Subgroups — C₅×#74402 #14331133

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#885	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5213	C₂	1	1	yes	maximal, characteristic
4	C₅×#5210	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4989	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4989	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4977	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4973	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4956	C₂	1	1	yes	maximal, characteristic
10	C₅×#4951	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4945	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4670	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4669	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4650	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4646	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2379	—	3	1	no	maximal, Hall
17	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
18	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₂²×C₅×Dic₆	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×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₅×#217	C₂²	1	1	yes	characteristic
26	C₂×C₅×#217	C₂²	1	1	yes	characteristic
27	C₂×C₅×#217	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×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
34	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
40	C₅×#885	C₄	1	8	yes	complemented
41	C₃×C₅×#95	C₂²	1	1	yes	characteristic
42	C₃×C₅×#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	#74402	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
54	C₂×C₅×#124	—	3	1	no	—
55	C₅×#391	—	3	1	no	—
56	C₅×#391	—	3	1	no	—
57	C₅×#388	—	3	1	no	—
58	C₅×#388	—	3	1	no	—
59	C₅×#388	—	3	1	no	—
60	C₅×#388	—	3	1	no	—
61	C₅×#386	—	3	1	no	—
62	C₅×#386	—	3	1	no	—
63	C₅×#385	—	3	1	no	—
64	C₅×#385	—	3	1	no	—
65	C₅×#385	—	3	1	no	—
66	C₅×#385	D₃	1	1	yes	characteristic, complemented
67	C₅×#382	—	3	1	no	—
68	C₅×#382	—	3	1	no	—
69	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
70	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
71	C₂²×C₃×C₄×C₅	—	4	1	no	—
72	C₂²×C₃×C₄×C₅	—	4	1	no	—
73	C₂²×C₃×C₄×C₅	—	4	1	no	—
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×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂×C₅×#67	—	4	1	no	—
81	C₂×C₅×#67	—	4	1	no	—
82	C₂×C₅×#67	C₂×C₄	1	4	yes	—
83	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
84	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
85	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
86	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
87	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
88	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
89	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
90	C₂×C₄×C₅×D₃	—	4	1	no	—
91	C₂×C₄×C₅×D₃	—	4	1	no	—
92	C₂×C₄×C₅×D₃	—	4	1	no	—
93	C₂×C₅×Dic₆	—	4	1	no	—
94	C₂×C₅×Dic₆	—	4	1	no	—
95	C₂×C₅×Dic₆	C₂×C₄	1	4	yes	complemented
