Subgroups — C₅×#75992 #14330982

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#896	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#4990	C₂	1	1	yes	maximal, characteristic
4	C₅×#4990	C₂	1	1	yes	maximal, characteristic
5	C₅×#4987	C₂	1	1	yes	maximal, characteristic
6	C₅×#4980	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4978	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4978	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4973	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4940	C₂	1	1	yes	maximal, characteristic
11	C₅×#4933	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4669	C₂	1	1	yes	maximal, characteristic
13	C₅×#4664	C₂	1	1	yes	maximal, characteristic
14	C₅×#4647	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4646	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2378	—	3	1	no	maximal, Hall
17	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
18	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
24	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
31	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
38	C₅×#896	C₄	1	8	yes	complemented
39	C₃×C₅×#95	C₂²	1	1	yes	characteristic
40	C₃×C₅×#95	C₂²	1	1	yes	characteristic
41	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
42	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
43	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
44	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
45	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
46	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
47	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
48	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
49	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
50	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
51	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
52	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
53	#75992	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
54	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
55	C₅×#391	—	3	1	no	—
56	C₅×#391	—	3	1	no	—
57	C₅×#389	—	3	1	no	—
58	C₅×#389	D₃	1	1	yes	characteristic, complemented
59	C₅×#388	—	3	1	no	—
60	C₅×#388	—	3	1	no	—
61	C₅×#388	—	3	1	no	—
62	C₅×#388	—	3	1	no	—
63	C₅×#387	—	3	1	no	—
64	C₅×#387	—	3	1	no	—
65	C₅×#387	—	3	1	no	—
66	C₅×#387	—	3	1	no	—
67	C₅×#381	—	3	1	no	—
68	C₅×#380	—	3	1	no	—
69	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
73	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
75	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
77	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
78	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
79	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
80	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
81	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
82	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
83	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
84	C₂×C₄×C₅×D₃	—	4	1	no	—
85	C₂×C₄×C₅×D₃	—	4	1	no	—
86	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
