Subgroups — C₅×#71604 #14297633

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 436 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	C₅×#4935	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4529	C₂	1	2	yes	maximal, complemented
6	C₅×#1802	—	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	—	2	1	no	—
15	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
16	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
17	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
18	C₅×#832	—	2	4	no	—
19	C₅×C₄⋊(C₃⋊C₈)	—	2	2	no	—
20	#71604	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic
22	C₂×C₅×C₄⋊C₈	—	3	1	no	—
23	C₂×C₅×#102	—	3	2	no	—
24	C₅×#384	—	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	1	no	—
29	C₂×C₃×C₅×D₄	—	2	1	no	—
30	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
31	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
32	C₂×C₃×C₅×D₄	Q₈	1	2	yes	—
33	C₂²×C₃×C₄×C₅	—	2	1	no	—
34	C₂²×C₃×C₄×C₅	—	2	4	no	—
35	C₂²×C₃×C₄×C₅	—	4	2	no	—
36	C₂²×C₃×C₄×C₅	—	4	2	no	—
37	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₅×Dic₃	—	2	2	no	—
41	C₃×C₅×C₄⋊C₄	—	2	1	no	—
42	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
43	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
44	C₃×C₄²×C₅	C₂×C₄	1	2	yes	—
45	C₃×C₄²×C₅	D₄	1	2	yes	—
46	C₅×C₄⋊Dic₃	—	2	2	no	—
47	C₅×C₄⋊Dic₃	—	2	2	no	—
48	C₅×C₄⋊Dic₃	—	4	2	no	—
49	C₅×C₄⋊Dic₃	—	4	2	no	—
50	C₂×C₅×C₃⋊C₈	—	2	2	no	—
51	C₂×C₅×C₃⋊C₈	—	2	2	no	—
52	C₂×C₅×C₃⋊C₈	—	2	2	no	—
53	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
54	C₂×#832	C₂×C₅	1	2	yes	—
55	#4935	C₂×C₅	1	1	yes	characteristic, complemented
56	C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	1	1	yes	characteristic, complemented
57	#4529	C₂×C₅	1	2	yes	complemented
58	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
59	C₂³×C₄×C₅	—	2	1	no	—
60	C₂²×C₅×C₈	—	3	2	no	—
61	C₄×C₅×D₄	—	2	2	no	—
62	C₄×C₅×D₄	Dic₃	1	4	yes	complemented
63	C₂×C₅×C₄⋊C₄	—	3	2	no	—
64	C₂×C₅×C₄⋊C₄	—	6	1	no	—
65	C₂×C₅×C₄⋊C₄	—	6	1	no	—
66	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
67	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
69	C₅×C₄⋊C₈	—	6	2	no	—
70	C₅×#102	—	6	4	no	—
71	#1802	—	3	1	no	Sylow
72	C₂³×C₃×C₅	—	2	2	no	—
73	C₂³×C₃×C₅	—	2	2	no	—
74	C₂³×C₃×C₅	—	2	2	no	—
75	C₂³×C₃×C₅	—	4	1	no	—
76	C₂³×C₃×C₅	—	4	1	no	—
77	C₂³×C₃×C₅	—	4	1	no	—
78	C₂³×C₃×C₅	—	4	1	no	—
79	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
80	C₃×C₅×D₄	—	2	2	no	—
81	C₃×C₅×D₄	—	2	2	no	—
82	C₃×C₅×D₄	—	2	2	no	—
83	C₃×C₅×D₄	C₄⋊C₄	1	4	yes	complemented
84	C₂×C₃×C₄×C₅	—	2	1	no	—
85	C₂×C₃×C₄×C₅	—	2	1	no	—
86	C₂×C₃×C₄×C₅	—	2	2	no	—
87	C₂×C₃×C₄×C₅	—	4	1	no	—
88	C₂×C₃×C₄×C₅	—	4	1	no	—
89	C₂×C₃×C₄×C₅	—	4	8	no	—
90	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
92	C₂×C₃×C₄×C₅	D₈	1	2	yes	—
93	C₂×C₃×C₄×C₅	SD₁₆	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
98	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
100	C₂×C₅×Dic₃	—	4	2	no	—
