Subgroups — C₃×C₅×#3122 #14276156

Order 1920.

836 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#482	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#478	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#459	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#447	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#442	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×C₅×D₈	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#433	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3122	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
13	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
14	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
15	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
16	C₃×C₅×#123	—	2	2	no	—
17	C₃×C₅×#121	—	2	2	no	—
18	C₃×C₅×#121	C₂²	1	2	yes	—
19	C₃×C₄×C₅×D₄	—	2	2	no	—
20	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
21	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
22	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
23	C₃×C₅×#117	C₂²	1	1	yes	characteristic
24	C₃×C₅×#117	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
26	C₃×C₅×#107	C₂²	1	2	yes	complemented
27	C₃×C₅×#106	C₂²	1	2	yes	complemented
28	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
29	C₃×C₅×#102	C₂²	1	2	yes	—
30	C₃×C₅×#102	C₂²	1	2	yes	—
31	C₃×C₅×#102	C₂²	1	2	yes	complemented
32	C₃×C₅×#102	C₂²	1	2	yes	complemented
33	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
34	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
36	C₃×#3122	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₅×#540	C₂×C₃	1	1	yes	characteristic, complemented
38	C₅×#518	C₂×C₃	1	1	yes	characteristic, complemented
39	C₅×#482	C₂×C₃	1	2	yes	complemented
40	C₅×#478	C₂×C₃	1	2	yes	complemented
41	C₅×#459	C₂×C₃	1	2	yes	complemented
42	C₅×#447	C₂×C₃	1	2	yes	complemented
43	C₅×#442	C₂×C₃	1	2	yes	complemented
44	C₄×C₅×D₈	C₂×C₃	1	2	yes	complemented
45	C₅×#433	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂⁴×C₃×C₅	—	2	1	no	—
47	C₂×C₃×C₅×D₄	—	2	4	no	—
48	C₂×C₃×C₅×D₄	—	2	2	no	—
49	C₂×C₃×C₅×D₄	—	2	1	no	—
50	C₂×C₃×C₅×D₄	—	2	2	no	—
51	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
52	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	—	2	2	no	—
54	C₂²×C₃×C₄×C₅	—	2	2	no	—
55	C₂²×C₃×C₄×C₅	—	2	2	no	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₃×C₅×D₈	—	2	4	no	—
58	C₃×C₅×D₈	—	2	4	no	—
59	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
60	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
61	C₃×C₅×C₄⋊C₄	—	2	2	no	—
62	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
63	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
64	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
65	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
66	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
67	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
68	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
69	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
70	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
71	C₃×C₄²×C₅	—	2	1	no	—
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₃×#540	C₂×C₅	1	1	yes	characteristic, complemented
75	C₃×#518	C₂×C₅	1	1	yes	characteristic, complemented
76	C₃×#482	C₂×C₅	1	2	yes	complemented
77	C₃×#478	C₂×C₅	1	2	yes	complemented
78	C₃×#459	C₂×C₅	1	2	yes	complemented
79	C₃×#447	C₂×C₅	1	2	yes	complemented
80	C₃×#442	C₂×C₅	1	2	yes	complemented
81	C₃×C₄×D₈	C₂×C₅	1	2	yes	complemented
82	C₃×#433	C₂×C₅	1	1	yes	characteristic, complemented
