Subgroups — C₃×#10617132 #14326422

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×#117	C₂	1	1	yes	maximal, characteristic
2	C₃×#65764	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₃×#65711	C₂	1	2	yes	maximal, complemented
5	C₃×#65711	C₂	1	2	yes	maximal, complemented
6	C₃×#65699	C₂	1	2	yes	maximal
7	C₃×C₂²⋊C₄×AGL(1,𝔽₅)	C₂	1	2	yes	maximal
8	C₃×#65690	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65689	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×C₄⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65686	C₂	1	1	yes	maximal, characteristic, complemented
12	#10617132	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₃×AGL(1,𝔽₅)	C₂²	1	2	yes	—
14	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
16	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
17	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
18	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
19	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
20	C₃×C₅×#117	C₄	1	1	yes	characteristic, complemented
21	C₃×#4072	C₄	1	1	yes	characteristic, complemented
22	C₃×#4038	C₄	1	1	yes	characteristic, complemented
23	C₃×#4038	C₄	1	1	yes	characteristic, complemented
24	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₃×D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₃×D₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₃×#4023	C₄	1	1	yes	characteristic, complemented
29	C₃×#4023	C₄	1	1	yes	characteristic, complemented
30	C₃×#4018	C₄	1	1	yes	characteristic, complemented
31	C₃×#4018	C₄	1	1	yes	characteristic, complemented
32	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
33	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
34	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
35	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
36	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
37	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
38	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
39	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
40	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
41	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
42	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
43	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
44	C₃×#2343	—	5	1	no	maximal, Hall
45	D₅×#117	C₂×C₃	1	1	yes	characteristic
46	#65764	C₂×C₃	1	1	yes	characteristic
47	C₂×(C₂×AGL(1,𝔽₅))⋊C₄	C₂×C₃	1	1	yes	characteristic
48	#65711	C₂×C₃	1	2	yes	complemented
49	#65711	C₂×C₃	1	2	yes	complemented
50	#65699	C₂×C₃	1	2	yes	—
51	C₂²⋊C₄×AGL(1,𝔽₅)	C₂×C₃	1	2	yes	—
52	#65690	C₂×C₃	1	1	yes	characteristic, complemented
53	#65689	C₂×C₃	1	1	yes	characteristic, complemented
54	C₄×C₄⋊AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic, complemented
55	#65686	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×AGL(1,𝔽₅)	—	2	4	no	—
58	C₂²×C₃×AGL(1,𝔽₅)	—	2	4	no	—
59	C₂²×C₃×AGL(1,𝔽₅)	—	4	2	no	—
60	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	2	yes	—
61	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	2	yes	—
62	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	2	yes	—
63	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	2	yes	—
64	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₃×C₄×D₅	—	2	4	no	—
67	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
68	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