87	C₂×C₅×Dic₆	—	4	1	no	—
88	C₂×C₅×Dic₆	—	4	1	no	—
89	C₂×C₅×Dic₆	C₂×C₄	1	4	yes	—
90	C₃×C₅×C₄⋊C₄	—	4	1	no	—
91	C₃×C₅×C₄⋊C₄	—	4	1	no	—
92	C₃×C₅×C₄⋊C₄	—	4	1	no	—
93	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
94	C₃×C₄²×C₅	—	4	1	no	—
95	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
96	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
97	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
98	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
99	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
100	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
101	C₅×C₄⋊Dic₃	—	4	1	no	—
102	C₅×Dic₃⋊C₄	—	4	1	no	—
103	C₅×Dic₃⋊C₄	—	4	1	no	—
104	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
105	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
106	C₄×C₅×Dic₃	—	4	1	no	—
107	C₄×C₅×Dic₃	—	4	1	no	—
108	C₄×C₅×Dic₃	—	4	1	no	—
109	C₂×#896	C₂×C₅	1	1	yes	characteristic
110	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
111	#4990	C₂×C₅	1	1	yes	characteristic
112	#4990	C₂×C₅	1	1	yes	characteristic
113	#4987	C₂×C₅	1	1	yes	characteristic
114	#4980	C₂×C₅	1	1	yes	characteristic, complemented
115	#4978	C₂×C₅	1	1	yes	characteristic, complemented
116	#4978	C₂×C₅	1	1	yes	characteristic, complemented
117	#4973	C₂×C₅	1	1	yes	characteristic, complemented
118	#4940	C₂×C₅	1	1	yes	characteristic
119	#4933	C₂×C₅	1	1	yes	characteristic, complemented
120	#4669	C₂×C₅	1	1	yes	characteristic
121	#4664	C₂×C₅	1	1	yes	characteristic
122	#4647	C₂×C₅	1	1	yes	characteristic, complemented
123	#4646	C₂×C₅	1	1	yes	characteristic, complemented
124	C₂²×C₅×Q₈	—	3	1	no	—
125	C₂³×C₄×C₅	—	3	1	no	—
126	C₅×C₂²⋊Q₈	—	3	8	no	—
127	C₂×C₅×C₄⋊C₄	—	3	1	no	—
128	C₂×C₅×C₄⋊C₄	—	3	1	no	—
129	C₂×C₅×C₄⋊C₄	—	3	1	no	—
130	C₂×C₅×C₄⋊C₄	—	3	1	no	—
131	C₂×C₅×C₄⋊C₄	—	3	1	no	—
132	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
133	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
134	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
135	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
136	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
137	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
138	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
139	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
140	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
141	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
142	C₂×C₄²×C₅	—	3	1	no	—
143	C₂×C₄²×C₅	—	3	1	no	—
144	C₂×C₄²×C₅	—	3	1	no	—
145	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
146	C₅×#95	—	3	1	no	—
147	C₅×#95	—	3	1	no	—
148	C₅×#95	—	3	1	no	—
149	C₅×#95	—	3	1	no	—
150	C₅×#95	—	3	1	no	—
151	C₅×#95	—	3	1	no	—
152	C₅×#95	—	3	1	no	—
153	C₅×#95	—	3	1	no	—
154	C₅×#95	—	3	1	no	—
155	C₅×#95	—	3	1	no	—
156	C₅×#95	—	3	1	no	—
157	C₅×#95	—	3	1	no	—
158	C₅×#95	C₂×D₃	1	1	yes	characteristic
159	C₅×#95	C₂×D₃	1	1	yes	characteristic
160	#2378	—	3	1	no	Sylow
161	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
162	C₂²×C₅×D₃	—	2	1	no	—
163	C₂²×C₅×D₃	—	2	1	no	—
164	C₂²×C₅×D₃	—	2	1	no	—
165	C₂²×C₅×D₃	—	2	1	no	—
