Subgroups — C₃×C₅×#3061 #14276095

Order 1920.

968 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	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#537	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#468	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#467	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#466	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#417	C₂	1	2	yes	maximal, complemented
9	C₅×#3061	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₃×C₅×#135	—	2	4	no	—
13	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
15	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×#131	—	2	4	no	—
17	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
18	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
20	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
22	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
23	C₃×C₅×#121	—	2	2	no	—
24	C₃×C₅×#121	—	2	4	no	—
25	C₃×C₅×#121	C₂²	1	4	yes	—
26	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
27	C₃×C₅×#107	C₂²	1	2	yes	—
28	C₃×C₅×#107	C₂²	1	2	yes	—
29	C₃×C₅×#103	C₂²	1	4	yes	—
30	C₃×C₅×#102	C₂²	1	4	yes	—
31	C₃×#3061	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×C₅×#131	C₂×C₃	1	1	yes	characteristic, complemented
34	C₅×#537	C₂×C₃	1	2	yes	complemented
35	C₅×#468	C₂×C₃	1	4	yes	complemented
36	C₅×#467	C₂×C₃	1	2	yes	complemented
37	C₅×#466	C₂×C₃	1	2	yes	complemented
38	C₂×C₅×#107	C₂×C₃	1	1	yes	characteristic, complemented
39	C₅×#417	C₂×C₃	1	2	yes	complemented
40	C₃×C₅×#41	—	2	2	no	—
41	C₃×C₅×#41	—	2	2	no	—
42	C₃×C₅×#41	—	2	4	no	—
43	C₃×C₅×#41	—	2	4	no	—
44	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
45	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
46	C₂×C₃×C₅×D₄	—	2	2	no	—
47	C₂×C₃×C₅×D₄	—	2	4	no	—
48	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
49	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
50	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	—	2	2	no	—
52	C₂²×C₃×C₄×C₅	—	2	2	no	—
53	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₃×C₅×Q₁₆	—	2	2	no	—
56	C₃×C₅×SD₁₆	—	2	4	no	—
57	C₃×C₅×D₈	—	2	2	no	—
58	C₃×C₅×M₁₆	—	2	2	no	—
59	C₃×C₅×M₁₆	—	2	4	no	—
60	C₂×C₃×C₅×C₈	—	2	4	no	—
61	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
62	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
63	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₃×C₅×C₄⋊C₄	—	2	2	no	—
66	C₃×C₅×C₄⋊C₄	—	2	4	no	—
67	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
68	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
69	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
70	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×C₃×#131	C₂×C₅	1	1	yes	characteristic, complemented
72	C₃×#537	C₂×C₅	1	2	yes	complemented
73	C₃×#468	C₂×C₅	1	4	yes	complemented
74	C₃×#467	C₂×C₅	1	2	yes	complemented
75	C₃×#466	C₂×C₅	1	2	yes	complemented
76	C₂×C₃×#107	C₂×C₅	1	1	yes	characteristic, complemented
77	C₃×#417	C₂×C₅	1	2	yes	complemented
78	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
79	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
80	C₅×#135	—	2	4	no	—
81	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
83	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
84	C₅×#131	—	2	4	no	—
85	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
87	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
88	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
89	C₅×C₂²⋊Q₈	—	2	2	no	—
90	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
91	C₅×#121	—	2	2	no	—
92	C₅×#121	—	2	4	no	—
93	C₅×#121	C₂²×C₃	1	4	yes	—
94	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
95	C₅×#107	C₂²×C₃	1	2	yes	—
96	C₅×#107	C₂²×C₃	1	2	yes	—
97	C₅×#103	C₂²×C₃	1	4	yes	—
98	C₅×#102	C₂²×C₃	1	4	yes	—
99	#3061	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
100	C₂³×C₃×C₅	—	2	2	no	—
101	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
102	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
103	C₃×C₅×Q₈	—	2	2	no	—
104	C₃×C₅×Q₈	—	2	2	no	—
105	C₃×C₅×Q₈	—	2	2	no	—
106	C₃×C₅×D₄	—	2	4	no	—
107	C₃×C₅×D₄	—	2	2	no	—
108	C₃×C₅×D₄	—	2	2	no	—
109	C₃×C₅×D₄	—	2	2	no	—
110	C₃×C₅×D₄	—	4	4	no	—
