Subgroups — C₅×#74005 #14322799

Order 1920.

1632 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₃×C₂²⋊C₄	C₂	1	2	yes	maximal
3	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5212	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4989	C₂	1	4	yes	maximal, complemented
6	C₅×#4942	C₂	1	2	yes	maximal, complemented
7	C₅×#4668	C₂	1	4	yes	maximal, complemented
8	C₅×#2315	—	3	1	no	maximal, Hall
9	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
14	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
15	C₂×C₅×#217	C₂²	1	2	yes	—
16	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	8	yes	complemented
17	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
18	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
19	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
20	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
21	C₂×C₅×Dic₃⋊C₄	C₂²	1	4	yes	complemented
22	C₅×D₃×C₂²⋊C₄	—	2	8	no	—
23	C₃×C₅×#95	C₂²	1	2	yes	complemented
24	C₅×C₃⋊#95	C₂²	1	4	yes	complemented
25	C₅×C₃⋊#95	C₂²	1	2	yes	complemented
26	#74005	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
27	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
28	C₂²×C₅×C₂²⋊C₄	—	3	2	no	—
29	C₅×#385	—	3	4	no	—
30	C₅×#385	—	3	4	no	—
31	C₅×#380	—	3	1	no	—
32	C₅×#380	—	3	2	no	—
33	C₅×#380	D₃	1	1	yes	characteristic, complemented
34	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
35	C₂³×C₅×D₃	—	4	2	no	—
36	C₂³×C₅×D₃	—	4	2	no	—
37	C₂³×C₅×D₃	C₂×C₄	1	4	yes	—
38	C₂³×C₅×D₃	D₄	1	4	yes	—
39	C₂³×C₅×D₃	Q₈	1	4	yes	—
40	C₂³×C₅×D₃	C₂³	1	2	yes	—
41	C₂²×C₃×C₄×C₅	—	4	2	no	—
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	complemented
43	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₅×Dic₃	—	4	2	no	—
47	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
48	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
49	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
50	C₂×C₄×C₅×D₃	—	2	8	no	—
51	C₂×C₄×C₅×D₃	—	4	4	no	—
52	C₂×C₄×C₅×D₃	—	4	4	no	—
53	C₃×C₅×C₄⋊C₄	—	4	2	no	—
54	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
55	C₅×#217	—	2	4	no	—
56	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
57	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	complemented
58	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	complemented
59	C₅×C₄⋊Dic₃	—	4	2	no	—
60	C₅×Dic₃⋊C₄	—	4	4	no	—
61	C₂²×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic
62	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	2	yes	—
63	C₃×#380	C₂×C₅	1	1	yes	characteristic, complemented
64	#5212	C₂×C₅	1	1	yes	characteristic, complemented
65	#4989	C₂×C₅	1	4	yes	complemented
66	#4942	C₂×C₅	1	2	yes	complemented
67	#4668	C₂×C₅	1	4	yes	complemented
68	C₂⁵×C₅	—	3	1	no	—
69	C₂³×C₄×C₅	—	3	1	no	—
70	C₂³×C₄×C₅	—	3	4	no	—
71	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
72	C₂×C₅×C₄⋊C₄	—	3	4	no	—
73	C₂×C₅×C₄⋊C₄	—	3	2	no	—
74	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
75	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
76	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
77	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
78	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
79	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
80	C₂×C₅×C₂²⋊C₄	—	6	8	no	—
81	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
82	C₅×#95	—	3	4	no	—
83	C₅×#95	—	3	2	no	—
84	C₅×#95	C₂×D₃	1	2	yes	complemented
85	#2315	—	3	1	no	Sylow
86	C₂³×C₃×C₅	—	2	2	no	—
