yes	complemented
39	C₅×#475	C₂×C₃	1	2	yes	complemented
40	C₅×#428	C₂×C₃	1	2	yes	—
41	C₅×#423	C₂×C₃	1	1	yes	characteristic
42	C₅×#419	C₂×C₃	1	2	yes	—
43	C₂×C₃×C₅×Q₈	—	2	1	no	—
44	C₂×C₃×C₅×Q₈	—	2	1	no	—
45	C₂×C₃×C₅×Q₈	—	2	1	no	—
46	C₂×C₃×C₅×Q₈	—	2	2	no	—
47	C₂×C₃×C₅×Q₈	Q₈	1	4	yes	complemented
48	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	—	2	1	no	—
50	C₂²×C₃×C₄×C₅	—	2	1	no	—
51	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₃×C₅×M₁₆	—	2	4	no	—
55	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
56	C₃×C₅×C₄⋊C₄	—	2	2	no	—
57	C₃×C₅×C₄⋊C₄	—	2	2	no	—
58	C₃×C₅×C₄⋊C₄	—	2	1	no	—
59	C₃×C₅×C₄⋊C₄	—	2	2	no	—
60	C₃×C₅×C₄⋊C₄	—	2	2	no	—
61	C₃×C₅×C₄⋊C₄	—	2	1	no	—
62	C₃×C₅×C₄⋊C₄	—	2	1	no	—
63	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
64	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
65	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
66	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
67	C₃×C₄²×C₅	—	2	2	no	—
68	C₃×C₄²×C₅	—	2	2	no	—
69	C₃×C₄²×C₅	—	2	2	no	—
70	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
71	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₃×#533	C₂×C₅	1	1	yes	characteristic
75	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic
76	C₃×#479	C₂×C₅	1	4	yes	complemented
77	C₃×#477	C₂×C₅	1	2	yes	complemented
78	C₃×#475	C₂×C₅	1	2	yes	complemented
79	C₃×#428	C₂×C₅	1	2	yes	—
80	C₃×#423	C₂×C₅	1	1	yes	characteristic
81	C₃×#419	C₂×C₅	1	2	yes	—
82	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
84	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
85	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
86	C₅×#125	C₂²×C₃	1	2	yes	—
87	C₅×C₂²⋊Q₈	—	2	1	no	—
88	C₅×C₂²⋊Q₈	—	2	1	no	—
89	C₄×C₅×Q₈	—	2	1	no	—
90	C₄×C₅×Q₈	—	2	1	no	—
91	C₄×C₅×Q₈	—	2	1	no	—
92	C₄×C₅×Q₈	—	2	1	no	—
93	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
94	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
95	C₅×#117	C₂²×C₃	1	2	yes	—
96	C₂×C₅×C₄⋊C₄	—	2	1	no	—
97	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₄²×C₅	—	2	1	no	—
99	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
100	C₅×#107	C₂²×C₃	1	4	yes	—
101	C₅×#106	C₂²×C₃	1	4	yes	—
102	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
103	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
104	C₅×#103	C₂²×C₃	1	4	yes	—
105	C₅×#103	C₂²×C₃	1	4	yes	—
106	#3078	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
107	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
108	C₃×C₅×Q₈	—	2	4	no	—
109	C₃×C₅×Q₈	—	2	2	no	—
110	C₃×C₅×Q₈	—	4	2	no	—
111	C₃×C₅×Q₈	—	4	2	no	—
112	C₃×C₅×Q₈	C₂×Q₈	1	4	yes	—
113	C₂×C₃×C₄×C₅	—	2	4	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	4	1	no	—
120	C₂×C₃×C₄×C₅	—	4	2	no	—
121	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
122	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
125	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
127	C₂×C₃×C₄×C₅	#41	1	2	yes	—
128	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
129	C₃×C₅×C₈	—	2	4	no	—
130	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
132	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
133	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
134	C₃×#125	C₂²×C₅	1	2	yes	—
135	C₃×C₂²⋊Q₈	—	2	1	no	—
136	C₃×C₂²⋊Q₈	—	2	1	no	—
137	C₃×C₄×Q₈	—	2	1	no	—
138	C₃×C₄×Q₈	—	2	1	no	—
139	C₃×C₄×Q₈	—	2	1	no	—
140	C₃×C₄×Q₈	—	2	1	no	—
141	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
142	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
143	C₃×#117	C₂²×C₅	1	2	yes	—
144	C₂×C₃×C₄⋊C₄	—	2	1	no	—
145	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₃×C₄²	—	2	1	no	—
147	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
148	C₃×#107	C₂²×C₅	1	4	yes	—
149	C₃×#106	C₂²×C₅	1	4	yes	—
150	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
151	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
152	C₃×#103	C₂²×C₅	1	4	yes	—
153	C₃×#103	C₂²×C₅	1	4	yes	—
154	C₂×C₅×Q₈	—	2	1	no	—
155	C₂×C₅×Q₈	—	2	1	no	—
156	C₂×C₅×Q₈	—	2	1	no	—
157	C₂×C₅×Q₈	—	2	2	no	—
158	C₂×C₅×Q₈	C₃×Q₈	1	4	yes	complemented
159	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
160	C₂²×C₄×C₅	—	2	1	no	—
161	C₂²×C₄×C₅	—	2	1	no	—
162	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
165	C₅×M₁₆	—	2	4	no	—
166	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
167	C₅×C₄⋊C₄	—	2	2	no	—
168	C₅×C₄⋊C₄	—	2	2	no	—
169	C₅×C₄⋊C₄	—	2	1	no	—
170	C₅×C₄⋊C₄	—	2	2	no	—
171	C₅×C₄⋊C₄	—	2	2	no	—
172	C₅×C₄⋊C₄	—	2	1	no	—
173	C₅×C₄⋊C₄	—	2	1	no	—
174	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
175	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