111	C₃×C₅×D₄	—	8	4	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	4	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	4	4	no	—
117	C₂×C₃×C₄×C₅	—	8	2	no	—
118	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
121	C₂×C₃×C₄×C₅	#41	1	2	yes	—
122	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
123	C₃×C₅×C₈	—	2	2	no	—
124	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
125	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
126	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
127	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
128	C₃×#135	—	2	4	no	—
129	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
130	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
131	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
132	C₃×#131	—	2	4	no	—
133	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
135	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
136	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
137	C₃×C₂²⋊Q₈	—	2	2	no	—
138	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
139	C₃×#121	—	2	2	no	—
140	C₃×#121	—	2	4	no	—
141	C₃×#121	C₂²×C₅	1	4	yes	—
142	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
143	C₃×#107	C₂²×C₅	1	2	yes	—
144	C₃×#107	C₂²×C₅	1	2	yes	—
145	C₃×#103	C₂²×C₅	1	4	yes	—
146	C₃×#102	C₂²×C₅	1	4	yes	—
147	C₅×#41	—	2	2	no	—
148	C₅×#41	—	2	2	no	—
149	C₅×#41	—	2	4	no	—
150	C₅×#41	—	2	4	no	—
151	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
152	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
153	C₂×C₅×D₄	—	2	2	no	—
154	C₂×C₅×D₄	—	2	4	no	—
155	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
156	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
157	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
158	C₂²×C₄×C₅	—	2	2	no	—
159	C₂²×C₄×C₅	—	2	2	no	—
160	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
161	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
162	C₅×Q₁₆	—	2	2	no	—
163	C₅×SD₁₆	—	2	4	no	—
164	C₅×D₈	—	2	2	no	—
165	C₅×M₁₆	—	2	2	no	—
166	C₅×M₁₆	—	2	4	no	—
167	C₂×C₅×C₈	—	2	4	no	—
168	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
169	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
170	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
171	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
172	C₅×C₄⋊C₄	—	2	2	no	—
173	C₅×C₄⋊C₄	—	2	4	no	—
174	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
175	C₅×C₂²⋊C₄	—	2	4	no	—
176	C₅×C₂²⋊C₄	—	2	4	no	—
177	C₂×#135	C₂×C₃×C₅	1	1	yes	characteristic, complemented
178	C₂×#131	C₂×C₃×C₅	1	1	yes	characteristic, complemented
179	#537	C₂×C₃×C₅	1	2	yes	complemented
180	#468	C₂×C₃×C₅	1	4	yes	complemented
181	#467	C₂×C₃×C₅	1	2	yes	complemented
182	#466	C₂×C₃×C₅	1	2	yes	complemented
183	C₂×#107	C₂×C₃×C₅	1	1	yes	characteristic, complemented
184	#417	C₂×C₃×C₅	1	2	yes	complemented
185	C₂²×C₃×C₅	—	2	1	no	—
186	C₂²×C₃×C₅	—	2	1	no	—
187	C₂²×C₃×C₅	—	2	2	no	—
188	C₂²×C₃×C₅	—	2	2	no	—
189	C₂²×C₃×C₅	—	2	2	no	—
190	C₂²×C₃×C₅	—	4	2	no	—
191	C₂²×C₃×C₅	—	4	2	no	—
192	C₂²×C₃×C₅	—	4	2	no	—
193	C₂²×C₃×C₅	#121	1	2	yes	—
194	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
195	C₃×C₄×C₅	—	2	2	no	—
196	C₃×C₄×C₅	—	4	2	no	—
197	C₃×C₄×C₅	—	4	4	no	—
198	C₃×C₄×C₅	#121	1	2	yes	—
199	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
200	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
201	C₃×#41	—	2	2	no	—
202	C₃×#41	—	2	2	no	—
203	C₃×#41	—	2	4	no	—
204	C₃×#41	—	2	4	no	—
205	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
206	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
207	C₂×C₃×D₄	—	2	2	no	—
208	C₂×C₃×D₄	—	2	4	no	—
209	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
210	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
211	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
212	C₂²×C₃×C₄	—	2	2	no	—
213	C₂²×C₃×C₄	—	2	2	no	—
214	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
215	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
216	C₃×Q₁₆	—	2	2	no	—
217	C₃×SD₁₆	—	2	4	no	—
218	C₃×D₈	—	2	2	no	—
219	C₃×M₁₆	—	2	2	no	—
220	C₃×M₁₆	—	2	4	no	—
221	C₂×C₃×C₈	—	2	4	no	—
222	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
223	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
