Subgroups — C₃×#65989 #11755666

Order 960.

584 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#711	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#709	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4085	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#683	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4042	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4040	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×D₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#4034	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#4032	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#4030	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#4029	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#4027	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#4027	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×#4024	C₂	1	1	yes	maximal, characteristic, complemented
16	#65989	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
23	C₂²×C₃×Dic₅	C₂²	1	1	yes	characteristic
24	C₂²×C₃×Dic₅	C₂²	1	1	yes	characteristic
25	C₂²×C₃×Dic₅	C₂²	1	1	yes	characteristic
26	C₃×#711	—	2	4	no	—
27	C₃×#709	—	2	4	no	—
28	C₂×C₃×D₂₀	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
33	C₂×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
34	C₂×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
35	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
37	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
41	C₃×#685	C₂²	1	1	yes	characteristic
42	C₃×#685	C₂²	1	1	yes	characteristic
43	C₃×#685	C₂²	1	1	yes	characteristic
44	C₃×#685	C₂²	1	1	yes	characteristic
45	C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
46	C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
47	C₃×#683	C₂²	1	1	yes	characteristic
48	C₃×#683	C₂²	1	1	yes	characteristic
49	C₃×#683	C₂²	1	1	yes	characteristic
50	C₃×#683	C₂²	1	1	yes	characteristic
51	C₃×#683	C₂²	1	1	yes	characteristic
52	C₃×#683	C₂²	1	1	yes	characteristic
53	C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
54	C₃×#547	—	5	1	no	maximal, Hall
55	C₂×#711	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×#709	C₂×C₃	1	1	yes	characteristic, complemented
57	C₅×#123	C₂×C₃	1	1	yes	characteristic, complemented
58	#4085	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×#683	C₂×C₃	1	1	yes	characteristic, complemented
60	#4042	C₂×C₃	1	1	yes	characteristic, complemented
61	#4040	C₂×C₃	1	1	yes	characteristic, complemented
62	D₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
63	#4034	C₂×C₃	1	1	yes	characteristic, complemented
64	#4032	C₂×C₃	1	1	yes	characteristic, complemented
