Subgroups — C₃×#10604723 #14297911

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic
2	C₃×#65765	C₂	1	2	yes	maximal
3	C₂×C₃×#3994	C₂	1	2	yes	maximal, complemented
4	C₃×#64893	C₂	1	2	yes	maximal, complemented
5	#10604723	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	2	no	—
8	C₂×C₃×C₄⋊AGL(1,𝔽₅)	C₂²	1	4	yes	—
9	C₂²×C₃×C₅×C₈	C₄	1	1	yes	characteristic, complemented
10	C₂²×C₃×#168	C₄	1	1	yes	characteristic, complemented
11	C₂×C₃×C₈×D₅	—	2	4	no	—
12	C₂×C₃×C₈×D₅	C₄	1	1	yes	characteristic, complemented
13	C₂×C₃×C₈×D₅	C₄	1	1	yes	characteristic, complemented
14	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
16	C₃×(C₂×AGL(1,𝔽₅))⋊C₄	—	2	2	no	—
17	C₃×#3994	—	2	4	no	—
18	C₃×#1808	—	5	1	no	maximal, Hall
19	C₂²×C₈×D₅	C₂×C₃	1	1	yes	characteristic
20	#65765	C₂×C₃	1	2	yes	—
21	C₂×#3994	C₂×C₃	1	2	yes	complemented
22	#64893	C₂×C₃	1	2	yes	complemented
23	C₂³×C₃×D₅	D₄	1	1	yes	characteristic
24	C₂²×C₃×AGL(1,𝔽₅)	—	2	4	no	—
25	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₃×Dic₅	Q₈	1	1	yes	characteristic
27	C₂×C₃×C₄×D₅	—	2	2	no	—
28	C₂×C₃×C₄×D₅	—	2	2	no	—
29	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
30	C₂×C₃×C₄×D₅	D₄	1	1	yes	characteristic
31	C₂×C₃×C₄×D₅	Q₈	1	1	yes	characteristic
32	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
33	C₃×C₂²⋊AGL(1,𝔽₅)	—	4	4	no	—
34	C₃×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
35	C₃×C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
36	C₂×C₃×C₅×C₈	—	2	2	no	—
37	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
38	C₂×C₃×C₅×C₈	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃×#168	—	2	2	no	—
40	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
41	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
42	C₃×C₈×D₅	—	2	2	no	—
43	C₃×C₈×D₅	—	2	2	no	—
44	C₃×C₈×D₅	—	2	2	no	—
45	C₃×C₈×D₅	D₄	1	4	yes	—
46	C₂³×C₃×C₈	—	5	1	no	—
47	C₂×C₃×#107	—	5	2	no	—
48	C₃×#380	—	5	2	no	—
49	C₃×#340	—	5	2	no	—
50	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
51	C₂×C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
52	C₂×C₄⋊AGL(1,𝔽₅)	C₂²×C₃	1	4	yes	—
53	C₂²×C₅×C₈	C₃×C₄	1	1	yes	characteristic, complemented
54	C₂²×#168	C₃×C₄	1	1	yes	characteristic, complemented
55	C₂×C₈×D₅	—	2	4	no	—
56	C₂×C₈×D₅	C₃×C₄	1	1	yes	characteristic, complemented
57	C₂×C₈×D₅	C₃×C₄	1	1	yes	characteristic, complemented
58	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
59	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
60	(C₂×AGL(1,𝔽₅))⋊C₄	—	2	2	no	—
61	#3994	—	2	4	no	—
62	#1808	—	5	1	no	Sylow
63	C₂³×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
64	C₂²×C₃×D₅	—	2	2	no	—
65	C₂²×C₃×D₅	—	2	2	no	—
66	C₂²×C₃×D₅	C₄⋊C₄	1	1	yes	characteristic
