Subgroups — C₃×D₅×#533 #14480109

Order 1920.

2336 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66062	C₂	1	2	yes	maximal, complemented
3	C₃×D₅×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
4	C₃×#66022	C₂	1	2	yes	maximal, complemented
5	C₃×D₅×#125	C₂	1	2	yes	maximal, complemented
6	C₃×D₅×C₂²⋊Q₈	C₂	1	4	yes	maximal
7	C₃×#65956	C₂	1	4	yes	maximal, complemented
8	C₃×#65912	C₂	1	4	yes	maximal, complemented
9	C₃×C₄×Q₈×D₅	C₂	1	4	yes	maximal, complemented
10	C₃×D₅×#117	C₂	1	2	yes	maximal
11	C₃×#65851	C₂	1	2	yes	maximal, complemented
12	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
13	C₃×#65804	C₂	1	1	yes	maximal, characteristic, complemented
14	D₅×#533	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₃×Q₈×D₅	C₂²	1	4	yes	—
16	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
17	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
18	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
19	C₃×C₅×#125	C₂²	1	2	yes	complemented
20	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
21	C₃×C₄×C₅×Q₈	C₂²	1	4	yes	complemented
22	C₃×C₅×#117	C₂²	1	2	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₃×#4092	C₂²	1	4	yes	—
25	C₃×Q₈×Dic₅	C₂²	1	4	yes	complemented
26	C₃×#4090	C₂²	1	4	yes	complemented
27	C₃×#4072	C₂²	1	2	yes	—
28	C₃×#4070	C₂²	1	4	yes	—
29	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
31	C₃×#4043	C₂²	1	4	yes	—
32	C₃×#4042	C₂²	1	8	yes	—
33	C₃×#4038	C₂²	1	4	yes	—
34	C₃×D₅×C₄⋊C₄	C₂²	1	4	yes	—
35	C₃×D₅×C₄⋊C₄	C₂²	1	8	yes	—
36	C₃×D₅×C₄⋊C₄	C₂²	1	4	yes	—
37	C₃×#4036	C₂²	1	4	yes	complemented
38	C₃×#4035	C₂²	1	8	yes	complemented
39	C₃×#4034	C₂²	1	4	yes	complemented
40	C₃×#4034	C₂²	1	4	yes	complemented
41	C₃×#4033	C₂²	1	8	yes	complemented
42	C₃×#4033	C₂²	1	4	yes	complemented
43	C₃×D₅×C₂²⋊C₄	C₂²	1	4	yes	—
44	C₃×#4024	C₂²	1	8	yes	—
45	C₃×#4023	C₂²	1	4	yes	—
46	C₃×#4018	C₂²	1	4	yes	—
47	C₃×C₄²×D₅	C₂²	1	4	yes	—
48	C₃×C₄²×D₅	C₂²	1	2	yes	—
49	C₃×C₄²×D₅	C₂²	1	2	yes	—
50	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
51	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
52	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
53	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
54	C₃×#4016	C₂²	1	2	yes	complemented
55	C₃×#4015	C₂²	1	2	yes	complemented
56	C₃×C₄×Dic₁₀	C₂²	1	8	yes	complemented
57	C₃×C₄×Dic₁₀	C₂²	1	4	yes	complemented
58	C₂×C₃×#533	—	5	1	no	maximal, Hall
59	C₅×#533	C₂×C₃	1	1	yes	characteristic, complemented
60	#66062	C₂×C₃	1	2	yes	complemented
61	D₅×C₄⋊Q₈	C₂×C₃	1	2	yes	complemented
62	#66022	C₂×C₃	1	2	yes	complemented
63	D₅×#125	C₂×C₃	1	2	yes	complemented
64	D₅×C₂²⋊Q₈	C₂×C₃	1	4	yes	—
65	#65956	C₂×C₃	1	4	yes	complemented
66	#65912	C₂×C₃	1	4	yes	complemented
67	C₄×Q₈×D₅	C₂×C₃	1	4	yes	complemented
68	D₅×#117	C₂×C₃	1	2	yes	—
69	#65851	C₂×C₃	1	2	yes	complemented
70	C₂×C₄²×D₅	C₂×C₃	1	1	yes	characteristic
71	#65804	C₂×C₃	1	1	yes	characteristic, complemented
72	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
74	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
75	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