96	C₃×C₅×C₄⋊C₄	—	4	1	no	—
97	C₃×C₅×C₄⋊C₄	—	4	1	no	—
98	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
99	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	complemented
100	C₅×#217	—	4	1	no	—
101	C₅×#217	—	4	1	no	—
102	C₅×#217	C₂×C₄	1	4	yes	complemented
103	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
104	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
105	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
106	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	complemented
107	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	complemented
108	C₅×C₄⋊Dic₃	—	4	1	no	—
109	C₅×Dic₃⋊C₄	—	4	1	no	—
110	C₅×Dic₃⋊C₄	—	4	1	no	—
111	C₅×Dic₃⋊C₄	—	4	1	no	—
112	C₄×C₅×Dic₃	—	4	1	no	—
113	C₄×C₅×Dic₃	—	4	1	no	—
114	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
115	C₂×#885	C₂×C₅	1	1	yes	characteristic
116	C₃×#385	C₂×C₅	1	1	yes	characteristic, complemented
117	#5213	C₂×C₅	1	1	yes	characteristic
118	#5210	C₂×C₅	1	1	yes	characteristic, complemented
119	#4989	C₂×C₅	1	1	yes	characteristic, complemented
120	#4989	C₂×C₅	1	1	yes	characteristic, complemented
121	#4977	C₂×C₅	1	1	yes	characteristic, complemented
122	#4973	C₂×C₅	1	1	yes	characteristic, complemented
123	#4956	C₂×C₅	1	1	yes	characteristic
124	#4951	C₂×C₅	1	1	yes	characteristic, complemented
125	#4945	C₂×C₅	1	1	yes	characteristic, complemented
126	#4670	C₂×C₅	1	1	yes	characteristic, complemented
127	#4669	C₂×C₅	1	1	yes	characteristic, complemented
128	#4650	C₂×C₅	1	1	yes	characteristic, complemented
129	#4646	C₂×C₅	1	1	yes	characteristic, complemented
130	C₂²×C₅×Q₈	—	3	1	no	—
131	C₂²×C₅×D₄	—	3	1	no	—
132	C₂³×C₄×C₅	—	3	1	no	—
133	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
134	C₅×#124	—	3	8	no	—
135	C₂×C₅×C₄⋊C₄	—	3	1	no	—
136	C₂×C₅×C₄⋊C₄	—	3	1	no	—
137	C₂×C₅×C₄⋊C₄	—	3	1	no	—
138	C₂×C₅×C₄⋊C₄	—	3	1	no	—
139	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
140	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
141	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
142	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
143	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
144	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
145	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
146	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
147	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
148	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
149	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
150	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
151	C₂×C₄²×C₅	—	3	1	no	—
152	C₂×C₄²×C₅	—	3	1	no	—
153	C₂×C₄²×C₅	—	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	—	3	1	no	—
159	C₅×#95	—	3	1	no	—
160	C₅×#95	—	3	1	no	—
161	C₅×#95	—	3	1	no	—
162	C₅×#95	—	3	1	no	—
163	C₅×#95	—	3	1	no	—
164	C₅×#95	C₂×D₃	1	1	yes	characteristic
165	C₅×#95	C₂×D₃	1	1	yes	characteristic
166	#2379	—	3	1	no	Sylow
167	C₂³×C₃×C₅	—	2	1	no	—
