Subgroups — C₄×C₅×#832 #14295689

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#832	C₂	1	2	yes	maximal
3	C₄×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4529	C₂	1	2	yes	maximal, complemented
6	C₄×C₅×#102	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
8	C₂³×C₃×C₄×C₅	—	2	1	no	—
9	C₃×C₄×C₅×D₄	—	2	2	no	—
10	C₃×C₄×C₅×D₄	C₄	1	4	yes	complemented
11	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
15	C₂×C₄×C₅×Dic₃	—	2	1	no	—
16	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
17	C₅×#832	C₄	1	8	yes	direct product factor
18	C₅×C₃⋊#95	—	2	1	no	—
19	C₄×C₅×C₃⋊C₈	—	2	2	no	—
20	C₄×#832	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic
22	C₂×C₅×#102	—	3	2	no	—
23	C₂×C₄×C₅×C₈	—	3	1	no	—
24	C₄×C₅×C₄⋊C₄	—	3	1	no	—
25	C₅×#340	—	3	2	no	—
26	C₂⁴×C₃×C₅	—	2	1	no	—
27	C₂×C₃×C₅×D₄	—	2	1	no	—
28	C₂×C₃×C₅×D₄	—	2	2	no	—
29	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
30	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
31	C₂²×C₃×C₄×C₅	—	2	1	no	—
32	C₂²×C₃×C₄×C₅	—	2	4	no	—
33	C₂²×C₃×C₄×C₅	—	4	2	no	—
34	C₂²×C₃×C₄×C₅	—	4	2	no	—
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂²×C₅×Dic₃	—	2	2	no	—
39	C₃×C₅×C₄⋊C₄	—	2	1	no	—
40	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
41	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
42	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
43	C₃×C₄²×C₅	D₄	1	2	yes	—
44	C₅×C₄⋊Dic₃	—	2	2	no	—
45	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	complemented
46	C₄×C₅×Dic₃	—	4	2	no	—
47	C₂×C₅×C₃⋊C₈	—	2	2	no	—
48	C₂×C₅×C₃⋊C₈	—	2	2	no	—
49	C₂×C₅×C₃⋊C₈	C₂×C₄	1	4	yes	complemented
50	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
51	C₂×#832	C₂×C₅	1	2	yes	—
52	C₄×C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
53	C₂×C₄×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
54	#4529	C₂×C₅	1	2	yes	complemented
55	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
56	C₂³×C₄×C₅	—	2	1	no	—
57	C₂²×C₅×C₈	—	3	2	no	—
58	C₄×C₅×D₄	—	2	2	no	—
59	C₄×C₅×D₄	Dic₃	1	4	yes	complemented
60	C₂×C₅×C₄⋊C₄	—	3	2	no	—
61	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
62	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
63	C₂×C₄²×C₅	—	6	1	no	—
64	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
65	C₅×#102	—	3	8	no	—
66	C₄×C₅×C₈	—	6	2	no	—
67	C₅×#95	—	6	1	no	—
68	C₄×#102	—	3	1	no	Sylow
69	C₂³×C₃×C₅	—	2	2	no	—
70	C₂³×C₃×C₅	—	2	4	no	—
71	C₂³×C₃×C₅	—	4	1	no	—
72	C₂³×C₃×C₅	—	4	1	no	—
73	C₂³×C₃×C₅	—	4	2	no	—
74	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
75	C₃×C₅×D₄	—	2	2	no	—
76	C₃×C₅×D₄	—	2	4	no	—
77	C₃×C₅×D₄	C₄²	1	4	yes	complemented
78	C₂×C₃×C₄×C₅	—	2	2	no	—
79	C₂×C₃×C₄×C₅	—	2	2	no	—
