Subgroups — C₃×#10618175 #14481802

Order 1920.

1992 conjugacy classes of subgroups.

The subgroup lattice has 500 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×#66063	C₂	1	4	yes	maximal, complemented
3	C₃×#66023	C₂	1	4	yes	maximal, complemented
4	C₃×#65968	C₂	1	4	yes	maximal
5	C₃×#65957	C₂	1	4	yes	maximal, complemented
6	C₃×#65912	C₂	1	8	yes	maximal, complemented
7	C₃×D₅×#117	C₂	1	2	yes	maximal
8	C₃×#65851	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#4018	C₂	1	1	yes	maximal, characteristic
10	C₃×#65804	C₂	1	1	yes	maximal, characteristic, complemented
11	#10618175	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
13	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
14	C₃×C₅×#125	C₂²	1	2	yes	complemented
15	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
16	C₃×C₄×C₅×Q₈	C₂²	1	4	yes	complemented
17	C₃×C₅×#117	C₂²	1	2	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₃×#4092	C₂²	1	8	yes	—
20	C₃×#4090	C₂²	1	8	yes	complemented
21	C₂×C₃×#685	C₂²	1	2	yes	—
22	C₃×#4072	C₂²	1	2	yes	—
23	C₃×#4070	C₂²	1	4	yes	—
24	C₂×C₃×#683	C₂²	1	2	yes	—
25	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
26	C₃×#4043	C₂²	1	8	yes	—
27	C₃×#4042	C₂²	1	8	yes	—
28	C₃×#4042	C₂²	1	8	yes	—
29	C₃×#4038	C₂²	1	4	yes	—
30	C₃×D₅×C₄⋊C₄	C₂²	1	4	yes	—
31	C₃×#4036	C₂²	1	4	yes	complemented
32	C₃×#4035	C₂²	1	8	yes	complemented
33	C₃×#4035	C₂²	1	8	yes	complemented
34	C₃×#4034	C₂²	1	4	yes	complemented
35	C₃×#4034	C₂²	1	8	yes	complemented
36	C₃×D₅×C₂²⋊C₄	C₂²	1	4	yes	—
37	C₃×#4024	C₂²	1	8	yes	—
38	C₃×#4023	C₂²	1	4	yes	—
39	C₃×#4018	C₂²	1	4	yes	—
40	C₃×#4018	C₂²	1	4	yes	—
41	C₃×#4018	C₂²	1	2	yes	—
42	C₃×#4018	C₂²	1	2	yes	—
43	C₃×C₄²×D₅	C₂²	1	4	yes	—
44	C₃×#4016	C₂²	1	2	yes	complemented
45	C₃×#4015	C₂²	1	2	yes	complemented
46	C₃×C₄×Dic₁₀	C₂²	1	8	yes	complemented
47	C₃×C₄×Dic₁₀	C₂²	1	4	yes	complemented
48	C₃×#3458	—	5	1	no	maximal, Hall
49	C₅×#533	C₂×C₃	1	1	yes	characteristic, complemented
50	#66063	C₂×C₃	1	4	yes	complemented
51	#66023	C₂×C₃	1	4	yes	complemented
52	#65968	C₂×C₃	1	4	yes	—
53	#65957	C₂×C₃	1	4	yes	complemented
54	#65912	C₂×C₃	1	8	yes	complemented
55	D₅×#117	C₂×C₃	1	2	yes	—
56	#65851	C₂×C₃	1	2	yes	complemented
57	C₂×#4018	C₂×C₃	1	1	yes	characteristic
58	#65804	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
61	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
64	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₄×D₅	Q₈	1	8	yes	complemented
66	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
67	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
68	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
69	C₂×C₃×Dic₁₀	C₂³	1	8	yes	—
