Subgroups — C₃×#10618137 #14481515

Order 1920.

2080 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66162	C₂	1	2	yes	maximal, complemented
3	C₃×#41×Dic₅	C₂	1	2	yes	maximal, complemented
4	C₃×#66065	C₂	1	2	yes	maximal, complemented
5	C₃×#66053	C₂	1	2	yes	maximal, complemented
6	C₃×#66016	C₂	1	4	yes	maximal, complemented
7	C₃×#65951	C₂	1	4	yes	maximal, complemented
8	C₃×#65936	C₂	1	4	yes	maximal, complemented
9	C₃×#65872	C₂	1	8	yes	maximal, complemented
10	C₂×C₃×#4018	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65804	C₂	1	1	yes	maximal, characteristic, complemented
12	#10618137	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
14	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
16	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
17	C₃×C₅×#124	C₂²	1	2	yes	complemented
18	C₃×C₅×#121	C₂²	1	4	yes	—
19	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₃×#4092	C₂²	1	4	yes	—
22	C₃×Q₈×Dic₅	C₂²	1	4	yes	complemented
23	C₃×#4085	C₂²	1	8	yes	—
24	C₃×#4084	C₂²	1	4	yes	—
25	C₃×#4083	C₂²	1	4	yes	—
26	C₃×#4081	C₂²	1	4	yes	—
27	C₃×#4081	C₂²	1	8	yes	complemented
28	C₃×D₄×Dic₅	C₂²	1	8	yes	—
29	C₃×D₄×Dic₅	C₂²	1	4	yes	complemented
30	C₃×C₄×C₂²⋊D₅	C₂²	1	8	yes	—
31	C₂×C₃×#685	C₂²	1	2	yes	—
32	C₃×#4072	C₂²	1	2	yes	—
33	C₃×#4072	C₂²	1	4	yes	complemented
34	C₃×#4070	C₂²	1	4	yes	—
35	C₂×C₃×#683	C₂²	1	2	yes	—
36	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×Dic₅	C₂²	1	4	yes	complemented
38	C₃×#4044	C₂²	1	8	yes	—
39	C₃×#4035	C₂²	1	8	yes	complemented
40	C₃×#4032	C₂²	1	8	yes	—
41	C₃×#4031	C₂²	1	8	yes	—
42	C₃×#4025	C₂²	1	8	yes	complemented
43	C₃×#4024	C₂²	1	8	yes	complemented
44	C₃×#4018	C₂²	1	4	yes	—
45	C₃×#4018	C₂²	1	2	yes	—
46	C₃×#4018	C₂²	1	2	yes	—
47	C₃×#4016	C₂²	1	2	yes	complemented
48	C₃×#4015	C₂²	1	2	yes	complemented
49	C₃×C₄×Dic₁₀	C₂²	1	4	yes	complemented
50	C₃×#3455	—	5	1	no	maximal, Hall
51	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
52	#66162	C₂×C₃	1	2	yes	complemented
53	#41×Dic₅	C₂×C₃	1	2	yes	complemented
54	#66065	C₂×C₃	1	2	yes	complemented
55	#66053	C₂×C₃	1	2	yes	complemented
56	#66016	C₂×C₃	1	4	yes	complemented
57	#65951	C₂×C₃	1	4	yes	complemented
58	#65936	C₂×C₃	1	4	yes	complemented
59	#65872	C₂×C₃	1	8	yes	complemented
60	C₂×#4018	C₂×C₃	1	1	yes	characteristic, complemented
61	#65804	C₂×C₃	1	1	yes	characteristic, complemented
62	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
63	C₃×C₅×#41	—	2	8	no	—
64	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
65	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
66	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
67	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
68	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
69	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
72	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
73	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
74	C₂²×C₃×Dic₅	C₂³	1	8	yes	—
75	C₂×C₃×C₄×D₅	—	2	4	no	—
76	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
