Subgroups — C₃×#10617214 #14327900

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×Q₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₃×(C₂×AGL(1,𝔽₅))⋊Q₈	C₂	1	2	yes	maximal
3	C₃×#65711	C₂	1	4	yes	maximal
4	C₃×C₄⋊C₄×AGL(1,𝔽₅)	C₂	1	2	yes	maximal
5	C₃×#65690	C₂	1	2	yes	maximal
6	C₃×#65689	C₂	1	1	yes	maximal, characteristic
7	C₃×C₄×C₄⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
8	C₃×#65686	C₂	1	2	yes	maximal
9	#10617214	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×Q₈×D₅	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
12	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
13	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	4	yes	—
14	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
15	C₃×C₄×C₅×Q₈	C₄	1	1	yes	characteristic, complemented
16	C₃×Q₈×Dic₅	C₄	1	1	yes	characteristic, complemented
17	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₃×#4033	C₄	1	2	yes	complemented
20	C₃×#4033	C₄	1	1	yes	characteristic, complemented
21	C₃×C₄²×D₅	C₂²	1	2	yes	—
22	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
23	C₃×C₄×Dic₁₀	C₄	1	1	yes	characteristic, complemented
24	C₃×C₄×Dic₁₀	C₄	1	2	yes	complemented
25	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
26	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
27	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	4	yes	—
28	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	1	yes	characteristic
29	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
30	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	4	yes	—
31	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	4	yes	—
32	C₃×#2356	—	5	1	no	maximal, Hall
33	C₄×Q₈×D₅	C₂×C₃	1	1	yes	characteristic
34	(C₂×AGL(1,𝔽₅))⋊Q₈	C₂×C₃	1	2	yes	—
35	#65711	C₂×C₃	1	4	yes	—
36	C₄⋊C₄×AGL(1,𝔽₅)	C₂×C₃	1	2	yes	—
37	#65690	C₂×C₃	1	2	yes	—
38	#65689	C₂×C₃	1	1	yes	characteristic
39	C₄×C₄⋊AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic
40	#65686	C₂×C₃	1	2	yes	—
41	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	4	yes	—
42	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	2	yes	—
43	C₂²×C₃×AGL(1,𝔽₅)	C₂³	1	2	yes	—
44	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
45	C₃×Q₈×D₅	—	2	2	no	—
46	C₃×Q₈×D₅	—	2	2	no	—
47	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
48	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
49	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
50	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
52	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
53	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
54	C₃×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
55	C₃×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
56	C₃×C₄×AGL(1,𝔽₅)	—	2	8	no	—
57	C₃×C₄×AGL(1,𝔽₅)	—	2	4	no	—
58	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
61	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
62	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
63	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
64	C₃×#683	C₂×C₄	1	2	yes	—
65	C₃×#683	C₂×C₄	1	2	yes	—
66	C₃×#683	C₂×C₄	1	2	yes	—
67	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
68	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
69	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
70	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
71	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
72	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
73	C₂×C₃×C₄×Q₈	—	5	1	no	—
74	C₃×#391	—	5	2	no	—
