Subgroups — C₃×#10614859 #14419593

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic
2	C₃×#65313	C₂	1	2	yes	maximal, complemented
3	C₃×#65300	C₂	1	2	yes	maximal, complemented
4	C₃×#65300	C₂	1	2	yes	maximal, complemented
5	C₃×D₄×#168	C₂	1	2	yes	maximal, complemented
6	C₃×#65289	C₂	1	2	yes	maximal, complemented
7	C₃×#65286	C₂	1	2	yes	maximal, complemented
8	C₃×#65214	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#3935	C₂	1	1	yes	maximal, characteristic, complemented
10	#10614859	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₅×#126	C₄	1	2	yes	—
12	C₃×C₅×#125	C₄	1	1	yes	characteristic
13	C₃×C₅×#124	C₄	1	1	yes	characteristic
14	C₃×C₅×#123	C₄	1	2	yes	—
15	C₃×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
16	C₃×C₅×#121	C₄	1	1	yes	characteristic
17	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
19	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₃×C₅×#117	C₂²	1	2	yes	—
21	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×#681	C₂²	1	2	yes	—
23	C₂²×C₃×#168	C₂²	1	2	yes	—
24	C₂²×C₃×#168	C₂²	1	2	yes	—
25	C₃×C₂²⋊#168	C₂²	1	2	yes	—
26	C₃×C₂²⋊#168	C₂²	1	2	yes	—
27	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic
28	C₃×C₂²⋊#168	C₂²	1	1	yes	characteristic
29	C₃×C₄⋊#168	C₂²	1	2	yes	—
30	C₃×C₄⋊#168	C₂²	1	2	yes	—
31	C₃×C₄⋊#168	C₂²	1	2	yes	—
32	C₃×#3935	C₂²	1	1	yes	characteristic
33	C₃×#3935	C₂²	1	2	yes	—
34	C₃×#3935	C₂²	1	1	yes	characteristic
35	C₃×#3935	C₂²	1	2	yes	—
36	C₃×C₄×#168	C₂²	1	2	yes	—
37	C₃×C₄×#168	C₂²	1	2	yes	—
38	C₃×#2968	—	5	1	no	maximal, Hall
39	C₅×#529	C₂×C₃	1	1	yes	characteristic
40	#65313	C₂×C₃	1	2	yes	complemented
41	#65300	C₂×C₃	1	2	yes	complemented
42	#65300	C₂×C₃	1	2	yes	complemented
43	D₄×#168	C₂×C₃	1	2	yes	complemented
44	#65289	C₂×C₃	1	2	yes	complemented
45	#65286	C₂×C₃	1	2	yes	complemented
46	#65214	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×#3935	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
50	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
55	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
56	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
57	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
61	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
62	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
63	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
64	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
65	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
66	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
67	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
68	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₃×C₄²×C₅	C₂³	1	2	yes	—
70	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₃×#681	—	2	4	no	—
72	C₂×C₃×#168	—	2	4	no	—
73	C₂×C₃×#168	—	2	4	no	—
74	C₂×C₃×#168	C₂³	1	2	yes	—
75	C₂×C₃×#168	C₂³	1	2	yes	—
76	C₂×C₃×#168	C₂³	1	2	yes	—
77	C₂×C₃×#168	C₂³	1	2	yes	—
78	C₃×#529	D₅	1	1	yes	characteristic
79	C₃×#446	—	5	2	no	—
80	C₃×#435	—	5	2	no	—
81	C₃×#435	—	5	2	no	—
82	C₃×C₈×D₄	—	5	2	no	—
83	C₃×#433	—	5	2	no	—
84	C₃×#431	—	5	1	no	—
85	C₃×#405	—	5	2	no	—
86	C₂×C₃×#97	—	5	1	no	—
87	C₅×#126	C₃×C₄	1	2	yes	—
88	C₅×#125	C₃×C₄	1	1	yes	characteristic
89	C₅×#124	C₃×C₄	1	1	yes	characteristic
90	C₅×#123	C₃×C₄	1	2	yes	—
91	C₅×C₂²⋊Q₈	C₃×C₄	1	1	yes	characteristic
92	C₅×#121	C₃×C₄	1	1	yes	characteristic
93	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
94	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
95	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
96	C₅×#117	C₂²×C₃	1	2	yes	—
97	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
98	C₂×#681	C₂²×C₃	1	2	yes	—
99	C₂²×#168	C₂²×C₃	1	2	yes	—
100	C₂²×#168	C₂²×C₃	1	2	yes	—
101	C₂²⋊#168	C₂²×C₃	1	2	yes	—
102	C₂²⋊#168	C₂²×C₃	1	2	yes	—
103	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic
104	C₂²⋊#168	C₂²×C₃	1	1	yes	characteristic
105	C₄⋊#168	C₂²×C₃	1	2	yes	—
106	C₄⋊#168	C₂²×C₃	1	2	yes	—
107	C₄⋊#168	C₂²×C₃	1	2	yes	—
108	#3935	C₂²×C₃	1	1	yes	characteristic
109	#3935	C₂²×C₃	1	2	yes	—