176	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
177	C₅×C₂²⋊C₄	—	2	2	no	—
178	C₄²×C₅	—	2	2	no	—
179	C₄²×C₅	—	2	2	no	—
180	C₄²×C₅	—	2	2	no	—
181	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
182	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
183	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
184	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
185	#533	C₂×C₃×C₅	1	1	yes	characteristic
186	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
187	#479	C₂×C₃×C₅	1	4	yes	complemented
188	#477	C₂×C₃×C₅	1	2	yes	complemented
189	#475	C₂×C₃×C₅	1	2	yes	complemented
190	#428	C₂×C₃×C₅	1	2	yes	—
191	#423	C₂×C₃×C₅	1	1	yes	characteristic
192	#419	C₂×C₃×C₅	1	2	yes	—
193	C₂²×C₃×C₅	—	2	1	no	—
194	C₂²×C₃×C₅	—	2	1	no	—
195	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
196	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
197	C₃×C₄×C₅	—	2	4	no	—
198	C₃×C₄×C₅	—	2	1	no	—
199	C₃×C₄×C₅	—	2	1	no	—
200	C₃×C₄×C₅	—	2	1	no	—
201	C₃×C₄×C₅	—	4	2	no	—
202	C₃×C₄×C₅	—	4	2	no	—
203	C₃×C₄×C₅	—	4	2	no	—
204	C₃×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
205	C₃×C₄×C₅	#137	1	2	yes	—
206	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
207	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
208	C₂×C₃×Q₈	—	2	1	no	—
209	C₂×C₃×Q₈	—	2	1	no	—
210	C₂×C₃×Q₈	—	2	1	no	—
211	C₂×C₃×Q₈	—	2	2	no	—
212	C₂×C₃×Q₈	C₅×Q₈	1	4	yes	complemented
213	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
214	C₂²×C₃×C₄	—	2	1	no	—
215	C₂²×C₃×C₄	—	2	1	no	—
216	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
217	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
218	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
219	C₃×M₁₆	—	2	4	no	—
220	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
221	C₃×C₄⋊C₄	—	2	2	no	—
222	C₃×C₄⋊C₄	—	2	2	no	—
223	C₃×C₄⋊C₄	—	2	1	no	—
224	C₃×C₄⋊C₄	—	2	2	no	—
225	C₃×C₄⋊C₄	—	2	2	no	—
226	C₃×C₄⋊C₄	—	2	1	no	—
227	C₃×C₄⋊C₄	—	2	1	no	—
228	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
229	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
230	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
231	C₃×C₂²⋊C₄	—	2	2	no	—
232	C₃×C₄²	—	2	2	no	—
233	C₃×C₄²	—	2	2	no	—
234	C₃×C₄²	—	2	2	no	—
235	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
236	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
237	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
238	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
239	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
240	C₅×Q₈	—	2	4	no	—
241	C₅×Q₈	—	2	2	no	—
242	C₅×Q₈	—	4	2	no	—
243	C₅×Q₈	—	4	2	no	—
244	C₅×Q₈	C₂×C₃×Q₈	1	4	yes	—
245	C₂×C₄×C₅	—	2	4	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	4	1	no	—
252	C₂×C₄×C₅	—	4	2	no	—
253	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
256	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
257	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
259	C₂×C₄×C₅	C₃×#41	1	2	yes	—
260	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
261	C₅×C₈	—	2	4	no	—
262	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
263	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
264	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
265	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
266	#125	C₂²×C₃×C₅	1	2	yes	—
267	C₂²⋊Q₈	—	2	1	no	—
268	C₂²⋊Q₈	—	2	1	no	—
269	C₄×Q₈	—	2	1	no	—
270	C₄×Q₈	—	2	1	no	—
271	C₄×Q₈	—	2	1	no	—
272	C₄×Q₈	—	2	1	no	—
273	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
274	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
275	#117	C₂²×C₃×C₅	1	2	yes	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
280	#107	C₂²×C₃×C₅	1	4	yes	—
281	#106	C₂²×C₃×C₅	1	4	yes	—
282	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
283	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
284	#103	C₂²×C₃×C₅	1	4	yes	—
285	#103	C₂²×C₃×C₅	1	4	yes	—
286	C₂×C₃×C₅	—	2	2	no	—
287	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
288	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
289	C₂×C₃×C₅	#575	1	1	yes	characteristic
290	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
291	C₃×Q₈	—	2	4	no	—
292	C₃×Q₈	—	2	2	no	—
293	C₃×Q₈	—	4	2	no	—
294	C₃×Q₈	—	4	2	no	—
295	C₃×Q₈	C₂×C₅×Q₈	1	4	yes	—
296	C₂×C₃×C₄	—	2	4	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	4	1	no	—
303	C₂×C₃×C₄	—	4	2	no	—
304	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
305	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
306	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
307	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
308	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