224	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
225	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
226	C₃×C₄⋊C₄	—	2	2	no	—
227	C₃×C₄⋊C₄	—	2	4	no	—
228	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
229	C₃×C₂²⋊C₄	—	2	4	no	—
230	C₃×C₂²⋊C₄	—	2	4	no	—
231	C₂³×C₅	—	2	2	no	—
232	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
233	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
234	C₅×Q₈	—	2	2	no	—
235	C₅×Q₈	—	2	2	no	—
236	C₅×Q₈	—	2	2	no	—
237	C₅×D₄	—	2	4	no	—
238	C₅×D₄	—	2	2	no	—
239	C₅×D₄	—	2	2	no	—
240	C₅×D₄	—	2	2	no	—
241	C₅×D₄	—	4	4	no	—
242	C₅×D₄	—	8	4	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	4	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	4	4	no	—
248	C₂×C₄×C₅	—	8	2	no	—
249	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
250	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
252	C₂×C₄×C₅	C₃×#41	1	2	yes	—
253	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
254	C₅×C₈	—	2	2	no	—
255	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
256	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
257	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
258	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
259	#135	—	2	4	no	—
260	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
261	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
262	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
263	#131	—	2	4	no	—
264	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
265	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
266	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
267	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
268	C₂²⋊Q₈	—	2	2	no	—
269	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	—
270	#121	—	2	2	no	—
271	#121	—	2	4	no	—
272	#121	C₂²×C₃×C₅	1	4	yes	—
273	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
274	#107	C₂²×C₃×C₅	1	2	yes	—
275	#107	C₂²×C₃×C₅	1	2	yes	—
276	#103	C₂²×C₃×C₅	1	4	yes	—
277	#102	C₂²×C₃×C₅	1	4	yes	—
278	C₂×C₃×C₅	—	2	2	no	—
279	C₂×C₃×C₅	—	4	2	no	—
280	C₂×C₃×C₅	—	8	2	no	—
281	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
282	C₂×C₃×C₅	#576	1	1	yes	characteristic
283	C₂×C₃×C₅	#578	1	1	yes	characteristic
284	C₂³×C₃	—	2	2	no	—
285	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
286	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
287	C₃×Q₈	—	2	2	no	—
288	C₃×Q₈	—	2	2	no	—
289	C₃×Q₈	—	2	2	no	—
290	C₃×D₄	—	2	4	no	—
291	C₃×D₄	—	2	2	no	—
292	C₃×D₄	—	2	2	no	—
293	C₃×D₄	—	2	2	no	—
294	C₃×D₄	—	4	4	no	—
295	C₃×D₄	—	8	4	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	4	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	4	4	no	—
301	C₂×C₃×C₄	—	8	2	no	—
302	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
303	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
304	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
305	C₂×C₃×C₄	C₅×#41	1	2	yes	—
306	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
307	C₃×C₈	—	2	2	no	—
308	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
309	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
310	C₂²×C₅	—	2	1	no	—
311	C₂²×C₅	—	2	1	no	—
312	C₂²×C₅	—	2	2	no	—
313	C₂²×C₅	—	2	2	no	—
314	C₂²×C₅	—	2	2	no	—
315	C₂²×C₅	—	4	2	no	—
316	C₂²×C₅	—	4	2	no	—
317	C₂²×C₅	—	4	2	no	—
318	C₂²×C₅	C₃×#121	1	2	yes	—
319	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
320	C₄×C₅	—	2	2	no	—
321	C₄×C₅	—	4	4	no	—
322	C₄×C₅	—	4	2	no	—
323	C₄×C₅	C₃×#121	1	2	yes	—
324	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
325	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	#41	—	2	4	no	—
329	#41	—	2	4	no	—
330	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
331	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
335	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
336	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
340	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
341	Q₁₆	—	2	2	no	—
342	SD₁₆	—	2	4	no	—
343	D₈	—	2	2	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	4	no	—
346	C₂×C₈	—	2	4	no	—
347	C₂×C₈	C₃×C₅×D₄	1	4	yes	complemented
348	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
