Subgroups — C₃×#10604376 #14294494

Order 1920.

808 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4130	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×D₅⋊M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₃×D₅×#117	C₂	1	1	yes	maximal, characteristic
4	C₃×#64862	C₂	1	4	yes	maximal, complemented
5	#10604376	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	—	2	1	no	—
8	C₂×C₃×#704	—	2	1	no	—
9	C₃×#4130	—	2	1	no	—
10	C₃×#4130	—	2	1	no	—
11	C₃×#4130	C₄	1	2	yes	complemented
12	C₃×#4130	C₂²	1	2	yes	—
13	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₄	1	2	yes	complemented
14	C₂×C₃×C₄×AGL(1,𝔽₅)	—	2	1	no	—
15	C₃×D₅⋊M₁₆	—	2	1	no	—
16	C₃×D₅⋊M₁₆	—	2	1	no	—
17	C₃×D₅⋊M₁₆	C₄	1	2	yes	complemented
18	C₃×D₅⋊M₁₆	C₂²	1	2	yes	—
19	C₂×C₃×#700	C₄	1	2	yes	complemented
20	C₂×C₃×D₅⋊C₈	—	2	1	no	—
21	C₃×C₅×#117	C₄	1	1	yes	characteristic, complemented
22	C₃×#4072	C₄	1	1	yes	characteristic, complemented
23	C₃×#4038	—	2	1	no	—
24	C₃×D₅×C₄⋊C₄	—	2	1	no	—
25	C₃×D₅×C₂²⋊C₄	—	2	1	no	—
26	C₃×#4023	—	2	1	no	—
27	C₃×#4018	C₄	1	2	yes	complemented
28	C₃×C₄²×D₅	C₂²	1	2	yes	—
29	C₃×#1733	—	5	1	no	maximal, Hall
30	C₂×#4130	C₂×C₃	1	1	yes	characteristic
31	C₂×D₅⋊M₁₆	C₂×C₃	1	1	yes	characteristic
32	D₅×#117	C₂×C₃	1	1	yes	characteristic
33	#64862	C₂×C₃	1	4	yes	complemented
34	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
35	C₂²×C₃×AGL(1,𝔽₅)	—	2	2	no	—
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×Dic₅	D₄	1	1	yes	characteristic
38	C₂×C₃×C₄×D₅	—	2	2	no	—
39	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
42	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
43	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
45	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
46	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
47	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
48	C₂×C₃×C₄×D₅	Q₈	1	1	yes	characteristic
49	C₂×C₃×C₄×D₅	Q₈	1	1	yes	characteristic
50	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
51	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
52	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
53	C₃×#704	—	2	2	no	—
54	C₃×#704	—	2	2	no	—
55	C₂×C₃×#170	—	2	2	no	—
56	C₃×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
57	C₃×C₄⋊AGL(1,𝔽₅)	C₂×C₄	1	4	yes	—
58	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
59	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
60	C₃×#700	—	2	2	no	—
61	C₃×#700	C₂×C₄	1	4	yes	complemented
62	C₃×D₅⋊C₈	—	2	2	no	—
63	C₃×D₅⋊C₈	—	2	2	no	—
64	C₃×C₅×C₄⋊C₄	—	2	1	no	—
65	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
66	C₃×C₄²×C₅	C₂×C₄	1	2	yes	complemented
67	C₃×C₂²⋊Dic₅	—	2	1	no	—
68	C₃×#685	—	2	2	no	—
69	C₃×C₄⋊Dic₅	—	2	1	no	—
70	C₃×#683	—	2	2	no	—
71	C₃×C₄×Dic₅	—	2	2	no	—
72	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	complemented
73	C₂²×C₃×M₁₆	—	5	1	no	—
74	C₂×C₃×#117	—	5	1	no	—
75	C₂×C₃×#117	—	5	1	no	—
76	C₃×#339	—	5	4	no	—
77	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₂²⋊AGL(1,𝔽₅)	—	2	1	no	—
