Subgroups — C₃×#10602352 #14300596

Order 1920.

808 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4070	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₂²⋊#168	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×#3942	C₂	1	2	yes	maximal, complemented
5	C₃×#64749	C₂	1	2	yes	maximal, complemented
6	#10602352	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂³×C₃×C₄×C₅	—	2	1	no	—
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
11	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₃×C₂²⋊Dic₅	—	2	1	no	—
14	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
15	C₃×#4070	—	2	2	no	—
16	C₃×#4070	C₄	1	4	yes	complemented
17	C₂×C₃×#683	—	2	1	no	—
18	C₂²×C₃×#168	C₂²	1	2	yes	—
19	C₃×C₂²⋊#168	—	2	2	no	—
20	C₃×#3942	—	2	4	no	—
21	C₃×#1872	—	5	1	no	maximal, Hall
22	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
23	C₂×#4070	C₂×C₃	1	1	yes	characteristic
24	C₂×C₂²⋊#168	C₂×C₃	1	1	yes	characteristic
25	C₂×#3942	C₂×C₃	1	2	yes	complemented
26	#64749	C₂×C₃	1	2	yes	complemented
27	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
28	C₂²×C₃×C₄×C₅	—	2	2	no	—
29	C₂²×C₃×C₄×C₅	—	2	2	no	—
30	C₂²×C₃×C₄×C₅	—	2	4	no	—
31	C₂²×C₃×C₄×C₅	—	2	2	no	—
32	C₂²×C₃×C₄×C₅	—	4	2	no	—
33	C₂²×C₃×C₄×C₅	—	4	2	no	—
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂²×C₃×Dic₅	—	2	1	no	—
39	C₂²×C₃×Dic₅	—	2	1	no	—
40	C₂×C₃×Dic₁₀	—	2	2	no	—
41	C₂×C₃×Dic₁₀	—	2	2	no	—
42	C₂×C₃×Dic₁₀	—	2	1	no	—
43	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	complemented
44	C₃×C₅×C₄⋊C₄	—	2	4	no	—
45	C₃×C₅×C₄⋊C₄	—	2	2	no	—
46	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	—
47	C₃×C₂²⋊Dic₅	—	2	4	no	—
48	C₃×C₄⋊Dic₅	—	2	1	no	—
49	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	complemented
50	C₃×#683	—	2	4	no	—
51	C₂×C₃×#168	—	2	2	no	—
52	C₂×C₃×#168	—	2	2	no	—
53	C₂×C₃×#168	—	2	2	no	—
54	C₂×C₃×C₂²⋊Q₈	—	5	1	no	—
55	C₂²×C₃×C₄⋊C₄	D₅	1	1	yes	characteristic
56	C₂×C₃×#103	—	5	2	no	—
57	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
58	C₃×#340	—	5	2	no	—
59	C₂³×C₄×C₅	—	2	1	no	—
60	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
61	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
62	C₂×C₅×C₄⋊C₄	—	2	1	no	—
63	C₂×C₅×C₄⋊C₄	—	2	4	no	—
64	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
65	C₂×C₂²⋊Dic₅	—	2	1	no	—
66	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
67	#4070	—	2	2	no	—
68	#4070	C₃×C₄	1	4	yes	complemented
69	C₂×#683	—	2	1	no	—
70	C₂²×#168	C₂²×C₃	1	2	yes	—
71	C₂²⋊#168	—	2	2	no	—
72	#3942	—	2	4	no	—
73	#1872	—	5	1	no	Sylow
74	C₂³×C₃×C₅	—	2	1	no	—
75	C₂³×C₃×C₅	—	2	1	no	—
76	C₂³×C₃×C₅	—	2	1	no	—
77	C₂³×C₃×C₅	—	2	1	no	—
78	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
79	C₂³×C₃×C₅	SD₁₆	1	2	yes	—
80	C₂³×C₃×C₅	Q₁₆	1	2	yes	—
81	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
82	C₂×C₃×C₄×C₅	—	2	1	no	—