166	C₂²×C₅×D₃	—	2	1	no	—
167	C₂²×C₅×D₃	—	2	1	no	—
168	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
169	C₂×C₃×C₄×C₅	—	2	1	no	—
170	C₂×C₃×C₄×C₅	—	2	1	no	—
171	C₂×C₃×C₄×C₅	—	2	1	no	—
172	C₂×C₃×C₄×C₅	—	2	1	no	—
173	C₂×C₃×C₄×C₅	—	2	1	no	—
174	C₂×C₃×C₄×C₅	—	2	1	no	—
175	C₂×C₃×C₄×C₅	—	2	1	no	—
176	C₂×C₃×C₄×C₅	—	2	1	no	—
177	C₂×C₃×C₄×C₅	—	2	1	no	—
178	C₂×C₃×C₄×C₅	—	2	1	no	—
179	C₂×C₃×C₄×C₅	—	2	1	no	—
180	C₂×C₃×C₄×C₅	—	2	1	no	—
181	C₂×C₃×C₄×C₅	—	2	1	no	—
182	C₂×C₃×C₄×C₅	—	2	1	no	—
183	C₂×C₃×C₄×C₅	—	2	1	no	—
184	C₂×C₃×C₄×C₅	—	2	1	no	—
185	C₂×C₃×C₄×C₅	—	2	1	no	—
186	C₂×C₃×C₄×C₅	—	2	1	no	—
187	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
188	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
189	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
190	C₂×C₅×Dic₃	—	2	1	no	—
191	C₂×C₅×Dic₃	—	2	1	no	—
192	C₂×C₅×Dic₃	—	2	1	no	—
193	C₂×C₅×Dic₃	—	2	1	no	—
194	C₂×C₅×Dic₃	—	2	1	no	—
195	C₂×C₅×Dic₃	—	2	1	no	—
196	C₂×C₅×Dic₃	—	2	1	no	—
197	C₂×C₅×Dic₃	—	2	1	no	—
198	C₂×C₅×Dic₃	—	2	1	no	—
199	C₂×C₅×Dic₃	—	2	1	no	—
200	C₂×C₅×Dic₃	—	2	1	no	—
201	C₂×C₅×Dic₃	—	2	1	no	—
202	C₂×C₅×Dic₃	—	2	1	no	—
203	C₂×C₅×Dic₃	—	2	1	no	—
204	C₂×C₅×Dic₃	—	2	1	no	—
205	C₂×C₅×Dic₃	—	2	1	no	—
206	C₂×C₅×Dic₃	—	2	1	no	—
207	C₂×C₅×Dic₃	—	2	1	no	—
208	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
209	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
210	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
211	C₄×C₅×D₃	—	4	4	no	—
212	C₅×Dic₆	—	4	4	no	—
213	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
214	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
215	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
216	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
217	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
218	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
219	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
220	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
221	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
222	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
223	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
224	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
225	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
227	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
228	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
229	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
230	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
231	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
233	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
234	#896	C₄×C₅	1	8	yes	complemented
235	C₃×#95	C₂²×C₅	1	1	yes	characteristic
236	C₃×#95	C₂²×C₅	1	1	yes	characteristic
237	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
238	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
239	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
240	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
241	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
242	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
