Subgroups — C₃×C₅×#3037 #14276071

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#137	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#464	C₂	1	4	yes	maximal, complemented
5	C₃×C₅×#462	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#460	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#417	C₂	1	2	yes	maximal, complemented
9	C₅×#3037	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₃×C₅×#137	—	2	8	no	—
13	C₂×C₃×C₅×Q₁₆	C₂²	1	4	yes	—
14	C₂×C₃×C₅×SD₁₆	C₂²	1	4	yes	—
15	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
16	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₃×C₅×#127	C₂²	1	1	yes	characteristic
18	C₃×C₅×#124	C₂²	1	2	yes	—
19	C₃×C₅×#121	—	2	1	no	—
20	C₃×C₅×#121	—	2	1	no	—
21	C₃×C₄×C₅×Q₈	—	2	1	no	—
22	C₃×C₄×C₅×Q₈	—	2	1	no	—
23	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
24	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
25	C₃×C₄×C₅×D₄	—	2	1	no	—
26	C₃×C₄×C₅×D₄	—	2	1	no	—
27	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
28	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄²×C₅	—	2	1	no	—
30	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
31	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
32	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
33	C₃×C₅×#103	C₂²	1	4	yes	—
34	C₃×C₅×#102	C₂²	1	4	yes	—
35	C₃×#3037	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
36	C₂×C₅×#137	C₂×C₃	1	2	yes	complemented
37	C₅×#532	C₂×C₃	1	1	yes	characteristic
38	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
39	C₅×#464	C₂×C₃	1	4	yes	complemented
40	C₅×#462	C₂×C₃	1	2	yes	complemented
41	C₅×#460	C₂×C₃	1	2	yes	complemented
42	C₅×#423	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#417	C₂×C₃	1	2	yes	complemented
44	C₃×C₅×#41	—	2	4	no	—
45	C₃×C₅×#41	—	2	4	no	—
46	C₂×C₃×C₅×Q₈	—	2	1	no	—
47	C₂×C₃×C₅×Q₈	—	2	2	no	—
48	C₂×C₃×C₅×Q₈	D₄	1	4	yes	complemented
49	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
50	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
51	C₂×C₃×C₅×D₄	—	2	2	no	—
52	C₂×C₃×C₅×D₄	—	2	1	no	—
53	C₂×C₃×C₅×D₄	—	2	1	no	—
54	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	—	2	1	no	—
56	C₂²×C₃×C₄×C₅	—	2	1	no	—
57	C₂²×C₃×C₄×C₅	—	2	2	no	—
58	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
59	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₃×C₅×Q₁₆	—	2	8	no	—
62	C₃×C₅×SD₁₆	—	2	8	no	—
63	C₃×C₅×M₁₆	—	2	4	no	—
64	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
65	C₃×C₅×C₄⋊C₄	—	2	2	no	—
66	C₃×C₅×C₄⋊C₄	—	2	2	no	—
67	C₃×C₅×C₄⋊C₄	—	2	1	no	—
68	C₃×C₅×C₄⋊C₄	—	2	1	no	—
69	C₃×C₅×C₄⋊C₄	—	2	1	no	—
70	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
71	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
72	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
73	C₃×C₄²×C₅	—	2	2	no	—
74	C₃×C₄²×C₅	—	2	2	no	—
75	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
76	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
77	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₃×#137	C₂×C₅	1	2	yes	complemented
80	C₃×#532	C₂×C₅	1	1	yes	characteristic
81	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
82	C₃×#464	C₂×C₅	1	4	yes	complemented
83	C₃×#462	C₂×C₅	1	2	yes	complemented
84	C₃×#460	C₂×C₅	1	2	yes	complemented
85	C₃×#423	C₂×C₅	1	1	yes	characteristic, complemented
86	C₃×#417	C₂×C₅	1	2	yes	complemented
87	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
88	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
89	C₅×#137	—	2	8	no	—
90	C₂×C₅×Q₁₆	C₂²×C₃	1	4	yes	—
91	C₂×C₅×SD₁₆	C₂²×C₃	1	4	yes	—
