Subgroups — C₃×C₅×#3035 #14276069

Order 1920.

992 conjugacy classes of subgroups.

The subgroup lattice has 604 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	2	yes	maximal, complemented
2	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#464	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#463	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#462	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#461	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#460	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#459	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#416	C₂	1	2	yes	maximal, complemented
12	C₅×#3035	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
14	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
15	C₃×C₅×#135	—	2	8	no	—
16	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
18	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
19	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
20	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
21	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₃×C₅×#127	C₂²	1	1	yes	characteristic
23	C₃×C₅×#124	C₂²	1	2	yes	—
24	C₃×C₅×#121	—	2	1	no	—
25	C₃×C₅×#121	—	2	1	no	—
26	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
28	C₃×C₄×C₅×D₄	—	2	1	no	—
29	C₃×C₄×C₅×D₄	—	2	1	no	—
30	C₃×C₄×C₅×D₄	—	2	1	no	—
31	C₃×C₄×C₅×D₄	—	2	1	no	—
32	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
33	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₃×C₅×#117	—	2	1	no	—
35	C₃×C₅×#117	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄²×C₅	—	2	1	no	—
37	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
38	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
41	C₃×C₅×#103	C₂²	1	2	yes	—
42	C₃×C₅×#103	C₂²	1	2	yes	—
43	C₃×C₅×#102	C₂²	1	2	yes	—
44	C₃×C₅×#102	C₂²	1	2	yes	—
45	C₃×#3035	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
46	C₂×C₅×#135	C₂×C₃	1	2	yes	complemented
47	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
48	C₄×C₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#464	C₂×C₃	1	2	yes	complemented
50	C₅×#463	C₂×C₃	1	2	yes	complemented
51	C₅×#462	C₂×C₃	1	1	yes	characteristic, complemented
52	C₅×#461	C₂×C₃	1	1	yes	characteristic, complemented
53	C₅×#460	C₂×C₃	1	1	yes	characteristic, complemented
54	C₅×#459	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×C₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
56	C₅×#416	C₂×C₃	1	2	yes	complemented
57	C₃×C₅×#41	—	2	2	no	—
58	C₃×C₅×#41	—	2	4	no	—
59	C₃×C₅×#41	—	2	4	no	—
60	C₃×C₅×#41	D₄	1	4	yes	complemented
61	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
62	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×D₄	—	2	1	no	—
64	C₂×C₃×C₅×D₄	—	2	2	no	—
65	C₂×C₃×C₅×D₄	—	2	1	no	—
66	C₂×C₃×C₅×D₄	—	2	1	no	—
67	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
68	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	—	2	1	no	—
70	C₂²×C₃×C₄×C₅	—	2	1	no	—
71	C₂²×C₃×C₄×C₅	—	2	1	no	—
72	C₂²×C₃×C₄×C₅	—	2	2	no	—
73	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
74	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
75	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₃×C₅×Q₁₆	—	2	4	no	—
77	C₃×C₅×SD₁₆	—	2	4	no	—
78	C₃×C₅×SD₁₆	—	2	4	no	—
79	C₃×C₅×D₈	—	2	4	no	—
80	C₂×C₃×C₅×C₈	—	2	4	no	—
81	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
82	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
83	C₃×C₅×C₄⋊C₄	—	2	1	no	—
84	C₃×C₅×C₄⋊C₄	—	2	1	no	—
85	C₃×C₅×C₄⋊C₄	—	2	1	no	—
86	C₃×C₅×C₄⋊C₄	—	2	1	no	—
87	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
90	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
91	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
92	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
93	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
94	C₃×C₄²×C₅	—	2	1	no	—
95	C₃×C₄²×C₅	—	2	1	no	—
96	C₃×C₄²×C₅	—	2	1	no	—
97	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