79	C₂×#704	—	2	1	no	—
80	#4130	—	2	1	no	—
81	#4130	—	2	1	no	—
82	#4130	C₃×C₄	1	2	yes	complemented
83	#4130	C₂²×C₃	1	2	yes	—
84	C₂×C₄⋊AGL(1,𝔽₅)	C₃×C₄	1	2	yes	complemented
85	C₂×C₄×AGL(1,𝔽₅)	—	2	1	no	—
86	D₅⋊M₁₆	—	2	1	no	—
87	D₅⋊M₁₆	—	2	1	no	—
88	D₅⋊M₁₆	C₃×C₄	1	2	yes	complemented
89	D₅⋊M₁₆	C₂²×C₃	1	2	yes	—
90	C₂×#700	C₃×C₄	1	2	yes	complemented
91	C₂×D₅⋊C₈	—	2	1	no	—
92	C₅×#117	C₃×C₄	1	1	yes	characteristic, complemented
93	#4072	C₃×C₄	1	1	yes	characteristic, complemented
94	#4038	—	2	1	no	—
95	D₅×C₄⋊C₄	—	2	1	no	—
96	D₅×C₂²⋊C₄	—	2	1	no	—
97	#4023	—	2	1	no	—
98	#4018	C₃×C₄	1	2	yes	complemented
99	C₄²×D₅	C₂²×C₃	1	2	yes	—
100	#1733	—	5	1	no	Sylow
101	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
102	C₂²×C₃×D₅	—	4	2	no	—
103	C₂²×C₃×D₅	C₂²⋊C₄	1	1	yes	characteristic
104	C₂²×C₃×D₅	C₂²⋊C₄	1	1	yes	characteristic
105	C₂²×C₃×D₅	C₂²⋊C₄	1	1	yes	characteristic
106	C₂²×C₃×D₅	C₄⋊C₄	1	1	yes	characteristic
107	C₂²×C₃×D₅	C₄⋊C₄	1	1	yes	characteristic
108	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
110	C₂×C₃×AGL(1,𝔽₅)	—	4	4	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₄²	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₃×Dic₅	—	2	2	no	—
119	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
120	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₃×Dic₅	C₂²⋊C₄	1	1	yes	characteristic
122	C₂×C₃×Dic₅	C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₃×Dic₅	C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
125	C₃×C₄×D₅	—	4	4	no	—
126	C₃×C₄×D₅	C₄²	1	1	yes	characteristic
127	C₃×C₄×D₅	C₄²	1	1	yes	characteristic
128	C₃×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
129	C₃×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
130	C₃×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
131	C₃×C₄×D₅	C₂²⋊C₄	1	1	yes	characteristic
132	C₃×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
133	C₃×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
134	C₃×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
135	C₃×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
136	C₃×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
137	C₃×C₄×D₅	C₄⋊C₄	1	1	yes	characteristic
138	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
139	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
140	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
141	C₃×C₄×D₅	C₂×Q₈	1	1	yes	characteristic
142	C₃×#170	—	2	4	no	—
143	C₂³×C₃×C₄	—	5	1	no	—
144	C₂×C₃×M₁₆	—	5	2	no	—
145	C₂×C₃×M₁₆	—	5	2	no	—
146	C₂×C₃×M₁₆	—	5	2	no	—
147	C₂×C₃×M₁₆	—	10	1	no	—
148	C₂×C₃×M₁₆	—	10	1	no	—
149	C₂×C₃×M₁₆	—	10	1	no	—
150	C₂²×C₃×C₈	—	10	1	no	—
151	C₃×#117	—	5	1	no	—
152	C₃×#117	—	5	2	no	—
153	C₃×#117	—	5	2	no	—
154	C₃×#117	—	5	2	no	—
155	C₃×#117	—	10	1	no	—
156	C₃×#117	—	10	1	no	—
157	C₃×#117	—	10	1	no	—
158	C₃×#117	—	10	1	no	—
159	C₃×#117	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
160	C₂×C₃×C₄⋊C₄	—	5	2	no	—
161	C₂×C₃×C₄⋊C₄	—	10	1	no	—
162	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
