Subgroups — C₃×C₅×#3113 #14276147

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 416 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×#483	C₂	1	2	yes	maximal
4	C₃×C₅×#475	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#462	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#451	C₂	1	2	yes	maximal
7	C₃×C₅×#441	C₂	1	4	yes	maximal, complemented
8	C₃×C₅×#432	C₂	1	1	yes	maximal, characteristic
9	C₅×#3113	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×Q₁₆	C₂²	1	4	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	—	2	1	no	—
15	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
16	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
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	C₂²	1	2	yes	—
21	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
22	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
23	C₃×C₅×#117	—	2	1	no	—
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×#106	C₂²	1	4	yes	—
29	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
30	C₃×C₅×#103	C₂²	1	4	yes	—
31	C₃×C₅×#103	C₂²	1	4	yes	—
32	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
33	C₃×C₅×#97	C₂²	1	2	yes	—
34	C₃×#3113	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×#483	C₂×C₃	1	2	yes	—
38	C₅×#475	C₂×C₃	1	2	yes	complemented
39	C₅×#462	C₂×C₃	1	2	yes	complemented
40	C₅×#451	C₂×C₃	1	2	yes	—
41	C₅×#441	C₂×C₃	1	4	yes	complemented
42	C₅×#432	C₂×C₃	1	1	yes	characteristic
43	C₂×C₃×C₅×Q₈	—	2	4	no	—
44	C₂×C₃×C₅×Q₈	—	2	1	no	—
45	C₂×C₃×C₅×Q₈	—	2	1	no	—
46	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
47	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	—	2	1	no	—
49	C₂²×C₃×C₄×C₅	—	2	1	no	—
50	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₃×C₅×Q₁₆	—	2	8	no	—
54	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
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	—	2	1	no	—
60	C₃×C₅×C₄⋊C₄	—	2	1	no	—
61	C₃×C₅×C₄⋊C₄	—	2	2	no	—
62	C₃×C₅×C₄⋊C₄	—	2	2	no	—
63	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
64	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
65	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
66	C₃×C₄²×C₅	—	2	2	no	—
67	C₃×C₄²×C₅	—	2	2	no	—
68	C₃×C₄²×C₅	—	2	2	no	—
69	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
70	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
71	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₃×#533	C₂×C₅	1	1	yes	characteristic
74	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic
75	C₃×#483	C₂×C₅	1	2	yes	—
76	C₃×#475	C₂×C₅	1	2	yes	complemented
77	C₃×#462	C₂×C₅	1	2	yes	complemented
78	C₃×#451	C₂×C₅	1	2	yes	—
79	C₃×#441	C₂×C₅	1	4	yes	complemented
80	C₃×#432	C₂×C₅	1	1	yes	characteristic
81	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₅×Q₁₆	C₂²×C₃	1	4	yes	—
83	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
84	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
85	C₅×#125	—	2	1	no	—
86	C₅×C₂²⋊Q₈	—	2	1	no	—
87	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
88	C₄×C₅×Q₈	—	2	1	no	—
89	C₄×C₅×Q₈	—	2	1	no	—
90	C₄×C₅×Q₈	—	2	1	no	—
91	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
92	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
93	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
94	C₅×#117	—	2	1	no	—
95	C₂×C₅×C₄⋊C₄	—	2	1	no	—
96	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₄²×C₅	—	2	1	no	—
98	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
99	C₅×#106	C₂²×C₃	1	4	yes	—
100	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
101	C₅×#103	C₂²×C₃	1	4	yes	—
102	C₅×#103	C₂²×C₃	1	4	yes	—
103	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
104	C₅×#97	C₂²×C₃	1	2	yes	—
105	#3113	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
106	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
107	C₃×C₅×Q₈	—	2	4	no	—
108	C₃×C₅×Q₈	—	2	2	no	—
109	C₃×C₅×Q₈	—	2	4	no	—
110	C₃×C₅×Q₈	—	4	2	no	—
111	C₃×C₅×Q₈	#41	1	4	yes	—
112	C₂×C₃×C₄×C₅	—	2	4	no	—
113	C₂×C₃×C₄×C₅	—	2	2	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	—	2	2	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	C₂⁴	1	1	yes	characteristic
127	C₃×C₅×C₈	—	2	4	no	—
128	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
129	C₂×C₃×Q₁₆	C₂²×C₅	1	4	yes	—
130	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
131	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
132	C₃×#125	—	2	1	no	—
133	C₃×C₂²⋊Q₈	—	2	1	no	—
134	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
135	C₃×C₄×Q₈	—	2	1	no	—
136	C₃×C₄×Q₈	—	2	1	no	—
137	C₃×C₄×Q₈	—	2	1	no	—
138	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
