Subgroups — C₅×#73573 #14326021

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₅×D₁₂	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5212	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4956	C₂	1	4	yes	maximal, complemented
6	C₅×#4929	C₂	1	2	yes	maximal, complemented
7	C₅×#4664	C₂	1	2	yes	maximal, complemented
8	C₅×D₃×#95	C₂	1	2	yes	maximal, complemented
9	C₅×#2339	—	3	1	no	maximal, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₅×#67	C₂²	1	2	yes	—
12	C₂×C₅×#235	—	2	8	no	—
13	C₂×C₅×#235	C₄	1	8	yes	complemented
14	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
16	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
17	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
20	C₂×C₅×#217	C₂²	1	2	yes	—
21	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
23	C₄×C₅×D₁₂	—	2	8	no	—
24	C₃×C₅×#95	C₂²	1	1	yes	characteristic
25	C₃×C₅×#95	C₂²	1	1	yes	characteristic
26	C₅×C₃⋊#95	C₂²	1	2	yes	—
27	C₅×C₃⋊#95	C₂²	1	4	yes	—
28	C₅×C₃⋊#95	C₂²	1	4	yes	—
29	#73573	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
30	C₂²×C₅×#41	—	3	1	no	—
31	C₂×C₄×C₅×D₄	—	3	2	no	—
32	C₅×#391	—	3	2	no	—
33	C₅×#386	—	3	4	no	—
34	C₅×#381	—	3	2	no	—
35	C₅×#380	—	3	1	no	—
36	C₄×C₅×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
37	C₂×C₅×#95	—	3	2	no	—
38	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
39	C₂³×C₅×D₃	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	—	2	4	no	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	complemented
42	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂×C₅×#67	—	2	8	no	—
47	C₂×C₅×#67	C₂×C₄	1	8	yes	complemented
48	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
49	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
50	C₅×#235	—	2	32	no	—
51	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
52	C₂×C₅×D₁₂	D₄	1	8	yes	—
53	C₂×C₄×C₅×D₃	—	2	8	no	—
54	C₂×C₄×C₅×D₃	—	2	8	no	—
55	C₂×C₄×C₅×D₃	—	2	8	no	—
56	C₂×C₄×C₅×D₃	—	4	4	no	—
57	C₂×C₄×C₅×D₃	C₂×C₄	1	8	yes	complemented
58	C₂×C₅×Dic₆	—	2	4	no	—
59	C₂×C₅×Dic₆	C₂×C₄	1	4	yes	complemented
60	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
61	C₃×C₄²×C₅	—	2	4	no	—
62	C₅×#217	—	4	2	no	—
63	C₅×(C₂×D₃)⋊C₄	—	2	8	no	—
64	C₅×C₄⋊Dic₃	—	2	4	no	—
65	C₂²×#235	C₂×C₅	1	1	yes	characteristic
66	C₂×C₄×D₁₂	C₂×C₅	1	2	yes	complemented
67	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
68	#5212	C₂×C₅	1	1	yes	characteristic, complemented
69	#4956	C₂×C₅	1	4	yes	complemented
70	#4929	C₂×C₅	1	2	yes	complemented
71	#4664	C₂×C₅	1	2	yes	complemented
72	D₃×#95	C₂×C₅	1	2	yes	complemented
73	C₂×C₅×#41	—	3	8	no	—
74	C₂×C₅×#41	—	6	8	no	—
75	C₂²×C₅×Q₈	—	3	1	no	—
76	C₂²×C₅×D₄	—	3	2	no	—
77	C₂²×C₅×D₄	—	3	1	no	—
78	C₂³×C₄×C₅	—	3	2	no	—
79	C₂³×C₄×C₅	—	3	4	no	—
80	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
81	C₄×C₅×D₄	—	6	8	no	—
82	C₂×C₅×C₄⋊C₄	—	3	2	no	—
83	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
84	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
85	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
86	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
87	C₅×#95	—	3	2	no	—
88	C₅×#95	—	3	4	no	—
89	C₅×#95	—	3	4	no	—
90	C₅×#95	C₂×D₃	1	1	yes	characteristic
91	C₅×#95	C₂×D₃	1	1	yes	characteristic
92	#2339	—	3	1	no	Sylow
93	C₂³×C₃×C₅	—	2	2	no	—
94	C₂³×C₃×C₅	—	2	2	no	—
