Subgroups — C₃×D₅×#464 #14426119

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₅×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₃×D₅×#124	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄×Q₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#464	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65455	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65343	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65317	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65134	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×D₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#65087	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×D₅×#102	C₂	1	1	yes	maximal, characteristic
15	C₃×#65056	C₂	1	1	yes	maximal, characteristic, complemented
16	D₅×#464	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
22	C₃×C₅×#124	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₃×#4093	C₂²	1	1	yes	characteristic
25	C₃×Q₈×Dic₅	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₃×#689	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×#689	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×#688	C₂²	1	1	yes	characteristic
29	C₃×#4082	C₂²	1	1	yes	characteristic
30	C₂×C₃×#687	C₂²	1	1	yes	characteristic
31	C₃×D₅×Q₁₆	—	2	4	no	—
32	C₃×D₅×SD₁₆	—	2	4	no	—
33	C₂×C₃×Dic₂₀	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₃×#677	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
37	C₃×D₅×C₄⋊C₄	—	2	1	no	—
38	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×#4033	—	2	1	no	—
40	C₃×#4033	C₂²	1	1	yes	characteristic, complemented
41	C₃×#4031	—	2	1	no	—
42	C₃×#4031	—	2	1	no	—
43	C₃×D₅×C₂²⋊C₄	—	2	1	no	—
44	C₃×D₅×C₂²⋊C₄	—	2	1	no	—
45	C₃×#4021	C₂²	1	1	yes	characteristic
46	C₃×C₄²×D₅	—	2	1	no	—
47	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
48	C₃×C₄×Dic₁₀	—	2	1	no	—
49	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
50	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic
53	C₃×#3967	C₂²	1	1	yes	characteristic, complemented
54	C₃×#3964	C₂²	1	1	yes	characteristic
55	C₃×#3953	C₂²	1	1	yes	characteristic
56	C₃×#3948	C₂²	1	1	yes	characteristic, complemented
57	C₃×#3946	C₂²	1	1	yes	characteristic, complemented
58	C₃×#3946	C₂²	1	1	yes	characteristic, complemented
59	C₃×#3942	C₂²	1	1	yes	characteristic, complemented
60	C₃×#3941	C₂²	1	1	yes	characteristic
61	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₃×#464	—	5	1	no	maximal, Hall
63	C₂×D₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂×D₅×SD₁₆	C₂×C₃	1	1	yes	characteristic
65	D₅×#124	C₂×C₃	1	1	yes	characteristic
66	C₄×Q₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#464	C₂×C₃	1	1	yes	characteristic, complemented
68	#65474	C₂×C₃	1	1	yes	characteristic, complemented
69	#65455	C₂×C₃	1	1	yes	characteristic, complemented
70	#65343	C₂×C₃	1	1	yes	characteristic, complemented
71	#65317	C₂×C₃	1	1	yes	characteristic, complemented
72	#65134	C₂×C₃	1	1	yes	characteristic, complemented
73	D₅×C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
74	D₅×#103	C₂×C₃	1	1	yes	characteristic, complemented
75	#65087	C₂×C₃	1	1	yes	characteristic, complemented
76	D₅×#102	C₂×C₃	1	1	yes	characteristic
77	#65056	C₂×C₃	1	1	yes	characteristic, complemented
78	C₂³×C₃×D₅	—	2	1	no	—
79	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
83	C₃×Q₈×D₅	—	2	2	no	—
84	C₃×Q₈×D₅	—	2	2	no	—
85	C₃×Q₈×D₅	—	2	2	no	—
86	C₃×Q₈×D₅	D₄	1	4	yes	—
