Subgroups — C₃×#10617209 #14320991

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 472 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×#65712	C₂	1	2	yes	maximal
4	C₃×#65711	C₂	1	4	yes	maximal
5	C₃×C₄×C₄⋊AGL(1,𝔽₅)	C₂	1	2	yes	maximal
6	C₃×C₄×C₄⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
7	C₃×#65686	C₂	1	2	yes	maximal
8	C₃×C₄²×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
9	#10617209	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	4	yes	—
12	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	2	yes	—
13	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄×AGL(1,𝔽₅)	C₂²	1	2	yes	—
15	C₂×C₃×C₄×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	1	yes	characteristic
18	C₃×C₄×C₅×Q₈	C₄	1	1	yes	characteristic, complemented
19	C₃×Q₈×Dic₅	C₄	1	1	yes	characteristic, complemented
20	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
21	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₃×#4033	C₄	1	2	yes	complemented
23	C₃×#4033	C₄	1	1	yes	characteristic, complemented
24	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
25	C₃×C₄²×D₅	C₂²	1	2	yes	—
26	C₃×C₄×Dic₁₀	C₄	1	1	yes	characteristic, complemented
27	C₃×C₄×Dic₁₀	C₄	1	2	yes	complemented
28	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	4	yes	—
29	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	4	yes	—
30	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	2	yes	—
31	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	4	yes	—
32	C₃×#2295	—	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	#65712	C₂×C₃	1	2	yes	—
36	#65711	C₂×C₃	1	4	yes	—
37	C₄×C₄⋊AGL(1,𝔽₅)	C₂×C₃	1	2	yes	—
38	C₄×C₄⋊AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic
39	#65686	C₂×C₃	1	2	yes	—
40	C₄²×AGL(1,𝔽₅)	C₂×C₃	1	1	yes	characteristic
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	4	no	—
46	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
47	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
48	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
49	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
50	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
51	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
52	C₂×C₃×Dic₁₀	C₂×C₄	1	2	yes	—
53	C₃×C₄⋊AGL(1,𝔽₅)	—	2	8	no	—
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	4	no	—
57	C₃×C₄×AGL(1,𝔽₅)	—	2	2	no	—
58	C₃×C₄×AGL(1,𝔽₅)	—	2	4	no	—
59	C₃×C₄×AGL(1,𝔽₅)	Q₈	1	4	yes	complemented
60	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
61	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
63	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
64	C₃×C₄⋊Dic₅	C₂×C₄	1	2	yes	—
65	C₃×C₄⋊Dic₅	C₂×C₄	1	1	yes	characteristic
66	C₃×#683	C₂×C₄	1	2	yes	—
67	C₃×#683	C₂×C₄	1	2	yes	—
68	C₃×#683	C₂×C₄	1	2	yes	—
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	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
74	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
75	C₂×C₃×C₄×Q₈	—	5	1	no	—
76	C₃×#391	—	5	2	no	—
77	C₃×#389	—	5	2	no	—
78	C₃×#387	—	5	4	no	—
79	C₃×C₄×C₄⋊C₄	—	5	1	no	—
80	C₃×C₄×C₄⋊C₄	—	5	2	no	—
81	C₃×#376	—	5	2	no	—
82	C₃×C₄³	—	5	1	no	—
83	C₂×Q₈×D₅	C₂²×C₃	1	1	yes	characteristic
84	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	—
85	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