77	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
78	C₃×Q₈×D₅	—	2	16	no	—
79	C₂×C₃×C₄×D₅	—	2	8	no	—
80	C₂×C₃×C₄×D₅	Q₈	1	8	yes	complemented
81	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
82	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
83	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
84	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
85	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
88	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
90	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
91	C₂×C₃×Dic₁₀	C₂³	1	8	yes	—
92	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
93	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
94	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
95	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
96	C₃×C₄²×C₅	C₂³	1	2	yes	—
97	C₃×C₄²×C₅	C₂³	1	4	yes	—
98	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
99	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
100	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
101	C₃×#685	C₂³	1	8	yes	—
102	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
103	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
104	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
105	C₃×#683	C₂³	1	8	yes	—
106	C₃×#683	C₂³	1	8	yes	—
107	C₃×#683	C₂³	1	8	yes	—
108	C₃×#683	C₂³	1	8	yes	—
109	C₃×C₄×Dic₅	C₂³	1	2	yes	—
110	C₃×C₄×Dic₅	C₂³	1	2	yes	—
111	C₃×C₄×Dic₅	C₂³	1	8	yes	—
112	C₃×C₄×Dic₅	C₂³	1	2	yes	—
113	C₃×C₄×Dic₅	C₂³	1	4	yes	—
114	C₃×C₄×Dic₅	C₂³	1	2	yes	—
115	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
116	C₃×C₄×Dic₅	C₂³	1	2	yes	—
117	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
118	C₃×#533	—	5	2	no	—
119	C₃×#533	—	5	2	no	—
120	C₃×#533	—	5	4	no	—
121	C₃×#533	—	5	4	no	—
122	C₃×#533	—	5	2	no	—
123	C₃×#533	—	5	1	no	—
124	C₃×#533	D₅	1	1	yes	characteristic, direct product factor
125	C₂×C₃×C₄⋊Q₈	—	5	2	no	—
126	C₂×C₃×#125	—	5	2	no	—
127	C₂×C₃×C₂²⋊Q₈	—	5	4	no	—
128	C₂×C₃×C₄×Q₈	—	5	4	no	—
129	C₂×C₃×#117	—	5	2	no	—
130	C₂²×C₃×C₄²	—	5	1	no	—
131	C₂×Q₈×D₅	C₂²×C₃	1	4	yes	—
132	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
133	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
134	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
135	C₅×#125	C₂²×C₃	1	2	yes	complemented
136	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
137	C₄×C₅×Q₈	C₂²×C₃	1	4	yes	complemented
138	C₅×#117	C₂²×C₃	1	2	yes	—
139	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
140	#4092	C₂²×C₃	1	4	yes	—
141	Q₈×Dic₅	C₂²×C₃	1	4	yes	complemented
142	#4090	C₂²×C₃	1	4	yes	complemented
143	#4072	C₂²×C₃	1	2	yes	—
144	#4070	C₂²×C₃	1	4	yes	—
145	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
146	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
147	#4043	C₂²×C₃	1	4	yes	—
148	#4042	C₂²×C₃	1	8	yes	—
149	#4038	C₂²×C₃	1	4	yes	—
150	D₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
151	D₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
152	D₅×C₄⋊C₄	C₂²×C₃	1	8	yes	—
153	#4036	C₂²×C₃	1	4	yes	complemented
154	#4035	C₂²×C₃	1	8	yes	complemented
