Subgroups — C₃×#10614647 #14414918

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#525	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4094	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×C₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65523	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65496	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65300	C₂	1	4	yes	maximal, complemented
7	C₃×D₄×#168	C₂	1	4	yes	maximal, complemented
8	C₃×#65288	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65286	C₂	1	1	yes	maximal, characteristic, complemented
10	#10614647	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₃×C₅×#123	C₄	1	2	yes	—
14	C₃×C₅×C₂²⋊Q₈	C₄	1	2	yes	—
15	C₃×C₅×#121	C₄	1	2	yes	—
16	C₃×C₅×#120	C₄	1	2	yes	—
17	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
18	C₃×C₅×#117	C₂²	1	1	yes	characteristic
19	C₃×#4094	—	2	4	no	—
20	C₂×C₃×#681	C₂²	1	1	yes	characteristic
21	C₂×C₃×#681	C₂²	1	1	yes	characteristic
22	C₂×C₃×#681	C₂²	1	2	yes	complemented
23	C₂²×C₃×#168	—	2	4	no	—
24	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
25	C₂²×C₃×#168	C₂²	1	2	yes	—
26	C₂²×C₃×#168	C₂²	1	2	yes	—
27	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
28	C₂²×C₃×#168	C₂²	1	2	yes	complemented
29	C₃×C₂²⋊#168	C₂²	1	4	yes	—
30	C₃×C₂²⋊#168	C₂²	1	4	yes	complemented
31	C₃×C₄⋊#168	C₂²	1	4	yes	complemented
32	C₃×#3935	C₂²	1	2	yes	complemented
33	C₃×C₄×#168	C₂²	1	2	yes	complemented
34	C₃×#2929	—	5	1	no	maximal, Hall
35	C₅×#525	C₂×C₃	1	1	yes	characteristic
36	C₂×#4094	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂³×#168	C₂×C₃	1	1	yes	characteristic, complemented
38	#65523	C₂×C₃	1	1	yes	characteristic, complemented
39	#65496	C₂×C₃	1	1	yes	characteristic, complemented
40	#65300	C₂×C₃	1	4	yes	complemented
41	D₄×#168	C₂×C₃	1	4	yes	complemented
42	#65288	C₂×C₃	1	1	yes	characteristic, complemented
43	#65286	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
45	C₃×C₅×#41	—	2	2	no	—
46	C₃×C₅×#41	—	2	2	no	—
47	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
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	—	2	2	no	—
52	C₂²×C₃×C₄×C₅	—	2	2	no	—
53	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
60	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
61	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
62	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
63	C₃×C₄²×C₅	C₂³	1	2	yes	—
64	C₃×#681	—	2	2	no	—
65	C₃×#681	—	2	2	no	—
66	C₃×#681	—	2	4	no	—
67	C₂×C₃×#168	—	2	2	no	—
68	C₂×C₃×#168	—	2	4	no	—
69	C₂×C₃×#168	—	2	4	no	—
70	C₂×C₃×#168	—	2	4	no	—
71	C₂×C₃×#168	D₄	1	4	yes	complemented
72	C₂×C₃×#168	C₂³	1	2	yes	—
73	C₂×C₃×#168	C₂³	1	2	yes	—
74	C₂×C₃×#168	C₂³	1	2	yes	—
75	C₂×C₃×#168	C₂³	1	1	yes	characteristic
76	C₂×C₃×#168	C₂³	1	1	yes	characteristic
77	C₂×C₃×#131	—	5	1	no	—
78	C₂³×C₃×C₈	—	5	1	no	—
79	C₃×#525	D₅	1	1	yes	characteristic
80	C₃×#435	—	5	4	no	—
81	C₃×C₈×D₄	—	5	4	no	—
82	C₃×#424	—	5	1	no	—
83	C₃×#408	—	5	1	no	—
84	C₃×#407	—	5	1	no	—
85	C₃×#405	—	5	1	no	—
86	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
87	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
88	C₅×#123	C₃×C₄	1	2	yes	—
89	C₅×C₂²⋊Q₈	C₃×C₄	1	2	yes	—
90	C₅×#121	C₃×C₄	1	2	yes	—
91	C₅×#120	C₃×C₄	1	2	yes	—
92	C₄×C₅×D₄	C₂²×C₃	1	4	yes	—