168	C₂³×C₃×C₅	—	2	1	no	—
169	C₂³×C₃×C₅	—	2	1	no	—
170	C₂³×C₃×C₅	—	2	1	no	—
171	C₂³×C₃×C₅	—	2	1	no	—
172	C₂³×C₃×C₅	—	2	1	no	—
173	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
174	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
175	C₂²×C₅×D₃	—	2	1	no	—
176	C₂²×C₅×D₃	—	2	1	no	—
177	C₂²×C₅×D₃	—	2	1	no	—
178	C₂²×C₅×D₃	—	2	1	no	—
179	C₂²×C₅×D₃	—	2	1	no	—
180	C₂²×C₅×D₃	—	2	1	no	—
181	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
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	—	2	1	no	—
188	C₂×C₃×C₄×C₅	—	2	1	no	—
189	C₂×C₃×C₄×C₅	—	2	1	no	—
190	C₂×C₃×C₄×C₅	—	2	1	no	—
191	C₂×C₃×C₄×C₅	—	2	1	no	—
192	C₂×C₃×C₄×C₅	—	2	1	no	—
193	C₂×C₃×C₄×C₅	—	2	1	no	—
194	C₂×C₃×C₄×C₅	—	2	1	no	—
195	C₂×C₃×C₄×C₅	—	2	1	no	—
196	C₂×C₃×C₄×C₅	—	2	1	no	—
197	C₂×C₃×C₄×C₅	—	2	1	no	—
198	C₂×C₃×C₄×C₅	—	4	4	no	—
199	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
200	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
201	C₅×#67	—	4	4	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	—	2	1	no	—
209	C₂×C₅×Dic₃	—	2	1	no	—
210	C₂×C₅×Dic₃	—	2	1	no	—
211	C₂×C₅×Dic₃	—	2	1	no	—
212	C₂×C₅×Dic₃	—	2	1	no	—
213	C₂×C₅×Dic₃	—	2	1	no	—
214	C₂×C₅×Dic₃	—	2	1	no	—
215	C₂×C₅×Dic₃	—	2	1	no	—
216	C₂×C₅×Dic₃	—	2	1	no	—
217	C₂×C₅×Dic₃	—	2	1	no	—
218	C₂×C₅×Dic₃	—	2	1	no	—
219	C₂×C₅×Dic₃	—	2	1	no	—
220	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
221	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
222	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
223	C₄×C₅×D₃	—	4	4	no	—
224	C₅×Dic₆	—	4	4	no	—
225	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
226	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
227	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
228	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
229	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
231	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
233	C₂×#217	C₂²×C₅	1	1	yes	characteristic
234	C₂×#217	C₂²×C₅	1	1	yes	characteristic
235	C₂×#217	C₂²×C₅	1	1	yes	characteristic
236	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
237	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
238	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
239	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
240	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
241	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
242	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
243	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
244	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
245	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
246	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
248	#885	C₄×C₅	1	8	yes	complemented
249	C₃×#95	C₂²×C₅	1	1	yes	characteristic
250	C₃×#95	C₂²×C₅	1	1	yes	characteristic
251	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
252	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