155	#4034	C₂²×C₃	1	4	yes	complemented
156	#4034	C₂²×C₃	1	4	yes	complemented
157	#4033	C₂²×C₃	1	4	yes	complemented
158	#4033	C₂²×C₃	1	8	yes	complemented
159	D₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
160	#4024	C₂²×C₃	1	8	yes	—
161	#4023	C₂²×C₃	1	4	yes	—
162	#4018	C₂²×C₃	1	4	yes	—
163	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
164	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
165	C₄²×D₅	C₂²×C₃	1	2	yes	—
166	C₄²×D₅	C₂²×C₃	1	2	yes	—
167	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
168	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
169	C₄²×D₅	C₂²×C₃	1	4	yes	—
170	#4016	C₂²×C₃	1	2	yes	complemented
171	#4015	C₂²×C₃	1	2	yes	complemented
172	C₄×Dic₁₀	C₂²×C₃	1	4	yes	complemented
173	C₄×Dic₁₀	C₂²×C₃	1	8	yes	complemented
174	C₂×#533	—	5	1	no	Sylow
175	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
176	C₂²×C₃×D₅	—	2	4	no	—
177	C₂²×C₃×D₅	C₂×Q₈	1	4	yes	—
178	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
179	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
180	C₃×C₅×Q₈	—	2	8	no	—
181	C₂×C₃×C₄×C₅	—	2	4	no	—
182	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	complemented
183	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
184	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
185	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
186	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
187	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
188	C₂×C₃×Dic₅	—	2	4	no	—
189	C₂×C₃×Dic₅	C₂×Q₈	1	4	yes	complemented
190	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
191	C₂×C₃×Dic₅	C₂⁴	1	8	yes	—
192	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
193	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
194	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
195	C₃×C₄×D₅	—	2	4	no	—
196	C₃×C₄×D₅	—	2	16	no	—
197	C₃×C₄×D₅	—	2	4	no	—
198	C₃×C₄×D₅	—	2	4	no	—
199	C₃×C₄×D₅	C₂×Q₈	1	4	yes	—
200	C₃×C₄×D₅	C₂×Q₈	1	4	yes	—
201	C₃×C₄×D₅	C₂×Q₈	1	4	yes	complemented
202	C₃×C₄×D₅	C₂×Q₈	1	4	yes	complemented
203	C₃×C₄×D₅	#41	1	8	yes	—
204	C₃×Dic₁₀	—	2	8	no	—
205	C₃×Dic₁₀	—	2	16	no	—
206	C₂²×C₃×Q₈	—	5	4	no	—
207	C₂³×C₃×C₄	—	5	1	no	—
208	C₂³×C₃×C₄	—	5	2	no	—
209	C₃×C₄⋊Q₈	—	5	4	no	—
210	C₃×C₄⋊Q₈	—	5	4	no	—
211	C₃×C₄⋊Q₈	—	5	4	no	—
212	C₃×C₄⋊Q₈	—	5	2	no	—
213	C₃×C₄⋊Q₈	C₂×D₅	1	2	yes	complemented
214	C₃×#125	—	5	8	no	—
215	C₃×#125	—	5	4	no	—
216	C₃×#125	—	5	2	no	—
217	C₃×#125	C₂×D₅	1	2	yes	complemented
218	C₃×C₂²⋊Q₈	—	5	4	no	—
219	C₃×C₂²⋊Q₈	—	5	4	no	—
220	C₃×C₂²⋊Q₈	—	5	8	no	—
221	C₃×C₂²⋊Q₈	—	5	4	no	—
222	C₃×C₂²⋊Q₈	—	5	8	no	—
223	C₃×C₂²⋊Q₈	C₂×D₅	1	4	yes	—
224	C₃×C₄×Q₈	—	5	4	no	—
225	C₃×C₄×Q₈	—	5	4	no	—
226	C₃×C₄×Q₈	—	5	8	no	—
227	C₃×C₄×Q₈	—	5	8	no	—
228	C₃×C₄×Q₈	—	5	4	no	—
229	C₃×C₄×Q₈	C₂×D₅	1	4	yes	complemented
230	C₃×#117	—	5	2	no	—
231	C₃×#117	—	5	4	no	—
232	C₃×#117	—	5	4	no	—
233	C₃×#117	—	5	4	no	—
234	C₃×#117	C₂×D₅	1	2	yes	—
235	C₂×C₃×C₄⋊C₄	—	5	4	no	—
236	C₂×C₃×C₄⋊C₄	—	5	8	no	—
237	C₂×C₃×C₄⋊C₄	—	5	4	no	—
238	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
239	C₂×C₃×C₄²	—	5	2	no	—
240	C₂×C₃×C₄²	—	5	1	no	—