93	C₅×#117	C₂²×C₃	1	1	yes	characteristic
94	#4094	—	2	4	no	—
95	C₂×#681	C₂²×C₃	1	1	yes	characteristic
96	C₂×#681	C₂²×C₃	1	1	yes	characteristic
97	C₂×#681	C₂²×C₃	1	2	yes	complemented
98	C₂²×#168	—	2	4	no	—
99	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
100	C₂²×#168	C₂²×C₃	1	2	yes	—
101	C₂²×#168	C₂²×C₃	1	2	yes	—
102	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
103	C₂²×#168	C₂²×C₃	1	2	yes	complemented
104	C₂²⋊#168	C₂²×C₃	1	4	yes	—
105	C₂²⋊#168	C₂²×C₃	1	4	yes	complemented
106	C₄⋊#168	C₂²×C₃	1	4	yes	complemented
107	#3935	C₂²×C₃	1	2	yes	complemented
108	C₄×#168	C₂²×C₃	1	2	yes	complemented
109	#2929	—	5	1	no	Sylow
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	—	2	4	no	—
112	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
113	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
114	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
115	C₃×C₅×Q₈	—	2	2	no	—
116	C₃×C₅×D₄	—	2	4	no	—
117	C₃×C₅×D₄	—	2	8	no	—
118	C₃×C₅×D₄	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	4	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	—	2	2	no	—
125	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
126	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	#41	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₃×#168	—	2	2	no	—
133	C₃×#168	—	2	2	no	—
134	C₃×#168	—	2	2	no	—
135	C₃×#168	C₂×D₄	1	2	yes	—
136	C₃×#168	C₂×D₄	1	2	yes	—
137	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
138	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
139	C₃×#131	—	10	4	no	—
140	C₂×C₃×M₁₆	—	5	1	no	—
141	C₂×C₃×M₁₆	—	5	2	no	—
142	C₂×C₃×M₁₆	—	5	1	no	—
143	C₂²×C₃×C₈	—	5	1	no	—
144	C₂²×C₃×C₈	—	5	1	no	—
145	C₂²×C₃×C₈	—	5	2	no	—
146	C₂²×C₃×C₈	—	5	2	no	—
147	C₂²×C₃×C₈	—	5	2	no	—
148	C₂²×C₃×C₈	—	10	4	no	—
149	C₃×#123	Dic₅	1	2	yes	—
150	C₃×C₂²⋊Q₈	Dic₅	1	2	yes	—
151	C₃×#121	Dic₅	1	2	yes	—
152	C₃×#120	Dic₅	1	2	yes	—
153	C₃×C₄×D₄	C₂×D₅	1	4	yes	—
154	C₃×#117	C₂×D₅	1	1	yes	characteristic
155	C₃×C₄⋊C₈	—	5	4	no	—
156	C₃×C₂²⋊C₈	—	5	4	no	—
157	C₃×C₂²⋊C₈	—	5	4	no	—
158	C₃×#97	—	5	2	no	—
159	C₃×C₄×C₈	—	5	2	no	—
160	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
161	C₅×#41	—	2	2	no	—
162	C₅×#41	—	2	2	no	—
163	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
164	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
165	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
166	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	—	2	2	no	—
168	C₂²×C₄×C₅	—	2	2	no	—
169	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
170	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
172	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
173	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
174	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
175	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	—
176	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
177	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
178	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	4	yes	—
179	C₄²×C₅	C₂³×C₃	1	2	yes	—
180	#681	—	2	2	no	—
181	#681	—	2	2	no	—
182	#681	—	2	4	no	—
183	C₂×#168	—	2	2	no	—
184	C₂×#168	—	2	4	no	—
185	C₂×#168	—	2	4	no	—
186	C₂×#168	—	2	4	no	—
187	C₂×#168	C₃×D₄	1	4	yes	complemented
188	C₂×#168	C₂³×C₃	1	2	yes	—