87	C₃×D₄×D₅	—	2	2	no	—
88	C₃×D₄×D₅	—	2	2	no	—
89	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₄×D₅	—	2	1	no	—
91	C₂×C₃×C₄×D₅	—	2	1	no	—
92	C₂×C₃×C₄×D₅	—	2	1	no	—
93	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
94	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
95	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
96	C₂×C₃×Dic₁₀	—	2	1	no	—
97	C₂×C₃×Dic₁₀	—	2	1	no	—
98	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
99	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
100	C₃×C₅×Q₁₆	—	2	2	no	—
101	C₃×C₅×SD₁₆	—	2	2	no	—
102	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
103	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
104	C₃×C₅×C₄⋊C₄	—	2	1	no	—
105	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
107	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
108	C₃×C₄²×C₅	—	2	1	no	—
109	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
110	C₃×C₂²⋊Dic₅	—	2	1	no	—
111	C₃×C₂²⋊Dic₅	—	2	1	no	—
112	C₃×#689	—	2	2	no	—
113	C₃×#689	—	2	2	no	—
114	C₃×#688	—	2	2	no	—
115	C₃×#687	—	2	2	no	—
116	C₃×#685	—	2	1	no	—
117	C₃×#685	—	2	1	no	—
118	C₃×#685	—	2	1	no	—
119	C₃×#685	—	2	1	no	—
120	C₃×C₄⋊Dic₅	—	2	1	no	—
121	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
122	C₃×#683	—	2	1	no	—
123	C₃×#683	—	2	1	no	—
124	C₃×#683	—	2	1	no	—
125	C₃×C₄×Dic₅	—	2	1	no	—
126	C₃×C₄×Dic₅	—	2	1	no	—
127	C₃×C₄×Dic₅	—	2	1	no	—
128	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
129	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
130	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
131	C₂×C₃×#168	C₂³	1	1	yes	characteristic
132	C₂×C₃×#168	C₂³	1	1	yes	characteristic
133	C₃×Dic₂₀	—	2	2	no	—
134	C₃×#677	—	2	2	no	—
135	C₃×C₈×D₅	—	2	2	no	—
136	C₃×C₈×D₅	—	2	2	no	—
137	C₂²×C₃×Q₁₆	—	5	1	no	—
138	C₂²×C₃×SD₁₆	—	5	1	no	—
139	C₂×C₃×#124	—	5	1	no	—
140	C₂×C₃×C₄×Q₈	—	5	1	no	—
141	C₃×#464	—	5	1	no	—
142	C₃×#464	—	5	1	no	—
143	C₃×#464	—	5	1	no	—
144	C₃×#464	—	5	1	no	—
145	C₃×#464	—	5	1	no	—
146	C₃×#464	—	5	1	no	—
147	C₃×#464	—	5	1	no	—
148	C₃×#464	D₅	1	1	yes	characteristic, direct product factor
149	C₂×C₃×C₄⋊C₈	—	5	1	no	—
150	C₂×C₃×#103	—	5	1	no	—
151	C₂×C₃×#102	—	5	1	no	—
152	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic
153	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic
154	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
156	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
157	C₅×#124	C₂²×C₃	1	1	yes	characteristic
158	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
159	#4093	C₂²×C₃	1	1	yes	characteristic
160	Q₈×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
161	C₂×#689	C₂²×C₃	1	1	yes	characteristic, complemented
162	C₂×#689	C₂²×C₃	1	1	yes	characteristic, complemented
163	C₂×#688	C₂²×C₃	1	1	yes	characteristic
164	#4082	C₂²×C₃	1	1	yes	characteristic
165	C₂×#687	C₂²×C₃	1	1	yes	characteristic
166	D₅×Q₁₆	—	2	4	no	—
167	D₅×SD₁₆	—	2	4	no	—
168	C₂×Dic₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₂×#677	C₂²×C₃	1	1	yes	characteristic
170	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
171	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
172	D₅×C₄⋊C₄	—	2	1	no	—
173	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
174	#4033	—	2	1	no	—
175	#4033	C₂²×C₃	1	1	yes	characteristic, complemented
176	#4031	—	2	1	no	—
177	#4031	—	2	1	no	—
178	D₅×C₂²⋊C₄	—	2	1	no	—
179	D₅×C₂²⋊C₄	—	2	1	no	—
