Subgroups — C₅×#71574 #14294481

Order 1920.

808 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅×#208	C₂	1	1	yes	maximal, characteristic
4	C₅×#4532	C₂	1	4	yes	maximal, complemented
5	C₅×#1733	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₃×C₅×#117	—	2	1	no	—
8	C₃×C₅×#117	—	2	1	no	—
9	C₃×C₅×#117	C₄	1	2	yes	complemented
10	C₃×C₅×#117	C₂²	1	2	yes	—
11	C₂×C₃×C₅×C₄⋊C₄	C₄	1	2	yes	complemented
12	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
13	C₂×C₃×C₄²×C₅	—	2	1	no	—
14	C₂×C₅×#217	—	2	1	no	—
15	C₅×#926	—	2	2	no	—
16	C₅×#926	C₄	1	4	yes	complemented
17	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
18	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
19	C₂×C₅×#208	—	2	2	no	—
20	C₂×C₅×#208	—	2	1	no	—
21	C₂×C₅×#208	C₄	1	4	yes	complemented
22	C₂×C₅×#208	C₂²	1	2	yes	—
23	C₂²×C₅×C₃⋊C₈	—	2	1	no	—
24	#71574	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂²×C₅×M₁₆	—	3	1	no	—
26	C₂×C₅×#117	—	3	1	no	—
27	C₂×C₅×#117	D₃	1	1	yes	characteristic
28	C₅×#339	—	3	4	no	—
29	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
30	C₂²×C₃×C₄×C₅	—	2	2	no	—
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
33	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
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	Q₈	1	2	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
41	C₂²×C₅×Dic₃	—	2	2	no	—
42	C₃×C₅×C₄⋊C₄	—	2	2	no	—
43	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
44	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
45	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
46	C₃×C₄²×C₅	—	2	2	no	—
47	C₃×C₄²×C₅	—	2	2	no	—
48	C₅×#217	—	2	4	no	—
49	C₅×C₄⋊Dic₃	—	2	4	no	—
50	C₄×C₅×Dic₃	—	2	2	no	—
51	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
52	C₅×#208	—	2	4	no	—
53	C₅×#208	—	2	2	no	—
54	C₅×#208	C₂×C₄	1	4	yes	complemented
55	C₂×C₅×C₃⋊C₈	—	2	4	no	—
56	C₂×C₅×C₃⋊C₈	—	2	2	no	—
57	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic
58	C₂×#926	C₂×C₅	1	1	yes	characteristic
59	C₂²×#208	C₂×C₅	1	1	yes	characteristic
60	#4532	C₂×C₅	1	4	yes	complemented
61	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
62	C₂×C₅×M₁₆	—	3	4	no	—
63	C₂×C₅×M₁₆	—	3	2	no	—
64	C₂×C₅×M₁₆	—	6	2	no	—
65	C₂×C₅×M₁₆	—	6	1	no	—
66	C₂²×C₅×C₈	—	6	1	no	—
67	C₅×#117	—	2	1	no	—
68	C₅×#117	—	2	1	no	—
69	C₅×#117	—	3	4	no	—
70	C₅×#117	—	6	2	no	—
71	C₅×#117	Dic₃	1	2	yes	complemented
72	C₅×#117	C₂×D₃	1	2	yes	—
73	C₂×C₅×C₄⋊C₄	—	6	1	no	—
74	C₂×C₅×C₄⋊C₄	Dic₃	1	2	yes	complemented
75	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
76	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
77	C₂×C₄²×C₅	—	2	1	no	—
78	C₂×C₄²×C₅	—	3	2	no	—
79	#1733	—	3	1	no	Sylow
80	C₂³×C₃×C₅	—	4	2	no	—
81	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
82	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
83	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
84	C₂³×C₃×C₅	C₄⋊C₄	1	2	yes	—
85	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
86	C₂×C₃×C₄×C₅	—	2	4	no	—
87	C₂×C₃×C₄×C₅	—	4	4	no	—
88	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