101	C₂×C₅×Dic₃	—	4	2	no	—
102	C₂×C₅×Dic₃	—	4	2	no	—
103	C₅×C₃⋊C₈	—	4	2	no	—
104	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
105	C₂³×C₃×C₄	—	2	1	no	—
106	C₃×C₄×D₄	—	2	2	no	—
107	C₃×C₄×D₄	C₄×C₅	1	4	yes	complemented
108	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
109	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
110	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
111	C₂×C₄⋊Dic₃	—	2	1	no	—
112	C₂×C₄⋊Dic₃	—	2	1	no	—
113	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
114	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
115	#832	—	2	4	no	—
116	C₄⋊(C₃⋊C₈)	—	2	2	no	—
117	C₂⁴×C₅	—	2	1	no	—
118	C₂×C₅×D₄	—	2	1	no	—
119	C₂×C₅×D₄	—	2	1	no	—
120	C₂×C₅×D₄	—	2	1	no	—
121	C₂×C₅×D₄	Dic₆	1	2	yes	—
122	C₂×C₅×D₄	D₁₂	1	2	yes	—
123	C₂×C₅×D₄	C₂×Dic₃	1	2	yes	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	2	4	no	—
126	C₂²×C₄×C₅	—	4	2	no	—
127	C₂²×C₄×C₅	—	4	2	no	—
128	C₂²×C₄×C₅	—	6	2	no	—
129	C₂²×C₄×C₅	#67	1	1	yes	characteristic
130	C₂²×C₄×C₅	#67	1	1	yes	characteristic
131	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
132	C₂×C₅×C₈	—	6	2	no	—
133	C₂×C₅×C₈	—	6	2	no	—
134	C₂×C₅×C₈	—	6	2	no	—
135	C₅×C₄⋊C₄	—	2	1	no	—
136	C₅×C₄⋊C₄	—	6	2	no	—
137	C₅×C₄⋊C₄	—	6	2	no	—
138	C₅×C₄⋊C₄	—	12	2	no	—
139	C₅×C₄⋊C₄	—	12	2	no	—
140	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
141	C₅×C₂²⋊C₄	—	2	4	no	—
142	C₄²×C₅	C₂×Dic₃	1	2	yes	—
143	C₄²×C₅	#67	1	2	yes	—
144	C₂×C₄×D₄	C₅×D₃	1	1	yes	characteristic
145	C₂×C₄⋊C₈	—	3	1	no	—
146	C₂×#102	—	3	2	no	—
147	#384	—	3	1	no	—
148	#340	—	3	2	no	—
149	C₂²×C₃×C₅	—	2	4	no	—
150	C₂²×C₃×C₅	—	4	2	no	—
151	C₂²×C₃×C₅	—	4	2	no	—
152	C₂²×C₃×C₅	—	4	2	no	—
153	C₂²×C₃×C₅	—	4	2	no	—
154	C₂²×C₃×C₅	—	4	2	no	—
155	C₂²×C₃×C₅	—	4	2	no	—
156	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₃×C₅	#121	1	1	yes	characteristic
158	C₂²×C₃×C₅	C₂²⋊Q₈	1	1	yes	characteristic
159	C₂²×C₃×C₅	C₂×D₈	1	1	yes	characteristic
160	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
161	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂²×C₃×C₅	#137	1	1	yes	characteristic
163	C₃×C₄×C₅	—	2	2	no	—
164	C₃×C₄×C₅	—	4	2	no	—
165	C₃×C₄×C₅	#102	1	4	yes	complemented
166	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₃×C₄×C₅	#117	1	1	yes	characteristic
168	C₃×C₄×C₅	#121	1	1	yes	characteristic
169	C₃×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
170	C₅×Dic₃	—	8	2	no	—
171	C₂⁴×C₃	—	2	1	no	—
172	C₂×C₃×D₄	—	2	1	no	—
173	C₂×C₃×D₄	—	2	1	no	—
174	C₂×C₃×D₄	—	2	1	no	—
175	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
176	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
177	C₂×C₃×D₄	C₅×Q₈	1	2	yes	—
178	C₂²×C₃×C₄	—	2	1	no	—
179	C₂²×C₃×C₄	—	2	4	no	—
180	C₂²×C₃×C₄	—	4	2	no	—
181	C₂²×C₃×C₄	—	4	2	no	—
182	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
184	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
185	C₂²×Dic₃	—	2	2	no	—
186	C₃×C₄⋊C₄	—	2	1	no	—
187	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