70	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
71	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
72	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
73	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
74	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
75	C₃×C₄²×C₅	C₂³	1	2	yes	—
76	C₃×C₄²×C₅	C₂³	1	4	yes	—
77	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
80	C₃×#685	C₂³	1	4	yes	—
81	C₃×#685	C₂³	1	8	yes	—
82	C₃×#685	C₂³	1	4	yes	—
83	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
84	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
85	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
86	C₃×#683	C₂³	1	4	yes	—
87	C₃×#683	C₂³	1	8	yes	—
88	C₃×#683	C₂³	1	8	yes	—
89	C₃×#683	C₂³	1	8	yes	—
90	C₃×#683	C₂³	1	8	yes	—
91	C₃×#683	C₂³	1	4	yes	—
92	C₃×C₄×Dic₅	C₂³	1	8	yes	—
93	C₃×C₄×Dic₅	C₂³	1	4	yes	—
94	C₃×C₄×Dic₅	C₂³	1	2	yes	—
95	C₃×C₄×Dic₅	C₂³	1	2	yes	—
96	C₃×#544	—	5	4	no	—
97	C₃×#544	—	5	4	no	—
98	C₃×#544	—	5	4	no	—
99	C₃×#543	—	5	4	no	—
100	C₃×#533	—	5	8	no	—
101	C₃×#533	—	5	2	no	—
102	C₃×#533	—	5	1	no	—
103	C₃×#533	D₅	1	1	yes	characteristic, complemented
104	C₂×C₃×#117	—	5	2	no	—
105	C₂×C₃×#117	—	5	1	no	—
106	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
107	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
108	C₅×#125	C₂²×C₃	1	2	yes	complemented
109	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	—
110	C₄×C₅×Q₈	C₂²×C₃	1	4	yes	complemented
111	C₅×#117	C₂²×C₃	1	2	yes	—
112	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
113	#4092	C₂²×C₃	1	8	yes	—
114	#4090	C₂²×C₃	1	8	yes	complemented
115	C₂×#685	C₂²×C₃	1	2	yes	—
116	#4072	C₂²×C₃	1	2	yes	—
117	#4070	C₂²×C₃	1	4	yes	—
118	C₂×#683	C₂²×C₃	1	2	yes	—
119	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
120	#4043	C₂²×C₃	1	8	yes	—
121	#4042	C₂²×C₃	1	8	yes	—
122	#4042	C₂²×C₃	1	8	yes	—
123	#4038	C₂²×C₃	1	4	yes	—
124	D₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
125	#4036	C₂²×C₃	1	4	yes	complemented
126	#4035	C₂²×C₃	1	8	yes	complemented
127	#4035	C₂²×C₃	1	8	yes	complemented
128	#4034	C₂²×C₃	1	4	yes	complemented
129	#4034	C₂²×C₃	1	8	yes	complemented
130	D₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
131	#4024	C₂²×C₃	1	8	yes	—
132	#4023	C₂²×C₃	1	4	yes	—
133	#4018	C₂²×C₃	1	2	yes	—
134	#4018	C₂²×C₃	1	4	yes	—
135	#4018	C₂²×C₃	1	2	yes	—
136	#4018	C₂²×C₃	1	4	yes	—
137	C₄²×D₅	C₂²×C₃	1	4	yes	—
138	#4016	C₂²×C₃	1	2	yes	complemented
139	#4015	C₂²×C₃	1	2	yes	complemented
140	C₄×Dic₁₀	C₂²×C₃	1	4	yes	complemented
141	C₄×Dic₁₀	C₂²×C₃	1	8	yes	complemented
142	#3458	—	5	1	no	Sylow
143	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
144	C₂²×C₃×D₅	—	4	2	no	—