180	#4021	C₂²×C₃	1	1	yes	characteristic
181	C₄²×D₅	—	2	1	no	—
182	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
183	C₄×Dic₁₀	—	2	1	no	—
184	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
185	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
186	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
187	C₅×#102	C₂²×C₃	1	1	yes	characteristic
188	#3967	C₂²×C₃	1	1	yes	characteristic, complemented
189	#3964	C₂²×C₃	1	1	yes	characteristic
190	#3953	C₂²×C₃	1	1	yes	characteristic
191	#3948	C₂²×C₃	1	1	yes	characteristic, complemented
192	#3946	C₂²×C₃	1	1	yes	characteristic, complemented
193	#3946	C₂²×C₃	1	1	yes	characteristic, complemented
194	#3942	C₂²×C₃	1	1	yes	characteristic, complemented
195	#3941	C₂²×C₃	1	1	yes	characteristic
196	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic, complemented
197	C₂×#464	—	5	1	no	Sylow
198	C₂³×C₃×C₅	—	2	1	no	—
199	C₂²×C₃×D₅	—	2	1	no	—
200	C₂²×C₃×D₅	—	4	2	no	—
201	C₂²×C₃×D₅	—	4	2	no	—
202	C₂²×C₃×D₅	—	4	2	no	—
203	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
204	C₃×C₅×Q₈	—	2	1	no	—
205	C₃×C₅×Q₈	—	2	1	no	—
206	C₃×C₅×Q₈	—	2	1	no	—
207	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
208	C₃×C₅×D₄	—	2	1	no	—
209	C₃×C₅×D₄	—	2	1	no	—
210	C₂×C₃×C₄×C₅	—	2	1	no	—
211	C₂×C₃×C₄×C₅	—	2	1	no	—
212	C₂×C₃×C₄×C₅	—	2	1	no	—
213	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
214	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
215	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
216	C₃×C₂²⋊D₅	—	4	2	no	—
217	C₂×C₃×Dic₅	—	2	1	no	—
218	C₂×C₃×Dic₅	—	2	1	no	—
219	C₂×C₃×Dic₅	—	2	1	no	—
220	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
221	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
222	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
223	C₃×D₂₀	—	2	1	no	—
224	C₃×D₂₀	—	2	1	no	—
225	C₃×C₄×D₅	—	2	4	no	—
226	C₃×C₄×D₅	—	2	2	no	—
227	C₃×C₄×D₅	—	2	2	no	—
228	C₃×C₄×D₅	—	4	2	no	—
229	C₃×C₄×D₅	—	4	2	no	—
230	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
231	C₃×C₄×D₅	#41	1	2	yes	—
232	C₃×Dic₁₀	—	2	1	no	—
233	C₃×Dic₁₀	—	2	4	no	—
234	C₃×Dic₁₀	—	2	1	no	—
235	C₃×Dic₁₀	—	2	1	no	—
236	C₃×Dic₁₀	—	4	2	no	—
237	C₃×Dic₁₀	C₂×D₄	1	2	yes	—
238	C₃×C₅×C₈	—	2	1	no	—
239	C₃×C₅×C₈	—	2	1	no	—
240	C₃×#168	—	2	1	no	—
241	C₃×#168	—	2	1	no	—
242	C₂²×C₃×Q₈	—	5	1	no	—
243	C₂²×C₃×Q₈	—	5	1	no	—
244	C₂²×C₃×D₄	—	5	1	no	—
245	C₂×C₃×Q₁₆	—	5	1	no	—
246	C₂×C₃×Q₁₆	—	5	1	no	—
247	C₂×C₃×Q₁₆	—	5	1	no	—
248	C₂×C₃×Q₁₆	—	10	4	no	—
249	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic, complemented
250	C₂×C₃×SD₁₆	—	5	1	no	—
251	C₂×C₃×SD₁₆	—	5	1	no	—
252	C₂×C₃×SD₁₆	—	5	1	no	—
253	C₂×C₃×SD₁₆	—	10	4	no	—
254	C₂×C₃×SD₁₆	C₂×D₅	1	1	yes	characteristic
255	C₂²×C₃×C₈	—	5	1	no	—
256	C₂²×C₃×C₈	—	5	1	no	—
257	C₃×#124	—	5	1	no	—
258	C₃×#124	—	5	1	no	—
259	C₃×#124	—	5	1	no	—
260	C₃×#124	—	10	1	no	—
261	C₃×#124	—	10	1	no	—
262	C₃×#124	C₂×D₅	1	1	yes	characteristic
263	C₃×C₄×Q₈	—	5	1	no	—
264	C₃×C₄×Q₈	—	5	1	no	—
265	C₃×C₄×Q₈	—	5	1	no	—
266	C₃×C₄×Q₈	—	10	1	no	—
267	C₃×C₄×Q₈	—	10	1	no	—
268	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
269	C₂×C₃×C₄⋊C₄	—	5	1	no	—
270	C₂×C₃×C₄⋊C₄	—	10	1	no	—
271	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
272	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
273	C₂×C₃×C₄²	—	5	1	no	—
274	C₂×C₃×C₄²	—	10	1	no	—
275	C₃×C₄⋊C₈	—	5	1	no	—
276	C₃×C₄⋊C₈	—	5	1	no	—
277	C₃×C₄⋊C₈	—	5	1	no	—
278	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic, complemented