86	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
88	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
89	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	—
90	C₂×C₄×AGL(1,𝔽₅)	C₂²×C₃	1	1	yes	characteristic
91	C₄×C₅×Q₈	C₃×C₄	1	1	yes	characteristic, complemented
92	Q₈×Dic₅	C₃×C₄	1	1	yes	characteristic, complemented
93	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
94	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
95	#4033	C₃×C₄	1	1	yes	characteristic, complemented
96	#4033	C₃×C₄	1	2	yes	complemented
97	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
98	C₄²×D₅	C₂²×C₃	1	2	yes	—
99	C₄×Dic₁₀	C₃×C₄	1	1	yes	characteristic, complemented
100	C₄×Dic₁₀	C₃×C₄	1	2	yes	complemented
101	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	4	yes	—
102	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	4	yes	—
103	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	2	yes	—
104	(C₂×AGL(1,𝔽₅))⋊C₄	C₂²×C₃	1	4	yes	—
105	#2295	—	5	1	no	Sylow
106	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
107	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
108	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
109	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
110	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
111	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
112	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
113	C₂×C₃×AGL(1,𝔽₅)	—	2	4	no	—
114	C₂×C₃×AGL(1,𝔽₅)	C₂×Q₈	1	4	yes	—
115	C₂×C₃×AGL(1,𝔽₅)	#41	1	4	yes	—
116	C₃×C₅×Q₈	—	2	2	no	—
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	2	yes	—
120	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
125	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
127	C₃×C₄×D₅	—	2	2	no	—
128	C₃×C₄×D₅	—	2	4	no	—
129	C₃×C₄×D₅	—	2	4	no	—
130	C₃×C₄×D₅	C₂×Q₈	1	2	yes	—
131	C₃×C₄×D₅	#41	1	4	yes	—
132	C₃×C₄×D₅	#41	1	2	yes	—
133	C₃×Dic₁₀	—	2	2	no	—
134	C₃×Dic₁₀	—	2	4	no	—
135	C₂²×C₃×Q₈	—	5	1	no	—
136	C₃×C₄×Q₈	—	5	1	no	—
137	C₃×C₄×Q₈	—	5	2	no	—
138	C₃×C₄×Q₈	—	5	1	no	—
139	C₃×C₄×Q₈	—	5	2	no	—
140	C₃×C₄×Q₈	—	5	1	no	—
141	C₃×C₄×Q₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
142	C₂×C₃×C₄⋊C₄	—	5	2	no	—
143	C₂×C₃×C₄⋊C₄	—	5	1	no	—
144	C₂×C₃×C₄⋊C₄	—	5	4	no	—
145	C₂×C₃×C₄⋊C₄	—	5	2	no	—
146	C₂×C₃×C₄²	—	5	1	no	—
147	C₂×C₃×C₄²	—	5	1	no	—
148	C₂×C₃×C₄²	—	5	2	no	—
149	C₂×C₃×C₄²	—	5	1	no	—
150	C₂×C₃×C₄²	—	5	2	no	—
151	C₂×C₃×C₄²	—	5	2	no	—
152	C₂×C₃×C₄²	—	5	2	no	—
153	C₃×#95	—	5	4	no	—
154	C₃×#95	—	5	4	no	—
155	C₃×#95	—	5	2	no	—
156	C₃×#95	—	5	4	no	—
157	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	4	yes	—
158	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
159	C₂²×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
160	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
161	Q₈×D₅	—	2	4	no	—
162	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
163	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
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	8	no	—
170	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
171	C₄×AGL(1,𝔽₅)	—	2	4	no	—
172	C₄×AGL(1,𝔽₅)	—	2	4	no	—
173	C₄×AGL(1,𝔽₅)	—	2	2	no	—
174	C₄×AGL(1,𝔽₅)	—	2	4	no	—
175	C₄×AGL(1,𝔽₅)	C₃×Q₈	1	4	yes	complemented
176	C₅×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
177	C₅×C₄⋊C₄	C₂×C₃×C₄	1	1	yes	characteristic
178	C₄²×C₅	C₂×C₃×C₄	1	2	yes	—
