Subgroups — C₃×#10610812 #14413168

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4053	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4047	C₂	1	1	yes	maximal, characteristic
3	C₃×#65856	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#424	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65407	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#3946	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65288	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65128	C₂	1	2	yes	maximal, complemented
9	C₃×#65128	C₂	1	2	yes	maximal, complemented
10	C₃×#65126	C₂	1	2	yes	maximal, complemented
11	C₃×D₅×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
12	#10610812	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#709	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×#117	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×#681	C₂²	1	1	yes	characteristic
19	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
20	C₃×#4053	—	2	4	no	—
21	C₃×#4047	—	2	4	no	—
22	C₂×C₃×#676	C₂²	1	2	yes	—
23	C₂×C₃×#676	C₂²	1	2	yes	—
24	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
25	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
26	C₃×#4039	C₄	1	1	yes	characteristic
27	C₃×#4039	C₄	1	1	yes	characteristic
28	C₃×#4033	C₄	1	1	yes	characteristic
29	C₃×#4033	C₄	1	1	yes	characteristic
30	C₃×#4027	C₄	1	2	yes	—
31	C₃×#4027	C₄	1	2	yes	—
32	C₃×#4018	C₂²	1	2	yes	—
33	C₃×C₄²×D₅	C₂²	1	2	yes	—
34	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
35	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
36	C₃×#3946	C₂²	1	1	yes	characteristic
37	C₃×#3946	C₂²	1	2	yes	—
38	C₃×#3946	C₂²	1	1	yes	characteristic
39	C₃×#3946	C₂²	1	1	yes	characteristic
40	C₃×#3946	C₂²	1	1	yes	characteristic
41	C₃×#3946	C₂²	1	2	yes	—
42	C₃×C₄⋊#168	C₂²	1	2	yes	—
43	C₃×C₄⋊#168	C₂²	1	2	yes	—
44	C₃×#2906	—	5	1	no	maximal, Hall
45	C₂×#4053	C₂×C₃	1	1	yes	characteristic
46	C₂×#4047	C₂×C₃	1	1	yes	characteristic
47	#65856	C₂×C₃	1	1	yes	characteristic
48	C₅×#424	C₂×C₃	1	1	yes	characteristic, complemented
49	#65407	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×#3946	C₂×C₃	1	1	yes	characteristic, complemented
51	#65288	C₂×C₃	1	1	yes	characteristic, complemented
52	#65128	C₂×C₃	1	2	yes	complemented
53	#65128	C₂×C₃	1	2	yes	complemented
54	#65126	C₂×C₃	1	2	yes	complemented
55	D₅×C₄⋊C₈	C₂×C₃	1	2	yes	complemented
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
58	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
60	C₃×#709	D₄	1	4	yes	—
61	C₃×#709	Q₈	1	4	yes	—
62	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
64	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
65	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
66	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
67	C₃×C₅×M₁₆	—	2	2	no	—
68	C₂×C₃×C₅×C₈	—	2	2	no	—
69	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
72	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
73	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
75	C₃×C₄²×C₅	C₂³	1	2	yes	—
76	C₃×#685	C₂×C₄	1	2	yes	—
77	C₃×#685	C₂×C₄	1	2	yes	—
78	C₃×#683	C₂×C₄	1	2	yes	—
79	C₃×#683	C₂×C₄	1	2	yes	—
80	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