80	C₂×C₃×C₄×C₅	—	4	1	no	—
81	C₂×C₃×C₄×C₅	—	4	1	no	—
82	C₂×C₃×C₄×C₅	—	4	8	no	—
83	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
84	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
85	C₂×C₃×C₄×C₅	D₈	1	2	yes	—
86	C₂×C₃×C₄×C₅	SD₁₆	1	2	yes	—
87	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
90	C₂×C₃×C₄×C₅	#41	1	2	yes	—
91	C₂×C₅×Dic₃	—	2	4	no	—
92	C₂×C₅×Dic₃	—	4	2	no	—
93	C₂×C₅×Dic₃	—	4	2	no	—
94	C₅×C₃⋊C₈	—	2	4	no	—
95	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
96	C₂³×C₃×C₄	—	2	1	no	—
97	C₃×C₄×D₄	—	2	2	no	—
98	C₃×C₄×D₄	C₄×C₅	1	4	yes	complemented
99	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
100	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
102	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
103	C₂×C₄×Dic₃	—	2	1	no	—
104	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
105	#832	C₄×C₅	1	8	yes	direct product factor
106	C₃⋊#95	—	2	1	no	—
107	C₄×C₃⋊C₈	—	2	2	no	—
108	C₂⁴×C₅	—	2	1	no	—
109	C₂×C₅×D₄	—	2	2	no	—
110	C₂×C₅×D₄	—	2	1	no	—
111	C₂×C₅×D₄	C₄×D₃	1	4	yes	—
112	C₂×C₅×D₄	C₂×Dic₃	1	2	yes	—
113	C₂²×C₄×C₅	—	2	1	no	—
114	C₂²×C₄×C₅	—	2	4	no	—
115	C₂²×C₄×C₅	—	4	2	no	—
116	C₂²×C₄×C₅	—	4	2	no	—
117	C₂²×C₄×C₅	—	6	2	no	—
118	C₂²×C₄×C₅	#67	1	1	yes	characteristic
119	C₂²×C₄×C₅	#67	1	1	yes	characteristic
120	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
121	C₂×C₅×C₈	—	3	4	no	—
122	C₂×C₅×C₈	—	6	2	no	—
123	C₂×C₅×C₈	—	6	2	no	—
124	C₅×C₄⋊C₄	—	2	1	no	—
125	C₅×C₄⋊C₄	—	3	4	no	—
126	C₅×C₄⋊C₄	—	6	2	no	—
127	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
128	C₅×C₂²⋊C₄	—	2	4	no	—
129	C₄²×C₅	—	12	2	no	—
130	C₄²×C₅	C₂×Dic₃	1	2	yes	—
131	C₄²×C₅	#67	1	2	yes	—
132	C₂×C₄×D₄	C₅×D₃	1	1	yes	characteristic
133	C₂×#102	—	3	2	no	—
134	C₂×C₄×C₈	—	3	1	no	—
135	C₄×C₄⋊C₄	—	3	1	no	—
136	#340	—	3	2	no	—
137	C₂²×C₃×C₅	—	2	4	no	—
138	C₂²×C₃×C₅	—	4	2	no	—
139	C₂²×C₃×C₅	—	4	2	no	—
140	C₂²×C₃×C₅	—	4	4	no	—
141	C₂²×C₃×C₅	—	4	4	no	—
142	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
144	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
145	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
146	C₂²×C₃×C₅	#135	1	2	yes	—
147	C₃×C₄×C₅	—	2	2	no	—
148	C₃×C₄×C₅	—	4	2	no	—
149	C₃×C₄×C₅	#102	1	4	yes	complemented
150	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
151	C₃×C₄×C₅	#117	1	1	yes	characteristic
152	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
153	C₅×Dic₃	—	4	4	no	—
154	C₂⁴×C₃	—	2	1	no	—
155	C₂×C₃×D₄	—	2	1	no	—
156	C₂×C₃×D₄	—	2	2	no	—
157	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
158	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
159	C₂²×C₃×C₄	—	2	1	no	—
160	C₂²×C₃×C₄	—	2	4	no	—
161	C₂²×C₃×C₄	—	4	2	no	—