83	C₂×C₃×C₄×C₅	—	2	1	no	—
84	C₂×C₃×C₄×C₅	—	2	4	no	—
85	C₂×C₃×C₄×C₅	—	2	4	no	—
86	C₂×C₃×C₄×C₅	—	2	4	no	—
87	C₂×C₃×C₄×C₅	—	4	8	no	—
88	C₂×C₃×C₄×C₅	—	4	2	no	—
89	C₂×C₃×C₄×C₅	—	4	2	no	—
90	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
93	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	#41	1	2	yes	—
95	C₂×C₃×Dic₅	—	2	2	no	—
96	C₂×C₃×Dic₅	—	2	2	no	—
97	C₂×C₃×Dic₅	—	4	1	no	—
98	C₂×C₃×Dic₅	—	4	1	no	—
99	C₂×C₃×Dic₅	—	4	1	no	—
100	C₂×C₃×Dic₅	—	4	1	no	—
101	C₃×Dic₁₀	—	2	4	no	—
102	C₃×Dic₁₀	—	4	2	no	—
103	C₃×#168	—	4	2	no	—
104	C₂²×C₃×Q₈	—	5	1	no	—
105	C₂³×C₃×C₄	—	2	1	no	—
106	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
107	C₂²×C₃×C₈	—	5	2	no	—
108	C₃×C₂²⋊Q₈	—	5	4	no	—
109	C₃×C₂²⋊Q₈	—	10	2	no	—
110	C₂×C₃×C₄⋊C₄	—	2	1	no	—
111	C₂×C₃×C₄⋊C₄	—	2	4	no	—
112	C₂×C₃×C₄⋊C₄	—	5	1	no	—
113	C₂×C₃×C₄⋊C₄	—	10	1	no	—
114	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
115	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
116	C₃×#103	—	10	4	no	—
117	C₃×C₂²⋊C₈	—	10	2	no	—
118	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	—	2	2	no	—
121	C₂²×C₄×C₅	—	2	4	no	—
122	C₂²×C₄×C₅	—	2	2	no	—
123	C₂²×C₄×C₅	—	4	2	no	—
124	C₂²×C₄×C₅	—	4	2	no	—
125	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
126	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
127	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
129	C₂²×Dic₅	—	2	1	no	—
130	C₂²×Dic₅	—	2	1	no	—
131	C₂×Dic₁₀	—	2	2	no	—
132	C₂×Dic₁₀	—	2	2	no	—
133	C₂×Dic₁₀	—	2	1	no	—
134	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	complemented
135	C₅×C₄⋊C₄	—	2	4	no	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	—
138	C₂²⋊Dic₅	—	2	4	no	—
139	C₄⋊Dic₅	—	2	1	no	—
140	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	complemented
141	#683	—	2	4	no	—
142	C₂×#168	—	2	2	no	—
143	C₂×#168	—	2	2	no	—
144	C₂×#168	—	2	2	no	—
145	C₂×C₂²⋊Q₈	—	5	1	no	—
146	C₂²×C₄⋊C₄	C₃×D₅	1	1	yes	characteristic
147	C₂×#103	—	5	2	no	—
148	C₂×C₂²⋊C₈	—	5	1	no	—
149	#340	—	5	2	no	—
150	C₂²×C₃×C₅	—	2	2	no	—
151	C₂²×C₃×C₅	—	2	2	no	—
152	C₂²×C₃×C₅	—	2	2	no	—
153	C₂²×C₃×C₅	—	2	2	no	—
154	C₂²×C₃×C₅	—	2	2	no	—
155	C₂²×C₃×C₅	—	2	2	no	—
156	C₂²×C₃×C₅	#103	1	4	yes	complemented
157	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₃×C₅	#120	1	1	yes	characteristic
159	C₂²×C₃×C₅	#123	1	1	yes	characteristic
160	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
161	C₂²×C₃×C₅	C₂×Q₁₆	1	1	yes	characteristic
162	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂²×C₃×C₅	#137	1	1	yes	characteristic
164	C₃×C₄×C₅	—	2	2	no	—
165	C₃×C₄×C₅	—	4	4	no	—
166	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
167	C₃×C₄×C₅	#121	1	2	yes	—
168	C₃×Dic₅	—	4	2	no	—
169	C₃×Dic₅	—	4	2	no	—
170	C₂⁴×C₃	C₂²⋊D₅	1	1	yes	characteristic
171	C₂×C₃×Q₈	—	5	2	no	—
172	C₂×C₃×Q₈	—	10	1	no	—
173	C₂×C₃×Q₈	—	10	2	no	—
174	C₂×C₃×Q₈	—	10	2	no	—