65	#4030	C₂×C₃	1	1	yes	characteristic, complemented
66	#4029	C₂×C₃	1	1	yes	characteristic, complemented
67	#4027	C₂×C₃	1	1	yes	characteristic, complemented
68	#4027	C₂×C₃	1	1	yes	characteristic, complemented
69	#4024	C₂×C₃	1	1	yes	characteristic, complemented
70	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
71	C₂³×C₃×C₅	C₂³	1	1	yes	characteristic
72	C₂²×C₃×D₅	C₂³	1	1	yes	characteristic
73	C₂²×C₃×D₅	C₂³	1	1	yes	characteristic
74	C₃×C₅×D₄	—	2	2	no	—
75	C₂×C₃×C₄×C₅	—	2	2	no	—
76	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₃×C₂²⋊D₅	—	2	2	no	—
82	C₃×C₂²⋊D₅	—	2	2	no	—
83	C₃×C₂²⋊D₅	—	2	2	no	—
84	C₃×C₂²⋊D₅	D₄	1	4	yes	complemented
85	C₂×C₃×Dic₅	—	2	2	no	—
86	C₂×C₃×Dic₅	—	2	2	no	—
87	C₂×C₃×Dic₅	—	2	2	no	—
88	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
89	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
90	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
91	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
92	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
93	C₂×C₃×Dic₅	C₂³	1	1	yes	characteristic
94	C₃×D₂₀	—	2	2	no	—
95	C₃×C₄×D₅	—	2	2	no	—
96	C₃×C₄×D₅	—	2	2	no	—
97	C₃×C₄×D₅	—	2	2	no	—
98	C₃×C₄×D₅	—	2	2	no	—
99	C₃×Dic₁₀	—	2	2	no	—
100	C₃×Dic₁₀	—	2	2	no	—
101	C₂×C₃×#41	—	5	1	no	—
102	C₂×C₃×#41	—	5	1	no	—
103	C₃×C₄⋊Q₈	—	5	1	no	—
104	C₃×#123	—	5	1	no	—
105	C₃×#123	—	5	1	no	—
106	C₃×#123	—	5	1	no	—
107	C₃×#123	D₅	1	1	yes	characteristic, complemented
108	C₃×C₂²⋊Q₈	—	5	1	no	—
109	C₃×C₂²⋊Q₈	—	5	1	no	—
110	C₃×#121	—	5	1	no	—
111	C₃×#121	—	5	1	no	—
112	C₃×C₄×D₄	—	5	1	no	—
113	C₃×C₄×D₄	—	5	1	no	—
114	C₂×C₃×C₄⋊C₄	—	5	1	no	—
115	C₂×C₃×C₄⋊C₄	—	5	1	no	—
116	C₂×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
118	C₂×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
120	C₂×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
122	C₂²×Dic₅	C₂²×C₃	1	1	yes	characteristic
123	C₂²×Dic₅	C₂²×C₃	1	1	yes	characteristic
124	C₂²×Dic₅	C₂²×C₃	1	1	yes	characteristic
125	#711	—	2	4	no	—
126	#709	—	2	4	no	—
127	C₂×D₂₀	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
130	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
132	C₂×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
133	C₂×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
134	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
135	C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
136	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
137	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
138	C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
139	C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
140	#685	C₂²×C₃	1	1	yes	characteristic
141	#685	C₂²×C₃	1	1	yes	characteristic