81	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
82	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
83	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
84	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
85	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
86	C₃×#681	—	2	2	no	—
87	C₂×C₃×#168	—	2	2	no	—
88	C₂×C₃×#168	C₂³	1	1	yes	characteristic
89	C₂×C₃×#168	C₂³	1	2	yes	—
90	C₂×C₃×#168	C₂³	1	1	yes	characteristic
91	C₃×#676	—	2	4	no	—
92	C₃×#676	—	2	4	no	—
93	C₃×C₈×D₅	—	2	4	no	—
94	C₃×C₈×D₅	—	2	4	no	—
95	C₂×C₃×#131	—	5	1	no	—
96	C₂×C₃×#131	—	5	1	no	—
97	C₃×C₄×#41	—	5	1	no	—
98	C₃×#424	—	5	1	no	—
99	C₃×#424	—	5	2	no	—
100	C₃×#424	—	5	2	no	—
101	C₃×#424	D₅	1	1	yes	characteristic, complemented
102	C₃×#423	—	5	1	no	—
103	C₃×#423	—	5	2	no	—
104	C₂×C₃×C₄⋊C₈	—	5	1	no	—
105	C₂×C₃×C₄⋊C₈	—	5	2	no	—
106	C₂×#709	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
108	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
109	C₅×#117	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
111	C₂×#681	C₂²×C₃	1	1	yes	characteristic
112	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
113	#4053	—	2	4	no	—
114	#4047	—	2	4	no	—
115	C₂×#676	C₂²×C₃	1	2	yes	—
116	C₂×#676	C₂²×C₃	1	2	yes	—
117	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
118	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
119	#4039	C₃×C₄	1	1	yes	characteristic
120	#4039	C₃×C₄	1	1	yes	characteristic
121	#4033	C₃×C₄	1	1	yes	characteristic
122	#4033	C₃×C₄	1	1	yes	characteristic
123	#4027	C₃×C₄	1	2	yes	—
124	#4027	C₃×C₄	1	2	yes	—
125	#4018	C₂²×C₃	1	2	yes	—
126	C₄²×D₅	C₂²×C₃	1	2	yes	—
127	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
128	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
129	#3946	C₂²×C₃	1	1	yes	characteristic
130	#3946	C₂²×C₃	1	2	yes	—
131	#3946	C₂²×C₃	1	1	yes	characteristic
132	#3946	C₂²×C₃	1	1	yes	characteristic
133	#3946	C₂²×C₃	1	1	yes	characteristic
134	#3946	C₂²×C₃	1	2	yes	—
135	C₄⋊#168	C₂²×C₃	1	2	yes	—
136	C₄⋊#168	C₂²×C₃	1	2	yes	—
137	#2906	—	5	1	no	Sylow
138	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
140	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
141	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
144	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
145	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
146	C₃×C₂²⋊D₅	C₄⋊C₄	1	8	yes	—
147	C₂×C₃×Dic₅	—	2	2	no	—
148	C₂×C₃×Dic₅	—	4	1	no	—
149	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
153	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
154	C₃×D₂₀	C₄⋊C₄	1	4	yes	—
155	C₃×C₄×D₅	—	2	4	no	—
156	C₃×C₄×D₅	—	4	2	no	—
157	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
158	C₃×C₄×D₅	C₂×Q₈	1	4	yes	—
159	C₃×Dic₁₀	C₄⋊C₄	1	4	yes	—
160	C₃×C₅×C₈	—	2	1	no	—
161	C₃×C₅×C₈	—	2	2	no	—
162	C₃×C₅×C₈	—	2	1	no	—
163	C₃×#168	—	2	1	no	—
164	C₃×#168	—	2	2	no	—
165	C₃×#168	—	2	1	no	—
166	C₂×C₃×#41	—	5	1	no	—
167	C₃×#131	—	10	4	no	—
168	C₃×#131	—	10	4	no	—
169	C₂×C₃×M₁₆	—	5	1	no	—
170	C₂×C₃×M₁₆	—	5	2	no	—
171	C₂×C₃×M₁₆	—	5	2	no	—
172	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
173	C₂²×C₃×C₈	—	5	1	no	—
174	C₂²×C₃×C₈	—	5	2	no	—
175	C₂²×C₃×C₈	—	5	2	no	—
176	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