98	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
99	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
100	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
101	C₂×C₃×#135	C₂×C₅	1	2	yes	complemented
102	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
103	C₃×C₄×#41	C₂×C₅	1	1	yes	characteristic, complemented
104	C₃×#464	C₂×C₅	1	2	yes	complemented
105	C₃×#463	C₂×C₅	1	2	yes	complemented
106	C₃×#462	C₂×C₅	1	1	yes	characteristic, complemented
107	C₃×#461	C₂×C₅	1	1	yes	characteristic, complemented
108	C₃×#460	C₂×C₅	1	1	yes	characteristic, complemented
109	C₃×#459	C₂×C₅	1	1	yes	characteristic, complemented
110	C₂×C₃×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
111	C₃×#416	C₂×C₅	1	2	yes	complemented
112	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
113	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
114	C₅×#135	—	2	8	no	—
115	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
116	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
117	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
118	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
119	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
120	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
121	C₅×#127	C₂²×C₃	1	1	yes	characteristic
122	C₅×#124	C₂²×C₃	1	2	yes	—
123	C₅×#121	—	2	1	no	—
124	C₅×#121	—	2	1	no	—
125	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
126	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
127	C₄×C₅×D₄	—	2	1	no	—
128	C₄×C₅×D₄	—	2	1	no	—
129	C₄×C₅×D₄	—	2	1	no	—
130	C₄×C₅×D₄	—	2	1	no	—
131	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
132	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
133	C₅×#117	—	2	1	no	—
134	C₅×#117	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₄²×C₅	—	2	1	no	—
136	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
137	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
138	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
139	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
140	C₅×#103	C₂²×C₃	1	2	yes	—
141	C₅×#103	C₂²×C₃	1	2	yes	—
142	C₅×#102	C₂²×C₃	1	2	yes	—
143	C₅×#102	C₂²×C₃	1	2	yes	—
144	#3035	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
145	C₂³×C₃×C₅	—	2	1	no	—
146	C₂³×C₃×C₅	—	2	2	no	—
147	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
148	C₃×C₅×Q₈	—	2	1	no	—
149	C₃×C₅×Q₈	—	2	2	no	—
150	C₃×C₅×Q₈	—	2	2	no	—
151	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
152	C₃×C₅×D₄	—	2	4	no	—
153	C₃×C₅×D₄	—	2	2	no	—
154	C₃×C₅×D₄	—	2	1	no	—
155	C₃×C₅×D₄	—	2	2	no	—
156	C₃×C₅×D₄	—	4	2	no	—
157	C₃×C₅×D₄	—	4	4	no	—
158	C₃×C₅×D₄	—	4	2	no	—
159	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
160	C₂×C₃×C₄×C₅	—	2	1	no	—
161	C₂×C₃×C₄×C₅	—	2	4	no	—
162	C₂×C₃×C₄×C₅	—	2	2	no	—
163	C₂×C₃×C₄×C₅	—	2	1	no	—
164	C₂×C₃×C₄×C₅	—	2	1	no	—
165	C₂×C₃×C₄×C₅	—	2	2	no	—
166	C₂×C₃×C₄×C₅	—	4	1	no	—
167	C₂×C₃×C₄×C₅	—	4	2	no	—
168	C₂×C₃×C₄×C₅	—	4	4	no	—
169	C₂×C₃×C₄×C₅	—	4	2	no	—
170	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
171	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
172	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
173	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
174	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
175	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
176	C₂×C₃×C₄×C₅	#41	1	2	yes	—
177	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
178	C₃×C₅×C₈	—	2	2	no	—
179	C₃×C₅×C₈	—	2	2	no	—
180	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
181	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
182	C₃×#135	—	2	8	no	—
183	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
184	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
185	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
186	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
187	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
