Subgroups — C₅×#73384 #14320970

Order 1920.

1000 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#376	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₅×#4932	C₂	1	1	yes	maximal, characteristic
5	C₄×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic
6	C₄×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic
7	C₄²×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic
8	C₅×#4655	C₂	1	2	yes	maximal
9	C₅×#4654	C₂	1	2	yes	maximal
10	C₅×#4647	C₂	1	2	yes	maximal
11	C₅×#4646	C₂	1	2	yes	maximal
12	C₅×#2295	—	3	1	no	maximal, Hall
13	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
20	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
21	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
24	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
25	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
29	C₄×C₅×Dic₆	C₄	1	8	yes	complemented
30	C₃×C₅×#95	C₂²	1	2	yes	—
31	C₃×C₅×#95	C₂²	1	2	yes	—
32	C₅×C₃⋊#95	C₂²	1	2	yes	—
33	C₅×C₃⋊#95	C₂²	1	2	yes	—
34	C₅×C₃⋊#95	C₂²	1	2	yes	—
35	C₅×C₃⋊#95	C₂²	1	2	yes	—
36	C₅×C₃⋊#95	C₂²	1	2	yes	—
37	#73384	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
38	C₂×C₄×C₅×Q₈	—	3	1	no	—
39	C₅×#391	—	3	2	no	—
40	C₅×#389	—	3	2	no	—
41	C₅×#387	—	3	2	no	—
42	C₅×#387	—	3	2	no	—
43	C₄×C₅×C₄⋊C₄	—	3	1	no	—
44	C₄×C₅×C₄⋊C₄	—	3	1	no	—
45	C₄×C₅×C₄⋊C₄	—	3	1	no	—
46	C₅×#376	—	3	1	no	—
47	C₅×#376	D₃	1	1	yes	characteristic
48	C₄³×C₅	—	3	1	no	—
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
55	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
56	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
57	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
58	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
59	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
60	C₂×C₅×Dic₆	—	2	4	no	—
61	C₂×C₅×Dic₆	C₂×C₄	1	4	yes	—
62	C₃×C₄²×C₅	—	2	2	no	—
63	C₃×C₄²×C₅	C₂×C₄	1	4	yes	—
64	C₃×C₄²×C₅	Q₈	1	4	yes	complemented
65	C₅×C₄⋊Dic₃	—	2	4	no	—
66	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	—
67	C₅×Dic₃⋊C₄	—	2	4	no	—
68	C₅×Dic₃⋊C₄	—	2	4	no	—
69	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
70	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
71	C₄×C₅×Dic₃	—	2	2	no	—
72	C₄×C₅×Dic₃	—	2	2	no	—
73	C₄×C₅×Dic₃	—	2	4	no	—
74	C₄×C₅×Dic₃	—	2	4	no	—
75	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
76	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
77	C₂×C₄×Dic₆	C₂×C₅	1	1	yes	characteristic
78	C₃×#376	C₂×C₅	1	1	yes	characteristic
79	C₄×C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic
80	#4932	C₂×C₅	1	1	yes	characteristic
81	C₄×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic
82	C₄×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic
83	C₄²×Dic₃	C₂×C₅	1	1	yes	characteristic
84	#4655	C₂×C₅	1	2	yes	—
85	#4654	C₂×C₅	1	2	yes	—
86	#4647	C₂×C₅	1	2	yes	—
87	#4646	C₂×C₅	1	2	yes	—
88	C₂²×C₅×Q₈	—	3	1	no	—
89	C₄×C₅×Q₈	—	3	8	no	—
90	C₂×C₅×C₄⋊C₄	—	3	1	no	—
91	C₂×C₅×C₄⋊C₄	—	3	1	no	—
92	C₂×C₅×C₄⋊C₄	—	3	1	no	—
93	C₂×C₅×C₄⋊C₄	—	3	2	no	—
94	C₂×C₅×C₄⋊C₄	—	3	2	no	—
95	C₂×C₅×C₄⋊C₄	—	3	2	no	—