110	#3935	C₂²×C₃	1	1	yes	characteristic
111	#3935	C₂²×C₃	1	2	yes	—
112	C₄×#168	C₂²×C₃	1	2	yes	—
113	C₄×#168	C₂²×C₃	1	2	yes	—
114	#2968	—	5	1	no	Sylow
115	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
116	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₃×C₅×Q₈	—	4	1	no	—
118	C₃×C₅×D₄	—	2	4	no	—
119	C₃×C₅×D₄	—	4	1	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	4	1	no	—
125	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
133	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
134	C₃×#168	—	2	2	no	—
135	C₃×#168	—	2	2	no	—
136	C₃×#168	—	2	2	no	—
137	C₃×#168	#41	1	4	yes	—
138	C₂×C₃×M₁₆	—	5	2	no	—
139	C₂²×C₃×C₈	—	5	2	no	—
140	C₂²×C₃×C₈	—	5	2	no	—
141	C₃×#126	Dic₅	1	2	yes	—
142	C₃×#125	Dic₅	1	1	yes	characteristic
143	C₃×#124	Dic₅	1	1	yes	characteristic
144	C₃×#123	Dic₅	1	2	yes	—
145	C₃×C₂²⋊Q₈	Dic₅	1	1	yes	characteristic
146	C₃×#121	Dic₅	1	1	yes	characteristic
147	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
148	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
149	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
150	C₃×#117	C₂×D₅	1	2	yes	—
151	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
152	C₃×C₄⋊C₈	—	5	2	no	—
153	C₃×C₄⋊C₈	—	5	2	no	—
154	C₃×C₄⋊C₈	—	5	2	no	—
155	C₃×C₂²⋊C₈	—	5	1	no	—
156	C₃×C₂²⋊C₈	—	5	1	no	—
157	C₃×C₂²⋊C₈	—	5	2	no	—
158	C₃×C₂²⋊C₈	—	5	2	no	—
159	C₃×#97	—	5	1	no	—
160	C₃×#97	—	5	1	no	—
161	C₃×#97	—	5	2	no	—
162	C₃×#97	—	5	2	no	—
163	C₃×C₄×C₈	—	5	2	no	—
164	C₃×C₄×C₈	—	5	2	no	—
165	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
166	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
167	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
172	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
173	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
174	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
175	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
176	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
177	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
178	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
179	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
180	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
181	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
182	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
183	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
184	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
185	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
186	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
187	C₄²×C₅	C₂³×C₃	1	2	yes	—
188	#681	—	2	4	no	—
189	C₂×#168	—	2	4	no	—
190	C₂×#168	—	2	4	no	—
191	C₂×#168	C₂³×C₃	1	2	yes	—
192	C₂×#168	C₂³×C₃	1	2	yes	—
193	C₂×#168	C₂³×C₃	1	2	yes	—
194	C₂×#168	C₂³×C₃	1	2	yes	—
195	#529	C₃×D₅	1	1	yes	characteristic
196	#446	—	5	2	no	—
197	#435	—	5	2	no	—
198	#435	—	5	2	no	—
199	C₈×D₄	—	5	2	no	—
200	#433	—	5	2	no	—
201	#431	—	5	1	no	—
202	#405	—	5	2	no	—
203	C₂×#97	—	5	1	no	—
204	C₂²×C₃×C₅	—	2	1	no	—
205	C₂²×C₃×C₅	—	2	1	no	—
206	C₂²×C₃×C₅	—	2	2	no	—
207	C₂²×C₃×C₅	—	2	2	no	—
208	C₂²×C₃×C₅	—	2	2	no	—
209	C₂²×C₃×C₅	#131	1	2	yes	—
210	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
211	C₃×C₄×C₅	—	2	1	no	—
212	C₃×C₄×C₅	—	2	2	no	—
213	C₃×C₄×C₅	—	2	1	no	—
214	C₃×C₄×C₅	—	2	1	no	—
215	C₃×C₄×C₅	—	2	2	no	—
216	C₃×C₄×C₅	—	2	1	no	—
217	C₃×C₄×C₅	—	2	1	no	—
218	C₃×C₄×C₅	—	2	2	no	—
219	C₃×C₄×C₅	C₂×#41	1	2	yes	—
220	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
221	C₂×C₃×D₄	C₂×Dic₅	1	2	yes	—
222	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
227	C₃×M₁₆	—	10	4	no	—
228	C₂×C₃×C₈	—	5	2	no	—
229	C₂×C₃×C₈	—	5	2	no	—
230	C₂×C₃×C₈	—	5	2	no	—
231	C₂×C₃×C₈	—	5	2	no	—
232	C₂×C₃×C₈	—	10	4	no	—
233	C₂×C₃×C₈	—	10	4	no	—
234	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
235	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
236	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
237	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
238	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