179	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
180	C₄⋊Dic₅	C₂×C₃×C₄	1	2	yes	—
181	C₄⋊Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
182	#683	C₂×C₃×C₄	1	2	yes	—
183	#683	C₂×C₃×C₄	1	2	yes	—
184	#683	C₂×C₃×C₄	1	2	yes	—
185	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
186	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
187	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
188	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
189	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
190	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
191	C₂×C₄×Q₈	—	5	1	no	—
192	#391	—	5	2	no	—
193	#389	—	5	2	no	—
194	#387	—	5	4	no	—
195	C₄×C₄⋊C₄	—	5	1	no	—
196	C₄×C₄⋊C₄	—	5	2	no	—
197	#376	—	5	2	no	—
198	C₄³	—	5	1	no	—
199	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₃×D₅	C₂²×Q₈	1	1	yes	characteristic
201	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
202	C₂×C₃×D₅	C₂×#41	1	2	yes	—
203	C₂×C₃×D₅	C₂×#41	1	2	yes	—
204	C₃×AGL(1,𝔽₅)	—	2	4	no	—
205	C₃×AGL(1,𝔽₅)	—	2	4	no	—
206	C₃×AGL(1,𝔽₅)	—	4	4	no	—
207	C₃×C₄×C₅	—	2	2	no	—
208	C₃×C₄×C₅	—	2	1	no	—
209	C₃×C₄×C₅	—	2	2	no	—
210	C₃×C₄×C₅	#117	1	2	yes	—
211	C₃×C₄×C₅	C₄×Q₈	1	2	yes	—
212	C₃×Dic₅	—	2	2	no	—
213	C₃×Dic₅	—	2	1	no	—
214	C₃×Dic₅	—	2	2	no	—
215	C₃×Dic₅	#117	1	2	yes	—
216	C₃×Dic₅	C₄×Q₈	1	2	yes	—
217	C₂×C₃×Q₈	—	5	2	no	—
218	C₂×C₃×Q₈	—	5	1	no	—
219	C₂×C₃×Q₈	—	10	4	no	—
220	C₂×C₃×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
221	C₂²×C₃×C₄	—	5	1	no	—
222	C₂²×C₃×C₄	—	5	1	no	—
223	C₂²×C₃×C₄	—	5	2	no	—
224	C₂²×C₃×C₄	—	5	2	no	—
225	C₂²×C₃×C₄	—	5	2	no	—
226	C₂²×C₃×C₄	—	5	1	no	—
227	C₂²×C₃×C₄	—	5	2	no	—
228	C₂²×C₃×C₄	—	5	4	no	—
229	C₃×C₄⋊C₄	—	5	2	no	—
230	C₃×C₄⋊C₄	—	5	2	no	—
231	C₃×C₄⋊C₄	—	5	2	no	—
232	C₃×C₄⋊C₄	—	5	2	no	—
233	C₃×C₄⋊C₄	—	5	1	no	—
234	C₃×C₄⋊C₄	—	10	4	no	—
235	C₃×C₄⋊C₄	—	10	8	no	—
236	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
237	C₃×C₄⋊C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
238	C₃×C₄²	—	5	4	no	—
239	C₃×C₄²	—	5	1	no	—
240	C₃×C₄²	—	5	2	no	—
241	C₃×C₄²	—	5	1	no	—
242	C₃×C₄²	—	5	2	no	—
243	C₃×C₄²	—	5	1	no	—
244	C₃×C₄²	—	5	2	no	—
245	C₃×C₄²	—	10	4	no	—
246	C₃×C₄²	—	10	2	no	—
247	C₃×C₄²	—	10	4	no	—
248	C₃×C₄²	—	10	4	no	—
249	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	2	yes	—
250	C₃×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
251	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
252	C₂×AGL(1,𝔽₅)	—	2	2	no	—
253	C₂×AGL(1,𝔽₅)	—	2	2	no	—
254	C₂×AGL(1,𝔽₅)	—	2	2	no	—
255	C₂×AGL(1,𝔽₅)	—	2	2	no	—
256	C₂×AGL(1,𝔽₅)	—	2	4	no	—
257	C₂×AGL(1,𝔽₅)	—	2	4	no	—
258	C₂×AGL(1,𝔽₅)	—	2	4	no	—
259	C₂×AGL(1,𝔽₅)	C₂×C₃×Q₈	1	4	yes	—
260	C₂×AGL(1,𝔽₅)	C₃×#41	1	4	yes	—
261	C₅×Q₈	—	2	2	no	—
262	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
264	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
265	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
267	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
268	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
269	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
270	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
271	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
272	C₄×D₅	—	2	2	no	—
273	C₄×D₅	—	2	4	no	—
274	C₄×D₅	—	2	4	no	—
275	C₄×D₅	C₂×C₃×Q₈	1	2	yes	—
276	C₄×D₅	C₃×#41	1	4	yes	—