243	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
244	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
245	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
246	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
247	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
248	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
249	C₂⁴×C₅	—	3	1	no	—
250	C₂×C₅×Q₈	—	3	4	no	—
251	C₂×C₅×Q₈	—	12	1	no	—
252	C₂×C₅×Q₈	—	12	1	no	—
253	C₂²×C₄×C₅	—	3	1	no	—
254	C₂²×C₄×C₅	—	3	1	no	—
255	C₂²×C₄×C₅	—	3	1	no	—
256	C₂²×C₄×C₅	—	3	4	no	—
257	C₂²×C₄×C₅	—	3	1	no	—
258	C₂²×C₄×C₅	—	3	1	no	—
259	C₂²×C₄×C₅	—	3	1	no	—
260	C₂²×C₄×C₅	—	3	1	no	—
261	C₂²×C₄×C₅	—	12	1	no	—
262	C₂²×C₄×C₅	—	12	1	no	—
263	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
264	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
265	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
266	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
267	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
268	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
269	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
270	C₅×C₄⋊C₄	—	3	4	no	—
271	C₅×C₄⋊C₄	—	3	4	no	—
272	C₅×C₄⋊C₄	—	4	1	no	—
273	C₅×C₄⋊C₄	—	4	1	no	—
274	C₅×C₄⋊C₄	—	4	1	no	—
275	C₅×C₄⋊C₄	—	12	1	no	—
276	C₅×C₄⋊C₄	—	12	1	no	—
277	C₅×C₄⋊C₄	—	12	1	no	—
278	C₅×C₄⋊C₄	C₄×D₃	1	4	yes	—
279	C₅×C₂²⋊C₄	—	3	4	no	—
280	C₅×C₂²⋊C₄	—	3	4	no	—
281	C₅×C₂²⋊C₄	—	12	1	no	—
282	C₅×C₂²⋊C₄	—	12	1	no	—
283	C₅×C₂²⋊C₄	—	12	1	no	—
284	C₅×C₂²⋊C₄	—	12	1	no	—
285	C₄²×C₅	—	4	1	no	—
286	C₄²×C₅	—	12	1	no	—
287	C₄²×C₅	—	12	1	no	—
288	C₄²×C₅	—	12	1	no	—
289	C₂×C₂²⋊Q₈	—	3	1	no	—
290	#391	—	3	1	no	—
291	#391	—	3	1	no	—
292	#389	—	3	1	no	—
293	#389	C₅×D₃	1	1	yes	characteristic, complemented
294	#388	—	3	1	no	—
295	#388	—	3	1	no	—
296	#388	—	3	1	no	—
297	#388	—	3	1	no	—
298	#387	—	3	1	no	—
299	#387	—	3	1	no	—
300	#387	—	3	1	no	—
301	#387	—	3	1	no	—
302	#381	—	3	1	no	—
303	#380	—	3	1	no	—
304	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
305	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
306	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
307	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
308	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
309	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
310	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
311	C₂×C₅×D₃	—	2	2	no	—
312	C₂×C₅×D₃	—	2	2	no	—
313	C₂×C₅×D₃	—	2	2	no	—
314	C₂×C₅×D₃	—	4	1	no	—
315	C₂×C₅×D₃	—	4	1	no	—
316	C₂×C₅×D₃	—	4	1	no	—
317	C₂×C₅×D₃	—	4	1	no	—
318	C₃×C₄×C₅	—	2	2	no	—
319	C₃×C₄×C₅	—	2	2	no	—
320	C₃×C₄×C₅	—	2	2	no	—
321	C₃×C₄×C₅	—	4	1	no	—
322	C₃×C₄×C₅	—	4	1	no	—
323	C₃×C₄×C₅	—	4	1	no	—
324	C₃×C₄×C₅	—	4	1	no	—
325	C₅×Dic₃	—	2	2	no	—
326	C₅×Dic₃	—	2	2	no	—
327	C₅×Dic₃	—	2	2	no	—
328	C₅×Dic₃	—	4	1	no	—
329	C₅×Dic₃	—	4	1	no	—
330	C₅×Dic₃	—	4	1	no	—
331	C₅×Dic₃	—	4	1	no	—
332	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
333	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
334	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
335	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