77	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
78	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
79	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
80	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
81	C₃×C₄²×C₅	C₂³	1	2	yes	—
82	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
83	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
85	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	—
86	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	—
87	C₃×#685	C₂³	1	8	yes	—
88	C₃×#685	C₂³	1	4	yes	—
89	C₃×#685	C₂³	1	4	yes	—
90	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
91	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
92	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
93	C₃×#683	C₂³	1	8	yes	—
94	C₃×#683	C₂³	1	4	yes	—
95	C₃×#683	C₂³	1	8	yes	—
96	C₃×#683	C₂³	1	4	yes	—
97	C₃×C₄×Dic₅	C₂³	1	8	yes	—
98	C₃×C₄×Dic₅	C₂³	1	2	yes	—
99	C₃×C₄×Dic₅	C₂³	1	4	yes	—
100	C₃×C₄×Dic₅	C₂³	1	2	yes	—
101	C₃×#542	—	5	4	no	—
102	C₃×#541	—	5	2	no	—
103	C₃×#540	—	5	2	no	—
104	C₃×#539	—	5	4	no	—
105	C₃×#538	—	5	4	no	—
106	C₃×#533	—	5	1	no	—
107	C₃×#532	D₅	1	1	yes	characteristic, complemented
108	C₃×#529	—	5	8	no	—
109	C₃×#525	—	5	2	no	—
110	C₃×C₄×#41	—	5	2	no	—
111	C₂×C₃×#117	—	5	1	no	—
112	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
113	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
114	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
115	C₅×#127	C₂²×C₃	1	1	yes	characteristic, complemented
116	C₅×#124	C₂²×C₃	1	2	yes	complemented
117	C₅×#121	C₂²×C₃	1	4	yes	—
118	C₄×C₅×D₄	C₂²×C₃	1	4	yes	complemented
119	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
120	#4092	C₂²×C₃	1	4	yes	—
121	Q₈×Dic₅	C₂²×C₃	1	4	yes	complemented
122	#4085	C₂²×C₃	1	8	yes	—
123	#4084	C₂²×C₃	1	4	yes	—
124	#4083	C₂²×C₃	1	4	yes	—
125	#4081	C₂²×C₃	1	4	yes	—
126	#4081	C₂²×C₃	1	8	yes	complemented
127	D₄×Dic₅	C₂²×C₃	1	8	yes	—
128	D₄×Dic₅	C₂²×C₃	1	4	yes	complemented
129	C₄×C₂²⋊D₅	C₂²×C₃	1	8	yes	—
130	C₂×#685	C₂²×C₃	1	2	yes	—
131	#4072	C₂²×C₃	1	2	yes	—
132	#4072	C₂²×C₃	1	4	yes	complemented
133	#4070	C₂²×C₃	1	4	yes	—
134	C₂×#683	C₂²×C₃	1	2	yes	—
135	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
136	C₂×C₄×Dic₅	C₂²×C₃	1	4	yes	complemented
137	#4044	C₂²×C₃	1	8	yes	—
138	#4035	C₂²×C₃	1	8	yes	complemented
139	#4032	C₂²×C₃	1	8	yes	—
140	#4031	C₂²×C₃	1	8	yes	—
141	#4025	C₂²×C₃	1	8	yes	complemented
142	#4024	C₂²×C₃	1	8	yes	complemented
143	#4018	C₂²×C₃	1	2	yes	—
144	#4018	C₂²×C₃	1	4	yes	—
145	#4018	C₂²×C₃	1	2	yes	—
146	#4016	C₂²×C₃	1	2	yes	complemented
147	#4015	C₂²×C₃	1	2	yes	complemented
148	C₄×Dic₁₀	C₂²×C₃	1	4	yes	complemented
149	#3455	—	5	1	no	Sylow
150	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
151	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
152	C₂²×C₃×D₅	—	2	2	no	—
153	C₂²×C₃×D₅	—	4	2	no	—
154	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
155	C₃×C₅×Q₈	—	2	4	no	—
156	C₃×C₅×D₄	—	2	8	no	—
157	C₃×C₅×D₄	—	2	4	no	—
158	C₃×C₅×D₄	—	4	4	no	—
159	C₂×C₃×C₄×C₅	—	2	8	no	—