241	C₂×C₃×C₄²	—	5	2	no	—
242	C₂×C₃×C₄²	—	5	1	no	—
243	C₂×C₃×C₄²	—	5	1	no	—
244	C₂×C₃×C₄²	—	5	1	no	—
245	C₂×C₃×C₄²	—	5	1	no	—
246	C₂×C₃×C₄²	—	5	2	no	—
247	C₂×C₃×C₄²	—	5	4	no	—
248	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
249	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
250	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
251	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
252	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
253	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
254	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
255	Q₈×D₅	—	2	16	no	—
256	C₂×C₄×D₅	—	2	8	no	—
257	C₂×C₄×D₅	C₃×Q₈	1	8	yes	complemented
258	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
259	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
260	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
261	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
262	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
263	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
264	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
265	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
266	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
267	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
268	C₂×Dic₁₀	C₂³×C₃	1	8	yes	—
269	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
270	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
271	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
272	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
273	C₄²×C₅	C₂³×C₃	1	2	yes	—
274	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
275	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
276	C₄²×C₅	C₂³×C₃	1	4	yes	—
277	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
278	#685	C₂³×C₃	1	8	yes	—
279	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
280	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
281	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
282	#683	C₂³×C₃	1	8	yes	—
283	#683	C₂³×C₃	1	8	yes	—
284	#683	C₂³×C₃	1	8	yes	—
285	#683	C₂³×C₃	1	8	yes	—
286	C₄×Dic₅	C₂³×C₃	1	2	yes	—
287	C₄×Dic₅	C₂³×C₃	1	4	yes	—
288	C₄×Dic₅	C₂³×C₃	1	2	yes	—
289	C₄×Dic₅	C₂³×C₃	1	2	yes	—
290	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
291	C₄×Dic₅	C₂³×C₃	1	2	yes	—
292	C₄×Dic₅	C₂³×C₃	1	2	yes	—
293	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
294	C₄×Dic₅	C₂³×C₃	1	8	yes	—
295	#533	—	5	2	no	—
296	#533	—	5	2	no	—
297	#533	—	5	4	no	—
298	#533	—	5	4	no	—
299	#533	—	5	2	no	—
300	#533	—	5	1	no	—
301	#533	C₃×D₅	1	1	yes	characteristic, direct product factor
302	C₂×C₄⋊Q₈	—	5	2	no	—
303	C₂×#125	—	5	2	no	—
304	C₂×C₂²⋊Q₈	—	5	4	no	—
305	C₂×C₄×Q₈	—	5	4	no	—
306	C₂×#117	—	5	2	no	—
307	C₂²×C₄²	—	5	1	no	—
308	C₂²×C₃×C₅	—	2	2	no	—
309	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
310	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
311	C₂×C₃×D₅	—	2	2	no	—
312	C₂×C₃×D₅	—	2	8	no	—
313	C₂×C₃×D₅	C₂²×Q₈	1	2	yes	—
314	C₂×C₃×D₅	C₂²×Q₈	1	2	yes	—
315	C₂×C₃×D₅	C₂×#41	1	4	yes	—
316	C₃×C₄×C₅	—	2	8	no	—
317	C₃×C₄×C₅	—	2	2	no	—