92	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
93	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
94	C₅×#127	C₂²×C₃	1	1	yes	characteristic
95	C₅×#124	C₂²×C₃	1	2	yes	—
96	C₅×#121	—	2	1	no	—
97	C₅×#121	—	2	1	no	—
98	C₄×C₅×Q₈	—	2	1	no	—
99	C₄×C₅×Q₈	—	2	1	no	—
100	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
101	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
102	C₄×C₅×D₄	—	2	1	no	—
103	C₄×C₅×D₄	—	2	1	no	—
104	C₂×C₅×C₄⋊C₄	—	2	1	no	—
105	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₄²×C₅	—	2	1	no	—
107	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
108	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
109	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
110	C₅×#103	C₂²×C₃	1	4	yes	—
111	C₅×#102	C₂²×C₃	1	4	yes	—
112	#3037	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
113	C₂³×C₃×C₅	—	2	2	no	—
114	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
115	C₃×C₅×Q₈	—	2	4	no	—
116	C₃×C₅×Q₈	—	2	2	no	—
117	C₃×C₅×Q₈	—	2	2	no	—
118	C₃×C₅×Q₈	—	2	2	no	—
119	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
120	C₃×C₅×D₄	—	2	2	no	—
121	C₃×C₅×D₄	—	2	2	no	—
122	C₃×C₅×D₄	—	4	2	no	—
123	C₃×C₅×D₄	—	4	4	no	—
124	C₃×C₅×D₄	—	4	2	no	—
125	C₂×C₃×C₄×C₅	—	2	4	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	4	1	no	—
131	C₂×C₃×C₄×C₅	—	4	2	no	—
132	C₂×C₃×C₄×C₅	—	4	4	no	—
133	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	#41	1	2	yes	—
140	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
141	C₃×C₅×C₈	—	2	4	no	—
142	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
143	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
144	C₃×#137	—	2	8	no	—
145	C₂×C₃×Q₁₆	C₂²×C₅	1	4	yes	—
146	C₂×C₃×SD₁₆	C₂²×C₅	1	4	yes	—
147	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
148	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
149	C₃×#127	C₂²×C₅	1	1	yes	characteristic
150	C₃×#124	C₂²×C₅	1	2	yes	—
151	C₃×#121	—	2	1	no	—
152	C₃×#121	—	2	1	no	—
153	C₃×C₄×Q₈	—	2	1	no	—
154	C₃×C₄×Q₈	—	2	1	no	—
155	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
156	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
157	C₃×C₄×D₄	—	2	1	no	—
158	C₃×C₄×D₄	—	2	1	no	—
159	C₂×C₃×C₄⋊C₄	—	2	1	no	—
160	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
161	C₂×C₃×C₄²	—	2	1	no	—
162	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
163	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
164	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
165	C₃×#103	C₂²×C₅	1	4	yes	—
166	C₃×#102	C₂²×C₅	1	4	yes	—
167	C₅×#41	—	2	4	no	—
168	C₅×#41	—	2	4	no	—
169	C₂×C₅×Q₈	—	2	1	no	—
170	C₂×C₅×Q₈	—	2	2	no	—
171	C₂×C₅×Q₈	C₃×D₄	1	4	yes	complemented
172	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
173	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
174	C₂×C₅×D₄	—	2	2	no	—
175	C₂×C₅×D₄	—	2	1	no	—
176	C₂×C₅×D₄	—	2	1	no	—
177	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
178	C₂²×C₄×C₅	—	2	1	no	—
179	C₂²×C₄×C₅	—	2	1	no	—
180	C₂²×C₄×C₅	—	2	2	no	—
181	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
184	C₅×Q₁₆	—	2	8	no	—
185	C₅×SD₁₆	—	2	8	no	—
186	C₅×M₁₆	—	2	4	no	—
187	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
188	C₅×C₄⋊C₄	—	2	2	no	—
189	C₅×C₄⋊C₄	—	2	2	no	—
190	C₅×C₄⋊C₄	—	2	1	no	—
191	C₅×C₄⋊C₄	—	2	1	no	—
192	C₅×C₄⋊C₄	—	2	1	no	—
193	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
194	C₅×C₂²⋊C₄	—	2	2	no	—
195	C₅×C₂²⋊C₄	—	2	2	no	—
196	C₄²×C₅	—	2	2	no	—
197	C₄²×C₅	—	2	2	no	—
198	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
199	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