277	C₄×D₅	C₃×#41	1	2	yes	—
278	Dic₁₀	—	2	2	no	—
279	Dic₁₀	—	2	4	no	—
280	C₂²×Q₈	—	5	1	no	—
281	C₄×Q₈	—	5	1	no	—
282	C₄×Q₈	—	5	2	no	—
283	C₄×Q₈	—	5	1	no	—
284	C₄×Q₈	—	5	2	no	—
285	C₄×Q₈	—	5	1	no	—
286	C₄×Q₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
287	C₂×C₄⋊C₄	—	5	2	no	—
288	C₂×C₄⋊C₄	—	5	1	no	—
289	C₂×C₄⋊C₄	—	5	4	no	—
290	C₂×C₄⋊C₄	—	5	2	no	—
291	C₂×C₄²	—	5	1	no	—
292	C₂×C₄²	—	5	1	no	—
293	C₂×C₄²	—	5	2	no	—
294	C₂×C₄²	—	5	1	no	—
295	C₂×C₄²	—	5	2	no	—
296	C₂×C₄²	—	5	2	no	—
297	C₂×C₄²	—	5	2	no	—
298	#95	—	5	4	no	—
299	#95	—	5	4	no	—
300	#95	—	5	2	no	—
301	#95	—	5	4	no	—
302	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
303	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
304	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
305	C₃×D₅	#529	1	2	yes	—
306	C₃×D₅	#533	1	2	yes	—
307	C₂³×C₃	—	5	1	no	—
308	C₃×Q₈	—	2	2	no	—
309	C₃×Q₈	—	10	4	no	—
310	C₃×Q₈	—	10	2	no	—
311	C₂×C₃×C₄	—	5	1	no	—
312	C₂×C₃×C₄	—	5	1	no	—
313	C₂×C₃×C₄	—	5	4	no	—
314	C₂×C₃×C₄	—	5	2	no	—
315	C₂×C₃×C₄	—	5	2	no	—
316	C₂×C₃×C₄	—	5	4	no	—
317	C₂×C₃×C₄	—	5	4	no	—
318	C₂×C₃×C₄	—	5	1	no	—
319	C₂×C₃×C₄	—	5	2	no	—
320	C₂×C₃×C₄	—	5	2	no	—
321	C₂×C₃×C₄	—	10	2	no	—
322	C₂×C₃×C₄	—	10	4	no	—
323	C₂×C₃×C₄	—	10	4	no	—
324	C₂×C₃×C₄	—	10	2	no	—
325	C₂×C₃×C₄	—	10	2	no	—
326	C₂×C₃×C₄	—	10	2	no	—
327	C₂×C₃×C₄	—	10	2	no	—
328	C₂×C₃×C₄	—	10	4	no	—
329	C₂×C₃×C₄	—	10	4	no	—
330	C₂×C₃×C₄	—	10	4	no	—
331	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
332	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
333	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
334	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
335	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
336	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
337	C₂×D₅	C₂²×C₃×Q₈	1	1	yes	characteristic
338	C₂×D₅	C₂×C₃×#41	1	1	yes	characteristic
339	C₂×D₅	C₂×C₃×#41	1	2	yes	—
340	C₂×D₅	C₂×C₃×#41	1	2	yes	—
341	AGL(1,𝔽₅)	—	2	4	no	—
342	AGL(1,𝔽₅)	—	2	4	no	—
343	AGL(1,𝔽₅)	—	4	4	no	—
344	C₄×C₅	—	2	2	no	—
345	C₄×C₅	—	2	1	no	—
346	C₄×C₅	—	2	2	no	—
347	C₄×C₅	C₃×#117	1	2	yes	—
348	C₄×C₅	C₃×C₄×Q₈	1	2	yes	—
349	Dic₅	—	2	2	no	—
350	Dic₅	—	2	1	no	—
351	Dic₅	—	2	2	no	—
352	Dic₅	C₃×#117	1	2	yes	—
353	Dic₅	C₃×C₄×Q₈	1	2	yes	—
354	C₂×Q₈	—	5	2	no	—
355	C₂×Q₈	—	5	1	no	—
356	C₂×Q₈	—	10	4	no	—
357	C₂×Q₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
358	C₂²×C₄	—	5	1	no	—
359	C₂²×C₄	—	5	1	no	—
360	C₂²×C₄	—	5	2	no	—
361	C₂²×C₄	—	5	2	no	—
362	C₂²×C₄	—	5	2	no	—
363	C₂²×C₄	—	5	1	no	—
364	C₂²×C₄	—	5	2	no	—
365	C₂²×C₄	—	5	4	no	—
366	C₄⋊C₄	—	5	2	no	—
367	C₄⋊C₄	—	5	2	no	—
368	C₄⋊C₄	—	5	2	no	—
369	C₄⋊C₄	—	5	2	no	—
370	C₄⋊C₄	—	5	1	no	—
371	C₄⋊C₄	—	10	4	no	—
372	C₄⋊C₄	—	10	8	no	—
373	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
374	C₄⋊C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
375	C₄²	—	5	4	no	—
376	C₄²	—	5	1	no	—
377	C₄²	—	5	2	no	—
378	C₄²	—	5	1	no	—
379	C₄²	—	5	2	no	—
380	C₄²	—	5	1	no	—
381	C₄²	—	5	2	no	—
382	C₄²	—	10	4	no	—
383	C₄²	—	10	2	no	—
384	C₄²	—	10	4	no	—
385	C₄²	—	10	4	no	—
386	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
387	C₄²	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
388	C₃×C₅	#2295	1	1	yes	characteristic, complemented, Hall
389	C₂²×C₃	—	5	2	no	—
390	C₂²×C₃	—	5	1	no	—
391	C₂²×C₃	—	5	1	no	—
392	C₂²×C₃	—	5	2	no	—