142	#685	C₂²×C₃	1	1	yes	characteristic
143	#685	C₂²×C₃	1	1	yes	characteristic
144	C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
145	C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
146	#683	C₂²×C₃	1	1	yes	characteristic
147	#683	C₂²×C₃	1	1	yes	characteristic
148	#683	C₂²×C₃	1	1	yes	characteristic
149	#683	C₂²×C₃	1	1	yes	characteristic
150	#683	C₂²×C₃	1	1	yes	characteristic
151	#683	C₂²×C₃	1	1	yes	characteristic
152	C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
153	#547	—	5	1	no	Sylow
154	C₂²×C₃×C₅	—	2	1	no	—
155	C₂²×C₃×C₅	—	2	1	no	—
156	C₂²×C₃×C₅	—	2	1	no	—
157	C₂²×C₃×C₅	—	2	1	no	—
158	C₂²×C₃×C₅	—	2	1	no	—
159	C₂²×C₃×C₅	C₂×D₄	1	2	yes	—
160	C₂²×C₃×C₅	C₂⁴	1	1	yes	characteristic
161	C₂×C₃×D₅	—	2	1	no	—
162	C₂×C₃×D₅	—	2	1	no	—
163	C₂×C₃×D₅	—	2	1	no	—
164	C₂×C₃×D₅	—	2	1	no	—
165	C₂×C₃×D₅	—	2	1	no	—
166	C₂×C₃×D₅	C₂×D₄	1	2	yes	—
167	C₃×C₄×C₅	—	2	1	no	—
168	C₃×C₄×C₅	—	2	1	no	—
169	C₃×C₄×C₅	—	2	1	no	—
170	C₃×C₄×C₅	—	2	1	no	—
171	C₃×C₄×C₅	—	2	1	no	—
172	C₃×Dic₅	—	2	1	no	—
173	C₃×Dic₅	—	2	1	no	—
174	C₃×Dic₅	—	2	1	no	—
175	C₃×Dic₅	—	2	1	no	—
176	C₃×Dic₅	C₂×D₄	1	2	yes	—
177	C₃×Dic₅	#41	1	2	yes	complemented
178	C₃×#41	—	10	4	no	—
179	C₃×#41	—	10	4	no	—
180	C₂×C₃×Q₈	—	5	1	no	—
181	C₂×C₃×Q₈	—	5	1	no	—
182	C₂×C₃×D₄	—	5	1	no	—
183	C₂×C₃×D₄	—	5	1	no	—
184	C₂×C₃×D₄	—	5	1	no	—
185	C₂×C₃×D₄	—	5	1	no	—
186	C₂×C₃×D₄	—	5	1	no	—
187	C₂×C₃×D₄	C₂×D₅	1	1	yes	characteristic
188	C₂²×C₃×C₄	—	5	1	no	—
189	C₂²×C₃×C₄	—	5	1	no	—
190	C₂²×C₃×C₄	—	5	1	no	—
191	C₂²×C₃×C₄	—	5	1	no	—
192	C₂²×C₃×C₄	—	5	1	no	—
193	C₂²×C₃×C₄	—	5	1	no	—
194	C₂²×C₃×C₄	—	5	1	no	—
195	C₂²×C₃×C₄	C₂×D₅	1	1	yes	characteristic
196	C₃×C₄⋊C₄	—	5	1	no	—
197	C₃×C₄⋊C₄	—	5	1	no	—
198	C₃×C₄⋊C₄	—	5	1	no	—
199	C₃×C₄⋊C₄	—	5	1	no	—
200	C₃×C₄⋊C₄	—	5	1	no	—
201	C₃×C₄⋊C₄	—	5	1	no	—
202	C₃×C₄⋊C₄	—	5	1	no	—
203	C₃×C₄⋊C₄	—	5	1	no	—
204	C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
205	C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
206	C₃×C₂²⋊C₄	—	5	1	no	—
207	C₃×C₂²⋊C₄	—	5	1	no	—
208	C₃×C₂²⋊C₄	—	5	1	no	—
209	C₃×C₂²⋊C₄	—	5	1	no	—
210	C₃×C₂²⋊C₄	—	5	1	no	—
211	C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
212	C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
213	C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
214	C₃×C₄²	—	5	1	no	—
215	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
216	C₂³×C₅	C₂³×C₃	1	1	yes	characteristic
217	C₂²×D₅	C₂³×C₃	1	1	yes	characteristic
218	C₂²×D₅	C₂³×C₃	1	1	yes	characteristic
219	C₅×D₄	—	2	2	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
225	C₂×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
226	C₂²⋊D₅	—	2	2	no	—
227	C₂²⋊D₅	—	2	2	no	—