95	C₂³×C₃×C₅	—	2	1	no	—
96	C₂³×C₃×C₅	—	2	1	no	—
97	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
98	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
99	C₂²×C₅×D₃	—	2	4	no	—
100	C₂²×C₅×D₃	—	2	2	no	—
101	C₂²×C₅×D₃	—	2	2	no	—
102	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
103	C₂²×C₅×D₃	C₂×D₄	1	8	yes	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	8	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
114	C₂×C₃×C₄×C₅	#41	1	4	yes	complemented
115	C₅×#67	—	2	16	no	—
116	C₂×C₅×Dic₃	—	2	4	no	—
117	C₂×C₅×Dic₃	—	2	4	no	—
118	C₂×C₅×Dic₃	—	2	4	no	—
119	C₂×C₅×Dic₃	—	2	4	no	—
120	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
121	C₅×D₁₂	C₂²⋊C₄	1	16	yes	complemented
122	C₄×C₅×D₃	—	2	16	no	—
123	C₄×C₅×D₃	—	4	16	no	—
124	C₅×Dic₆	—	2	8	no	—
125	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
126	C₂²×#67	C₂²×C₅	1	2	yes	—
127	C₂×#235	—	2	8	no	—
128	C₂×#235	C₄×C₅	1	8	yes	complemented
129	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
130	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
131	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
132	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
133	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
134	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
135	C₂×#217	C₂²×C₅	1	2	yes	—
136	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
137	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
138	C₄×D₁₂	—	2	8	no	—
139	C₃×#95	C₂²×C₅	1	1	yes	characteristic
140	C₃×#95	C₂²×C₅	1	1	yes	characteristic
141	C₃⋊#95	C₂²×C₅	1	2	yes	—
142	C₃⋊#95	C₂²×C₅	1	4	yes	—
143	C₃⋊#95	C₂²×C₅	1	4	yes	—
144	C₂⁴×C₅	—	3	2	no	—
145	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
146	C₅×#41	—	6	32	no	—
147	C₂×C₅×Q₈	—	3	4	no	—
148	C₂×C₅×Q₈	—	6	4	no	—
149	C₂×C₅×D₄	—	3	8	no	—
150	C₂×C₅×D₄	—	3	4	no	—
151	C₂×C₅×D₄	—	3	8	no	—
152	C₂×C₅×D₄	—	6	8	no	—
153	C₂²×C₄×C₅	—	2	4	no	—
154	C₂²×C₄×C₅	—	3	2	no	—
155	C₂²×C₄×C₅	—	3	8	no	—
156	C₂²×C₄×C₅	—	3	4	no	—
157	C₂²×C₄×C₅	—	6	8	no	—
158	C₂²×C₄×C₅	—	6	8	no	—
159	C₂²×C₄×C₅	—	6	8	no	—
160	C₂²×C₄×C₅	—	12	4	no	—
161	C₂²×C₄×C₅	C₄×D₃	1	4	yes	complemented
162	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
163	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
165	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
166	C₅×C₄⋊C₄	—	6	4	no	—
167	C₅×C₂²⋊C₄	—	2	4	no	—
168	C₅×C₂²⋊C₄	—	6	8	no	—
169	C₅×C₂²⋊C₄	—	12	2	no	—
170	C₄²×C₅	—	2	4	no	—
171	C₂²×#41	—	3	1	no	—
172	C₂×C₄×D₄	—	3	2	no	—
173	#391	—	3	2	no	—
174	#386	—	3	4	no	—
175	#381	—	3	2	no	—
176	#380	—	3	1	no	—
177	C₄×C₂²⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
178	C₂×#95	—	3	2	no	—
179	C₂²×C₃×C₅	—	2	2	no	—
180	C₂²×C₃×C₅	—	2	2	no	—
181	C₂²×C₃×C₅	—	2	2	no	—
182	C₂²×C₃×C₅	—	4	2	no	—
183	C₂²×C₃×C₅	—	4	2	no	—
184	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
185	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
186	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
187	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
189	C₂×C₅×D₃	—	2	4	no	—
190	C₂×C₅×D₃	—	2	4	no	—
191	C₂×C₅×D₃	—	2	8	no	—
192	C₂×C₅×D₃	—	2	8	no	—
193	C₂×C₅×D₃	C₂×C₂²⋊C₄	1	8	yes	—
194	C₃×C₄×C₅	—	2	2	no	—
195	C₃×C₄×C₅	—	2	4	no	—
196	C₃×C₄×C₅	—	4	2	no	—
197	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