336	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
337	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
338	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
339	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
340	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
341	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
342	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
343	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
344	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
345	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
346	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
347	C₂×C₄×D₃	—	4	1	no	—
348	C₂×C₄×D₃	—	4	1	no	—
349	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
350	C₂×Dic₆	—	4	1	no	—
351	C₂×Dic₆	—	4	1	no	—
352	C₂×Dic₆	C₂×C₄×C₅	1	4	yes	—
353	C₃×C₄⋊C₄	—	4	1	no	—
354	C₃×C₄⋊C₄	—	4	1	no	—
355	C₃×C₄⋊C₄	—	4	1	no	—
356	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
357	C₃×C₄²	—	4	1	no	—
358	(C₂×D₃)⋊C₄	—	4	1	no	—
359	(C₂×D₃)⋊C₄	—	4	1	no	—
360	(C₂×D₃)⋊C₄	—	4	1	no	—
361	(C₂×D₃)⋊C₄	—	4	1	no	—
362	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
363	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
364	C₄⋊Dic₃	—	4	1	no	—
365	Dic₃⋊C₄	—	4	1	no	—
366	Dic₃⋊C₄	—	4	1	no	—
367	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	—
368	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	—
369	C₄×Dic₃	—	4	1	no	—
370	C₄×Dic₃	—	4	1	no	—
371	C₄×Dic₃	—	4	1	no	—
372	C₂³×C₅	—	3	2	no	—
373	C₂³×C₅	—	6	1	no	—
374	C₂³×C₅	—	6	1	no	—
375	C₂³×C₅	—	6	1	no	—
376	C₂³×C₅	—	6	1	no	—
377	C₂³×C₅	—	6	1	no	—
378	C₂³×C₅	—	6	1	no	—
379	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
380	C₅×Q₈	—	12	4	no	—
381	C₂×C₄×C₅	—	2	1	no	—
382	C₂×C₄×C₅	—	2	1	no	—
383	C₂×C₄×C₅	—	2	1	no	—
384	C₂×C₄×C₅	—	2	1	no	—
385	C₂×C₄×C₅	—	2	1	no	—
386	C₂×C₄×C₅	—	2	1	no	—
387	C₂×C₄×C₅	—	2	1	no	—
388	C₂×C₄×C₅	—	2	1	no	—
389	C₂×C₄×C₅	—	2	1	no	—
390	C₂×C₄×C₅	—	2	1	no	—
391	C₂×C₄×C₅	—	2	1	no	—
392	C₂×C₄×C₅	—	2	1	no	—
393	C₂×C₄×C₅	—	2	1	no	—
394	C₂×C₄×C₅	—	2	1	no	—
395	C₂×C₄×C₅	—	2	1	no	—
396	C₂×C₄×C₅	—	2	1	no	—
397	C₂×C₄×C₅	—	2	1	no	—
398	C₂×C₄×C₅	—	2	1	no	—
399	C₂×C₄×C₅	—	3	2	no	—
400	C₂×C₄×C₅	—	3	2	no	—
401	C₂×C₄×C₅	—	3	2	no	—
402	C₂×C₄×C₅	—	6	1	no	—
403	C₂×C₄×C₅	—	6	1	no	—
404	C₂×C₄×C₅	—	6	1	no	—
405	C₂×C₄×C₅	—	6	1	no	—
406	C₂×C₄×C₅	—	6	1	no	—
407	C₂×C₄×C₅	—	6	1	no	—
408	C₂×C₄×C₅	—	6	1	no	—
409	C₂×C₄×C₅	—	6	1	no	—
410	C₂×C₄×C₅	—	6	1	no	—
411	C₂×C₄×C₅	—	6	1	no	—
412	C₂×C₄×C₅	—	6	1	no	—
413	C₂×C₄×C₅	—	6	1	no	—
414	C₂×C₄×C₅	—	6	1	no	—
415	C₂×C₄×C₅	—	6	1	no	—
416	C₂×C₄×C₅	—	6	1	no	—
417	C₂×C₄×C₅	—	6	1	no	—
418	C₂×C₄×C₅	—	6	1	no	—
419	C₂×C₄×C₅	—	6	1	no	—
420	C₂×C₄×C₅	—	12	4	no	—
421	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
422	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
423	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
424	C₂²×Q₈	—	3	1	no	—
425	C₂³×C₄	—	3	1	no	—
426	C₂²⋊Q₈	—	3	8	no	—
427	C₂×C₄⋊C₄	—	3	1	no	—
428	C₂×C₄⋊C₄	—	3	1	no	—
429	C₂×C₄⋊C₄	—	3	1	no	—
430	C₂×C₄⋊C₄	—	3	1	no	—
431	C₂×C₄⋊C₄	—	3	1	no	—