318	C₃×C₄×C₅	C₂²×Q₈	1	2	yes	—
319	C₃×C₄×C₅	C₂²×Q₈	1	2	yes	—
320	C₃×C₄×C₅	C₂×#41	1	4	yes	—
321	C₃×Dic₅	—	2	8	no	—
322	C₃×Dic₅	—	2	2	no	—
323	C₃×Dic₅	C₂²×Q₈	1	2	yes	—
324	C₃×Dic₅	C₂²×Q₈	1	2	yes	—
325	C₃×Dic₅	C₂×#41	1	4	yes	—
326	C₂⁴×C₃	—	5	1	no	—
327	C₂×C₃×Q₈	—	5	8	no	—
328	C₂×C₃×Q₈	—	5	4	no	—
329	C₂×C₃×Q₈	—	10	16	no	—
330	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	—
331	C₂²×C₃×C₄	—	5	1	no	—
332	C₂²×C₃×C₄	—	5	8	no	—
333	C₂²×C₃×C₄	—	5	1	no	—
334	C₂²×C₃×C₄	—	5	2	no	—
335	C₂²×C₃×C₄	—	5	1	no	—
336	C₂²×C₃×C₄	—	5	1	no	—
337	C₂²×C₃×C₄	—	5	1	no	—
338	C₂²×C₃×C₄	—	5	2	no	—
339	C₂²×C₃×C₄	—	5	2	no	—
340	C₂²×C₃×C₄	—	5	2	no	—
341	C₂²×C₃×C₄	—	5	2	no	—
342	C₂²×C₃×C₄	—	5	8	no	—
343	C₂²×C₃×C₄	—	10	8	no	—
344	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
345	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
346	C₃×C₄⋊C₄	—	5	8	no	—
347	C₃×C₄⋊C₄	—	5	8	no	—
348	C₃×C₄⋊C₄	—	5	8	no	—
349	C₃×C₄⋊C₄	—	5	8	no	—
350	C₃×C₄⋊C₄	—	5	4	no	—
351	C₃×C₄⋊C₄	—	5	8	no	—
352	C₃×C₄⋊C₄	—	5	4	no	—
353	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
354	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
355	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
356	C₃×C₂²⋊C₄	—	5	4	no	—
357	C₃×C₂²⋊C₄	—	5	8	no	—
358	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
359	C₃×C₄²	—	5	2	no	—
360	C₃×C₄²	—	5	2	no	—
361	C₃×C₄²	—	5	2	no	—
362	C₃×C₄²	—	5	1	no	—
363	C₃×C₄²	—	5	2	no	—
364	C₃×C₄²	—	5	1	no	—
365	C₃×C₄²	—	5	8	no	—
366	C₃×C₄²	—	5	2	no	—
367	C₃×C₄²	—	5	4	no	—
368	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
369	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
370	C₃×C₄²	C₂²×D₅	1	2	yes	—
371	C₃×C₄²	C₂²×D₅	1	4	yes	—
372	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
373	C₂²×D₅	—	2	4	no	—
374	C₂²×D₅	C₂×C₃×Q₈	1	4	yes	—
375	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
376	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
377	C₅×Q₈	—	2	8	no	—
378	C₂×C₄×C₅	—	2	4	no	—
379	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	complemented
380	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
381	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
382	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
383	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
384	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
385	C₂×Dic₅	—	2	4	no	—
386	C₂×Dic₅	C₂×C₃×Q₈	1	4	yes	complemented
387	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
388	C₂×Dic₅	C₂⁴×C₃	1	8	yes	—
389	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
390	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
391	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
392	C₄×D₅	—	2	4	no	—
393	C₄×D₅	—	2	16	no	—
394	C₄×D₅	—	2	4	no	—
395	C₄×D₅	—	2	4	no	—
396	C₄×D₅	C₂×C₃×Q₈	1	4	yes	—
397	C₄×D₅	C₂×C₃×Q₈	1	4	yes	—
398	C₄×D₅	C₂×C₃×Q₈	1	4	yes	complemented
399	C₄×D₅	C₂×C₃×Q₈	1	4	yes	complemented
400	C₄×D₅	C₃×#41	1	8	yes	—
401	Dic₁₀	—	2	8	no	—
402	Dic₁₀	—	2	16	no	—
403	C₂²×Q₈	—	5	4	no	—
404	C₂³×C₄	—	5	1	no	—
405	C₂³×C₄	—	5	2	no	—
406	C₄⋊Q₈	—	5	4	no	—
407	C₄⋊Q₈	—	5	4	no	—
408	C₄⋊Q₈	—	5	4	no	—