279	C₃×#103	—	5	1	no	—
280	C₃×#103	—	5	1	no	—
281	C₃×#103	—	5	1	no	—
282	C₃×#103	C₂×D₅	1	1	yes	characteristic, complemented
283	C₃×#102	—	5	1	no	—
284	C₃×#102	—	5	1	no	—
285	C₃×#102	—	5	1	no	—
286	C₃×#102	C₂×D₅	1	1	yes	characteristic
287	C₂³×D₅	—	2	1	no	—
288	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
289	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
290	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
291	C₂×C₂²⋊D₅	—	2	1	no	—
292	Q₈×D₅	—	2	2	no	—
293	Q₈×D₅	—	2	2	no	—
294	Q₈×D₅	—	2	2	no	—
295	Q₈×D₅	C₃×D₄	1	4	yes	—
296	D₄×D₅	—	2	2	no	—
297	D₄×D₅	—	2	2	no	—
298	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
299	C₂×C₄×D₅	—	2	1	no	—
300	C₂×C₄×D₅	—	2	1	no	—
301	C₂×C₄×D₅	—	2	1	no	—
302	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
303	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
304	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
305	C₂×Dic₁₀	—	2	1	no	—
306	C₂×Dic₁₀	—	2	1	no	—
307	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
308	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
309	C₅×Q₁₆	—	2	2	no	—
310	C₅×SD₁₆	—	2	2	no	—
311	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
312	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
313	C₅×C₄⋊C₄	—	2	1	no	—
314	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
315	C₅×C₂²⋊C₄	—	2	1	no	—
316	C₅×C₂²⋊C₄	—	2	1	no	—
317	C₄²×C₅	—	2	1	no	—
318	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
319	C₂²⋊Dic₅	—	2	1	no	—
320	C₂²⋊Dic₅	—	2	1	no	—
321	#689	—	2	2	no	—
322	#689	—	2	2	no	—
323	#688	—	2	2	no	—
324	#687	—	2	2	no	—
325	#685	—	2	1	no	—
326	#685	—	2	1	no	—
327	#685	—	2	1	no	—
328	#685	—	2	1	no	—
329	C₄⋊Dic₅	—	2	1	no	—
330	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
331	#683	—	2	1	no	—
332	#683	—	2	1	no	—
333	#683	—	2	1	no	—
334	C₄×Dic₅	—	2	1	no	—
335	C₄×Dic₅	—	2	1	no	—
336	C₄×Dic₅	—	2	1	no	—
337	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
338	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
339	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
340	C₂×#168	C₂³×C₃	1	1	yes	characteristic
341	C₂×#168	C₂³×C₃	1	1	yes	characteristic
342	Dic₂₀	—	2	2	no	—
343	#677	—	2	2	no	—
344	C₈×D₅	—	2	2	no	—
345	C₈×D₅	—	2	2	no	—
346	C₂²×Q₁₆	—	5	1	no	—
347	C₂²×SD₁₆	—	5	1	no	—
348	C₂×#124	—	5	1	no	—
349	C₂×C₄×Q₈	—	5	1	no	—
350	#464	—	5	1	no	—
351	#464	—	5	1	no	—
352	#464	—	5	1	no	—
353	#464	—	5	1	no	—
354	#464	—	5	1	no	—
355	#464	—	5	1	no	—
356	#464	—	5	1	no	—
357	#464	C₃×D₅	1	1	yes	characteristic, direct product factor
358	C₂×C₄⋊C₈	—	5	1	no	—
359	C₂×#103	—	5	1	no	—
360	C₂×#102	—	5	1	no	—
361	C₂²×C₃×C₅	—	4	1	no	—
362	C₂²×C₃×C₅	—	4	1	no	—
363	C₂²×C₃×C₅	—	4	1	no	—
364	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
365	C₂×C₃×D₅	—	4	1	no	—
366	C₂×C₃×D₅	—	4	1	no	—
367	C₂×C₃×D₅	—	4	1	no	—
368	C₂×C₃×D₅	—	8	4	no	—
369	C₂×C₃×D₅	#121	1	2	yes	—
370	C₂×C₃×D₅	#135	1	2	yes	—
371	C₂×C₃×D₅	#137	1	2	yes	—
372	C₃×C₄×C₅	—	2	2	no	—
373	C₃×C₄×C₅	—	2	1	no	—
374	C₃×C₄×C₅	—	2	1	no	—
375	C₃×C₄×C₅	—	4	1	no	—
376	C₃×C₄×C₅	—	4	1	no	—
377	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
378	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
379	C₃×Dic₅	—	2	2	no	—
380	C₃×Dic₅	—	2	1	no	—
381	C₃×Dic₅	—	2	1	no	—
382	C₃×Dic₅	—	4	1	no	—
383	C₃×Dic₅	—	4	1	no	—
384	C₃×Dic₅	#121	1	2	yes	—
385	C₂⁴×C₃	—	10	1	no	—
386	C₂×C₃×Q₈	—	5	4	no	—
387	C₂×C₃×Q₈	—	5	1	no	—