253	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
254	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
255	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
256	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
257	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
258	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
259	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
260	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
261	C₂⁴×C₅	—	3	1	no	—
262	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
263	C₂×C₅×Q₈	—	3	4	no	—
264	C₂×C₅×Q₈	—	12	1	no	—
265	C₂×C₅×Q₈	—	12	1	no	—
266	C₂×C₅×D₄	—	3	4	no	—
267	C₂×C₅×D₄	—	12	1	no	—
268	C₂×C₅×D₄	—	12	1	no	—
269	C₂²×C₄×C₅	—	3	1	no	—
270	C₂²×C₄×C₅	—	3	1	no	—
271	C₂²×C₄×C₅	—	3	1	no	—
272	C₂²×C₄×C₅	—	3	1	no	—
273	C₂²×C₄×C₅	—	3	1	no	—
274	C₂²×C₄×C₅	—	3	1	no	—
275	C₂²×C₄×C₅	—	3	1	no	—
276	C₂²×C₄×C₅	—	4	1	no	—
277	C₂²×C₄×C₅	—	4	1	no	—
278	C₂²×C₄×C₅	—	4	1	no	—
279	C₂²×C₄×C₅	—	12	1	no	—
280	C₂²×C₄×C₅	—	12	1	no	—
281	C₂²×C₄×C₅	—	12	1	no	—
282	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
283	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
284	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
285	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
286	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
287	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
288	C₅×C₄⋊C₄	—	4	1	no	—
289	C₅×C₄⋊C₄	—	4	1	no	—
290	C₅×C₄⋊C₄	—	12	1	no	—
291	C₅×C₄⋊C₄	—	12	1	no	—
292	C₅×C₄⋊C₄	—	12	1	no	—
293	C₅×C₄⋊C₄	—	12	1	no	—
294	C₅×C₂²⋊C₄	—	3	4	no	—
295	C₅×C₂²⋊C₄	—	3	4	no	—
296	C₅×C₂²⋊C₄	—	3	4	no	—
297	C₅×C₂²⋊C₄	—	4	1	no	—
298	C₅×C₂²⋊C₄	—	12	1	no	—
299	C₅×C₂²⋊C₄	—	12	1	no	—
300	C₅×C₂²⋊C₄	—	12	1	no	—
301	C₅×C₂²⋊C₄	—	12	1	no	—
302	C₅×C₂²⋊C₄	—	12	1	no	—
303	C₅×C₂²⋊C₄	C₄×D₃	1	4	yes	complemented
304	C₄²×C₅	—	3	4	no	—
305	C₄²×C₅	—	12	1	no	—
306	C₄²×C₅	—	12	1	no	—
307	C₂×#124	—	3	1	no	—
308	#391	—	3	1	no	—
309	#391	—	3	1	no	—
310	#388	—	3	1	no	—
311	#388	—	3	1	no	—
312	#388	—	3	1	no	—
313	#388	—	3	1	no	—
314	#386	—	3	1	no	—
315	#386	—	3	1	no	—
316	#385	—	3	1	no	—
317	#385	—	3	1	no	—
318	#385	—	3	1	no	—
319	#385	C₅×D₃	1	1	yes	characteristic, complemented
320	#382	—	3	1	no	—
321	#382	—	3	1	no	—
322	C₂²×C₃×C₅	—	2	2	no	—
323	C₂²×C₃×C₅	—	2	2	no	—
324	C₂²×C₃×C₅	—	2	2	no	—
325	C₂²×C₃×C₅	—	4	1	no	—
326	C₂²×C₃×C₅	—	4	1	no	—
327	C₂²×C₃×C₅	—	4	1	no	—
328	C₂²×C₃×C₅	—	4	1	no	—
329	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
330	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
331	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
332	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
333	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
334	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
335	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
336	C₂×C₅×D₃	—	2	2	no	—
337	C₂×C₅×D₃	—	2	2	no	—
338	C₂×C₅×D₃	—	2	2	no	—
339	C₂×C₅×D₃	—	4	1	no	—
340	C₂×C₅×D₃	—	4	1	no	—