145	C₂²×C₃×D₅	C₂×Q₈	1	4	yes	—
146	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
147	C₃×C₅×Q₈	—	4	4	no	—
148	C₂×C₃×C₄×C₅	—	4	2	no	—
149	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
150	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
151	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
152	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
153	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
155	C₂×C₃×Dic₅	—	4	2	no	—
156	C₂×C₃×Dic₅	C₂×Q₈	1	4	yes	—
157	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
158	C₂×C₃×Dic₅	C₂⁴	1	8	yes	—
159	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
160	C₃×C₄×D₅	—	4	8	no	—
161	C₃×C₄×D₅	C₂×Q₈	1	8	yes	—
162	C₃×C₄×D₅	C₂×Q₈	1	8	yes	—
163	C₃×Dic₁₀	—	4	4	no	—
164	C₃×Dic₁₀	—	4	8	no	—
165	C₂³×C₃×C₄	—	5	1	no	—
166	C₃×C₄⋊Q₈	—	5	8	no	—
167	C₃×C₄⋊Q₈	—	5	8	no	—
168	C₃×C₄⋊Q₈	—	5	4	no	—
169	C₃×C₄⋊Q₈	—	5	2	no	—
170	C₃×C₄⋊Q₈	C₂×D₅	1	2	yes	complemented
171	C₃×#125	—	5	8	no	—
172	C₃×#125	—	5	8	no	—
173	C₃×#125	—	5	4	no	—
174	C₃×#125	—	5	2	no	—
175	C₃×#125	C₂×D₅	1	2	yes	complemented
176	C₃×C₂²⋊Q₈	—	5	8	no	—
177	C₃×C₂²⋊Q₈	—	5	4	no	—
178	C₃×C₂²⋊Q₈	—	5	8	no	—
179	C₃×C₂²⋊Q₈	—	5	8	no	—
180	C₃×C₂²⋊Q₈	—	5	8	no	—
181	C₃×C₂²⋊Q₈	—	5	8	no	—
182	C₃×C₂²⋊Q₈	C₂×D₅	1	4	yes	—
183	C₃×C₄×Q₈	—	5	8	no	—
184	C₃×C₄×Q₈	—	5	4	no	—
185	C₃×C₄×Q₈	C₂×D₅	1	4	yes	complemented
186	C₃×#117	—	5	2	no	—
187	C₃×#117	—	5	4	no	—
188	C₃×#117	—	5	4	no	—
189	C₃×#117	—	5	4	no	—
190	C₃×#117	—	5	4	no	—
191	C₃×#117	—	5	2	no	—
192	C₃×#117	—	5	2	no	—
193	C₃×#117	C₂×D₅	1	2	yes	—
194	C₂×C₃×C₄⋊C₄	—	5	2	no	—
195	C₂×C₃×C₄⋊C₄	—	5	4	no	—
196	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
197	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
198	C₂×C₃×C₄²	—	5	1	no	—
199	C₂×C₃×C₄²	—	5	4	no	—
200	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
201	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
202	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
203	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
204	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
205	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
206	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
207	C₂×C₄×D₅	C₃×Q₈	1	8	yes	complemented
208	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
209	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
210	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
211	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
212	C₂×Dic₁₀	C₂³×C₃	1	8	yes	—
213	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
214	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
215	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