388	C₂×C₃×Q₈	—	5	1	no	—
389	C₂×C₃×Q₈	—	10	1	no	—
390	C₂×C₃×Q₈	—	10	1	no	—
391	C₂×C₃×Q₈	—	10	2	no	—
392	C₂×C₃×Q₈	—	10	2	no	—
393	C₂×C₃×Q₈	—	10	2	no	—
394	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
395	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
396	C₂×C₃×D₄	—	5	1	no	—
397	C₂×C₃×D₄	—	10	2	no	—
398	C₂×C₃×D₄	—	10	2	no	—
399	C₂×C₃×D₄	—	10	1	no	—
400	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
401	C₂²×C₃×C₄	—	5	1	no	—
402	C₂²×C₃×C₄	—	5	1	no	—
403	C₂²×C₃×C₄	—	5	1	no	—
404	C₂²×C₃×C₄	—	10	1	no	—
405	C₂²×C₃×C₄	—	10	1	no	—
406	C₂²×C₃×C₄	—	10	1	no	—
407	C₃×Q₁₆	—	2	2	no	—
408	C₃×Q₁₆	—	10	2	no	—
409	C₃×Q₁₆	—	10	2	no	—
410	C₃×Q₁₆	—	10	2	no	—
411	C₃×SD₁₆	—	2	2	no	—
412	C₃×SD₁₆	—	10	2	no	—
413	C₃×SD₁₆	—	10	2	no	—
414	C₃×SD₁₆	—	10	2	no	—
415	C₂×C₃×C₈	—	5	1	no	—
416	C₂×C₃×C₈	—	5	1	no	—
417	C₂×C₃×C₈	—	10	2	no	—
418	C₂×C₃×C₈	—	10	2	no	—
419	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
420	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
421	C₃×C₄⋊C₄	—	2	1	no	—
422	C₃×C₄⋊C₄	—	5	1	no	—
423	C₃×C₄⋊C₄	—	10	1	no	—
424	C₃×C₄⋊C₄	—	10	1	no	—
425	C₃×C₄⋊C₄	—	10	1	no	—
426	C₃×C₄⋊C₄	—	10	1	no	—
427	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
428	C₃×C₂²⋊C₄	—	2	1	no	—
429	C₃×C₂²⋊C₄	—	2	1	no	—
430	C₃×C₂²⋊C₄	—	10	1	no	—
431	C₃×C₂²⋊C₄	—	10	1	no	—
432	C₃×C₂²⋊C₄	—	10	1	no	—
433	C₃×C₂²⋊C₄	—	10	1	no	—
434	C₃×C₂²⋊C₄	—	10	1	no	—
435	C₃×C₂²⋊C₄	—	10	1	no	—
436	C₃×C₄²	—	2	1	no	—
437	C₃×C₄²	—	5	1	no	—
438	C₃×C₄²	—	5	1	no	—
439	C₃×C₄²	—	5	1	no	—
440	C₃×C₄²	—	10	1	no	—
441	C₃×C₄²	—	10	1	no	—
442	C₃×C₄²	—	10	1	no	—
443	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
444	C₂³×C₅	—	2	1	no	—
445	C₂²×D₅	—	2	1	no	—
446	C₂²×D₅	—	4	2	no	—
447	C₂²×D₅	—	4	2	no	—
448	C₂²×D₅	—	4	2	no	—
449	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
450	C₅×Q₈	—	2	1	no	—
451	C₅×Q₈	—	2	1	no	—
452	C₅×Q₈	—	2	1	no	—
453	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
454	C₅×D₄	—	2	1	no	—
455	C₅×D₄	—	2	1	no	—
456	C₂×C₄×C₅	—	2	1	no	—
457	C₂×C₄×C₅	—	2	1	no	—
458	C₂×C₄×C₅	—	2	1	no	—
459	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
460	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
461	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
462	C₂²⋊D₅	—	4	2	no	—
463	C₂×Dic₅	—	2	1	no	—
464	C₂×Dic₅	—	2	1	no	—
465	C₂×Dic₅	—	2	1	no	—
466	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
467	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
468	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
469	D₂₀	—	2	1	no	—
470	D₂₀	—	2	1	no	—
471	C₄×D₅	—	2	4	no	—
472	C₄×D₅	—	2	2	no	—
473	C₄×D₅	—	2	2	no	—
474	C₄×D₅	—	4	2	no	—
475	C₄×D₅	—	4	2	no	—
476	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
477	C₄×D₅	C₃×#41	1	2	yes	—
478	Dic₁₀	—	2	1	no	—
479	Dic₁₀	—	2	4	no	—
480	Dic₁₀	—	2	1	no	—
481	Dic₁₀	—	2	1	no	—
482	Dic₁₀	—	4	2	no	—
483	Dic₁₀	C₂×C₃×D₄	1	2	yes	—
484	C₅×C₈	—	2	1	no	—
485	C₅×C₈	—	2	1	no	—
486	#168	—	2	1	no	—
487	#168	—	2	1	no	—
488	C₂²×Q₈	—	5	1	no	—
489	C₂²×Q₈	—	5	1	no	—
490	C₂²×D₄	—	5	1	no	—
491	C₂×Q₁₆	—	5	1	no	—
492	C₂×Q₁₆	—	5	1	no	—
493	C₂×Q₁₆	—	5	1	no	—
494	C₂×Q₁₆	—	10	4	no	—
495	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
496	C₂×SD₁₆	—	5	1	no	—
497	C₂×SD₁₆	—	5	1	no	—
498	C₂×SD₁₆	—	5	1	no	—
499	C₂×SD₁₆	—	10	4	no	—
500	C₂×SD₁₆	C₂×C₃×D₅	1	1	yes	characteristic
501	C₂²×C₈	—	5	1	no	—
502	C₂²×C₈	—	5	1	no	—
503	#124	—	5	1	no	—
504	#124	—	5	1	no	—
505	#124	—	5	1	no	—
