Subgroups — C₃×#10617114 #14418899

Order 1920.

912 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×#65856	C₂	1	1	yes	maximal, characteristic
2	C₃×#65748	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×#170	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65703	C₂	1	2	yes	maximal, complemented
5	C₃×#65702	C₂	1	2	yes	maximal, complemented
6	C₃×#65692	C₂	1	4	yes	maximal, complemented
7	C₃×#65678	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×D₅⋊C₈	C₂	1	2	yes	maximal, complemented
9	#10617114	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×#709	C₄	1	1	yes	characteristic
11	C₂²×C₃×#170	C₂²	1	2	yes	—
12	C₂×C₃×D₅⋊C₈	C₂²	1	4	yes	—
13	C₃×C₅×#117	C₄	1	1	yes	characteristic
14	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
15	C₃×#4039	C₄	1	1	yes	characteristic
16	C₃×#4039	C₂²	1	1	yes	characteristic
17	C₃×#4033	C₄	1	1	yes	characteristic
18	C₃×#4033	C₂²	1	1	yes	characteristic
19	C₃×#4027	C₄	1	2	yes	—
20	C₃×#4027	C₂²	1	2	yes	—
21	C₃×#4018	C₄	1	2	yes	—
22	C₃×C₄²×D₅	C₂²	1	2	yes	—
23	C₃×C₂²⋊#170	C₂²	1	2	yes	—
24	C₃×#4004	C₂²	1	4	yes	—
25	C₃×#4003	C₂²	1	4	yes	—
26	C₃×C₄⋊#170	C₂²	1	2	yes	—
27	C₃×C₄×#170	C₂²	1	1	yes	characteristic
28	C₃×C₄×#170	C₂²	1	2	yes	—
29	C₃×C₄×#170	C₂²	1	4	yes	—
30	C₃×C₄×#170	C₂²	1	1	yes	characteristic
31	C₃×C₄×#170	C₂²	1	2	yes	—
32	C₃×C₈×#41	—	5	1	no	maximal, Hall
33	#65856	C₂×C₃	1	1	yes	characteristic
34	#65748	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×C₄×#170	C₂×C₃	1	1	yes	characteristic, complemented
36	#65703	C₂×C₃	1	2	yes	complemented
37	#65702	C₂×C₃	1	2	yes	complemented
38	#65692	C₂×C₃	1	4	yes	complemented
39	#65678	C₂×C₃	1	2	yes	complemented
40	C₄×D₅⋊C₈	C₂×C₃	1	2	yes	complemented
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
43	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
45	C₃×#709	C₈	1	8	yes	complemented
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×#170	—	2	4	no	—
52	C₂×C₃×#170	C₂³	1	4	yes	—
53	C₂×C₃×#170	C₂³	1	2	yes	—
54	C₂×C₃×#170	C₂³	1	2	yes	—
55	C₃×D₅⋊C₈	—	2	8	no	—
56	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
59	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
60	C₃×#685	C₂×C₄	1	2	yes	—
61	C₃×#685	C₂×C₄	1	2	yes	—
62	C₃×#683	C₂×C₄	1	2	yes	—
63	C₃×#683	C₂×C₄	1	2	yes	—
64	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
65	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
66	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
67	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
68	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
69	C₃×C₄×Dic₅	C₂³	1	2	yes	—
70	C₃×C₄×#41	—	5	1	no	—
71	C₃×C₈×Q₈	—	5	2	no	—
72	C₃×C₈×D₄	—	5	4	no	—
73	C₃×C₈×D₄	—	5	2	no	—
74	C₃×#431	—	5	2	no	—
75	C₃×#431	—	5	1	no	—
76	C₂×C₃×C₄×C₈	—	5	2	no	—
77	C₂×C₃×C₄×C₈	—	5	1	no	—
78	C₂×#709	C₃×C₄	1	1	yes	characteristic
79	C₂²×#170	C₂²×C₃	1	2	yes	—
80	C₂×D₅⋊C₈	C₂²×C₃	1	4	yes	—
81	C₅×#117	C₃×C₄	1	1	yes	characteristic