160	C₂×C₃×C₄×C₅	—	4	2	no	—
161	C₂×C₃×C₄×C₅	#41	1	4	yes	—
162	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
163	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
164	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
165	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
166	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
167	C₃×C₂²⋊D₅	—	4	8	no	—
168	C₂×C₃×Dic₅	—	2	2	no	—
169	C₂×C₃×Dic₅	—	4	8	no	—
170	C₂×C₃×Dic₅	—	4	2	no	—
171	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
172	C₂×C₃×Dic₅	C₂⁴	1	8	yes	—
173	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
174	C₃×C₄×D₅	—	2	4	no	—
175	C₃×C₄×D₅	—	2	4	no	—
176	C₃×Dic₁₀	—	4	4	no	—
177	C₂×C₃×#41	C₂×D₅	1	2	yes	—
178	C₂³×C₃×C₄	—	5	1	no	—
179	C₃×C₄⋊Q₈	—	5	2	no	—
180	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
181	C₃×#127	C₂×D₅	1	1	yes	characteristic, complemented
182	C₃×#126	—	5	8	no	—
183	C₃×#126	—	5	8	no	—
184	C₃×#125	—	5	8	no	—
185	C₃×#125	—	5	2	no	—
186	C₃×#124	—	5	8	no	—
187	C₃×#124	C₂×D₅	1	2	yes	complemented
188	C₃×#123	—	5	4	no	—
189	C₃×#123	—	5	8	no	—
190	C₃×#123	—	5	8	no	—
191	C₃×C₂²⋊Q₈	—	5	4	no	—
192	C₃×C₂²⋊Q₈	—	5	4	no	—
193	C₃×C₂²⋊Q₈	—	5	8	no	—
194	C₃×#121	—	5	4	no	—
195	C₃×#121	—	5	8	no	—
196	C₃×#121	C₂×D₅	1	4	yes	—
197	C₃×#120	—	5	4	no	—
198	C₃×C₄×Q₈	—	5	4	no	—
199	C₃×C₄×Q₈	—	5	4	no	—
200	C₃×C₄×D₄	—	5	8	no	—
201	C₃×C₄×D₄	—	5	4	no	—
202	C₃×C₄×D₄	—	5	8	no	—
203	C₃×C₄×D₄	C₂×D₅	1	4	yes	complemented
204	C₃×#117	—	5	2	no	—
205	C₃×#117	—	5	4	no	—
206	C₃×#117	—	5	4	no	—
207	C₃×#117	—	5	2	no	—
208	C₃×#117	—	5	2	no	—
209	C₂×C₃×C₄⋊C₄	—	5	2	no	—
210	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
211	C₂×C₃×C₄²	—	5	1	no	—
212	C₂×C₃×C₄²	—	5	4	no	—
213	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
214	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
215	C₅×#41	—	2	8	no	—
216	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
217	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
218	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
219	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
220	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
221	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
222	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
223	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	—
224	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
225	C₂²×Dic₅	C₂³×C₃	1	8	yes	—
226	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
227	C₂×C₄×D₅	—	2	4	no	—
228	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
229	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
230	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
231	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
232	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
233	C₄²×C₅	C₂³×C₃	1	2	yes	—
234	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
235	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
236	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	—