189	C₂×#168	C₂³×C₃	1	2	yes	—
190	C₂×#168	C₂³×C₃	1	2	yes	—
191	C₂×#168	C₂³×C₃	1	1	yes	characteristic
192	C₂×#168	C₂³×C₃	1	1	yes	characteristic
193	C₂×#131	—	5	1	no	—
194	C₂³×C₈	—	5	1	no	—
195	#525	C₃×D₅	1	1	yes	characteristic
196	#435	—	5	4	no	—
197	C₈×D₄	—	5	4	no	—
198	#424	—	5	1	no	—
199	#408	—	5	1	no	—
200	#407	—	5	1	no	—
201	#405	—	5	1	no	—
202	C₂²×C₃×C₅	—	2	8	no	—
203	C₂²×C₃×C₅	—	2	2	no	—
204	C₂²×C₃×C₅	—	2	2	no	—
205	C₂²×C₃×C₅	—	2	2	no	—
206	C₂²×C₃×C₅	—	2	2	no	—
207	C₂²×C₃×C₅	—	2	4	no	—
208	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
209	C₂²×C₃×C₅	#131	1	4	yes	complemented
210	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
211	C₃×C₄×C₅	—	2	2	no	—
212	C₃×C₄×C₅	—	2	2	no	—
213	C₃×C₄×C₅	—	2	4	no	—
214	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
215	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
216	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
217	C₂⁴×C₃	C₂×Dic₅	1	1	yes	characteristic
218	C₃×#41	—	2	2	no	—
219	C₃×#41	—	2	2	no	—
220	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
221	C₂×C₃×D₄	C₂×Dic₅	1	4	yes	—
222	C₂×C₃×D₄	C₂×Dic₅	1	2	yes	—
223	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
224	C₂²×C₃×C₄	—	2	2	no	—
225	C₂²×C₃×C₄	—	2	2	no	—
226	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
227	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
228	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
229	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
230	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
231	C₃×M₁₆	—	10	4	no	—
232	C₃×M₁₆	—	10	2	no	—
233	C₃×M₁₆	—	10	2	no	—
234	C₂×C₃×C₈	—	5	4	no	—
235	C₂×C₃×C₈	—	5	1	no	—
236	C₂×C₃×C₈	—	5	1	no	—
237	C₂×C₃×C₈	—	5	2	no	—
238	C₂×C₃×C₈	—	5	2	no	—
239	C₂×C₃×C₈	—	5	2	no	—
240	C₂×C₃×C₈	—	10	4	no	—
241	C₂×C₃×C₈	—	10	4	no	—
242	C₂×C₃×C₈	—	10	4	no	—
243	C₂×C₃×C₈	—	10	2	no	—
244	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
245	C₃×C₄⋊C₄	C₂×Dic₅	1	4	yes	—
246	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
247	C₃×C₂²⋊C₄	C₂×Dic₅	1	4	yes	—
248	C₃×C₂²⋊C₄	C₂×Dic₅	1	4	yes	—
249	C₃×C₄²	C₂²×D₅	1	2	yes	—
250	C₂³×C₅	—	2	2	no	—
251	C₂³×C₅	—	2	4	no	—
252	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
253	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
254	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
255	C₅×Q₈	—	2	2	no	—
256	C₅×D₄	—	2	4	no	—
257	C₅×D₄	—	2	8	no	—
258	C₅×D₄	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	4	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	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	C₂²×C₃×C₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
270	C₂×C₄×C₅	C₃×#41	1	2	yes	—
271	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
272	#168	—	2	2	no	—
273	#168	—	2	2	no	—
274	#168	—	2	2	no	—
275	#168	C₂×C₃×D₄	1	2	yes	—
276	#168	C₂×C₃×D₄	1	2	yes	—
277	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
278	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
279	#131	—	10	4	no	—
280	C₂×M₁₆	—	5	1	no	—
281	C₂×M₁₆	—	5	2	no	—
282	C₂×M₁₆	—	5	1	no	—
283	C₂²×C₈	—	5	1	no	—
284	C₂²×C₈	—	5	1	no	—
285	C₂²×C₈	—	5	2	no	—
286	C₂²×C₈	—	5	2	no	—
287	C₂²×C₈	—	5	2	no	—
288	C₂²×C₈	—	10	4	no	—
289	#123	C₃×Dic₅	1	2	yes	—
290	C₂²⋊Q₈	C₃×Dic₅	1	2	yes	—
291	#121	C₃×Dic₅	1	2	yes	—
292	#120	C₃×Dic₅	1	2	yes	—