96	C₂×C₄²×C₅	—	3	1	no	—
97	C₂×C₄²×C₅	—	3	1	no	—
98	C₂×C₄²×C₅	—	3	2	no	—
99	C₂×C₄²×C₅	—	3	2	no	—
100	C₂×C₄²×C₅	—	3	1	no	—
101	C₂×C₄²×C₅	—	3	1	no	—
102	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
103	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
104	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
105	C₅×#95	—	3	2	no	—
106	C₅×#95	—	3	2	no	—
107	C₅×#95	—	3	2	no	—
108	C₅×#95	—	3	2	no	—
109	C₅×#95	—	3	2	no	—
110	C₅×#95	C₂×D₃	1	2	yes	—
111	C₅×#95	C₂×D₃	1	2	yes	—
112	#2295	—	3	1	no	Sylow
113	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
122	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
124	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
125	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
126	C₂×C₃×C₄×C₅	#41	1	2	yes	—
127	C₂×C₅×Dic₃	—	2	2	no	—
128	C₂×C₅×Dic₃	—	2	2	no	—
129	C₂×C₅×Dic₃	—	2	2	no	—
130	C₂×C₅×Dic₃	—	2	2	no	—
131	C₂×C₅×Dic₃	—	2	2	no	—
132	C₂×C₅×Dic₃	—	2	2	no	—
133	C₂×C₅×Dic₃	—	2	2	no	—
134	C₂×C₅×Dic₃	—	2	2	no	—
135	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
136	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
137	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
138	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
139	C₂×C₅×Dic₃	#41	1	4	yes	—
140	C₂×C₅×Dic₃	#41	1	4	yes	—
141	C₅×Dic₆	—	2	8	no	—
142	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
143	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
145	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
147	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
148	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
149	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
150	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
151	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
153	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
154	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
155	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
158	C₄×Dic₆	C₄×C₅	1	8	yes	complemented
159	C₃×#95	C₂²×C₅	1	2	yes	—
160	C₃×#95	C₂²×C₅	1	2	yes	—
161	C₃⋊#95	C₂²×C₅	1	2	yes	—
162	C₃⋊#95	C₂²×C₅	1	2	yes	—
163	C₃⋊#95	C₂²×C₅	1	2	yes	—
164	C₃⋊#95	C₂²×C₅	1	2	yes	—
165	C₃⋊#95	C₂²×C₅	1	2	yes	—
166	C₂×C₅×Q₈	—	3	4	no	—
167	C₂×C₅×Q₈	—	6	4	no	—
168	C₂²×C₄×C₅	—	3	1	no	—
169	C₂²×C₄×C₅	—	3	1	no	—
170	C₂²×C₄×C₅	—	3	2	no	—
171	C₂²×C₄×C₅	—	3	1	no	—
172	C₂²×C₄×C₅	—	3	1	no	—
173	C₂²×C₄×C₅	—	3	2	no	—
174	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
175	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
176	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
179	C₅×C₄⋊C₄	—	3	4	no	—
180	C₅×C₄⋊C₄	—	3	4	no	—
181	C₅×C₄⋊C₄	—	3	4	no	—
182	C₅×C₄⋊C₄	—	6	4	no	—
183	C₅×C₄⋊C₄	—	6	4	no	—
184	C₅×C₄⋊C₄	—	6	4	no	—
185	C₄²×C₅	—	2	2	no	—
186	C₄²×C₅	—	3	4	no	—
187	C₄²×C₅	—	3	4	no	—
188	C₄²×C₅	—	6	4	no	—
189	C₄²×C₅	—	6	4	no	—
190	C₄²×C₅	—	6	2	no	—
191	C₄²×C₅	—	6	2	no	—
192	C₄²×C₅	Dic₆	1	4	yes	complemented
193	C₄²×C₅	C₄×D₃	1	4	yes	—
194	C₂×C₄×Q₈	—	3	1	no	—
195	#391	—	3	2	no	—
196	#389	—	3	2	no	—
197	#387	—	3	2	no	—
198	#387	—	3	2	no	—
199	C₄×C₄⋊C₄	—	3	1	no	—
