Subgroups — C₃×#10610178 #14418982

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×#709	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65400	C₂	1	4	yes	maximal, complemented
4	C₃×#65214	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#64977	C₂	1	2	yes	maximal, complemented
6	C₃×C₄×#676	C₂	1	2	yes	maximal, complemented
7	C₃×#64974	C₂	1	2	yes	maximal, complemented
8	C₃×#64968	C₂	1	2	yes	maximal, complemented
9	#10610178	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×#709	C₄	1	1	yes	characteristic
11	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
12	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
13	C₃×C₄×C₂²⋊D₅	C₄	1	2	yes	—
14	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
15	C₃×#4072	C₄	1	1	yes	characteristic
16	C₂×C₃×#676	C₂²	1	4	yes	—
17	C₃×C₄×D₂₀	C₄	1	1	yes	characteristic
18	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
19	C₃×#4018	C₄	1	2	yes	—
20	C₃×C₄²×D₅	C₂²	1	2	yes	—
21	C₃×C₄×Dic₁₀	C₄	1	1	yes	characteristic
22	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
24	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₃×C₂²⋊#168	C₂²	1	2	yes	—
27	C₃×#3952	C₂²	1	4	yes	—
28	C₃×#3947	C₂²	1	4	yes	—
29	C₃×#3946	C₂²	1	4	yes	—
30	C₃×C₄⋊#168	C₂²	1	2	yes	—
31	C₃×C₄×#168	C₂²	1	2	yes	—
32	C₃×#2965	—	5	1	no	maximal, Hall
33	C₄×#709	C₂×C₃	1	1	yes	characteristic
34	C₂×C₄×C₅×C₈	C₂×C₃	1	1	yes	characteristic, complemented
35	#65400	C₂×C₃	1	4	yes	complemented
36	#65214	C₂×C₃	1	1	yes	characteristic, complemented
37	#64977	C₂×C₃	1	2	yes	complemented
38	C₄×#676	C₂×C₃	1	2	yes	complemented
39	#64974	C₂×C₃	1	2	yes	complemented
40	#64968	C₂×C₃	1	2	yes	complemented
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
45	C₃×#709	—	2	4	no	—
46	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
47	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
48	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
49	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
50	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×C₅×C₈	—	2	4	no	—
52	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
53	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
54	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
55	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
56	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
57	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
58	C₃×C₂²⋊Dic₅	C₂×C₄	1	2	yes	—
59	C₃×#685	C₂×C₄	1	2	yes	—
60	C₃×#685	C₂×C₄	1	2	yes	—
61	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
62	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
63	C₃×#683	C₂×C₄	1	2	yes	—
64	C₃×#683	C₂×C₄	1	2	yes	—
65	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
66	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
67	C₃×C₄×Dic₅	C₂³	1	2	yes	—
68	C₂×C₃×#168	C₂³	1	4	yes	—
69	C₃×#676	—	2	8	no	—
70	C₃×C₄×#41	—	5	1	no	—
71	C₃×#446	—	5	2	no	—
72	C₃×#436	—	5	2	no	—
73	C₃×#435	—	5	4	no	—
74	C₃×#431	—	5	1	no	—
75	C₃×#431	—	5	2	no	—
76	C₃×C₄×M₁₆	—	5	2	no	—
77	C₂×C₃×C₄×C₈	D₅	1	1	yes	characteristic, complemented
78	C₂×#709	C₃×C₄	1	1	yes	characteristic
79	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
80	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
81	C₄×C₂²⋊D₅	C₃×C₄	1	2	yes	—
82	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
83	#4072	C₃×C₄	1	1	yes	characteristic
84	C₂×#676	C₂²×C₃	1	4	yes	—
85	C₄×D₂₀	C₃×C₄	1	1	yes	characteristic
86	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
87	#4018	C₃×C₄	1	2	yes	—
88	C₄²×D₅	C₂²×C₃	1	2	yes	—
89	C₄×Dic₁₀	C₃×C₄	1	1	yes	characteristic
90	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
91	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
92	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