75	C₃×#387	—	5	4	no	—
76	C₃×#383	—	5	2	no	—
77	C₃×#382	—	5	1	no	—
78	C₃×C₄×C₄⋊C₄	—	5	1	no	—
79	C₃×C₄×C₄⋊C₄	—	5	2	no	—
80	C₃×#376	—	5	2	no	—
81	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic
82	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
83	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
84	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	—
85	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
86	C₄×C₅×Q₈	C₃×C₄	1	1	yes	characteristic, complemented
87	Q₈×Dic₅	C₃×C₄	1	1	yes	characteristic, complemented
88	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
90	#4033	C₃×C₄	1	1	yes	characteristic, complemented
91	#4033	C₃×C₄	1	2	yes	complemented
92	C₄²×D₅	C₂²×C₃	1	2	yes	—
93	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
94	C₄×Dic₁₀	C₃×C₄	1	1	yes	characteristic, complemented
95	C₄×Dic₁₀	C₃×C₄	1	2	yes	complemented
96	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
97	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
98	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	4	yes	—
99	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	1	yes	characteristic
100	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
101	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	4	yes	—
102	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	4	yes	—
103	#2356	—	5	1	no	Sylow
104	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
105	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
106	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
107	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
108	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
109	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
110	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
111	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
112	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
113	C₂×C₃×AGL(1,𝔽₅)	#41	1	4	yes	—
114	C₃×C₅×Q₈	—	2	2	no	—
115	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
122	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
124	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
125	C₃×C₄×D₅	—	2	4	no	—
126	C₃×C₄×D₅	—	2	2	no	—
127	C₃×C₄×D₅	—	2	2	no	—
128	C₃×C₄×D₅	—	2	2	no	—
129	C₃×C₄×D₅	—	2	2	no	—
130	C₃×C₄×D₅	#41	1	2	yes	—
131	C₃×C₄×D₅	#41	1	2	yes	—
132	C₃×Dic₁₀	—	2	2	no	—
133	C₃×Dic₁₀	—	2	4	no	—
134	C₂²×C₃×Q₈	—	5	1	no	—
135	C₃×C₄×Q₈	—	5	1	no	—
136	C₃×C₄×Q₈	—	5	2	no	—
137	C₃×C₄×Q₈	—	5	1	no	—
138	C₃×C₄×Q₈	—	5	2	no	—
139	C₃×C₄×Q₈	—	5	1	no	—
140	C₃×C₄×Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
141	C₂×C₃×C₄⋊C₄	—	5	1	no	—
142	C₂×C₃×C₄⋊C₄	—	5	2	no	—
143	C₂×C₃×C₄⋊C₄	—	5	2	no	—
144	C₂×C₃×C₄⋊C₄	—	5	2	no	—
145	C₂×C₃×C₄²	—	5	2	no	—
146	C₂×C₃×C₄²	—	5	1	no	—
147	C₂×C₃×C₄²	—	5	4	no	—
148	C₂×C₃×C₄²	—	5	2	no	—
149	C₃×#95	—	5	1	no	—
150	C₃×#95	—	5	2	no	—
151	C₃×#95	—	5	4	no	—
152	C₃×#95	—	5	1	no	—
153	C₃×#95	—	5	4	no	—
154	C₃×#95	—	5	2	no	—
155	C₃×#95	—	5	4	no	—
156	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	4	yes	—
157	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
158	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
159	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
160	Q₈×D₅	—	2	2	no	—
161	Q₈×D₅	—	2	2	no	—
162	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
163	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
164	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
165	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
166	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