341	C₂×C₅×D₃	—	4	1	no	—
342	C₂×C₅×D₃	—	4	1	no	—
343	C₃×C₄×C₅	—	2	2	no	—
344	C₃×C₄×C₅	—	2	2	no	—
345	C₃×C₄×C₅	—	4	1	no	—
346	C₃×C₄×C₅	—	4	1	no	—
347	C₃×C₄×C₅	—	4	1	no	—
348	C₃×C₄×C₅	—	4	1	no	—
349	C₅×Dic₃	—	2	2	no	—
350	C₅×Dic₃	—	2	2	no	—
351	C₅×Dic₃	—	2	2	no	—
352	C₅×Dic₃	—	4	1	no	—
353	C₅×Dic₃	—	4	1	no	—
354	C₅×Dic₃	—	4	1	no	—
355	C₅×Dic₃	—	4	1	no	—
356	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
357	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
358	C₂²×C₃×C₄	—	4	1	no	—
359	C₂²×C₃×C₄	—	4	1	no	—
360	C₂²×C₃×C₄	—	4	1	no	—
361	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
362	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
363	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
364	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
365	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
366	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
367	C₂×#67	—	4	1	no	—
368	C₂×#67	—	4	1	no	—
369	C₂×#67	C₂×C₄×C₅	1	4	yes	—
370	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
371	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
372	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
373	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
374	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
375	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
376	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
377	C₂×C₄×D₃	—	4	1	no	—
378	C₂×C₄×D₃	—	4	1	no	—
379	C₂×C₄×D₃	—	4	1	no	—
380	C₂×Dic₆	—	4	1	no	—
381	C₂×Dic₆	—	4	1	no	—
382	C₂×Dic₆	C₂×C₄×C₅	1	4	yes	complemented
383	C₃×C₄⋊C₄	—	4	1	no	—
384	C₃×C₄⋊C₄	—	4	1	no	—
385	C₃×C₂²⋊C₄	—	4	1	no	—
386	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
387	#217	—	4	1	no	—
388	#217	—	4	1	no	—
389	#217	C₂×C₄×C₅	1	4	yes	complemented
390	(C₂×D₃)⋊C₄	—	4	1	no	—
391	(C₂×D₃)⋊C₄	—	4	1	no	—
392	(C₂×D₃)⋊C₄	—	4	1	no	—
393	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
394	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
395	C₄⋊Dic₃	—	4	1	no	—
396	Dic₃⋊C₄	—	4	1	no	—
397	Dic₃⋊C₄	—	4	1	no	—
398	Dic₃⋊C₄	—	4	1	no	—
399	C₄×Dic₃	—	4	1	no	—
400	C₄×Dic₃	—	4	1	no	—
401	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
402	C₂³×C₅	—	2	1	no	—
403	C₂³×C₅	—	2	1	no	—
404	C₂³×C₅	—	2	1	no	—
405	C₂³×C₅	—	2	1	no	—
406	C₂³×C₅	—	2	1	no	—
407	C₂³×C₅	—	2	1	no	—
408	C₂³×C₅	—	3	2	no	—
409	C₂³×C₅	—	6	1	no	—
410	C₂³×C₅	—	6	1	no	—
411	C₂³×C₅	—	6	1	no	—
412	C₂³×C₅	—	6	1	no	—
413	C₂³×C₅	—	6	1	no	—
414	C₂³×C₅	—	6	1	no	—
415	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
416	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
417	C₅×Q₈	—	12	4	no	—
418	C₅×D₄	—	12	4	no	—
419	C₂×C₄×C₅	—	2	1	no	—
420	C₂×C₄×C₅	—	2	1	no	—
421	C₂×C₄×C₅	—	2	1	no	—
422	C₂×C₄×C₅	—	2	1	no	—
423	C₂×C₄×C₅	—	2	1	no	—
424	C₂×C₄×C₅	—	2	1	no	—
425	C₂×C₄×C₅	—	2	1	no	—
426	C₂×C₄×C₅	—	2	1	no	—
427	C₂×C₄×C₅	—	2	1	no	—
428	C₂×C₄×C₅	—	2	1	no	—
429	C₂×C₄×C₅	—	2	1	no	—
430	C₂×C₄×C₅	—	2	1	no	—
431	C₂×C₄×C₅	—	2	1	no	—