349	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
350	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
354	C₂²⋊C₄	—	2	4	no	—
355	C₂²⋊C₄	—	2	4	no	—
356	C₃×C₅	#3061	1	1	yes	characteristic, direct product factor, Hall
357	C₂²×C₃	—	2	1	no	—
358	C₂²×C₃	—	2	1	no	—
359	C₂²×C₃	—	2	2	no	—
360	C₂²×C₃	—	2	2	no	—
361	C₂²×C₃	—	2	2	no	—
362	C₂²×C₃	—	4	2	no	—
363	C₂²×C₃	—	4	2	no	—
364	C₂²×C₃	—	4	2	no	—
365	C₂²×C₃	C₅×#121	1	2	yes	—
366	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
367	C₃×C₄	—	2	2	no	—
368	C₃×C₄	—	4	2	no	—
369	C₃×C₄	—	4	4	no	—
370	C₃×C₄	C₅×#121	1	2	yes	—
371	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
372	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
373	C₂×C₅	—	2	2	no	—
374	C₂×C₅	—	4	2	no	—
375	C₂×C₅	—	8	2	no	—
376	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
377	C₂×C₅	C₃×#576	1	1	yes	characteristic
378	C₂×C₅	C₃×#578	1	1	yes	characteristic
379	C₂³	—	2	2	no	—
380	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
381	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
382	Q₈	—	2	2	no	—
383	Q₈	—	2	2	no	—
384	Q₈	—	2	2	no	—
385	D₄	—	2	4	no	—
386	D₄	—	2	2	no	—
387	D₄	—	2	2	no	—
388	D₄	—	2	2	no	—
389	D₄	—	4	4	no	—
390	D₄	—	8	4	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	8	2	no	—
397	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
398	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
399	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
400	C₂×C₄	C₃×C₅×#41	1	2	yes	—
401	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
404	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
405	C₂×C₃	—	2	2	no	—
406	C₂×C₃	—	4	2	no	—
407	C₂×C₃	—	8	2	no	—
408	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
409	C₂×C₃	C₅×#576	1	1	yes	characteristic
410	C₂×C₃	C₅×#578	1	1	yes	characteristic
411	C₅	C₃×#3061	1	1	yes	characteristic, direct product factor, Sylow
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	C₃×C₅×#121	1	2	yes	—
421	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
422	C₄	—	2	2	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	4	no	—
425	C₄	C₃×C₅×#121	1	2	yes	—
426	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
427	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
428	C₃	C₅×#3061	1	1	yes	characteristic, direct product factor, Sylow
429	C₂	—	2	2	no	—
430	C₂	—	4	2	no	—
431	C₂	—	8	2	no	—
432	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
433	C₂	C₃×C₅×#576	1	1	yes	characteristic
434	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
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#135	C₂	semidirect
2. C₂×C₃×C₅×#131	C₂	semidirect
3. C₃×C₅×#537	C₂	semidirect
4. C₃×C₅×#468	C₂	semidirect
5. C₃×C₅×#467	C₂	semidirect
6. C₃×C₅×#466	C₂	semidirect
7. C₂×C₃×C₅×#107	C₂	semidirect
8. C₃×C₅×#417	C₂	semidirect
9. C₅×#3061	C₃	direct (N × H)
31. C₃×#3061	C₅	direct (N × H)
32. C₂×C₅×#135	C₂×C₃	semidirect
33. C₂×C₅×#131	C₂×C₃	semidirect
34. C₅×#537	C₂×C₃	semidirect
35. C₅×#468	C₂×C₃	semidirect
36. C₅×#467	C₂×C₃	semidirect
37. C₅×#466	C₂×C₃	semidirect
38. C₂×C₅×#107	C₂×C₃	semidirect
39. C₅×#417	C₂×C₃	semidirect
61. C₂×C₃×C₅×C₈	D₄	semidirect
70. C₂×C₃×#135	C₂×C₅	semidirect
71. C₂×C₃×#131	C₂×C₅	semidirect
72. C₃×#537	C₂×C₅	semidirect
73. C₃×#468	C₂×C₅	semidirect
74. C₃×#467	C₂×C₅	semidirect
75. C₃×#466	C₂×C₅	semidirect
76. C₂×C₃×#107	C₂×C₅	semidirect
77. C₃×#417	C₂×C₅	semidirect
99. #3061	C₃×C₅	direct (N × H)
168. C₂×C₅×C₈	C₃×D₄	semidirect
177. C₂×#135	C₂×C₃×C₅	semidirect
178. C₂×#131	C₂×C₃×C₅	semidirect
179. #537	C₂×C₃×C₅	semidirect
180. #468	C₂×C₃×C₅	semidirect
181. #467	C₂×C₃×C₅	semidirect
182. #466	C₂×C₃×C₅	semidirect
183. C₂×#107	C₂×C₃×C₅	semidirect
184. #417	C₂×C₃×C₅	semidirect
222. C₂×C₃×C₈	C₅×D₄	semidirect
347. C₂×C₈	C₃×C₅×D₄	semidirect
356. C₃×C₅	#3061	direct (N × H)
411. C₅	C₃×#3061	direct (N × H)
428. C₃	C₅×#3061	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×#135	2
C₂×C₃×C₅×#131	2
C₃×C₅×#537	2
C₃×C₅×#468	2
C₃×C₅×#467	2
C₃×C₅×#466	2
C₂×C₃×C₅×#107	2
C₃×C₅×#417	2
C₅×#3061	3
C₃×#3061	5

Subgroups — C3×C5×#3061 #14276095

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3061 #14276095