237	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	—
238	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
239	#685	C₂³×C₃	1	4	yes	—
240	#685	C₂³×C₃	1	4	yes	—
241	#685	C₂³×C₃	1	8	yes	—
242	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
243	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
244	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
245	#683	C₂³×C₃	1	8	yes	—
246	#683	C₂³×C₃	1	4	yes	—
247	#683	C₂³×C₃	1	4	yes	—
248	#683	C₂³×C₃	1	8	yes	—
249	C₄×Dic₅	C₂³×C₃	1	4	yes	—
250	C₄×Dic₅	C₂³×C₃	1	2	yes	—
251	C₄×Dic₅	C₂³×C₃	1	2	yes	—
252	C₄×Dic₅	C₂³×C₃	1	8	yes	—
253	#542	—	5	4	no	—
254	#541	—	5	2	no	—
255	#540	—	5	2	no	—
256	#539	—	5	4	no	—
257	#538	—	5	4	no	—
258	#533	—	5	1	no	—
259	#532	C₃×D₅	1	1	yes	characteristic, complemented
260	#529	—	5	8	no	—
261	#525	—	5	2	no	—
262	C₄×#41	—	5	2	no	—
263	C₂×#117	—	5	1	no	—
264	C₂²×C₃×C₅	—	2	2	no	—
265	C₂²×C₃×C₅	—	2	4	no	—
266	C₂²×C₃×C₅	—	2	8	no	—
267	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
268	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
269	C₂×C₃×D₅	—	2	2	no	—
270	C₂×C₃×D₅	—	2	4	no	—
271	C₂×C₃×D₅	—	4	4	no	—
272	C₃×C₄×C₅	—	2	4	no	—
273	C₃×C₄×C₅	—	2	2	no	—
274	C₃×C₄×C₅	—	2	2	no	—
275	C₃×C₄×C₅	C₂×#41	1	2	yes	—
276	C₃×C₄×C₅	C₂×#41	1	2	yes	—
277	C₃×Dic₅	—	2	2	no	—
278	C₃×Dic₅	—	2	8	no	—
279	C₃×Dic₅	—	2	4	no	—
280	C₂⁴×C₃	—	5	1	no	—
281	C₃×#41	—	2	8	no	—
282	C₂×C₃×Q₈	—	5	4	no	—
283	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
284	C₂×C₃×D₄	—	5	8	no	—
285	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
286	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
287	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
288	C₂²×C₃×C₄	—	5	1	no	—
289	C₂²×C₃×C₄	—	5	2	no	—
290	C₂²×C₃×C₄	—	5	8	no	—
291	C₂²×C₃×C₄	—	5	2	no	—
292	C₂²×C₃×C₄	—	5	2	no	—
293	C₂²×C₃×C₄	—	10	4	no	—
294	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
295	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
296	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
297	C₃×C₄⋊C₄	—	5	4	no	—
298	C₃×C₄⋊C₄	—	5	4	no	—
299	C₃×C₄⋊C₄	—	5	8	no	—
300	C₃×C₄⋊C₄	—	5	8	no	—
301	C₃×C₄⋊C₄	—	5	4	no	—
302	C₃×C₄⋊C₄	—	5	8	no	—
303	C₃×C₄⋊C₄	—	5	4	no	—
304	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
305	C₃×C₂²⋊C₄	—	5	4	no	—
306	C₃×C₂²⋊C₄	—	5	8	no	—
307	C₃×C₂²⋊C₄	—	5	8	no	—
308	C₃×C₂²⋊C₄	—	5	4	no	—
309	C₃×C₂²⋊C₄	—	5	4	no	—
310	C₃×C₂²⋊C₄	—	5	8	no	—
311	C₃×C₂²⋊C₄	C₂²×D₅	1	8	yes	—
312	C₃×C₄²	—	5	2	no	—
313	C₃×C₄²	—	5	8	no	—
314	C₃×C₄²	—	5	2	no	—
315	C₃×C₄²	—	5	4	no	—
316	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
317	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
318	C₃×C₄²	C₂²×D₅	1	2	yes	—
319	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
320	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
321	C₂²×D₅	—	2	2	no	—
322	C₂²×D₅	—	4	2	no	—
323	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
324	C₅×Q₈	—	2	4	no	—
325	C₅×D₄	—	2	8	no	—
326	C₅×D₄	—	2	4	no	—
327	C₅×D₄	—	4	4	no	—
328	C₂×C₄×C₅	—	2	8	no	—
329	C₂×C₄×C₅	—	4	2	no	—
330	C₂×C₄×C₅	C₃×#41	1	4	yes	—