82	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
83	#4039	C₃×C₄	1	1	yes	characteristic
84	#4039	C₂²×C₃	1	1	yes	characteristic
85	#4033	C₃×C₄	1	1	yes	characteristic
86	#4033	C₂²×C₃	1	1	yes	characteristic
87	#4027	C₃×C₄	1	2	yes	—
88	#4027	C₂²×C₃	1	2	yes	—
89	#4018	C₃×C₄	1	2	yes	—
90	C₄²×D₅	C₂²×C₃	1	2	yes	—
91	C₂²⋊#170	C₂²×C₃	1	2	yes	—
92	#4004	C₂²×C₃	1	4	yes	—
93	#4003	C₂²×C₃	1	4	yes	—
94	C₄⋊#170	C₂²×C₃	1	2	yes	—
95	C₄×#170	C₂²×C₃	1	1	yes	characteristic
96	C₄×#170	C₂²×C₃	1	2	yes	—
97	C₄×#170	C₂²×C₃	1	4	yes	—
98	C₄×#170	C₂²×C₃	1	1	yes	characteristic
99	C₄×#170	C₂²×C₃	1	2	yes	—
100	C₈×#41	—	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	C₂×C₈	1	4	yes	complemented
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₃×C₂²⋊D₅	C₂×C₈	1	8	yes	complemented
109	C₂×C₃×Dic₅	—	2	2	no	—
110	C₂×C₃×Dic₅	—	2	2	no	—
111	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
114	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
116	C₃×D₂₀	C₂×C₈	1	4	yes	complemented
117	C₃×C₄×D₅	—	2	4	no	—
118	C₃×C₄×D₅	—	2	4	no	—
119	C₃×C₄×D₅	C₂×C₈	1	8	yes	complemented
120	C₃×Dic₁₀	C₂×C₈	1	4	yes	complemented
121	C₃×#170	—	2	4	no	—
122	C₃×#170	—	2	2	no	—
123	C₃×#170	#41	1	4	yes	complemented
124	C₂×C₃×#41	—	5	1	no	—
125	C₂²×C₃×C₈	—	5	4	no	—
126	C₂²×C₃×C₈	—	5	2	no	—
127	C₃×C₄×Q₈	—	5	1	no	—
128	C₃×C₄×Q₈	—	5	1	no	—
129	C₃×C₄×D₄	—	5	1	no	—
130	C₃×C₄×D₄	—	5	1	no	—
131	C₃×C₄×D₄	—	5	2	no	—
132	C₃×C₄×D₄	—	5	2	no	—
133	C₃×#117	—	5	2	no	—
134	C₃×#117	AGL(1,𝔽₅)	1	1	yes	characteristic
135	C₂×C₃×C₄²	—	5	1	no	—
136	C₂×C₃×C₄²	—	5	2	no	—
137	C₃×C₄⋊C₈	—	5	2	no	—
138	C₃×C₄⋊C₈	—	5	4	no	—
139	C₃×C₂²⋊C₈	—	5	4	no	—
140	C₃×C₂²⋊C₈	—	5	2	no	—
141	C₃×C₄×C₈	—	5	1	no	—
142	C₃×C₄×C₈	—	5	2	no	—
143	C₃×C₄×C₈	—	5	1	no	—
144	C₃×C₄×C₈	—	5	4	no	—
145	C₃×C₄×C₈	—	5	2	no	—
146	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
147	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	2	yes	—
148	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
149	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
150	#709	C₃×C₈	1	8	yes	complemented
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×#170	—	2	4	no	—
157	C₂×#170	C₂³×C₃	1	4	yes	—
158	C₂×#170	C₂³×C₃	1	2	yes	—
159	C₂×#170	C₂³×C₃	1	2	yes	—
160	D₅⋊C₈	—	2	8	no	—
161	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
162	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
163	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	2	yes	—
164	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
165	#685	C₂×C₃×C₄	1	2	yes	—
166	#685	C₂×C₃×C₄	1	2	yes	—
167	#683	C₂×C₃×C₄	1	2	yes	—
168	#683	C₂×C₃×C₄	1	2	yes	—
169	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
170	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
171	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
172	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
173	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
174	C₄×Dic₅	C₂³×C₃	1	2	yes	—
175	C₄×#41	—	5	1	no	—