163	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
164	C₂×C₃×C₄²	—	5	2	no	—
165	C₂×C₃×C₄²	—	10	1	no	—
166	C₂³×D₅	C₃×D₄	1	1	yes	characteristic
167	C₂²×AGL(1,𝔽₅)	—	2	2	no	—
168	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
169	C₂²×Dic₅	C₃×D₄	1	1	yes	characteristic
170	C₂×C₄×D₅	—	2	2	no	—
171	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
172	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
173	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
174	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
175	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
176	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
177	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
178	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
179	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
180	C₂×C₄×D₅	C₃×Q₈	1	1	yes	characteristic
181	C₂×C₄×D₅	C₃×Q₈	1	1	yes	characteristic
182	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
183	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
184	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
185	#704	—	2	2	no	—
186	#704	—	2	2	no	—
187	C₂×#170	—	2	2	no	—
188	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
189	C₄⋊AGL(1,𝔽₅)	C₂×C₃×C₄	1	4	yes	—
190	C₄×AGL(1,𝔽₅)	—	2	2	no	—
191	C₄×AGL(1,𝔽₅)	—	2	2	no	—
192	#700	—	2	2	no	—
193	#700	C₂×C₃×C₄	1	4	yes	complemented
194	D₅⋊C₈	—	2	2	no	—
195	D₅⋊C₈	—	2	2	no	—
196	C₅×C₄⋊C₄	—	2	1	no	—
197	C₅×C₂²⋊C₄	—	2	1	no	—
198	C₄²×C₅	C₂×C₃×C₄	1	2	yes	complemented
199	C₂²⋊Dic₅	—	2	1	no	—
200	#685	—	2	2	no	—
201	C₄⋊Dic₅	—	2	1	no	—
202	#683	—	2	2	no	—
203	C₄×Dic₅	—	2	2	no	—
204	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	complemented
205	C₂²×M₁₆	—	5	1	no	—
206	C₂×#117	—	5	1	no	—
207	C₂×#117	—	5	1	no	—
208	#339	—	5	4	no	—
209	C₂²×C₃×C₅	—	4	1	no	—
210	C₂²×C₃×C₅	#95	1	1	yes	characteristic
211	C₂²×C₃×C₅	#95	1	1	yes	characteristic
212	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
213	C₂×C₃×D₅	—	2	2	no	—
214	C₂×C₃×D₅	—	2	2	no	—
215	C₂×C₃×D₅	—	2	2	no	—
216	C₂×C₃×D₅	—	4	1	no	—
217	C₂×C₃×D₅	—	4	1	no	—
218	C₂×C₃×D₅	—	4	1	no	—
219	C₂×C₃×D₅	#95	1	1	yes	characteristic
220	C₂×C₃×D₅	#95	1	1	yes	characteristic
221	C₂×C₃×D₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	C₂×C₃×D₅	C₂×C₄⋊C₄	1	1	yes	characteristic
223	C₃×AGL(1,𝔽₅)	—	4	4	no	—
224	C₃×C₄×C₅	—	4	2	no	—
225	C₃×C₄×C₅	#95	1	1	yes	characteristic
226	C₃×C₄×C₅	#95	1	1	yes	characteristic
227	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
228	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
229	C₃×Dic₅	—	4	2	no	—
230	C₃×Dic₅	#95	1	1	yes	characteristic
231	C₃×Dic₅	#95	1	1	yes	characteristic
232	C₃×Dic₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₃×Dic₅	C₂×C₄⋊C₄	1	1	yes	characteristic
234	C₂⁴×C₃	—	5	1	no	—
235	C₂²×C₃×C₄	—	5	1	no	—
236	C₂²×C₃×C₄	—	5	1	no	—
237	C₂²×C₃×C₄	—	5	1	no	—
238	C₂²×C₃×C₄	—	5	1	no	—
239	C₂²×C₃×C₄	—	5	1	no	—
240	C₂²×C₃×C₄	—	5	1	no	—
241	C₂²×C₃×C₄	—	5	1	no	—
242	C₂²×C₃×C₄	—	5	1	no	—