432	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
436	C₂×C₂²⋊C₄	—	3	1	no	—
437	C₂×C₂²⋊C₄	—	3	1	no	—
438	C₂×C₂²⋊C₄	—	3	1	no	—
439	C₂×C₂²⋊C₄	—	3	1	no	—
440	C₂×C₂²⋊C₄	—	3	1	no	—
441	C₂×C₂²⋊C₄	—	3	1	no	—
442	C₂×C₄²	—	3	1	no	—
443	C₂×C₄²	—	3	1	no	—
444	C₂×C₄²	—	3	1	no	—
445	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
446	#95	—	3	1	no	—
447	#95	—	3	1	no	—
448	#95	—	3	1	no	—
449	#95	—	3	1	no	—
450	#95	—	3	1	no	—
451	#95	—	3	1	no	—
452	#95	—	3	1	no	—
453	#95	—	3	1	no	—
454	#95	—	3	1	no	—
455	#95	—	3	1	no	—
456	#95	—	3	1	no	—
457	#95	—	3	1	no	—
458	#95	C₂×C₅×D₃	1	1	yes	characteristic
459	#95	C₂×C₅×D₃	1	1	yes	characteristic
460	C₂×C₃×C₅	#518	1	1	yes	characteristic
461	C₂×C₃×C₅	#519	1	1	yes	characteristic
462	C₂×C₃×C₅	#520	1	1	yes	characteristic
463	C₂×C₃×C₅	#562	1	1	yes	characteristic
464	C₂×C₃×C₅	#562	1	1	yes	characteristic
465	C₂×C₃×C₅	#563	1	1	yes	characteristic
466	C₂×C₃×C₅	#563	1	1	yes	characteristic
467	C₅×D₃	—	4	2	no	—
468	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
469	C₂²×D₃	—	2	1	no	—
470	C₂²×D₃	—	2	1	no	—
471	C₂²×D₃	—	2	1	no	—
472	C₂²×D₃	—	2	1	no	—
473	C₂²×D₃	—	2	1	no	—
474	C₂²×D₃	—	2	1	no	—
475	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
476	C₂×C₃×C₄	—	2	1	no	—
477	C₂×C₃×C₄	—	2	1	no	—
478	C₂×C₃×C₄	—	2	1	no	—
479	C₂×C₃×C₄	—	2	1	no	—
480	C₂×C₃×C₄	—	2	1	no	—
481	C₂×C₃×C₄	—	2	1	no	—
482	C₂×C₃×C₄	—	2	1	no	—
483	C₂×C₃×C₄	—	2	1	no	—
484	C₂×C₃×C₄	—	2	1	no	—
485	C₂×C₃×C₄	—	2	1	no	—
486	C₂×C₃×C₄	—	2	1	no	—
487	C₂×C₃×C₄	—	2	1	no	—
488	C₂×C₃×C₄	—	2	1	no	—
489	C₂×C₃×C₄	—	2	1	no	—
490	C₂×C₃×C₄	—	2	1	no	—
491	C₂×C₃×C₄	—	2	1	no	—
492	C₂×C₃×C₄	—	2	1	no	—
493	C₂×C₃×C₄	—	2	1	no	—
494	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
495	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
496	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
497	C₂×Dic₃	—	2	1	no	—
498	C₂×Dic₃	—	2	1	no	—
499	C₂×Dic₃	—	2	1	no	—
500	C₂×Dic₃	—	2	1	no	—
501	C₂×Dic₃	—	2	1	no	—
502	C₂×Dic₃	—	2	1	no	—
503	C₂×Dic₃	—	2	1	no	—
504	C₂×Dic₃	—	2	1	no	—
505	C₂×Dic₃	—	2	1	no	—
506	C₂×Dic₃	—	2	1	no	—
507	C₂×Dic₃	—	2	1	no	—
508	C₂×Dic₃	—	2	1	no	—
509	C₂×Dic₃	—	2	1	no	—
510	C₂×Dic₃	—	2	1	no	—
511	C₂×Dic₃	—	2	1	no	—
512	C₂×Dic₃	—	2	1	no	—
513	C₂×Dic₃	—	2	1	no	—
514	C₂×Dic₃	—	2	1	no	—
515	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
516	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
517	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
518	C₄×D₃	—	4	4	no	—
519	Dic₆	—	4	4	no	—
520	C₂²×C₅	—	6	2	no	—
521	C₂²×C₅	—	6	2	no	—
522	C₂²×C₅	—	6	2	no	—
523	C₂²×C₅	—	12	1	no	—
524	C₂²×C₅	—	12	1	no	—
525	C₂²×C₅	—	12	1	no	—
526	C₂²×C₅	—	12	1	no	—
527	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
528	C₂²×C₅	#1004	1	1	yes	characteristic
529	C₂²×C₅	#1004	1	1	yes	characteristic
530	C₂²×C₅	#1007	1	1	yes	characteristic
531	C₂²×C₅	#1007	1	1	yes	characteristic
532	C₂²×C₅	#1009	1	1	yes	characteristic
533	C₂²×C₅	#1010	1	1	yes	characteristic
534	C₄×C₅	—	2	2	no	—
535	C₄×C₅	—	2	2	no	—
536	C₄×C₅	—	2	2	no	—
537	C₄×C₅	—	4	1	no	—
538	C₄×C₅	—	4	1	no	—
539	C₄×C₅	—	4	1	no	—