93	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
94	C₂²⋊#168	C₂²×C₃	1	2	yes	—
95	#3952	C₂²×C₃	1	4	yes	—
96	#3947	C₂²×C₃	1	4	yes	—
97	#3946	C₂²×C₃	1	4	yes	—
98	C₄⋊#168	C₂²×C₃	1	2	yes	—
99	C₄×#168	C₂²×C₃	1	2	yes	—
100	#2965	—	5	1	no	Sylow
101	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	M₁₆	1	4	yes	complemented
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
112	C₃×C₂²⋊D₅	—	2	4	no	—
113	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
114	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
115	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
116	C₃×D₂₀	—	2	2	no	—
117	C₃×C₄×D₅	—	2	4	no	—
118	C₃×C₄×D₅	—	2	4	no	—
119	C₃×C₄×D₅	—	2	4	no	—
120	C₃×Dic₁₀	—	2	2	no	—
121	C₃×C₅×C₈	—	2	2	no	—
122	C₃×C₅×C₈	#41	1	4	yes	complemented
123	C₃×#168	—	2	4	no	—
124	C₂×C₃×#41	—	5	1	no	—
125	C₂×C₃×M₁₆	—	5	4	no	—
126	C₂²×C₃×C₈	C₂×D₅	1	2	yes	—
127	C₃×C₄×Q₈	—	5	1	no	—
128	C₃×C₄×Q₈	—	5	1	no	—
129	C₃×C₄×D₄	—	5	2	no	—
130	C₃×C₄×D₄	—	5	2	no	—
131	C₃×C₄×D₄	—	5	1	no	—
132	C₃×C₄×D₄	—	5	1	no	—
133	C₃×#117	—	5	1	no	—
134	C₃×#117	—	5	2	no	—
135	C₂×C₃×C₄²	—	5	2	no	—
136	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
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	C₂×D₅	1	2	yes	—
144	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
145	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
146	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
149	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
150	#709	—	2	4	no	—
151	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
152	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
153	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
154	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
155	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
156	C₂×C₅×C₈	—	2	4	no	—
157	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
158	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
159	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
160	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
161	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
162	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
163	C₂²⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
164	#685	C₂×C₃×C₄	1	2	yes	—
165	#685	C₂×C₃×C₄	1	2	yes	—
166	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
167	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
168	#683	C₂×C₃×C₄	1	2	yes	—
169	#683	C₂×C₃×C₄	1	2	yes	—
170	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
171	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
172	C₄×Dic₅	C₂³×C₃	1	2	yes	—
173	C₂×#168	C₂³×C₃	1	4	yes	—
174	#676	—	2	8	no	—
175	C₄×#41	—	5	1	no	—
176	#446	—	5	2	no	—
177	#436	—	5	2	no	—
178	#435	—	5	4	no	—
179	#431	—	5	1	no	—
180	#431	—	5	2	no	—
181	C₄×M₁₆	—	5	2	no	—
182	C₂×C₄×C₈	C₃×D₅	1	1	yes	characteristic, complemented
183	C₂²×C₃×C₅	—	2	1	no	—
184	C₂²×C₃×C₅	—	2	1	no	—
185	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
186	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₃×D₅	—	2	2	no	—
188	C₂×C₃×D₅	—	2	2	no	—
189	C₂×C₃×D₅	—	2	2	no	—
190	C₃×C₄×C₅	—	2	1	no	—
191	C₃×C₄×C₅	—	2	1	no	—
192	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
193	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
194	C₃×C₄×C₅	#131	1	2	yes	—
195	C₃×C₄×C₅	C₂×#41	1	2	yes	—
196	C₃×Dic₅	—	2	2	no	—
197	C₃×Dic₅	—	2	2	no	—
198	C₃×Dic₅	—	2	2	no	—
199	C₃×#41	—	10	4	no	—
200	C₂×C₃×Q₈	—	5	1	no	—
201	C₂×C₃×D₄	—	5	2	no	—
202	C₂×C₃×D₄	—	5	1	no	—
203	C₂²×C₃×C₄	—	5	2	no	—
204	C₂²×C₃×C₄	—	5	2	no	—
205	C₂²×C₃×C₄	—	5	2	no	—
206	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
208	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
209	C₃×M₁₆	—	10	8	no	—
210	C₂×C₃×C₈	—	2	4	no	—
