Subgroups — C₅×#79279 #14419571

Order 1920.

744 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	C₅×#5479	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#803	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4836	C₂	1	2	yes	maximal, complemented
5	C₅×#4828	C₂	1	2	yes	maximal, complemented
6	C₅×#4730	C₂	1	2	yes	maximal, complemented
7	C₅×#67⋊C₈	C₂	1	2	yes	maximal, complemented
8	C₅×#4690	C₂	1	2	yes	maximal, complemented
9	C₅×#4689	C₂	1	2	yes	maximal, complemented
10	C₅×#2968	—	3	1	no	maximal, Hall
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₅×#930	C₄	1	1	yes	characteristic
13	C₅×#929	C₄	1	2	yes	—
14	C₄×C₅×#67	C₂²	1	2	yes	—
15	C₅×#924	C₄	1	1	yes	characteristic
16	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
17	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
18	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
19	C₅×#876	C₄	1	2	yes	—
20	C₅×#875	C₄	1	1	yes	characteristic
21	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
22	C₅×#872	C₂²	1	2	yes	—
23	C₅×#870	C₄	1	1	yes	characteristic
24	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
25	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
26	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
29	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
30	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
31	C₅×#815	C₂²	1	2	yes	—
32	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
33	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
34	C₅×C₈×Dic₃	C₂²	1	2	yes	—
35	C₅×#803	C₂²	1	1	yes	characteristic
36	C₅×#803	C₂²	1	1	yes	characteristic
37	C₅×#803	C₂²	1	2	yes	—
38	#79279	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₅×#529	—	3	1	no	—
40	C₅×#446	—	3	2	no	—
41	C₅×#435	—	3	2	no	—
42	C₅×#435	—	3	2	no	—
43	C₅×C₈×D₄	—	3	2	no	—
44	C₅×#433	—	3	2	no	—
45	C₅×#431	D₃	1	1	yes	characteristic, complemented
46	C₅×#405	—	3	2	no	—
47	C₂×C₅×#97	—	3	1	no	—
48	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₅×#67	C₂×C₄	1	2	yes	—
52	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
54	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
55	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
56	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
57	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
58	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
59	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
60	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
61	C₅×#217	C₂×C₄	1	2	yes	—
62	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
63	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
64	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
65	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
66	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
67	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
68	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
69	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
70	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
71	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
72	C₄×C₅×Dic₃	C₂³	1	2	yes	—
73	C₂×C₅×C₃⋊C₈	—	2	4	no	—
74	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
75	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
76	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
77	C₅×D₃×C₈	—	2	4	no	—
78	#5479	C₂×C₅	1	1	yes	characteristic
79	C₃×#431	C₂×C₅	1	1	yes	characteristic, complemented
80	C₂×#803	C₂×C₅	1	1	yes	characteristic, complemented
81	#4836	C₂×C₅	1	2	yes	complemented
82	#4828	C₂×C₅	1	2	yes	complemented
83	#4730	C₂×C₅	1	2	yes	complemented
84	#67⋊C₈	C₂×C₅	1	2	yes	complemented
85	#4690	C₂×C₅	1	2	yes	complemented
86	#4689	C₂×C₅	1	2	yes	complemented
87	C₂×C₅×M₁₆	—	3	2	no	—
88	C₂²×C₅×C₈	—	3	2	no	—
89	C₂²×C₅×C₈	—	3	2	no	—
90	C₅×#126	—	3	2	no	—
91	C₅×#125	—	3	1	no	—
92	C₅×#124	—	3	1	no	—
93	C₅×#123	—	3	2	no	—
94	C₅×C₂²⋊Q₈	—	3	1	no	—
95	C₅×#121	—	3	1	no	—
96	C₄×C₅×Q₈	—	3	1	no	—
97	C₄×C₅×D₄	—	3	2	no	—
98	C₄×C₅×D₄	—	3	1	no	—
99	C₅×#117	—	3	2	no	—
100	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
101	C₅×C₄⋊C₈	—	3	2	no	—
102	C₅×C₄⋊C₈	—	3	2	no	—