87	C₂³×C₃×C₅	—	2	2	no	—
88	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
89	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
90	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
91	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
92	C₂²×C₅×D₃	—	2	4	no	—
93	C₂²×C₅×D₃	—	2	4	no	—
94	C₂²×C₅×D₃	—	4	4	no	—
95	C₂²×C₅×D₃	—	4	4	no	—
96	C₂²×C₅×D₃	—	4	8	no	—
97	C₂²×C₅×D₃	—	4	8	no	—
98	C₂²×C₅×D₃	C₄⋊C₄	1	16	yes	complemented
99	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
100	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
101	C₂²×C₅×D₃	C₂×Q₈	1	4	yes	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	2	no	—
104	C₂×C₃×C₄×C₅	—	2	4	no	—
105	C₂×C₃×C₄×C₅	—	2	4	no	—
106	C₂×C₃×C₄×C₅	—	2	4	no	—
107	C₂×C₃×C₄×C₅	—	4	4	no	—
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
109	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
110	C₂×C₅×Dic₃	—	2	4	no	—
111	C₂×C₅×Dic₃	—	2	4	no	—
112	C₂×C₅×Dic₃	—	2	4	no	—
113	C₂×C₅×Dic₃	—	2	4	no	—
114	C₂×C₅×Dic₃	—	4	4	no	—
115	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
116	C₄×C₅×D₃	—	4	16	no	—
117	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
118	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
119	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
120	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
121	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
122	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
123	C₂×#217	C₂²×C₅	1	2	yes	—
124	C₂×(C₂×D₃)⋊C₄	C₄×C₅	1	8	yes	complemented
125	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
126	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
127	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
128	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	complemented
129	C₂×Dic₃⋊C₄	C₂²×C₅	1	4	yes	complemented
130	D₃×C₂²⋊C₄	—	2	8	no	—
131	C₃×#95	C₂²×C₅	1	2	yes	complemented
132	C₃⋊#95	C₂²×C₅	1	4	yes	complemented
133	C₃⋊#95	C₂²×C₅	1	2	yes	complemented
134	C₂⁴×C₅	—	3	2	no	—
135	C₂⁴×C₅	—	3	4	no	—
136	C₂⁴×C₅	—	3	4	no	—
137	C₂⁴×C₅	—	3	4	no	—
138	C₂⁴×C₅	—	12	2	no	—
139	C₂⁴×C₅	—	12	2	no	—
140	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
141	C₂²×C₄×C₅	—	3	2	no	—
142	C₂²×C₄×C₅	—	3	4	no	—
143	C₂²×C₄×C₅	—	3	4	no	—
144	C₂²×C₄×C₅	—	4	2	no	—
145	C₂²×C₄×C₅	—	6	8	no	—
146	C₂²×C₄×C₅	—	12	4	no	—
147	C₂²×C₄×C₅	—	12	4	no	—
148	C₂²×C₄×C₅	—	12	2	no	—
149	C₂²×C₄×C₅	C₄×D₃	1	4	yes	complemented
150	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
151	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
153	C₅×C₄⋊C₄	—	4	2	no	—
154	C₅×C₄⋊C₄	—	12	4	no	—
155	C₅×C₄⋊C₄	—	12	2	no	—
156	C₅×C₂²⋊C₄	—	2	4	no	—
157	C₅×C₂²⋊C₄	—	3	8	no	—
158	C₅×C₂²⋊C₄	—	3	8	no	—
159	C₅×C₂²⋊C₄	—	6	8	no	—
160	C₅×C₂²⋊C₄	—	6	4	no	—
161	C₂²×C₂²⋊C₄	—	3	1	no	—
162	C₂²×C₂²⋊C₄	—	3	2	no	—
163	#385	—	3	4	no	—
164	#385	—	3	4	no	—
165	#380	—	3	1	no	—
166	#380	—	3	2	no	—
167	#380	C₅×D₃	1	1	yes	characteristic, complemented
168	C₂²×C₃×C₅	—	2	2	no	—
169	C₂²×C₃×C₅	—	2	2	no	—
170	C₂²×C₃×C₅	—	2	4	no	—
171	C₂²×C₃×C₅	—	2	4	no	—
172	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	4	yes	—
173	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
174	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
175	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
176	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
177	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
178	C₂×C₅×D₃	—	2	4	no	—
179	C₂×C₅×D₃	—	2	4	no	—
180	C₂×C₅×D₃	—	2	8	no	—