239	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
240	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
241	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
242	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
243	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
244	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
245	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
246	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
247	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
248	C₃×C₄²	C₂²×D₅	1	2	yes	—
249	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
250	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
251	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
252	C₅×Q₈	—	4	1	no	—
253	C₅×D₄	—	2	4	no	—
254	C₅×D₄	—	4	1	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	4	1	no	—
260	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
266	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
267	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
268	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
269	#168	—	2	2	no	—
270	#168	—	2	2	no	—
271	#168	—	2	2	no	—
272	#168	C₃×#41	1	4	yes	—
273	C₂×M₁₆	—	5	2	no	—
274	C₂²×C₈	—	5	2	no	—
275	C₂²×C₈	—	5	2	no	—
276	#126	C₃×Dic₅	1	2	yes	—
277	#125	C₃×Dic₅	1	1	yes	characteristic
278	#124	C₃×Dic₅	1	1	yes	characteristic
279	#123	C₃×Dic₅	1	2	yes	—
280	C₂²⋊Q₈	C₃×Dic₅	1	1	yes	characteristic
281	#121	C₃×Dic₅	1	1	yes	characteristic
282	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
283	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
284	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
285	#117	C₂×C₃×D₅	1	2	yes	—
286	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
287	C₄⋊C₈	—	5	2	no	—
288	C₄⋊C₈	—	5	2	no	—
289	C₄⋊C₈	—	5	2	no	—
290	C₂²⋊C₈	—	5	1	no	—
291	C₂²⋊C₈	—	5	1	no	—
292	C₂²⋊C₈	—	5	2	no	—
293	C₂²⋊C₈	—	5	2	no	—
294	#97	—	5	1	no	—
295	#97	—	5	1	no	—
296	#97	—	5	2	no	—
297	#97	—	5	2	no	—
298	C₄×C₈	—	5	2	no	—
299	C₄×C₈	—	5	2	no	—
300	C₂×C₃×C₅	—	2	2	no	—
301	C₂×C₃×C₅	—	4	2	no	—
302	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
303	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
304	C₂×C₃×C₅	#568	1	1	yes	characteristic
305	C₂³×C₃	C₂²×Dic₅	1	2	yes	—
306	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
307	C₃×Q₈	—	4	1	no	—
308	C₃×D₄	—	2	4	no	—
309	C₃×D₄	—	4	1	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	4	1	no	—
315	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
316	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
317	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
318	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
319	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
320	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
321	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
322	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
323	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
324	C₃×C₈	—	5	4	no	—
325	C₃×C₈	—	10	2	no	—
326	C₃×C₈	—	10	2	no	—
327	C₃×C₈	—	10	2	no	—
328	C₂²×C₅	—	2	1	no	—
329	C₂²×C₅	—	2	1	no	—
330	C₂²×C₅	—	2	2	no	—
331	C₂²×C₅	—	2	2	no	—
332	C₂²×C₅	—	2	2	no	—
333	C₂²×C₅	C₃×#131	1	2	yes	—
334	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
335	C₄×C₅	—	2	1	no	—
336	C₄×C₅	—	2	1	no	—
337	C₄×C₅	—	2	2	no	—
338	C₄×C₅	—	2	1	no	—
339	C₄×C₅	—	2	1	no	—
340	C₄×C₅	—	2	2	no	—
341	C₄×C₅	—	2	1	no	—
342	C₄×C₅	—	2	2	no	—
343	C₄×C₅	C₂×C₃×#41	1	2	yes	—
344	C₂×Q₈	C₂×C₃×Dic₅	1	1	yes	characteristic
345	C₂×D₄	C₂×C₃×Dic₅	1	2	yes	—
346	C₂×D₄	C₂×C₃×Dic₅	1	1	yes	characteristic
347	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
348	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
351	M₁₆	—	10	4	no	—
352	C₂×C₈	—	5	2	no	—
353	C₂×C₈	—	5	2	no	—
354	C₂×C₈	—	5	2	no	—
355	C₂×C₈	—	5	2	no	—
356	C₂×C₈	—	10	4	no	—
357	C₂×C₈	—	10	4	no	—
358	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
359	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