103	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	—
104	C₅×C₂²⋊C₈	—	3	2	no	—
105	C₅×C₂²⋊C₈	—	3	2	no	—
106	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
107	C₅×C₂²⋊C₈	C₂×D₃	1	1	yes	characteristic
108	C₅×#97	—	3	2	no	—
109	C₅×#97	—	3	1	no	—
110	C₅×#97	—	3	1	no	—
111	C₅×#97	—	3	2	no	—
112	C₄×C₅×C₈	—	3	2	no	—
113	C₄×C₅×C₈	C₂×D₃	1	2	yes	—
114	#2968	—	3	1	no	Sylow
115	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	4	1	no	—
120	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
126	C₅×#67	—	2	4	no	—
127	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
128	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
129	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
130	C₅×D₁₂	—	4	1	no	—
131	C₄×C₅×D₃	—	2	2	no	—
132	C₄×C₅×D₃	—	2	2	no	—
133	C₅×Dic₆	—	4	1	no	—
134	C₃×C₅×C₈	—	2	2	no	—
135	C₃×C₅×C₈	—	2	2	no	—
136	C₅×C₃⋊C₈	—	2	2	no	—
137	C₅×C₃⋊C₈	#41	1	4	yes	—
138	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
139	#930	C₄×C₅	1	1	yes	characteristic
140	#929	C₄×C₅	1	2	yes	—
141	C₄×#67	C₂²×C₅	1	2	yes	—
142	#924	C₄×C₅	1	1	yes	characteristic
143	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
144	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
145	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
146	#876	C₄×C₅	1	2	yes	—
147	#875	C₄×C₅	1	1	yes	characteristic
148	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
149	#872	C₂²×C₅	1	2	yes	—
150	#870	C₄×C₅	1	1	yes	characteristic
151	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
152	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
153	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
154	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
155	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
156	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	—
157	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	—
158	#815	C₂²×C₅	1	2	yes	—
159	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
160	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
161	C₈×Dic₃	C₂²×C₅	1	2	yes	—
162	#803	C₂²×C₅	1	1	yes	characteristic
163	#803	C₂²×C₅	1	1	yes	characteristic
164	#803	C₂²×C₅	1	2	yes	—
165	C₂×C₅×Q₈	—	3	1	no	—
166	C₂×C₅×D₄	—	3	2	no	—
167	C₂×C₅×D₄	—	3	1	no	—
168	C₂²×C₄×C₅	—	3	2	no	—
169	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
172	C₅×M₁₆	—	6	4	no	—
173	C₂×C₅×C₈	—	3	2	no	—
174	C₂×C₅×C₈	—	3	2	no	—
175	C₂×C₅×C₈	—	6	4	no	—
176	C₂×C₅×C₈	—	6	4	no	—
177	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
178	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
179	C₅×C₄⋊C₄	—	3	2	no	—
180	C₅×C₄⋊C₄	—	3	2	no	—
181	C₅×C₄⋊C₄	—	3	1	no	—
182	C₅×C₄⋊C₄	—	3	2	no	—
183	C₅×C₄⋊C₄	—	3	1	no	—
184	C₅×C₄⋊C₄	—	3	2	no	—
185	C₅×C₂²⋊C₄	—	3	2	no	—
186	C₅×C₂²⋊C₄	—	3	2	no	—
187	C₅×C₂²⋊C₄	—	3	2	no	—
188	C₅×C₂²⋊C₄	—	3	2	no	—
189	C₅×C₂²⋊C₄	—	3	2	no	—
190	C₄²×C₅	—	3	2	no	—
191	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
192	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
193	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
194	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
195	#529	—	3	1	no	—
196	#446	—	3	2	no	—
197	#435	—	3	2	no	—
198	#435	—	3	2	no	—
199	C₈×D₄	—	3	2	no	—
200	#433	—	3	2	no	—
201	#431	C₅×D₃	1	1	yes	characteristic, complemented
202	#405	—	3	2	no	—
203	C₂×#97	—	3	1	no	—
204	C₂²×C₃×C₅	—	2	1	no	—
205	C₂²×C₃×C₅	—	2	1	no	—
206	C₂²×C₃×C₅	#131	1	2	yes	—
207	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₅×D₃	—	2	2	no	—
209	C₂×C₅×D₃	—	2	2	no	—
210	C₂×C₅×D₃	—	2	2	no	—
211	C₃×C₄×C₅	—	2	1	no	—
212	C₃×C₄×C₅	—	2	1	no	—
213	C₃×C₄×C₅	—	2	1	no	—
214	C₃×C₄×C₅	—	2	1	no	—
215	C₃×C₄×C₅	—	2	1	no	—
216	C₃×C₄×C₅	C₂×#41	1	2	yes	—
217	C₅×Dic₃	—	2	2	no	—
218	C₅×Dic₃	—	2	2	no	—
219	C₅×Dic₃	—	2	2	no	—
220	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
221	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
222	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
223	C₂×#67	C₂×C₄×C₅	1	2	yes	—
224	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
225	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
226	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
227	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