89	C₂×C₃×C₄×C₅	C₄²	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
91	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
94	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
95	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
96	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
99	C₂×C₃×C₄×C₅	C₄⋊C₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
106	C₂×C₅×Dic₃	—	2	4	no	—
107	C₂×C₅×Dic₃	—	4	4	no	—
108	C₅×C₃⋊C₈	—	2	4	no	—
109	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
110	C₃×#117	—	2	1	no	—
111	C₃×#117	—	2	1	no	—
112	C₃×#117	C₄×C₅	1	2	yes	complemented
113	C₃×#117	C₂²×C₅	1	2	yes	—
114	C₂×C₃×C₄⋊C₄	C₄×C₅	1	2	yes	complemented
115	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₃×C₄²	—	2	1	no	—
117	C₂×#217	—	2	1	no	—
118	#926	—	2	2	no	—
119	#926	C₄×C₅	1	4	yes	complemented
120	C₂×C₄⋊Dic₃	—	2	1	no	—
121	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
122	C₂×#208	—	2	2	no	—
123	C₂×#208	—	2	1	no	—
124	C₂×#208	C₄×C₅	1	4	yes	complemented
125	C₂×#208	C₂²×C₅	1	2	yes	—
126	C₂²×C₃⋊C₈	—	2	1	no	—
127	C₂⁴×C₅	#67	1	1	yes	characteristic
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	—	6	2	no	—
130	C₂²×C₄×C₅	Dic₆	1	2	yes	—
131	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
132	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
133	C₂²×C₄×C₅	D₁₂	1	2	yes	—
134	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
135	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
136	C₂²×C₄×C₅	#67	1	1	yes	characteristic
137	C₂²×C₄×C₅	#67	1	1	yes	characteristic
138	C₂²×C₄×C₅	#67	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
140	C₅×M₁₆	—	3	4	no	—
141	C₅×M₁₆	—	6	4	no	—
142	C₅×M₁₆	—	6	2	no	—
143	C₂×C₅×C₈	—	6	4	no	—
144	C₂×C₅×C₈	—	6	2	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	6	4	no	—
147	C₅×C₄⋊C₄	C₂×Dic₃	1	4	yes	—
148	C₅×C₂²⋊C₄	—	2	2	no	—
149	C₅×C₂²⋊C₄	—	2	2	no	—
150	C₅×C₂²⋊C₄	—	6	4	no	—
151	C₄²×C₅	—	2	2	no	—
152	C₄²×C₅	—	2	2	no	—
153	C₄²×C₅	—	3	4	no	—
154	C₄²×C₅	—	6	2	no	—
155	C₂²×M₁₆	—	3	1	no	—
156	C₂×#117	—	3	1	no	—
157	C₂×#117	C₅×D₃	1	1	yes	characteristic
158	#339	—	3	4	no	—
159	C₂²×C₃×C₅	—	2	2	no	—
160	C₂²×C₃×C₅	—	2	2	no	—
161	C₂²×C₃×C₅	—	2	2	no	—
162	C₂²×C₃×C₅	—	4	2	no	—
163	C₂²×C₃×C₅	—	4	2	no	—
164	C₂²×C₃×C₅	#95	1	2	yes	—
165	C₂²×C₃×C₅	#95	1	2	yes	—
166	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
169	C₃×C₄×C₅	—	4	4	no	—
170	C₃×C₄×C₅	#95	1	2	yes	—
171	C₃×C₄×C₅	#95	1	2	yes	—
172	C₃×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
173	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₃×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₅×Dic₃	—	4	4	no	—
177	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
178	C₂²×C₃×C₄	—	2	2	no	—
179	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
180	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
181	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
182	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
183	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
184	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
185	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