409	C₄⋊Q₈	—	5	2	no	—
410	C₄⋊Q₈	C₂×C₃×D₅	1	2	yes	complemented
411	#125	—	5	8	no	—
412	#125	—	5	4	no	—
413	#125	—	5	2	no	—
414	#125	C₂×C₃×D₅	1	2	yes	complemented
415	C₂²⋊Q₈	—	5	4	no	—
416	C₂²⋊Q₈	—	5	4	no	—
417	C₂²⋊Q₈	—	5	8	no	—
418	C₂²⋊Q₈	—	5	4	no	—
419	C₂²⋊Q₈	—	5	8	no	—
420	C₂²⋊Q₈	C₂×C₃×D₅	1	4	yes	—
421	C₄×Q₈	—	5	4	no	—
422	C₄×Q₈	—	5	4	no	—
423	C₄×Q₈	—	5	8	no	—
424	C₄×Q₈	—	5	8	no	—
425	C₄×Q₈	—	5	4	no	—
426	C₄×Q₈	C₂×C₃×D₅	1	4	yes	complemented
427	#117	—	5	2	no	—
428	#117	—	5	4	no	—
429	#117	—	5	4	no	—
430	#117	—	5	4	no	—
431	#117	C₂×C₃×D₅	1	2	yes	—
432	C₂×C₄⋊C₄	—	5	4	no	—
433	C₂×C₄⋊C₄	—	5	8	no	—
434	C₂×C₄⋊C₄	—	5	4	no	—
435	C₂×C₂²⋊C₄	—	5	4	no	—
436	C₂×C₄²	—	5	2	no	—
437	C₂×C₄²	—	5	1	no	—
438	C₂×C₄²	—	5	4	no	—
439	C₂×C₄²	—	5	2	no	—
440	C₂×C₄²	—	5	1	no	—
441	C₂×C₄²	—	5	1	no	—
442	C₂×C₄²	—	5	1	no	—
443	C₂×C₄²	—	5	1	no	—
444	C₂×C₄²	—	5	2	no	—
445	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
446	C₂×C₃×C₅	—	2	2	no	—
447	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
448	C₂×C₃×C₅	C₂²×#41	1	2	yes	—
449	C₃×D₅	—	2	2	no	—
450	C₃×D₅	#533	1	4	yes	direct product factor
451	C₂³×C₃	—	5	1	no	—
452	C₂³×C₃	—	5	4	no	—
453	C₂³×C₃	—	5	1	no	—
454	C₂³×C₃	—	10	4	no	—
455	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
456	C₃×Q₈	—	2	8	no	—
457	C₃×Q₈	—	10	16	no	—
458	C₃×Q₈	—	10	8	no	—
459	C₂×C₃×C₄	—	2	4	no	—
460	C₂×C₃×C₄	—	5	4	no	—
461	C₂×C₃×C₄	—	5	1	no	—
462	C₂×C₃×C₄	—	5	1	no	—
463	C₂×C₃×C₄	—	5	2	no	—
464	C₂×C₃×C₄	—	5	4	no	—
465	C₂×C₃×C₄	—	5	4	no	—
466	C₂×C₃×C₄	—	5	4	no	—
467	C₂×C₃×C₄	—	5	4	no	—
468	C₂×C₃×C₄	—	5	8	no	—
469	C₂×C₃×C₄	—	5	2	no	—
470	C₂×C₃×C₄	—	5	8	no	—
471	C₂×C₃×C₄	—	10	4	no	—
472	C₂×C₃×C₄	—	10	4	no	—
473	C₂×C₃×C₄	—	10	16	no	—
474	C₂×C₃×C₄	—	10	4	no	—
475	C₂×C₃×C₄	—	10	4	no	—
476	C₂×C₃×C₄	Q₈×D₅	1	4	yes	complemented
477	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
478	C₂×C₃×C₄	C₂³×D₅	1	8	yes	—
479	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
480	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
481	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
482	C₂²×C₅	—	2	2	no	—
483	C₂²×C₅	C₂²×C₃×Q₈	1	2	yes	—
484	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
485	C₂×D₅	—	2	2	no	—
486	C₂×D₅	—	2	8	no	—
487	C₂×D₅	C₂²×C₃×Q₈	1	2	yes	—
488	C₂×D₅	C₂²×C₃×Q₈	1	2	yes	—
489	C₂×D₅	C₂×C₃×#41	1	4	yes	—
490	C₄×C₅	—	2	8	no	—
491	C₄×C₅	—	2	2	no	—
492	C₄×C₅	C₂²×C₃×Q₈	1	2	yes	—
493	C₄×C₅	C₂²×C₃×Q₈	1	2	yes	—
494	C₄×C₅	C₂×C₃×#41	1	4	yes	—
495	Dic₅	—	2	8	no	—
496	Dic₅	—	2	2	no	—
497	Dic₅	C₂²×C₃×Q₈	1	2	yes	—
498	Dic₅	C₂²×C₃×Q₈	1	2	yes	—
499	Dic₅	C₂×C₃×#41	1	4	yes	—
500	C₂⁴	—	5	1	no	—
501	C₂×Q₈	—	5	8	no	—
502	C₂×Q₈	—	5	4	no	—
503	C₂×Q₈	—	10	16	no	—
504	C₂×Q₈	C₂²×C₃×D₅	1	4	yes	—
505	C₂²×C₄	—	5	1	no	—
506	C₂²×C₄	—	5	8	no	—
507	C₂²×C₄	—	5	1	no	—
508	C₂²×C₄	—	5	1	no	—
509	C₂²×C₄	—	5	2	no	—
510	C₂²×C₄	—	5	1	no	—
511	C₂²×C₄	—	5	1	no	—
512	C₂²×C₄	—	5	2	no	—
513	C₂²×C₄	—	5	2	no	—
514	C₂²×C₄	—	5	2	no	—
515	C₂²×C₄	—	5	2	no	—
516	C₂²×C₄	—	5	8	no	—
517	C₂²×C₄	—	10	8	no	—
518	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
519	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