211	C₂×C₃×C₈	—	5	4	no	—
212	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
213	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
214	C₃×C₄⋊C₄	—	5	2	no	—
215	C₃×C₄⋊C₄	—	5	2	no	—
216	C₃×C₄⋊C₄	—	5	1	no	—
217	C₃×C₄⋊C₄	—	5	1	no	—
218	C₃×C₂²⋊C₄	—	5	2	no	—
219	C₃×C₂²⋊C₄	—	5	2	no	—
220	C₃×C₂²⋊C₄	—	5	2	no	—
221	C₃×C₄²	—	5	2	no	—
222	C₃×C₄²	—	5	2	no	—
223	C₃×C₄²	—	5	2	no	—
224	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
225	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
226	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
227	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
228	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
229	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	C₃×M₁₆	1	4	yes	complemented
233	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
239	C₂²⋊D₅	—	2	4	no	—
240	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
241	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
242	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
243	D₂₀	—	2	2	no	—
244	C₄×D₅	—	2	4	no	—
245	C₄×D₅	—	2	4	no	—
246	C₄×D₅	—	2	4	no	—
247	Dic₁₀	—	2	2	no	—
248	C₅×C₈	—	2	2	no	—
249	C₅×C₈	C₃×#41	1	4	yes	complemented
250	#168	—	2	4	no	—
251	C₂×#41	—	5	1	no	—
252	C₂×M₁₆	—	5	4	no	—
253	C₂²×C₈	C₂×C₃×D₅	1	2	yes	—
254	C₄×Q₈	—	5	1	no	—
255	C₄×Q₈	—	5	1	no	—
256	C₄×D₄	—	5	2	no	—
257	C₄×D₄	—	5	2	no	—
258	C₄×D₄	—	5	1	no	—
259	C₄×D₄	—	5	1	no	—
260	#117	—	5	1	no	—
261	#117	—	5	2	no	—
262	C₂×C₄²	—	5	2	no	—
263	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
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	2	no	—
270	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
271	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
272	C₄×C₈	C₂×C₃×D₅	1	2	yes	—
273	C₂×C₃×C₅	—	2	2	no	—
274	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
275	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
277	C₃×D₅	—	4	2	no	—
278	C₂³×C₃	—	5	2	no	—
279	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
280	C₃×Q₈	—	10	2	no	—
281	C₃×D₄	—	10	4	no	—
282	C₃×D₄	—	10	2	no	—
283	C₂×C₃×C₄	—	2	2	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	5	2	no	—
286	C₂×C₃×C₄	—	5	2	no	—
287	C₂×C₃×C₄	—	5	2	no	—
288	C₂×C₃×C₄	—	10	4	no	—
289	C₂×C₃×C₄	—	10	4	no	—
290	C₂×C₃×C₄	—	10	4	no	—
291	C₂×C₃×C₄	#676	1	4	yes	complemented
292	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
295	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
298	C₃×C₈	—	2	2	no	—
299	C₃×C₈	—	10	4	no	—
300	C₃×C₈	#709	1	4	yes	complemented
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	2	1	no	—
303	C₂²×C₅	C₂×C₃×M₁₆	1	2	yes	—
304	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
305	C₂×D₅	—	2	2	no	—
306	C₂×D₅	—	2	2	no	—
307	C₂×D₅	—	2	2	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	C₂×C₃×M₁₆	1	2	yes	—
311	C₄×C₅	C₂×C₃×M₁₆	1	2	yes	—
312	C₄×C₅	C₃×#131	1	2	yes	—
313	C₄×C₅	C₂×C₃×#41	1	2	yes	—
314	Dic₅	—	2	2	no	—
315	Dic₅	—	2	2	no	—
316	Dic₅	—	2	2	no	—
317	#41	—	10	4	no	—
318	C₂×Q₈	—	5	1	no	—
319	C₂×D₄	—	5	2	no	—
320	C₂×D₄	—	5	1	no	—
321	C₂²×C₄	—	5	2	no	—
322	C₂²×C₄	—	5	2	no	—
323	C₂²×C₄	—	5	2	no	—
324	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
325	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
326	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
327	M₁₆	—	10	8	no	—
328	C₂×C₈	—	2	4	no	—
329	C₂×C₈	—	5	4	no	—
330	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
331	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
332	C₄⋊C₄	—	5	2	no	—
333	C₄⋊C₄	—	5	2	no	—
334	C₄⋊C₄	—	5	1	no	—
335	C₄⋊C₄	—	5	1	no	—
336	C₂²⋊C₄	—	5	2	no	—
337	C₂²⋊C₄	—	5	2	no	—
338	C₂²⋊C₄	—	5	2	no	—
339	C₄²	—	5	2	no	—
340	C₄²	—	5	2	no	—
341	C₄²	—	5	2	no	—
342	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
