Subgroups — C₃×#10614248 #14418985

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₃×#65313	C₂	1	2	yes	maximal, complemented
3	C₃×#65301	C₂	1	2	yes	maximal, complemented
4	C₃×#65300	C₂	1	4	yes	maximal, complemented
5	C₃×#65214	C₂	1	2	yes	maximal, complemented
6	C₃×#65214	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄×#681	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×C₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
9	#10614248	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×#41	C₄	1	1	yes	characteristic
11	C₃×C₄×C₅×Q₈	C₄	1	1	yes	characteristic
12	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
13	C₃×C₄×C₅×D₄	C₄	1	2	yes	—
14	C₃×C₄×C₅×D₄	C₄	1	1	yes	characteristic
15	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
16	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₃×C₅×#117	C₄	1	2	yes	—
18	C₃×C₅×#117	C₄	1	1	yes	characteristic
19	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
21	C₂×C₃×#681	C₂²	1	4	yes	—
22	C₂²×C₃×#168	C₂²	1	2	yes	—
23	C₃×C₂²⋊#168	C₂²	1	2	yes	—
24	C₃×C₂²⋊#168	C₂²	1	4	yes	—
25	C₃×C₄⋊#168	C₂²	1	4	yes	—
26	C₃×C₄⋊#168	C₂²	1	2	yes	—
27	C₃×#3935	C₂²	1	4	yes	—
28	C₃×C₄×#168	C₂²	1	2	yes	—
29	C₃×C₄×#168	C₂²	1	1	yes	characteristic
30	C₃×C₄×#168	C₂²	1	1	yes	characteristic
31	C₃×C₄×#168	C₂²	1	2	yes	—
32	C₃×#2965	—	5	1	no	maximal, Hall
33	C₄×C₅×#41	C₂×C₃	1	1	yes	characteristic
34	#65313	C₂×C₃	1	2	yes	complemented
35	#65301	C₂×C₃	1	2	yes	complemented
36	#65300	C₂×C₃	1	4	yes	complemented
37	#65214	C₂×C₃	1	1	yes	characteristic, complemented
38	#65214	C₂×C₃	1	2	yes	complemented
39	C₄×#681	C₂×C₃	1	2	yes	complemented
40	C₂×C₄×#168	C₂×C₃	1	1	yes	characteristic, complemented
41	C₃×C₅×#41	—	2	4	no	—
42	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
44	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
52	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
54	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
56	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
57	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
58	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
59	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
60	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
61	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
62	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
63	C₃×C₄²×C₅	C₂³	1	2	yes	—
64	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
65	C₃×#681	—	2	8	no	—
66	C₂×C₃×#168	—	2	4	no	—
67	C₂×C₃×#168	C₂³	1	2	yes	—
68	C₂×C₃×#168	C₂³	1	4	yes	—
69	C₂×C₃×#168	C₂³	1	2	yes	—
70	C₃×C₄×#41	D₅	1	1	yes	characteristic
71	C₃×#446	—	5	2	no	—
72	C₃×#436	—	5	2	no	—
73	C₃×#435	—	5	4	no	—
74	C₃×#431	—	5	2	no	—
75	C₃×#431	—	5	1	no	—
76	C₃×C₄×M₁₆	—	5	2	no	—
77	C₂×C₃×C₄×C₈	—	5	1	no	—
78	C₂×C₅×#41	C₃×C₄	1	1	yes	characteristic
79	C₄×C₅×Q₈	C₃×C₄	1	1	yes	characteristic
80	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
81	C₄×C₅×D₄	C₃×C₄	1	2	yes	—
82	C₄×C₅×D₄	C₃×C₄	1	1	yes	characteristic
83	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
84	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
85	C₅×#117	C₃×C₄	1	2	yes	—
86	C₅×#117	C₃×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
88	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
89	C₂×#681	C₂²×C₃	1	4	yes	—
90	C₂²×#168	C₂²×C₃	1	2	yes	—
91	C₂²⋊#168	C₂²×C₃	1	2	yes	—
92	C₂²⋊#168	C₂²×C₃	1	4	yes	—
93	C₄⋊#168	C₂²×C₃	1	4	yes	—
94	C₄⋊#168	C₂²×C₃	1	2	yes	—
95	#3935	C₂²×C₃	1	4	yes	—
96	C₄×#168	C₂²×C₃	1	2	yes	—
97	C₄×#168	C₂²×C₃	1	1	yes	characteristic
98	C₄×#168	C₂²×C₃	1	1	yes	characteristic
99	C₄×#168	C₂²×C₃	1	2	yes	—
100	#2965	—	5	1	no	Sylow
101	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
102	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₃×C₅×Q₈	—	2	2	no	—
104	C₃×C₅×D₄	—	2	4	no	—
105	C₃×C₅×D₄	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	4	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	4	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	4	no	—