188	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
189	C₃×#127	C₂²×C₅	1	1	yes	characteristic
190	C₃×#124	C₂²×C₅	1	2	yes	—
191	C₃×#121	—	2	1	no	—
192	C₃×#121	—	2	1	no	—
193	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
194	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
195	C₃×C₄×D₄	—	2	1	no	—
196	C₃×C₄×D₄	—	2	1	no	—
197	C₃×C₄×D₄	—	2	1	no	—
198	C₃×C₄×D₄	—	2	1	no	—
199	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
200	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
201	C₃×#117	—	2	1	no	—
202	C₃×#117	C₂²×C₅	1	1	yes	characteristic
203	C₂×C₃×C₄²	—	2	1	no	—
204	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
205	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
206	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
207	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
208	C₃×#103	C₂²×C₅	1	2	yes	—
209	C₃×#103	C₂²×C₅	1	2	yes	—
210	C₃×#102	C₂²×C₅	1	2	yes	—
211	C₃×#102	C₂²×C₅	1	2	yes	—
212	C₅×#41	—	2	2	no	—
213	C₅×#41	—	2	4	no	—
214	C₅×#41	—	2	4	no	—
215	C₅×#41	C₃×D₄	1	4	yes	complemented
216	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
217	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
218	C₂×C₅×D₄	—	2	1	no	—
219	C₂×C₅×D₄	—	2	2	no	—
220	C₂×C₅×D₄	—	2	1	no	—
221	C₂×C₅×D₄	—	2	1	no	—
222	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
223	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
224	C₂²×C₄×C₅	—	2	1	no	—
225	C₂²×C₄×C₅	—	2	1	no	—
226	C₂²×C₄×C₅	—	2	1	no	—
227	C₂²×C₄×C₅	—	2	2	no	—
228	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
231	C₅×Q₁₆	—	2	4	no	—
232	C₅×SD₁₆	—	2	4	no	—
233	C₅×SD₁₆	—	2	4	no	—
234	C₅×D₈	—	2	4	no	—
235	C₂×C₅×C₈	—	2	4	no	—
236	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
237	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
238	C₅×C₄⋊C₄	—	2	1	no	—
239	C₅×C₄⋊C₄	—	2	1	no	—
240	C₅×C₄⋊C₄	—	2	1	no	—
241	C₅×C₄⋊C₄	—	2	1	no	—
242	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
243	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
244	C₅×C₂²⋊C₄	—	2	1	no	—
245	C₅×C₂²⋊C₄	—	2	1	no	—
246	C₅×C₂²⋊C₄	—	2	1	no	—
247	C₅×C₂²⋊C₄	—	2	2	no	—
248	C₅×C₂²⋊C₄	—	2	2	no	—
249	C₄²×C₅	—	2	1	no	—
250	C₄²×C₅	—	2	1	no	—
251	C₄²×C₅	—	2	1	no	—
252	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
253	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
254	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
255	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
256	C₂×#135	C₂×C₃×C₅	1	2	yes	complemented
257	#532	C₂×C₃×C₅	1	1	yes	characteristic, complemented
258	C₄×#41	C₂×C₃×C₅	1	1	yes	characteristic, complemented
259	#464	C₂×C₃×C₅	1	2	yes	complemented
260	#463	C₂×C₃×C₅	1	2	yes	complemented
261	#462	C₂×C₃×C₅	1	1	yes	characteristic, complemented
262	#461	C₂×C₃×C₅	1	1	yes	characteristic, complemented
263	#460	C₂×C₃×C₅	1	1	yes	characteristic, complemented
264	#459	C₂×C₃×C₅	1	1	yes	characteristic, complemented
265	C₂×C₄⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
266	#416	C₂×C₃×C₅	1	2	yes	complemented
267	C₂²×C₃×C₅	—	2	1	no	—
268	C₂²×C₃×C₅	—	2	1	no	—
269	C₂²×C₃×C₅	—	2	2	no	—
270	C₂²×C₃×C₅	—	4	1	no	—
271	C₂²×C₃×C₅	—	4	1	no	—
272	C₂²×C₃×C₅	—	4	2	no	—
273	C₂²×C₃×C₅	—	4	2	no	—
274	C₂²×C₃×C₅	—	4	2	no	—
275	C₂²×C₃×C₅	#121	1	2	yes	—
276	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
277	C₃×C₄×C₅	—	2	2	no	—
278	C₃×C₄×C₅	—	2	1	no	—
279	C₃×C₄×C₅	—	2	1	no	—
280	C₃×C₄×C₅	—	2	1	no	—
281	C₃×C₄×C₅	—	4	2	no	—
282	C₃×C₄×C₅	—	4	1	no	—
283	C₃×C₄×C₅	—	4	1	no	—
284	C₃×C₄×C₅	#121	1	2	yes	—
285	C₃×C₄×C₅	#135	1	2	yes	complemented
286	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
287	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
288	C₃×#41	—	2	2	no	—
289	C₃×#41	—	2	4	no	—
290	C₃×#41	—	2	4	no	—
291	C₃×#41	C₅×D₄	1	4	yes	complemented
292	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
293	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
294	C₂×C₃×D₄	—	2	1	no	—
295	C₂×C₃×D₄	—	2	2	no	—
296	C₂×C₃×D₄	—	2	1	no	—