188	C₃×C₂²⋊C₄	—	2	4	no	—
189	C₃×C₄²	C₂×C₄×C₅	1	2	yes	—
190	C₃×C₄²	C₅×D₄	1	2	yes	—
191	C₄⋊Dic₃	—	2	2	no	—
192	C₄⋊Dic₃	—	2	2	no	—
193	C₄⋊Dic₃	—	4	2	no	—
194	C₄⋊Dic₃	—	4	2	no	—
195	C₂×C₃⋊C₈	—	2	2	no	—
196	C₂×C₃⋊C₈	—	2	2	no	—
197	C₂×C₃⋊C₈	—	2	2	no	—
198	C₂³×C₅	—	2	2	no	—
199	C₂³×C₅	—	2	2	no	—
200	C₂³×C₅	—	2	2	no	—
201	C₂³×C₅	—	4	1	no	—
202	C₂³×C₅	—	4	1	no	—
203	C₂³×C₅	—	4	1	no	—
204	C₂³×C₅	—	4	1	no	—
205	C₂³×C₅	C₂×#67	1	1	yes	characteristic
206	C₅×D₄	—	2	2	no	—
207	C₅×D₄	—	2	2	no	—
208	C₅×D₄	—	2	2	no	—
209	C₅×D₄	C₄⋊Dic₃	1	4	yes	complemented
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	4	1	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	—	4	8	no	—
216	C₂×C₄×C₅	—	12	2	no	—
217	C₂×C₄×C₅	—	12	2	no	—
218	C₂×C₄×C₅	—	12	2	no	—
219	C₂×C₄×C₅	#213	1	2	yes	—
220	C₂×C₄×C₅	#214	1	2	yes	—
221	C₂×C₄×C₅	#217	1	2	yes	—
222	C₂×C₄×C₅	#217	1	2	yes	—
223	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
225	C₂×C₄×C₅	#235	1	1	yes	characteristic
226	C₂×C₄×C₅	#235	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
229	C₅×C₈	—	12	2	no	—
230	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
231	C₂³×C₄	—	2	1	no	—
232	C₂²×C₈	—	3	2	no	—
233	C₄×D₄	—	2	2	no	—
234	C₄×D₄	C₅×Dic₃	1	4	yes	complemented
235	C₂×C₄⋊C₄	—	3	2	no	—
236	C₂×C₄⋊C₄	—	6	1	no	—
237	C₂×C₄⋊C₄	—	6	1	no	—
238	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
239	C₂×C₂²⋊C₄	—	2	1	no	—
240	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
241	C₄⋊C₈	—	6	2	no	—
242	#102	—	6	4	no	—
243	C₂×C₃×C₅	—	4	4	no	—
244	C₂×C₃×C₅	#380	1	1	yes	characteristic
245	C₂×C₃×C₅	C₂×#102	1	1	yes	characteristic
246	C₂×C₃×C₅	#417	1	1	yes	characteristic
247	C₂×C₃×C₅	#459	1	1	yes	characteristic
248	C₂×C₃×C₅	#461	1	1	yes	characteristic
249	C₂×C₃×C₅	#474	1	1	yes	characteristic
250	C₂×C₃×C₅	#476	1	1	yes	characteristic
251	C₂³×C₃	—	2	2	no	—
252	C₂³×C₃	—	2	2	no	—
253	C₂³×C₃	—	2	2	no	—
254	C₂³×C₃	—	4	1	no	—
255	C₂³×C₃	—	4	1	no	—
256	C₂³×C₃	—	4	1	no	—
257	C₂³×C₃	—	4	1	no	—
258	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
259	C₃×D₄	—	2	2	no	—
260	C₃×D₄	—	2	2	no	—
261	C₃×D₄	—	2	2	no	—
262	C₃×D₄	C₅×C₄⋊C₄	1	4	yes	complemented
263	C₂×C₃×C₄	—	2	1	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	2	2	no	—
266	C₂×C₃×C₄	—	4	1	no	—
267	C₂×C₃×C₄	—	4	1	no	—
268	C₂×C₃×C₄	—	4	8	no	—
269	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
270	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
271	C₂×C₃×C₄	C₅×D₈	1	2	yes	—
272	C₂×C₃×C₄	C₅×SD₁₆	1	2	yes	—
273	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
274	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
275	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
276	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
277	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
278	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
279	C₂×Dic₃	—	4	2	no	—
280	C₂×Dic₃	—	4	2	no	—
281	C₂×Dic₃	—	4	2	no	—
282	C₃⋊C₈	—	4	2	no	—