200	C₄×C₄⋊C₄	—	3	1	no	—
201	C₄×C₄⋊C₄	—	3	1	no	—
202	#376	—	3	1	no	—
203	#376	C₅×D₃	1	1	yes	characteristic
204	C₄³	—	3	1	no	—
205	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
206	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
207	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
208	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
209	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
210	C₃×C₄×C₅	—	2	2	no	—
211	C₃×C₄×C₅	—	2	2	no	—
212	C₃×C₄×C₅	—	2	4	no	—
213	C₃×C₄×C₅	—	4	2	no	—
214	C₃×C₄×C₅	C₄×Q₈	1	4	yes	—
215	C₅×Dic₃	—	2	2	no	—
216	C₅×Dic₃	—	2	2	no	—
217	C₅×Dic₃	—	2	2	no	—
218	C₅×Dic₃	—	2	4	no	—
219	C₅×Dic₃	—	4	2	no	—
220	C₅×Dic₃	#117	1	4	yes	—
221	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
222	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
223	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
224	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
225	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
226	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
227	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
228	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
229	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
230	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
231	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
232	C₂×Dic₆	—	2	4	no	—
233	C₂×Dic₆	C₂×C₄×C₅	1	4	yes	—
234	C₃×C₄²	—	2	2	no	—
235	C₃×C₄²	C₂×C₄×C₅	1	4	yes	—
236	C₃×C₄²	C₅×Q₈	1	4	yes	complemented
237	C₄⋊Dic₃	—	2	4	no	—
238	C₄⋊Dic₃	C₂×C₄×C₅	1	4	yes	—
239	Dic₃⋊C₄	—	2	4	no	—
240	Dic₃⋊C₄	—	2	4	no	—
241	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	—
242	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	—
243	C₄×Dic₃	—	2	2	no	—
244	C₄×Dic₃	—	2	2	no	—
245	C₄×Dic₃	—	2	4	no	—
246	C₄×Dic₃	—	2	4	no	—
247	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
248	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
249	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
250	C₅×Q₈	—	6	8	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	3	2	no	—
259	C₂×C₄×C₅	—	3	4	no	—
260	C₂×C₄×C₅	—	3	2	no	—
261	C₂×C₄×C₅	—	3	2	no	—
262	C₂×C₄×C₅	—	3	2	no	—
263	C₂×C₄×C₅	—	3	4	no	—
264	C₂×C₄×C₅	—	6	2	no	—
265	C₂×C₄×C₅	—	6	2	no	—
266	C₂×C₄×C₅	—	6	2	no	—
267	C₂×C₄×C₅	—	6	2	no	—
268	C₂×C₄×C₅	—	6	2	no	—
269	C₂×C₄×C₅	—	6	2	no	—
270	C₂×C₄×C₅	—	6	2	no	—
271	C₂×C₄×C₅	—	6	2	no	—
272	C₂×C₄×C₅	C₂×Dic₆	1	4	yes	—
273	C₂×C₄×C₅	C₂×Dic₆	1	2	yes	—
274	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
275	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
276	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
277	C₂×C₄×C₅	#235	1	2	yes	—
278	C₂²×Q₈	—	3	1	no	—
279	C₄×Q₈	—	3	8	no	—
280	C₂×C₄⋊C₄	—	3	1	no	—
281	C₂×C₄⋊C₄	—	3	1	no	—
282	C₂×C₄⋊C₄	—	3	1	no	—
283	C₂×C₄⋊C₄	—	3	2	no	—
284	C₂×C₄⋊C₄	—	3	2	no	—
285	C₂×C₄⋊C₄	—	3	2	no	—
286	C₂×C₄²	—	3	1	no	—
287	C₂×C₄²	—	3	1	no	—
288	C₂×C₄²	—	3	1	no	—
289	C₂×C₄²	—	3	2	no	—
290	C₂×C₄²	—	3	2	no	—
291	C₂×C₄²	—	3	1	no	—
292	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