309	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
310	C₂×C₃×C₄	C₅×#41	1	2	yes	—
311	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
312	C₃×C₈	—	2	4	no	—
313	C₂²×C₅	—	2	1	no	—
314	C₂²×C₅	—	2	1	no	—
315	C₂²×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
316	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
317	C₄×C₅	—	2	1	no	—
318	C₄×C₅	—	2	1	no	—
319	C₄×C₅	—	2	1	no	—
320	C₄×C₅	—	2	4	no	—
321	C₄×C₅	—	4	2	no	—
322	C₄×C₅	—	4	2	no	—
323	C₄×C₅	—	4	2	no	—
324	C₄×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
325	C₄×C₅	C₃×#137	1	2	yes	—
326	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
327	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	C₃×C₅×Q₈	1	4	yes	complemented
333	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
337	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
338	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
339	M₁₆	—	2	4	no	—
340	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
349	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
350	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	2	2	no	—
355	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
356	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
357	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
358	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
359	C₃×C₅	#3078	1	1	yes	characteristic, direct product factor, Hall
360	C₂²×C₃	—	2	1	no	—
361	C₂²×C₃	—	2	1	no	—
362	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
363	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
364	C₃×C₄	—	2	4	no	—
365	C₃×C₄	—	2	1	no	—
366	C₃×C₄	—	2	1	no	—
367	C₃×C₄	—	2	1	no	—
368	C₃×C₄	—	4	2	no	—
369	C₃×C₄	—	4	2	no	—
370	C₃×C₄	—	4	2	no	—
371	C₃×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
372	C₃×C₄	C₅×#137	1	2	yes	—
373	C₃×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
374	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
375	C₂×C₅	—	2	2	no	—
376	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
377	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
378	C₂×C₅	C₃×#575	1	1	yes	characteristic
379	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
380	Q₈	—	2	4	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	4	2	no	—
384	Q₈	C₂×C₃×C₅×Q₈	1	4	yes	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
394	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
395	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
396	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
397	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
398	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
399	C₂×C₄	C₃×C₅×#41	1	2	yes	—
400	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
401	C₈	—	2	4	no	—
402	C₂×C₃	—	2	2	no	—
403	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
404	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
405	C₂×C₃	C₅×#575	1	1	yes	characteristic
406	C₅	C₃×#3078	1	1	yes	characteristic, direct product factor, Sylow
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
410	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
411	C₄	—	2	4	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
419	C₄	C₃×C₅×#137	1	2	yes	—
420	C₄	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
421	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
422	C₃	C₅×#3078	1	1	yes	characteristic, direct product factor, Sylow
423	C₂	—	2	2	no	—
424	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
425	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic
426	C₂	C₃×C₅×#575	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 ◁ C₂×C₃×C₄²×C₅ ◁ 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×#477	C₂	semidirect
5. C₃×C₅×#475	C₂	semidirect
9. C₅×#3078	C₃	direct (N × H)
34. C₃×#3078	C₅	direct (N × H)
37. C₅×#479	C₂×C₃	semidirect
38. C₅×#477	C₂×C₃	semidirect
39. C₅×#475	C₂×C₃	semidirect
47. C₂×C₃×C₅×Q₈	Q₈	semidirect
76. C₃×#479	C₂×C₅	semidirect
77. C₃×#477	C₂×C₅	semidirect
78. C₃×#475	C₂×C₅	semidirect
106. #3078	C₃×C₅	direct (N × H)
158. C₂×C₅×Q₈	C₃×Q₈	semidirect
187. #479	C₂×C₃×C₅	semidirect
188. #477	C₂×C₃×C₅	semidirect
189. #475	C₂×C₃×C₅	semidirect
212. C₂×C₃×Q₈	C₅×Q₈	semidirect
332. C₂×Q₈	C₃×C₅×Q₈	semidirect
359. C₃×C₅	#3078	direct (N × H)
406. C₅	C₃×#3078	direct (N × H)
422. C₃	C₅×#3078	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
C₂×C₃×C₄×C₅×Q₈	2
C₃×C₅×#479	2
C₃×C₅×#477	2
C₃×C₅×#475	2
C₃×C₅×#428	2
C₃×C₅×#423	2
C₃×C₅×#419	2
C₅×#3078	3
C₃×#3078	5

Subgroups — C3×C5×#3078 #14276112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3078 #14276112