293	C₄×D₄	C₂×C₃×D₅	1	4	yes	—
294	#117	C₂×C₃×D₅	1	1	yes	characteristic
295	C₄⋊C₈	—	5	4	no	—
296	C₂²⋊C₈	—	5	4	no	—
297	C₂²⋊C₈	—	5	4	no	—
298	#97	—	5	2	no	—
299	C₄×C₈	—	5	2	no	—
300	C₂×C₃×C₅	—	2	2	no	—
301	C₂×C₃×C₅	—	2	4	no	—
302	C₂×C₃×C₅	—	4	2	no	—
303	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
304	C₂×C₃×C₅	C₂×#131	1	2	yes	—
305	C₂³×C₃	—	2	2	no	—
306	C₂³×C₃	—	2	4	no	—
307	C₂³×C₃	C₂²×Dic₅	1	2	yes	—
308	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
309	C₂³×C₃	C₂²×Dic₅	1	2	yes	—
310	C₃×Q₈	—	2	2	no	—
311	C₃×D₄	—	2	4	no	—
312	C₃×D₄	—	2	8	no	—
313	C₃×D₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	2	no	—
319	C₂×C₃×C₄	—	2	4	no	—
320	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
321	C₂×C₃×C₄	#711	1	2	yes	—
322	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
323	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
324	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
325	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
327	C₃×C₈	—	5	2	no	—
328	C₃×C₈	—	5	2	no	—
329	C₃×C₈	—	10	2	no	—
330	C₃×C₈	—	10	2	no	—
331	C₃×C₈	—	10	2	no	—
332	C₂²×C₅	—	2	8	no	—
333	C₂²×C₅	—	2	2	no	—
334	C₂²×C₅	—	2	2	no	—
335	C₂²×C₅	—	2	2	no	—
336	C₂²×C₅	—	2	4	no	—
337	C₂²×C₅	—	2	2	no	—
338	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
339	C₂²×C₅	C₃×#131	1	4	yes	complemented
340	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
341	C₄×C₅	—	2	4	no	—
342	C₄×C₅	—	2	2	no	—
343	C₄×C₅	—	2	2	no	—
344	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
345	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
346	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
347	C₂⁴	C₂×C₃×Dic₅	1	1	yes	characteristic
348	#41	—	2	2	no	—
349	#41	—	2	2	no	—
350	C₂×Q₈	C₂×C₃×Dic₅	1	1	yes	characteristic
351	C₂×D₄	C₂×C₃×Dic₅	1	4	yes	—
352	C₂×D₄	C₂×C₃×Dic₅	1	2	yes	—
353	C₂×D₄	C₂×C₃×Dic₅	1	1	yes	characteristic
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	C₂×C₃×Dic₅	1	2	yes	—
357	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
358	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
359	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
360	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
361	M₁₆	—	10	4	no	—
362	M₁₆	—	10	2	no	—
363	M₁₆	—	10	2	no	—
364	C₂×C₈	—	5	4	no	—
365	C₂×C₈	—	5	1	no	—
366	C₂×C₈	—	5	1	no	—
367	C₂×C₈	—	5	2	no	—
368	C₂×C₈	—	5	2	no	—
369	C₂×C₈	—	5	2	no	—
370	C₂×C₈	—	10	4	no	—
371	C₂×C₈	—	10	4	no	—
372	C₂×C₈	—	10	4	no	—
373	C₂×C₈	—	10	2	no	—
374	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
375	C₄⋊C₄	C₂×C₃×Dic₅	1	4	yes	—
376	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
377	C₂²⋊C₄	C₂×C₃×Dic₅	1	4	yes	—
378	C₂²⋊C₄	C₂×C₃×Dic₅	1	4	yes	—
379	C₄²	C₂²×C₃×D₅	1	2	yes	—
380	C₃×C₅	#2929	1	1	yes	characteristic, complemented, Hall
381	C₂²×C₃	—	2	8	no	—
382	C₂²×C₃	—	2	2	no	—
383	C₂²×C₃	—	2	2	no	—
384	C₂²×C₃	—	2	2	no	—
385	C₂²×C₃	—	2	2	no	—
386	C₂²×C₃	—	2	4	no	—
387	C₂²×C₃	D₄×Dic₅	1	2	yes	—
388	C₂²×C₃	#4094	1	4	yes	complemented
389	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
390	C₃×C₄	—	2	2	no	—
391	C₃×C₄	—	2	2	no	—
392	C₃×C₄	—	2	4	no	—
393	C₃×C₄	D₄×Dic₅	1	2	yes	—
394	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
395	C₃×C₄	C₂×#711	1	1	yes	characteristic
396	C₂×C₅	—	2	2	no	—