297	C₂×C₃×D₄	—	2	1	no	—
298	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
299	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
300	C₂²×C₃×C₄	—	2	1	no	—
301	C₂²×C₃×C₄	—	2	1	no	—
302	C₂²×C₃×C₄	—	2	1	no	—
303	C₂²×C₃×C₄	—	2	2	no	—
304	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
305	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
306	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
307	C₃×Q₁₆	—	2	4	no	—
308	C₃×SD₁₆	—	2	4	no	—
309	C₃×SD₁₆	—	2	4	no	—
310	C₃×D₈	—	2	4	no	—
311	C₂×C₃×C₈	—	2	4	no	—
312	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
313	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
314	C₃×C₄⋊C₄	—	2	1	no	—
315	C₃×C₄⋊C₄	—	2	1	no	—
316	C₃×C₄⋊C₄	—	2	1	no	—
317	C₃×C₄⋊C₄	—	2	1	no	—
318	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
319	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
320	C₃×C₂²⋊C₄	—	2	1	no	—
321	C₃×C₂²⋊C₄	—	2	1	no	—
322	C₃×C₂²⋊C₄	—	2	1	no	—
323	C₃×C₂²⋊C₄	—	2	2	no	—
324	C₃×C₂²⋊C₄	—	2	2	no	—
325	C₃×C₄²	—	2	1	no	—
326	C₃×C₄²	—	2	1	no	—
327	C₃×C₄²	—	2	1	no	—
328	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
329	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
330	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
331	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
332	C₂³×C₅	—	2	1	no	—
333	C₂³×C₅	—	2	2	no	—
334	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
335	C₅×Q₈	—	2	1	no	—
336	C₅×Q₈	—	2	2	no	—
337	C₅×Q₈	—	2	2	no	—
338	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
339	C₅×D₄	—	2	4	no	—
340	C₅×D₄	—	2	2	no	—
341	C₅×D₄	—	2	1	no	—
342	C₅×D₄	—	2	2	no	—
343	C₅×D₄	—	4	2	no	—
344	C₅×D₄	—	4	4	no	—
345	C₅×D₄	—	4	2	no	—
346	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
347	C₂×C₄×C₅	—	2	1	no	—
348	C₂×C₄×C₅	—	2	4	no	—
349	C₂×C₄×C₅	—	2	2	no	—
350	C₂×C₄×C₅	—	2	1	no	—
351	C₂×C₄×C₅	—	2	1	no	—
352	C₂×C₄×C₅	—	2	2	no	—
353	C₂×C₄×C₅	—	4	1	no	—
354	C₂×C₄×C₅	—	4	2	no	—
355	C₂×C₄×C₅	—	4	4	no	—
356	C₂×C₄×C₅	—	4	2	no	—
357	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
358	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
359	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
360	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
361	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
362	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
363	C₂×C₄×C₅	C₃×#41	1	2	yes	—
364	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
365	C₅×C₈	—	2	2	no	—
366	C₅×C₈	—	2	2	no	—
367	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
368	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
369	#135	—	2	8	no	—
370	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
371	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
372	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
373	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
374	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
375	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
376	#127	C₂²×C₃×C₅	1	1	yes	characteristic
377	#124	C₂²×C₃×C₅	1	2	yes	—
378	#121	—	2	1	no	—
379	#121	—	2	1	no	—
380	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
381	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	—	2	1	no	—
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
387	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
388	#117	—	2	1	no	—
389	#117	C₂²×C₃×C₅	1	1	yes	characteristic
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
392	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
393	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
394	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
395	#103	C₂²×C₃×C₅	1	2	yes	—
396	#103	C₂²×C₃×C₅	1	2	yes	—
397	#102	C₂²×C₃×C₅	1	2	yes	—
398	#102	C₂²×C₃×C₅	1	2	yes	—
399	C₂×C₃×C₅	—	2	2	no	—
400	C₂×C₃×C₅	—	4	2	no	—
401	C₂×C₃×C₅	—	8	2	no	—
402	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
403	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