111	C₂×C₃×C₄×C₅	M₁₆	1	4	yes	complemented
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
121	C₃×#168	—	2	2	no	—
122	C₃×#168	—	2	4	no	—
123	C₃×#168	#41	1	4	yes	complemented
124	C₂×C₃×#41	Dic₅	1	1	yes	characteristic
125	C₂×C₃×M₁₆	—	5	4	no	—
126	C₂²×C₃×C₈	—	5	2	no	—
127	C₃×C₄×Q₈	Dic₅	1	1	yes	characteristic
128	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
129	C₃×C₄×D₄	Dic₅	1	2	yes	—
130	C₃×C₄×D₄	Dic₅	1	1	yes	characteristic
131	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
132	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
133	C₃×#117	Dic₅	1	2	yes	—
134	C₃×#117	Dic₅	1	1	yes	characteristic
135	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
136	C₂×C₃×C₄²	C₂×D₅	1	2	yes	—
137	C₃×C₄⋊C₈	—	5	4	no	—
138	C₃×C₄⋊C₈	—	5	2	no	—
139	C₃×C₂²⋊C₈	—	5	2	no	—
140	C₃×C₂²⋊C₈	—	5	4	no	—
141	C₃×#97	—	5	4	no	—
142	C₃×C₄×C₈	—	5	2	no	—
143	C₃×C₄×C₈	—	5	1	no	—
144	C₃×C₄×C₈	—	5	1	no	—
145	C₃×C₄×C₈	—	5	2	no	—
146	C₅×#41	—	2	4	no	—
147	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
148	C₂×C₅×D₄	C₂×C₃×C₄	1	2	yes	—
149	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
151	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
152	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
156	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
157	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
158	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
159	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
160	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
161	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
162	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
163	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
164	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
165	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
166	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
167	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
168	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
169	C₄²×C₅	C₂³×C₃	1	2	yes	—
170	#681	—	2	8	no	—
171	C₂×#168	—	2	4	no	—
172	C₂×#168	C₂³×C₃	1	2	yes	—
173	C₂×#168	C₂³×C₃	1	4	yes	—
174	C₂×#168	C₂³×C₃	1	2	yes	—
175	C₄×#41	C₃×D₅	1	1	yes	characteristic
176	#446	—	5	2	no	—
177	#436	—	5	2	no	—
178	#435	—	5	4	no	—
179	#431	—	5	2	no	—
180	#431	—	5	1	no	—
181	C₄×M₁₆	—	5	2	no	—
182	C₂×C₄×C₈	—	5	1	no	—
183	C₂²×C₃×C₅	—	2	1	no	—
184	C₂²×C₃×C₅	—	2	1	no	—
185	C₂²×C₃×C₅	—	2	2	no	—
186	C₂²×C₃×C₅	—	2	2	no	—
187	C₂²×C₃×C₅	—	2	2	no	—
188	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
189	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
190	C₃×C₄×C₅	—	2	1	no	—
191	C₃×C₄×C₅	—	2	2	no	—
192	C₃×C₄×C₅	—	2	2	no	—
193	C₃×C₄×C₅	—	2	1	no	—
194	C₃×C₄×C₅	—	2	2	no	—
195	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
196	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
197	C₃×C₄×C₅	#131	1	2	yes	—
198	C₃×C₄×C₅	C₂×#41	1	2	yes	—
199	C₃×#41	—	2	4	no	—
200	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
201	C₂×C₃×D₄	C₂×Dic₅	1	2	yes	—
202	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
203	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
204	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
205	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
208	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
209	C₃×M₁₆	—	10	8	no	—
210	C₂×C₃×C₈	—	5	2	no	—
211	C₂×C₃×C₈	—	5	2	no	—
212	C₂×C₃×C₈	—	5	4	no	—
213	C₂×C₃×C₈	—	10	4	no	—
214	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
215	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
216	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
217	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
218	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
219	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
220	C₃×C₂²⋊C₄	C₂×Dic₅	1	2	yes	—