186	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
187	C₂²×C₃×C₄	C₅×Q₈	1	2	yes	—
188	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
189	C₂²×Dic₃	—	2	2	no	—
190	C₃×C₄⋊C₄	—	2	2	no	—
191	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
192	C₃×C₂²⋊C₄	—	2	2	no	—
193	C₃×C₂²⋊C₄	—	2	2	no	—
194	C₃×C₄²	—	2	2	no	—
195	C₃×C₄²	—	2	2	no	—
196	#217	—	2	4	no	—
197	C₄⋊Dic₃	—	2	4	no	—
198	C₄×Dic₃	—	2	2	no	—
199	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
200	#208	—	2	4	no	—
201	#208	—	2	2	no	—
202	#208	C₂×C₄×C₅	1	4	yes	complemented
203	C₂×C₃⋊C₈	—	2	4	no	—
204	C₂×C₃⋊C₈	—	2	2	no	—
205	C₂³×C₅	—	4	2	no	—
206	C₂³×C₅	Dic₃⋊C₄	1	2	yes	—
207	C₂³×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
208	C₂³×C₅	#217	1	1	yes	characteristic
209	C₂³×C₅	#217	1	1	yes	characteristic
210	C₂³×C₅	C₂×#67	1	1	yes	characteristic
211	C₂×C₄×C₅	—	2	4	no	—
212	C₂×C₄×C₅	—	4	4	no	—
213	C₂×C₄×C₅	—	6	4	no	—
214	C₂×C₄×C₅	—	12	4	no	—
215	C₂×C₄×C₅	C₄×Dic₃	1	2	yes	—
216	C₂×C₄×C₅	C₄×Dic₃	1	2	yes	—
217	C₂×C₄×C₅	Dic₃⋊C₄	1	2	yes	—
218	C₂×C₄×C₅	Dic₃⋊C₄	1	2	yes	—
219	C₂×C₄×C₅	Dic₃⋊C₄	1	2	yes	—
220	C₂×C₄×C₅	C₄⋊Dic₃	1	2	yes	—
221	C₂×C₄×C₅	C₄⋊Dic₃	1	2	yes	—
222	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
223	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
224	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	2	yes	—
225	C₂×C₄×C₅	#217	1	1	yes	characteristic
226	C₂×C₄×C₅	#217	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂×Dic₆	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
233	C₅×C₈	—	6	4	no	—
234	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
235	C₂×M₁₆	—	3	4	no	—
236	C₂×M₁₆	—	3	2	no	—
237	C₂×M₁₆	—	6	2	no	—
238	C₂×M₁₆	—	6	1	no	—
239	C₂²×C₈	—	6	1	no	—
240	#117	—	2	1	no	—
241	#117	—	2	1	no	—
242	#117	—	3	4	no	—
243	#117	—	6	2	no	—
244	#117	C₅×Dic₃	1	2	yes	complemented
245	#117	C₂×C₅×D₃	1	2	yes	—
246	C₂×C₄⋊C₄	—	6	1	no	—
247	C₂×C₄⋊C₄	C₅×Dic₃	1	2	yes	complemented
248	C₂×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₂²⋊C₄	—	6	1	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	—	3	2	no	—
252	C₂×C₃×C₅	—	2	1	no	—
253	C₂×C₃×C₅	—	2	2	no	—
254	C₂×C₃×C₅	—	2	2	no	—
255	C₂×C₃×C₅	—	2	1	no	—
256	C₂×C₃×C₅	C₂×#95	1	1	yes	characteristic
257	C₂×C₃×C₅	#421	1	2	yes	—
258	C₂³×C₃	—	4	2	no	—
259	C₂³×C₃	C₅×C₂²⋊C₄	1	2	yes	—
260	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
261	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
262	C₂³×C₃	C₅×C₄⋊C₄	1	2	yes	—
263	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
264	C₂×C₃×C₄	—	2	4	no	—
265	C₂×C₃×C₄	—	4	4	no	—
266	C₂×C₃×C₄	C₄²×C₅	1	2	yes	—
267	C₂×C₃×C₄	C₄²×C₅	1	2	yes	—
268	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
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×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
274	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
275	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
276	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
277	C₂×C₃×C₄	C₅×C₄⋊C₄	1	2	yes	—
278	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