432	C₂×C₄×C₅	—	2	1	no	—
433	C₂×C₄×C₅	—	2	1	no	—
434	C₂×C₄×C₅	—	2	1	no	—
435	C₂×C₄×C₅	—	3	2	no	—
436	C₂×C₄×C₅	—	3	2	no	—
437	C₂×C₄×C₅	—	3	2	no	—
438	C₂×C₄×C₅	—	4	4	no	—
439	C₂×C₄×C₅	—	6	1	no	—
440	C₂×C₄×C₅	—	6	1	no	—
441	C₂×C₄×C₅	—	6	1	no	—
442	C₂×C₄×C₅	—	6	1	no	—
443	C₂×C₄×C₅	—	6	1	no	—
444	C₂×C₄×C₅	—	6	1	no	—
445	C₂×C₄×C₅	—	6	1	no	—
446	C₂×C₄×C₅	—	6	1	no	—
447	C₂×C₄×C₅	—	6	1	no	—
448	C₂×C₄×C₅	—	6	1	no	—
449	C₂×C₄×C₅	—	6	1	no	—
450	C₂×C₄×C₅	—	6	1	no	—
451	C₂×C₄×C₅	—	6	1	no	—
452	C₂×C₄×C₅	—	6	1	no	—
453	C₂×C₄×C₅	—	6	1	no	—
454	C₂×C₄×C₅	—	6	1	no	—
455	C₂×C₄×C₅	—	6	1	no	—
456	C₂×C₄×C₅	—	6	1	no	—
457	C₂×C₄×C₅	—	12	4	no	—
458	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
459	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
460	C₂²×Q₈	—	3	1	no	—
461	C₂²×D₄	—	3	1	no	—
462	C₂³×C₄	—	3	1	no	—
463	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
464	#124	—	3	8	no	—
465	C₂×C₄⋊C₄	—	3	1	no	—
466	C₂×C₄⋊C₄	—	3	1	no	—
467	C₂×C₄⋊C₄	—	3	1	no	—
468	C₂×C₄⋊C₄	—	3	1	no	—
469	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
470	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
471	C₂×C₂²⋊C₄	—	3	1	no	—
472	C₂×C₂²⋊C₄	—	3	1	no	—
473	C₂×C₂²⋊C₄	—	3	1	no	—
474	C₂×C₂²⋊C₄	—	3	1	no	—
475	C₂×C₂²⋊C₄	—	3	1	no	—
476	C₂×C₂²⋊C₄	—	3	1	no	—
477	C₂×C₂²⋊C₄	—	3	1	no	—
478	C₂×C₂²⋊C₄	—	3	1	no	—
479	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
481	C₂×C₄²	—	3	1	no	—
482	C₂×C₄²	—	3	1	no	—
483	C₂×C₄²	—	3	1	no	—
484	#95	—	3	1	no	—
485	#95	—	3	1	no	—
486	#95	—	3	1	no	—
487	#95	—	3	1	no	—
488	#95	—	3	1	no	—
489	#95	—	3	1	no	—
490	#95	—	3	1	no	—
491	#95	—	3	1	no	—
492	#95	—	3	1	no	—
493	#95	—	3	1	no	—
494	#95	C₂×C₅×D₃	1	1	yes	characteristic
495	#95	C₂×C₅×D₃	1	1	yes	characteristic
496	C₂×C₃×C₅	—	4	2	no	—
497	C₂×C₃×C₅	#518	1	1	yes	characteristic
498	C₂×C₃×C₅	#520	1	1	yes	characteristic
499	C₂×C₃×C₅	#520	1	1	yes	characteristic
500	C₂×C₃×C₅	H(3,𝔽₄)	1	1	yes	characteristic
501	C₂×C₃×C₅	#562	1	1	yes	characteristic
502	C₂×C₃×C₅	#562	1	1	yes	characteristic
503	C₂×C₃×C₅	#563	1	1	yes	characteristic
504	C₅×D₃	—	4	2	no	—
505	C₂³×C₃	—	2	1	no	—
506	C₂³×C₃	—	2	1	no	—
507	C₂³×C₃	—	2	1	no	—
508	C₂³×C₃	—	2	1	no	—
509	C₂³×C₃	—	2	1	no	—
510	C₂³×C₃	—	2	1	no	—
511	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
512	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
513	C₂²×D₃	—	2	1	no	—
514	C₂²×D₃	—	2	1	no	—
515	C₂²×D₃	—	2	1	no	—
516	C₂²×D₃	—	2	1	no	—
517	C₂²×D₃	—	2	1	no	—
518	C₂²×D₃	—	2	1	no	—
519	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
520	C₂×C₃×C₄	—	2	1	no	—
521	C₂×C₃×C₄	—	2	1	no	—
522	C₂×C₃×C₄	—	2	1	no	—
523	C₂×C₃×C₄	—	2	1	no	—
524	C₂×C₃×C₄	—	2	1	no	—
525	C₂×C₃×C₄	—	2	1	no	—
526	C₂×C₃×C₄	—	2	1	no	—
527	C₂×C₃×C₄	—	2	1	no	—
528	C₂×C₃×C₄	—	2	1	no	—
529	C₂×C₃×C₄	—	2	1	no	—
530	C₂×C₃×C₄	—	2	1	no	—
531	C₂×C₃×C₄	—	2	1	no	—
532	C₂×C₃×C₄	—	2	1	no	—
533	C₂×C₃×C₄	—	2	1	no	—
534	C₂×C₃×C₄	—	2	1	no	—
535	C₂×C₃×C₄	—	2	1	no	—
536	C₂×C₃×C₄	—	4	4	no	—