181	C₂×C₅×D₃	—	2	8	no	—
182	C₂×C₅×D₃	—	4	16	no	—
183	C₂×C₅×D₃	C₂×C₄⋊C₄	1	8	yes	—
184	C₃×C₄×C₅	—	2	2	no	—
185	C₃×C₄×C₅	—	2	2	no	—
186	C₃×C₄×C₅	—	4	4	no	—
187	C₅×Dic₃	—	2	4	no	—
188	C₅×Dic₃	—	4	4	no	—
189	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
190	C₂³×D₃	—	4	2	no	—
191	C₂³×D₃	—	4	2	no	—
192	C₂³×D₃	C₂×C₄×C₅	1	4	yes	—
193	C₂³×D₃	C₅×D₄	1	4	yes	—
194	C₂³×D₃	C₅×Q₈	1	4	yes	—
195	C₂³×D₃	C₂³×C₅	1	2	yes	—
196	C₂²×C₃×C₄	—	4	2	no	—
197	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	complemented
198	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
199	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
201	C₂²×Dic₃	—	4	2	no	—
202	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
203	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
204	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
205	C₂×C₄×D₃	—	2	8	no	—
206	C₂×C₄×D₃	—	4	4	no	—
207	C₂×C₄×D₃	—	4	4	no	—
208	C₃×C₄⋊C₄	—	4	2	no	—
209	C₃×C₂²⋊C₄	—	2	4	no	—
210	#217	—	2	4	no	—
211	(C₂×D₃)⋊C₄	—	2	8	no	—
212	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
213	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
214	C₄⋊Dic₃	—	4	2	no	—
215	Dic₃⋊C₄	—	4	4	no	—
216	C₂³×C₅	—	2	2	no	—
217	C₂³×C₅	—	2	2	no	—
218	C₂³×C₅	—	3	4	no	—
219	C₂³×C₅	—	3	4	no	—
220	C₂³×C₅	—	3	4	no	—
221	C₂³×C₅	—	3	16	no	—
222	C₂³×C₅	—	6	4	no	—
223	C₂³×C₅	—	6	4	no	—
224	C₂³×C₅	—	12	8	no	—
225	C₂³×C₅	—	12	4	no	—
226	C₂³×C₅	—	12	4	no	—
227	C₂³×C₅	—	12	8	no	—
228	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
229	C₂³×C₅	D₃×D₄	1	2	yes	—
230	C₂³×C₅	D₃×Q₈	1	2	yes	—
231	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	2	4	no	—
236	C₂×C₄×C₅	—	2	4	no	—
237	C₂×C₄×C₅	—	3	4	no	—
238	C₂×C₄×C₅	—	4	4	no	—
239	C₂×C₄×C₅	—	6	4	no	—
240	C₂×C₄×C₅	—	6	4	no	—
241	C₂×C₄×C₅	—	6	4	no	—
242	C₂×C₄×C₅	—	6	4	no	—
243	C₂×C₄×C₅	—	12	16	no	—
244	C₂×C₄×C₅	—	12	4	no	—
245	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
246	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
247	C₂⁵	—	3	1	no	—
248	C₂³×C₄	—	3	1	no	—
249	C₂³×C₄	—	3	4	no	—
250	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
251	C₂×C₄⋊C₄	—	3	4	no	—
252	C₂×C₄⋊C₄	—	3	2	no	—
253	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
254	C₂×C₂²⋊C₄	—	3	8	no	—
255	C₂×C₂²⋊C₄	—	3	2	no	—
256	C₂×C₂²⋊C₄	—	3	2	no	—
257	C₂×C₂²⋊C₄	—	3	2	no	—
258	C₂×C₂²⋊C₄	—	3	4	no	—
259	C₂×C₂²⋊C₄	—	6	8	no	—
260	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
261	#95	—	3	4	no	—
262	#95	—	3	2	no	—
263	#95	C₂×C₅×D₃	1	2	yes	complemented
264	C₂×C₃×C₅	—	2	4	no	—
265	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
266	C₂×C₃×C₅	#518	1	1	yes	characteristic
267	C₂×C₃×C₅	#518	1	1	yes	characteristic
268	C₂×C₃×C₅	#534	1	2	yes	—
269	C₂×C₃×C₅	#543	1	2	yes	—
270	C₅×D₃	—	2	8	no	—
271	C₂³×C₃	—	2	2	no	—
272	C₂³×C₃	—	2	2	no	—
273	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
274	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
275	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
276	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
277	C₂²×D₃	—	2	4	no	—
278	C₂²×D₃	—	2	4	no	—
279	C₂²×D₃	—	4	4	no	—
280	C₂²×D₃	—	4	4	no	—
281	C₂²×D₃	—	4	8	no	—
282	C₂²×D₃	—	4	8	no	—
283	C₂²×D₃	C₅×C₄⋊C₄	1	16	yes	complemented
284	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
285	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
286	C₂²×D₃	C₂×C₅×Q₈	1	4	yes	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	4	no	—
290	C₂×C₃×C₄	—	2	4	no	—