177	C₃×C₄×Q₈	—	5	1	no	—
178	C₃×C₄×Q₈	—	5	1	no	—
179	C₃×C₄×D₄	—	5	1	no	—
180	C₃×C₄×D₄	—	5	1	no	—
181	C₃×C₄×D₄	—	5	2	no	—
182	C₃×C₄×D₄	—	5	2	no	—
183	C₃×#117	—	5	2	no	—
184	C₃×#117	C₂×D₅	1	1	yes	characteristic
185	C₂×C₃×C₄²	—	5	1	no	—
186	C₂×C₃×C₄²	—	5	2	no	—
187	C₃×C₄⋊C₈	—	5	1	no	—
188	C₃×C₄⋊C₈	—	5	2	no	—
189	C₃×C₄⋊C₈	—	5	1	no	—
190	C₃×C₄⋊C₈	—	5	1	no	—
191	C₃×C₄⋊C₈	—	5	1	no	—
192	C₃×C₄⋊C₈	—	5	2	no	—
193	C₃×C₄⋊C₈	—	5	2	no	—
194	C₃×C₄⋊C₈	—	5	2	no	—
195	C₃×C₄⋊C₈	C₂×D₅	1	2	yes	—
196	C₃×C₄⋊C₈	C₂×D₅	1	2	yes	—
197	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
198	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
199	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
200	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
201	#709	C₃×D₄	1	4	yes	—
202	#709	C₃×Q₈	1	4	yes	—
203	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
204	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
205	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
206	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
207	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
208	C₅×M₁₆	—	2	2	no	—
209	C₂×C₅×C₈	—	2	2	no	—
210	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
211	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
212	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
213	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
214	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
215	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
216	C₄²×C₅	C₂³×C₃	1	2	yes	—
217	#685	C₂×C₃×C₄	1	2	yes	—
218	#685	C₂×C₃×C₄	1	2	yes	—
219	#683	C₂×C₃×C₄	1	2	yes	—
220	#683	C₂×C₃×C₄	1	2	yes	—
221	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
222	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
223	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
224	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
225	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
226	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
227	#681	—	2	2	no	—
228	C₂×#168	—	2	2	no	—
229	C₂×#168	C₂³×C₃	1	1	yes	characteristic
230	C₂×#168	C₂³×C₃	1	2	yes	—
231	C₂×#168	C₂³×C₃	1	1	yes	characteristic
232	#676	—	2	4	no	—
233	#676	—	2	4	no	—
234	C₈×D₅	—	2	4	no	—
235	C₈×D₅	—	2	4	no	—
236	C₂×#131	—	5	1	no	—
237	C₂×#131	—	5	1	no	—
238	C₄×#41	—	5	1	no	—
239	#424	—	5	1	no	—
240	#424	—	5	2	no	—
241	#424	—	5	2	no	—
242	#424	C₃×D₅	1	1	yes	characteristic, complemented
243	#423	—	5	1	no	—
244	#423	—	5	2	no	—
245	C₂×C₄⋊C₈	—	5	1	no	—
246	C₂×C₄⋊C₈	—	5	2	no	—
247	C₂²×C₃×C₅	—	2	1	no	—
248	C₂²×C₃×C₅	—	2	1	no	—
249	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	2	yes	—
250	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
251	C₂×C₃×D₅	—	2	2	no	—
252	C₂×C₃×D₅	—	2	2	no	—
253	C₂×C₃×D₅	C₂×C₄⋊C₄	1	4	yes	—
254	C₃×C₄×C₅	—	2	2	no	—
255	C₃×C₄×C₅	—	2	2	no	—
256	C₃×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
257	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
258	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
259	C₃×Dic₅	—	2	1	no	—
260	C₃×Dic₅	—	2	1	no	—
261	C₃×Dic₅	—	2	1	no	—
262	C₃×Dic₅	C₂×C₄⋊C₄	1	4	yes	—
263	C₃×Dic₅	#131	1	2	yes	complemented
264	C₃×#41	—	5	4	no	—
265	C₃×#41	—	5	4	no	—