331	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
332	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
333	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
334	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
335	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
336	C₂²⋊D₅	—	4	8	no	—
337	C₂×Dic₅	—	2	2	no	—
338	C₂×Dic₅	—	4	8	no	—
339	C₂×Dic₅	—	4	2	no	—
340	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
341	C₂×Dic₅	C₂⁴×C₃	1	8	yes	—
342	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
343	C₄×D₅	—	2	4	no	—
344	C₄×D₅	—	2	4	no	—
345	Dic₁₀	—	4	4	no	—
346	C₂×#41	C₂×C₃×D₅	1	2	yes	—
347	C₂³×C₄	—	5	1	no	—
348	C₄⋊Q₈	—	5	2	no	—
349	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
350	#127	C₂×C₃×D₅	1	1	yes	characteristic, complemented
351	#126	—	5	8	no	—
352	#126	—	5	8	no	—
353	#125	—	5	8	no	—
354	#125	—	5	2	no	—
355	#124	—	5	8	no	—
356	#124	C₂×C₃×D₅	1	2	yes	complemented
357	#123	—	5	4	no	—
358	#123	—	5	8	no	—
359	#123	—	5	8	no	—
360	C₂²⋊Q₈	—	5	4	no	—
361	C₂²⋊Q₈	—	5	4	no	—
362	C₂²⋊Q₈	—	5	8	no	—
363	#121	—	5	4	no	—
364	#121	—	5	8	no	—
365	#121	C₂×C₃×D₅	1	4	yes	—
366	#120	—	5	4	no	—
367	C₄×Q₈	—	5	4	no	—
368	C₄×Q₈	—	5	4	no	—
369	C₄×D₄	—	5	8	no	—
370	C₄×D₄	—	5	4	no	—
371	C₄×D₄	—	5	8	no	—
372	C₄×D₄	C₂×C₃×D₅	1	4	yes	complemented
373	#117	—	5	2	no	—
374	#117	—	5	4	no	—
375	#117	—	5	4	no	—
376	#117	—	5	2	no	—
377	#117	—	5	2	no	—
378	C₂×C₄⋊C₄	—	5	2	no	—
379	C₂×C₂²⋊C₄	—	5	2	no	—
380	C₂×C₄²	—	5	1	no	—
381	C₂×C₄²	—	5	4	no	—
382	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
383	C₂×C₃×C₅	—	2	2	no	—
384	C₂×C₃×C₅	—	4	4	no	—
385	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
386	C₂×C₃×C₅	#585	1	2	yes	—
387	C₃×D₅	—	4	2	no	—
388	C₂³×C₃	—	5	2	no	—
389	C₂³×C₃	—	10	2	no	—
390	C₂³×C₃	—	20	2	no	—
391	C₂³×C₃	C₂³×D₅	1	4	yes	—
392	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
393	C₃×Q₈	—	2	4	no	—
394	C₃×Q₈	—	20	4	no	—
395	C₃×D₄	—	2	8	no	—
396	C₃×D₄	—	2	4	no	—
397	C₃×D₄	—	4	4	no	—
398	C₃×D₄	—	20	8	no	—
399	C₂×C₃×C₄	—	2	8	no	—
400	C₂×C₃×C₄	—	4	2	no	—
401	C₂×C₃×C₄	—	5	4	no	—
402	C₂×C₃×C₄	—	5	8	no	—
403	C₂×C₃×C₄	—	5	2	no	—
404	C₂×C₃×C₄	—	10	2	no	—
405	C₂×C₃×C₄	—	10	4	no	—
406	C₂×C₃×C₄	—	10	4	no	—
407	C₂×C₃×C₄	—	20	2	no	—
408	C₂×C₃×C₄	—	20	8	no	—
409	C₂×C₃×C₄	#711	1	4	yes	—
410	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
411	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
412	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
413	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
414	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
415	C₂²×C₅	—	2	2	no	—
416	C₂²×C₅	—	2	4	no	—
417	C₂²×C₅	—	2	8	no	—
418	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
419	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
420	C₂×D₅	—	2	2	no	—
421	C₂×D₅	—	2	4	no	—
422	C₂×D₅	—	4	4	no	—
423	C₄×C₅	—	2	4	no	—
424	C₄×C₅	—	2	2	no	—
425	C₄×C₅	—	2	2	no	—
426	C₄×C₅	C₂×C₃×#41	1	2	yes	—
427	C₄×C₅	C₂×C₃×#41	1	2	yes	—
428	Dic₅	—	2	2	no	—
429	Dic₅	—	2	8	no	—