540	C₄×C₅	—	4	1	no	—
541	C₄×C₅	—	6	2	no	—
542	C₄×C₅	—	6	2	no	—
543	C₄×C₅	—	6	2	no	—
544	C₄×C₅	—	12	1	no	—
545	C₄×C₅	—	12	1	no	—
546	C₄×C₅	—	12	1	no	—
547	C₄×C₅	—	12	1	no	—
548	C₂⁴	—	3	1	no	—
549	C₂×Q₈	—	3	4	no	—
550	C₂×Q₈	—	12	1	no	—
551	C₂×Q₈	—	12	1	no	—
552	C₂²×C₄	—	3	1	no	—
553	C₂²×C₄	—	3	1	no	—
554	C₂²×C₄	—	3	1	no	—
555	C₂²×C₄	—	3	4	no	—
556	C₂²×C₄	—	3	1	no	—
557	C₂²×C₄	—	3	1	no	—
558	C₂²×C₄	—	3	1	no	—
559	C₂²×C₄	—	3	1	no	—
560	C₂²×C₄	—	12	1	no	—
561	C₂²×C₄	—	12	1	no	—
562	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
563	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
564	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
565	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
566	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
567	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
568	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
569	C₄⋊C₄	—	3	4	no	—
570	C₄⋊C₄	—	3	4	no	—
571	C₄⋊C₄	—	4	1	no	—
572	C₄⋊C₄	—	4	1	no	—
573	C₄⋊C₄	—	4	1	no	—
574	C₄⋊C₄	—	12	1	no	—
575	C₄⋊C₄	—	12	1	no	—
576	C₄⋊C₄	—	12	1	no	—
577	C₄⋊C₄	C₄×C₅×D₃	1	4	yes	—
578	C₂²⋊C₄	—	3	4	no	—
579	C₂²⋊C₄	—	3	4	no	—
580	C₂²⋊C₄	—	12	1	no	—
581	C₂²⋊C₄	—	12	1	no	—
582	C₂²⋊C₄	—	12	1	no	—
583	C₂²⋊C₄	—	12	1	no	—
584	C₄²	—	4	1	no	—
585	C₄²	—	12	1	no	—
586	C₄²	—	12	1	no	—
587	C₄²	—	12	1	no	—
588	C₃×C₅	#2378	1	1	yes	characteristic, complemented, Hall
589	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
590	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
591	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
592	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
593	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
594	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
595	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
596	C₂×D₃	—	2	2	no	—
597	C₂×D₃	—	2	2	no	—
598	C₂×D₃	—	2	2	no	—
599	C₂×D₃	—	4	1	no	—
600	C₂×D₃	—	4	1	no	—
601	C₂×D₃	—	4	1	no	—
602	C₂×D₃	—	4	1	no	—
603	C₃×C₄	—	2	2	no	—
604	C₃×C₄	—	2	2	no	—
605	C₃×C₄	—	2	2	no	—
606	C₃×C₄	—	4	1	no	—
607	C₃×C₄	—	4	1	no	—
608	C₃×C₄	—	4	1	no	—
609	C₃×C₄	—	4	1	no	—
610	Dic₃	—	2	2	no	—
611	Dic₃	—	2	2	no	—
612	Dic₃	—	2	2	no	—
613	Dic₃	—	4	1	no	—
614	Dic₃	—	4	1	no	—
615	Dic₃	—	4	1	no	—
616	Dic₃	—	4	1	no	—
617	C₂×C₅	—	12	2	no	—
618	C₂×C₅	#5504	1	1	yes	characteristic
619	C₂×C₅	#5545	1	1	yes	characteristic
620	C₂×C₅	#5572	1	1	yes	characteristic
621	C₂×C₅	#5621	1	1	yes	characteristic
622	C₂×C₅	#5647	1	1	yes	characteristic
623	C₂×C₅	#5699	1	1	yes	characteristic
624	C₂×C₅	#5735	1	1	yes	characteristic
625	C₂³	—	3	2	no	—
626	C₂³	—	6	1	no	—
627	C₂³	—	6	1	no	—
628	C₂³	—	6	1	no	—
629	C₂³	—	6	1	no	—
630	C₂³	—	6	1	no	—
631	C₂³	—	6	1	no	—
632	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
633	Q₈	—	12	4	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	3	2	no	—
653	C₂×C₄	—	3	2	no	—
654	C₂×C₄	—	3	2	no	—
655	C₂×C₄	—	6	1	no	—
656	C₂×C₄	—	6	1	no	—
657	C₂×C₄	—	6	1	no	—
658	C₂×C₄	—	6	1	no	—
659	C₂×C₄	—	6	1	no	—
660	C₂×C₄	—	6	1	no	—
661	C₂×C₄	—	6	1	no	—
662	C₂×C₄	—	6	1	no	—
663	C₂×C₄	—	6	1	no	—
664	C₂×C₄	—	6	1	no	—