175	C₂²×C₃×C₄	—	2	2	no	—
176	C₂²×C₃×C₄	—	2	2	no	—
177	C₂²×C₃×C₄	—	2	4	no	—
178	C₂²×C₃×C₄	—	2	2	no	—
179	C₂²×C₃×C₄	—	4	2	no	—
180	C₂²×C₃×C₄	—	4	2	no	—
181	C₂²×C₃×C₄	—	10	1	no	—
182	C₂²×C₃×C₄	—	10	1	no	—
183	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
184	C₂²×C₃×C₄	D₂₀	1	2	yes	—
185	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
186	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
187	C₂×C₃×C₈	—	10	2	no	—
188	C₂×C₃×C₈	—	10	2	no	—
189	C₂×C₃×C₈	—	10	2	no	—
190	C₃×C₄⋊C₄	—	2	4	no	—
191	C₃×C₄⋊C₄	—	2	2	no	—
192	C₃×C₄⋊C₄	—	5	2	no	—
193	C₃×C₄⋊C₄	—	10	4	no	—
194	C₃×C₄⋊C₄	—	10	1	no	—
195	C₃×C₄⋊C₄	C₂²⋊D₅	1	4	yes	—
196	C₃×C₂²⋊C₄	—	10	4	no	—
197	C₂³×C₅	—	2	1	no	—
198	C₂³×C₅	—	2	1	no	—
199	C₂³×C₅	—	2	1	no	—
200	C₂³×C₅	—	2	1	no	—
201	C₂³×C₅	C₃×C₂²⋊C₄	1	2	yes	—
202	C₂³×C₅	C₃×SD₁₆	1	2	yes	—
203	C₂³×C₅	C₃×Q₁₆	1	2	yes	—
204	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	4	no	—
208	C₂×C₄×C₅	—	2	4	no	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	—	4	8	no	—
211	C₂×C₄×C₅	—	4	2	no	—
212	C₂×C₄×C₅	—	4	2	no	—
213	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
214	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
216	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
217	C₂×C₄×C₅	C₃×#41	1	2	yes	—
218	C₂×Dic₅	—	2	2	no	—
219	C₂×Dic₅	—	2	2	no	—
220	C₂×Dic₅	—	4	1	no	—
221	C₂×Dic₅	—	4	1	no	—
222	C₂×Dic₅	—	4	1	no	—
223	C₂×Dic₅	—	4	1	no	—
224	Dic₁₀	—	2	4	no	—
225	Dic₁₀	—	4	2	no	—
226	#168	—	4	2	no	—
227	C₂²×Q₈	—	5	1	no	—
228	C₂³×C₄	—	2	1	no	—
229	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
230	C₂²×C₈	—	5	2	no	—
231	C₂²⋊Q₈	—	5	4	no	—
232	C₂²⋊Q₈	—	10	2	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	2	4	no	—
235	C₂×C₄⋊C₄	—	5	1	no	—
236	C₂×C₄⋊C₄	—	10	1	no	—
237	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
238	C₂×C₂²⋊C₄	—	10	1	no	—
239	#103	—	10	4	no	—
240	C₂²⋊C₈	—	10	2	no	—
241	C₂×C₃×C₅	—	2	4	no	—
242	C₂×C₃×C₅	#386	1	1	yes	characteristic
243	C₂×C₃×C₅	C₂×#103	1	1	yes	characteristic
244	C₂×C₃×C₅	#417	1	1	yes	characteristic
245	C₂×C₃×C₅	#450	1	1	yes	characteristic
246	C₂×C₃×C₅	#451	1	1	yes	characteristic
247	C₂×C₃×C₅	#483	1	1	yes	characteristic
248	C₂×C₃×C₅	#484	1	1	yes	characteristic
249	C₂³×C₃	—	2	1	no	—
250	C₂³×C₃	—	2	1	no	—
251	C₂³×C₃	—	2	1	no	—
252	C₂³×C₃	—	2	1	no	—
253	C₂³×C₃	#685	1	2	yes	—
254	C₂³×C₃	#687	1	2	yes	—
255	C₂³×C₃	#689	1	2	yes	—
256	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
257	C₃×Q₈	—	10	4	no	—
258	C₃×Q₈	—	20	2	no	—
259	C₂×C₃×C₄	—	2	1	no	—
260	C₂×C₃×C₄	—	2	1	no	—
261	C₂×C₃×C₄	—	2	4	no	—
262	C₂×C₃×C₄	—	2	4	no	—
263	C₂×C₃×C₄	—	2	4	no	—
264	C₂×C₃×C₄	—	4	8	no	—
265	C₂×C₃×C₄	—	4	2	no	—
266	C₂×C₃×C₄	—	4	2	no	—
267	C₂×C₃×C₄	—	10	2	no	—
268	C₂×C₃×C₄	—	10	2	no	—
269	C₂×C₃×C₄	—	20	1	no	—
270	C₂×C₃×C₄	—	20	1	no	—
271	C₂×C₃×C₄	—	20	1	no	—
272	C₂×C₃×C₄	—	20	1	no	—