430	Dic₅	—	2	4	no	—
431	C₂⁴	—	5	1	no	—
432	#41	—	2	8	no	—
433	C₂×Q₈	—	5	4	no	—
434	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
435	C₂×D₄	—	5	8	no	—
436	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
437	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
438	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
439	C₂²×C₄	—	5	1	no	—
440	C₂²×C₄	—	5	2	no	—
441	C₂²×C₄	—	5	8	no	—
442	C₂²×C₄	—	5	2	no	—
443	C₂²×C₄	—	5	2	no	—
444	C₂²×C₄	—	10	4	no	—
445	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
446	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
447	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
448	C₄⋊C₄	—	5	4	no	—
449	C₄⋊C₄	—	5	4	no	—
450	C₄⋊C₄	—	5	4	no	—
451	C₄⋊C₄	—	5	8	no	—
452	C₄⋊C₄	—	5	8	no	—
453	C₄⋊C₄	—	5	8	no	—
454	C₄⋊C₄	—	5	4	no	—
455	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
456	C₂²⋊C₄	—	5	4	no	—
457	C₂²⋊C₄	—	5	8	no	—
458	C₂²⋊C₄	—	5	8	no	—
459	C₂²⋊C₄	—	5	4	no	—
460	C₂²⋊C₄	—	5	4	no	—
461	C₂²⋊C₄	—	5	8	no	—
462	C₂²⋊C₄	C₂²×C₃×D₅	1	8	yes	—
463	C₄²	—	5	2	no	—
464	C₄²	—	5	2	no	—
465	C₄²	—	5	4	no	—
466	C₄²	—	5	8	no	—
467	C₄²	C₂²×C₃×D₅	1	2	yes	—
468	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
469	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
470	C₃×C₅	#3455	1	1	yes	characteristic, complemented, Hall
471	C₂²×C₃	—	2	2	no	—
472	C₂²×C₃	—	2	4	no	—
473	C₂²×C₃	—	2	8	no	—
474	C₂²×C₃	—	10	2	no	—
475	C₂²×C₃	—	10	4	no	—
476	C₂²×C₃	—	20	4	no	—
477	C₂²×C₃	C₂×#711	1	2	yes	—
478	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
479	C₃×C₄	—	2	4	no	—
480	C₃×C₄	—	2	2	no	—
481	C₃×C₄	—	2	2	no	—
482	C₃×C₄	—	10	2	no	—
483	C₃×C₄	—	10	4	no	—
484	C₃×C₄	—	10	8	no	—
485	C₃×C₄	C₂×#711	1	2	yes	—
486	C₃×C₄	C₂×#711	1	2	yes	—
487	C₂×C₅	—	2	2	no	—
488	C₂×C₅	—	4	4	no	—
489	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
490	C₂×C₅	C₃×#585	1	2	yes	—
491	D₅	—	4	2	no	—
492	C₂³	—	5	2	no	—
493	C₂³	—	10	2	no	—
494	C₂³	—	20	2	no	—
495	C₂³	C₂³×C₃×D₅	1	4	yes	—
496	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
497	Q₈	—	2	4	no	—
498	Q₈	—	20	4	no	—
499	D₄	—	2	8	no	—
500	D₄	—	2	4	no	—
501	D₄	—	4	4	no	—
502	D₄	—	20	8	no	—
503	C₂×C₄	—	2	8	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	5	4	no	—
506	C₂×C₄	—	5	8	no	—
507	C₂×C₄	—	5	2	no	—
508	C₂×C₄	—	10	2	no	—
509	C₂×C₄	—	10	4	no	—
510	C₂×C₄	—	10	4	no	—
511	C₂×C₄	—	20	2	no	—
512	C₂×C₄	—	20	8	no	—
513	C₂×C₄	C₃×#711	1	4	yes	—
514	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
515	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
516	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
517	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
518	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
519	C₂×C₃	—	2	2	no	—
520	C₂×C₃	—	4	4	no	—
521	C₂×C₃	—	20	2	no	—
522	C₂×C₃	C₂²×#711	1	1	yes	characteristic
523	C₂×C₃	#66283	1	2	yes	—
524	C₅	C₃×#3455	1	1	yes	characteristic, complemented, Sylow
525	C₂²	—	2	2	no	—
526	C₂²	—	2	4	no	—
527	C₂²	—	2	8	no	—
528	C₂²	—	10	2	no	—
529	C₂²	—	10	4	no	—
530	C₂²	—	20	4	no	—