200	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
201	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
202	C₂×#137	C₂×C₃×C₅	1	2	yes	complemented
203	#532	C₂×C₃×C₅	1	1	yes	characteristic
204	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
205	#464	C₂×C₃×C₅	1	4	yes	complemented
206	#462	C₂×C₃×C₅	1	2	yes	complemented
207	#460	C₂×C₃×C₅	1	2	yes	complemented
208	#423	C₂×C₃×C₅	1	1	yes	characteristic, complemented
209	#417	C₂×C₃×C₅	1	2	yes	complemented
210	C₂²×C₃×C₅	—	2	1	no	—
211	C₂²×C₃×C₅	—	2	1	no	—
212	C₂²×C₃×C₅	—	4	2	no	—
213	C₂²×C₃×C₅	—	4	2	no	—
214	C₂²×C₃×C₅	—	4	2	no	—
215	C₂²×C₃×C₅	#121	1	2	yes	—
216	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
217	C₃×C₄×C₅	—	2	4	no	—
218	C₃×C₄×C₅	—	2	1	no	—
219	C₃×C₄×C₅	—	2	1	no	—
220	C₃×C₄×C₅	—	2	1	no	—
221	C₃×C₄×C₅	—	4	2	no	—
222	C₃×C₄×C₅	—	4	2	no	—
223	C₃×C₄×C₅	#121	1	2	yes	—
224	C₃×C₄×C₅	#137	1	2	yes	complemented
225	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
226	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
227	C₃×#41	—	2	4	no	—
228	C₃×#41	—	2	4	no	—
229	C₂×C₃×Q₈	—	2	1	no	—
230	C₂×C₃×Q₈	—	2	2	no	—
231	C₂×C₃×Q₈	C₅×D₄	1	4	yes	complemented
232	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
233	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
234	C₂×C₃×D₄	—	2	2	no	—
235	C₂×C₃×D₄	—	2	1	no	—
236	C₂×C₃×D₄	—	2	1	no	—
237	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
238	C₂²×C₃×C₄	—	2	1	no	—
239	C₂²×C₃×C₄	—	2	1	no	—
240	C₂²×C₃×C₄	—	2	2	no	—
241	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
242	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
243	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
244	C₃×Q₁₆	—	2	8	no	—
245	C₃×SD₁₆	—	2	8	no	—
246	C₃×M₁₆	—	2	4	no	—
247	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
248	C₃×C₄⋊C₄	—	2	2	no	—
249	C₃×C₄⋊C₄	—	2	2	no	—
250	C₃×C₄⋊C₄	—	2	1	no	—
251	C₃×C₄⋊C₄	—	2	1	no	—
252	C₃×C₄⋊C₄	—	2	1	no	—
253	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
254	C₃×C₂²⋊C₄	—	2	2	no	—
255	C₃×C₂²⋊C₄	—	2	2	no	—
256	C₃×C₄²	—	2	2	no	—
257	C₃×C₄²	—	2	2	no	—
258	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
259	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
260	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
261	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
262	C₂³×C₅	—	2	2	no	—
263	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
264	C₅×Q₈	—	2	4	no	—
265	C₅×Q₈	—	2	2	no	—
266	C₅×Q₈	—	2	2	no	—
267	C₅×Q₈	—	2	2	no	—
268	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
269	C₅×D₄	—	2	2	no	—
270	C₅×D₄	—	2	2	no	—
271	C₅×D₄	—	4	2	no	—
272	C₅×D₄	—	4	4	no	—
273	C₅×D₄	—	4	2	no	—
274	C₂×C₄×C₅	—	2	4	no	—
275	C₂×C₄×C₅	—	2	2	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	4	1	no	—
280	C₂×C₄×C₅	—	4	2	no	—
281	C₂×C₄×C₅	—	4	4	no	—
282	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
283	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
287	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
288	C₂×C₄×C₅	C₃×#41	1	2	yes	—
289	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
290	C₅×C₈	—	2	4	no	—
291	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
292	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
293	#137	—	2	8	no	—
294	C₂×Q₁₆	C₂²×C₃×C₅	1	4	yes	—
295	C₂×SD₁₆	C₂²×C₃×C₅	1	4	yes	—
296	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
297	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
298	#127	C₂²×C₃×C₅	1	1	yes	characteristic
299	#124	C₂²×C₃×C₅	1	2	yes	—
300	#121	—	2	1	no	—
301	#121	—	2	1	no	—
302	C₄×Q₈	—	2	1	no	—