393	C₂²×C₃	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
394	C₃×C₄	—	2	2	no	—
395	C₃×C₄	—	2	1	no	—
396	C₃×C₄	—	2	2	no	—
397	C₃×C₄	—	5	2	no	—
398	C₃×C₄	—	5	2	no	—
399	C₃×C₄	—	10	4	no	—
400	C₃×C₄	—	10	4	no	—
401	C₃×C₄	—	10	2	no	—
402	C₃×C₄	—	10	1	no	—
403	C₃×C₄	—	10	2	no	—
404	C₃×C₄	—	20	4	no	—
405	C₃×C₄	#4130	1	2	yes	—
406	C₃×C₄	Q₈×AGL(1,𝔽₅)	1	2	yes	—
407	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
408	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
409	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
410	D₅	C₃×#529	1	2	yes	—
411	D₅	C₃×#533	1	2	yes	—
412	C₂³	—	5	1	no	—
413	Q₈	—	2	2	no	—
414	Q₈	—	10	4	no	—
415	Q₈	—	10	2	no	—
416	C₂×C₄	—	5	1	no	—
417	C₂×C₄	—	5	1	no	—
418	C₂×C₄	—	5	4	no	—
419	C₂×C₄	—	5	2	no	—
420	C₂×C₄	—	5	2	no	—
421	C₂×C₄	—	5	4	no	—
422	C₂×C₄	—	5	4	no	—
423	C₂×C₄	—	5	1	no	—
424	C₂×C₄	—	5	2	no	—
425	C₂×C₄	—	5	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	2	no	—
432	C₂×C₄	—	10	2	no	—
433	C₂×C₄	—	10	4	no	—
434	C₂×C₄	—	10	4	no	—
435	C₂×C₄	—	10	4	no	—
436	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
437	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
438	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
439	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
440	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
441	C₂×C₃	—	5	2	no	—
442	C₂×C₃	—	5	2	no	—
443	C₂×C₃	C₂×#4130	1	1	yes	characteristic
444	C₂×C₃	C₂×Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic
445	C₂×C₃	#41×AGL(1,𝔽₅)	1	1	yes	characteristic
446	C₅	C₃×#2295	1	1	yes	characteristic, complemented, Sylow
447	C₂²	—	5	2	no	—
448	C₂²	—	5	1	no	—
449	C₂²	—	5	1	no	—
450	C₂²	—	5	2	no	—
451	C₂²	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	2	no	—
455	C₄	—	5	2	no	—
456	C₄	—	5	2	no	—
457	C₄	—	10	4	no	—
458	C₄	—	10	4	no	—
459	C₄	—	10	2	no	—
460	C₄	—	10	1	no	—
461	C₄	—	10	2	no	—
462	C₄	—	20	4	no	—
463	C₄	C₃×#4130	1	2	yes	—
464	C₄	C₃×Q₈×AGL(1,𝔽₅)	1	2	yes	—
465	C₃	#10617209	1	1	yes	characteristic, direct product factor, Sylow
466	C₂	—	5	2	no	—
467	C₂	—	5	2	no	—
468	C₂	C₂×C₃×#4130	1	1	yes	characteristic
469	C₂	C₂×C₃×Q₈×AGL(1,𝔽₅)	1	1	yes	characteristic
470	C₂	C₃×#41×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×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×#2295
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×Q₈

Complements

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

N	H ≅ G/N	type
9. #10617209	C₃	direct (N × H)
18. C₃×C₄×C₅×Q₈	C₄	semidirect
19. C₃×Q₈×Dic₅	C₄	semidirect
22. C₃×#4033	C₄	semidirect
23. C₃×#4033	C₄	semidirect
26. C₃×C₄×Dic₁₀	C₄	semidirect
27. C₃×C₄×Dic₁₀	C₄	semidirect
59. C₃×C₄×AGL(1,𝔽₅)	Q₈	semidirect
91. C₄×C₅×Q₈	C₃×C₄	semidirect
92. Q₈×Dic₅	C₃×C₄	semidirect
95. #4033	C₃×C₄	semidirect
96. #4033	C₃×C₄	semidirect
99. C₄×Dic₁₀	C₃×C₄	semidirect
100. C₄×Dic₁₀	C₃×C₄	semidirect
141. C₃×C₄×Q₈	AGL(1,𝔽₅)	semidirect
175. C₄×AGL(1,𝔽₅)	C₃×Q₈	semidirect
286. C₄×Q₈	C₃×AGL(1,𝔽₅)	semidirect
388. C₃×C₅	#2295	semidirect
446. C₅	C₃×#2295	semidirect
465. C₃	#10617209	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×#65712	2
C₃×#65711	2
C₃×C₄×C₄⋊AGL(1,𝔽₅)	2
C₃×#65686	2
C₃×C₄²×AGL(1,𝔽₅)	2
#10617209	3
C₃×#2295	5

Subgroups — C3×#10617209 #14320991

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617209 #14320991