506	#124	—	10	1	no	—
507	#124	—	10	1	no	—
508	#124	C₂×C₃×D₅	1	1	yes	characteristic
509	C₄×Q₈	—	5	1	no	—
510	C₄×Q₈	—	5	1	no	—
511	C₄×Q₈	—	5	1	no	—
512	C₄×Q₈	—	10	1	no	—
513	C₄×Q₈	—	10	1	no	—
514	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
515	C₂×C₄⋊C₄	—	5	1	no	—
516	C₂×C₄⋊C₄	—	10	1	no	—
517	C₂×C₂²⋊C₄	—	10	1	no	—
518	C₂×C₂²⋊C₄	—	10	1	no	—
519	C₂×C₄²	—	5	1	no	—
520	C₂×C₄²	—	10	1	no	—
521	C₄⋊C₈	—	5	1	no	—
522	C₄⋊C₈	—	5	1	no	—
523	C₄⋊C₈	—	5	1	no	—
524	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
525	#103	—	5	1	no	—
526	#103	—	5	1	no	—
527	#103	—	5	1	no	—
528	#103	C₂×C₃×D₅	1	1	yes	characteristic, complemented
529	#102	—	5	1	no	—
530	#102	—	5	1	no	—
531	#102	—	5	1	no	—
532	#102	C₂×C₃×D₅	1	1	yes	characteristic
533	C₂×C₃×C₅	—	8	1	no	—
534	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
535	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
536	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
537	C₃×D₅	—	8	1	no	—
538	C₃×D₅	#464	1	4	yes	direct product factor
539	C₂³×C₃	—	2	1	no	—
540	C₂³×C₃	—	5	1	no	—
541	C₂³×C₃	—	10	1	no	—
542	C₂³×C₃	—	20	2	no	—
543	C₂³×C₃	—	20	2	no	—
544	C₂³×C₃	—	20	2	no	—
545	C₃×Q₈	—	2	1	no	—
546	C₃×Q₈	—	2	1	no	—
547	C₃×Q₈	—	2	1	no	—
548	C₃×Q₈	—	5	2	no	—
549	C₃×Q₈	—	10	4	no	—
550	C₃×Q₈	—	10	1	no	—
551	C₃×Q₈	—	10	1	no	—
552	C₃×Q₈	—	10	1	no	—
553	C₃×Q₈	—	20	2	no	—
554	C₃×Q₈	D₄×D₅	1	2	yes	—
555	C₃×D₄	—	2	1	no	—
556	C₃×D₄	—	2	1	no	—
557	C₃×D₄	—	10	1	no	—
558	C₃×D₄	—	10	1	no	—
559	C₃×D₄	—	20	2	no	—
560	C₂×C₃×C₄	—	2	1	no	—
561	C₂×C₃×C₄	—	2	1	no	—
562	C₂×C₃×C₄	—	2	1	no	—
563	C₂×C₃×C₄	—	5	1	no	—
564	C₂×C₃×C₄	—	5	2	no	—
565	C₂×C₃×C₄	—	5	2	no	—
566	C₂×C₃×C₄	—	5	1	no	—
567	C₂×C₃×C₄	—	5	1	no	—
568	C₂×C₃×C₄	—	10	2	no	—
569	C₂×C₃×C₄	—	10	2	no	—
570	C₂×C₃×C₄	—	10	4	no	—
571	C₂×C₃×C₄	—	10	1	no	—
572	C₂×C₃×C₄	—	10	1	no	—
573	C₂×C₃×C₄	—	10	1	no	—
574	C₂×C₃×C₄	—	20	2	no	—
575	C₂×C₃×C₄	—	20	2	no	—
576	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
577	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
578	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
579	C₃×C₈	—	2	1	no	—
580	C₃×C₈	—	2	1	no	—
581	C₃×C₈	—	10	1	no	—
582	C₃×C₈	—	10	1	no	—
583	C₂²×C₅	—	4	1	no	—
584	C₂²×C₅	—	4	1	no	—
585	C₂²×C₅	—	4	1	no	—
586	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
587	C₂×D₅	—	4	1	no	—
588	C₂×D₅	—	4	1	no	—
589	C₂×D₅	—	4	1	no	—
590	C₂×D₅	—	8	4	no	—
591	C₂×D₅	C₃×#121	1	2	yes	—
592	C₂×D₅	C₃×#135	1	2	yes	—
593	C₂×D₅	C₃×#137	1	2	yes	—
594	C₄×C₅	—	2	1	no	—
595	C₄×C₅	—	2	1	no	—
596	C₄×C₅	—	2	2	no	—
597	C₄×C₅	—	4	1	no	—
598	C₄×C₅	—	4	1	no	—
599	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
600	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
601	Dic₅	—	2	1	no	—
602	Dic₅	—	2	1	no	—
603	Dic₅	—	2	2	no	—
604	Dic₅	—	4	1	no	—
605	Dic₅	—	4	1	no	—
606	Dic₅	C₃×#121	1	2	yes	—
607	C₂⁴	—	10	1	no	—
608	C₂×Q₈	—	5	4	no	—
609	C₂×Q₈	—	5	1	no	—
610	C₂×Q₈	—	5	1	no	—
611	C₂×Q₈	—	10	1	no	—
612	C₂×Q₈	—	10	1	no	—
613	C₂×Q₈	—	10	2	no	—
614	C₂×Q₈	—	10	2	no	—
615	C₂×Q₈	—	10	2	no	—
616	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
617	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
618	C₂×D₄	—	5	1	no	—
619	C₂×D₄	—	10	2	no	—
620	C₂×D₄	—	10	2	no	—
621	C₂×D₄	—	10	1	no	—
622	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
623	C₂²×C₄	—	5	1	no	—
624	C₂²×C₄	—	5	1	no	—
625	C₂²×C₄	—	5	1	no	—
626	C₂²×C₄	—	10	1	no	—
627	C₂²×C₄	—	10	1	no	—
628	C₂²×C₄	—	10	1	no	—