216	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
217	C₄²×C₅	C₂³×C₃	1	2	yes	—
218	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
219	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
220	C₄²×C₅	C₂³×C₃	1	4	yes	—
221	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
222	#685	C₂³×C₃	1	4	yes	—
223	#685	C₂³×C₃	1	4	yes	—
224	#685	C₂³×C₃	1	8	yes	—
225	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
226	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
227	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
228	#683	C₂³×C₃	1	8	yes	—
229	#683	C₂³×C₃	1	8	yes	—
230	#683	C₂³×C₃	1	8	yes	—
231	#683	C₂³×C₃	1	4	yes	—
232	#683	C₂³×C₃	1	4	yes	—
233	#683	C₂³×C₃	1	8	yes	—
234	C₄×Dic₅	C₂³×C₃	1	4	yes	—
235	C₄×Dic₅	C₂³×C₃	1	2	yes	—
236	C₄×Dic₅	C₂³×C₃	1	8	yes	—
237	C₄×Dic₅	C₂³×C₃	1	2	yes	—
238	#544	—	5	4	no	—
239	#544	—	5	4	no	—
240	#544	—	5	4	no	—
241	#543	—	5	4	no	—
242	#533	—	5	8	no	—
243	#533	—	5	2	no	—
244	#533	—	5	1	no	—
245	#533	C₃×D₅	1	1	yes	characteristic, complemented
246	C₂×#117	—	5	2	no	—
247	C₂×#117	—	5	1	no	—
248	C₂²×C₃×C₅	—	2	2	no	—
249	C₂²×C₃×C₅	C₂²×Q₈	1	2	yes	—
250	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
251	C₂×C₃×D₅	—	2	4	no	—
252	C₂×C₃×D₅	—	4	4	no	—
253	C₂×C₃×D₅	C₂²×Q₈	1	4	yes	—
254	C₃×C₄×C₅	—	2	2	no	—
255	C₃×C₄×C₅	—	2	8	no	—
256	C₃×C₄×C₅	—	2	2	no	—
257	C₃×C₄×C₅	C₂²×Q₈	1	2	yes	—
258	C₃×C₄×C₅	C₂²×Q₈	1	2	yes	—
259	C₃×Dic₅	—	2	8	no	—
260	C₃×Dic₅	—	2	4	no	—
261	C₃×Dic₅	C₂²×Q₈	1	4	yes	—
262	C₂⁴×C₃	—	5	1	no	—
263	C₂×C₃×Q₈	—	5	8	no	—
264	C₂×C₃×Q₈	—	5	4	no	—
265	C₂×C₃×Q₈	C₂²×D₅	1	4	yes	—
266	C₂²×C₃×C₄	—	5	1	no	—
267	C₂²×C₃×C₄	—	5	8	no	—
268	C₂²×C₃×C₄	—	5	2	no	—
269	C₂²×C₃×C₄	—	5	2	no	—
270	C₂²×C₃×C₄	—	5	2	no	—
271	C₂²×C₃×C₄	—	5	8	no	—
272	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
273	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
274	C₃×C₄⋊C₄	—	5	8	no	—
275	C₃×C₄⋊C₄	—	5	4	no	—
276	C₃×C₄⋊C₄	—	5	4	no	—
277	C₃×C₄⋊C₄	—	5	8	no	—
278	C₃×C₄⋊C₄	—	5	8	no	—
279	C₃×C₄⋊C₄	—	5	8	no	—
280	C₃×C₄⋊C₄	—	5	4	no	—
281	C₃×C₄⋊C₄	—	5	8	no	—
282	C₃×C₄⋊C₄	—	5	4	no	—
283	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
284	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
285	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
286	C₃×C₂²⋊C₄	—	5	4	no	—
287	C₃×C₂²⋊C₄	—	5	8	no	—
288	C₃×C₂²⋊C₄	—	5	4	no	—
289	C₃×C₂²⋊C₄	—	5	4	no	—
290	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
291	C₃×C₄²	—	5	8	no	—
292	C₃×C₄²	—	5	2	no	—
293	C₃×C₄²	—	5	4	no	—
294	C₃×C₄²	—	5	2	no	—
295	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
296	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
297	C₃×C₄²	C₂²×D₅	1	4	yes	—
298	C₃×C₄²	C₂²×D₅	1	2	yes	—