228	C₂²⋊D₅	—	2	2	no	—
229	C₂²⋊D₅	C₃×D₄	1	4	yes	complemented
230	C₂×Dic₅	—	2	2	no	—
231	C₂×Dic₅	—	2	2	no	—
232	C₂×Dic₅	—	2	2	no	—
233	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
234	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
235	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
236	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
237	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
238	C₂×Dic₅	C₂³×C₃	1	1	yes	characteristic
239	D₂₀	—	2	2	no	—
240	C₄×D₅	—	2	2	no	—
241	C₄×D₅	—	2	2	no	—
242	C₄×D₅	—	2	2	no	—
243	C₄×D₅	—	2	2	no	—
244	Dic₁₀	—	2	2	no	—
245	Dic₁₀	—	2	2	no	—
246	C₂×#41	—	5	1	no	—
247	C₂×#41	—	5	1	no	—
248	C₄⋊Q₈	—	5	1	no	—
249	#123	—	5	1	no	—
250	#123	—	5	1	no	—
251	#123	—	5	1	no	—
252	#123	C₃×D₅	1	1	yes	characteristic, complemented
253	C₂²⋊Q₈	—	5	1	no	—
254	C₂²⋊Q₈	—	5	1	no	—
255	#121	—	5	1	no	—
256	#121	—	5	1	no	—
257	C₄×D₄	—	5	1	no	—
258	C₄×D₄	—	5	1	no	—
259	C₂×C₄⋊C₄	—	5	1	no	—
260	C₂×C₄⋊C₄	—	5	1	no	—
261	C₂×C₃×C₅	—	2	2	no	—
262	C₂×C₃×C₅	—	4	1	no	—
263	C₂×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₃×C₅	C₂×#41	1	1	yes	characteristic
265	C₂×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
266	C₃×D₅	—	2	2	no	—
267	C₃×D₅	—	4	1	no	—
268	C₂³×C₃	—	5	1	no	—
269	C₂³×C₃	—	5	1	no	—
270	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
271	C₂³×C₃	C₂²×D₅	1	1	yes	characteristic
272	C₃×Q₈	—	10	2	no	—
273	C₃×Q₈	—	10	2	no	—
274	C₃×D₄	—	2	2	no	—
275	C₃×D₄	—	5	4	no	—
276	C₃×D₄	—	10	2	no	—
277	C₃×D₄	—	10	2	no	—
278	C₃×D₄	—	10	2	no	—
279	C₃×D₄	—	10	2	no	—
280	C₂×C₃×C₄	—	2	2	no	—
281	C₂×C₃×C₄	—	5	1	no	—
282	C₂×C₃×C₄	—	5	1	no	—
283	C₂×C₃×C₄	—	5	1	no	—
284	C₂×C₃×C₄	—	5	1	no	—
285	C₂×C₃×C₄	—	5	1	no	—
286	C₂×C₃×C₄	—	5	1	no	—
287	C₂×C₃×C₄	—	10	2	no	—
288	C₂×C₃×C₄	—	10	2	no	—
289	C₂×C₃×C₄	—	10	2	no	—
290	C₂×C₃×C₄	—	10	2	no	—
291	C₂×C₃×C₄	—	10	2	no	—
292	C₂×C₃×C₄	—	10	2	no	—
293	C₂×C₃×C₄	—	10	2	no	—
294	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
298	C₂×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
299	C₂²×C₅	—	2	1	no	—
300	C₂²×C₅	—	2	1	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	2	1	no	—
303	C₂²×C₅	—	2	1	no	—
304	C₂²×C₅	C₂×C₃×D₄	1	2	yes	—
305	C₂²×C₅	C₂⁴×C₃	1	1	yes	characteristic
306	C₂×D₅	—	2	1	no	—
307	C₂×D₅	—	2	1	no	—
308	C₂×D₅	—	2	1	no	—
309	C₂×D₅	—	2	1	no	—
310	C₂×D₅	—	2	1	no	—
311	C₂×D₅	C₂×C₃×D₄	1	2	yes	—
312	C₄×C₅	—	2	1	no	—
313	C₄×C₅	—	2	1	no	—
314	C₄×C₅	—	2	1	no	—
315	C₄×C₅	—	2	1	no	—
316	C₄×C₅	—	2	1	no	—
317	Dic₅	—	2	1	no	—
318	Dic₅	—	2	1	no	—
319	Dic₅	—	2	1	no	—
320	Dic₅	—	2	1	no	—
321	Dic₅	C₂×C₃×D₄	1	2	yes	—
322	Dic₅	C₃×#41	1	2	yes	complemented
323	#41	—	10	4	no	—
324	#41	—	10	4	no	—