139	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
140	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
141	C₃×#117	—	2	1	no	—
142	C₂×C₃×C₄⋊C₄	—	2	1	no	—
143	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₃×C₄²	—	2	1	no	—
145	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
146	C₃×#106	C₂²×C₅	1	4	yes	—
147	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
148	C₃×#103	C₂²×C₅	1	4	yes	—
149	C₃×#103	C₂²×C₅	1	4	yes	—
150	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
151	C₃×#97	C₂²×C₅	1	2	yes	—
152	C₂×C₅×Q₈	—	2	4	no	—
153	C₂×C₅×Q₈	—	2	1	no	—
154	C₂×C₅×Q₈	—	2	1	no	—
155	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
156	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
157	C₂²×C₄×C₅	—	2	1	no	—
158	C₂²×C₄×C₅	—	2	1	no	—
159	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
162	C₅×Q₁₆	—	2	8	no	—
163	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
164	C₅×C₄⋊C₄	—	2	2	no	—
165	C₅×C₄⋊C₄	—	2	2	no	—
166	C₅×C₄⋊C₄	—	2	1	no	—
167	C₅×C₄⋊C₄	—	2	1	no	—
168	C₅×C₄⋊C₄	—	2	1	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	C₂³×C₃	1	2	yes	—
173	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
174	C₅×C₂²⋊C₄	—	2	2	no	—
175	C₄²×C₅	—	2	2	no	—
176	C₄²×C₅	—	2	2	no	—
177	C₄²×C₅	—	2	2	no	—
178	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
179	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
180	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
181	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
182	#533	C₂×C₃×C₅	1	1	yes	characteristic
183	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
184	#483	C₂×C₃×C₅	1	2	yes	—
185	#475	C₂×C₃×C₅	1	2	yes	complemented
186	#462	C₂×C₃×C₅	1	2	yes	complemented
187	#451	C₂×C₃×C₅	1	2	yes	—
188	#441	C₂×C₃×C₅	1	4	yes	complemented
189	#432	C₂×C₃×C₅	1	1	yes	characteristic
190	C₂²×C₃×C₅	—	2	1	no	—
191	C₂²×C₃×C₅	—	2	1	no	—
192	C₂²×C₃×C₅	#137	1	2	yes	—
193	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
194	C₃×C₄×C₅	—	2	4	no	—
195	C₃×C₄×C₅	—	2	1	no	—
196	C₃×C₄×C₅	—	2	1	no	—
197	C₃×C₄×C₅	—	2	1	no	—
198	C₃×C₄×C₅	—	2	1	no	—
199	C₃×C₄×C₅	—	4	2	no	—
200	C₃×C₄×C₅	—	4	2	no	—
201	C₃×C₄×C₅	—	4	2	no	—
202	C₃×C₄×C₅	#137	1	2	yes	—
203	C₃×C₄×C₅	C₂×#41	1	2	yes	—
204	C₂×C₃×Q₈	—	2	4	no	—
205	C₂×C₃×Q₈	—	2	1	no	—
206	C₂×C₃×Q₈	—	2	1	no	—
207	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
208	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
209	C₂²×C₃×C₄	—	2	1	no	—
210	C₂²×C₃×C₄	—	2	1	no	—
211	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
212	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
213	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
214	C₃×Q₁₆	—	2	8	no	—
215	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
216	C₃×C₄⋊C₄	—	2	2	no	—
217	C₃×C₄⋊C₄	—	2	2	no	—
218	C₃×C₄⋊C₄	—	2	1	no	—
219	C₃×C₄⋊C₄	—	2	1	no	—
220	C₃×C₄⋊C₄	—	2	1	no	—
221	C₃×C₄⋊C₄	—	2	1	no	—
222	C₃×C₄⋊C₄	—	2	2	no	—
223	C₃×C₄⋊C₄	—	2	2	no	—
224	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
225	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
226	C₃×C₂²⋊C₄	—	2	2	no	—
227	C₃×C₄²	—	2	2	no	—
228	C₃×C₄²	—	2	2	no	—
229	C₃×C₄²	—	2	2	no	—
230	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
231	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
232	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
233	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
234	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
235	C₅×Q₈	—	2	4	no	—
236	C₅×Q₈	—	2	2	no	—
237	C₅×Q₈	—	2	4	no	—
238	C₅×Q₈	—	4	2	no	—
239	C₅×Q₈	C₃×#41	1	4	yes	—
240	C₂×C₄×C₅	—	2	4	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	4	2	no	—
249	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
252	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
253	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
255	C₅×C₈	—	2	4	no	—
256	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
257	C₂×Q₁₆	C₂²×C₃×C₅	1	4	yes	—
258	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
259	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
260	#125	—	2	1	no	—
261	C₂²⋊Q₈	—	2	1	no	—
262	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
263	C₄×Q₈	—	2	1	no	—
264	C₄×Q₈	—	2	1	no	—
265	C₄×Q₈	—	2	1	no	—
266	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
267	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
268	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
269	#117	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
274	#106	C₂²×C₃×C₅	1	4	yes	—
275	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