162	C₂²×C₃×C₄	—	4	2	no	—
163	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
164	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
165	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
166	C₂²×Dic₃	—	2	2	no	—
167	C₃×C₄⋊C₄	—	2	1	no	—
168	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
169	C₃×C₂²⋊C₄	—	2	4	no	—
170	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
171	C₃×C₄²	C₅×D₄	1	2	yes	—
172	C₄⋊Dic₃	—	2	2	no	—
173	C₄⋊Dic₃	C₂×C₄×C₅	1	4	yes	complemented
174	C₄×Dic₃	—	4	2	no	—
175	C₂×C₃⋊C₈	—	2	2	no	—
176	C₂×C₃⋊C₈	—	2	2	no	—
177	C₂×C₃⋊C₈	C₂×C₄×C₅	1	4	yes	complemented
178	C₂³×C₅	—	2	4	no	—
179	C₂³×C₅	—	2	2	no	—
180	C₂³×C₅	—	4	1	no	—
181	C₂³×C₅	—	4	1	no	—
182	C₂³×C₅	—	4	2	no	—
183	C₂³×C₅	C₂×#67	1	1	yes	characteristic
184	C₅×D₄	—	2	2	no	—
185	C₅×D₄	—	2	4	no	—
186	C₅×D₄	C₄×Dic₃	1	4	yes	complemented
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	4	1	no	—
190	C₂×C₄×C₅	—	4	1	no	—
191	C₂×C₄×C₅	—	4	8	no	—
192	C₂×C₄×C₅	—	6	4	no	—
193	C₂×C₄×C₅	—	12	2	no	—
194	C₂×C₄×C₅	—	12	2	no	—
195	C₂×C₄×C₅	#213	1	2	yes	—
196	C₂×C₄×C₅	#214	1	2	yes	—
197	C₂×C₄×C₅	#217	1	2	yes	—
198	C₂×C₄×C₅	#217	1	2	yes	—
199	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
200	C₂×C₄×C₅	#235	1	2	yes	—
201	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
202	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
203	C₅×C₈	—	6	4	no	—
204	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
205	C₂³×C₄	—	2	1	no	—
206	C₂²×C₈	—	3	2	no	—
207	C₄×D₄	—	2	2	no	—
208	C₄×D₄	C₅×Dic₃	1	4	yes	complemented
209	C₂×C₄⋊C₄	—	3	2	no	—
210	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
211	C₂×C₂²⋊C₄	—	2	1	no	—
212	C₂×C₄²	—	6	1	no	—
213	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
214	#102	—	3	8	no	—
215	C₄×C₈	—	6	2	no	—
216	#95	—	6	1	no	—
217	C₂×C₃×C₅	—	4	4	no	—
218	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
220	C₂×C₃×C₅	#416	1	1	yes	characteristic
221	C₂×C₃×C₅	C₄×D₈	1	2	yes	—
222	C₂×C₃×C₅	C₄×SD₁₆	1	2	yes	—
223	C₂³×C₃	—	2	2	no	—
224	C₂³×C₃	—	2	4	no	—
225	C₂³×C₃	—	4	1	no	—
226	C₂³×C₃	—	4	1	no	—
227	C₂³×C₃	—	4	2	no	—
228	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
229	C₃×D₄	—	2	2	no	—
230	C₃×D₄	—	2	4	no	—
231	C₃×D₄	C₄²×C₅	1	4	yes	complemented
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	4	1	no	—
235	C₂×C₃×C₄	—	4	1	no	—
236	C₂×C₃×C₄	—	4	8	no	—
237	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
238	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
239	C₂×C₃×C₄	C₅×D₈	1	2	yes	—
240	C₂×C₃×C₄	C₅×SD₁₆	1	2	yes	—
241	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
242	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