283	C₂²×C₅	—	2	4	no	—
284	C₂²×C₅	—	4	2	no	—
285	C₂²×C₅	—	4	2	no	—
286	C₂²×C₅	—	4	2	no	—
287	C₂²×C₅	—	4	2	no	—
288	C₂²×C₅	—	4	2	no	—
289	C₂²×C₅	—	4	2	no	—
290	C₂²×C₅	#924	1	1	yes	characteristic
291	C₂²×C₅	#930	1	1	yes	characteristic
292	C₂²×C₅	C₂×#213	1	1	yes	characteristic
293	C₂²×C₅	C₂×#214	1	1	yes	characteristic
294	C₂²×C₅	#949	1	1	yes	characteristic
295	C₂²×C₅	#951	1	1	yes	characteristic
296	C₂²×C₅	C₂×#217	1	1	yes	characteristic
297	C₄×C₅	—	2	2	no	—
298	C₄×C₅	—	4	2	no	—
299	C₄×C₅	—	24	2	no	—
300	C₄×C₅	#832	1	4	yes	complemented
301	C₄×C₅	#924	1	1	yes	characteristic
302	C₄×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
303	C₄×C₅	#926	1	1	yes	characteristic
304	C₄×C₅	#930	1	1	yes	characteristic
305	C₂⁴	—	2	1	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	C₅×Dic₆	1	2	yes	—
310	C₂×D₄	C₅×D₁₂	1	2	yes	—
311	C₂×D₄	C₂×C₅×Dic₃	1	2	yes	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	4	2	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	—	6	2	no	—
317	C₂²×C₄	C₅×#67	1	1	yes	characteristic
318	C₂²×C₄	C₅×#67	1	1	yes	characteristic
319	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
320	C₂×C₈	—	6	2	no	—
321	C₂×C₈	—	6	2	no	—
322	C₂×C₈	—	6	2	no	—
323	C₄⋊C₄	—	2	1	no	—
324	C₄⋊C₄	—	6	2	no	—
325	C₄⋊C₄	—	6	2	no	—
326	C₄⋊C₄	—	12	2	no	—
327	C₄⋊C₄	—	12	2	no	—
328	C₄⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
329	C₂²⋊C₄	—	2	4	no	—
330	C₄²	C₂×C₅×Dic₃	1	2	yes	—
331	C₄²	C₅×#67	1	2	yes	—
332	C₃×C₅	#1802	1	1	yes	characteristic, complemented, Hall
333	C₂²×C₃	—	2	4	no	—
334	C₂²×C₃	—	4	2	no	—
335	C₂²×C₃	—	4	2	no	—
336	C₂²×C₃	—	4	2	no	—
337	C₂²×C₃	—	4	2	no	—
338	C₂²×C₃	—	4	2	no	—
339	C₂²×C₃	—	4	2	no	—
340	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
341	C₂²×C₃	C₅×#121	1	1	yes	characteristic
342	C₂²×C₃	C₅×C₂²⋊Q₈	1	1	yes	characteristic
343	C₂²×C₃	C₂×C₅×D₈	1	1	yes	characteristic
344	C₂²×C₃	C₂×C₅×SD₁₆	1	1	yes	characteristic
345	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
346	C₂²×C₃	C₅×#137	1	1	yes	characteristic
347	C₃×C₄	—	2	2	no	—
348	C₃×C₄	—	4	2	no	—
349	C₃×C₄	C₅×#102	1	4	yes	complemented
350	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
351	C₃×C₄	C₅×#117	1	1	yes	characteristic
352	C₃×C₄	C₅×#121	1	1	yes	characteristic
353	C₃×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
354	Dic₃	—	8	2	no	—
355	C₂×C₅	—	4	4	no	—
356	C₂×C₅	#5007	1	1	yes	characteristic
357	C₂×C₅	#5008	1	1	yes	characteristic
358	C₂×C₅	#5015	1	1	yes	characteristic
359	C₂×C₅	#5019	1	1	yes	characteristic
360	C₂×C₅	#5212	1	1	yes	characteristic
361	C₂×C₅	C₂×#832	1	1	yes	characteristic
362	C₂×C₅	#5232	1	1	yes	characteristic
363	C₂³	—	2	2	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	1	no	—
368	C₂³	—	4	1	no	—
369	C₂³	—	4	1	no	—
370	C₂³	C₂×C₅×#67	1	1	yes	characteristic
371	D₄	—	2	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	2	2	no	—
374	D₄	C₅×C₄⋊Dic₃	1	4	yes	complemented
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	8	no	—