299	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
300	C₂²×D₅	—	4	2	no	—
301	C₂²×D₅	C₂×C₃×Q₈	1	4	yes	—
302	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
303	C₅×Q₈	—	4	4	no	—
304	C₂×C₄×C₅	—	4	2	no	—
305	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
306	C₂×C₄×C₅	C₂⁴×C₃	1	8	yes	—
307	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
308	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
309	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
311	C₂×Dic₅	—	4	2	no	—
312	C₂×Dic₅	C₂×C₃×Q₈	1	4	yes	—
313	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
314	C₂×Dic₅	C₂⁴×C₃	1	8	yes	—
315	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
316	C₄×D₅	—	4	8	no	—
317	C₄×D₅	C₂×C₃×Q₈	1	8	yes	—
318	C₄×D₅	C₂×C₃×Q₈	1	8	yes	—
319	Dic₁₀	—	4	4	no	—
320	Dic₁₀	—	4	8	no	—
321	C₂³×C₄	—	5	1	no	—
322	C₄⋊Q₈	—	5	8	no	—
323	C₄⋊Q₈	—	5	8	no	—
324	C₄⋊Q₈	—	5	4	no	—
325	C₄⋊Q₈	—	5	2	no	—
326	C₄⋊Q₈	C₂×C₃×D₅	1	2	yes	complemented
327	#125	—	5	8	no	—
328	#125	—	5	8	no	—
329	#125	—	5	4	no	—
330	#125	—	5	2	no	—
331	#125	C₂×C₃×D₅	1	2	yes	complemented
332	C₂²⋊Q₈	—	5	8	no	—
333	C₂²⋊Q₈	—	5	4	no	—
334	C₂²⋊Q₈	—	5	8	no	—
335	C₂²⋊Q₈	—	5	8	no	—
336	C₂²⋊Q₈	—	5	8	no	—
337	C₂²⋊Q₈	—	5	8	no	—
338	C₂²⋊Q₈	C₂×C₃×D₅	1	4	yes	—
339	C₄×Q₈	—	5	8	no	—
340	C₄×Q₈	—	5	4	no	—
341	C₄×Q₈	C₂×C₃×D₅	1	4	yes	complemented
342	#117	—	5	2	no	—
343	#117	—	5	4	no	—
344	#117	—	5	4	no	—
345	#117	—	5	4	no	—
346	#117	—	5	4	no	—
347	#117	—	5	2	no	—
348	#117	—	5	2	no	—
349	#117	C₂×C₃×D₅	1	2	yes	—
350	C₂×C₄⋊C₄	—	5	2	no	—
351	C₂×C₄⋊C₄	—	5	4	no	—
352	C₂×C₂²⋊C₄	—	5	2	no	—
353	C₂×C₂²⋊C₄	—	5	4	no	—
354	C₂×C₄²	—	5	1	no	—
355	C₂×C₄²	—	5	4	no	—
356	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
357	C₂×C₃×C₅	—	2	2	no	—
358	C₂×C₃×C₅	C₂³×Q₈	1	1	yes	characteristic
359	C₂×C₃×C₅	#585	1	2	yes	—
360	C₃×D₅	—	2	4	no	—
361	C₂³×C₃	—	5	2	no	—
362	C₂³×C₃	—	5	4	no	—
363	C₂³×C₃	—	20	2	no	—
364	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
365	C₃×Q₈	—	4	4	no	—
366	C₃×Q₈	—	20	4	no	—
367	C₃×Q₈	—	20	8	no	—
368	C₂×C₃×C₄	—	4	2	no	—
369	C₂×C₃×C₄	—	5	4	no	—
370	C₂×C₃×C₄	—	5	2	no	—
371	C₂×C₃×C₄	—	5	8	no	—
372	C₂×C₃×C₄	—	5	8	no	—
373	C₂×C₃×C₄	—	5	4	no	—
374	C₂×C₃×C₄	—	5	8	no	—
375	C₂×C₃×C₄	—	20	8	no	—
376	C₂×C₃×C₄	—	20	2	no	—
377	C₂×C₃×C₄	Q₈×D₅	1	4	yes	—
378	C₂×C₃×C₄	C₂³×D₅	1	8	yes	—
379	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
380	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
381	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
382	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
383	C₂²×C₅	—	2	2	no	—
384	C₂²×C₅	C₂²×C₃×Q₈	1	2	yes	—
385	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