244	C₂×C₃×C₄	C₅×#41	1	2	yes	—
245	C₂×Dic₃	—	2	4	no	—
246	C₂×Dic₃	—	4	2	no	—
247	C₂×Dic₃	—	4	2	no	—
248	C₃⋊C₈	—	2	4	no	—
249	C₂²×C₅	—	2	4	no	—
250	C₂²×C₅	—	4	2	no	—
251	C₂²×C₅	—	4	2	no	—
252	C₂²×C₅	—	4	4	no	—
253	C₂²×C₅	—	4	4	no	—
254	C₂²×C₅	C₄×#67	1	2	yes	—
255	C₂²×C₅	C₂×#213	1	1	yes	characteristic
256	C₂²×C₅	C₂×#214	1	1	yes	characteristic
257	C₂²×C₅	#950	1	2	yes	—
258	C₂²×C₅	C₂×#217	1	1	yes	characteristic
259	C₄×C₅	—	2	2	no	—
260	C₄×C₅	—	4	2	no	—
261	C₄×C₅	—	12	4	no	—
262	C₄×C₅	#832	1	4	yes	direct product factor
263	C₄×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
264	C₄×C₅	#926	1	1	yes	characteristic
265	C₄×C₅	C₄×#67	1	2	yes	—
266	C₂⁴	—	2	1	no	—
267	C₂×D₄	—	2	2	no	—
268	C₂×D₄	—	2	1	no	—
269	C₂×D₄	C₄×C₅×D₃	1	4	yes	—
270	C₂×D₄	C₂×C₅×Dic₃	1	2	yes	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	—	4	2	no	—
275	C₂²×C₄	—	6	2	no	—
276	C₂²×C₄	C₅×#67	1	1	yes	characteristic
277	C₂²×C₄	C₅×#67	1	1	yes	characteristic
278	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
279	C₂×C₈	—	3	4	no	—
280	C₂×C₈	—	6	2	no	—
281	C₂×C₈	—	6	2	no	—
282	C₄⋊C₄	—	2	1	no	—
283	C₄⋊C₄	—	3	4	no	—
284	C₄⋊C₄	—	6	2	no	—
285	C₄⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
286	C₂²⋊C₄	—	2	4	no	—
287	C₄²	—	12	2	no	—
288	C₄²	C₂×C₅×Dic₃	1	2	yes	—
289	C₄²	C₅×#67	1	2	yes	—
290	C₃×C₅	C₄×#102	1	1	yes	characteristic, complemented, Hall
291	C₂²×C₃	—	2	4	no	—
292	C₂²×C₃	—	4	2	no	—
293	C₂²×C₃	—	4	2	no	—
294	C₂²×C₃	—	4	4	no	—
295	C₂²×C₃	—	4	4	no	—
296	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
297	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
298	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
299	C₂²×C₃	C₂×C₅×SD₁₆	1	1	yes	characteristic
300	C₂²×C₃	C₅×#135	1	2	yes	—
301	C₃×C₄	—	2	2	no	—
302	C₃×C₄	—	4	2	no	—
303	C₃×C₄	C₅×#102	1	4	yes	complemented
304	C₃×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
305	C₃×C₄	C₅×#117	1	1	yes	characteristic
306	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
307	Dic₃	—	4	4	no	—
308	C₂×C₅	—	4	4	no	—
309	C₂×C₅	C₄×#213	1	2	yes	—
310	C₂×C₅	C₄×#214	1	2	yes	—
311	C₂×C₅	C₄×#217	1	1	yes	characteristic
312	C₂×C₅	C₂×#832	1	1	yes	characteristic
313	C₂×C₅	#5233	1	1	yes	characteristic
314	C₂³	—	2	4	no	—
315	C₂³	—	2	2	no	—
316	C₂³	—	4	1	no	—
317	C₂³	—	4	1	no	—
318	C₂³	—	4	2	no	—
319	C₂³	C₂×C₅×#67	1	1	yes	characteristic
320	D₄	—	2	2	no	—
321	D₄	—	2	4	no	—
322	D₄	C₄×C₅×Dic₃	1	4	yes	complemented
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	8	no	—
328	C₂×C₄	—	6	4	no	—
329	C₂×C₄	—	12	2	no	—
330	C₂×C₄	—	12	2	no	—
331	C₂×C₄	C₅×#213	1	2	yes	—
332	C₂×C₄	C₅×#214	1	2	yes	—
333	C₂×C₄	C₅×#217	1	2	yes	—
334	C₂×C₄	C₅×#217	1	2	yes	—