67	C₂²×C₃×D₅	D₈	1	2	yes	—
68	C₂²×C₃×D₅	Q₁₆	1	2	yes	—
69	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
70	C₂×C₃×AGL(1,𝔽₅)	—	4	4	no	—
71	C₂×C₃×AGL(1,𝔽₅)	—	4	4	no	—
72	C₂×C₃×AGL(1,𝔽₅)	—	4	4	no	—
73	C₂×C₃×C₄×C₅	—	2	1	no	—
74	C₂×C₃×C₄×C₅	—	2	1	no	—
75	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
76	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₃×Dic₅	—	2	2	no	—
78	C₂×C₃×Dic₅	C₄⋊C₄	1	1	yes	characteristic
79	C₂×C₃×Dic₅	C₂×Q₈	1	1	yes	characteristic
80	C₃×C₄×D₅	—	2	2	no	—
81	C₃×C₄×D₅	—	2	1	no	—
82	C₃×C₄×D₅	—	2	1	no	—
83	C₃×C₄×D₅	—	2	2	no	—
84	C₃×C₄×D₅	C₂×D₄	1	2	yes	—
85	C₃×C₄×D₅	#41	1	2	yes	—
86	C₃×C₅×C₈	—	2	1	no	—
87	C₃×C₅×C₈	C₂²⋊C₄	1	2	yes	complemented
88	C₃×#168	—	2	1	no	—
89	C₃×#168	C₂²⋊C₄	1	2	yes	complemented
90	C₂³×C₃×C₄	—	5	1	no	—
91	C₂²×C₃×C₈	—	5	1	no	—
92	C₂²×C₃×C₈	—	5	1	no	—
93	C₂²×C₃×C₈	—	5	1	no	—
94	C₂²×C₃×C₈	—	5	1	no	—
95	C₂²×C₃×C₈	—	5	1	no	—
96	C₂²×C₃×C₈	—	10	4	no	—
97	C₂²×C₃×C₈	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
98	C₂×C₃×C₄⋊C₄	—	5	4	no	—
99	C₂×C₃×C₂²⋊C₄	—	10	2	no	—
100	C₃×#107	—	10	4	no	—
101	C₃×#95	—	10	2	no	—
102	C₂³×D₅	C₃×D₄	1	1	yes	characteristic
103	C₂²×AGL(1,𝔽₅)	—	2	4	no	—
104	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
105	C₂²×Dic₅	C₃×Q₈	1	1	yes	characteristic
106	C₂×C₄×D₅	—	2	2	no	—
107	C₂×C₄×D₅	—	2	2	no	—
108	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
109	C₂×C₄×D₅	C₃×D₄	1	1	yes	characteristic
110	C₂×C₄×D₅	C₃×Q₈	1	1	yes	characteristic
111	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
112	C₂²⋊AGL(1,𝔽₅)	—	4	4	no	—
113	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
114	C₄⋊AGL(1,𝔽₅)	—	2	4	no	—
115	C₂×C₅×C₈	—	2	2	no	—
116	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
117	C₂×C₅×C₈	C₂×C₃×C₄	1	1	yes	characteristic
118	C₂×#168	—	2	2	no	—
119	C₂×#168	C₂×C₃×C₄	1	1	yes	characteristic
120	C₂×#168	C₂×C₃×C₄	1	1	yes	characteristic
121	C₈×D₅	—	2	2	no	—
122	C₈×D₅	—	2	2	no	—
123	C₈×D₅	—	2	2	no	—
124	C₈×D₅	C₃×D₄	1	4	yes	—
125	C₂³×C₈	—	5	1	no	—
126	C₂×#107	—	5	2	no	—
127	#380	—	5	2	no	—
128	#340	—	5	2	no	—
129	C₂²×C₃×C₅	—	2	1	no	—
130	C₂²×C₃×C₅	—	2	1	no	—
131	C₂²×C₃×C₅	#107	1	2	yes	complemented
132	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₃×D₅	—	2	1	no	—
134	C₂×C₃×D₅	—	2	1	no	—
135	C₂×C₃×D₅	—	2	4	no	—
136	C₂×C₃×D₅	—	2	4	no	—
137	C₂×C₃×D₅	#107	1	2	yes	complemented
138	C₂×C₃×D₅	#121	1	2	yes	—
139	C₂×C₃×D₅	C₂×D₈	1	1	yes	characteristic
140	C₂×C₃×D₅	C₂×Q₁₆	1	1	yes	characteristic
141	C₂×C₃×D₅	#135	1	2	yes	—
142	C₃×AGL(1,𝔽₅)	—	8	4	no	—
143	C₃×C₄×C₅	—	2	1	no	—
144	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₃×C₄×C₅	#117	1	1	yes	characteristic
146	C₃×Dic₅	—	2	1	no	—
147	C₃×Dic₅	C₂²⋊Q₈	1	2	yes	—