228	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
229	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
230	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
231	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
232	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
233	#217	C₂×C₄×C₅	1	2	yes	—
234	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
235	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
236	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
237	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
238	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
239	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
240	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
241	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
242	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
243	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
244	C₄×Dic₃	C₂³×C₅	1	2	yes	—
245	C₂×C₃⋊C₈	—	2	4	no	—
246	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
247	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
248	ΓL(1,𝔽₂₅)	—	2	4	no	—
249	D₃×C₈	—	2	4	no	—
250	C₂³×C₅	—	3	2	no	—
251	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
252	C₅×Q₈	—	12	1	no	—
253	C₅×D₄	—	6	4	no	—
254	C₅×D₄	—	12	1	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	3	2	no	—
258	C₂×C₄×C₅	—	3	2	no	—
259	C₂×C₄×C₅	—	3	2	no	—
260	C₂×C₄×C₅	—	4	1	no	—
261	C₂×C₄×C₅	—	6	2	no	—
262	C₂×C₄×C₅	—	6	2	no	—
263	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
265	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
266	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
268	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
269	C₅×C₈	—	2	2	no	—
270	C₅×C₈	—	2	2	no	—
271	C₅×C₈	—	3	4	no	—
272	C₅×C₈	—	6	2	no	—
273	C₂×M₁₆	—	3	2	no	—
274	C₂²×C₈	—	3	2	no	—
275	C₂²×C₈	—	3	2	no	—
276	#126	—	3	2	no	—
277	#125	—	3	1	no	—
278	#124	—	3	1	no	—
279	#123	—	3	2	no	—
280	C₂²⋊Q₈	—	3	1	no	—
281	#121	—	3	1	no	—
282	C₄×Q₈	—	3	1	no	—
283	C₄×D₄	—	3	2	no	—
284	C₄×D₄	—	3	1	no	—
285	#117	—	3	2	no	—
286	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
287	C₄⋊C₈	—	3	2	no	—
288	C₄⋊C₈	—	3	2	no	—
289	C₄⋊C₈	C₂×C₅×D₃	1	2	yes	—
290	C₂²⋊C₈	—	3	2	no	—
291	C₂²⋊C₈	—	3	2	no	—
292	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
293	C₂²⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
294	#97	—	3	2	no	—
295	#97	—	3	1	no	—
296	#97	—	3	1	no	—
297	#97	—	3	2	no	—
298	C₄×C₈	—	3	2	no	—
299	C₄×C₈	C₂×C₅×D₃	1	2	yes	—
300	C₂×C₃×C₅	—	2	2	no	—
301	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
302	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
303	C₂×C₃×C₅	#568	1	1	yes	characteristic
304	C₅×D₃	—	4	2	no	—
305	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
306	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
307	C₂×C₃×C₄	—	2	2	no	—
308	C₂×C₃×C₄	—	2	2	no	—
309	C₂×C₃×C₄	—	4	1	no	—
310	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
311	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
312	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
313	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
314	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
315	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
316	#67	—	2	4	no	—
317	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
318	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
319	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
320	D₁₂	—	4	1	no	—
321	C₄×D₃	—	2	2	no	—
322	C₄×D₃	—	2	2	no	—
323	Dic₆	—	4	1	no	—
324	C₃×C₈	—	2	2	no	—
325	C₃×C₈	—	2	2	no	—
326	C₃⋊C₈	—	2	2	no	—
327	C₃⋊C₈	C₅×#41	1	4	yes	—
328	C₂²×C₅	—	2	1	no	—
329	C₂²×C₅	—	2	1	no	—
330	C₂²×C₅	—	6	2	no	—
331	C₂²×C₅	—	6	2	no	—
332	C₂²×C₅	—	6	2	no	—
333	C₂²×C₅	#901	1	2	yes	—
334	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
335	C₄×C₅	—	2	1	no	—
336	C₄×C₅	—	2	1	no	—
337	C₄×C₅	—	2	1	no	—
338	C₄×C₅	—	2	1	no	—
339	C₄×C₅	—	2	1	no	—
340	C₄×C₅	—	6	2	no	—
341	C₄×C₅	—	6	2	no	—
342	C₄×C₅	—	6	2	no	—
343	C₄×C₅	D₃×#41	1	2	yes	—
344	C₂×Q₈	—	3	1	no	—
345	C₂×D₄	—	3	2	no	—
346	C₂×D₄	—	3	1	no	—
347	C₂²×C₄	—	3	2	no	—