273	C₂×C₃×C₄	#685	1	2	yes	—
274	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
276	C₂×C₃×C₄	#709	1	2	yes	—
277	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
278	C₃×C₈	—	20	2	no	—
279	C₂²×C₅	—	2	2	no	—
280	C₂²×C₅	—	2	2	no	—
281	C₂²×C₅	—	2	2	no	—
282	C₂²×C₅	—	2	2	no	—
283	C₂²×C₅	—	2	2	no	—
284	C₂²×C₅	—	2	2	no	—
285	C₂²×C₅	C₃×#103	1	4	yes	complemented
286	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
287	C₂²×C₅	C₃×#120	1	1	yes	characteristic
288	C₂²×C₅	C₃×#123	1	1	yes	characteristic
289	C₂²×C₅	C₂×C₃×SD₁₆	1	1	yes	characteristic
290	C₂²×C₅	C₂×C₃×Q₁₆	1	1	yes	characteristic
291	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
292	C₂²×C₅	C₃×#137	1	1	yes	characteristic
293	C₄×C₅	—	2	2	no	—
294	C₄×C₅	—	4	4	no	—
295	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
296	C₄×C₅	C₃×#121	1	2	yes	—
297	Dic₅	—	4	2	no	—
298	Dic₅	—	4	2	no	—
299	C₂⁴	C₃×C₂²⋊D₅	1	1	yes	characteristic
300	C₂×Q₈	—	5	2	no	—
301	C₂×Q₈	—	10	1	no	—
302	C₂×Q₈	—	10	2	no	—
303	C₂×Q₈	—	10	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	—	10	1	no	—
311	C₂²×C₄	—	10	1	no	—
312	C₂²×C₄	C₃×C₄×D₅	1	2	yes	—
313	C₂²×C₄	C₃×D₂₀	1	2	yes	—
314	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
315	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
316	C₂×C₈	—	10	2	no	—
317	C₂×C₈	—	10	2	no	—
318	C₂×C₈	—	10	2	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	5	2	no	—
322	C₄⋊C₄	—	10	4	no	—
323	C₄⋊C₄	—	10	1	no	—
324	C₄⋊C₄	C₃×C₂²⋊D₅	1	4	yes	—
325	C₂²⋊C₄	—	10	4	no	—
326	C₃×C₅	#1872	1	1	yes	characteristic, complemented, Hall
327	C₂²×C₃	—	2	2	no	—
328	C₂²×C₃	—	2	2	no	—
329	C₂²×C₃	—	2	2	no	—
330	C₂²×C₃	—	2	2	no	—
331	C₂²×C₃	—	2	2	no	—
332	C₂²×C₃	—	2	2	no	—
333	C₂²×C₃	#3942	1	4	yes	complemented
334	C₂²×C₃	C₂×#685	1	1	yes	characteristic
335	C₂²×C₃	#4075	1	1	yes	characteristic
336	C₂²×C₃	#4078	1	1	yes	characteristic
337	C₂²×C₃	C₂×#687	1	1	yes	characteristic
338	C₂²×C₃	#4088	1	1	yes	characteristic
339	C₂²×C₃	C₂×#689	1	1	yes	characteristic
340	C₂²×C₃	#4099	1	1	yes	characteristic
341	C₃×C₄	—	2	2	no	—
342	C₃×C₄	—	4	4	no	—
343	C₃×C₄	—	20	2	no	—
344	C₃×C₄	—	20	2	no	—
345	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
346	C₃×C₄	#4076	1	2	yes	—
347	C₂×C₅	—	2	4	no	—
348	C₂×C₅	C₃×#386	1	1	yes	characteristic
349	C₂×C₅	C₂×C₃×#103	1	1	yes	characteristic
350	C₂×C₅	C₃×#417	1	1	yes	characteristic
351	C₂×C₅	C₃×#450	1	1	yes	characteristic
352	C₂×C₅	C₃×#451	1	1	yes	characteristic
353	C₂×C₅	C₃×#483	1	1	yes	characteristic
354	C₂×C₅	C₃×#484	1	1	yes	characteristic
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	C₃×#685	1	2	yes	—
360	C₂³	C₃×#687	1	2	yes	—
361	C₂³	C₃×#689	1	2	yes	—
362	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
363	Q₈	—	10	4	no	—
364	Q₈	—	20	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	4	8	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	10	2	no	—