148	C₂⁴×C₃	—	5	1	no	—
149	C₂²×C₃×C₄	—	5	1	no	—
150	C₂²×C₃×C₄	—	5	1	no	—
151	C₂²×C₃×C₄	—	5	1	no	—
152	C₂²×C₃×C₄	—	5	1	no	—
153	C₂²×C₃×C₄	—	5	1	no	—
154	C₂²×C₃×C₄	—	10	2	no	—
155	C₂²×C₃×C₄	—	10	2	no	—
156	C₂²×C₃×C₄	—	10	4	no	—
157	C₂²×C₃×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
158	C₂×C₃×C₈	—	2	2	no	—
159	C₂×C₃×C₈	—	5	1	no	—
160	C₂×C₃×C₈	—	5	4	no	—
161	C₂×C₃×C₈	—	5	1	no	—
162	C₂×C₃×C₈	—	10	2	no	—
163	C₂×C₃×C₈	—	10	2	no	—
164	C₂×C₃×C₈	—	10	2	no	—
165	C₂×C₃×C₈	—	10	2	no	—
166	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
167	C₂×C₃×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
168	C₃×C₄⋊C₄	—	10	4	no	—
169	C₃×C₄⋊C₄	—	10	4	no	—
170	C₃×C₂²⋊C₄	—	20	4	no	—
171	C₂³×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
172	C₂²×D₅	—	2	2	no	—
173	C₂²×D₅	—	2	2	no	—
174	C₂²×D₅	C₃×C₄⋊C₄	1	1	yes	characteristic
175	C₂²×D₅	C₃×D₈	1	2	yes	—
176	C₂²×D₅	C₃×Q₁₆	1	2	yes	—
177	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
178	C₂×AGL(1,𝔽₅)	—	4	4	no	—
179	C₂×AGL(1,𝔽₅)	—	4	4	no	—
180	C₂×AGL(1,𝔽₅)	—	4	4	no	—
181	C₂×C₄×C₅	—	2	1	no	—
182	C₂×C₄×C₅	—	2	1	no	—
183	C₂×C₄×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
185	C₂×Dic₅	—	2	2	no	—
186	C₂×Dic₅	C₃×C₄⋊C₄	1	1	yes	characteristic
187	C₂×Dic₅	C₂×C₃×Q₈	1	1	yes	characteristic
188	C₄×D₅	—	2	2	no	—
189	C₄×D₅	—	2	1	no	—
190	C₄×D₅	—	2	1	no	—
191	C₄×D₅	—	2	2	no	—
192	C₄×D₅	C₂×C₃×D₄	1	2	yes	—
193	C₄×D₅	C₃×#41	1	2	yes	—
194	C₅×C₈	—	2	1	no	—
195	C₅×C₈	C₃×C₂²⋊C₄	1	2	yes	complemented
196	#168	—	2	1	no	—
197	#168	C₃×C₂²⋊C₄	1	2	yes	complemented
198	C₂³×C₄	—	5	1	no	—
199	C₂²×C₈	—	5	1	no	—
200	C₂²×C₈	—	5	1	no	—
201	C₂²×C₈	—	5	1	no	—
202	C₂²×C₈	—	5	1	no	—
203	C₂²×C₈	—	5	1	no	—
204	C₂²×C₈	—	10	4	no	—
205	C₂²×C₈	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
206	C₂×C₄⋊C₄	—	5	4	no	—
207	C₂×C₂²⋊C₄	—	10	2	no	—
208	#107	—	10	4	no	—
209	#95	—	10	2	no	—
210	C₂×C₃×C₅	—	2	2	no	—
211	C₂×C₃×C₅	#380	1	1	yes	characteristic
212	C₂×C₃×C₅	C₂×#107	1	1	yes	characteristic
213	C₂×C₃×C₅	#427	1	1	yes	characteristic
214	C₃×D₅	—	2	2	no	—
215	C₃×D₅	#466	1	2	yes	—
216	C₃×D₅	#467	1	2	yes	—
217	C₂³×C₃	—	5	1	no	—
218	C₂³×C₃	—	5	1	no	—
219	C₂³×C₃	—	5	2	no	—
220	C₂³×C₃	—	5	2	no	—
221	C₂³×C₃	—	10	2	no	—
222	C₂³×C₃	—	10	2	no	—
223	C₂³×C₃	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
224	C₂×C₃×C₄	—	2	1	no	—
225	C₂×C₃×C₄	—	2	1	no	—
226	C₂×C₃×C₄	—	5	1	no	—
227	C₂×C₃×C₄	—	5	2	no	—
228	C₂×C₃×C₄	—	5	2	no	—
229	C₂×C₃×C₄	—	5	1	no	—
230	C₂×C₃×C₄	—	10	2	no	—
231	C₂×C₃×C₄	—	10	2	no	—
232	C₂×C₃×C₄	—	10	2	no	—
233	C₂×C₃×C₄	—	10	1	no	—
234	C₂×C₃×C₄	—	10	1	no	—
235	C₂×C₃×C₄	—	20	4	no	—
236	C₂×C₃×C₄	—	20	4	no	—
237	C₂×C₃×C₄	—	20	4	no	—
238	C₂×C₃×C₄	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
