Subgroups — C₂×C₃×#65300 #14414691

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂²×C₃×C₅×D₄	C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×C₄×D₄	D₅
hypocenter	C₅	C₂×C₃×#435
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×#681	C₂	semidirect
3. C₂³×C₃×#168	C₂	semidirect
4. C₂×C₃×C₂²⋊#168	C₂	semidirect
5. C₂×C₃×C₂²⋊#168	C₂	semidirect
6. C₃×#65300	C₂	direct (N × H)
7. C₂×C₃×C₄⋊#168	C₂	semidirect
8. C₂×C₃×#3935	C₂	semidirect
9. C₂×#65300	C₃	direct (N × H)
20. C₂×C₃×#681	C₂²	semidirect
26. C₂²×C₃×#168	C₂²	semidirect
27. C₃×C₂²⋊#168	C₂²	semidirect
28. C₃×C₂²⋊#168	C₂²	semidirect
29. C₃×C₄⋊#168	C₂²	semidirect
30. C₃×#3935	C₂²	semidirect
33. C₂²×#681	C₂×C₃	semidirect
34. C₂³×#168	C₂×C₃	semidirect
35. C₂×C₂²⋊#168	C₂×C₃	semidirect
36. C₂×C₂²⋊#168	C₂×C₃	semidirect
37. #65300	C₂×C₃	direct (N × H)
38. C₂×C₄⋊#168	C₂×C₃	semidirect
39. C₂×#3935	C₂×C₃	semidirect
67. C₂×C₃×#168	D₄	semidirect
90. C₂×#681	C₂²×C₃	semidirect
96. C₂²×#168	C₂²×C₃	semidirect
97. C₂²⋊#168	C₂²×C₃	semidirect
98. C₂²⋊#168	C₂²×C₃	semidirect
99. C₄⋊#168	C₂²×C₃	semidirect
100. #3935	C₂²×C₃	semidirect
107. C₂³×C₃×C₅	M₁₆	semidirect
133. C₃×#168	C₂×D₄	semidirect
182. C₂×#168	C₃×D₄	semidirect
204. C₂²×C₃×C₅	C₂×M₁₆	semidirect
251. C₂³×C₅	C₃×M₁₆	semidirect
277. #168	C₂×C₃×D₄	semidirect
301. C₂×C₃×C₅	#435	semidirect
310. C₂³×C₃	#681	semidirect
346. C₂²×C₅	C₂×C₃×M₁₆	semidirect
388. C₃×C₅	C₂×#435	semidirect
397. C₂²×C₃	C₂×#681	semidirect
410. C₂×C₅	C₃×#435	semidirect
419. C₂³	C₃×#681	semidirect
448. C₂×C₃	#65300	direct (N × H)
452. C₅	C₂×C₃×#435	semidirect
461. C₂²	C₂×C₃×#681	semidirect
472. C₃	C₂×#65300	direct (N × H)
475. C₂	C₃×#65300	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×C₄×C₅×D₄	2
C₂²×C₃×#681	2
C₂³×C₃×#168	2
C₂×C₃×C₂²⋊#168	2
C₃×#65300	2
C₂×C₃×C₄⋊#168	2
C₂×C₃×#3935	2
C₂×#65300	3
C₂×C₃×#435	5

Subgroups — C2×C3×#65300 #14414691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65300 #14414691