325	C₂×Q₈	—	5	1	no	—
326	C₂×Q₈	—	5	1	no	—
327	C₂×D₄	—	5	1	no	—
328	C₂×D₄	—	5	1	no	—
329	C₂×D₄	—	5	1	no	—
330	C₂×D₄	—	5	1	no	—
331	C₂×D₄	—	5	1	no	—
332	C₂×D₄	C₂×C₃×D₅	1	1	yes	characteristic
333	C₂²×C₄	—	5	1	no	—
334	C₂²×C₄	—	5	1	no	—
335	C₂²×C₄	—	5	1	no	—
336	C₂²×C₄	—	5	1	no	—
337	C₂²×C₄	—	5	1	no	—
338	C₂²×C₄	—	5	1	no	—
339	C₂²×C₄	—	5	1	no	—
340	C₂²×C₄	C₂×C₃×D₅	1	1	yes	characteristic
341	C₄⋊C₄	—	5	1	no	—
342	C₄⋊C₄	—	5	1	no	—
343	C₄⋊C₄	—	5	1	no	—
344	C₄⋊C₄	—	5	1	no	—
345	C₄⋊C₄	—	5	1	no	—
346	C₄⋊C₄	—	5	1	no	—
347	C₄⋊C₄	—	5	1	no	—
348	C₄⋊C₄	—	5	1	no	—
349	C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
350	C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
351	C₂²⋊C₄	—	5	1	no	—
352	C₂²⋊C₄	—	5	1	no	—
353	C₂²⋊C₄	—	5	1	no	—
354	C₂²⋊C₄	—	5	1	no	—
355	C₂²⋊C₄	—	5	1	no	—
356	C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
357	C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
358	C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
359	C₄²	—	5	1	no	—
360	C₃×C₅	#547	1	1	yes	characteristic, complemented, Hall
361	C₂²×C₃	—	2	1	no	—
362	C₂²×C₃	—	2	1	no	—
363	C₂²×C₃	—	2	1	no	—
364	C₂²×C₃	—	2	1	no	—
365	C₂²×C₃	—	2	1	no	—
366	C₂²×C₃	—	5	2	no	—
367	C₂²×C₃	—	10	1	no	—
368	C₂²×C₃	—	10	1	no	—
369	C₂²×C₃	—	10	1	no	—
370	C₂²×C₃	—	10	1	no	—
371	C₂²×C₃	—	10	1	no	—
372	C₂²×C₃	D₄×D₅	1	2	yes	—
373	C₂²×C₃	C₂³×D₅	1	1	yes	characteristic
374	C₃×C₄	—	2	1	no	—
375	C₃×C₄	—	2	1	no	—
376	C₃×C₄	—	2	1	no	—
377	C₃×C₄	—	2	1	no	—
378	C₃×C₄	—	2	1	no	—
379	C₃×C₄	—	5	2	no	—
380	C₃×C₄	—	5	2	no	—
381	C₃×C₄	—	10	1	no	—
382	C₃×C₄	—	10	1	no	—
383	C₃×C₄	—	10	1	no	—
384	C₃×C₄	—	10	1	no	—
385	C₂×C₅	—	2	2	no	—
386	C₂×C₅	—	4	1	no	—
387	C₂×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
388	C₂×C₅	C₂×C₃×#41	1	1	yes	characteristic
389	C₂×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
390	D₅	—	2	2	no	—
391	D₅	—	4	1	no	—
392	C₂³	—	5	1	no	—
393	C₂³	—	5	1	no	—
394	C₂³	C₂²×C₃×D₅	1	1	yes	characteristic
395	C₂³	C₂²×C₃×D₅	1	1	yes	characteristic
396	Q₈	—	10	2	no	—
397	Q₈	—	10	2	no	—
398	D₄	—	2	2	no	—
399	D₄	—	5	4	no	—
400	D₄	—	10	2	no	—
401	D₄	—	10	2	no	—
402	D₄	—	10	2	no	—
403	D₄	—	10	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	5	1	no	—
406	C₂×C₄	—	5	1	no	—
407	C₂×C₄	—	5	1	no	—
408	C₂×C₄	—	5	1	no	—
409	C₂×C₄	—	5	1	no	—
410	C₂×C₄	—	5	1	no	—
411	C₂×C₄	—	10	2	no	—
412	C₂×C₄	—	10	2	no	—
413	C₂×C₄	—	10	2	no	—
414	C₂×C₄	—	10	2	no	—
415	C₂×C₄	—	10	2	no	—
416	C₂×C₄	—	10	2	no	—
417	C₂×C₄	—	10	2	no	—
418	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
419	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
420	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