386	C₂×D₅	—	2	4	no	—
387	C₂×D₅	—	4	4	no	—
388	C₂×D₅	C₂²×C₃×Q₈	1	4	yes	—
389	C₄×C₅	—	2	2	no	—
390	C₄×C₅	—	2	8	no	—
391	C₄×C₅	—	2	2	no	—
392	C₄×C₅	C₂²×C₃×Q₈	1	2	yes	—
393	C₄×C₅	C₂²×C₃×Q₈	1	2	yes	—
394	Dic₅	—	2	8	no	—
395	Dic₅	—	2	4	no	—
396	Dic₅	C₂²×C₃×Q₈	1	4	yes	—
397	C₂⁴	—	5	1	no	—
398	C₂×Q₈	—	5	8	no	—
399	C₂×Q₈	—	5	4	no	—
400	C₂×Q₈	C₂²×C₃×D₅	1	4	yes	—
401	C₂²×C₄	—	5	1	no	—
402	C₂²×C₄	—	5	8	no	—
403	C₂²×C₄	—	5	2	no	—
404	C₂²×C₄	—	5	2	no	—
405	C₂²×C₄	—	5	2	no	—
406	C₂²×C₄	—	5	8	no	—
407	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
408	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
409	C₄⋊C₄	—	5	8	no	—
410	C₄⋊C₄	—	5	4	no	—
411	C₄⋊C₄	—	5	4	no	—
412	C₄⋊C₄	—	5	4	no	—
413	C₄⋊C₄	—	5	8	no	—
414	C₄⋊C₄	—	5	8	no	—
415	C₄⋊C₄	—	5	8	no	—
416	C₄⋊C₄	—	5	8	no	—
417	C₄⋊C₄	—	5	4	no	—
418	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
419	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
420	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
421	C₂²⋊C₄	—	5	4	no	—
422	C₂²⋊C₄	—	5	8	no	—
423	C₂²⋊C₄	—	5	4	no	—
424	C₂²⋊C₄	—	5	4	no	—
425	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
426	C₄²	—	5	2	no	—
427	C₄²	—	5	4	no	—
428	C₄²	—	5	8	no	—
429	C₄²	—	5	2	no	—
430	C₄²	C₂²×C₃×D₅	1	4	yes	—
431	C₄²	C₂²×C₃×D₅	1	2	yes	—
432	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
433	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
434	C₃×C₅	#3458	1	1	yes	characteristic, complemented, Hall
435	C₂²×C₃	—	2	2	no	—
436	C₂²×C₃	—	5	4	no	—
437	C₂²×C₃	—	10	4	no	—
438	C₂²×C₃	—	20	4	no	—
439	C₂²×C₃	C₂×Q₈×D₅	1	2	yes	—
440	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
441	C₃×C₄	—	2	2	no	—
442	C₃×C₄	—	2	2	no	—
443	C₃×C₄	—	2	8	no	—
444	C₃×C₄	—	5	4	no	—
445	C₃×C₄	—	10	8	no	—
446	C₃×C₄	—	10	4	no	—
447	C₃×C₄	C₂×Q₈×D₅	1	2	yes	—
448	C₃×C₄	C₂×Q₈×D₅	1	2	yes	—
449	C₂×C₅	—	2	2	no	—
450	C₂×C₅	C₂³×C₃×Q₈	1	1	yes	characteristic
451	C₂×C₅	C₃×#585	1	2	yes	—
452	D₅	—	2	4	no	—
453	C₂³	—	5	2	no	—
454	C₂³	—	5	4	no	—
455	C₂³	—	20	2	no	—
456	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
457	Q₈	—	4	4	no	—
458	Q₈	—	20	4	no	—
459	Q₈	—	20	8	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	5	4	no	—
462	C₂×C₄	—	5	2	no	—
463	C₂×C₄	—	5	8	no	—
464	C₂×C₄	—	5	8	no	—
465	C₂×C₄	—	5	8	no	—
466	C₂×C₄	—	5	4	no	—
467	C₂×C₄	—	20	8	no	—
468	C₂×C₄	—	20	2	no	—
469	C₂×C₄	C₃×Q₈×D₅	1	4	yes	—
470	C₂×C₄	C₂³×C₃×D₅	1	8	yes	—
471	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
472	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
473	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
474	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
475	C₂×C₃	—	2	2	no	—
476	C₂×C₃	—	10	4	no	—