69	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
75	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
76	C₃×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
77	C₃×C₄⋊AGL(1,𝔽₅)	—	4	2	no	—
78	C₃×C₄×AGL(1,𝔽₅)	—	2	4	no	—
79	C₃×C₄×AGL(1,𝔽₅)	—	4	2	no	—
80	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic, complemented
81	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic, complemented
82	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic, complemented
85	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic, complemented
86	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
87	C₃×C₂²⋊Dic₅	C₂×C₄	1	1	yes	characteristic
88	C₃×#685	C₂×C₄	1	1	yes	characteristic
89	C₃×#685	C₂×C₄	1	1	yes	characteristic
90	C₃×#685	C₂×C₄	1	1	yes	characteristic
91	C₃×#685	C₂×C₄	1	1	yes	characteristic
92	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
93	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
94	C₃×#683	C₂×C₄	1	1	yes	characteristic, complemented
95	C₃×#683	C₂×C₄	1	1	yes	characteristic, complemented
96	C₃×#683	C₂×C₄	1	1	yes	characteristic, complemented
97	C₃×#683	C₂×C₄	1	1	yes	characteristic, complemented
98	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
99	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
100	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
101	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
102	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
103	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
104	C₂×C₃×#117	—	5	1	no	—
105	C₃×#387	—	5	2	no	—
106	C₃×#387	—	5	2	no	—
107	C₃×#385	—	5	2	no	—
108	C₃×#383	—	5	1	no	—
109	C₃×#382	—	5	1	no	—
110	C₃×#381	—	5	1	no	—
111	C₃×C₄×C₄⋊C₄	—	5	1	no	—
112	C₃×C₄×C₂²⋊C₄	—	5	2	no	—
113	C₃×#376	—	5	1	no	—
114	C₂×C₃×#95	—	5	1	no	—
115	C₂³×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
116	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₂²⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
118	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
119	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
120	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
121	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
122	C₅×#117	C₃×C₄	1	1	yes	characteristic, complemented
123	#4072	C₃×C₄	1	1	yes	characteristic, complemented
124	#4038	C₃×C₄	1	1	yes	characteristic, complemented
125	#4038	C₃×C₄	1	1	yes	characteristic, complemented
126	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	D₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
129	D₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
130	#4023	C₃×C₄	1	1	yes	characteristic, complemented
131	#4023	C₃×C₄	1	1	yes	characteristic, complemented
132	#4018	C₃×C₄	1	1	yes	characteristic, complemented
133	#4018	C₃×C₄	1	1	yes	characteristic, complemented
134	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
135	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
136	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
137	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
138	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
139	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
140	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
141	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
142	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