279	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
280	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
281	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
282	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
283	C₂×C₃×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
284	C₂×Dic₃	—	2	4	no	—
285	C₂×Dic₃	—	4	4	no	—
286	C₃⋊C₈	—	2	4	no	—
287	C₂²×C₅	—	2	2	no	—
288	C₂²×C₅	—	2	2	no	—
289	C₂²×C₅	—	2	2	no	—
290	C₂²×C₅	—	4	2	no	—
291	C₂²×C₅	—	4	2	no	—
292	C₂²×C₅	C₃⋊#95	1	2	yes	—
293	C₂²×C₅	C₃⋊#95	1	2	yes	—
294	C₂²×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
295	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
296	C₂²×C₅	C₂×#217	1	1	yes	characteristic
297	C₄×C₅	—	4	4	no	—
298	C₄×C₅	—	12	4	no	—
299	C₄×C₅	C₃⋊#95	1	2	yes	—
300	C₄×C₅	C₃⋊#95	1	2	yes	—
301	C₄×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
302	C₄×C₅	C₂×Dic₃⋊C₄	1	1	yes	characteristic
303	C₄×C₅	C₂×C₄⋊Dic₃	1	1	yes	characteristic
304	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
305	C₂⁴	C₅×#67	1	1	yes	characteristic
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	6	2	no	—
308	C₂²×C₄	C₅×Dic₆	1	2	yes	—
309	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
310	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
311	C₂²×C₄	C₅×D₁₂	1	2	yes	—
312	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
314	C₂²×C₄	C₅×#67	1	1	yes	characteristic
315	C₂²×C₄	C₅×#67	1	1	yes	characteristic
316	C₂²×C₄	C₅×#67	1	1	yes	characteristic
317	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
318	M₁₆	—	3	4	no	—
319	M₁₆	—	6	4	no	—
320	M₁₆	—	6	2	no	—
321	C₂×C₈	—	6	4	no	—
322	C₂×C₈	—	6	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	6	4	no	—
325	C₄⋊C₄	C₂×C₅×Dic₃	1	4	yes	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	6	4	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	3	4	no	—
332	C₄²	—	6	2	no	—
333	C₃×C₅	#1733	1	1	yes	characteristic, complemented, Hall
334	C₂²×C₃	—	2	2	no	—
335	C₂²×C₃	—	2	2	no	—
336	C₂²×C₃	—	2	2	no	—
337	C₂²×C₃	—	4	2	no	—
338	C₂²×C₃	—	4	2	no	—
339	C₂²×C₃	C₅×#95	1	2	yes	—
340	C₂²×C₃	C₅×#95	1	2	yes	—
341	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
342	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
343	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
344	C₃×C₄	—	4	4	no	—
345	C₃×C₄	C₅×#95	1	2	yes	—
346	C₃×C₄	C₅×#95	1	2	yes	—
347	C₃×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
348	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
349	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
350	C₃×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
351	Dic₃	—	4	4	no	—
352	C₂×C₅	—	2	1	no	—
353	C₂×C₅	—	2	2	no	—
354	C₂×C₅	—	2	2	no	—
355	C₂×C₅	—	2	1	no	—
356	C₂×C₅	C₂×C₃⋊#95	1	1	yes	characteristic
357	C₂×C₅	#5236	1	2	yes	—
358	C₂³	—	4	2	no	—
359	C₂³	C₅×Dic₃⋊C₄	1	2	yes	—
360	C₂³	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
361	C₂³	C₅×#217	1	1	yes	characteristic
362	C₂³	C₅×#217	1	1	yes	characteristic
363	C₂³	C₂×C₅×#67	1	1	yes	characteristic
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	6	4	no	—
367	C₂×C₄	—	12	4	no	—