293	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
294	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
295	#95	—	3	2	no	—
296	#95	—	3	2	no	—
297	#95	—	3	2	no	—
298	#95	—	3	2	no	—
299	#95	—	3	2	no	—
300	#95	C₂×C₅×D₃	1	2	yes	—
301	#95	C₂×C₅×D₃	1	2	yes	—
302	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
303	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
304	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
305	C₂×C₃×C₅	#529	1	2	yes	—
306	C₂×C₃×C₅	#533	1	2	yes	—
307	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
308	C₂×C₃×C₄	—	2	2	no	—
309	C₂×C₃×C₄	—	2	2	no	—
310	C₂×C₃×C₄	—	2	2	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	2	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
316	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
317	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
318	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
319	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
320	C₂×C₃×C₄	C₅×#41	1	2	yes	—
321	C₂×Dic₃	—	2	2	no	—
322	C₂×Dic₃	—	2	2	no	—
323	C₂×Dic₃	—	2	2	no	—
324	C₂×Dic₃	—	2	2	no	—
325	C₂×Dic₃	—	2	2	no	—
326	C₂×Dic₃	—	2	2	no	—
327	C₂×Dic₃	—	2	2	no	—
328	C₂×Dic₃	—	2	2	no	—
329	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
330	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
331	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
332	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
333	C₂×Dic₃	C₅×#41	1	4	yes	—
334	C₂×Dic₃	C₅×#41	1	4	yes	—
335	Dic₆	—	2	8	no	—
336	C₂²×C₅	C₂²×Dic₆	1	1	yes	characteristic
337	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
338	C₂²×C₅	C₂×#235	1	1	yes	characteristic
339	C₂²×C₅	D₃×#41	1	2	yes	—
340	C₂²×C₅	D₃×#41	1	2	yes	—
341	C₄×C₅	—	2	4	no	—
342	C₄×C₅	—	2	2	no	—
343	C₄×C₅	—	2	2	no	—
344	C₄×C₅	—	3	4	no	—
345	C₄×C₅	—	4	2	no	—
346	C₄×C₅	—	6	2	no	—
347	C₄×C₅	—	6	2	no	—
348	C₄×C₅	—	6	2	no	—
349	C₄×C₅	—	6	4	no	—
350	C₄×C₅	—	12	2	no	—
351	C₄×C₅	C₄×Dic₆	1	4	yes	—
352	C₂×Q₈	—	3	4	no	—
353	C₂×Q₈	—	6	4	no	—
354	C₂²×C₄	—	3	1	no	—
355	C₂²×C₄	—	3	1	no	—
356	C₂²×C₄	—	3	1	no	—
357	C₂²×C₄	—	3	2	no	—
358	C₂²×C₄	—	3	1	no	—
359	C₂²×C₄	—	3	2	no	—
360	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
361	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
362	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
363	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
364	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
365	C₄⋊C₄	—	3	4	no	—
366	C₄⋊C₄	—	3	4	no	—
367	C₄⋊C₄	—	3	4	no	—
368	C₄⋊C₄	—	6	4	no	—
369	C₄⋊C₄	—	6	4	no	—
370	C₄⋊C₄	—	6	4	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	3	4	no	—
373	C₄²	—	3	4	no	—
374	C₄²	—	6	4	no	—
375	C₄²	—	6	4	no	—
376	C₄²	—	6	2	no	—
377	C₄²	—	6	2	no	—
378	C₄²	C₅×Dic₆	1	4	yes	complemented
379	C₄²	C₄×C₅×D₃	1	4	yes	—
380	C₃×C₅	#2295	1	1	yes	characteristic, complemented, Hall
381	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
382	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
383	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
384	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