143	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
144	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
145	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
146	#2343	—	5	1	no	Sylow
147	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₃×D₅	—	2	2	no	—
149	C₂²×C₃×D₅	—	2	1	no	—
150	C₂²×C₃×D₅	—	2	1	no	—
151	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₃×D₅	#41	1	4	yes	—
153	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
154	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
155	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
156	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
157	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
158	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
159	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
160	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
161	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
162	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
163	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
164	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
165	C₂×C₃×AGL(1,𝔽₅)	—	4	8	no	—
166	C₂×C₃×AGL(1,𝔽₅)	#41	1	4	yes	—
167	C₂×C₃×C₄×C₅	—	2	2	no	—
168	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
174	C₂×C₃×Dic₅	—	2	2	no	—
175	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
181	C₃×C₄×D₅	—	2	2	no	—
182	C₃×C₄×D₅	—	2	2	no	—
183	C₃×C₄×D₅	—	2	2	no	—
184	C₃×C₄×D₅	—	2	2	no	—
185	C₃×C₄×D₅	—	2	2	no	—
186	C₃×C₄×D₅	—	2	2	no	—
187	C₃×C₄×D₅	—	2	1	no	—
188	C₃×C₄×D₅	—	2	1	no	—
189	C₃×C₄×D₅	—	2	1	no	—
190	C₃×C₄×D₅	—	2	1	no	—
191	C₂³×C₃×C₄	—	5	1	no	—
192	C₂³×C₃×C₄	—	5	2	no	—
193	C₃×#117	—	5	1	no	—
194	C₃×#117	—	5	1	no	—
195	C₃×#117	—	5	1	no	—
196	C₃×#117	—	5	1	no	—
197	C₃×#117	—	5	1	no	—
198	C₃×#117	—	5	1	no	—
199	C₃×#117	—	5	1	no	—
200	C₃×#117	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
201	C₂×C₃×C₄⋊C₄	—	5	1	no	—
202	C₂×C₃×C₄⋊C₄	—	5	1	no	—
203	C₂×C₃×C₄⋊C₄	—	5	2	no	—
204	C₂×C₃×C₄⋊C₄	—	5	2	no	—
205	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
206	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
207	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
208	C₂×C₃×C₄²	—	5	1	no	—
209	C₂×C₃×C₄²	—	5	1	no	—
210	C₂×C₃×C₄²	—	5	2	no	—
211	C₂×C₃×C₄²	—	5	2	no	—
212	C₃×#95	—	5	1	no	—
213	C₃×#95	—	5	1	no	—
214	C₃×#95	—	5	2	no	—
215	C₃×#95	—	5	1	no	—
216	C₃×#95	—	5	2	no	—
217	C₃×#95	—	5	2	no	—
218	C₃×#95	—	5	2	no	—
219	C₃×#95	—	5	1	no	—
220	C₃×#95	—	5	2	no	—
221	C₃×#95	—	5	2	no	—
222	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
223	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
224	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
225	C₂²×AGL(1,𝔽₅)	—	4	2	no	—
226	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
227	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
228	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
229	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
230	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
231	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
232	C₂×C₄×D₅	—	2	4	no	—
233	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
234	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
235	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
236	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
237	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