243	C₂²×C₃×C₄	—	5	1	no	—
244	C₂²×C₃×C₄	—	5	1	no	—
245	C₂²×C₃×C₄	—	5	1	no	—
246	C₂²×C₃×C₄	—	5	1	no	—
247	C₂²×C₃×C₄	—	5	1	no	—
248	C₂²×C₃×C₄	—	10	2	no	—
249	C₂²×C₃×C₄	—	10	2	no	—
250	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
251	C₃×M₁₆	—	5	4	no	—
252	C₃×M₁₆	—	10	2	no	—
253	C₃×M₁₆	—	10	2	no	—
254	C₃×M₁₆	—	10	2	no	—
255	C₂×C₃×C₈	—	10	2	no	—
256	C₂×C₃×C₈	—	10	2	no	—
257	C₂×C₃×C₈	—	10	2	no	—
258	C₃×C₄⋊C₄	—	2	1	no	—
259	C₃×C₄⋊C₄	—	5	4	no	—
260	C₃×C₄⋊C₄	—	10	2	no	—
261	C₃×C₄⋊C₄	—	10	2	no	—
262	C₃×C₄⋊C₄	—	10	1	no	—
263	C₃×C₂²⋊C₄	—	2	1	no	—
264	C₃×C₂²⋊C₄	—	10	2	no	—
265	C₃×C₂²⋊C₄	—	10	2	no	—
266	C₃×C₂²⋊C₄	—	10	2	no	—
267	C₃×C₂²⋊C₄	—	10	1	no	—
268	C₃×C₄²	—	5	2	no	—
269	C₃×C₄²	—	10	2	no	—
270	C₃×C₄²	—	10	2	no	—
271	C₃×C₄²	—	10	2	no	—
272	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
273	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
274	C₂²×D₅	—	4	2	no	—
275	C₂²×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
276	C₂²×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
277	C₂²×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
278	C₂²×D₅	C₃×C₄⋊C₄	1	1	yes	characteristic
279	C₂²×D₅	C₃×C₄⋊C₄	1	1	yes	characteristic
280	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
281	C₂×AGL(1,𝔽₅)	—	2	4	no	—
282	C₂×AGL(1,𝔽₅)	—	4	4	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
285	C₂×C₄×C₅	C₃×C₄²	1	1	yes	characteristic
286	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
287	C₂×C₄×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
288	C₂×C₄×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
290	C₂×Dic₅	—	2	2	no	—
291	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
292	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
293	C₂×Dic₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
294	C₂×Dic₅	C₃×C₄⋊C₄	1	1	yes	characteristic
295	C₂×Dic₅	C₃×C₄⋊C₄	1	1	yes	characteristic
296	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
297	C₄×D₅	—	4	4	no	—
298	C₄×D₅	C₃×C₄²	1	1	yes	characteristic
299	C₄×D₅	C₃×C₄²	1	1	yes	characteristic
300	C₄×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
301	C₄×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
302	C₄×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
303	C₄×D₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
304	C₄×D₅	C₃×C₄⋊C₄	1	1	yes	characteristic
305	C₄×D₅	C₃×C₄⋊C₄	1	1	yes	characteristic
306	C₄×D₅	C₃×C₄⋊C₄	1	1	yes	characteristic
307	C₄×D₅	C₃×C₄⋊C₄	1	1	yes	characteristic
308	C₄×D₅	C₃×C₄⋊C₄	1	1	yes	characteristic
309	C₄×D₅	C₃×C₄⋊C₄	1	1	yes	characteristic
310	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
311	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
312	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
313	C₄×D₅	C₂×C₃×Q₈	1	1	yes	characteristic
314	#170	—	2	4	no	—
315	C₂³×C₄	—	5	1	no	—
316	C₂×M₁₆	—	5	2	no	—
317	C₂×M₁₆	—	5	2	no	—
318	C₂×M₁₆	—	5	2	no	—
319	C₂×M₁₆	—	10	1	no	—
320	C₂×M₁₆	—	10	1	no	—
321	C₂×M₁₆	—	10	1	no	—
322	C₂²×C₈	—	10	1	no	—
323	#117	—	5	1	no	—