629	Q₁₆	—	2	2	no	—
630	Q₁₆	—	10	2	no	—
631	Q₁₆	—	10	2	no	—
632	Q₁₆	—	10	2	no	—
633	SD₁₆	—	2	2	no	—
634	SD₁₆	—	10	2	no	—
635	SD₁₆	—	10	2	no	—
636	SD₁₆	—	10	2	no	—
637	C₂×C₈	—	5	1	no	—
638	C₂×C₈	—	5	1	no	—
639	C₂×C₈	—	10	2	no	—
640	C₂×C₈	—	10	2	no	—
641	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
642	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
643	C₄⋊C₄	—	2	1	no	—
644	C₄⋊C₄	—	5	1	no	—
645	C₄⋊C₄	—	10	1	no	—
646	C₄⋊C₄	—	10	1	no	—
647	C₄⋊C₄	—	10	1	no	—
648	C₄⋊C₄	—	10	1	no	—
649	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
650	C₂²⋊C₄	—	2	1	no	—
651	C₂²⋊C₄	—	2	1	no	—
652	C₂²⋊C₄	—	10	1	no	—
653	C₂²⋊C₄	—	10	1	no	—
654	C₂²⋊C₄	—	10	1	no	—
655	C₂²⋊C₄	—	10	1	no	—
656	C₂²⋊C₄	—	10	1	no	—
657	C₂²⋊C₄	—	10	1	no	—
658	C₄²	—	2	1	no	—
659	C₄²	—	5	1	no	—
660	C₄²	—	5	1	no	—
661	C₄²	—	5	1	no	—
662	C₄²	—	10	1	no	—
663	C₄²	—	10	1	no	—
664	C₄²	—	10	1	no	—
665	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
666	C₃×C₅	C₂×#464	1	1	yes	characteristic, complemented, Hall
667	C₂²×C₃	—	4	1	no	—
668	C₂²×C₃	—	4	1	no	—
669	C₂²×C₃	—	4	1	no	—
670	C₂²×C₃	—	5	2	no	—
671	C₂²×C₃	—	5	2	no	—
672	C₂²×C₃	—	5	2	no	—
673	C₂²×C₃	—	20	1	no	—
674	C₂²×C₃	—	20	1	no	—
675	C₂²×C₃	—	20	1	no	—
676	C₂²×C₃	—	40	4	no	—
677	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
678	C₃×C₄	—	2	1	no	—
679	C₃×C₄	—	2	1	no	—
680	C₃×C₄	—	2	2	no	—
681	C₃×C₄	—	4	1	no	—
682	C₃×C₄	—	4	1	no	—
683	C₃×C₄	—	5	2	no	—
684	C₃×C₄	—	10	1	no	—
685	C₃×C₄	—	10	1	no	—
686	C₃×C₄	—	10	2	no	—
687	C₃×C₄	—	20	1	no	—
688	C₃×C₄	—	20	1	no	—
689	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
690	C₃×C₄	D₅×#41	1	1	yes	characteristic
691	C₂×C₅	—	8	1	no	—
692	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
693	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
694	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
695	D₅	—	8	1	no	—
696	D₅	C₃×#464	1	4	yes	direct product factor
697	C₂³	—	2	1	no	—
698	C₂³	—	5	1	no	—
699	C₂³	—	10	1	no	—
700	C₂³	—	20	2	no	—
701	C₂³	—	20	2	no	—
702	C₂³	—	20	2	no	—
703	Q₈	—	2	1	no	—
704	Q₈	—	2	1	no	—
705	Q₈	—	2	1	no	—
706	Q₈	—	5	2	no	—
707	Q₈	—	10	4	no	—
708	Q₈	—	10	1	no	—
709	Q₈	—	10	1	no	—
710	Q₈	—	10	1	no	—
711	Q₈	—	20	2	no	—
712	Q₈	C₃×D₄×D₅	1	2	yes	—
713	D₄	—	2	1	no	—
714	D₄	—	2	1	no	—
715	D₄	—	10	1	no	—
716	D₄	—	10	1	no	—
717	D₄	—	20	2	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	2	1	no	—
721	C₂×C₄	—	5	1	no	—
722	C₂×C₄	—	5	2	no	—
723	C₂×C₄	—	5	2	no	—
724	C₂×C₄	—	5	1	no	—
725	C₂×C₄	—	5	1	no	—
726	C₂×C₄	—	10	2	no	—
727	C₂×C₄	—	10	2	no	—
728	C₂×C₄	—	10	4	no	—
729	C₂×C₄	—	10	1	no	—
730	C₂×C₄	—	10	1	no	—
731	C₂×C₄	—	10	1	no	—
732	C₂×C₄	—	20	2	no	—
733	C₂×C₄	—	20	2	no	—
734	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
735	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
736	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
737	C₈	—	2	1	no	—
738	C₈	—	2	1	no	—
739	C₈	—	10	1	no	—
740	C₈	—	10	1	no	—
741	C₂×C₃	—	5	4	no	—
742	C₂×C₃	—	8	1	no	—
743	C₂×C₃	—	40	1	no	—
744	C₂×C₃	D₅×#121	1	1	yes	characteristic
745	C₂×C₃	D₅×#135	1	1	yes	characteristic
746	C₂×C₃	D₅×#137	1	1	yes	characteristic
747	C₅	C₂×C₃×#464	1	1	yes	characteristic, complemented, Sylow
748	C₂²	—	4	1	no	—
749	C₂²	—	4	1	no	—
750	C₂²	—	4	1	no	—
751	C₂²	—	5	2	no	—
752	C₂²	—	5	2	no	—
753	C₂²	—	5	2	no	—
754	C₂²	—	20	1	no	—
755	C₂²	—	20	1	no	—
756	C₂²	—	20	1	no	—
757	C₂²	—	40	4	no	—
758	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