83	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
85	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
86	C₅×#127	C₂²×C₃	1	1	yes	characteristic, complemented
87	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
88	C₅×#123	—	2	2	no	—
89	C₅×#121	—	2	2	no	—
90	C₅×#121	C₂²×C₃	1	2	yes	—
91	C₄×C₅×D₄	—	2	2	no	—
92	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
93	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
94	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
95	C₅×#117	C₂²×C₃	1	1	yes	characteristic
96	C₅×#117	C₂²×C₃	1	1	yes	characteristic
97	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
98	C₅×#107	C₂²×C₃	1	2	yes	complemented
99	C₅×#106	C₂²×C₃	1	2	yes	complemented
100	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
101	C₅×#102	C₂²×C₃	1	2	yes	—
102	C₅×#102	C₂²×C₃	1	2	yes	—
103	C₅×#102	C₂²×C₃	1	2	yes	complemented
104	C₅×#102	C₂²×C₃	1	2	yes	complemented
105	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
106	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
107	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
108	#3122	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
109	C₂³×C₃×C₅	—	2	4	no	—
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	—	2	2	no	—
112	C₂³×C₃×C₅	—	8	2	no	—
113	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
114	C₃×C₅×D₄	—	2	4	no	—
115	C₃×C₅×D₄	—	2	2	no	—
116	C₃×C₅×D₄	—	2	2	no	—
117	C₃×C₅×D₄	—	2	2	no	—
118	C₃×C₅×D₄	—	8	2	no	—
119	C₃×C₅×D₄	—	8	2	no	—
120	C₃×C₅×D₄	#41	1	4	yes	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	8	2	no	—
125	C₂×C₃×C₄×C₅	—	8	2	no	—
126	C₂×C₃×C₄×C₅	—	8	2	no	—
127	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
131	C₃×C₅×C₈	—	2	2	no	—
132	C₃×C₅×C₈	—	2	2	no	—
133	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
135	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
136	C₃×#127	C₂²×C₅	1	1	yes	characteristic, complemented
137	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
138	C₃×#123	—	2	2	no	—
139	C₃×#121	—	2	2	no	—
140	C₃×#121	C₂²×C₅	1	2	yes	—
141	C₃×C₄×D₄	—	2	2	no	—
142	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
143	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
144	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
145	C₃×#117	C₂²×C₅	1	1	yes	characteristic
146	C₃×#117	C₂²×C₅	1	1	yes	characteristic
147	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
148	C₃×#107	C₂²×C₅	1	2	yes	complemented
149	C₃×#106	C₂²×C₅	1	2	yes	complemented
150	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
151	C₃×#102	C₂²×C₅	1	2	yes	—
152	C₃×#102	C₂²×C₅	1	2	yes	—
153	C₃×#102	C₂²×C₅	1	2	yes	complemented
154	C₃×#102	C₂²×C₅	1	2	yes	complemented
155	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
156	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
157	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
158	C₂⁴×C₅	—	2	1	no	—
159	C₂×C₅×D₄	—	2	4	no	—
160	C₂×C₅×D₄	—	2	2	no	—
161	C₂×C₅×D₄	—	2	1	no	—
162	C₂×C₅×D₄	—	2	2	no	—
163	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
164	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
165	C₂²×C₄×C₅	—	2	2	no	—
166	C₂²×C₄×C₅	—	2	2	no	—
167	C₂²×C₄×C₅	—	2	2	no	—
168	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
169	C₅×D₈	—	2	4	no	—
170	C₅×D₈	—	2	4	no	—
171	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
172	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
173	C₅×C₄⋊C₄	—	2	2	no	—
174	C₅×C₄⋊C₄	C₃×D₄	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	1	no	—
178	C₅×C₂²⋊C₄	—	2	2	no	—
179	C₅×C₂²⋊C₄	—	2	2	no	—