324	#117	—	5	2	no	—
325	#117	—	5	2	no	—
326	#117	—	5	2	no	—
327	#117	—	10	1	no	—
328	#117	—	10	1	no	—
329	#117	—	10	1	no	—
330	#117	—	10	1	no	—
331	#117	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
332	C₂×C₄⋊C₄	—	5	2	no	—
333	C₂×C₄⋊C₄	—	10	1	no	—
334	C₂×C₂²⋊C₄	—	10	1	no	—
335	C₂×C₂²⋊C₄	—	10	1	no	—
336	C₂×C₄²	—	5	2	no	—
337	C₂×C₄²	—	10	1	no	—
338	C₂×C₃×C₅	—	2	1	no	—
339	C₂×C₃×C₅	—	2	1	no	—
340	C₂×C₃×C₅	—	2	1	no	—
341	C₂×C₃×C₅	C₂×#95	1	1	yes	characteristic
342	C₃×D₅	—	2	1	no	—
343	C₃×D₅	—	2	1	no	—
344	C₃×D₅	—	2	1	no	—
345	C₃×D₅	#421	1	2	yes	—
346	C₂³×C₃	—	5	1	no	—
347	C₂³×C₃	—	5	1	no	—
348	C₂³×C₃	—	5	1	no	—
349	C₂³×C₃	—	5	1	no	—
350	C₂³×C₃	—	5	1	no	—
351	C₂³×C₃	—	5	1	no	—
352	C₂³×C₃	—	20	2	no	—
353	C₂³×C₃	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	—	5	1	no	—
356	C₂×C₃×C₄	—	5	1	no	—
357	C₂×C₃×C₄	—	5	1	no	—
358	C₂×C₃×C₄	—	5	1	no	—
359	C₂×C₃×C₄	—	5	1	no	—
360	C₂×C₃×C₄	—	5	1	no	—
361	C₂×C₃×C₄	—	5	1	no	—
362	C₂×C₃×C₄	—	5	1	no	—
363	C₂×C₃×C₄	—	5	1	no	—
364	C₂×C₃×C₄	—	5	1	no	—
365	C₂×C₃×C₄	—	5	1	no	—
366	C₂×C₃×C₄	—	5	1	no	—
367	C₂×C₃×C₄	—	5	1	no	—
368	C₂×C₃×C₄	—	5	1	no	—
369	C₂×C₃×C₄	—	5	1	no	—
370	C₂×C₃×C₄	—	5	1	no	—
371	C₂×C₃×C₄	—	5	1	no	—
372	C₂×C₃×C₄	—	5	1	no	—
373	C₂×C₃×C₄	—	5	1	no	—
374	C₂×C₃×C₄	—	5	1	no	—
375	C₂×C₃×C₄	—	5	1	no	—
376	C₂×C₃×C₄	—	5	1	no	—
377	C₂×C₃×C₄	—	10	4	no	—
378	C₂×C₃×C₄	—	10	2	no	—
379	C₂×C₃×C₄	—	20	4	no	—
380	C₂×C₃×C₄	—	20	4	no	—
381	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
382	C₂×C₃×C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
383	C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
384	C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
385	C₂×C₃×C₄	C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
386	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
387	C₃×C₈	—	10	4	no	—
388	C₂²×C₅	—	4	1	no	—
389	C₂²×C₅	C₃×#95	1	1	yes	characteristic
390	C₂²×C₅	C₃×#95	1	1	yes	characteristic
391	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
392	C₂×D₅	—	2	2	no	—
393	C₂×D₅	—	2	2	no	—
394	C₂×D₅	—	2	2	no	—
395	C₂×D₅	—	4	1	no	—
396	C₂×D₅	—	4	1	no	—
397	C₂×D₅	—	4	1	no	—
398	C₂×D₅	C₃×#95	1	1	yes	characteristic
399	C₂×D₅	C₃×#95	1	1	yes	characteristic
400	C₂×D₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
401	C₂×D₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
402	AGL(1,𝔽₅)	—	4	4	no	—
403	C₄×C₅	—	4	2	no	—
404	C₄×C₅	C₃×#95	1	1	yes	characteristic
405	C₄×C₅	C₃×#95	1	1	yes	characteristic
406	C₄×C₅	C₂×C₃×C₄²	1	1	yes	characteristic
407	C₄×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
408	Dic₅	—	4	2	no	—
409	Dic₅	C₃×#95	1	1	yes	characteristic
410	Dic₅	C₃×#95	1	1	yes	characteristic
411	Dic₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
412	Dic₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
413	C₂⁴	—	5	1	no	—
414	C₂²×C₄	—	5	1	no	—
415	C₂²×C₄	—	5	1	no	—
416	C₂²×C₄	—	5	1	no	—
417	C₂²×C₄	—	5	1	no	—
418	C₂²×C₄	—	5	1	no	—
419	C₂²×C₄	—	5	1	no	—
420	C₂²×C₄	—	5	1	no	—
421	C₂²×C₄	—	5	1	no	—
422	C₂²×C₄	—	5	1	no	—