421	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
423	C₂×C₃	—	2	2	no	—
424	C₂×C₃	—	4	1	no	—
425	C₂×C₃	—	10	2	no	—
426	C₂×C₃	—	20	1	no	—
427	C₂×C₃	C₂×D₄×D₅	1	1	yes	characteristic
428	C₂×C₃	D₅×#41	1	1	yes	characteristic
429	C₂×C₃	#4150	1	1	yes	characteristic
430	C₅	C₃×#547	1	1	yes	characteristic, complemented, Sylow
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	5	2	no	—
437	C₂²	—	10	1	no	—
438	C₂²	—	10	1	no	—
439	C₂²	—	10	1	no	—
440	C₂²	—	10	1	no	—
441	C₂²	—	10	1	no	—
442	C₂²	C₃×D₄×D₅	1	2	yes	—
443	C₂²	C₂³×C₃×D₅	1	1	yes	characteristic
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	5	2	no	—
450	C₄	—	5	2	no	—
451	C₄	—	10	1	no	—
452	C₄	—	10	1	no	—
453	C₄	—	10	1	no	—
454	C₄	—	10	1	no	—
455	C₃	#65989	1	1	yes	characteristic, direct product factor, Sylow
456	C₂	—	2	2	no	—
457	C₂	—	4	1	no	—
458	C₂	—	10	2	no	—
459	C₂	—	20	1	no	—
460	C₂	C₂×C₃×D₄×D₅	1	1	yes	characteristic
461	C₂	C₃×D₅×#41	1	1	yes	characteristic
462	C₂	C₃×#4150	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₅
Fitting	C₃×C₅×#123	C₂
socle	C₂²×C₃×C₅	C₂⁴
hypercenter	C₃×#123	D₅
hypocenter	C₅	C₃×#547
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#123

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#711	C₂	semidirect
2. C₂×C₃×#709	C₂	semidirect
3. C₃×C₅×#123	C₂	semidirect
4. C₃×#4085	C₂	semidirect
5. C₂×C₃×#683	C₂	semidirect
6. C₃×#4042	C₂	semidirect
7. C₃×#4040	C₂	semidirect
8. C₃×D₅×C₄⋊C₄	C₂	semidirect
9. C₃×#4034	C₂	semidirect
10. C₃×#4032	C₂	semidirect
11. C₃×#4030	C₂	semidirect
12. C₃×#4029	C₂	semidirect
13. C₃×#4027	C₂	semidirect
14. C₃×#4027	C₂	semidirect
15. C₃×#4024	C₂	semidirect
16. #65989	C₃	direct (N × H)
55. C₂×#711	C₂×C₃	semidirect
56. C₂×#709	C₂×C₃	semidirect
57. C₅×#123	C₂×C₃	semidirect
58. #4085	C₂×C₃	semidirect
59. C₂×#683	C₂×C₃	semidirect
60. #4042	C₂×C₃	semidirect
61. #4040	C₂×C₃	semidirect
62. D₅×C₄⋊C₄	C₂×C₃	semidirect
63. #4034	C₂×C₃	semidirect
64. #4032	C₂×C₃	semidirect
65. #4030	C₂×C₃	semidirect
66. #4029	C₂×C₃	semidirect
67. #4027	C₂×C₃	semidirect
68. #4027	C₂×C₃	semidirect
69. #4024	C₂×C₃	semidirect
84. C₃×C₂²⋊D₅	D₄	semidirect
107. C₃×#123	D₅	semidirect
177. C₃×Dic₅	#41	semidirect
229. C₂²⋊D₅	C₃×D₄	semidirect
252. #123	C₃×D₅	semidirect
322. Dic₅	C₃×#41	semidirect
360. C₃×C₅	#547	semidirect
430. C₅	C₃×#547	semidirect
455. C₃	#65989	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×#711	2
C₂×C₃×#709	2
C₃×C₅×#123	2
C₃×#4085	2
C₂×C₃×#683	2
C₃×#4042	2
C₃×#4040	2
C₃×D₅×C₄⋊C₄	2
C₃×#4034	2
C₃×#4032	2
C₃×#4030	2
C₃×#4029	2
C₃×#4027	2
C₃×#4024	2
#65989	3
C₃×#547	5

Subgroups — C3×#65989 #11755666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#65989 #11755666