360	C₄⋊C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
361	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
362	C₄⋊C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
363	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
364	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
365	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
366	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
367	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
368	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
369	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
370	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
371	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
372	C₄²	C₂²×C₃×D₅	1	2	yes	—
373	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
374	C₃×C₅	#2968	1	1	yes	characteristic, complemented, Hall
375	C₂²×C₃	—	2	1	no	—
376	C₂²×C₃	—	2	1	no	—
377	C₂²×C₃	—	2	2	no	—
378	C₂²×C₃	—	2	2	no	—
379	C₂²×C₃	—	2	2	no	—
380	C₂²×C₃	#4094	1	2	yes	—
381	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
382	C₃×C₄	—	2	1	no	—
383	C₃×C₄	—	2	1	no	—
384	C₃×C₄	—	2	2	no	—
385	C₃×C₄	—	2	1	no	—
386	C₃×C₄	—	2	1	no	—
387	C₃×C₄	—	2	2	no	—
388	C₃×C₄	—	2	1	no	—
389	C₃×C₄	—	2	2	no	—
390	C₃×C₄	D₅×#41	1	2	yes	—
391	C₂×C₅	—	2	2	no	—
392	C₂×C₅	—	4	2	no	—
393	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
394	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
395	C₂×C₅	C₃×#568	1	1	yes	characteristic
396	C₂³	C₂²×C₃×Dic₅	1	2	yes	—
397	C₂³	C₂²×C₃×Dic₅	1	1	yes	characteristic
398	Q₈	—	4	1	no	—
399	D₄	—	2	4	no	—
400	D₄	—	4	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
407	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
408	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
409	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
410	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
411	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
412	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
413	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
414	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
415	C₈	—	5	4	no	—
416	C₈	—	10	2	no	—
417	C₈	—	10	2	no	—
418	C₈	—	10	2	no	—
419	C₂×C₃	—	2	2	no	—
420	C₂×C₃	—	4	2	no	—
421	C₂×C₃	C₂×#4094	1	1	yes	characteristic
422	C₂×C₃	#66153	1	1	yes	characteristic
423	C₂×C₃	#41×Dic₅	1	1	yes	characteristic
424	C₅	C₃×#2968	1	1	yes	characteristic, complemented, Sylow
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	C₃×#4094	1	2	yes	—
431	C₂²	C₂³×C₃×Dic₅	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	2	no	—
440	C₄	C₃×D₅×#41	1	2	yes	—
441	C₃	#10614859	1	1	yes	characteristic, direct product factor, Sylow
442	C₂	—	2	2	no	—
443	C₂	—	4	2	no	—
444	C₂	C₂×C₃×#4094	1	1	yes	characteristic
445	C₂	C₃×#66153	1	1	yes	characteristic
446	C₂	C₃×#41×Dic₅	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×#529	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₃×C₅×#121	C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#529	D₅
hypocenter	C₅	C₃×#2968
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#529

Complements

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

N	H ≅ G/N	type
2. C₃×#65313	C₂	semidirect
3. C₃×#65300	C₂	semidirect
4. C₃×#65300	C₂	semidirect
5. C₃×D₄×#168	C₂	semidirect
6. C₃×#65289	C₂	semidirect
7. C₃×#65286	C₂	semidirect
8. C₃×#65214	C₂	semidirect
9. C₂×C₃×#3935	C₂	semidirect
10. #10614859	C₃	direct (N × H)
40. #65313	C₂×C₃	semidirect
41. #65300	C₂×C₃	semidirect
42. #65300	C₂×C₃	semidirect
43. D₄×#168	C₂×C₃	semidirect
44. #65289	C₂×C₃	semidirect
45. #65286	C₂×C₃	semidirect
46. #65214	C₂×C₃	semidirect
47. C₂×#3935	C₂×C₃	semidirect
374. C₃×C₅	#2968	semidirect
424. C₅	C₃×#2968	semidirect
441. C₃	#10614859	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×#529	2
C₃×#65313	2
C₃×#65300	2
C₃×D₄×#168	2
C₃×#65289	2
C₃×#65286	2
C₃×#65214	2
C₂×C₃×#3935	2
#10614859	3
C₃×#2968	5

Subgroups — C3×#10614859 #14419593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10614859 #14419593