238	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
239	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
240	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
241	C₂²⋊AGL(1,𝔽₅)	—	2	4	no	—
242	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
243	C₄⋊AGL(1,𝔽₅)	—	4	2	no	—
244	C₄×AGL(1,𝔽₅)	—	2	4	no	—
245	C₄×AGL(1,𝔽₅)	—	4	2	no	—
246	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic, complemented
247	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic, complemented
248	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
249	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
250	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
251	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
252	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
253	C₂²⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
254	#685	C₂×C₃×C₄	1	1	yes	characteristic
255	#685	C₂×C₃×C₄	1	1	yes	characteristic
256	#685	C₂×C₃×C₄	1	1	yes	characteristic
257	#685	C₂×C₃×C₄	1	1	yes	characteristic
258	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
259	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
260	#683	C₂×C₃×C₄	1	1	yes	characteristic, complemented
261	#683	C₂×C₃×C₄	1	1	yes	characteristic, complemented
262	#683	C₂×C₃×C₄	1	1	yes	characteristic, complemented
263	#683	C₂×C₃×C₄	1	1	yes	characteristic, complemented
264	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
265	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
266	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
267	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
268	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
269	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
270	C₂×#117	—	5	1	no	—
271	#387	—	5	2	no	—
272	#387	—	5	2	no	—
273	#385	—	5	2	no	—
274	#383	—	5	1	no	—
275	#382	—	5	1	no	—
276	#381	—	5	1	no	—
277	C₄×C₄⋊C₄	—	5	1	no	—
278	C₄×C₂²⋊C₄	—	5	2	no	—
279	#376	—	5	1	no	—
280	C₂×#95	—	5	1	no	—
281	C₂²×C₃×C₅	—	2	1	no	—
282	C₂²×C₃×C₅	—	2	1	no	—
283	C₂²×C₃×C₅	#117	1	2	yes	—
284	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
285	C₂×C₃×D₅	—	2	1	no	—
286	C₂×C₃×D₅	—	2	1	no	—
287	C₂×C₃×D₅	—	2	4	no	—
288	C₂×C₃×D₅	—	2	4	no	—
289	C₂×C₃×D₅	#117	1	2	yes	—
290	C₂×C₃×D₅	C₂×#41	1	2	yes	—
291	C₂×C₃×D₅	C₂×#41	1	2	yes	—
292	C₂×C₃×D₅	H(5,𝔽₂)	1	1	yes	characteristic
293	C₂×C₃×D₅	2₋¹⁺⁴	1	1	yes	characteristic
294	C₃×AGL(1,𝔽₅)	—	2	4	no	—
295	C₃×AGL(1,𝔽₅)	—	4	2	no	—
296	C₃×AGL(1,𝔽₅)	—	4	2	no	—
297	C₃×AGL(1,𝔽₅)	—	4	2	no	—
298	C₃×C₄×C₅	—	2	1	no	—
299	C₃×C₄×C₅	—	2	1	no	—
300	C₃×C₄×C₅	—	2	1	no	—
301	C₃×C₄×C₅	—	2	1	no	—
302	C₃×C₄×C₅	—	2	1	no	—
303	C₃×C₄×C₅	—	2	1	no	—
304	C₃×Dic₅	—	2	1	no	—
305	C₃×Dic₅	—	2	1	no	—
306	C₃×Dic₅	—	2	1	no	—
307	C₃×Dic₅	—	2	1	no	—
308	C₃×Dic₅	—	2	1	no	—
309	C₃×Dic₅	—	2	1	no	—
310	C₂⁴×C₃	—	5	1	no	—
311	C₂²×C₃×C₄	—	5	2	no	—
312	C₂²×C₃×C₄	—	5	1	no	—
313	C₂²×C₃×C₄	—	5	1	no	—
314	C₂²×C₃×C₄	—	5	1	no	—
315	C₂²×C₃×C₄	—	5	1	no	—
316	C₂²×C₃×C₄	—	5	1	no	—
317	C₂²×C₃×C₄	—	5	1	no	—
318	C₂²×C₃×C₄	—	5	1	no	—
319	C₂²×C₃×C₄	—	5	1	no	—
320	C₂²×C₃×C₄	—	5	1	no	—
321	C₂²×C₃×C₄	—	5	2	no	—
322	C₂²×C₃×C₄	—	5	2	no	—
323	C₂²×C₃×C₄	—	5	2	no	—
324	C₂²×C₃×C₄	—	10	4	no	—
325	C₂²×C₃×C₄	—	10	4	no	—
326	C₂²×C₃×C₄	—	10	4	no	—
327	C₂²×C₃×C₄	—	20	2	no	—
328	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
329	C₃×C₄⋊C₄	—	5	1	no	—
330	C₃×C₄⋊C₄	—	5	1	no	—
331	C₃×C₄⋊C₄	—	5	1	no	—