477	C₂×C₃	C₂²×Q₈×D₅	1	1	yes	characteristic
478	C₂×C₃	#66283	1	2	yes	—
479	C₅	C₃×#3458	1	1	yes	characteristic, complemented, Sylow
480	C₂²	—	2	2	no	—
481	C₂²	—	5	4	no	—
482	C₂²	—	10	4	no	—
483	C₂²	—	20	4	no	—
484	C₂²	C₂×C₃×Q₈×D₅	1	2	yes	—
485	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
486	C₄	—	2	2	no	—
487	C₄	—	2	2	no	—
488	C₄	—	2	8	no	—
489	C₄	—	5	4	no	—
490	C₄	—	10	8	no	—
491	C₄	—	10	4	no	—
492	C₄	C₂×C₃×Q₈×D₅	1	2	yes	—
493	C₄	C₂×C₃×Q₈×D₅	1	2	yes	—
494	C₃	#10618175	1	1	yes	characteristic, direct product factor, Sylow
495	C₂	—	2	2	no	—
496	C₂	—	10	4	no	—
497	C₂	C₂²×C₃×Q₈×D₅	1	1	yes	characteristic
498	C₂	C₃×#66283	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	C₃×#3458
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×#66063	C₂	semidirect
3. C₃×#66023	C₂	semidirect
5. C₃×#65957	C₂	semidirect
6. C₃×#65912	C₂	semidirect
8. C₃×#65851	C₂	semidirect
10. C₃×#65804	C₂	semidirect
11. #10618175	C₃	direct (N × H)
13. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
14. C₃×C₅×#125	C₂²	semidirect
16. C₃×C₄×C₅×Q₈	C₂²	semidirect
20. C₃×#4090	C₂²	semidirect
31. C₃×#4036	C₂²	semidirect
32. C₃×#4035	C₂²	semidirect
33. C₃×#4035	C₂²	semidirect
34. C₃×#4034	C₂²	semidirect
35. C₃×#4034	C₂²	semidirect
44. C₃×#4016	C₂²	semidirect
45. C₃×#4015	C₂²	semidirect
46. C₃×C₄×Dic₁₀	C₂²	semidirect
47. C₃×C₄×Dic₁₀	C₂²	semidirect
49. C₅×#533	C₂×C₃	semidirect
50. #66063	C₂×C₃	semidirect
51. #66023	C₂×C₃	semidirect
53. #65957	C₂×C₃	semidirect
54. #65912	C₂×C₃	semidirect
56. #65851	C₂×C₃	semidirect
58. #65804	C₂×C₃	semidirect
65. C₂×C₃×C₄×D₅	Q₈	semidirect
103. C₃×#533	D₅	semidirect
107. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
108. C₅×#125	C₂²×C₃	semidirect
110. C₄×C₅×Q₈	C₂²×C₃	semidirect
114. #4090	C₂²×C₃	semidirect
125. #4036	C₂²×C₃	semidirect
126. #4035	C₂²×C₃	semidirect
127. #4035	C₂²×C₃	semidirect
128. #4034	C₂²×C₃	semidirect
129. #4034	C₂²×C₃	semidirect
138. #4016	C₂²×C₃	semidirect
139. #4015	C₂²×C₃	semidirect
140. C₄×Dic₁₀	C₂²×C₃	semidirect
141. C₄×Dic₁₀	C₂²×C₃	semidirect
170. C₃×C₄⋊Q₈	C₂×D₅	semidirect
175. C₃×#125	C₂×D₅	semidirect
185. C₃×C₄×Q₈	C₂×D₅	semidirect
207. C₂×C₄×D₅	C₃×Q₈	semidirect
245. #533	C₃×D₅	semidirect
326. C₄⋊Q₈	C₂×C₃×D₅	semidirect
331. #125	C₂×C₃×D₅	semidirect
341. C₄×Q₈	C₂×C₃×D₅	semidirect
434. C₃×C₅	#3458	semidirect
479. C₅	C₃×#3458	semidirect
494. C₃	#10618175	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×#66063	2
C₃×#66023	2
C₃×#65968	2
C₃×#65957	2
C₃×#65912	2
C₃×D₅×#117	2
C₃×#65851	2
C₂×C₃×#4018	2
C₃×#65804	2
#10618175	3
C₃×#3458	5

Subgroups — C3×#10618175 #14481802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10618175 #14481802