240	C₃×C₈	—	2	1	no	—
241	C₃×C₈	—	5	2	no	—
242	C₃×C₈	—	10	1	no	—
243	C₃×C₈	C₂²⋊AGL(1,𝔽₅)	1	2	yes	complemented
244	C₂²×C₅	—	2	1	no	—
245	C₂²×C₅	—	2	1	no	—
246	C₂²×C₅	C₃×#107	1	2	yes	complemented
247	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
248	C₂×D₅	—	2	1	no	—
249	C₂×D₅	—	2	1	no	—
250	C₂×D₅	—	2	4	no	—
251	C₂×D₅	—	2	4	no	—
252	C₂×D₅	C₃×#107	1	2	yes	complemented
253	C₂×D₅	C₃×#121	1	2	yes	—
254	C₂×D₅	C₂×C₃×D₈	1	1	yes	characteristic
255	C₂×D₅	C₂×C₃×Q₁₆	1	1	yes	characteristic
256	C₂×D₅	C₃×#135	1	2	yes	—
257	AGL(1,𝔽₅)	—	8	4	no	—
258	C₄×C₅	—	2	1	no	—
259	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
260	C₄×C₅	C₃×#117	1	1	yes	characteristic
261	Dic₅	—	2	1	no	—
262	Dic₅	C₃×C₂²⋊Q₈	1	2	yes	—
263	C₂⁴	—	5	1	no	—
264	C₂²×C₄	—	5	1	no	—
265	C₂²×C₄	—	5	1	no	—
266	C₂²×C₄	—	5	1	no	—
267	C₂²×C₄	—	5	1	no	—
268	C₂²×C₄	—	5	1	no	—
269	C₂²×C₄	—	10	2	no	—
270	C₂²×C₄	—	10	2	no	—
271	C₂²×C₄	—	10	4	no	—
272	C₂²×C₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
273	C₂×C₈	—	2	2	no	—
274	C₂×C₈	—	5	1	no	—
275	C₂×C₈	—	5	4	no	—
276	C₂×C₈	—	5	1	no	—
277	C₂×C₈	—	10	2	no	—
278	C₂×C₈	—	10	2	no	—
279	C₂×C₈	—	10	2	no	—
280	C₂×C₈	—	10	2	no	—
281	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
282	C₂×C₈	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
283	C₄⋊C₄	—	10	4	no	—
284	C₄⋊C₄	—	10	4	no	—
285	C₂²⋊C₄	—	20	4	no	—
286	C₃×C₅	#1808	1	1	yes	characteristic, complemented, Hall
287	C₂²×C₃	—	2	1	no	—
288	C₂²×C₃	—	2	1	no	—
289	C₂²×C₃	—	5	1	no	—
290	C₂²×C₃	—	5	1	no	—
291	C₂²×C₃	—	5	2	no	—
292	C₂²×C₃	—	5	2	no	—
293	C₂²×C₃	—	5	2	no	—
294	C₂²×C₃	—	10	4	no	—
295	C₂²×C₃	—	10	4	no	—
296	C₂²×C₃	—	10	1	no	—
297	C₂²×C₃	—	10	1	no	—
298	C₂²×C₃	#3994	1	2	yes	complemented
299	C₂²×C₃	C₂×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
300	C₃×C₄	—	2	1	no	—
301	C₃×C₄	—	5	2	no	—
302	C₃×C₄	—	10	1	no	—
303	C₃×C₄	—	40	4	no	—
304	C₃×C₄	#4130	1	1	yes	characteristic
305	C₃×C₄	C₂×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
306	C₂×C₅	—	2	2	no	—
307	C₂×C₅	C₃×#380	1	1	yes	characteristic
308	C₂×C₅	C₂×C₃×#107	1	1	yes	characteristic
309	C₂×C₅	C₃×#427	1	1	yes	characteristic
310	D₅	—	2	2	no	—
311	D₅	C₃×#466	1	2	yes	—
312	D₅	C₃×#467	1	2	yes	—
313	C₂³	—	5	1	no	—
314	C₂³	—	5	2	no	—
315	C₂³	—	5	2	no	—
316	C₂³	—	5	1	no	—
317	C₂³	—	10	2	no	—
318	C₂³	—	10	2	no	—
319	C₂³	C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	5	1	no	—
323	C₂×C₄	—	5	2	no	—
324	C₂×C₄	—	5	2	no	—
325	C₂×C₄	—	5	1	no	—
326	C₂×C₄	—	10	2	no	—
327	C₂×C₄	—	10	2	no	—
328	C₂×C₄	—	10	2	no	—
329	C₂×C₄	—	10	1	no	—
330	C₂×C₄	—	10	1	no	—
331	C₂×C₄	—	20	4	no	—
332	C₂×C₄	—	20	4	no	—
333	C₂×C₄	—	20	4	no	—
334	C₂×C₄	C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