332	C₃×C₄⋊C₄	—	5	1	no	—
333	C₃×C₄⋊C₄	—	5	1	no	—
334	C₃×C₄⋊C₄	—	5	1	no	—
335	C₃×C₄⋊C₄	—	10	4	no	—
336	C₃×C₄⋊C₄	—	20	2	no	—
337	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
338	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
339	C₃×C₂²⋊C₄	—	5	1	no	—
340	C₃×C₂²⋊C₄	—	5	1	no	—
341	C₃×C₂²⋊C₄	—	5	1	no	—
342	C₃×C₂²⋊C₄	—	5	1	no	—
343	C₃×C₂²⋊C₄	—	5	1	no	—
344	C₃×C₂²⋊C₄	—	5	1	no	—
345	C₃×C₂²⋊C₄	—	10	4	no	—
346	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
347	C₃×C₂²⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
348	C₃×C₄²	—	5	1	no	—
349	C₃×C₄²	—	5	1	no	—
350	C₃×C₄²	—	5	1	no	—
351	C₃×C₄²	—	5	1	no	—
352	C₃×C₄²	—	5	1	no	—
353	C₃×C₄²	—	5	1	no	—
354	C₃×C₄²	—	10	4	no	—
355	C₃×C₄²	—	20	2	no	—
356	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
357	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
358	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
359	C₂²×D₅	—	2	2	no	—
360	C₂²×D₅	—	2	1	no	—
361	C₂²×D₅	—	2	1	no	—
362	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
363	C₂²×D₅	C₃×#41	1	4	yes	—
364	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
365	C₂×AGL(1,𝔽₅)	—	2	2	no	—
366	C₂×AGL(1,𝔽₅)	—	2	2	no	—
367	C₂×AGL(1,𝔽₅)	—	2	2	no	—
368	C₂×AGL(1,𝔽₅)	—	2	2	no	—
369	C₂×AGL(1,𝔽₅)	—	2	2	no	—
370	C₂×AGL(1,𝔽₅)	—	2	2	no	—
371	C₂×AGL(1,𝔽₅)	—	2	2	no	—
372	C₂×AGL(1,𝔽₅)	—	2	2	no	—
373	C₂×AGL(1,𝔽₅)	—	2	2	no	—
374	C₂×AGL(1,𝔽₅)	—	2	2	no	—
375	C₂×AGL(1,𝔽₅)	—	2	2	no	—
376	C₂×AGL(1,𝔽₅)	—	4	8	no	—
377	C₂×AGL(1,𝔽₅)	C₃×#41	1	4	yes	—
378	C₂×C₄×C₅	—	2	2	no	—
379	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
380	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
381	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
382	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
383	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
384	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
385	C₂×Dic₅	—	2	2	no	—
386	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
387	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
388	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
389	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
390	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
391	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
392	C₄×D₅	—	2	2	no	—
393	C₄×D₅	—	2	2	no	—
394	C₄×D₅	—	2	2	no	—
395	C₄×D₅	—	2	2	no	—
396	C₄×D₅	—	2	2	no	—
397	C₄×D₅	—	2	2	no	—
398	C₄×D₅	—	2	1	no	—
399	C₄×D₅	—	2	1	no	—
400	C₄×D₅	—	2	1	no	—
401	C₄×D₅	—	2	1	no	—
402	C₂³×C₄	—	5	1	no	—
403	C₂³×C₄	—	5	2	no	—
404	#117	—	5	1	no	—
405	#117	—	5	1	no	—
406	#117	—	5	1	no	—
407	#117	—	5	1	no	—
408	#117	—	5	1	no	—
409	#117	—	5	1	no	—
410	#117	—	5	1	no	—
411	#117	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
412	C₂×C₄⋊C₄	—	5	1	no	—
413	C₂×C₄⋊C₄	—	5	1	no	—
414	C₂×C₄⋊C₄	—	5	2	no	—
415	C₂×C₄⋊C₄	—	5	2	no	—
416	C₂×C₂²⋊C₄	—	5	1	no	—
417	C₂×C₂²⋊C₄	—	5	1	no	—
418	C₂×C₂²⋊C₄	—	5	2	no	—
419	C₂×C₄²	—	5	1	no	—
420	C₂×C₄²	—	5	1	no	—
421	C₂×C₄²	—	5	2	no	—
422	C₂×C₄²	—	5	2	no	—
423	#95	—	5	1	no	—
424	#95	—	5	1	no	—
425	#95	—	5	2	no	—
426	#95	—	5	1	no	—
427	#95	—	5	2	no	—
428	#95	—	5	2	no	—
429	#95	—	5	2	no	—
430	#95	—	5	1	no	—
431	#95	—	5	2	no	—
432	#95	—	5	2	no	—
433	C₂×C₃×C₅	—	2	2	no	—
434	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
435	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
436	C₂×C₃×C₅	#520	1	1	yes	characteristic
437	C₃×D₅	—	2	2	no	—