198	C₅×Dic₃	—	2	4	no	—
199	C₅×Dic₃	—	4	4	no	—
200	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
201	C₂³×D₃	C₂³×C₅	1	2	yes	—
202	C₂²×C₃×C₄	—	2	4	no	—
203	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	complemented
204	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
205	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
206	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
207	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
208	C₂×#67	—	2	8	no	—
209	C₂×#67	C₂×C₄×C₅	1	8	yes	complemented
210	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
211	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
212	#235	—	2	32	no	—
213	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
214	C₂×D₁₂	C₅×D₄	1	8	yes	—
215	C₂×C₄×D₃	—	2	8	no	—
216	C₂×C₄×D₃	—	2	8	no	—
217	C₂×C₄×D₃	—	2	8	no	—
218	C₂×C₄×D₃	—	4	4	no	—
219	C₂×C₄×D₃	C₂×C₄×C₅	1	8	yes	complemented
220	C₂×Dic₆	—	2	4	no	—
221	C₂×Dic₆	C₂×C₄×C₅	1	4	yes	complemented
222	C₃×C₂²⋊C₄	—	2	4	no	—
223	C₃×C₄²	—	2	4	no	—
224	#217	—	4	2	no	—
225	(C₂×D₃)⋊C₄	—	2	8	no	—
226	C₄⋊Dic₃	—	2	4	no	—
227	C₂³×C₅	—	2	2	no	—
228	C₂³×C₅	—	2	2	no	—
229	C₂³×C₅	—	2	1	no	—
230	C₂³×C₅	—	2	1	no	—
231	C₂³×C₅	—	3	4	no	—
232	C₂³×C₅	—	3	8	no	—
233	C₂³×C₅	—	6	4	no	—
234	C₂³×C₅	—	6	2	no	—
235	C₂³×C₅	—	6	2	no	—
236	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
237	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
238	C₅×Q₈	—	6	8	no	—
239	C₅×D₄	—	3	16	no	—
240	C₅×D₄	—	6	16	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	8	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	3	4	no	—
249	C₂×C₄×C₅	—	6	16	no	—
250	C₂×C₄×C₅	—	6	4	no	—
251	C₂×C₄×C₅	—	6	4	no	—
252	C₂×C₄×C₅	—	6	4	no	—
253	C₂×C₄×C₅	—	6	4	no	—
254	C₂×C₄×C₅	—	12	16	no	—
255	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
256	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
257	C₂×C₄×C₅	#235	1	4	yes	complemented
258	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
259	C₂×#41	—	3	8	no	—
260	C₂×#41	—	6	8	no	—
261	C₂²×Q₈	—	3	1	no	—
262	C₂²×D₄	—	3	2	no	—
263	C₂²×D₄	—	3	1	no	—
264	C₂³×C₄	—	3	2	no	—
265	C₂³×C₄	—	3	4	no	—
266	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
267	C₄×D₄	—	6	8	no	—
268	C₂×C₄⋊C₄	—	3	2	no	—
269	C₂×C₂²⋊C₄	—	3	4	no	—
270	C₂×C₂²⋊C₄	—	3	2	no	—
271	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
272	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
273	#95	—	3	2	no	—
274	#95	—	3	4	no	—
275	#95	—	3	4	no	—
276	#95	C₂×C₅×D₃	1	1	yes	characteristic
277	#95	C₂×C₅×D₃	1	1	yes	characteristic
278	C₂×C₃×C₅	—	4	2	no	—
279	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
281	C₂×C₃×C₅	#520	1	1	yes	characteristic
282	C₂×C₃×C₅	#546	1	2	yes	—
283	C₂×C₃×C₅	#547	1	2	yes	—
284	C₅×D₃	—	2	8	no	—
285	C₂³×C₃	—	2	2	no	—
286	C₂³×C₃	—	2	2	no	—
287	C₂³×C₃	—	2	1	no	—
288	C₂³×C₃	—	2	1	no	—
289	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
290	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
291	C₂²×D₃	—	2	4	no	—
292	C₂²×D₃	—	2	2	no	—
293	C₂²×D₃	—	2	2	no	—
294	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
295	C₂²×D₃	C₂×C₅×D₄	1	8	yes	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	8	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
304	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