176	C₈×Q₈	—	5	2	no	—
177	C₈×D₄	—	5	4	no	—
178	C₈×D₄	—	5	2	no	—
179	#431	—	5	2	no	—
180	#431	—	5	1	no	—
181	C₂×C₄×C₈	—	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	C₂²×C₈	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	C₂²×C₈	1	4	yes	—
190	C₃×C₄×C₅	—	2	2	no	—
191	C₃×C₄×C₅	—	2	2	no	—
192	C₃×C₄×C₅	C₂²×C₈	1	2	yes	—
193	C₃×C₄×C₅	C₂²×C₈	1	2	yes	—
194	C₃×Dic₅	—	2	1	no	—
195	C₃×Dic₅	—	2	1	no	—
196	C₃×Dic₅	C₂²×C₈	1	4	yes	—
197	C₃×Dic₅	#131	1	2	yes	—
198	C₃×Dic₅	C₂×#41	1	2	yes	—
199	C₃×#41	—	5	8	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	1	no	—
205	C₂²×C₃×C₄	—	5	1	no	—
206	C₂²×C₃×C₄	—	5	2	no	—
207	C₂²×C₃×C₄	—	5	2	no	—
208	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
209	C₂×C₃×C₈	—	5	2	no	—
210	C₂×C₃×C₈	—	5	2	no	—
211	C₂×C₃×C₈	—	5	4	no	—
212	C₂×C₃×C₈	—	10	8	no	—
213	C₂×C₃×C₈	—	10	4	no	—
214	C₃×C₄⋊C₄	—	5	2	no	—
215	C₃×C₄⋊C₄	—	5	2	no	—
216	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
217	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
218	C₃×C₂²⋊C₄	—	5	2	no	—
219	C₃×C₂²⋊C₄	—	5	2	no	—
220	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
221	C₃×C₄²	—	5	2	no	—
222	C₃×C₄²	—	5	1	no	—
223	C₃×C₄²	—	5	2	no	—
224	C₃×C₄²	—	5	1	no	—
225	C₃×C₄²	—	5	1	no	—
226	C₃×C₄²	—	5	1	no	—
227	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	2	yes	—
228	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
229	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
230	C₂×C₄×C₅	C₂×C₃×C₈	1	4	yes	complemented
231	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
232	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
233	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
235	C₂²⋊D₅	C₂×C₃×C₈	1	8	yes	complemented
236	C₂×Dic₅	—	2	2	no	—
237	C₂×Dic₅	—	2	2	no	—
238	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
239	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
240	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
241	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
242	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
243	D₂₀	C₂×C₃×C₈	1	4	yes	complemented
244	C₄×D₅	—	2	4	no	—
245	C₄×D₅	—	2	4	no	—
246	C₄×D₅	C₂×C₃×C₈	1	8	yes	complemented
247	Dic₁₀	C₂×C₃×C₈	1	4	yes	complemented
248	#170	—	2	4	no	—
249	#170	—	2	2	no	—
250	#170	C₃×#41	1	4	yes	complemented
251	C₂×#41	—	5	1	no	—
252	C₂²×C₈	—	5	4	no	—
253	C₂²×C₈	—	5	2	no	—
254	C₄×Q₈	—	5	1	no	—
255	C₄×Q₈	—	5	1	no	—
256	C₄×D₄	—	5	1	no	—
257	C₄×D₄	—	5	1	no	—
258	C₄×D₄	—	5	2	no	—
259	C₄×D₄	—	5	2	no	—
260	#117	—	5	2	no	—
261	#117	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
262	C₂×C₄²	—	5	1	no	—
263	C₂×C₄²	—	5	2	no	—
264	C₄⋊C₈	—	5	2	no	—
265	C₄⋊C₈	—	5	4	no	—
266	C₂²⋊C₈	—	5	4	no	—
267	C₂²⋊C₈	—	5	2	no	—
268	C₄×C₈	—	5	1	no	—
269	C₄×C₈	—	5	2	no	—
270	C₄×C₈	—	5	1	no	—
271	C₄×C₈	—	5	4	no	—
272	C₄×C₈	—	5	2	no	—
273	C₂×C₃×C₅	—	2	2	no	—
274	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
275	C₂×C₃×C₅	C₂³×C₈	1	1	yes	characteristic