520	C₄⋊C₄	—	5	8	no	—
521	C₄⋊C₄	—	5	4	no	—
522	C₄⋊C₄	—	5	8	no	—
523	C₄⋊C₄	—	5	8	no	—
524	C₄⋊C₄	—	5	8	no	—
525	C₄⋊C₄	—	5	8	no	—
526	C₄⋊C₄	—	5	4	no	—
527	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
528	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
529	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
530	C₂²⋊C₄	—	5	4	no	—
531	C₂²⋊C₄	—	5	8	no	—
532	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
533	C₄²	—	5	2	no	—
534	C₄²	—	5	2	no	—
535	C₄²	—	5	2	no	—
536	C₄²	—	5	2	no	—
537	C₄²	—	5	1	no	—
538	C₄²	—	5	2	no	—
539	C₄²	—	5	1	no	—
540	C₄²	—	5	8	no	—
541	C₄²	—	5	4	no	—
542	C₄²	C₂²×C₃×D₅	1	2	yes	—
543	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
544	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
545	C₄²	C₂²×C₃×D₅	1	4	yes	—
546	C₃×C₅	C₂×#533	1	1	yes	characteristic, complemented, Hall
547	C₂²×C₃	—	2	2	no	—
548	C₂²×C₃	—	5	2	no	—
549	C₂²×C₃	—	5	4	no	—
550	C₂²×C₃	—	5	2	no	—
551	C₂²×C₃	—	10	8	no	—
552	C₂²×C₃	—	10	2	no	—
553	C₂²×C₃	C₂×Q₈×D₅	1	2	yes	—
554	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
555	C₃×C₄	—	2	2	no	—
556	C₃×C₄	—	2	8	no	—
557	C₃×C₄	—	5	2	no	—
558	C₃×C₄	—	5	2	no	—
559	C₃×C₄	—	5	4	no	—
560	C₃×C₄	—	10	2	no	—
561	C₃×C₄	—	10	8	no	—
562	C₃×C₄	C₂×Q₈×D₅	1	2	yes	—
563	C₃×C₄	C₂×Q₈×D₅	1	2	yes	—
564	C₃×C₄	D₅×#41	1	4	yes	—
565	C₂×C₅	—	2	2	no	—
566	C₂×C₅	C₂³×C₃×Q₈	1	1	yes	characteristic
567	C₂×C₅	C₂²×C₃×#41	1	2	yes	—
568	D₅	—	2	2	no	—
569	D₅	C₃×#533	1	4	yes	direct product factor
570	C₂³	—	5	1	no	—
571	C₂³	—	5	4	no	—
572	C₂³	—	5	1	no	—
573	C₂³	—	10	4	no	—
574	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
575	Q₈	—	2	8	no	—
576	Q₈	—	10	16	no	—
577	Q₈	—	10	8	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	5	4	no	—
580	C₂×C₄	—	5	1	no	—
581	C₂×C₄	—	5	1	no	—
582	C₂×C₄	—	5	2	no	—
583	C₂×C₄	—	5	4	no	—
584	C₂×C₄	—	5	4	no	—
585	C₂×C₄	—	5	4	no	—
586	C₂×C₄	—	5	4	no	—
587	C₂×C₄	—	5	8	no	—
588	C₂×C₄	—	5	2	no	—
589	C₂×C₄	—	5	8	no	—
590	C₂×C₄	—	10	4	no	—
591	C₂×C₄	—	10	4	no	—
592	C₂×C₄	—	10	16	no	—
593	C₂×C₄	—	10	4	no	—
594	C₂×C₄	—	10	4	no	—
595	C₂×C₄	C₃×Q₈×D₅	1	4	yes	complemented
596	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
597	C₂×C₄	C₂³×C₃×D₅	1	8	yes	—
598	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
599	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
600	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
601	C₂×C₃	—	2	2	no	—
602	C₂×C₃	—	5	4	no	—
603	C₂×C₃	—	10	2	no	—
604	C₂×C₃	C₂²×Q₈×D₅	1	1	yes	characteristic
605	C₂×C₃	C₂×D₅×#41	1	2	yes	—
606	C₅	C₂×C₃×#533	1	1	yes	characteristic, complemented, Sylow
607	C₂²	—	2	2	no	—
608	C₂²	—	5	2	no	—
609	C₂²	—	5	4	no	—
610	C₂²	—	5	2	no	—
611	C₂²	—	10	8	no	—
612	C₂²	—	10	2	no	—
613	C₂²	C₂×C₃×Q₈×D₅	1	2	yes	—
614	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
615	C₄	—	2	2	no	—
616	C₄	—	2	8	no	—
617	C₄	—	5	2	no	—
618	C₄	—	5	2	no	—
619	C₄	—	5	4	no	—
620	C₄	—	10	2	no	—
621	C₄	—	10	8	no	—
622	C₄	C₂×C₃×Q₈×D₅	1	2	yes	—
623	C₄	C₂×C₃×Q₈×D₅	1	2	yes	—
624	C₄	C₃×D₅×#41	1	4	yes	—
625	C₃	D₅×#533	1	1	yes	characteristic, direct product factor, Sylow