305	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
306	C₂×C₃×C₄	C₅×#41	1	4	yes	complemented
307	#67	—	2	16	no	—
308	C₂×Dic₃	—	2	4	no	—
309	C₂×Dic₃	—	2	4	no	—
310	C₂×Dic₃	—	2	4	no	—
311	C₂×Dic₃	—	2	4	no	—
312	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
313	D₁₂	C₅×C₂²⋊C₄	1	16	yes	complemented
314	C₄×D₃	—	2	16	no	—
315	C₄×D₃	—	4	16	no	—
316	Dic₆	—	2	8	no	—
317	C₂²×C₅	—	2	2	no	—
318	C₂²×C₅	—	2	2	no	—
319	C₂²×C₅	—	2	2	no	—
320	C₂²×C₅	—	3	8	no	—
321	C₂²×C₅	—	4	2	no	—
322	C₂²×C₅	—	4	2	no	—
323	C₂²×C₅	—	6	4	no	—
324	C₂²×C₅	—	6	4	no	—
325	C₂²×C₅	—	6	8	no	—
326	C₂²×C₅	—	6	8	no	—
327	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
328	C₂²×C₅	C₂×#235	1	2	yes	—
329	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
330	C₂²×C₅	#1009	1	1	yes	characteristic
331	C₂²×C₅	#1010	1	1	yes	characteristic
332	C₄×C₅	—	2	2	no	—
333	C₄×C₅	—	2	4	no	—
334	C₄×C₅	—	4	2	no	—
335	C₄×C₅	—	6	4	no	—
336	C₄×C₅	—	12	4	no	—
337	C₄×C₅	D₃×C₂²⋊C₄	1	4	yes	—
338	C₂⁴	—	3	2	no	—
339	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
340	#41	—	6	32	no	—
341	C₂×Q₈	—	3	4	no	—
342	C₂×Q₈	—	6	4	no	—
343	C₂×D₄	—	3	8	no	—
344	C₂×D₄	—	3	4	no	—
345	C₂×D₄	—	3	8	no	—
346	C₂×D₄	—	6	8	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	3	2	no	—
349	C₂²×C₄	—	3	8	no	—
350	C₂²×C₄	—	3	4	no	—
351	C₂²×C₄	—	6	8	no	—
352	C₂²×C₄	—	6	8	no	—
353	C₂²×C₄	—	6	8	no	—
354	C₂²×C₄	—	12	4	no	—
355	C₂²×C₄	C₄×C₅×D₃	1	4	yes	complemented
356	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
357	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
358	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
359	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
360	C₄⋊C₄	—	6	4	no	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	6	8	no	—
363	C₂²⋊C₄	—	12	2	no	—
364	C₄²	—	2	4	no	—
365	C₃×C₅	#2339	1	1	yes	characteristic, complemented, Hall
366	C₂²×C₃	—	2	2	no	—
367	C₂²×C₃	—	2	2	no	—
368	C₂²×C₃	—	2	2	no	—
369	C₂²×C₃	—	4	2	no	—
370	C₂²×C₃	—	4	2	no	—
371	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
372	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
373	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
374	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
375	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
376	C₂×D₃	—	2	4	no	—
377	C₂×D₃	—	2	4	no	—
378	C₂×D₃	—	2	8	no	—
379	C₂×D₃	—	2	8	no	—
380	C₂×D₃	C₂×C₅×C₂²⋊C₄	1	8	yes	—
381	C₃×C₄	—	2	2	no	—
382	C₃×C₄	—	2	4	no	—
383	C₃×C₄	—	4	2	no	—
384	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
385	Dic₃	—	2	4	no	—
386	Dic₃	—	4	4	no	—
387	C₂×C₅	—	4	2	no	—
388	C₂×C₅	—	6	8	no	—
389	C₂×C₅	C₄×#235	1	1	yes	characteristic
390	C₂×C₅	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
391	C₂×C₅	#5523	1	1	yes	characteristic
392	C₂×C₅	#5550	1	2	yes	—
393	C₂×C₅	#5551	1	2	yes	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	1	no	—
397	C₂³	—	2	1	no	—
398	C₂³	—	3	4	no	—
399	C₂³	—	3	8	no	—
400	C₂³	—	6	4	no	—
401	C₂³	—	6	2	no	—
402	C₂³	—	6	2	no	—
403	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
404	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
405	Q₈	—	6	8	no	—
406	D₄	—	3	16	no	—
407	D₄	—	6	16	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	8	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	3	4	no	—
416	C₂×C₄	—	6	16	no	—
417	C₂×C₄	—	6	4	no	—