348	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
349	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
350	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
351	M₁₆	—	6	4	no	—
352	C₂×C₈	—	3	2	no	—
353	C₂×C₈	—	3	2	no	—
354	C₂×C₈	—	6	4	no	—
355	C₂×C₈	—	6	4	no	—
356	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
357	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
358	C₄⋊C₄	—	3	2	no	—
359	C₄⋊C₄	—	3	2	no	—
360	C₄⋊C₄	—	3	1	no	—
361	C₄⋊C₄	—	3	2	no	—
362	C₄⋊C₄	—	3	1	no	—
363	C₄⋊C₄	—	3	2	no	—
364	C₂²⋊C₄	—	3	2	no	—
365	C₂²⋊C₄	—	3	2	no	—
366	C₂²⋊C₄	—	3	2	no	—
367	C₂²⋊C₄	—	3	2	no	—
368	C₂²⋊C₄	—	3	2	no	—
369	C₄²	—	3	2	no	—
370	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
371	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
372	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
373	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
374	C₃×C₅	#2968	1	1	yes	characteristic, complemented, Hall
375	C₂²×C₃	—	2	1	no	—
376	C₂²×C₃	—	2	1	no	—
377	C₂²×C₃	C₅×#131	1	2	yes	—
378	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
379	C₂×D₃	—	2	2	no	—
380	C₂×D₃	—	2	2	no	—
381	C₂×D₃	—	2	2	no	—
382	C₃×C₄	—	2	1	no	—
383	C₃×C₄	—	2	1	no	—
384	C₃×C₄	—	2	1	no	—
385	C₃×C₄	—	2	1	no	—
386	C₃×C₄	—	2	1	no	—
387	C₃×C₄	C₂×C₅×#41	1	2	yes	—
388	Dic₃	—	2	2	no	—
389	Dic₃	—	2	2	no	—
390	Dic₃	—	2	2	no	—
391	C₂×C₅	—	2	2	no	—
392	C₂×C₅	—	12	2	no	—
393	C₂×C₅	#5522	1	1	yes	characteristic
394	C₂×C₅	C₂×#901	1	1	yes	characteristic
395	C₂×C₅	#5745	1	1	yes	characteristic
396	C₂³	—	3	2	no	—
397	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
398	Q₈	—	12	1	no	—
399	D₄	—	6	4	no	—
400	D₄	—	12	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	3	2	no	—
404	C₂×C₄	—	3	2	no	—
405	C₂×C₄	—	3	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	6	2	no	—
408	C₂×C₄	—	6	2	no	—
409	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
410	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
411	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
412	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
413	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
414	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	2	2	no	—
417	C₈	—	3	4	no	—
418	C₈	—	6	2	no	—
419	C₂×C₃	—	2	2	no	—
420	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
421	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
422	C₂×C₃	C₅×#568	1	1	yes	characteristic
423	D₃	—	4	2	no	—
424	C₅	#79279	1	1	yes	characteristic, direct product factor, Sylow
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	6	2	no	—
428	C₂²	—	6	2	no	—
429	C₂²	—	6	2	no	—
430	C₂²	C₅×#901	1	2	yes	—
431	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	6	2	no	—
438	C₄	—	6	2	no	—
439	C₄	—	6	2	no	—
440	C₄	C₅×D₃×#41	1	2	yes	—
441	C₃	C₅×#2968	1	1	yes	characteristic, complemented, Sylow
442	C₂	—	2	2	no	—
443	C₂	—	12	2	no	—
444	C₂	C₅×#5522	1	1	yes	characteristic
445	C₂	C₂×C₅×#901	1	1	yes	characteristic
446	C₂	C₅×#5745	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#431	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₅×#930	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#431	D₃
hypocenter	C₃	C₅×#2968
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#431

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#431	C₂	semidirect
3. C₂×C₅×#803	C₂	semidirect
4. C₅×#4836	C₂	semidirect
5. C₅×#4828	C₂	semidirect
6. C₅×#4730	C₂	semidirect
7. C₅×#67⋊C₈	C₂	semidirect
8. C₅×#4690	C₂	semidirect
9. C₅×#4689	C₂	semidirect
38. #79279	C₅	direct (N × H)
45. C₅×#431	D₃	semidirect
79. C₃×#431	C₂×C₅	semidirect
80. C₂×#803	C₂×C₅	semidirect
81. #4836	C₂×C₅	semidirect
82. #4828	C₂×C₅	semidirect
83. #4730	C₂×C₅	semidirect
84. #67⋊C₈	C₂×C₅	semidirect
85. #4690	C₂×C₅	semidirect
86. #4689	C₂×C₅	semidirect
201. #431	C₅×D₃	semidirect
374. C₃×C₅	#2968	semidirect
424. C₅	#79279	direct (N × H)
441. C₃	C₅×#2968	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5479	2
C₃×C₅×#431	2
C₂×C₅×#803	2
C₅×#4836	2
C₅×#4828	2
C₅×#4730	2
C₅×#67⋊C₈	2
C₅×#4690	2
C₅×#4689	2
C₅×#2968	3
#79279	5

Subgroups — C5×#79279 #14419571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79279 #14419571