343	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
344	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
345	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
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	—	10	2	no	—
350	C₂²×C₃	—	10	2	no	—
351	C₂²×C₃	—	10	2	no	—
352	C₂²×C₃	C₂×#676	1	2	yes	—
353	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
354	C₃×C₄	—	2	1	no	—
355	C₃×C₄	—	2	1	no	—
356	C₃×C₄	—	10	2	no	—
357	C₃×C₄	—	10	2	no	—
358	C₃×C₄	—	10	2	no	—
359	C₃×C₄	C₂×#676	1	2	yes	—
360	C₃×C₄	C₂×#676	1	2	yes	—
361	C₃×C₄	#4047	1	2	yes	—
362	C₃×C₄	C₂×#709	1	2	yes	—
363	C₂×C₅	—	2	2	no	—
364	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
365	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
366	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
367	D₅	—	4	2	no	—
368	C₂³	—	5	2	no	—
369	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
370	Q₈	—	10	2	no	—
371	D₄	—	10	4	no	—
372	D₄	—	10	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	5	2	no	—
376	C₂×C₄	—	5	2	no	—
377	C₂×C₄	—	5	2	no	—
378	C₂×C₄	—	10	4	no	—
379	C₂×C₄	—	10	4	no	—
380	C₂×C₄	—	10	4	no	—
381	C₂×C₄	C₃×#676	1	4	yes	complemented
382	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
383	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
384	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
385	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
386	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
387	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
388	C₈	—	2	2	no	—
389	C₈	—	10	4	no	—
390	C₈	C₃×#709	1	4	yes	complemented
391	C₂×C₃	—	2	2	no	—
392	C₂×C₃	—	20	2	no	—
393	C₂×C₃	C₄×#709	1	1	yes	characteristic
394	C₂×C₃	C₂²×#676	1	1	yes	characteristic
395	C₂×C₃	C₂×#4047	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	—	10	2	no	—
400	C₂²	—	10	2	no	—
401	C₂²	—	10	2	no	—
402	C₂²	C₂×C₃×#676	1	2	yes	—
403	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	10	2	no	—
407	C₄	—	10	2	no	—
408	C₄	—	10	2	no	—
409	C₄	C₂×C₃×#676	1	2	yes	—
410	C₄	C₂×C₃×#676	1	2	yes	—
411	C₄	C₃×#4047	1	2	yes	—
412	C₄	C₂×C₃×#709	1	2	yes	—
413	C₃	#10610178	1	1	yes	characteristic, direct product factor, Sylow
414	C₂	—	2	2	no	—
415	C₂	—	20	2	no	—
416	C₂	C₃×C₄×#709	1	1	yes	characteristic
417	C₂	C₂²×C₃×#676	1	1	yes	characteristic
418	C₂	C₂×C₃×#4047	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	C₂×C₃×C₄×C₅×C₈	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₃×#709	C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×C₄×C₈	D₅
hypocenter	C₅	C₃×#2965
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄² ◁ C₂×C₃×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄×C₅×C₈	C₂	semidirect
3. C₃×#65400	C₂	semidirect
4. C₃×#65214	C₂	semidirect
5. C₃×#64977	C₂	semidirect
6. C₃×C₄×#676	C₂	semidirect
7. C₃×#64974	C₂	semidirect
8. C₃×#64968	C₂	semidirect
9. #10610178	C₃	direct (N × H)
34. C₂×C₄×C₅×C₈	C₂×C₃	semidirect
35. #65400	C₂×C₃	semidirect
36. #65214	C₂×C₃	semidirect
37. #64977	C₂×C₃	semidirect
38. C₄×#676	C₂×C₃	semidirect
39. #64974	C₂×C₃	semidirect
40. #64968	C₂×C₃	semidirect
77. C₂×C₃×C₄×C₈	D₅	semidirect
105. C₂×C₃×C₄×C₅	M₁₆	semidirect
122. C₃×C₅×C₈	#41	semidirect
182. C₂×C₄×C₈	C₃×D₅	semidirect
232. C₂×C₄×C₅	C₃×M₁₆	semidirect
249. C₅×C₈	C₃×#41	semidirect
291. C₂×C₃×C₄	#676	semidirect
300. C₃×C₈	#709	semidirect
346. C₃×C₅	#2965	semidirect
381. C₂×C₄	C₃×#676	semidirect
390. C₈	C₃×#709	semidirect
396. C₅	C₃×#2965	semidirect
413. C₃	#10610178	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×#709	2
C₂×C₃×C₄×C₅×C₈	2
C₃×#65400	2
C₃×#65214	2
C₃×#64977	2
C₃×C₄×#676	2
C₃×#64974	2
C₃×#64968	2
#10610178	3
C₃×#2965	5

Subgroups — C3×#10610178 #14418982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610178 #14418982