167	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
168	C₂×Dic₁₀	C₂×C₃×C₄	1	2	yes	—
169	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
170	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
171	C₄×AGL(1,𝔽₅)	—	2	8	no	—
172	C₄×AGL(1,𝔽₅)	—	2	4	no	—
173	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
174	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
175	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
176	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
177	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
178	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
179	#683	C₂×C₃×C₄	1	2	yes	—
180	#683	C₂×C₃×C₄	1	2	yes	—
181	#683	C₂×C₃×C₄	1	2	yes	—
182	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
183	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
184	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
185	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
186	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
187	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
188	C₂×C₄×Q₈	—	5	1	no	—
189	#391	—	5	2	no	—
190	#387	—	5	4	no	—
191	#383	—	5	2	no	—
192	#382	—	5	1	no	—
193	C₄×C₄⋊C₄	—	5	1	no	—
194	C₄×C₄⋊C₄	—	5	2	no	—
195	#376	—	5	2	no	—
196	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
198	C₂×C₃×D₅	C₂×#41	1	2	yes	—
199	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
200	C₂×C₃×D₅	2₋¹⁺⁴	1	2	yes	—
201	C₃×AGL(1,𝔽₅)	—	2	4	no	—
202	C₃×AGL(1,𝔽₅)	—	4	2	no	—
203	C₃×AGL(1,𝔽₅)	—	4	4	no	—
204	C₃×C₄×C₅	—	2	2	no	—
205	C₃×C₄×C₅	—	2	2	no	—
206	C₃×C₄×C₅	—	2	1	no	—
207	C₃×C₄×C₅	—	2	1	no	—
208	C₃×C₄×C₅	#117	1	2	yes	—
209	C₃×Dic₅	—	2	2	no	—
210	C₃×Dic₅	—	2	2	no	—
211	C₃×Dic₅	—	2	1	no	—
212	C₃×Dic₅	—	2	1	no	—
213	C₃×Dic₅	#117	1	2	yes	—
214	C₂×C₃×Q₈	—	5	2	no	—
215	C₂×C₃×Q₈	—	5	1	no	—
216	C₂×C₃×Q₈	—	10	2	no	—
217	C₂×C₃×Q₈	—	10	2	no	—
218	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
219	C₂²×C₃×C₄	—	5	1	no	—
220	C₂²×C₃×C₄	—	5	2	no	—
221	C₂²×C₃×C₄	—	5	1	no	—
222	C₂²×C₃×C₄	—	5	2	no	—
223	C₂²×C₃×C₄	—	5	2	no	—
224	C₂²×C₃×C₄	—	5	1	no	—
225	C₂²×C₃×C₄	—	5	4	no	—
226	C₂²×C₃×C₄	—	5	2	no	—
227	C₃×C₄⋊C₄	—	5	2	no	—
228	C₃×C₄⋊C₄	—	5	2	no	—
229	C₃×C₄⋊C₄	—	5	2	no	—
230	C₃×C₄⋊C₄	—	5	2	no	—
231	C₃×C₄⋊C₄	—	5	1	no	—
232	C₃×C₄⋊C₄	—	10	4	no	—
233	C₃×C₄⋊C₄	—	10	4	no	—
234	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
235	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
236	C₃×C₄²	—	5	1	no	—
237	C₃×C₄²	—	5	1	no	—
238	C₃×C₄²	—	5	2	no	—
239	C₃×C₄²	—	5	1	no	—
240	C₃×C₄²	—	5	2	no	—
241	C₃×C₄²	—	5	2	no	—
242	C₃×C₄²	—	10	4	no	—
243	C₃×C₄²	—	10	8	no	—
244	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	2	yes	—
245	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
246	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
247	C₂×AGL(1,𝔽₅)	—	2	2	no	—
248	C₂×AGL(1,𝔽₅)	—	2	2	no	—
249	C₂×AGL(1,𝔽₅)	—	2	2	no	—
250	C₂×AGL(1,𝔽₅)	—	2	4	no	—
251	C₂×AGL(1,𝔽₅)	—	2	2	no	—
252	C₂×AGL(1,𝔽₅)	—	2	4	no	—
253	C₂×AGL(1,𝔽₅)	—	2	2	no	—
254	C₂×AGL(1,𝔽₅)	—	2	4	no	—
255	C₂×AGL(1,𝔽₅)	C₃×#41	1	4	yes	—
256	C₅×Q₈	—	2	2	no	—
257	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
259	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
260	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
261	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
262	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
263	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
264	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