303	C₄×Q₈	—	2	1	no	—
304	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
305	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
310	C₂×C₄²	—	2	1	no	—
311	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
312	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
313	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
314	#103	C₂²×C₃×C₅	1	4	yes	—
315	#102	C₂²×C₃×C₅	1	4	yes	—
316	C₂×C₃×C₅	—	2	2	no	—
317	C₂×C₃×C₅	—	8	2	no	—
318	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
319	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
320	C₂×C₃×C₅	#575	1	1	yes	characteristic
321	C₂³×C₃	—	2	2	no	—
322	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
323	C₃×Q₈	—	2	4	no	—
324	C₃×Q₈	—	2	2	no	—
325	C₃×Q₈	—	2	2	no	—
326	C₃×Q₈	—	2	2	no	—
327	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
328	C₃×D₄	—	2	2	no	—
329	C₃×D₄	—	2	2	no	—
330	C₃×D₄	—	4	2	no	—
331	C₃×D₄	—	4	4	no	—
332	C₃×D₄	—	4	2	no	—
333	C₂×C₃×C₄	—	2	4	no	—
334	C₂×C₃×C₄	—	2	2	no	—
335	C₂×C₃×C₄	—	2	2	no	—
336	C₂×C₃×C₄	—	2	2	no	—
337	C₂×C₃×C₄	—	2	2	no	—
338	C₂×C₃×C₄	—	4	1	no	—
339	C₂×C₃×C₄	—	4	2	no	—
340	C₂×C₃×C₄	—	4	4	no	—
341	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
342	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
343	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
344	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
346	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
347	C₂×C₃×C₄	C₅×#41	1	2	yes	—
348	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
349	C₃×C₈	—	2	4	no	—
350	C₂²×C₅	—	2	1	no	—
351	C₂²×C₅	—	2	1	no	—
352	C₂²×C₅	—	4	2	no	—
353	C₂²×C₅	—	4	2	no	—
354	C₂²×C₅	—	4	2	no	—
355	C₂²×C₅	C₃×#121	1	2	yes	—
356	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
357	C₄×C₅	—	2	1	no	—
358	C₄×C₅	—	2	1	no	—
359	C₄×C₅	—	2	1	no	—
360	C₄×C₅	—	2	4	no	—
361	C₄×C₅	—	4	2	no	—
362	C₄×C₅	—	4	2	no	—
363	C₄×C₅	C₃×#121	1	2	yes	—
364	C₄×C₅	C₃×#137	1	2	yes	complemented
365	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
366	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
367	#41	—	2	4	no	—
368	#41	—	2	4	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	C₃×C₅×D₄	1	4	yes	complemented
372	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
373	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
382	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
383	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
384	Q₁₆	—	2	8	no	—
385	SD₁₆	—	2	8	no	—
386	M₁₆	—	2	4	no	—
387	C₂×C₈	C₂³×C₃×C₅	1	4	yes	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
399	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
400	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
401	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
402	C₃×C₅	#3037	1	1	yes	characteristic, direct product factor, Hall
403	C₂²×C₃	—	2	1	no	—
404	C₂²×C₃	—	2	1	no	—
405	C₂²×C₃	—	4	2	no	—
406	C₂²×C₃	—	4	2	no	—
407	C₂²×C₃	—	4	2	no	—
408	C₂²×C₃	C₅×#121	1	2	yes	—
409	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
410	C₃×C₄	—	2	4	no	—
411	C₃×C₄	—	2	1	no	—
412	C₃×C₄	—	2	1	no	—
413	C₃×C₄	—	2	1	no	—
414	C₃×C₄	—	4	2	no	—
415	C₃×C₄	—	4	2	no	—
416	C₃×C₄	C₅×#121	1	2	yes	—
417	C₃×C₄	C₅×#137	1	2	yes	complemented
418	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
419	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
420	C₂×C₅	—	2	2	no	—
421	C₂×C₅	—	8	2	no	—
422	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
423	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
424	C₂×C₅	C₃×#575	1	1	yes	characteristic
425	C₂³	—	2	2	no	—