385	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
386	C₃×C₄	—	2	2	no	—
387	C₃×C₄	—	2	2	no	—
388	C₃×C₄	—	2	4	no	—
389	C₃×C₄	—	4	2	no	—
390	C₃×C₄	C₄×C₅×Q₈	1	4	yes	—
391	Dic₃	—	2	2	no	—
392	Dic₃	—	2	2	no	—
393	Dic₃	—	2	2	no	—
394	Dic₃	—	2	4	no	—
395	Dic₃	—	4	2	no	—
396	Dic₃	C₅×#117	1	4	yes	—
397	C₂×C₅	C₂×C₄×Dic₆	1	1	yes	characteristic
398	C₂×C₅	#5517	1	2	yes	—
399	C₂×C₅	D₃×#117	1	1	yes	characteristic
400	C₂×C₅	#5522	1	1	yes	characteristic
401	C₂×C₅	#5528	1	2	yes	—
402	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
403	Q₈	—	6	8	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	3	2	no	—
412	C₂×C₄	—	3	4	no	—
413	C₂×C₄	—	3	2	no	—
414	C₂×C₄	—	3	2	no	—
415	C₂×C₄	—	3	2	no	—
416	C₂×C₄	—	3	4	no	—
417	C₂×C₄	—	6	2	no	—
418	C₂×C₄	—	6	2	no	—
419	C₂×C₄	—	6	2	no	—
420	C₂×C₄	—	6	2	no	—
421	C₂×C₄	—	6	2	no	—
422	C₂×C₄	—	6	2	no	—
423	C₂×C₄	—	6	2	no	—
424	C₂×C₄	—	6	2	no	—
425	C₂×C₄	C₂×C₅×Dic₆	1	4	yes	—
426	C₂×C₄	C₂×C₅×Dic₆	1	2	yes	—
427	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
428	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
429	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
430	C₂×C₄	C₅×#235	1	2	yes	—
431	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
432	C₂×C₃	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
433	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
434	C₂×C₃	C₅×#529	1	2	yes	—
435	C₂×C₃	C₅×#533	1	2	yes	—
436	C₅	#73384	1	1	yes	characteristic, direct product factor, Sylow
437	C₂²	C₂²×C₅×Dic₆	1	1	yes	characteristic
438	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
439	C₂²	C₂×C₅×#235	1	1	yes	characteristic
440	C₂²	C₅×D₃×#41	1	2	yes	—
441	C₂²	C₅×D₃×#41	1	2	yes	—
442	C₄	—	2	4	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	2	no	—
445	C₄	—	3	4	no	—
446	C₄	—	4	2	no	—
447	C₄	—	6	2	no	—
448	C₄	—	6	2	no	—
449	C₄	—	6	2	no	—
450	C₄	—	6	4	no	—
451	C₄	—	12	2	no	—
452	C₄	C₄×C₅×Dic₆	1	4	yes	—
453	C₃	C₅×#2295	1	1	yes	characteristic, complemented, Sylow
454	C₂	C₂×C₄×C₅×Dic₆	1	1	yes	characteristic
455	C₂	C₅×#5517	1	2	yes	—
456	C₂	C₅×D₃×#117	1	1	yes	characteristic
457	C₂	C₅×#5522	1	1	yes	characteristic
458	C₂	C₅×#5528	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#376	C₂
socle, prime radical	C₂³×C₃×C₅	C₂⁴
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#376	D₃
hypocenter	C₃	C₅×#2295
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₅×#376

Complements

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

N	H ≅ G/N	type
29. C₄×C₅×Dic₆	C₄	semidirect
37. #73384	C₅	direct (N × H)
64. C₃×C₄²×C₅	Q₈	semidirect
158. C₄×Dic₆	C₄×C₅	semidirect
192. C₄²×C₅	Dic₆	semidirect
236. C₃×C₄²	C₅×Q₈	semidirect
378. C₄²	C₅×Dic₆	semidirect
380. C₃×C₅	#2295	semidirect
436. C₅	#73384	direct (N × H)
453. C₃	C₅×#2295	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×Dic₆	2
C₃×C₅×#376	2
C₄×C₅×C₄⋊Dic₃	2
C₅×#4932	2
C₄×C₅×Dic₃⋊C₄	2
C₄²×C₅×Dic₃	2
C₅×#4655	2
C₅×#4654	2
C₅×#4647	2
C₅×#4646	2
C₅×#2295	3
#73384	5

Subgroups — C5×#73384 #14320970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73384 #14320970