368	C₂×C₄	C₄×C₅×Dic₃	1	2	yes	—
369	C₂×C₄	C₄×C₅×Dic₃	1	2	yes	—
370	C₂×C₄	C₅×Dic₃⋊C₄	1	2	yes	—
371	C₂×C₄	C₅×Dic₃⋊C₄	1	2	yes	—
372	C₂×C₄	C₅×Dic₃⋊C₄	1	2	yes	—
373	C₂×C₄	C₅×C₄⋊Dic₃	1	2	yes	—
374	C₂×C₄	C₅×C₄⋊Dic₃	1	2	yes	—
375	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
376	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
377	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	2	yes	—
378	C₂×C₄	C₅×#217	1	1	yes	characteristic
379	C₂×C₄	C₅×#217	1	1	yes	characteristic
380	C₂×C₄	C₂×C₅×Dic₆	1	1	yes	characteristic
381	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
382	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
383	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
384	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
385	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
386	C₈	—	6	4	no	—
387	C₂×C₃	—	2	1	no	—
388	C₂×C₃	—	2	1	no	—
389	C₂×C₃	—	2	2	no	—
390	C₂×C₃	—	2	2	no	—
391	C₂×C₃	C₂×C₅×#95	1	1	yes	characteristic
392	C₂×C₃	C₅×#421	1	2	yes	—
393	C₅	#71574	1	1	yes	characteristic, direct product factor, Sylow
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	C₅×C₃⋊#95	1	2	yes	—
400	C₂²	C₅×C₃⋊#95	1	2	yes	—
401	C₂²	C₂×C₅×Dic₃⋊C₄	1	1	yes	characteristic
402	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
403	C₂²	C₂×C₅×#217	1	1	yes	characteristic
404	C₄	—	4	4	no	—
405	C₄	—	12	4	no	—
406	C₄	C₅×C₃⋊#95	1	2	yes	—
407	C₄	C₅×C₃⋊#95	1	2	yes	—
408	C₄	C₂×C₄×C₅×Dic₃	1	1	yes	characteristic
409	C₄	C₂×C₅×Dic₃⋊C₄	1	1	yes	characteristic
410	C₄	C₂×C₅×C₄⋊Dic₃	1	1	yes	characteristic
411	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
412	C₃	C₅×#1733	1	1	yes	characteristic, complemented, Sylow
413	C₂	—	2	1	no	—
414	C₂	—	2	1	no	—
415	C₂	—	2	2	no	—
416	C₂	—	2	2	no	—
417	C₂	C₂×C₅×C₃⋊#95	1	1	yes	characteristic
418	C₂	C₅×#5236	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂×#67
commutator	C₃×C₄	C₂×C₄²×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₃×C₅	D₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×#117	D₃
hypocenter	C₃	C₅×#1733
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂³×C₄×C₅ ◁ C₂×C₅×#117

Complements

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

N	H ≅ G/N	type
4. C₅×#4532	C₂	semidirect
9. C₃×C₅×#117	C₄	semidirect
11. C₂×C₃×C₅×C₄⋊C₄	C₄	semidirect
16. C₅×#926	C₄	semidirect
21. C₂×C₅×#208	C₄	semidirect
24. #71574	C₅	direct (N × H)
51. C₄×C₅×Dic₃	C₂×C₄	semidirect
54. C₅×#208	C₂×C₄	semidirect
60. #4532	C₂×C₅	semidirect
71. C₅×#117	Dic₃	semidirect
74. C₂×C₅×C₄⋊C₄	Dic₃	semidirect
112. C₃×#117	C₄×C₅	semidirect
114. C₂×C₃×C₄⋊C₄	C₄×C₅	semidirect
119. #926	C₄×C₅	semidirect
124. C₂×#208	C₄×C₅	semidirect
199. C₄×Dic₃	C₂×C₄×C₅	semidirect
202. #208	C₂×C₄×C₅	semidirect
244. #117	C₅×Dic₃	semidirect
247. C₂×C₄⋊C₄	C₅×Dic₃	semidirect
333. C₃×C₅	#1733	semidirect
393. C₅	#71574	direct (N × H)
412. C₃	C₅×#1733	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#117	2
C₂×C₅×#926	2
C₂²×C₅×#208	2
C₅×#4532	2
C₅×#1733	3
#71574	5

Subgroups — C5×#71574 #14294481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71574 #14294481