265	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
266	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
267	C₄×D₅	—	2	4	no	—
268	C₄×D₅	—	2	2	no	—
269	C₄×D₅	—	2	2	no	—
270	C₄×D₅	—	2	2	no	—
271	C₄×D₅	—	2	2	no	—
272	C₄×D₅	C₃×#41	1	2	yes	—
273	C₄×D₅	C₃×#41	1	2	yes	—
274	Dic₁₀	—	2	2	no	—
275	Dic₁₀	—	2	4	no	—
276	C₂²×Q₈	—	5	1	no	—
277	C₄×Q₈	—	5	1	no	—
278	C₄×Q₈	—	5	2	no	—
279	C₄×Q₈	—	5	1	no	—
280	C₄×Q₈	—	5	2	no	—
281	C₄×Q₈	—	5	1	no	—
282	C₄×Q₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
283	C₂×C₄⋊C₄	—	5	1	no	—
284	C₂×C₄⋊C₄	—	5	2	no	—
285	C₂×C₄⋊C₄	—	5	2	no	—
286	C₂×C₄⋊C₄	—	5	2	no	—
287	C₂×C₄²	—	5	2	no	—
288	C₂×C₄²	—	5	1	no	—
289	C₂×C₄²	—	5	4	no	—
290	C₂×C₄²	—	5	2	no	—
291	#95	—	5	1	no	—
292	#95	—	5	2	no	—
293	#95	—	5	4	no	—
294	#95	—	5	1	no	—
295	#95	—	5	4	no	—
296	#95	—	5	2	no	—
297	#95	—	5	4	no	—
298	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
299	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
300	C₂×C₃×C₅	#519	1	1	yes	characteristic
301	C₃×D₅	#552	1	2	yes	—
302	C₃×D₅	#556	1	2	yes	—
303	C₂³×C₃	—	5	1	no	—
304	C₃×Q₈	—	2	2	no	—
305	C₃×Q₈	—	10	4	no	—
306	C₃×Q₈	—	10	2	no	—
307	C₂×C₃×C₄	—	5	1	no	—
308	C₂×C₃×C₄	—	5	2	no	—
309	C₂×C₃×C₄	—	5	2	no	—
310	C₂×C₃×C₄	—	5	4	no	—
311	C₂×C₃×C₄	—	5	1	no	—
312	C₂×C₃×C₄	—	5	2	no	—
313	C₂×C₃×C₄	—	5	1	no	—
314	C₂×C₃×C₄	—	5	2	no	—
315	C₂×C₃×C₄	—	10	4	no	—
316	C₂×C₃×C₄	—	10	2	no	—
317	C₂×C₃×C₄	—	10	2	no	—
318	C₂×C₃×C₄	—	10	2	no	—
319	C₂×C₃×C₄	—	10	2	no	—
320	C₂×C₃×C₄	—	10	2	no	—
321	C₂×C₃×C₄	—	10	2	no	—
322	C₂×C₃×C₄	—	10	2	no	—
323	C₂×C₃×C₄	—	10	4	no	—
324	C₂×C₃×C₄	—	10	4	no	—
325	C₂×C₃×C₄	—	10	2	no	—
326	C₂×C₃×C₄	—	10	2	no	—
327	C₂×C₃×C₄	—	10	4	no	—
328	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
329	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
330	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
331	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
332	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
333	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
334	C₂×D₅	C₂×C₃×#41	1	1	yes	characteristic
335	C₂×D₅	C₂×C₃×#41	1	2	yes	—
336	C₂×D₅	C₂×C₃×#41	1	1	yes	characteristic
337	C₂×D₅	C₃×2₋¹⁺⁴	1	2	yes	—
338	AGL(1,𝔽₅)	—	2	4	no	—
339	AGL(1,𝔽₅)	—	4	2	no	—
340	AGL(1,𝔽₅)	—	4	4	no	—
341	C₄×C₅	—	2	2	no	—
342	C₄×C₅	—	2	2	no	—
343	C₄×C₅	—	2	1	no	—
344	C₄×C₅	—	2	1	no	—
345	C₄×C₅	C₃×#117	1	2	yes	—
346	Dic₅	—	2	2	no	—
347	Dic₅	—	2	2	no	—
348	Dic₅	—	2	1	no	—
349	Dic₅	—	2	1	no	—
350	Dic₅	C₃×#117	1	2	yes	—
351	C₂×Q₈	—	5	2	no	—
352	C₂×Q₈	—	5	1	no	—
353	C₂×Q₈	—	10	2	no	—
354	C₂×Q₈	—	10	2	no	—
355	C₂×Q₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
356	C₂²×C₄	—	5	1	no	—
357	C₂²×C₄	—	5	2	no	—
358	C₂²×C₄	—	5	1	no	—
359	C₂²×C₄	—	5	2	no	—
360	C₂²×C₄	—	5	2	no	—
361	C₂²×C₄	—	5	1	no	—
362	C₂²×C₄	—	5	4	no	—
363	C₂²×C₄	—	5	2	no	—
364	C₄⋊C₄	—	5	2	no	—
365	C₄⋊C₄	—	5	2	no	—
366	C₄⋊C₄	—	5	2	no	—
367	C₄⋊C₄	—	5	2	no	—
368	C₄⋊C₄	—	5	1	no	—
369	C₄⋊C₄	—	10	4	no	—
370	C₄⋊C₄	—	10	4	no	—
371	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
372	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
373	C₄²	—	5	1	no	—
374	C₄²	—	5	1	no	—
375	C₄²	—	5	2	no	—
376	C₄²	—	5	1	no	—
377	C₄²	—	5	2	no	—
378	C₄²	—	5	2	no	—
379	C₄²	—	10	4	no	—
380	C₄²	—	10	8	no	—
381	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
382	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
383	C₃×C₅	#2356	1	1	yes	characteristic, complemented, Hall
384	C₂²×C₃	—	5	1	no	—
385	C₂²×C₃	—	5	1	no	—
386	C₂²×C₃	—	5	2	no	—
387	C₂²×C₃	—	5	2	no	—