335	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
336	C₂×C₄	C₅×#235	1	2	yes	—
337	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
338	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
339	C₈	—	6	4	no	—
340	C₂×C₃	—	4	4	no	—
341	C₂×C₃	C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
342	C₂×C₃	C₂×C₅×#102	1	1	yes	characteristic
343	C₂×C₃	C₅×#416	1	1	yes	characteristic
344	C₂×C₃	C₄×C₅×D₈	1	2	yes	—
345	C₂×C₃	C₄×C₅×SD₁₆	1	2	yes	—
346	C₅	C₄×#832	1	1	yes	characteristic, direct product factor, Sylow
347	C₂²	—	2	4	no	—
348	C₂²	—	4	2	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	4	4	no	—
351	C₂²	—	4	4	no	—
352	C₂²	C₄×C₅×#67	1	2	yes	—
353	C₂²	C₂×C₅×#213	1	1	yes	characteristic
354	C₂²	C₂×C₅×#214	1	1	yes	characteristic
355	C₂²	C₅×#950	1	2	yes	—
356	C₂²	C₂×C₅×#217	1	1	yes	characteristic
357	C₄	—	2	2	no	—
358	C₄	—	4	2	no	—
359	C₄	—	12	4	no	—
360	C₄	C₅×#832	1	4	yes	direct product factor
361	C₄	C₂×C₄×C₅×Dic₃	1	1	yes	characteristic
362	C₄	C₅×#926	1	1	yes	characteristic
363	C₄	C₄×C₅×#67	1	2	yes	—
364	C₃	C₄×C₅×#102	1	1	yes	characteristic, complemented, Sylow
365	C₂	—	4	4	no	—
366	C₂	C₄×C₅×#213	1	2	yes	—
367	C₂	C₄×C₅×#214	1	2	yes	—
368	C₂	C₄×C₅×#217	1	1	yes	characteristic
369	C₂	C₂×C₅×#832	1	1	yes	characteristic
370	C₂	C₅×#5233	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	#67
commutator	C₃×C₄	C₂×C₄²×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂²×C₃×C₅×D₄	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₄×C₅×D₄	D₃
hypocenter	C₃	C₄×C₅×#102
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
3. C₄×C₅×C₄⋊Dic₃	C₂	semidirect
4. C₂×C₄×C₅×C₃⋊C₈	C₂	semidirect
5. C₅×#4529	C₂	semidirect
10. C₃×C₄×C₅×D₄	C₄	semidirect
17. C₅×#832	C₄	direct (N × H)
20. C₄×#832	C₅	direct (N × H)
45. C₅×C₄⋊Dic₃	C₂×C₄	semidirect
49. C₂×C₅×C₃⋊C₈	C₂×C₄	semidirect
52. C₄×C₄⋊Dic₃	C₂×C₅	semidirect
53. C₂×C₄×C₃⋊C₈	C₂×C₅	semidirect
54. #4529	C₂×C₅	semidirect
59. C₄×C₅×D₄	Dic₃	semidirect
77. C₃×C₅×D₄	C₄²	semidirect
98. C₃×C₄×D₄	C₄×C₅	semidirect
105. #832	C₄×C₅	direct (N × H)
149. C₃×C₄×C₅	#102	semidirect
173. C₄⋊Dic₃	C₂×C₄×C₅	semidirect
177. C₂×C₃⋊C₈	C₂×C₄×C₅	semidirect
186. C₅×D₄	C₄×Dic₃	semidirect
208. C₄×D₄	C₅×Dic₃	semidirect
231. C₃×D₄	C₄²×C₅	semidirect
262. C₄×C₅	#832	direct (N × H)
290. C₃×C₅	C₄×#102	semidirect
303. C₃×C₄	C₅×#102	semidirect
322. D₄	C₄×C₅×Dic₃	semidirect
346. C₅	C₄×#832	direct (N × H)
360. C₄	C₅×#832	direct (N × H)
364. C₃	C₄×C₅×#102	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₅×D₄	2
C₂×C₅×#832	2
C₄×C₅×C₄⋊Dic₃	2
C₂×C₄×C₅×C₃⋊C₈	2
C₅×#4529	2
C₄×C₅×#102	3
C₄×#832	5

Subgroups — C4×C5×#832 #14295689

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#832 #14295689