266	C₂×C₃×Q₈	—	5	1	no	—
267	C₂×C₃×D₄	—	5	2	no	—
268	C₂×C₃×D₄	—	5	1	no	—
269	C₂²×C₃×C₄	—	5	2	no	—
270	C₂²×C₃×C₄	—	5	1	no	—
271	C₂²×C₃×C₄	—	5	1	no	—
272	C₂²×C₃×C₄	—	5	2	no	—
273	C₂²×C₃×C₄	—	5	2	no	—
274	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
275	C₃×M₁₆	—	2	2	no	—
276	C₃×M₁₆	—	10	4	no	—
277	C₃×M₁₆	—	10	4	no	—
278	C₃×M₁₆	—	10	2	no	—
279	C₂×C₃×C₈	—	2	2	no	—
280	C₂×C₃×C₈	—	5	1	no	—
281	C₂×C₃×C₈	—	5	2	no	—
282	C₂×C₃×C₈	—	5	1	no	—
283	C₂×C₃×C₈	—	10	4	no	—
284	C₂×C₃×C₈	—	10	4	no	—
285	C₂×C₃×C₈	—	10	2	no	—
286	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
287	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
288	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
289	C₃×C₄⋊C₄	—	5	2	no	—
290	C₃×C₄⋊C₄	—	5	2	no	—
291	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
292	C₃×C₄⋊C₄	C₄×D₅	1	1	yes	characteristic
293	C₃×C₂²⋊C₄	—	5	2	no	—
294	C₃×C₂²⋊C₄	—	5	2	no	—
295	C₃×C₂²⋊C₄	C₄×D₅	1	2	yes	—
296	C₃×C₄²	—	5	2	no	—
297	C₃×C₄²	—	5	1	no	—
298	C₃×C₄²	—	5	2	no	—
299	C₃×C₄²	—	5	1	no	—
300	C₃×C₄²	—	5	1	no	—
301	C₃×C₄²	—	5	1	no	—
302	C₃×C₄²	C₂²×D₅	1	2	yes	—
303	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
304	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
305	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
306	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
307	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
308	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
309	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
310	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
311	C₂²⋊D₅	C₃×C₄⋊C₄	1	8	yes	—
312	C₂×Dic₅	—	2	2	no	—
313	C₂×Dic₅	—	4	1	no	—
314	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
315	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
316	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
317	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
318	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
319	D₂₀	C₃×C₄⋊C₄	1	4	yes	—
320	C₄×D₅	—	2	4	no	—
321	C₄×D₅	—	4	2	no	—
322	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
323	C₄×D₅	C₂×C₃×Q₈	1	4	yes	—
324	Dic₁₀	C₃×C₄⋊C₄	1	4	yes	—
325	C₅×C₈	—	2	1	no	—
326	C₅×C₈	—	2	2	no	—
327	C₅×C₈	—	2	1	no	—
328	#168	—	2	1	no	—
329	#168	—	2	2	no	—
330	#168	—	2	1	no	—
331	C₂×#41	—	5	1	no	—
332	#131	—	10	4	no	—
333	#131	—	10	4	no	—
334	C₂×M₁₆	—	5	1	no	—
335	C₂×M₁₆	—	5	2	no	—
336	C₂×M₁₆	—	5	2	no	—
337	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
338	C₂²×C₈	—	5	1	no	—
339	C₂²×C₈	—	5	2	no	—
340	C₂²×C₈	—	5	2	no	—
341	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
342	C₄×Q₈	—	5	1	no	—
343	C₄×Q₈	—	5	1	no	—
344	C₄×D₄	—	5	1	no	—
345	C₄×D₄	—	5	1	no	—
346	C₄×D₄	—	5	2	no	—
347	C₄×D₄	—	5	2	no	—
348	#117	—	5	2	no	—
349	#117	C₂×C₃×D₅	1	1	yes	characteristic
350	C₂×C₄²	—	5	1	no	—
351	C₂×C₄²	—	5	2	no	—
352	C₄⋊C₈	—	5	1	no	—
353	C₄⋊C₈	—	5	2	no	—
354	C₄⋊C₈	—	5	1	no	—
355	C₄⋊C₈	—	5	1	no	—
356	C₄⋊C₈	—	5	1	no	—
357	C₄⋊C₈	—	5	2	no	—
358	C₄⋊C₈	—	5	2	no	—
359	C₄⋊C₈	—	5	2	no	—
360	C₄⋊C₈	C₂×C₃×D₅	1	2	yes	—
361	C₄⋊C₈	C₂×C₃×D₅	1	2	yes	—
362	C₂×C₃×C₅	—	2	2	no	—
363	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
364	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
365	C₂×C₃×C₅	#568	1	1	yes	characteristic