388	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
389	C₃×C₄	—	2	2	no	—
390	C₃×C₄	—	2	1	no	—
391	C₃×C₄	—	2	2	no	—
392	C₃×C₄	—	2	1	no	—
393	C₃×C₄	—	5	2	no	—
394	C₃×C₄	—	10	4	no	—
395	C₃×C₄	—	10	2	no	—
396	C₃×C₄	—	10	1	no	—
397	C₃×C₄	—	10	2	no	—
398	C₃×C₄	—	10	1	no	—
399	C₃×C₄	—	20	2	no	—
400	C₃×C₄	—	20	4	no	—
401	C₃×C₄	#4130	1	2	yes	—
402	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
403	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
404	C₂×C₅	C₃×#519	1	1	yes	characteristic
405	D₅	C₃×#552	1	2	yes	—
406	D₅	C₃×#556	1	2	yes	—
407	C₂³	—	5	1	no	—
408	Q₈	—	2	2	no	—
409	Q₈	—	10	4	no	—
410	Q₈	—	10	2	no	—
411	C₂×C₄	—	5	1	no	—
412	C₂×C₄	—	5	2	no	—
413	C₂×C₄	—	5	2	no	—
414	C₂×C₄	—	5	4	no	—
415	C₂×C₄	—	5	1	no	—
416	C₂×C₄	—	5	2	no	—
417	C₂×C₄	—	5	1	no	—
418	C₂×C₄	—	5	2	no	—
419	C₂×C₄	—	10	4	no	—
420	C₂×C₄	—	10	2	no	—
421	C₂×C₄	—	10	2	no	—
422	C₂×C₄	—	10	2	no	—
423	C₂×C₄	—	10	2	no	—
424	C₂×C₄	—	10	2	no	—
425	C₂×C₄	—	10	2	no	—
426	C₂×C₄	—	10	2	no	—
427	C₂×C₄	—	10	4	no	—
428	C₂×C₄	—	10	4	no	—
429	C₂×C₄	—	10	2	no	—
430	C₂×C₄	—	10	2	no	—
431	C₂×C₄	—	10	4	no	—
432	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
433	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
434	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
435	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
436	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
437	C₂×C₃	—	5	2	no	—
438	C₂×C₃	—	5	2	no	—
439	C₂×C₃	C₂×#4130	1	1	yes	characteristic
440	C₂×C₃	#66262	1	1	yes	characteristic
441	C₂×C₃	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
442	C₅	C₃×#2356	1	1	yes	characteristic, complemented, Sylow
443	C₂²	—	5	1	no	—
444	C₂²	—	5	1	no	—
445	C₂²	—	5	2	no	—
446	C₂²	—	5	2	no	—
447	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
448	C₄	—	2	2	no	—
449	C₄	—	2	1	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	1	no	—
452	C₄	—	5	2	no	—
453	C₄	—	10	4	no	—
454	C₄	—	10	2	no	—
455	C₄	—	10	1	no	—
456	C₄	—	10	2	no	—
457	C₄	—	10	1	no	—
458	C₄	—	20	2	no	—
459	C₄	—	20	4	no	—
460	C₄	C₃×#4130	1	2	yes	—
461	C₃	#10617214	1	1	yes	characteristic, direct product factor, Sylow
462	C₂	—	5	2	no	—
463	C₂	—	5	2	no	—
464	C₂	C₂×C₃×#4130	1	1	yes	characteristic
465	C₂	C₃×#66262	1	1	yes	characteristic
466	C₂	C₃×#41×AGL(1,𝔽₅)	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×C₄×C₅×Q₈	C₄
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂²×C₃×D₅	C₂⁴
cosocle	C₂²×D₅	C₂⁴×C₃
hypercenter	C₃×C₄×Q₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2356
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×Q₈

Complements

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

N	H ≅ G/N	type
9. #10617214	C₃	direct (N × H)
15. C₃×C₄×C₅×Q₈	C₄	semidirect
16. C₃×Q₈×Dic₅	C₄	semidirect
19. C₃×#4033	C₄	semidirect
20. C₃×#4033	C₄	semidirect
23. C₃×C₄×Dic₁₀	C₄	semidirect
24. C₃×C₄×Dic₁₀	C₄	semidirect
86. C₄×C₅×Q₈	C₃×C₄	semidirect
87. Q₈×Dic₅	C₃×C₄	semidirect
90. #4033	C₃×C₄	semidirect
91. #4033	C₃×C₄	semidirect
94. C₄×Dic₁₀	C₃×C₄	semidirect
95. C₄×Dic₁₀	C₃×C₄	semidirect
140. C₃×C₄×Q₈	AGL(1,𝔽₅)	semidirect
282. C₄×Q₈	C₃×AGL(1,𝔽₅)	semidirect
383. C₃×C₅	#2356	semidirect
442. C₅	C₃×#2356	semidirect
461. C₃	#10617214	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×Q₈×D₅	2
C₃×(C₂×AGL(1,𝔽₅))⋊Q₈	2
C₃×#65711	2
C₃×C₄⋊C₄×AGL(1,𝔽₅)	2
C₃×#65690	2
C₃×#65689	2
C₃×C₄×C₄⋊AGL(1,𝔽₅)	2
C₃×#65686	2
#10617214	3
C₃×#2356	5

Subgroups — C3×#10617214 #14327900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617214 #14327900