180	C₅×C₂²⋊C₄	—	2	2	no	—
181	C₅×C₂²⋊C₄	—	2	2	no	—
182	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
183	C₄²×C₅	—	2	1	no	—
184	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
185	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
186	#540	C₂×C₃×C₅	1	1	yes	characteristic, complemented
187	#518	C₂×C₃×C₅	1	1	yes	characteristic, complemented
188	#482	C₂×C₃×C₅	1	2	yes	complemented
189	#478	C₂×C₃×C₅	1	2	yes	complemented
190	#459	C₂×C₃×C₅	1	2	yes	complemented
191	#447	C₂×C₃×C₅	1	2	yes	complemented
192	#442	C₂×C₃×C₅	1	2	yes	complemented
193	C₄×D₈	C₂×C₃×C₅	1	2	yes	complemented
194	#433	C₂×C₃×C₅	1	1	yes	characteristic, complemented
195	C₂²×C₃×C₅	—	2	1	no	—
196	C₂²×C₃×C₅	—	2	4	no	—
197	C₂²×C₃×C₅	—	2	2	no	—
198	C₂²×C₃×C₅	—	4	2	no	—
199	C₂²×C₃×C₅	—	4	2	no	—
200	C₂²×C₃×C₅	—	4	2	no	—
201	C₂²×C₃×C₅	—	4	2	no	—
202	C₂²×C₃×C₅	—	4	2	no	—
203	C₂²×C₃×C₅	—	8	4	no	—
204	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
205	C₃×C₄×C₅	—	2	1	no	—
206	C₃×C₄×C₅	—	2	2	no	—
207	C₃×C₄×C₅	—	2	2	no	—
208	C₃×C₄×C₅	—	4	2	no	—
209	C₃×C₄×C₅	—	4	2	no	—
210	C₃×C₄×C₅	C₂×#41	1	2	yes	—
211	C₂⁴×C₃	—	2	1	no	—
212	C₂×C₃×D₄	—	2	4	no	—
213	C₂×C₃×D₄	—	2	2	no	—
214	C₂×C₃×D₄	—	2	1	no	—
215	C₂×C₃×D₄	—	2	2	no	—
216	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
217	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
218	C₂²×C₃×C₄	—	2	2	no	—
219	C₂²×C₃×C₄	—	2	2	no	—
220	C₂²×C₃×C₄	—	2	2	no	—
221	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
222	C₃×D₈	—	2	4	no	—
223	C₃×D₈	—	2	4	no	—
224	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
225	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
226	C₃×C₄⋊C₄	—	2	2	no	—
227	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
228	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
229	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
230	C₃×C₂²⋊C₄	—	2	1	no	—
231	C₃×C₂²⋊C₄	—	2	2	no	—
232	C₃×C₂²⋊C₄	—	2	2	no	—
233	C₃×C₂²⋊C₄	—	2	2	no	—
234	C₃×C₂²⋊C₄	—	2	2	no	—
235	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
236	C₃×C₄²	—	2	1	no	—
237	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
238	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
239	C₂³×C₅	—	2	4	no	—
240	C₂³×C₅	—	2	2	no	—
241	C₂³×C₅	—	2	2	no	—
242	C₂³×C₅	—	8	2	no	—
243	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
244	C₅×D₄	—	2	4	no	—
245	C₅×D₄	—	2	2	no	—
246	C₅×D₄	—	2	2	no	—
247	C₅×D₄	—	2	2	no	—
248	C₅×D₄	—	8	2	no	—
249	C₅×D₄	—	8	2	no	—
250	C₅×D₄	C₃×#41	1	4	yes	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	8	2	no	—
255	C₂×C₄×C₅	—	8	2	no	—
256	C₂×C₄×C₅	—	8	2	no	—
257	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
259	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
260	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
261	C₅×C₈	—	2	2	no	—
262	C₅×C₈	—	2	2	no	—
263	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
264	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
265	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
266	#127	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
267	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
268	#123	—	2	2	no	—
269	#121	—	2	2	no	—
270	#121	C₂²×C₃×C₅	1	2	yes	—
271	C₄×D₄	—	2	2	no	—
272	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
273	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
274	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
275	#117	C₂²×C₃×C₅	1	1	yes	characteristic
276	#117	C₂²×C₃×C₅	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	—	2	2	no	—
278	#107	C₂²×C₃×C₅	1	2	yes	complemented