759	C₄	—	2	1	no	—
760	C₄	—	2	1	no	—
761	C₄	—	2	2	no	—
762	C₄	—	4	1	no	—
763	C₄	—	4	1	no	—
764	C₄	—	5	2	no	—
765	C₄	—	10	1	no	—
766	C₄	—	10	1	no	—
767	C₄	—	10	2	no	—
768	C₄	—	20	1	no	—
769	C₄	—	20	1	no	—
770	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
771	C₄	C₃×D₅×#41	1	1	yes	characteristic
772	C₃	D₅×#464	1	1	yes	characteristic, direct product factor, Sylow
773	C₂	—	5	4	no	—
774	C₂	—	8	1	no	—
775	C₂	—	40	1	no	—
776	C₂	C₃×D₅×#121	1	1	yes	characteristic
777	C₂	C₃×D₅×#135	1	1	yes	characteristic
778	C₂	C₃×D₅×#137	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#464	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×D₄×D₅	C₂²
hypercenter	C₃×#464	D₅
hypocenter	C₅	C₂×C₃×#464
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#464

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₅×Q₁₆	C₂	semidirect
4. C₃×C₄×Q₈×D₅	C₂	semidirect
5. C₃×C₅×#464	C₂	semidirect
6. C₃×#65474	C₂	semidirect
7. C₃×#65455	C₂	semidirect
8. C₃×#65343	C₂	semidirect
9. C₃×#65317	C₂	semidirect
10. C₃×#65134	C₂	semidirect
11. C₃×D₅×C₄⋊C₈	C₂	semidirect
12. C₃×D₅×#103	C₂	semidirect
13. C₃×#65087	C₂	semidirect
15. C₃×#65056	C₂	semidirect
16. D₅×#464	C₃	direct (N × H)
20. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
23. C₃×C₄×C₅×Q₈	C₂²	semidirect
25. C₃×Q₈×Dic₅	C₂²	semidirect
26. C₂×C₃×#689	C₂²	semidirect
27. C₂×C₃×#689	C₂²	semidirect
33. C₂×C₃×Dic₂₀	C₂²	semidirect
40. C₃×#4033	C₂²	semidirect
49. C₃×C₄×Dic₁₀	C₂²	semidirect
50. C₃×C₅×C₄⋊C₈	C₂²	semidirect
51. C₃×C₅×#103	C₂²	semidirect
53. C₃×#3967	C₂²	semidirect
56. C₃×#3948	C₂²	semidirect
57. C₃×#3946	C₂²	semidirect
58. C₃×#3946	C₂²	semidirect
59. C₃×#3942	C₂²	semidirect
61. C₃×C₄⋊#168	C₂²	semidirect
63. C₂×D₅×Q₁₆	C₂×C₃	semidirect
66. C₄×Q₈×D₅	C₂×C₃	semidirect
67. C₅×#464	C₂×C₃	semidirect
68. #65474	C₂×C₃	semidirect
69. #65455	C₂×C₃	semidirect
70. #65343	C₂×C₃	semidirect
71. #65317	C₂×C₃	semidirect
72. #65134	C₂×C₃	semidirect
73. D₅×C₄⋊C₈	C₂×C₃	semidirect
74. D₅×#103	C₂×C₃	semidirect
75. #65087	C₂×C₃	semidirect
77. #65056	C₂×C₃	semidirect
148. C₃×#464	D₅	direct (N × H)
155. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
158. C₄×C₅×Q₈	C₂²×C₃	semidirect
160. Q₈×Dic₅	C₂²×C₃	semidirect
161. C₂×#689	C₂²×C₃	semidirect
162. C₂×#689	C₂²×C₃	semidirect
168. C₂×Dic₂₀	C₂²×C₃	semidirect
175. #4033	C₂²×C₃	semidirect
184. C₄×Dic₁₀	C₂²×C₃	semidirect
185. C₅×C₄⋊C₈	C₂²×C₃	semidirect
186. C₅×#103	C₂²×C₃	semidirect
188. #3967	C₂²×C₃	semidirect
191. #3948	C₂²×C₃	semidirect
192. #3946	C₂²×C₃	semidirect
193. #3946	C₂²×C₃	semidirect
194. #3942	C₂²×C₃	semidirect
196. C₄⋊#168	C₂²×C₃	semidirect
249. C₂×C₃×Q₁₆	C₂×D₅	semidirect
268. C₃×C₄×Q₈	C₂×D₅	semidirect
278. C₃×C₄⋊C₈	C₂×D₅	semidirect
282. C₃×#103	C₂×D₅	semidirect
357. #464	C₃×D₅	direct (N × H)
495. C₂×Q₁₆	C₂×C₃×D₅	semidirect
514. C₄×Q₈	C₂×C₃×D₅	semidirect
524. C₄⋊C₈	C₂×C₃×D₅	semidirect
528. #103	C₂×C₃×D₅	semidirect
538. C₃×D₅	#464	direct (N × H)
666. C₃×C₅	C₂×#464	semidirect
696. D₅	C₃×#464	direct (N × H)
747. C₅	C₂×C₃×#464	semidirect
772. C₃	D₅×#464	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×D₅×Q₁₆	2
C₂×C₃×D₅×SD₁₆	2
C₃×D₅×#124	2
C₃×C₄×Q₈×D₅	2
C₃×C₅×#464	2
C₃×#65474	2
C₃×#65455	2
C₃×#65343	2
C₃×#65317	2
C₃×#65134	2
C₃×D₅×C₄⋊C₈	2
C₃×D₅×#103	2
C₃×#65087	2
C₃×D₅×#102	2
C₃×#65056	2
D₅×#464	3
C₂×C₃×#464	5

Subgroups — C3×D5×#464 #14426119

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#464 #14426119