276	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
277	C₃×D₅	—	2	4	no	—
278	C₂³×C₃	—	5	2	no	—
279	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
280	C₃×Q₈	—	5	4	no	—
281	C₃×D₄	—	5	8	no	—
282	C₃×D₄	—	5	4	no	—
283	C₂×C₃×C₄	—	5	1	no	—
284	C₂×C₃×C₄	—	5	2	no	—
285	C₂×C₃×C₄	—	5	1	no	—
286	C₂×C₃×C₄	—	5	8	no	—
287	C₂×C₃×C₄	—	5	1	no	—
288	C₂×C₃×C₄	—	5	1	no	—
289	C₂×C₃×C₄	—	10	4	no	—
290	C₂×C₃×C₄	—	10	4	no	—
291	C₂×C₃×C₄	—	10	2	no	—
292	C₂×C₃×C₄	—	10	2	no	—
293	C₂×C₃×C₄	D₅⋊C₈	1	4	yes	complemented
294	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
295	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
296	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
297	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
298	C₃×C₈	—	5	4	no	—
299	C₃×C₈	—	10	4	no	—
300	C₃×C₈	—	10	2	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	2	1	no	—
303	C₂²×C₅	C₂²×C₃×C₈	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	C₂²×C₃×C₈	1	4	yes	—
308	C₄×C₅	—	2	2	no	—
309	C₄×C₅	—	2	2	no	—
310	C₄×C₅	C₂²×C₃×C₈	1	2	yes	—
311	C₄×C₅	C₂²×C₃×C₈	1	2	yes	—
312	Dic₅	—	2	1	no	—
313	Dic₅	—	2	1	no	—
314	Dic₅	C₂²×C₃×C₈	1	4	yes	—
315	Dic₅	C₃×#131	1	2	yes	—
316	Dic₅	C₂×C₃×#41	1	2	yes	—
317	#41	—	5	8	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	1	no	—
323	C₂²×C₄	—	5	1	no	—
324	C₂²×C₄	—	5	2	no	—
325	C₂²×C₄	—	5	2	no	—
326	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
327	C₂×C₈	—	5	2	no	—
328	C₂×C₈	—	5	2	no	—
329	C₂×C₈	—	5	4	no	—
330	C₂×C₈	—	10	8	no	—
331	C₂×C₈	—	10	4	no	—
332	C₄⋊C₄	—	5	2	no	—
333	C₄⋊C₄	—	5	2	no	—
334	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
335	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
336	C₂²⋊C₄	—	5	2	no	—
337	C₂²⋊C₄	—	5	2	no	—
338	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
339	C₄²	—	5	1	no	—
340	C₄²	—	5	2	no	—
341	C₄²	—	5	1	no	—
342	C₄²	—	5	1	no	—
343	C₄²	—	5	2	no	—
344	C₄²	—	5	1	no	—
345	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
346	C₃×C₅	C₈×#41	1	1	yes	characteristic, complemented, Hall
347	C₂²×C₃	—	2	1	no	—
348	C₂²×C₃	—	2	1	no	—
349	C₂²×C₃	—	5	4	no	—
350	C₂²×C₃	—	10	2	no	—
351	C₂²×C₃	—	10	2	no	—
352	C₂²×C₃	C₂×D₅⋊C₈	1	2	yes	—
353	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
354	C₃×C₄	—	2	2	no	—
355	C₃×C₄	—	2	2	no	—
356	C₃×C₄	—	5	4	no	—
357	C₃×C₄	—	5	2	no	—
358	C₃×C₄	—	5	2	no	—
359	C₃×C₄	—	10	1	no	—
360	C₃×C₄	—	10	1	no	—
361	C₃×C₄	C₂×D₅⋊C₈	1	2	yes	—
362	C₃×C₄	C₂×D₅⋊C₈	1	2	yes	—
363	C₂×C₅	—	2	2	no	—
364	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
365	C₂×C₅	C₂³×C₃×C₈	1	1	yes	characteristic
366	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
367	D₅	—	2	4	no	—
368	C₂³	—	5	2	no	—
369	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
370	Q₈	—	5	4	no	—
371	D₄	—	5	8	no	—
372	D₄	—	5	4	no	—
373	C₂×C₄	—	5	1	no	—
374	C₂×C₄	—	5	1	no	—
375	C₂×C₄	—	5	2	no	—
376	C₂×C₄	—	5	8	no	—
377	C₂×C₄	—	5	1	no	—
378	C₂×C₄	—	5	1	no	—
379	C₂×C₄	—	10	4	no	—
380	C₂×C₄	—	10	4	no	—