335	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
336	C₈	—	2	1	no	—
337	C₈	—	5	2	no	—
338	C₈	—	10	1	no	—
339	C₈	C₃×C₂²⋊AGL(1,𝔽₅)	1	2	yes	complemented
340	C₂×C₃	—	2	2	no	—
341	C₂×C₃	—	5	2	no	—
342	C₂×C₃	—	5	2	no	—
343	C₂×C₃	—	10	2	no	—
344	C₂×C₃	C₂×#3994	1	1	yes	characteristic
345	C₂×C₃	#65721	1	1	yes	characteristic
346	C₂×C₃	#65765	1	1	yes	characteristic
347	C₅	C₃×#1808	1	1	yes	characteristic, complemented, Sylow
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	5	1	no	—
351	C₂²	—	5	1	no	—
352	C₂²	—	5	2	no	—
353	C₂²	—	5	2	no	—
354	C₂²	—	5	2	no	—
355	C₂²	—	10	4	no	—
356	C₂²	—	10	4	no	—
357	C₂²	—	10	1	no	—
358	C₂²	—	10	1	no	—
359	C₂²	C₃×#3994	1	2	yes	complemented
360	C₂²	C₂×C₃×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	5	2	no	—
363	C₄	—	10	1	no	—
364	C₄	—	40	4	no	—
365	C₄	C₃×#4130	1	1	yes	characteristic
366	C₄	C₂×C₃×C₂²⋊AGL(1,𝔽₅)	1	1	yes	characteristic
367	C₃	#10604723	1	1	yes	characteristic, direct product factor, Sylow
368	C₂	—	2	2	no	—
369	C₂	—	5	2	no	—
370	C₂	—	5	2	no	—
371	C₂	—	10	2	no	—
372	C₂	C₂×C₃×#3994	1	1	yes	characteristic
373	C₂	C₃×#65721	1	1	yes	characteristic
374	C₂	C₃×#65765	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×C₄⋊AGL(1,𝔽₅)
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₂²×C₃×C₅×C₈	C₄
socle	C₂²×C₃×C₅	C₂×C₄⋊C₄
prime radical	C₂³×C₃×D₅	D₄
cosocle	C₂×C₄×D₅	C₂³×C₃
hypercenter	C₂²×C₃×C₈	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#1808
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×#3994	C₂	semidirect
4. C₃×#64893	C₂	semidirect
5. #10604723	C₃	direct (N × H)
9. C₂²×C₃×C₅×C₈	C₄	semidirect
10. C₂²×C₃×#168	C₄	semidirect
12. C₂×C₃×C₈×D₅	C₄	semidirect
13. C₂×C₃×C₈×D₅	C₄	semidirect
21. C₂×#3994	C₂×C₃	semidirect
22. #64893	C₂×C₃	semidirect
53. C₂²×C₅×C₈	C₃×C₄	semidirect
54. C₂²×#168	C₃×C₄	semidirect
56. C₂×C₈×D₅	C₃×C₄	semidirect
57. C₂×C₈×D₅	C₃×C₄	semidirect
87. C₃×C₅×C₈	C₂²⋊C₄	semidirect
89. C₃×#168	C₂²⋊C₄	semidirect
97. C₂²×C₃×C₈	AGL(1,𝔽₅)	semidirect
131. C₂²×C₃×C₅	#107	semidirect
137. C₂×C₃×D₅	#107	semidirect
195. C₅×C₈	C₃×C₂²⋊C₄	semidirect
197. #168	C₃×C₂²⋊C₄	semidirect
205. C₂²×C₈	C₃×AGL(1,𝔽₅)	semidirect
243. C₃×C₈	C₂²⋊AGL(1,𝔽₅)	semidirect
246. C₂²×C₅	C₃×#107	semidirect
252. C₂×D₅	C₃×#107	semidirect
286. C₃×C₅	#1808	semidirect
298. C₂²×C₃	#3994	semidirect
339. C₈	C₃×C₂²⋊AGL(1,𝔽₅)	semidirect
347. C₅	C₃×#1808	semidirect
359. C₂²	C₃×#3994	semidirect
367. C₃	#10604723	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃×C₈×D₅	2
C₃×#65765	2
C₂×C₃×#3994	2
C₃×#64893	2
#10604723	3
C₃×#1808	5

Subgroups — C3×#10604723 #14297911

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10604723 #14297911