531	C₂²	C₂×C₃×#711	1	2	yes	—
532	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
533	C₄	—	2	4	no	—
534	C₄	—	2	2	no	—
535	C₄	—	2	2	no	—
536	C₄	—	10	2	no	—
537	C₄	—	10	4	no	—
538	C₄	—	10	8	no	—
539	C₄	C₂×C₃×#711	1	2	yes	—
540	C₄	C₂×C₃×#711	1	2	yes	—
541	C₃	#10618137	1	1	yes	characteristic, direct product factor, Sylow
542	C₂	—	2	2	no	—
543	C₂	—	4	4	no	—
544	C₂	—	20	2	no	—
545	C₂	C₂²×C₃×#711	1	1	yes	characteristic
546	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×#532	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×#532	D₅
hypocenter	C₅	C₃×#3455
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#532

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#532	C₂	semidirect
2. C₃×#66162	C₂	semidirect
3. C₃×#41×Dic₅	C₂	semidirect
4. C₃×#66065	C₂	semidirect
5. C₃×#66053	C₂	semidirect
6. C₃×#66016	C₂	semidirect
7. C₃×#65951	C₂	semidirect
8. C₃×#65936	C₂	semidirect
9. C₃×#65872	C₂	semidirect
10. C₂×C₃×#4018	C₂	semidirect
11. C₃×#65804	C₂	semidirect
12. #10618137	C₃	direct (N × H)
15. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
16. C₃×C₅×#127	C₂²	semidirect
17. C₃×C₅×#124	C₂²	semidirect
19. C₃×C₄×C₅×D₄	C₂²	semidirect
22. C₃×Q₈×Dic₅	C₂²	semidirect
27. C₃×#4081	C₂²	semidirect
29. C₃×D₄×Dic₅	C₂²	semidirect
33. C₃×#4072	C₂²	semidirect
37. C₂×C₃×C₄×Dic₅	C₂²	semidirect
39. C₃×#4035	C₂²	semidirect
42. C₃×#4025	C₂²	semidirect
43. C₃×#4024	C₂²	semidirect
47. C₃×#4016	C₂²	semidirect
48. C₃×#4015	C₂²	semidirect
49. C₃×C₄×Dic₁₀	C₂²	semidirect
51. C₅×#532	C₂×C₃	semidirect
52. #66162	C₂×C₃	semidirect
53. #41×Dic₅	C₂×C₃	semidirect
54. #66065	C₂×C₃	semidirect
55. #66053	C₂×C₃	semidirect
56. #66016	C₂×C₃	semidirect
57. #65951	C₂×C₃	semidirect
58. #65936	C₂×C₃	semidirect
59. #65872	C₂×C₃	semidirect
60. C₂×#4018	C₂×C₃	semidirect
61. #65804	C₂×C₃	semidirect
107. C₃×#532	D₅	semidirect
114. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
115. C₅×#127	C₂²×C₃	semidirect
116. C₅×#124	C₂²×C₃	semidirect
118. C₄×C₅×D₄	C₂²×C₃	semidirect
121. Q₈×Dic₅	C₂²×C₃	semidirect
126. #4081	C₂²×C₃	semidirect
128. D₄×Dic₅	C₂²×C₃	semidirect
132. #4072	C₂²×C₃	semidirect
136. C₂×C₄×Dic₅	C₂²×C₃	semidirect
138. #4035	C₂²×C₃	semidirect
141. #4025	C₂²×C₃	semidirect
142. #4024	C₂²×C₃	semidirect
146. #4016	C₂²×C₃	semidirect
147. #4015	C₂²×C₃	semidirect
148. C₄×Dic₁₀	C₂²×C₃	semidirect
180. C₃×C₄⋊Q₈	C₂×D₅	semidirect
181. C₃×#127	C₂×D₅	semidirect
187. C₃×#124	C₂×D₅	semidirect
203. C₃×C₄×D₄	C₂×D₅	semidirect
259. #532	C₃×D₅	semidirect
349. C₄⋊Q₈	C₂×C₃×D₅	semidirect
350. #127	C₂×C₃×D₅	semidirect
356. #124	C₂×C₃×D₅	semidirect
372. C₄×D₄	C₂×C₃×D₅	semidirect
470. C₃×C₅	#3455	semidirect
524. C₅	C₃×#3455	semidirect
541. C₃	#10618137	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×#532	2
C₃×#66162	2
C₃×#41×Dic₅	2
C₃×#66065	2
C₃×#66053	2
C₃×#66016	2
C₃×#65951	2
C₃×#65936	2
C₃×#65872	2
C₂×C₃×#4018	2
C₃×#65804	2
#10618137	3
C₃×#3455	5

Subgroups — C3×#10618137 #14481515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10618137 #14481515