381	C₂×C₄	—	12	2	no	—
382	C₂×C₄	—	12	2	no	—
383	C₂×C₄	—	12	2	no	—
384	C₂×C₄	C₅×#213	1	2	yes	—
385	C₂×C₄	C₅×#214	1	2	yes	—
386	C₂×C₄	C₅×#217	1	2	yes	—
387	C₂×C₄	C₅×#217	1	2	yes	—
388	C₂×C₄	C₂×C₅×Dic₆	1	1	yes	characteristic
389	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
390	C₂×C₄	C₅×#235	1	1	yes	characteristic
391	C₂×C₄	C₅×#235	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
393	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
394	C₈	—	12	2	no	—
395	C₂×C₃	—	4	4	no	—
396	C₂×C₃	C₅×#380	1	1	yes	characteristic
397	C₂×C₃	C₂×C₅×#102	1	1	yes	characteristic
398	C₂×C₃	C₅×#417	1	1	yes	characteristic
399	C₂×C₃	C₅×#459	1	1	yes	characteristic
400	C₂×C₃	C₅×#461	1	1	yes	characteristic
401	C₂×C₃	C₅×#474	1	1	yes	characteristic
402	C₂×C₃	C₅×#476	1	1	yes	characteristic
403	C₅	#71604	1	1	yes	characteristic, direct product factor, Sylow
404	C₂²	—	2	4	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	C₅×#924	1	1	yes	characteristic
412	C₂²	C₅×#930	1	1	yes	characteristic
413	C₂²	C₂×C₅×#213	1	1	yes	characteristic
414	C₂²	C₂×C₅×#214	1	1	yes	characteristic
415	C₂²	C₅×#949	1	1	yes	characteristic
416	C₂²	C₅×#951	1	1	yes	characteristic
417	C₂²	C₂×C₅×#217	1	1	yes	characteristic
418	C₄	—	2	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	24	2	no	—
421	C₄	C₅×#832	1	4	yes	complemented
422	C₄	C₅×#924	1	1	yes	characteristic
423	C₄	C₂×C₅×C₄⋊Dic₃	1	1	yes	characteristic
424	C₄	C₅×#926	1	1	yes	characteristic
425	C₄	C₅×#930	1	1	yes	characteristic
426	C₃	C₅×#1802	1	1	yes	characteristic, complemented, Sylow
427	C₂	—	4	4	no	—
428	C₂	C₅×#5007	1	1	yes	characteristic
429	C₂	C₅×#5008	1	1	yes	characteristic
430	C₂	C₅×#5015	1	1	yes	characteristic
431	C₂	C₅×#5019	1	1	yes	characteristic
432	C₂	C₅×#5212	1	1	yes	characteristic
433	C₂	C₂×C₅×#832	1	1	yes	characteristic
434	C₂	C₅×#5232	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator	C₂×C₃×C₄	C₂²×C₄×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	C₅×#1802
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×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. C₅×#4935	C₂	semidirect
4. C₂×C₅×C₄⋊(C₃⋊C₈)	C₂	semidirect
5. C₅×#4529	C₂	semidirect
10. C₃×C₄×C₅×D₄	C₄	semidirect
20. #71604	C₅	direct (N × H)
55. #4935	C₂×C₅	semidirect
56. C₂×C₄⋊(C₃⋊C₈)	C₂×C₅	semidirect
57. #4529	C₂×C₅	semidirect
62. C₄×C₅×D₄	Dic₃	semidirect
83. C₃×C₅×D₄	C₄⋊C₄	semidirect
107. C₃×C₄×D₄	C₄×C₅	semidirect
165. C₃×C₄×C₅	#102	semidirect
209. C₅×D₄	C₄⋊Dic₃	semidirect
234. C₄×D₄	C₅×Dic₃	semidirect
262. C₃×D₄	C₅×C₄⋊C₄	semidirect
300. C₄×C₅	#832	semidirect
332. C₃×C₅	#1802	semidirect
349. C₃×C₄	C₅×#102	semidirect
374. D₄	C₅×C₄⋊Dic₃	semidirect
403. C₅	#71604	direct (N × H)
421. C₄	C₅×#832	semidirect
426. C₃	C₅×#1802	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
C₅×#4935	2
C₂×C₅×C₄⋊(C₃⋊C₈)	2
C₅×#4529	2
C₅×#1802	3
#71604	5

Subgroups — C5×#71604 #14297633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71604 #14297633