279	#106	C₂²×C₃×C₅	1	2	yes	complemented
280	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	complemented
281	#102	C₂²×C₃×C₅	1	2	yes	—
282	#102	C₂²×C₃×C₅	1	2	yes	—
283	#102	C₂²×C₃×C₅	1	2	yes	complemented
284	#102	C₂²×C₃×C₅	1	2	yes	complemented
285	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
286	#97	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
287	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
288	C₂×C₃×C₅	—	4	1	no	—
289	C₂×C₃×C₅	—	4	4	no	—
290	C₂×C₃×C₅	—	8	2	no	—
291	C₂×C₃×C₅	#525	1	1	yes	characteristic
292	C₂×C₃×C₅	#576	1	2	yes	—
293	C₂³×C₃	—	2	4	no	—
294	C₂³×C₃	—	2	2	no	—
295	C₂³×C₃	—	2	2	no	—
296	C₂³×C₃	—	8	2	no	—
297	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
298	C₃×D₄	—	2	4	no	—
299	C₃×D₄	—	2	2	no	—
300	C₃×D₄	—	2	2	no	—
301	C₃×D₄	—	2	2	no	—
302	C₃×D₄	—	8	2	no	—
303	C₃×D₄	—	8	2	no	—
304	C₃×D₄	C₅×#41	1	4	yes	—
305	C₂×C₃×C₄	—	2	2	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	2	2	no	—
308	C₂×C₃×C₄	—	8	2	no	—
309	C₂×C₃×C₄	—	8	2	no	—
310	C₂×C₃×C₄	—	8	2	no	—
311	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
312	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
313	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
314	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
315	C₃×C₈	—	2	2	no	—
316	C₃×C₈	—	2	2	no	—
317	C₂²×C₅	—	2	2	no	—
318	C₂²×C₅	—	2	1	no	—
319	C₂²×C₅	—	2	4	no	—
320	C₂²×C₅	—	4	2	no	—
321	C₂²×C₅	—	4	2	no	—
322	C₂²×C₅	—	4	2	no	—
323	C₂²×C₅	—	4	2	no	—
324	C₂²×C₅	—	4	2	no	—
325	C₂²×C₅	—	8	4	no	—
326	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
327	C₄×C₅	—	2	2	no	—
328	C₄×C₅	—	2	2	no	—
329	C₄×C₅	—	2	1	no	—
330	C₄×C₅	—	4	2	no	—
331	C₄×C₅	—	4	2	no	—
332	C₄×C₅	C₂×C₃×#41	1	2	yes	—
333	C₂⁴	—	2	1	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
339	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
344	D₈	—	2	4	no	—
345	D₈	—	2	4	no	—
346	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
347	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
350	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
351	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	2	2	no	—
355	C₂²⋊C₄	—	2	2	no	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
358	C₄²	—	2	1	no	—
359	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
360	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
361	C₃×C₅	#3122	1	1	yes	characteristic, direct product factor, Hall
362	C₂²×C₃	—	2	1	no	—
363	C₂²×C₃	—	2	4	no	—
364	C₂²×C₃	—	2	2	no	—
365	C₂²×C₃	—	4	2	no	—
366	C₂²×C₃	—	4	2	no	—
367	C₂²×C₃	—	4	2	no	—
368	C₂²×C₃	—	4	2	no	—
369	C₂²×C₃	—	4	2	no	—
370	C₂²×C₃	—	8	4	no	—
371	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
372	C₃×C₄	—	2	1	no	—
373	C₃×C₄	—	2	2	no	—
374	C₃×C₄	—	2	2	no	—
375	C₃×C₄	—	4	2	no	—
376	C₃×C₄	—	4	2	no	—
377	C₃×C₄	C₂×C₅×#41	1	2	yes	—
378	C₂×C₅	—	4	1	no	—
379	C₂×C₅	—	4	4	no	—
380	C₂×C₅	—	8	2	no	—
381	C₂×C₅	C₃×#525	1	1	yes	characteristic
382	C₂×C₅	C₃×#576	1	2	yes	—
383	C₂³	—	2	4	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	8	2	no	—
387	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
388	D₄	—	2	4	no	—
389	D₄	—	2	2	no	—
390	D₄	—	2	2	no	—
391	D₄	—	2	2	no	—
392	D₄	—	8	2	no	—
393	D₄	—	8	2	no	—
394	D₄	C₃×C₅×#41	1	4	yes	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	8	2	no	—
399	C₂×C₄	—	8	2	no	—
400	C₂×C₄	—	8	2	no	—
401	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
402	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
403	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
404	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
405	C₈	—	2	2	no	—