537	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
538	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
539	#67	—	4	4	no	—
540	C₂×Dic₃	—	2	1	no	—
541	C₂×Dic₃	—	2	1	no	—
542	C₂×Dic₃	—	2	1	no	—
543	C₂×Dic₃	—	2	1	no	—
544	C₂×Dic₃	—	2	1	no	—
545	C₂×Dic₃	—	2	1	no	—
546	C₂×Dic₃	—	2	1	no	—
547	C₂×Dic₃	—	2	1	no	—
548	C₂×Dic₃	—	2	1	no	—
549	C₂×Dic₃	—	2	1	no	—
550	C₂×Dic₃	—	2	1	no	—
551	C₂×Dic₃	—	2	1	no	—
552	C₂×Dic₃	—	2	1	no	—
553	C₂×Dic₃	—	2	1	no	—
554	C₂×Dic₃	—	2	1	no	—
555	C₂×Dic₃	—	2	1	no	—
556	C₂×Dic₃	—	2	1	no	—
557	C₂×Dic₃	—	2	1	no	—
558	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
559	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
560	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
561	C₄×D₃	—	4	4	no	—
562	Dic₆	—	4	4	no	—
563	C₂²×C₅	—	2	2	no	—
564	C₂²×C₅	—	2	2	no	—
565	C₂²×C₅	—	2	2	no	—
566	C₂²×C₅	—	4	1	no	—
567	C₂²×C₅	—	4	1	no	—
568	C₂²×C₅	—	4	1	no	—
569	C₂²×C₅	—	4	1	no	—
570	C₂²×C₅	—	6	2	no	—
571	C₂²×C₅	—	6	2	no	—
572	C₂²×C₅	—	6	2	no	—
573	C₂²×C₅	—	12	1	no	—
574	C₂²×C₅	—	12	1	no	—
575	C₂²×C₅	—	12	1	no	—
576	C₂²×C₅	—	12	1	no	—
577	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
578	C₂²×C₅	#1004	1	1	yes	characteristic
579	C₂²×C₅	#1004	1	1	yes	characteristic
580	C₂²×C₅	#1004	1	1	yes	characteristic
581	C₂²×C₅	#1007	1	1	yes	characteristic
582	C₂²×C₅	#1009	1	1	yes	characteristic
583	C₂²×C₅	#1010	1	1	yes	characteristic
584	C₄×C₅	—	2	2	no	—
585	C₄×C₅	—	2	2	no	—
586	C₄×C₅	—	4	1	no	—
587	C₄×C₅	—	4	1	no	—
588	C₄×C₅	—	4	1	no	—
589	C₄×C₅	—	4	1	no	—
590	C₄×C₅	—	6	2	no	—
591	C₄×C₅	—	6	2	no	—
592	C₄×C₅	—	6	2	no	—
593	C₄×C₅	—	12	1	no	—
594	C₄×C₅	—	12	1	no	—
595	C₄×C₅	—	12	1	no	—
596	C₄×C₅	—	12	1	no	—
597	C₂⁴	—	3	1	no	—
598	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
599	C₂×Q₈	—	3	4	no	—
600	C₂×Q₈	—	12	1	no	—
601	C₂×Q₈	—	12	1	no	—
602	C₂×D₄	—	3	4	no	—
603	C₂×D₄	—	12	1	no	—
604	C₂×D₄	—	12	1	no	—
605	C₂²×C₄	—	3	1	no	—
606	C₂²×C₄	—	3	1	no	—
607	C₂²×C₄	—	3	1	no	—
608	C₂²×C₄	—	3	1	no	—
609	C₂²×C₄	—	3	1	no	—
610	C₂²×C₄	—	3	1	no	—
611	C₂²×C₄	—	3	1	no	—
612	C₂²×C₄	—	4	1	no	—
613	C₂²×C₄	—	4	1	no	—
614	C₂²×C₄	—	4	1	no	—
615	C₂²×C₄	—	12	1	no	—
616	C₂²×C₄	—	12	1	no	—
617	C₂²×C₄	—	12	1	no	—
618	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
619	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
620	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
621	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
622	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
623	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
624	C₄⋊C₄	—	4	1	no	—
625	C₄⋊C₄	—	4	1	no	—
626	C₄⋊C₄	—	12	1	no	—
627	C₄⋊C₄	—	12	1	no	—
628	C₄⋊C₄	—	12	1	no	—
629	C₄⋊C₄	—	12	1	no	—
630	C₂²⋊C₄	—	3	4	no	—
631	C₂²⋊C₄	—	3	4	no	—
632	C₂²⋊C₄	—	3	4	no	—
633	C₂²⋊C₄	—	4	1	no	—
634	C₂²⋊C₄	—	12	1	no	—
635	C₂²⋊C₄	—	12	1	no	—
636	C₂²⋊C₄	—	12	1	no	—
637	C₂²⋊C₄	—	12	1	no	—
638	C₂²⋊C₄	—	12	1	no	—
639	C₂²⋊C₄	C₄×C₅×D₃	1	4	yes	complemented
640	C₄²	—	3	4	no	—