423	C₂²×C₄	—	5	1	no	—
424	C₂²×C₄	—	5	1	no	—
425	C₂²×C₄	—	5	1	no	—
426	C₂²×C₄	—	5	1	no	—
427	C₂²×C₄	—	10	2	no	—
428	C₂²×C₄	—	10	2	no	—
429	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
430	M₁₆	—	5	4	no	—
431	M₁₆	—	10	2	no	—
432	M₁₆	—	10	2	no	—
433	M₁₆	—	10	2	no	—
434	C₂×C₈	—	10	2	no	—
435	C₂×C₈	—	10	2	no	—
436	C₂×C₈	—	10	2	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	5	4	no	—
439	C₄⋊C₄	—	10	2	no	—
440	C₄⋊C₄	—	10	2	no	—
441	C₄⋊C₄	—	10	1	no	—
442	C₂²⋊C₄	—	2	1	no	—
443	C₂²⋊C₄	—	10	2	no	—
444	C₂²⋊C₄	—	10	2	no	—
445	C₂²⋊C₄	—	10	2	no	—
446	C₂²⋊C₄	—	10	1	no	—
447	C₄²	—	5	2	no	—
448	C₄²	—	10	2	no	—
449	C₄²	—	10	2	no	—
450	C₄²	—	10	2	no	—
451	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	complemented
452	C₃×C₅	#1733	1	1	yes	characteristic, complemented, Hall
453	C₂²×C₃	—	4	1	no	—
454	C₂²×C₃	—	5	1	no	—
455	C₂²×C₃	—	5	1	no	—
456	C₂²×C₃	—	5	1	no	—
457	C₂²×C₃	—	5	1	no	—
458	C₂²×C₃	—	10	2	no	—
459	C₂²×C₃	—	10	2	no	—
460	C₂²×C₃	—	10	2	no	—
461	C₂²×C₃	—	20	1	no	—
462	C₂²×C₃	—	20	1	no	—
463	C₂²×C₃	—	20	1	no	—
464	C₂²×C₃	(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
465	C₂²×C₃	(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
466	C₂²×C₃	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
467	C₃×C₄	—	4	2	no	—
468	C₃×C₄	—	5	1	no	—
469	C₃×C₄	—	5	1	no	—
470	C₃×C₄	—	5	1	no	—
471	C₃×C₄	—	5	1	no	—
472	C₃×C₄	—	20	2	no	—
473	C₃×C₄	—	20	4	no	—
474	C₃×C₄	(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
475	C₃×C₄	(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
476	C₃×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
477	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
478	C₂×C₅	—	2	1	no	—
479	C₂×C₅	—	2	1	no	—
480	C₂×C₅	—	2	1	no	—
481	C₂×C₅	C₂×C₃×#95	1	1	yes	characteristic
482	D₅	—	2	1	no	—
483	D₅	—	2	1	no	—
484	D₅	—	2	1	no	—
485	D₅	C₃×#421	1	2	yes	—
486	C₂³	—	5	1	no	—
487	C₂³	—	5	1	no	—
488	C₂³	—	5	1	no	—
489	C₂³	—	5	1	no	—
490	C₂³	—	5	1	no	—
491	C₂³	—	5	1	no	—
492	C₂³	—	20	2	no	—
493	C₂³	C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	5	1	no	—
496	C₂×C₄	—	5	1	no	—
497	C₂×C₄	—	5	1	no	—
498	C₂×C₄	—	5	1	no	—
499	C₂×C₄	—	5	1	no	—
500	C₂×C₄	—	5	1	no	—
501	C₂×C₄	—	5	1	no	—
502	C₂×C₄	—	5	1	no	—
503	C₂×C₄	—	5	1	no	—
504	C₂×C₄	—	5	1	no	—
505	C₂×C₄	—	5	1	no	—
506	C₂×C₄	—	5	1	no	—
507	C₂×C₄	—	5	1	no	—
508	C₂×C₄	—	5	1	no	—
509	C₂×C₄	—	5	1	no	—
510	C₂×C₄	—	5	1	no	—
511	C₂×C₄	—	5	1	no	—
512	C₂×C₄	—	5	1	no	—
513	C₂×C₄	—	5	1	no	—
514	C₂×C₄	—	5	1	no	—
515	C₂×C₄	—	5	1	no	—
516	C₂×C₄	—	5	1	no	—
517	C₂×C₄	—	10	4	no	—
518	C₂×C₄	—	10	2	no	—
519	C₂×C₄	—	20	4	no	—
520	C₂×C₄	—	20	4	no	—
521	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
522	C₂×C₄	C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
523	C₂×C₄	C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
524	C₂×C₄	C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
525	C₂×C₄	C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
526	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