404	C₂×C₃×C₅	#575	1	1	yes	characteristic
405	C₂³×C₃	—	2	1	no	—
406	C₂³×C₃	—	2	2	no	—
407	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
408	C₃×Q₈	—	2	1	no	—
409	C₃×Q₈	—	2	2	no	—
410	C₃×Q₈	—	2	2	no	—
411	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
412	C₃×D₄	—	2	4	no	—
413	C₃×D₄	—	2	2	no	—
414	C₃×D₄	—	2	1	no	—
415	C₃×D₄	—	2	2	no	—
416	C₃×D₄	—	4	2	no	—
417	C₃×D₄	—	4	4	no	—
418	C₃×D₄	—	4	2	no	—
419	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
420	C₂×C₃×C₄	—	2	1	no	—
421	C₂×C₃×C₄	—	2	4	no	—
422	C₂×C₃×C₄	—	2	2	no	—
423	C₂×C₃×C₄	—	2	1	no	—
424	C₂×C₃×C₄	—	2	1	no	—
425	C₂×C₃×C₄	—	2	2	no	—
426	C₂×C₃×C₄	—	4	1	no	—
427	C₂×C₃×C₄	—	4	2	no	—
428	C₂×C₃×C₄	—	4	4	no	—
429	C₂×C₃×C₄	—	4	2	no	—
430	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
431	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
432	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
433	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
434	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
435	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
436	C₂×C₃×C₄	C₅×#41	1	2	yes	—
437	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
438	C₃×C₈	—	2	2	no	—
439	C₃×C₈	—	2	2	no	—
440	C₂²×C₅	—	2	1	no	—
441	C₂²×C₅	—	2	1	no	—
442	C₂²×C₅	—	2	2	no	—
443	C₂²×C₅	—	4	1	no	—
444	C₂²×C₅	—	4	1	no	—
445	C₂²×C₅	—	4	2	no	—
446	C₂²×C₅	—	4	2	no	—
447	C₂²×C₅	—	4	2	no	—
448	C₂²×C₅	C₃×#121	1	2	yes	—
449	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
450	C₄×C₅	—	2	1	no	—
451	C₄×C₅	—	2	1	no	—
452	C₄×C₅	—	2	1	no	—
453	C₄×C₅	—	2	2	no	—
454	C₄×C₅	—	4	1	no	—
455	C₄×C₅	—	4	1	no	—
456	C₄×C₅	—	4	2	no	—
457	C₄×C₅	C₃×#121	1	2	yes	—
458	C₄×C₅	C₃×#135	1	2	yes	complemented
459	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
460	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
461	#41	—	2	2	no	—
462	#41	—	2	4	no	—
463	#41	—	2	4	no	—
464	#41	C₃×C₅×D₄	1	4	yes	complemented
465	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
466	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
467	C₂×D₄	—	2	1	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
472	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
478	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
479	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
480	Q₁₆	—	2	4	no	—
481	SD₁₆	—	2	4	no	—
482	SD₁₆	—	2	4	no	—
483	D₈	—	2	4	no	—
484	C₂×C₈	—	2	4	no	—
485	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
486	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
492	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₂²⋊C₄	—	2	1	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
502	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
503	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
504	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
505	C₃×C₅	#3035	1	1	yes	characteristic, direct product factor, Hall
506	C₂²×C₃	—	2	1	no	—
507	C₂²×C₃	—	2	1	no	—
508	C₂²×C₃	—	2	2	no	—
509	C₂²×C₃	—	4	1	no	—
510	C₂²×C₃	—	4	1	no	—
511	C₂²×C₃	—	4	2	no	—
512	C₂²×C₃	—	4	2	no	—
513	C₂²×C₃	—	4	2	no	—
514	C₂²×C₃	C₅×#121	1	2	yes	—
515	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
516	C₃×C₄	—	2	2	no	—
517	C₃×C₄	—	2	1	no	—
518	C₃×C₄	—	2	1	no	—
519	C₃×C₄	—	2	1	no	—
520	C₃×C₄	—	4	2	no	—
521	C₃×C₄	—	4	1	no	—
522	C₃×C₄	—	4	1	no	—
523	C₃×C₄	C₅×#121	1	2	yes	—
524	C₃×C₄	C₅×#135	1	2	yes	complemented
525	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
526	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
527	C₂×C₅	—	2	2	no	—
528	C₂×C₅	—	4	2	no	—
529	C₂×C₅	—	8	2	no	—
530	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
531	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
532	C₂×C₅	C₃×#575	1	1	yes	characteristic
533	C₂³	—	2	1	no	—
534	C₂³	—	2	2	no	—
535	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
536	Q₈	—	2	1	no	—
537	Q₈	—	2	2	no	—
538	Q₈	—	2	2	no	—
539	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