418	C₂×C₄	—	6	4	no	—
419	C₂×C₄	—	6	4	no	—
420	C₂×C₄	—	6	4	no	—
421	C₂×C₄	—	12	16	no	—
422	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
423	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
424	C₂×C₄	C₅×#235	1	4	yes	complemented
425	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
426	C₂×C₃	—	4	2	no	—
427	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
428	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
429	C₂×C₃	C₅×#520	1	1	yes	characteristic
430	C₂×C₃	C₅×#546	1	2	yes	—
431	C₂×C₃	C₅×#547	1	2	yes	—
432	D₃	—	2	8	no	—
433	C₅	#73573	1	1	yes	characteristic, direct product factor, Sylow
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	3	8	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	6	4	no	—
441	C₂²	—	6	4	no	—
442	C₂²	—	6	8	no	—
443	C₂²	—	6	8	no	—
444	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
445	C₂²	C₂×C₅×#235	1	2	yes	—
446	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
447	C₂²	C₅×#1009	1	1	yes	characteristic
448	C₂²	C₅×#1010	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	2	4	no	—
451	C₄	—	4	2	no	—
452	C₄	—	6	4	no	—
453	C₄	—	12	4	no	—
454	C₄	C₅×D₃×C₂²⋊C₄	1	4	yes	—
455	C₃	C₅×#2339	1	1	yes	characteristic, complemented, Sylow
456	C₂	—	4	2	no	—
457	C₂	—	6	8	no	—
458	C₂	C₄×C₅×#235	1	1	yes	characteristic
459	C₂	C₂×C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
460	C₂	C₅×#5523	1	1	yes	characteristic
461	C₂	C₅×#5550	1	2	yes	—
462	C₂	C₅×#5551	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×C₂²⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×#235	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₄×C₅×C₂²⋊C₄	D₃
hypocenter	C₃	C₅×#2339
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₅×D₁₂	C₂	semidirect
3. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
4. C₅×#5212	C₂	semidirect
5. C₅×#4956	C₂	semidirect
6. C₅×#4929	C₂	semidirect
7. C₅×#4664	C₂	semidirect
8. C₅×D₃×#95	C₂	semidirect
13. C₂×C₅×#235	C₄	semidirect
29. #73573	C₅	direct (N × H)
36. C₄×C₅×C₂²⋊C₄	D₃	semidirect
41. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
47. C₂×C₅×#67	C₂×C₄	semidirect
57. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
59. C₂×C₅×Dic₆	C₂×C₄	semidirect
66. C₂×C₄×D₁₂	C₂×C₅	semidirect
67. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
68. #5212	C₂×C₅	semidirect
69. #4956	C₂×C₅	semidirect
70. #4929	C₂×C₅	semidirect
71. #4664	C₂×C₅	semidirect
72. D₃×#95	C₂×C₅	semidirect
114. C₂×C₃×C₄×C₅	#41	semidirect
121. C₅×D₁₂	C₂²⋊C₄	semidirect
128. C₂×#235	C₄×C₅	semidirect
161. C₂²×C₄×C₅	C₄×D₃	semidirect
177. C₄×C₂²⋊C₄	C₅×D₃	semidirect
203. C₂²×C₃×C₄	C₂×C₄×C₅	semidirect
209. C₂×#67	C₂×C₄×C₅	semidirect
219. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
221. C₂×Dic₆	C₂×C₄×C₅	semidirect
257. C₂×C₄×C₅	#235	semidirect
306. C₂×C₃×C₄	C₅×#41	semidirect
313. D₁₂	C₅×C₂²⋊C₄	semidirect
355. C₂²×C₄	C₄×C₅×D₃	semidirect
365. C₃×C₅	#2339	semidirect
424. C₂×C₄	C₅×#235	semidirect
433. C₅	#73573	direct (N × H)
455. C₃	C₅×#2339	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₅×#235	2
C₂×C₄×C₅×D₁₂	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#5212	2
C₅×#4956	2
C₅×#4929	2
C₅×#4664	2
C₅×D₃×#95	2
C₅×#2339	3
#73573	5

Subgroups — C5×#73573 #14326021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73573 #14326021