665	C₂×C₄	—	6	1	no	—
666	C₂×C₄	—	6	1	no	—
667	C₂×C₄	—	6	1	no	—
668	C₂×C₄	—	6	1	no	—
669	C₂×C₄	—	6	1	no	—
670	C₂×C₄	—	6	1	no	—
671	C₂×C₄	—	6	1	no	—
672	C₂×C₄	—	6	1	no	—
673	C₂×C₄	—	12	4	no	—
674	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
675	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
676	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
677	C₂×C₃	C₅×#518	1	1	yes	characteristic
678	C₂×C₃	C₅×#519	1	1	yes	characteristic
679	C₂×C₃	C₅×#520	1	1	yes	characteristic
680	C₂×C₃	C₅×#562	1	1	yes	characteristic
681	C₂×C₃	C₅×#562	1	1	yes	characteristic
682	C₂×C₃	C₅×#563	1	1	yes	characteristic
683	C₂×C₃	C₅×#563	1	1	yes	characteristic
684	D₃	—	4	2	no	—
685	C₅	#75992	1	1	yes	characteristic, direct product factor, Sylow
686	C₂²	—	6	2	no	—
687	C₂²	—	6	2	no	—
688	C₂²	—	6	2	no	—
689	C₂²	—	12	1	no	—
690	C₂²	—	12	1	no	—
691	C₂²	—	12	1	no	—
692	C₂²	—	12	1	no	—
693	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
694	C₂²	C₅×#1004	1	1	yes	characteristic
695	C₂²	C₅×#1004	1	1	yes	characteristic
696	C₂²	C₅×#1007	1	1	yes	characteristic
697	C₂²	C₅×#1007	1	1	yes	characteristic
698	C₂²	C₅×#1009	1	1	yes	characteristic
699	C₂²	C₅×#1010	1	1	yes	characteristic
700	C₄	—	2	2	no	—
701	C₄	—	2	2	no	—
702	C₄	—	2	2	no	—
703	C₄	—	4	1	no	—
704	C₄	—	4	1	no	—
705	C₄	—	4	1	no	—
706	C₄	—	4	1	no	—
707	C₄	—	6	2	no	—
708	C₄	—	6	2	no	—
709	C₄	—	6	2	no	—
710	C₄	—	12	1	no	—
711	C₄	—	12	1	no	—
712	C₄	—	12	1	no	—
713	C₄	—	12	1	no	—
714	C₃	C₅×#2378	1	1	yes	characteristic, complemented, Sylow
715	C₂	—	12	2	no	—
716	C₂	C₅×#5504	1	1	yes	characteristic
717	C₂	C₅×#5545	1	1	yes	characteristic
718	C₂	C₅×#5572	1	1	yes	characteristic
719	C₂	C₅×#5621	1	1	yes	characteristic
720	C₂	C₅×#5647	1	1	yes	characteristic
721	C₂	C₅×#5699	1	1	yes	characteristic
722	C₂	C₅×#5735	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#389	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₅×D₃	C₂³
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#389	D₃
hypocenter	C₃	C₅×#2378
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#389

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#389	C₂	semidirect
6. C₅×#4980	C₂	semidirect
7. C₅×#4978	C₂	semidirect
8. C₅×#4978	C₂	semidirect
9. C₅×#4973	C₂	semidirect
11. C₅×#4933	C₂	semidirect
14. C₅×#4647	C₂	semidirect
15. C₅×#4646	C₂	semidirect
38. C₅×#896	C₄	semidirect
53. #75992	C₅	direct (N × H)
58. C₅×#389	D₃	semidirect
110. C₃×#389	C₂×C₅	semidirect
114. #4980	C₂×C₅	semidirect
115. #4978	C₂×C₅	semidirect
116. #4978	C₂×C₅	semidirect
117. #4973	C₂×C₅	semidirect
119. #4933	C₂×C₅	semidirect
122. #4647	C₂×C₅	semidirect
123. #4646	C₂×C₅	semidirect
234. #896	C₄×C₅	semidirect
293. #389	C₅×D₃	semidirect
588. C₃×C₅	#2378	semidirect
685. C₅	#75992	direct (N × H)
714. C₃	C₅×#2378	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#896	2
C₃×C₅×#389	2
C₅×#4990	2
C₅×#4987	2
C₅×#4980	2
C₅×#4978	2
C₅×#4973	2
C₅×#4940	2
C₅×#4933	2
C₅×#4669	2
C₅×#4664	2
C₅×#4647	2
C₅×#4646	2
C₅×#2378	3
#75992	5

Subgroups — C5×#75992 #14330982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#75992 #14330982