291	C₂×C₃×C₄	—	2	4	no	—
292	C₂×C₃×C₄	—	4	4	no	—
293	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
294	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
295	C₂×Dic₃	—	2	4	no	—
296	C₂×Dic₃	—	2	4	no	—
297	C₂×Dic₃	—	2	4	no	—
298	C₂×Dic₃	—	2	4	no	—
299	C₂×Dic₃	—	4	4	no	—
300	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
301	C₄×D₃	—	4	16	no	—
302	C₂²×C₅	—	2	4	no	—
303	C₂²×C₅	—	2	2	no	—
304	C₂²×C₅	—	2	2	no	—
305	C₂²×C₅	—	2	4	no	—
306	C₂²×C₅	—	3	8	no	—
307	C₂²×C₅	—	6	8	no	—
308	C₂²×C₅	—	6	4	no	—
309	C₂²×C₅	—	6	4	no	—
310	C₂²×C₅	—	6	8	no	—
311	C₂²×C₅	—	12	16	no	—
312	C₂²×C₅	D₃×C₄⋊C₄	1	4	yes	—
313	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
314	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
315	C₂²×C₅	#1004	1	2	yes	—
316	C₂²×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
317	C₂²×C₅	#1009	1	2	yes	—
318	C₄×C₅	—	2	2	no	—
319	C₄×C₅	—	2	2	no	—
320	C₄×C₅	—	4	4	no	—
321	C₄×C₅	—	6	4	no	—
322	C₄×C₅	—	12	4	no	—
323	C₂⁴	—	3	2	no	—
324	C₂⁴	—	3	4	no	—
325	C₂⁴	—	3	4	no	—
326	C₂⁴	—	3	4	no	—
327	C₂⁴	—	12	2	no	—
328	C₂⁴	—	12	2	no	—
329	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
330	C₂²×C₄	—	3	2	no	—
331	C₂²×C₄	—	3	4	no	—
332	C₂²×C₄	—	3	4	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	6	8	no	—
335	C₂²×C₄	—	12	4	no	—
336	C₂²×C₄	—	12	4	no	—
337	C₂²×C₄	—	12	2	no	—
338	C₂²×C₄	C₄×C₅×D₃	1	4	yes	complemented
339	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
340	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
341	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	—	12	4	no	—
344	C₄⋊C₄	—	12	2	no	—
345	C₂²⋊C₄	—	2	4	no	—
346	C₂²⋊C₄	—	3	8	no	—
347	C₂²⋊C₄	—	3	8	no	—
348	C₂²⋊C₄	—	6	8	no	—
349	C₂²⋊C₄	—	6	4	no	—
350	C₃×C₅	#2315	1	1	yes	characteristic, complemented, Hall
351	C₂²×C₃	—	2	2	no	—
352	C₂²×C₃	—	2	2	no	—
353	C₂²×C₃	—	2	4	no	—
354	C₂²×C₃	—	2	4	no	—
355	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
356	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
357	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
358	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
359	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
360	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
361	C₂×D₃	—	2	4	no	—
362	C₂×D₃	—	2	4	no	—
363	C₂×D₃	—	2	8	no	—
364	C₂×D₃	—	2	8	no	—
365	C₂×D₃	—	4	16	no	—
366	C₂×D₃	C₂×C₅×C₄⋊C₄	1	8	yes	—
367	C₃×C₄	—	2	2	no	—
368	C₃×C₄	—	2	2	no	—
369	C₃×C₄	—	4	4	no	—
370	Dic₃	—	2	4	no	—
371	Dic₃	—	4	4	no	—
372	C₂×C₅	—	2	4	no	—
373	C₂×C₅	—	6	8	no	—
374	C₂×C₅	#5486	1	1	yes	characteristic
375	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
376	C₂×C₅	#5521	1	1	yes	characteristic
377	C₂×C₅	#5605	1	2	yes	—
378	C₂×C₅	#5634	1	2	yes	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	3	4	no	—
382	C₂³	—	3	4	no	—
383	C₂³	—	3	4	no	—
384	C₂³	—	3	16	no	—
385	C₂³	—	6	4	no	—
386	C₂³	—	6	4	no	—
387	C₂³	—	12	4	no	—
388	C₂³	—	12	4	no	—
389	C₂³	—	12	8	no	—
390	C₂³	—	12	8	no	—
391	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
392	C₂³	C₅×D₃×D₄	1	2	yes	—
393	C₂³	C₅×D₃×Q₈	1	2	yes	—
394	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	3	4	no	—
401	C₂×C₄	—	4	4	no	—
402	C₂×C₄	—	6	4	no	—
403	C₂×C₄	—	6	4	no	—
404	C₂×C₄	—	6	4	no	—
405	C₂×C₄	—	6	4	no	—
406	C₂×C₄	—	12	16	no	—
407	C₂×C₄	—	12	4	no	—
408	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
409	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
410	C₂×C₃	—	2	4	no	—
411	C₂×C₃	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