381	C₂×C₄	—	10	2	no	—
382	C₂×C₄	—	10	2	no	—
383	C₂×C₄	C₃×D₅⋊C₈	1	4	yes	complemented
384	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
385	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
386	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
387	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
388	C₈	—	5	4	no	—
389	C₈	—	10	4	no	—
390	C₈	—	10	2	no	—
391	C₂×C₃	—	2	2	no	—
392	C₂×C₃	—	10	4	no	—
393	C₂×C₃	C₂²×D₅⋊C₈	1	1	yes	characteristic
394	C₂×C₃	D₅⋊#131	1	1	yes	characteristic
395	C₂×C₃	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
396	C₅	C₃×C₈×#41	1	1	yes	characteristic, complemented, Sylow
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	5	4	no	—
400	C₂²	—	10	2	no	—
401	C₂²	—	10	2	no	—
402	C₂²	C₂×C₃×D₅⋊C₈	1	2	yes	—
403	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
404	C₄	—	2	2	no	—
405	C₄	—	2	2	no	—
406	C₄	—	5	4	no	—
407	C₄	—	5	2	no	—
408	C₄	—	5	2	no	—
409	C₄	—	10	1	no	—
410	C₄	—	10	1	no	—
411	C₄	C₂×C₃×D₅⋊C₈	1	2	yes	—
412	C₄	C₂×C₃×D₅⋊C₈	1	2	yes	—
413	C₃	#10617114	1	1	yes	characteristic, direct product factor, Sylow
414	C₂	—	2	2	no	—
415	C₂	—	10	4	no	—
416	C₂	C₂²×C₃×D₅⋊C₈	1	1	yes	characteristic
417	C₂	C₃×D₅⋊#131	1	1	yes	characteristic
418	C₂	C₃×#41×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂³×C₃×C₈
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×#117	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₃×#709	C₄
cosocle	C₂×Dic₅	C₂⁴×C₃
hypercenter	C₃×#117	AGL(1,𝔽₅)
hypocenter	C₅	C₃×C₈×#41
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#117

Complements

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

N	H ≅ G/N	type
2. C₃×#65748	C₂	semidirect
3. C₂×C₃×C₄×#170	C₂	semidirect
4. C₃×#65703	C₂	semidirect
5. C₃×#65702	C₂	semidirect
6. C₃×#65692	C₂	semidirect
7. C₃×#65678	C₂	semidirect
8. C₃×C₄×D₅⋊C₈	C₂	semidirect
9. #10617114	C₃	direct (N × H)
34. #65748	C₂×C₃	semidirect
35. C₂×C₄×#170	C₂×C₃	semidirect
36. #65703	C₂×C₃	semidirect
37. #65702	C₂×C₃	semidirect
38. #65692	C₂×C₃	semidirect
39. #65678	C₂×C₃	semidirect
40. C₄×D₅⋊C₈	C₂×C₃	semidirect
45. C₃×#709	C₈	semidirect
103. C₂×C₃×C₄×C₅	C₂×C₈	semidirect
108. C₃×C₂²⋊D₅	C₂×C₈	semidirect
116. C₃×D₂₀	C₂×C₈	semidirect
119. C₃×C₄×D₅	C₂×C₈	semidirect
120. C₃×Dic₁₀	C₂×C₈	semidirect
123. C₃×#170	#41	semidirect
150. #709	C₃×C₈	semidirect
230. C₂×C₄×C₅	C₂×C₃×C₈	semidirect
235. C₂²⋊D₅	C₂×C₃×C₈	semidirect
243. D₂₀	C₂×C₃×C₈	semidirect
246. C₄×D₅	C₂×C₃×C₈	semidirect
247. Dic₁₀	C₂×C₃×C₈	semidirect
250. #170	C₃×#41	semidirect
293. C₂×C₃×C₄	D₅⋊C₈	semidirect
346. C₃×C₅	C₈×#41	semidirect
383. C₂×C₄	C₃×D₅⋊C₈	semidirect
396. C₅	C₃×C₈×#41	semidirect
413. C₃	#10617114	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×#65856	2
C₃×#65748	2
C₂×C₃×C₄×#170	2
C₃×#65703	2
C₃×#65702	2
C₃×#65692	2
C₃×#65678	2
C₃×C₄×D₅⋊C₈	2
#10617114	3
C₃×C₈×#41	5

Subgroups — C3×#10617114 #14418899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617114 #14418899