527	C₈	—	10	4	no	—
528	C₂×C₃	—	2	1	no	—
529	C₂×C₃	—	2	1	no	—
530	C₂×C₃	—	2	1	no	—
531	C₂×C₃	—	5	2	no	—
532	C₂×C₃	—	10	1	no	—
533	C₂×C₃	—	10	1	no	—
534	C₂×C₃	—	10	1	no	—
535	C₂×C₃	C₂×(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
536	C₅	C₃×#1733	1	1	yes	characteristic, complemented, Sylow
537	C₂²	—	4	1	no	—
538	C₂²	—	5	1	no	—
539	C₂²	—	5	1	no	—
540	C₂²	—	5	1	no	—
541	C₂²	—	5	1	no	—
542	C₂²	—	10	2	no	—
543	C₂²	—	10	2	no	—
544	C₂²	—	10	2	no	—
545	C₂²	—	20	1	no	—
546	C₂²	—	20	1	no	—
547	C₂²	—	20	1	no	—
548	C₂²	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
549	C₂²	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
550	C₂²	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
551	C₄	—	4	2	no	—
552	C₄	—	5	1	no	—
553	C₄	—	5	1	no	—
554	C₄	—	5	1	no	—
555	C₄	—	5	1	no	—
556	C₄	—	20	2	no	—
557	C₄	—	20	4	no	—
558	C₄	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
559	C₄	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic
560	C₄	C₂×C₃×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
561	C₄	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
562	C₃	#10604376	1	1	yes	characteristic, direct product factor, Sylow
563	C₂	—	2	1	no	—
564	C₂	—	2	1	no	—
565	C₂	—	2	1	no	—
566	C₂	—	5	2	no	—
567	C₂	—	10	1	no	—
568	C₂	—	10	1	no	—
569	C₂	—	10	1	no	—
570	C₂	C₂×C₃×(C₂×AGL(1,𝔽₅))⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	C₂×C₄⋊AGL(1,𝔽₅)
commutator	C₄×C₅	C₂×C₃×C₄²
Frattini	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×#117	C₄
socle	C₂×C₃×C₅	C₂×#95
prime radical	C₂³×C₃×D₅	D₄
cosocle	C₂×C₄×D₅	C₂³×C₃
hypercenter	C₃×#117	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#1733
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₃×#117

Complements

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

N	H ≅ G/N	type
4. C₃×#64862	C₂	semidirect
5. #10604376	C₃	direct (N × H)
11. C₃×#4130	C₄	semidirect
13. C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₄	semidirect
17. C₃×D₅⋊M₁₆	C₄	semidirect
19. C₂×C₃×#700	C₄	semidirect
21. C₃×C₅×#117	C₄	semidirect
22. C₃×#4072	C₄	semidirect
27. C₃×#4018	C₄	semidirect
33. #64862	C₂×C₃	semidirect
61. C₃×#700	C₂×C₄	semidirect
66. C₃×C₄²×C₅	C₂×C₄	semidirect
72. C₃×C₄×Dic₅	C₂×C₄	semidirect
82. #4130	C₃×C₄	semidirect
84. C₂×C₄⋊AGL(1,𝔽₅)	C₃×C₄	semidirect
88. D₅⋊M₁₆	C₃×C₄	semidirect
90. C₂×#700	C₃×C₄	semidirect
92. C₅×#117	C₃×C₄	semidirect
93. #4072	C₃×C₄	semidirect
98. #4018	C₃×C₄	semidirect
159. C₃×#117	AGL(1,𝔽₅)	semidirect
193. #700	C₂×C₃×C₄	semidirect
198. C₄²×C₅	C₂×C₃×C₄	semidirect
204. C₄×Dic₅	C₂×C₃×C₄	semidirect
272. C₃×C₄²	C₂×AGL(1,𝔽₅)	semidirect
331. #117	C₃×AGL(1,𝔽₅)	semidirect
451. C₄²	C₂×C₃×AGL(1,𝔽₅)	semidirect
452. C₃×C₅	#1733	semidirect
536. C₅	C₃×#1733	semidirect
562. C₃	#10604376	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×#4130	2
C₂×C₃×D₅⋊M₁₆	2
C₃×D₅×#117	2
C₃×#64862	2
#10604376	3
C₃×#1733	5

Subgroups — C3×#10604376 #14294494

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10604376 #14294494