438	C₃×D₅	#551	1	2	yes	—
439	C₃×D₅	#552	1	2	yes	—
440	C₂³×C₃	—	5	1	no	—
441	C₂³×C₃	—	5	4	no	—
442	C₂³×C₃	—	5	1	no	—
443	C₂³×C₃	—	10	2	no	—
444	C₂³×C₃	—	10	1	no	—
445	C₂³×C₃	—	10	1	no	—
446	C₂³×C₃	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
447	C₂×C₃×C₄	—	2	2	no	—
448	C₂×C₃×C₄	—	5	4	no	—
449	C₂×C₃×C₄	—	5	1	no	—
450	C₂×C₃×C₄	—	5	1	no	—
451	C₂×C₃×C₄	—	5	1	no	—
452	C₂×C₃×C₄	—	5	1	no	—
453	C₂×C₃×C₄	—	5	1	no	—
454	C₂×C₃×C₄	—	5	1	no	—
455	C₂×C₃×C₄	—	10	2	no	—
456	C₂×C₃×C₄	—	10	1	no	—
457	C₂×C₃×C₄	—	10	2	no	—
458	C₂×C₃×C₄	—	10	1	no	—
459	C₂×C₃×C₄	—	10	1	no	—
460	C₂×C₃×C₄	—	10	1	no	—
461	C₂×C₃×C₄	—	10	2	no	—
462	C₂×C₃×C₄	—	10	2	no	—
463	C₂×C₃×C₄	—	10	2	no	—
464	C₂×C₃×C₄	—	10	2	no	—
465	C₂×C₃×C₄	—	10	2	no	—
466	C₂×C₃×C₄	—	10	2	no	—
467	C₂×C₃×C₄	—	10	2	no	—
468	C₂×C₃×C₄	—	10	2	no	—
469	C₂×C₃×C₄	—	10	2	no	—
470	C₂×C₃×C₄	—	10	2	no	—
471	C₂×C₃×C₄	—	10	2	no	—
472	C₂×C₃×C₄	—	10	2	no	—
473	C₂×C₃×C₄	—	10	2	no	—
474	C₂×C₃×C₄	—	10	2	no	—
475	C₂×C₃×C₄	—	10	2	no	—
476	C₂×C₃×C₄	—	10	2	no	—
477	C₂×C₃×C₄	—	20	8	no	—
478	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
479	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
480	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
481	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
482	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
483	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
484	C₂²×C₅	—	2	1	no	—
485	C₂²×C₅	—	2	1	no	—
486	C₂²×C₅	C₃×#117	1	2	yes	—
487	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
488	C₂×D₅	—	2	1	no	—
489	C₂×D₅	—	2	1	no	—
490	C₂×D₅	—	2	4	no	—
491	C₂×D₅	—	2	4	no	—
492	C₂×D₅	C₃×#117	1	2	yes	—
493	C₂×D₅	C₂×C₃×#41	1	2	yes	—
494	C₂×D₅	C₂×C₃×#41	1	2	yes	—
495	C₂×D₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
496	C₂×D₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
497	AGL(1,𝔽₅)	—	2	4	no	—
498	AGL(1,𝔽₅)	—	4	2	no	—
499	AGL(1,𝔽₅)	—	4	2	no	—
500	AGL(1,𝔽₅)	—	4	2	no	—
501	C₄×C₅	—	2	1	no	—
502	C₄×C₅	—	2	1	no	—
503	C₄×C₅	—	2	1	no	—
504	C₄×C₅	—	2	1	no	—
505	C₄×C₅	—	2	1	no	—
506	C₄×C₅	—	2	1	no	—
507	Dic₅	—	2	1	no	—
508	Dic₅	—	2	1	no	—
509	Dic₅	—	2	1	no	—
510	Dic₅	—	2	1	no	—
511	Dic₅	—	2	1	no	—
512	Dic₅	—	2	1	no	—
513	C₂⁴	—	5	1	no	—
514	C₂²×C₄	—	5	2	no	—
515	C₂²×C₄	—	5	1	no	—
516	C₂²×C₄	—	5	1	no	—
517	C₂²×C₄	—	5	1	no	—
518	C₂²×C₄	—	5	1	no	—
519	C₂²×C₄	—	5	1	no	—
520	C₂²×C₄	—	5	1	no	—
521	C₂²×C₄	—	5	1	no	—
522	C₂²×C₄	—	5	1	no	—
523	C₂²×C₄	—	5	1	no	—
524	C₂²×C₄	—	5	2	no	—
525	C₂²×C₄	—	5	2	no	—
526	C₂²×C₄	—	5	2	no	—
527	C₂²×C₄	—	10	4	no	—
528	C₂²×C₄	—	10	4	no	—
529	C₂²×C₄	—	10	4	no	—
530	C₂²×C₄	—	20	2	no	—
531	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
532	C₄⋊C₄	—	5	1	no	—
533	C₄⋊C₄	—	5	1	no	—
534	C₄⋊C₄	—	5	1	no	—
535	C₄⋊C₄	—	5	1	no	—
536	C₄⋊C₄	—	5	1	no	—
537	C₄⋊C₄	—	5	1	no	—
538	C₄⋊C₄	—	10	4	no	—
539	C₄⋊C₄	—	20	2	no	—
540	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
541	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
542	C₂²⋊C₄	—	5	1	no	—
543	C₂²⋊C₄	—	5	1	no	—
544	C₂²⋊C₄	—	5	1	no	—
545	C₂²⋊C₄	—	5	1	no	—
546	C₂²⋊C₄	—	5	1	no	—
547	C₂²⋊C₄	—	5	1	no	—
548	C₂²⋊C₄	—	10	4	no	—
549	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
550	C₂²⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
551	C₄²	—	5	1	no	—
552	C₄²	—	5	1	no	—
553	C₄²	—	5	1	no	—
554	C₄²	—	5	1	no	—
555	C₄²	—	5	1	no	—
556	C₄²	—	5	1	no	—
557	C₄²	—	10	4	no	—
558	C₄²	—	20	2	no	—