540	D₄	—	2	4	no	—
541	D₄	—	2	2	no	—
542	D₄	—	2	1	no	—
543	D₄	—	2	2	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	4	no	—
546	D₄	—	4	2	no	—
547	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	4	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	4	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
559	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
560	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
561	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
562	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
563	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
564	C₂×C₄	C₃×C₅×#41	1	2	yes	—
565	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
566	C₈	—	2	2	no	—
567	C₈	—	2	2	no	—
568	C₂×C₃	—	2	2	no	—
569	C₂×C₃	—	4	2	no	—
570	C₂×C₃	—	8	2	no	—
571	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
572	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
573	C₂×C₃	C₅×#575	1	1	yes	characteristic
574	C₅	C₃×#3035	1	1	yes	characteristic, direct product factor, Sylow
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	C₃×C₅×#121	1	2	yes	—
584	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
585	C₄	—	2	2	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	4	2	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	C₃×C₅×#121	1	2	yes	—
593	C₄	C₃×C₅×#135	1	2	yes	complemented
594	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
595	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
596	C₃	C₅×#3035	1	1	yes	characteristic, direct product factor, Sylow
597	C₂	—	2	2	no	—
598	C₂	—	4	2	no	—
599	C₂	—	8	2	no	—
600	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
601	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
602	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
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. C₂×C₃×C₅×#135	C₂	semidirect
2. C₃×C₅×#532	C₂	semidirect
3. C₃×C₄×C₅×#41	C₂	semidirect
4. C₃×C₅×#464	C₂	semidirect
5. C₃×C₅×#463	C₂	semidirect
6. C₃×C₅×#462	C₂	semidirect
7. C₃×C₅×#461	C₂	semidirect
8. C₃×C₅×#460	C₂	semidirect
9. C₃×C₅×#459	C₂	semidirect
10. C₂×C₃×C₅×C₄⋊C₈	C₂	semidirect
11. C₃×C₅×#416	C₂	semidirect
12. C₅×#3035	C₃	direct (N × H)
45. C₃×#3035	C₅	direct (N × H)
46. C₂×C₅×#135	C₂×C₃	semidirect
47. C₅×#532	C₂×C₃	semidirect
48. C₄×C₅×#41	C₂×C₃	semidirect
49. C₅×#464	C₂×C₃	semidirect
50. C₅×#463	C₂×C₃	semidirect
51. C₅×#462	C₂×C₃	semidirect
52. C₅×#461	C₂×C₃	semidirect
53. C₅×#460	C₂×C₃	semidirect
54. C₅×#459	C₂×C₃	semidirect
55. C₂×C₅×C₄⋊C₈	C₂×C₃	semidirect
56. C₅×#416	C₂×C₃	semidirect
60. C₃×C₅×#41	D₄	semidirect
101. C₂×C₃×#135	C₂×C₅	semidirect
102. C₃×#532	C₂×C₅	semidirect
103. C₃×C₄×#41	C₂×C₅	semidirect
104. C₃×#464	C₂×C₅	semidirect
105. C₃×#463	C₂×C₅	semidirect
106. C₃×#462	C₂×C₅	semidirect
107. C₃×#461	C₂×C₅	semidirect
108. C₃×#460	C₂×C₅	semidirect
109. C₃×#459	C₂×C₅	semidirect
110. C₂×C₃×C₄⋊C₈	C₂×C₅	semidirect
111. C₃×#416	C₂×C₅	semidirect
144. #3035	C₃×C₅	direct (N × H)
215. C₅×#41	C₃×D₄	semidirect
256. C₂×#135	C₂×C₃×C₅	semidirect
257. #532	C₂×C₃×C₅	semidirect
258. C₄×#41	C₂×C₃×C₅	semidirect
259. #464	C₂×C₃×C₅	semidirect
260. #463	C₂×C₃×C₅	semidirect
261. #462	C₂×C₃×C₅	semidirect
262. #461	C₂×C₃×C₅	semidirect
263. #460	C₂×C₃×C₅	semidirect
264. #459	C₂×C₃×C₅	semidirect
265. C₂×C₄⋊C₈	C₂×C₃×C₅	semidirect
266. #416	C₂×C₃×C₅	semidirect
285. C₃×C₄×C₅	#135	semidirect
291. C₃×#41	C₅×D₄	semidirect
458. C₄×C₅	C₃×#135	semidirect
464. #41	C₃×C₅×D₄	semidirect
505. C₃×C₅	#3035	direct (N × H)
524. C₃×C₄	C₅×#135	semidirect
574. C₅	C₃×#3035	direct (N × H)
593. C₄	C₃×C₅×#135	semidirect
596. C₃	C₅×#3035	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
C₃×C₅×#532	2
C₃×C₄×C₅×#41	2
C₃×C₅×#464	2
C₃×C₅×#463	2
C₃×C₅×#462	2
C₃×C₅×#461	2
C₃×C₅×#460	2
C₃×C₅×#459	2
C₂×C₃×C₅×C₄⋊C₈	2
C₃×C₅×#416	2
C₅×#3035	3
C₃×#3035	5

Subgroups — C3×C5×#3035 #14276069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3035 #14276069