626	C₂	—	2	2	no	—
627	C₂	—	5	4	no	—
628	C₂	—	10	2	no	—
629	C₂	C₂²×C₃×Q₈×D₅	1	1	yes	characteristic
630	C₂	C₂×C₃×D₅×#41	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₅×#533	C₂
socle	C₂²×C₃×C₅	C₂⁵
prime radical	C₂³×C₃×D₅	C₂³
hypercenter	C₃×#533	D₅
hypocenter	C₅	C₂×C₃×#533
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#533

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#533	C₂	semidirect
2. C₃×#66062	C₂	semidirect
3. C₃×D₅×C₄⋊Q₈	C₂	semidirect
4. C₃×#66022	C₂	semidirect
5. C₃×D₅×#125	C₂	semidirect
7. C₃×#65956	C₂	semidirect
8. C₃×#65912	C₂	semidirect
9. C₃×C₄×Q₈×D₅	C₂	semidirect
11. C₃×#65851	C₂	semidirect
13. C₃×#65804	C₂	semidirect
14. D₅×#533	C₃	direct (N × H)
18. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
19. C₃×C₅×#125	C₂²	semidirect
21. C₃×C₄×C₅×Q₈	C₂²	semidirect
25. C₃×Q₈×Dic₅	C₂²	semidirect
26. C₃×#4090	C₂²	semidirect
37. C₃×#4036	C₂²	semidirect
38. C₃×#4035	C₂²	semidirect
39. C₃×#4034	C₂²	semidirect
40. C₃×#4034	C₂²	semidirect
41. C₃×#4033	C₂²	semidirect
42. C₃×#4033	C₂²	semidirect
54. C₃×#4016	C₂²	semidirect
55. C₃×#4015	C₂²	semidirect
56. C₃×C₄×Dic₁₀	C₂²	semidirect
57. C₃×C₄×Dic₁₀	C₂²	semidirect
59. C₅×#533	C₂×C₃	semidirect
60. #66062	C₂×C₃	semidirect
61. D₅×C₄⋊Q₈	C₂×C₃	semidirect
62. #66022	C₂×C₃	semidirect
63. D₅×#125	C₂×C₃	semidirect
65. #65956	C₂×C₃	semidirect
66. #65912	C₂×C₃	semidirect
67. C₄×Q₈×D₅	C₂×C₃	semidirect
69. #65851	C₂×C₃	semidirect
71. #65804	C₂×C₃	semidirect
80. C₂×C₃×C₄×D₅	Q₈	semidirect
124. C₃×#533	D₅	direct (N × H)
134. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
135. C₅×#125	C₂²×C₃	semidirect
137. C₄×C₅×Q₈	C₂²×C₃	semidirect
141. Q₈×Dic₅	C₂²×C₃	semidirect
142. #4090	C₂²×C₃	semidirect
153. #4036	C₂²×C₃	semidirect
154. #4035	C₂²×C₃	semidirect
155. #4034	C₂²×C₃	semidirect
156. #4034	C₂²×C₃	semidirect
157. #4033	C₂²×C₃	semidirect
158. #4033	C₂²×C₃	semidirect
170. #4016	C₂²×C₃	semidirect
171. #4015	C₂²×C₃	semidirect
172. C₄×Dic₁₀	C₂²×C₃	semidirect
173. C₄×Dic₁₀	C₂²×C₃	semidirect
182. C₂×C₃×C₄×C₅	C₂×Q₈	semidirect
189. C₂×C₃×Dic₅	C₂×Q₈	semidirect
201. C₃×C₄×D₅	C₂×Q₈	semidirect
202. C₃×C₄×D₅	C₂×Q₈	semidirect
213. C₃×C₄⋊Q₈	C₂×D₅	semidirect
217. C₃×#125	C₂×D₅	semidirect
229. C₃×C₄×Q₈	C₂×D₅	semidirect
257. C₂×C₄×D₅	C₃×Q₈	semidirect
301. #533	C₃×D₅	direct (N × H)
379. C₂×C₄×C₅	C₂×C₃×Q₈	semidirect
386. C₂×Dic₅	C₂×C₃×Q₈	semidirect
398. C₄×D₅	C₂×C₃×Q₈	semidirect
399. C₄×D₅	C₂×C₃×Q₈	semidirect
410. C₄⋊Q₈	C₂×C₃×D₅	semidirect
414. #125	C₂×C₃×D₅	semidirect
426. C₄×Q₈	C₂×C₃×D₅	semidirect
450. C₃×D₅	#533	direct (N × H)
476. C₂×C₃×C₄	Q₈×D₅	semidirect
546. C₃×C₅	C₂×#533	semidirect
569. D₅	C₃×#533	direct (N × H)
595. C₂×C₄	C₃×Q₈×D₅	semidirect
606. C₅	C₂×C₃×#533	semidirect
625. C₃	D₅×#533	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×#533	2
C₃×#66062	2
C₃×D₅×C₄⋊Q₈	2
C₃×#66022	2
C₃×D₅×#125	2
C₃×D₅×C₂²⋊Q₈	2
C₃×#65956	2
C₃×#65912	2
C₃×C₄×Q₈×D₅	2
C₃×D₅×#117	2
C₃×#65851	2
C₂×C₃×C₄²×D₅	2
C₃×#65804	2
D₅×#533	3
C₂×C₃×#533	5

Subgroups — C3×D5×#533 #14480109

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#533 #14480109