559	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
560	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
561	C₃×C₅	#2343	1	1	yes	characteristic, complemented, Hall
562	C₂²×C₃	—	2	1	no	—
563	C₂²×C₃	—	2	1	no	—
564	C₂²×C₃	—	5	2	no	—
565	C₂²×C₃	—	5	2	no	—
566	C₂²×C₃	—	5	1	no	—
567	C₂²×C₃	—	5	1	no	—
568	C₂²×C₃	—	5	2	no	—
569	C₂²×C₃	—	10	4	no	—
570	C₂²×C₃	—	10	4	no	—
571	C₂²×C₃	—	10	1	no	—
572	C₂²×C₃	—	10	1	no	—
573	C₂²×C₃	#4130	1	2	yes	—
574	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
575	C₃×C₄	—	2	1	no	—
576	C₃×C₄	—	2	1	no	—
577	C₃×C₄	—	2	1	no	—
578	C₃×C₄	—	2	1	no	—
579	C₃×C₄	—	2	1	no	—
580	C₃×C₄	—	2	1	no	—
581	C₃×C₄	—	10	4	no	—
582	C₃×C₄	—	10	1	no	—
583	C₃×C₄	—	10	1	no	—
584	C₃×C₄	—	10	1	no	—
585	C₃×C₄	—	10	1	no	—
586	C₃×C₄	—	10	1	no	—
587	C₃×C₄	—	10	1	no	—
588	C₃×C₄	—	20	2	no	—
589	C₃×C₄	—	20	2	no	—
590	C₃×C₄	—	20	2	no	—
591	C₂×C₅	—	2	2	no	—
592	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
593	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
594	C₂×C₅	C₃×#520	1	1	yes	characteristic
595	D₅	—	2	2	no	—
596	D₅	C₃×#551	1	2	yes	—
597	D₅	C₃×#552	1	2	yes	—
598	C₂³	—	5	1	no	—
599	C₂³	—	5	4	no	—
600	C₂³	—	5	1	no	—
601	C₂³	—	10	2	no	—
602	C₂³	—	10	1	no	—
603	C₂³	—	10	1	no	—
604	C₂³	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	5	4	no	—
607	C₂×C₄	—	5	1	no	—
608	C₂×C₄	—	5	1	no	—
609	C₂×C₄	—	5	1	no	—
610	C₂×C₄	—	5	1	no	—
611	C₂×C₄	—	5	1	no	—
612	C₂×C₄	—	5	1	no	—
613	C₂×C₄	—	10	2	no	—
614	C₂×C₄	—	10	1	no	—
615	C₂×C₄	—	10	2	no	—
616	C₂×C₄	—	10	1	no	—
617	C₂×C₄	—	10	2	no	—
618	C₂×C₄	—	10	2	no	—
619	C₂×C₄	—	10	2	no	—
620	C₂×C₄	—	10	2	no	—
621	C₂×C₄	—	10	1	no	—
622	C₂×C₄	—	10	1	no	—
623	C₂×C₄	—	10	2	no	—
624	C₂×C₄	—	10	2	no	—
625	C₂×C₄	—	10	2	no	—
626	C₂×C₄	—	10	2	no	—
627	C₂×C₄	—	10	2	no	—
628	C₂×C₄	—	10	2	no	—
629	C₂×C₄	—	10	2	no	—
630	C₂×C₄	—	10	2	no	—
631	C₂×C₄	—	10	2	no	—
632	C₂×C₄	—	10	2	no	—
633	C₂×C₄	—	10	2	no	—
634	C₂×C₄	—	10	2	no	—
635	C₂×C₄	—	20	8	no	—
636	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
637	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
638	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
639	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
640	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
641	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
642	C₂×C₃	—	2	2	no	—
643	C₂×C₃	—	5	2	no	—
644	C₂×C₃	—	5	2	no	—
645	C₂×C₃	—	10	2	no	—
646	C₂×C₃	C₂×#4130	1	1	yes	characteristic
647	C₂×C₃	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
648	C₂×C₃	#66266	1	1	yes	characteristic
649	C₅	C₃×#2343	1	1	yes	characteristic, complemented, Sylow
650	C₂²	—	2	1	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	5	2	no	—
653	C₂²	—	5	2	no	—
654	C₂²	—	5	1	no	—
655	C₂²	—	5	1	no	—
656	C₂²	—	5	2	no	—
657	C₂²	—	10	4	no	—
658	C₂²	—	10	4	no	—
659	C₂²	—	10	1	no	—
660	C₂²	—	10	1	no	—
661	C₂²	C₃×#4130	1	2	yes	—
662	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	1	no	—
667	C₄	—	2	1	no	—
668	C₄	—	2	1	no	—
669	C₄	—	10	4	no	—
670	C₄	—	10	1	no	—
671	C₄	—	10	1	no	—
672	C₄	—	10	1	no	—
673	C₄	—	10	1	no	—
674	C₄	—	10	1	no	—
675	C₄	—	10	1	no	—
676	C₄	—	20	2	no	—
677	C₄	—	20	2	no	—
678	C₄	—	20	2	no	—
679	C₃	#10617132	1	1	yes	characteristic, direct product factor, Sylow
680	C₂	—	2	2	no	—
681	C₂	—	5	2	no	—
682	C₂	—	5	2	no	—
683	C₂	—	10	2	no	—
684	C₂	C₂×C₃×#4130	1	1	yes	characteristic