426	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
427	Q₈	—	2	4	no	—
428	Q₈	—	2	2	no	—
429	Q₈	—	2	2	no	—
430	Q₈	—	2	2	no	—
431	Q₈	C₂×C₃×C₅×D₄	1	4	yes	—
432	D₄	—	2	2	no	—
433	D₄	—	2	2	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	4	no	—
436	D₄	—	4	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	4	no	—
445	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
446	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
447	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
448	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
449	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
450	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
451	C₂×C₄	C₃×C₅×#41	1	2	yes	—
452	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
453	C₈	—	2	4	no	—
454	C₂×C₃	—	2	2	no	—
455	C₂×C₃	—	8	2	no	—
456	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
457	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
458	C₂×C₃	C₅×#575	1	1	yes	characteristic
459	C₅	C₃×#3037	1	1	yes	characteristic, direct product factor, Sylow
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	4	2	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	C₃×C₅×#121	1	2	yes	—
466	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
467	C₄	—	2	4	no	—
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	2	1	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	C₃×C₅×#121	1	2	yes	—
474	C₄	C₃×C₅×#137	1	2	yes	complemented
475	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
476	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
477	C₃	C₅×#3037	1	1	yes	characteristic, direct product factor, Sylow
478	C₂	—	2	2	no	—
479	C₂	—	8	2	no	—
480	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
481	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic
482	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	C₃×C₅×#532	C₂
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
1. C₂×C₃×C₅×#137	C₂	semidirect
3. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
4. C₃×C₅×#464	C₂	semidirect
5. C₃×C₅×#462	C₂	semidirect
6. C₃×C₅×#460	C₂	semidirect
7. C₃×C₅×#423	C₂	semidirect
8. C₃×C₅×#417	C₂	semidirect
9. C₅×#3037	C₃	direct (N × H)
35. C₃×#3037	C₅	direct (N × H)
36. C₂×C₅×#137	C₂×C₃	semidirect
38. C₂×C₄×C₅×Q₈	C₂×C₃	semidirect
39. C₅×#464	C₂×C₃	semidirect
40. C₅×#462	C₂×C₃	semidirect
41. C₅×#460	C₂×C₃	semidirect
42. C₅×#423	C₂×C₃	semidirect
43. C₅×#417	C₂×C₃	semidirect
48. C₂×C₃×C₅×Q₈	D₄	semidirect
79. C₂×C₃×#137	C₂×C₅	semidirect
81. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
82. C₃×#464	C₂×C₅	semidirect
83. C₃×#462	C₂×C₅	semidirect
84. C₃×#460	C₂×C₅	semidirect
85. C₃×#423	C₂×C₅	semidirect
86. C₃×#417	C₂×C₅	semidirect
112. #3037	C₃×C₅	direct (N × H)
171. C₂×C₅×Q₈	C₃×D₄	semidirect
202. C₂×#137	C₂×C₃×C₅	semidirect
204. C₂×C₄×Q₈	C₂×C₃×C₅	semidirect
205. #464	C₂×C₃×C₅	semidirect
206. #462	C₂×C₃×C₅	semidirect
207. #460	C₂×C₃×C₅	semidirect
208. #423	C₂×C₃×C₅	semidirect
209. #417	C₂×C₃×C₅	semidirect
224. C₃×C₄×C₅	#137	semidirect
231. C₂×C₃×Q₈	C₅×D₄	semidirect
364. C₄×C₅	C₃×#137	semidirect
371. C₂×Q₈	C₃×C₅×D₄	semidirect
402. C₃×C₅	#3037	direct (N × H)
417. C₃×C₄	C₅×#137	semidirect
459. C₅	C₃×#3037	direct (N × H)
474. C₄	C₃×C₅×#137	semidirect
477. C₃	C₅×#3037	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×#137	2
C₃×C₅×#532	2
C₂×C₃×C₄×C₅×Q₈	2
C₃×C₅×#464	2
C₃×C₅×#462	2
C₃×C₅×#460	2
C₃×C₅×#423	2
C₃×C₅×#417	2
C₅×#3037	3
C₃×#3037	5

Subgroups — C3×C5×#3037 #14276071

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3037 #14276071