366	C₃×D₅	—	2	4	no	—
367	C₂³×C₃	—	5	2	no	—
368	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
369	C₃×Q₈	—	5	4	no	—
370	C₃×D₄	—	5	8	no	—
371	C₃×D₄	—	5	4	no	—
372	C₂×C₃×C₄	—	5	1	no	—
373	C₂×C₃×C₄	—	5	2	no	—
374	C₂×C₃×C₄	—	5	4	no	—
375	C₂×C₃×C₄	—	5	4	no	—
376	C₂×C₃×C₄	—	5	1	no	—
377	C₂×C₃×C₄	—	5	1	no	—
378	C₂×C₃×C₄	—	5	1	no	—
379	C₂×C₃×C₄	—	10	4	no	—
380	C₂×C₃×C₄	—	10	2	no	—
381	C₂×C₃×C₄	—	20	2	no	—
382	C₂×C₃×C₄	—	20	1	no	—
383	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
384	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
385	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
386	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
387	C₂×C₃×C₄	Q₈×D₅	1	2	yes	—
388	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
389	C₃×C₈	—	2	1	no	—
390	C₃×C₈	—	2	1	no	—
391	C₃×C₈	—	2	2	no	—
392	C₃×C₈	—	10	1	no	—
393	C₃×C₈	—	10	2	no	—
394	C₃×C₈	—	10	1	no	—
395	C₂²×C₅	—	2	1	no	—
396	C₂²×C₅	—	2	1	no	—
397	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
398	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
399	C₂×D₅	—	2	2	no	—
400	C₂×D₅	—	2	2	no	—
401	C₂×D₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
402	C₄×C₅	—	2	2	no	—
403	C₄×C₅	—	2	2	no	—
404	C₄×C₅	C₂×C₃×C₄⋊C₄	1	2	yes	—
405	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
406	C₄×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
407	Dic₅	—	2	1	no	—
408	Dic₅	—	2	1	no	—
409	Dic₅	—	2	1	no	—
410	Dic₅	C₂×C₃×C₄⋊C₄	1	4	yes	—
411	Dic₅	C₃×#131	1	2	yes	complemented
412	#41	—	5	4	no	—
413	#41	—	5	4	no	—
414	C₂×Q₈	—	5	1	no	—
415	C₂×D₄	—	5	2	no	—
416	C₂×D₄	—	5	1	no	—
417	C₂²×C₄	—	5	2	no	—
418	C₂²×C₄	—	5	1	no	—
419	C₂²×C₄	—	5	1	no	—
420	C₂²×C₄	—	5	2	no	—
421	C₂²×C₄	—	5	2	no	—
422	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
423	M₁₆	—	2	2	no	—
424	M₁₆	—	10	4	no	—
425	M₁₆	—	10	4	no	—
426	M₁₆	—	10	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	5	1	no	—
429	C₂×C₈	—	5	1	no	—
430	C₂×C₈	—	5	2	no	—
431	C₂×C₈	—	10	4	no	—
432	C₂×C₈	—	10	4	no	—
433	C₂×C₈	—	10	2	no	—
434	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
435	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
436	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
437	C₄⋊C₄	—	5	2	no	—
438	C₄⋊C₄	—	5	2	no	—
439	C₄⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
440	C₄⋊C₄	C₃×C₄×D₅	1	1	yes	characteristic
441	C₂²⋊C₄	—	5	2	no	—
442	C₂²⋊C₄	—	5	2	no	—
443	C₂²⋊C₄	C₃×C₄×D₅	1	2	yes	—
444	C₄²	—	5	2	no	—
445	C₄²	—	5	1	no	—
446	C₄²	—	5	2	no	—
447	C₄²	—	5	1	no	—
448	C₄²	—	5	1	no	—
449	C₄²	—	5	1	no	—
450	C₄²	C₂²×C₃×D₅	1	2	yes	—
451	C₃×C₅	#2906	1	1	yes	characteristic, complemented, Hall
452	C₂²×C₃	—	2	1	no	—
453	C₂²×C₃	—	2	1	no	—
454	C₂²×C₃	—	5	4	no	—
455	C₂²×C₃	—	10	2	no	—
456	C₂²×C₃	—	10	2	no	—
457	C₂²×C₃	D₅×C₄⋊C₄	1	2	yes	—
458	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
459	C₃×C₄	—	2	2	no	—
460	C₃×C₄	—	2	2	no	—
461	C₃×C₄	—	5	2	no	—
462	C₃×C₄	—	5	4	no	—
463	C₃×C₄	—	10	1	no	—
464	C₃×C₄	—	10	1	no	—
465	C₃×C₄	—	10	1	no	—
466	C₃×C₄	D₅×C₄⋊C₄	1	2	yes	—
467	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
468	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
469	C₂×C₅	—	2	2	no	—
470	C₂×C₅	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