374	C₂×C₄	—	10	2	no	—
375	C₂×C₄	—	20	1	no	—
376	C₂×C₄	—	20	1	no	—
377	C₂×C₄	—	20	1	no	—
378	C₂×C₄	—	20	1	no	—
379	C₂×C₄	C₃×#685	1	2	yes	—
380	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
381	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
382	C₂×C₄	C₃×#709	1	2	yes	—
383	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
384	C₈	—	20	2	no	—
385	C₂×C₃	—	2	4	no	—
386	C₂×C₃	#65255	1	1	yes	characteristic
387	C₂×C₃	C₂×#3942	1	1	yes	characteristic
388	C₂×C₃	#65259	1	1	yes	characteristic
389	C₂×C₃	#65260	1	1	yes	characteristic
390	C₂×C₃	#65502	1	1	yes	characteristic
391	C₂×C₃	#65507	1	1	yes	characteristic
392	C₂×C₃	#65517	1	1	yes	characteristic
393	C₅	C₃×#1872	1	1	yes	characteristic, complemented, Sylow
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	2	2	no	—
400	C₂²	C₃×#3942	1	4	yes	complemented
401	C₂²	C₂×C₃×#685	1	1	yes	characteristic
402	C₂²	C₃×#4075	1	1	yes	characteristic
403	C₂²	C₃×#4078	1	1	yes	characteristic
404	C₂²	C₂×C₃×#687	1	1	yes	characteristic
405	C₂²	C₃×#4088	1	1	yes	characteristic
406	C₂²	C₂×C₃×#689	1	1	yes	characteristic
407	C₂²	C₃×#4099	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	4	4	no	—
410	C₄	—	20	2	no	—
411	C₄	—	20	2	no	—
412	C₄	C₃×C₄×C₂²⋊D₅	1	2	yes	—
413	C₄	C₃×#4076	1	2	yes	—
414	C₃	#10602352	1	1	yes	characteristic, direct product factor, Sylow
415	C₂	—	2	4	no	—
416	C₂	C₃×#65255	1	1	yes	characteristic
417	C₂	C₂×C₃×#3942	1	1	yes	characteristic
418	C₂	C₃×#65259	1	1	yes	characteristic
419	C₂	C₃×#65260	1	1	yes	characteristic
420	C₂	C₃×#65502	1	1	yes	characteristic
421	C₂	C₃×#65507	1	1	yes	characteristic
422	C₂	C₃×#65517	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×C₂²⋊D₅
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₂²×C₃×C₅×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂⁴×C₃×C₅	D₄
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₂²×C₃×C₄⋊C₄	D₅
hypocenter	C₅	C₃×#1872
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×C₄ ◁ C₂²×C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. C₂×C₃×#3942	C₂	semidirect
5. C₃×#64749	C₂	semidirect
6. #10602352	C₃	direct (N × H)
16. C₃×#4070	C₄	semidirect
25. C₂×#3942	C₂×C₃	semidirect
26. #64749	C₂×C₃	semidirect
43. C₂×C₃×Dic₁₀	C₂×C₄	semidirect
49. C₃×C₄⋊Dic₅	C₂×C₄	semidirect
68. #4070	C₃×C₄	semidirect
134. C₂×Dic₁₀	C₂×C₃×C₄	semidirect
140. C₄⋊Dic₅	C₂×C₃×C₄	semidirect
156. C₂²×C₃×C₅	#103	semidirect
285. C₂²×C₅	C₃×#103	semidirect
326. C₃×C₅	#1872	semidirect
333. C₂²×C₃	#3942	semidirect
393. C₅	C₃×#1872	semidirect
400. C₂²	C₃×#3942	semidirect
414. C₃	#10602352	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₅×C₄⋊C₄	2
C₂×C₃×#4070	2
C₂×C₃×C₂²⋊#168	2
C₂×C₃×#3942	2
C₃×#64749	2
#10602352	3
C₃×#1872	5

Subgroups — C3×#10602352 #14300596

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10602352 #14300596