221	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
222	C₃×C₄²	C₂×Dic₅	1	2	yes	—
223	C₃×C₄²	C₂×Dic₅	1	2	yes	—
224	C₃×C₄²	C₂×Dic₅	1	1	yes	characteristic
225	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
226	C₃×C₄²	C₂²×D₅	1	2	yes	—
227	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
228	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
229	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
230	C₅×Q₈	—	2	2	no	—
231	C₅×D₄	—	2	4	no	—
232	C₅×D₄	—	2	2	no	—
233	C₂×C₄×C₅	—	2	4	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	4	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	4	no	—
238	C₂×C₄×C₅	C₃×M₁₆	1	4	yes	complemented
239	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
241	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
243	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
244	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
248	#168	—	2	2	no	—
249	#168	—	2	4	no	—
250	#168	C₃×#41	1	4	yes	complemented
251	C₂×#41	C₃×Dic₅	1	1	yes	characteristic
252	C₂×M₁₆	—	5	4	no	—
253	C₂²×C₈	—	5	2	no	—
254	C₄×Q₈	C₃×Dic₅	1	1	yes	characteristic
255	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
256	C₄×D₄	C₃×Dic₅	1	2	yes	—
257	C₄×D₄	C₃×Dic₅	1	1	yes	characteristic
258	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
259	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
260	#117	C₃×Dic₅	1	2	yes	—
261	#117	C₃×Dic₅	1	1	yes	characteristic
262	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
263	C₂×C₄²	C₂×C₃×D₅	1	2	yes	—
264	C₄⋊C₈	—	5	4	no	—
265	C₄⋊C₈	—	5	2	no	—
266	C₂²⋊C₈	—	5	2	no	—
267	C₂²⋊C₈	—	5	4	no	—
268	#97	—	5	4	no	—
269	C₄×C₈	—	5	1	no	—
270	C₄×C₈	—	5	1	no	—
271	C₄×C₈	—	5	2	no	—
272	C₄×C₈	—	5	2	no	—
273	C₂×C₃×C₅	—	2	2	no	—
274	C₂×C₃×C₅	—	4	2	no	—
275	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
277	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
278	C₂³×C₃	C₂²×Dic₅	1	2	yes	—
279	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
280	C₃×Q₈	—	2	2	no	—
281	C₃×D₄	—	2	4	no	—
282	C₃×D₄	—	2	2	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	2	4	no	—
285	C₂×C₃×C₄	—	2	4	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	2	4	no	—
288	C₂×C₃×C₄	#681	1	4	yes	complemented
289	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
290	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
291	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
293	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
294	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
298	C₃×C₈	—	5	4	no	—
299	C₃×C₈	—	10	2	no	—
300	C₃×C₈	—	10	4	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	2	1	no	—
303	C₂²×C₅	—	2	2	no	—
304	C₂²×C₅	—	2	2	no	—
305	C₂²×C₅	—	2	2	no	—
306	C₂²×C₅	C₂×C₃×M₁₆	1	2	yes	—
307	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
308	C₄×C₅	—	2	2	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	—	2	2	no	—
311	C₄×C₅	—	2	1	no	—
312	C₄×C₅	—	2	2	no	—
313	C₄×C₅	C₂×C₃×M₁₆	1	2	yes	—
314	C₄×C₅	C₂×C₃×M₁₆	1	2	yes	—
315	C₄×C₅	C₃×#131	1	2	yes	—
316	C₄×C₅	C₂×C₃×#41	1	2	yes	—
317	#41	—	2	4	no	—
318	C₂×Q₈	C₂×C₃×Dic₅	1	1	yes	characteristic
319	C₂×D₄	C₂×C₃×Dic₅	1	2	yes	—
320	C₂×D₄	C₂×C₃×Dic₅	1	1	yes	characteristic
321	C₂²×C₄	C₂×C₃×Dic₅	1	2	yes	—
322	C₂²×C₄	C₂×C₃×Dic₅	1	2	yes	—
323	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
324	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
325	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
326	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
327	M₁₆	—	10	8	no	—
328	C₂×C₈	—	5	2	no	—
329	C₂×C₈	—	5	2	no	—
330	C₂×C₈	—	5	4	no	—
331	C₂×C₈	—	10	4	no	—
332	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
333	C₄⋊C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
334	C₄⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
335	C₄⋊C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
336	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