276	#103	C₂²×C₃×C₅	1	4	yes	—
277	#103	C₂²×C₃×C₅	1	4	yes	—
278	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
279	#97	C₂²×C₃×C₅	1	2	yes	—
280	C₂×C₃×C₅	—	2	2	no	—
281	C₂×C₃×C₅	#525	1	1	yes	characteristic
282	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
283	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
284	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
285	C₃×Q₈	—	2	4	no	—
286	C₃×Q₈	—	2	2	no	—
287	C₃×Q₈	—	2	4	no	—
288	C₃×Q₈	—	4	2	no	—
289	C₃×Q₈	C₅×#41	1	4	yes	—
290	C₂×C₃×C₄	—	2	4	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	4	2	no	—
299	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
304	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
305	C₃×C₈	—	2	4	no	—
306	C₂²×C₅	—	2	1	no	—
307	C₂²×C₅	—	2	1	no	—
308	C₂²×C₅	C₃×#137	1	2	yes	—
309	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
310	C₄×C₅	—	2	1	no	—
311	C₄×C₅	—	2	1	no	—
312	C₄×C₅	—	2	1	no	—
313	C₄×C₅	—	2	4	no	—
314	C₄×C₅	—	2	1	no	—
315	C₄×C₅	—	4	2	no	—
316	C₄×C₅	—	4	2	no	—
317	C₄×C₅	—	4	2	no	—
318	C₄×C₅	C₃×#137	1	2	yes	—
319	C₄×C₅	C₂×C₃×#41	1	2	yes	—
320	C₂×Q₈	—	2	4	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
324	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
328	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
329	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
330	Q₁₆	—	2	8	no	—
331	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
341	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
342	C₂²⋊C₄	—	2	2	no	—
343	C₄²	—	2	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	2	no	—
346	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
347	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
348	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
349	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
350	C₃×C₅	#3113	1	1	yes	characteristic, direct product factor, Hall
351	C₂²×C₃	—	2	1	no	—
352	C₂²×C₃	—	2	1	no	—
353	C₂²×C₃	C₅×#137	1	2	yes	—
354	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
355	C₃×C₄	—	2	4	no	—
356	C₃×C₄	—	2	1	no	—
357	C₃×C₄	—	2	1	no	—
358	C₃×C₄	—	2	1	no	—
359	C₃×C₄	—	2	1	no	—
360	C₃×C₄	—	4	2	no	—
361	C₃×C₄	—	4	2	no	—
362	C₃×C₄	—	4	2	no	—
363	C₃×C₄	C₅×#137	1	2	yes	—
364	C₃×C₄	C₂×C₅×#41	1	2	yes	—
365	C₂×C₅	—	2	2	no	—
366	C₂×C₅	C₃×#525	1	1	yes	characteristic
367	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
368	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
369	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
370	Q₈	—	2	4	no	—
371	Q₈	—	2	2	no	—
372	Q₈	—	2	4	no	—
373	Q₈	—	4	2	no	—
374	Q₈	C₃×C₅×#41	1	4	yes	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
385	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
386	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
387	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
388	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
389	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
390	C₈	—	2	4	no	—
391	C₂×C₃	—	2	2	no	—
392	C₂×C₃	C₅×#525	1	1	yes	characteristic
393	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
394	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
395	C₅	C₃×#3113	1	1	yes	characteristic, direct product factor, Sylow
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	C₃×C₅×#137	1	2	yes	—
399	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
400	C₄	—	2	4	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	C₃×C₅×#137	1	2	yes	—
409	C₄	C₂×C₃×C₅×#41	1	2	yes	—
410	C₃	C₅×#3113	1	1	yes	characteristic, direct product factor, Sylow
411	C₂	—	2	2	no	—
412	C₂	C₃×C₅×#525	1	1	yes	characteristic
413	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic
414	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	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
4. C₃×C₅×#475	C₂	semidirect
5. C₃×C₅×#462	C₂	semidirect
7. C₃×C₅×#441	C₂	semidirect
9. C₅×#3113	C₃	direct (N × H)
34. C₃×#3113	C₅	direct (N × H)
38. C₅×#475	C₂×C₃	semidirect
39. C₅×#462	C₂×C₃	semidirect
41. C₅×#441	C₂×C₃	semidirect
76. C₃×#475	C₂×C₅	semidirect
77. C₃×#462	C₂×C₅	semidirect
79. C₃×#441	C₂×C₅	semidirect
105. #3113	C₃×C₅	direct (N × H)
185. #475	C₂×C₃×C₅	semidirect
186. #462	C₂×C₃×C₅	semidirect
188. #441	C₂×C₃×C₅	semidirect
350. C₃×C₅	#3113	direct (N × H)
395. C₅	C₃×#3113	direct (N × H)
410. C₃	C₅×#3113	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×#483	2
C₃×C₅×#475	2
C₃×C₅×#462	2
C₃×C₅×#451	2
C₃×C₅×#441	2
C₃×C₅×#432	2
C₅×#3113	3
C₃×#3113	5

Subgroups — C3×C5×#3113 #14276147

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3113 #14276147