471	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
472	C₂×C₅	C₃×#568	1	1	yes	characteristic
473	D₅	—	2	4	no	—
474	C₂³	—	5	2	no	—
475	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
476	Q₈	—	5	4	no	—
477	D₄	—	5	8	no	—
478	D₄	—	5	4	no	—
479	C₂×C₄	—	5	1	no	—
480	C₂×C₄	—	5	2	no	—
481	C₂×C₄	—	5	4	no	—
482	C₂×C₄	—	5	4	no	—
483	C₂×C₄	—	5	1	no	—
484	C₂×C₄	—	5	1	no	—
485	C₂×C₄	—	5	1	no	—
486	C₂×C₄	—	10	4	no	—
487	C₂×C₄	—	10	2	no	—
488	C₂×C₄	—	20	2	no	—
489	C₂×C₄	—	20	1	no	—
490	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
491	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
492	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
493	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
494	C₂×C₄	C₃×Q₈×D₅	1	2	yes	—
495	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
496	C₈	—	2	1	no	—
497	C₈	—	2	1	no	—
498	C₈	—	2	2	no	—
499	C₈	—	10	1	no	—
500	C₈	—	10	2	no	—
501	C₈	—	10	1	no	—
502	C₂×C₃	—	2	2	no	—
503	C₂×C₃	—	10	4	no	—
504	C₂×C₃	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic
505	C₂×C₃	D₅×#131	1	1	yes	characteristic
506	C₂×C₃	#66084	1	1	yes	characteristic
507	C₅	C₃×#2906	1	1	yes	characteristic, complemented, Sylow
508	C₂²	—	2	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	5	4	no	—
511	C₂²	—	10	2	no	—
512	C₂²	—	10	2	no	—
513	C₂²	C₃×D₅×C₄⋊C₄	1	2	yes	—
514	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	5	2	no	—
518	C₄	—	5	4	no	—
519	C₄	—	10	1	no	—
520	C₄	—	10	1	no	—
521	C₄	—	10	1	no	—
522	C₄	C₃×D₅×C₄⋊C₄	1	2	yes	—
523	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
524	C₄	C₂×C₃×Q₈×D₅	1	1	yes	characteristic
525	C₃	#10610812	1	1	yes	characteristic, direct product factor, Sylow
526	C₂	—	2	2	no	—
527	C₂	—	10	4	no	—
528	C₂	C₂×C₃×D₅×C₄⋊C₄	1	1	yes	characteristic
529	C₂	C₃×D₅×#131	1	1	yes	characteristic
530	C₂	C₃×#66084	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#424	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₃×#709	C₂²
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#424	D₅
hypocenter	C₅	C₃×#2906
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#424

Complements

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

N	H ≅ G/N	type
4. C₃×C₅×#424	C₂	semidirect
5. C₃×#65407	C₂	semidirect
6. C₂×C₃×#3946	C₂	semidirect
7. C₃×#65288	C₂	semidirect
8. C₃×#65128	C₂	semidirect
9. C₃×#65128	C₂	semidirect
10. C₃×#65126	C₂	semidirect
11. C₃×D₅×C₄⋊C₈	C₂	semidirect
12. #10610812	C₃	direct (N × H)
48. C₅×#424	C₂×C₃	semidirect
49. #65407	C₂×C₃	semidirect
50. C₂×#3946	C₂×C₃	semidirect
51. #65288	C₂×C₃	semidirect
52. #65128	C₂×C₃	semidirect
53. #65128	C₂×C₃	semidirect
54. #65126	C₂×C₃	semidirect
55. D₅×C₄⋊C₈	C₂×C₃	semidirect
101. C₃×#424	D₅	semidirect
242. #424	C₃×D₅	semidirect
263. C₃×Dic₅	#131	semidirect
411. Dic₅	C₃×#131	semidirect
451. C₃×C₅	#2906	semidirect
507. C₅	C₃×#2906	semidirect
525. C₃	#10610812	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×#4053	2
C₂×C₃×#4047	2
C₃×#65856	2
C₃×C₅×#424	2
C₃×#65407	2
C₂×C₃×#3946	2
C₃×#65288	2
C₃×#65128	2
C₃×#65126	2
C₃×D₅×C₄⋊C₈	2
#10610812	3
C₃×#2906	5

Subgroups — C3×#10610812 #14413168

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610812 #14413168