337	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
338	C₂²⋊C₄	C₂×C₃×Dic₅	1	2	yes	—
339	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
340	C₄²	C₂×C₃×Dic₅	1	2	yes	—
341	C₄²	C₂×C₃×Dic₅	1	2	yes	—
342	C₄²	C₂×C₃×Dic₅	1	1	yes	characteristic
343	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
344	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
345	C₄²	C₂²×C₃×D₅	1	2	yes	—
346	C₃×C₅	#2965	1	1	yes	characteristic, complemented, Hall
347	C₂²×C₃	—	2	1	no	—
348	C₂²×C₃	—	2	1	no	—
349	C₂²×C₃	—	2	2	no	—
350	C₂²×C₃	—	2	2	no	—
351	C₂²×C₃	—	2	2	no	—
352	C₂²×C₃	C₂×#681	1	2	yes	—
353	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
354	C₃×C₄	—	2	2	no	—
355	C₃×C₄	—	2	1	no	—
356	C₃×C₄	—	2	2	no	—
357	C₃×C₄	—	2	1	no	—
358	C₃×C₄	—	2	2	no	—
359	C₃×C₄	C₂×#681	1	2	yes	—
360	C₃×C₄	C₂×#681	1	2	yes	—
361	C₃×C₄	#4094	1	2	yes	—
362	C₃×C₄	D₅×#41	1	2	yes	—
363	C₂×C₅	—	2	2	no	—
364	C₂×C₅	—	4	2	no	—
365	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
366	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
367	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
368	C₂³	C₂²×C₃×Dic₅	1	2	yes	—
369	C₂³	C₂²×C₃×Dic₅	1	1	yes	characteristic
370	Q₈	—	2	2	no	—
371	D₄	—	2	4	no	—
372	D₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	C₃×#681	1	4	yes	complemented
379	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
381	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
382	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
383	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
384	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
385	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
386	C₂×C₄	C₂²×C₃×Dic₅	1	1	yes	characteristic
387	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
388	C₈	—	5	4	no	—
389	C₈	—	10	2	no	—
390	C₈	—	10	4	no	—
391	C₂×C₃	—	2	2	no	—
392	C₂×C₃	—	4	2	no	—
393	C₂×C₃	C₂²×#681	1	1	yes	characteristic
394	C₂×C₃	C₂×#4094	1	1	yes	characteristic
395	C₂×C₃	#41×Dic₅	1	1	yes	characteristic
396	C₅	C₃×#2965	1	1	yes	characteristic, complemented, Sylow
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	C₂×C₃×#681	1	2	yes	—
403	C₂²	C₂³×C₃×Dic₅	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	2	no	—
407	C₄	—	2	1	no	—
408	C₄	—	2	2	no	—
409	C₄	C₂×C₃×#681	1	2	yes	—
410	C₄	C₂×C₃×#681	1	2	yes	—
411	C₄	C₃×#4094	1	2	yes	—
412	C₄	C₃×D₅×#41	1	2	yes	—
413	C₃	#10614248	1	1	yes	characteristic, direct product factor, Sylow
414	C₂	—	2	2	no	—
415	C₂	—	4	2	no	—
416	C₂	C₂²×C₃×#681	1	1	yes	characteristic
417	C₂	C₂×C₃×#4094	1	1	yes	characteristic
418	C₂	C₃×#41×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄²	C₂²×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₃×C₅×#41	C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×#41	D₅
hypocenter	C₅	C₃×#2965
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄² ◁ C₃×C₄×#41

Complements

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

N	H ≅ G/N	type
2. C₃×#65313	C₂	semidirect
3. C₃×#65301	C₂	semidirect
4. C₃×#65300	C₂	semidirect
5. C₃×#65214	C₂	semidirect
6. C₃×#65214	C₂	semidirect
7. C₃×C₄×#681	C₂	semidirect
8. C₂×C₃×C₄×#168	C₂	semidirect
9. #10614248	C₃	direct (N × H)
34. #65313	C₂×C₃	semidirect
35. #65301	C₂×C₃	semidirect
36. #65300	C₂×C₃	semidirect
37. #65214	C₂×C₃	semidirect
38. #65214	C₂×C₃	semidirect
39. C₄×#681	C₂×C₃	semidirect
40. C₂×C₄×#168	C₂×C₃	semidirect
111. C₂×C₃×C₄×C₅	M₁₆	semidirect
123. C₃×#168	#41	semidirect
238. C₂×C₄×C₅	C₃×M₁₆	semidirect
250. #168	C₃×#41	semidirect
288. C₂×C₃×C₄	#681	semidirect
346. C₃×C₅	#2965	semidirect
378. C₂×C₄	C₃×#681	semidirect
396. C₅	C₃×#2965	semidirect
413. C₃	#10614248	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×C₄×C₅×#41	2
C₃×#65313	2
C₃×#65301	2
C₃×#65300	2
C₃×#65214	2
C₃×C₄×#681	2
C₂×C₃×C₄×#168	2
#10614248	3
C₃×#2965	5

Subgroups — C3×#10614248 #14418985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10614248 #14418985