412	C₂×C₃	C₅×#518	1	1	yes	characteristic
413	C₂×C₃	C₅×#518	1	1	yes	characteristic
414	C₂×C₃	C₅×#534	1	2	yes	—
415	C₂×C₃	C₅×#543	1	2	yes	—
416	D₃	—	2	8	no	—
417	C₅	#74005	1	1	yes	characteristic, direct product factor, Sylow
418	C₂²	—	2	2	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	4	no	—
421	C₂²	—	2	4	no	—
422	C₂²	—	3	8	no	—
423	C₂²	—	6	4	no	—
424	C₂²	—	6	4	no	—
425	C₂²	—	6	8	no	—
426	C₂²	—	6	8	no	—
427	C₂²	—	12	16	no	—
428	C₂²	C₅×D₃×C₄⋊C₄	1	4	yes	—
429	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
430	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
431	C₂²	C₅×#1004	1	2	yes	—
432	C₂²	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
433	C₂²	C₅×#1009	1	2	yes	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	4	no	—
437	C₄	—	6	4	no	—
438	C₄	—	12	4	no	—
439	C₃	C₅×#2315	1	1	yes	characteristic, complemented, Sylow
440	C₂	—	2	4	no	—
441	C₂	—	6	8	no	—
442	C₂	C₅×#5486	1	1	yes	characteristic
443	C₂	C₂×C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
444	C₂	C₅×#5521	1	1	yes	characteristic
445	C₂	C₅×#5605	1	2	yes	—
446	C₂	C₅×#5634	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#380	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₅×D₃	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#380	D₃
hypocenter	C₃	C₅×#2315
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#380

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×#380	C₂	semidirect
4. C₅×#5212	C₂	semidirect
5. C₅×#4989	C₂	semidirect
6. C₅×#4942	C₂	semidirect
7. C₅×#4668	C₂	semidirect
13. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
16. C₂×C₅×(C₂×D₃)⋊C₄	C₄	semidirect
20. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
21. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
23. C₃×C₅×#95	C₂²	semidirect
24. C₅×C₃⋊#95	C₂²	semidirect
25. C₅×C₃⋊#95	C₂²	semidirect
26. #74005	C₅	direct (N × H)
33. C₅×#380	D₃	semidirect
42. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
47. C₂²×C₅×Dic₃	C₂×C₄	semidirect
57. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
58. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
63. C₃×#380	C₂×C₅	semidirect
64. #5212	C₂×C₅	semidirect
65. #4989	C₂×C₅	semidirect
66. #4942	C₂×C₅	semidirect
67. #4668	C₂×C₅	semidirect
74. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
84. C₅×#95	C₂×D₃	semidirect
98. C₂²×C₅×D₃	C₄⋊C₄	semidirect
121. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
124. C₂×(C₂×D₃)⋊C₄	C₄×C₅	semidirect
128. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
129. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
131. C₃×#95	C₂²×C₅	semidirect
132. C₃⋊#95	C₂²×C₅	semidirect
133. C₃⋊#95	C₂²×C₅	semidirect
149. C₂²×C₄×C₅	C₄×D₃	semidirect
167. #380	C₅×D₃	semidirect
197. C₂²×C₃×C₄	C₂×C₄×C₅	semidirect
202. C₂²×Dic₃	C₂×C₄×C₅	semidirect
212. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
213. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
253. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
263. #95	C₂×C₅×D₃	semidirect
283. C₂²×D₃	C₅×C₄⋊C₄	semidirect
338. C₂²×C₄	C₄×C₅×D₃	semidirect
350. C₃×C₅	#2315	semidirect
417. C₅	#74005	direct (N × H)
439. C₃	C₅×#2315	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×(C₂×D₃)⋊C₄	2
C₂×C₅×D₃×C₂²⋊C₄	2
C₃×C₅×#380	2
C₅×#5212	2
C₅×#4989	2
C₅×#4942	2
C₅×#4668	2
C₅×#2315	3
#74005	5

Subgroups — C5×#74005 #14322799

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#74005 #14322799