685	C₂	C₃×#41×AGL(1,𝔽₅)	1	1	yes	characteristic
686	C₂	C₃×#66266	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂²	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×#117	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₃×D₅	C₂³
cosocle	C₂²×D₅	C₂⁴×C₃
hypercenter	C₃×#117	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2343
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117

Complements

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

N	H ≅ G/N	type
4. C₃×#65711	C₂	semidirect
5. C₃×#65711	C₂	semidirect
8. C₃×#65690	C₂	semidirect
9. C₃×#65689	C₂	semidirect
10. C₃×C₄×C₄⋊AGL(1,𝔽₅)	C₂	semidirect
11. C₃×#65686	C₂	semidirect
12. #10617132	C₃	direct (N × H)
20. C₃×C₅×#117	C₄	semidirect
21. C₃×#4072	C₄	semidirect
22. C₃×#4038	C₄	semidirect
23. C₃×#4038	C₄	semidirect
28. C₃×#4023	C₄	semidirect
29. C₃×#4023	C₄	semidirect
30. C₃×#4018	C₄	semidirect
31. C₃×#4018	C₄	semidirect
48. #65711	C₂×C₃	semidirect
49. #65711	C₂×C₃	semidirect
52. #65690	C₂×C₃	semidirect
53. #65689	C₂×C₃	semidirect
54. C₄×C₄⋊AGL(1,𝔽₅)	C₂×C₃	semidirect
55. #65686	C₂×C₃	semidirect
80. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
81. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
84. C₃×C₄²×C₅	C₂×C₄	semidirect
85. C₃×C₄²×C₅	C₂×C₄	semidirect
92. C₃×C₄⋊Dic₅	C₂×C₄	semidirect
93. C₃×C₄⋊Dic₅	C₂×C₄	semidirect
94. C₃×#683	C₂×C₄	semidirect
95. C₃×#683	C₂×C₄	semidirect
96. C₃×#683	C₂×C₄	semidirect
97. C₃×#683	C₂×C₄	semidirect
98. C₃×C₄×Dic₅	C₂×C₄	semidirect
99. C₃×C₄×Dic₅	C₂×C₄	semidirect
100. C₃×C₄×Dic₅	C₂×C₄	semidirect
101. C₃×C₄×Dic₅	C₂×C₄	semidirect
102. C₃×C₄×Dic₅	C₂×C₄	semidirect
103. C₃×C₄×Dic₅	C₂×C₄	semidirect
122. C₅×#117	C₃×C₄	semidirect
123. #4072	C₃×C₄	semidirect
124. #4038	C₃×C₄	semidirect
125. #4038	C₃×C₄	semidirect
130. #4023	C₃×C₄	semidirect
131. #4023	C₃×C₄	semidirect
132. #4018	C₃×C₄	semidirect
133. #4018	C₃×C₄	semidirect
200. C₃×#117	AGL(1,𝔽₅)	semidirect
246. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
247. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
250. C₄²×C₅	C₂×C₃×C₄	semidirect
251. C₄²×C₅	C₂×C₃×C₄	semidirect
258. C₄⋊Dic₅	C₂×C₃×C₄	semidirect
259. C₄⋊Dic₅	C₂×C₃×C₄	semidirect
260. #683	C₂×C₃×C₄	semidirect
261. #683	C₂×C₃×C₄	semidirect
262. #683	C₂×C₃×C₄	semidirect
263. #683	C₂×C₃×C₄	semidirect
264. C₄×Dic₅	C₂×C₃×C₄	semidirect
265. C₄×Dic₅	C₂×C₃×C₄	semidirect
266. C₄×Dic₅	C₂×C₃×C₄	semidirect
267. C₄×Dic₅	C₂×C₃×C₄	semidirect
268. C₄×Dic₅	C₂×C₃×C₄	semidirect
269. C₄×Dic₅	C₂×C₃×C₄	semidirect
337. C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	semidirect
338. C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	semidirect
356. C₃×C₄²	C₂×AGL(1,𝔽₅)	semidirect
357. C₃×C₄²	C₂×AGL(1,𝔽₅)	semidirect
411. #117	C₃×AGL(1,𝔽₅)	semidirect
540. C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	semidirect
541. C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	semidirect
559. C₄²	C₂×C₃×AGL(1,𝔽₅)	semidirect
560. C₄²	C₂×C₃×AGL(1,𝔽₅)	semidirect
561. C₃×C₅	#2343	semidirect
649. C₅	C₃×#2343	semidirect
679. C₃	#10617132	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×D₅×#117	2
C₃×#65764	2
C₂×C₃×(C₂×AGL(1,𝔽₅))⋊C₄	2
C₃×#65711	2
C₃×#65699	2
C₃×C₂²⋊C₄×AGL(1,𝔽₅)	2
C₃×#65690	2
C₃×#65689	2
C₃×C₄×C₄⋊AGL(1,𝔽₅)	2
C₃×#65686	2
#10617132	3
C₃×#2343	5

Subgroups — C3×#10617132 #14326422

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617132 #14326422