397	C₂×C₅	—	2	4	no	—
398	C₂×C₅	—	4	2	no	—
399	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
400	C₂×C₅	C₂×C₃×#131	1	2	yes	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	4	no	—
403	C₂³	C₂²×C₃×Dic₅	1	2	yes	—
404	C₂³	C₂²×C₃×Dic₅	1	1	yes	characteristic
405	C₂³	C₂²×C₃×Dic₅	1	2	yes	—
406	Q₈	—	2	2	no	—
407	D₄	—	2	4	no	—
408	D₄	—	2	8	no	—
409	D₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
417	C₂×C₄	C₃×#711	1	2	yes	—
418	C₂×C₄	C₂²×C₃×Dic₅	1	4	yes	—
419	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
420	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
421	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
422	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
423	C₈	—	5	2	no	—
424	C₈	—	5	2	no	—
425	C₈	—	10	2	no	—
426	C₈	—	10	2	no	—
427	C₈	—	10	2	no	—
428	C₂×C₃	—	2	2	no	—
429	C₂×C₃	—	2	4	no	—
430	C₂×C₃	—	4	2	no	—
431	C₂×C₃	C₂×D₄×Dic₅	1	1	yes	characteristic
432	C₂×C₃	C₂×#4094	1	2	yes	—
433	C₅	C₃×#2929	1	1	yes	characteristic, complemented, Sylow
434	C₂²	—	2	8	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	4	no	—
440	C₂²	C₃×D₄×Dic₅	1	2	yes	—
441	C₂²	C₃×#4094	1	4	yes	complemented
442	C₂²	C₂³×C₃×Dic₅	1	1	yes	characteristic
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	4	no	—
446	C₄	C₃×D₄×Dic₅	1	2	yes	—
447	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
448	C₄	C₂×C₃×#711	1	1	yes	characteristic
449	C₃	#10614647	1	1	yes	characteristic, direct product factor, Sylow
450	C₂	—	2	2	no	—
451	C₂	—	2	4	no	—
452	C₂	—	4	2	no	—
453	C₂	C₂×C₃×D₄×Dic₅	1	1	yes	characteristic
454	C₂	C₂×C₃×#4094	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting, prime radical	C₃×C₅×#525	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#525	D₅
hypocenter	C₅	C₃×#2929
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#525

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4094	C₂	semidirect
3. C₂³×C₃×#168	C₂	semidirect
4. C₃×#65523	C₂	semidirect
5. C₃×#65496	C₂	semidirect
6. C₃×#65300	C₂	semidirect
7. C₃×D₄×#168	C₂	semidirect
8. C₃×#65288	C₂	semidirect
9. C₃×#65286	C₂	semidirect
10. #10614647	C₃	direct (N × H)
22. C₂×C₃×#681	C₂²	semidirect
28. C₂²×C₃×#168	C₂²	semidirect
30. C₃×C₂²⋊#168	C₂²	semidirect
31. C₃×C₄⋊#168	C₂²	semidirect
32. C₃×#3935	C₂²	semidirect
33. C₃×C₄×#168	C₂²	semidirect
36. C₂×#4094	C₂×C₃	semidirect
37. C₂³×#168	C₂×C₃	semidirect
38. #65523	C₂×C₃	semidirect
39. #65496	C₂×C₃	semidirect
40. #65300	C₂×C₃	semidirect
41. D₄×#168	C₂×C₃	semidirect
42. #65288	C₂×C₃	semidirect
43. #65286	C₂×C₃	semidirect
71. C₂×C₃×#168	D₄	semidirect
97. C₂×#681	C₂²×C₃	semidirect
103. C₂²×#168	C₂²×C₃	semidirect
105. C₂²⋊#168	C₂²×C₃	semidirect
106. C₄⋊#168	C₂²×C₃	semidirect
107. #3935	C₂²×C₃	semidirect
108. C₄×#168	C₂²×C₃	semidirect
187. C₂×#168	C₃×D₄	semidirect
209. C₂²×C₃×C₅	#131	semidirect
339. C₂²×C₅	C₃×#131	semidirect
380. C₃×C₅	#2929	semidirect
388. C₂²×C₃	#4094	semidirect
433. C₅	C₃×#2929	semidirect
441. C₂²	C₃×#4094	semidirect
449. C₃	#10614647	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×#525	2
C₂×C₃×#4094	2
C₂³×C₃×#168	2
C₃×#65523	2
C₃×#65496	2
C₃×#65300	2
C₃×D₄×#168	2
C₃×#65288	2
C₃×#65286	2
#10614647	3
C₃×#2929	5

Subgroups — C3×#10614647 #14414918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10614647 #14414918