406	C₈	—	2	2	no	—
407	C₂×C₃	—	4	1	no	—
408	C₂×C₃	—	4	4	no	—
409	C₂×C₃	—	8	2	no	—
410	C₂×C₃	C₅×#525	1	1	yes	characteristic
411	C₂×C₃	C₅×#576	1	2	yes	—
412	C₅	C₃×#3122	1	1	yes	characteristic, direct product factor, Sylow
413	C₂²	—	2	1	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	8	4	no	—
422	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
423	C₄	—	2	1	no	—
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	C₂×C₃×C₅×#41	1	2	yes	—
429	C₃	C₅×#3122	1	1	yes	characteristic, direct product factor, Sylow
430	C₂	—	4	1	no	—
431	C₂	—	4	4	no	—
432	C₂	—	8	2	no	—
433	C₂	C₃×C₅×#525	1	1	yes	characteristic
434	C₂	C₃×C₅×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
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
1. C₃×C₅×#540	C₂	semidirect
2. C₃×C₅×#518	C₂	semidirect
3. C₃×C₅×#482	C₂	semidirect
4. C₃×C₅×#478	C₂	semidirect
5. C₃×C₅×#459	C₂	semidirect
6. C₃×C₅×#447	C₂	semidirect
7. C₃×C₅×#442	C₂	semidirect
8. C₃×C₄×C₅×D₈	C₂	semidirect
9. C₃×C₅×#433	C₂	semidirect
10. C₅×#3122	C₃	direct (N × H)
14. C₃×C₅×#127	C₂²	semidirect
15. C₃×C₅×#125	C₂²	semidirect
22. C₃×C₄×C₅×D₄	C₂²	semidirect
26. C₃×C₅×#107	C₂²	semidirect
27. C₃×C₅×#106	C₂²	semidirect
28. C₃×C₅×C₄⋊C₈	C₂²	semidirect
31. C₃×C₅×#102	C₂²	semidirect
32. C₃×C₅×#102	C₂²	semidirect
34. C₃×C₅×#97	C₂²	semidirect
35. C₃×C₄×C₅×C₈	C₂²	semidirect
36. C₃×#3122	C₅	direct (N × H)
37. C₅×#540	C₂×C₃	semidirect
38. C₅×#518	C₂×C₃	semidirect
39. C₅×#482	C₂×C₃	semidirect
40. C₅×#478	C₂×C₃	semidirect
41. C₅×#459	C₂×C₃	semidirect
42. C₅×#447	C₂×C₃	semidirect
43. C₅×#442	C₂×C₃	semidirect
44. C₄×C₅×D₈	C₂×C₃	semidirect
45. C₅×#433	C₂×C₃	semidirect
74. C₃×#540	C₂×C₅	semidirect
75. C₃×#518	C₂×C₅	semidirect
76. C₃×#482	C₂×C₅	semidirect
77. C₃×#478	C₂×C₅	semidirect
78. C₃×#459	C₂×C₅	semidirect
79. C₃×#447	C₂×C₅	semidirect
80. C₃×#442	C₂×C₅	semidirect
81. C₃×C₄×D₈	C₂×C₅	semidirect
82. C₃×#433	C₂×C₅	semidirect
86. C₅×#127	C₂²×C₃	semidirect
87. C₅×#125	C₂²×C₃	semidirect
94. C₄×C₅×D₄	C₂²×C₃	semidirect
98. C₅×#107	C₂²×C₃	semidirect
99. C₅×#106	C₂²×C₃	semidirect
100. C₅×C₄⋊C₈	C₂²×C₃	semidirect
103. C₅×#102	C₂²×C₃	semidirect
104. C₅×#102	C₂²×C₃	semidirect
106. C₅×#97	C₂²×C₃	semidirect
107. C₄×C₅×C₈	C₂²×C₃	semidirect
108. #3122	C₃×C₅	direct (N × H)
136. C₃×#127	C₂²×C₅	semidirect
137. C₃×#125	C₂²×C₅	semidirect
144. C₃×C₄×D₄	C₂²×C₅	semidirect
148. C₃×#107	C₂²×C₅	semidirect
149. C₃×#106	C₂²×C₅	semidirect
150. C₃×C₄⋊C₈	C₂²×C₅	semidirect
153. C₃×#102	C₂²×C₅	semidirect
154. C₃×#102	C₂²×C₅	semidirect
156. C₃×#97	C₂²×C₅	semidirect
157. C₃×C₄×C₈	C₂²×C₅	semidirect
186. #540	C₂×C₃×C₅	semidirect
187. #518	C₂×C₃×C₅	semidirect
188. #482	C₂×C₃×C₅	semidirect
189. #478	C₂×C₃×C₅	semidirect
190. #459	C₂×C₃×C₅	semidirect
191. #447	C₂×C₃×C₅	semidirect
192. #442	C₂×C₃×C₅	semidirect
193. C₄×D₈	C₂×C₃×C₅	semidirect
194. #433	C₂×C₃×C₅	semidirect
266. #127	C₂²×C₃×C₅	semidirect
267. #125	C₂²×C₃×C₅	semidirect
274. C₄×D₄	C₂²×C₃×C₅	semidirect
278. #107	C₂²×C₃×C₅	semidirect
279. #106	C₂²×C₃×C₅	semidirect
280. C₄⋊C₈	C₂²×C₃×C₅	semidirect
283. #102	C₂²×C₃×C₅	semidirect
284. #102	C₂²×C₃×C₅	semidirect
286. #97	C₂²×C₃×C₅	semidirect
287. C₄×C₈	C₂²×C₃×C₅	semidirect
361. C₃×C₅	#3122	direct (N × H)
412. C₅	C₃×#3122	direct (N × H)
429. C₃	C₅×#3122	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×#540	2
C₃×C₅×#518	2
C₃×C₅×#482	2
C₃×C₅×#478	2
C₃×C₅×#459	2
C₃×C₅×#447	2
C₃×C₅×#442	2
C₃×C₄×C₅×D₈	2
C₃×C₅×#433	2
C₅×#3122	3
C₃×#3122	5

Subgroups — C3×C5×#3122 #14276156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3122 #14276156