641	C₄²	—	12	1	no	—
642	C₄²	—	12	1	no	—
643	C₃×C₅	#2379	1	1	yes	characteristic, complemented, Hall
644	C₂²×C₃	—	2	2	no	—
645	C₂²×C₃	—	2	2	no	—
646	C₂²×C₃	—	2	2	no	—
647	C₂²×C₃	—	4	1	no	—
648	C₂²×C₃	—	4	1	no	—
649	C₂²×C₃	—	4	1	no	—
650	C₂²×C₃	—	4	1	no	—
651	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
652	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
653	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
654	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
655	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
656	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
657	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
658	C₂×D₃	—	2	2	no	—
659	C₂×D₃	—	2	2	no	—
660	C₂×D₃	—	2	2	no	—
661	C₂×D₃	—	4	1	no	—
662	C₂×D₃	—	4	1	no	—
663	C₂×D₃	—	4	1	no	—
664	C₂×D₃	—	4	1	no	—
665	C₃×C₄	—	2	2	no	—
666	C₃×C₄	—	2	2	no	—
667	C₃×C₄	—	4	1	no	—
668	C₃×C₄	—	4	1	no	—
669	C₃×C₄	—	4	1	no	—
670	C₃×C₄	—	4	1	no	—
671	Dic₃	—	2	2	no	—
672	Dic₃	—	2	2	no	—
673	Dic₃	—	2	2	no	—
674	Dic₃	—	4	1	no	—
675	Dic₃	—	4	1	no	—
676	Dic₃	—	4	1	no	—
677	Dic₃	—	4	1	no	—
678	C₂×C₅	—	4	2	no	—
679	C₂×C₅	—	12	2	no	—
680	C₂×C₅	#5504	1	1	yes	characteristic
681	C₂×C₅	#5545	1	1	yes	characteristic
682	C₂×C₅	#5546	1	1	yes	characteristic
683	C₂×C₅	#5594	1	1	yes	characteristic
684	C₂×C₅	#5646	1	1	yes	characteristic
685	C₂×C₅	#5647	1	1	yes	characteristic
686	C₂×C₅	#5667	1	1	yes	characteristic
687	C₂³	—	2	1	no	—
688	C₂³	—	2	1	no	—
689	C₂³	—	2	1	no	—
690	C₂³	—	2	1	no	—
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	3	2	no	—
694	C₂³	—	6	1	no	—
695	C₂³	—	6	1	no	—
696	C₂³	—	6	1	no	—
697	C₂³	—	6	1	no	—
698	C₂³	—	6	1	no	—
699	C₂³	—	6	1	no	—
700	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
701	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
702	Q₈	—	12	4	no	—
703	D₄	—	12	4	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	2	1	no	—
718	C₂×C₄	—	2	1	no	—
719	C₂×C₄	—	2	1	no	—
720	C₂×C₄	—	3	2	no	—
721	C₂×C₄	—	3	2	no	—
722	C₂×C₄	—	3	2	no	—
723	C₂×C₄	—	4	4	no	—
724	C₂×C₄	—	6	1	no	—
725	C₂×C₄	—	6	1	no	—
726	C₂×C₄	—	6	1	no	—
727	C₂×C₄	—	6	1	no	—
728	C₂×C₄	—	6	1	no	—
729	C₂×C₄	—	6	1	no	—
730	C₂×C₄	—	6	1	no	—
731	C₂×C₄	—	6	1	no	—
732	C₂×C₄	—	6	1	no	—
733	C₂×C₄	—	6	1	no	—
734	C₂×C₄	—	6	1	no	—
735	C₂×C₄	—	6	1	no	—
736	C₂×C₄	—	6	1	no	—
737	C₂×C₄	—	6	1	no	—
738	C₂×C₄	—	6	1	no	—
739	C₂×C₄	—	6	1	no	—
740	C₂×C₄	—	6	1	no	—
741	C₂×C₄	—	6	1	no	—
742	C₂×C₄	—	12	4	no	—
743	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
744	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
745	C₂×C₃	—	4	2	no	—
746	C₂×C₃	C₅×#518	1	1	yes	characteristic
747	C₂×C₃	C₅×#520	1	1	yes	characteristic
748	C₂×C₃	C₅×#520	1	1	yes	characteristic
749	C₂×C₃	C₅×H(3,𝔽₄)	1	1	yes	characteristic
750	C₂×C₃	C₅×#562	1	1	yes	characteristic
751	C₂×C₃	C₅×#562	1	1	yes	characteristic
752	C₂×C₃	C₅×#563	1	1	yes	characteristic
753	D₃	—	4	2	no	—
754	C₅	#74402	1	1	yes	characteristic, direct product factor, Sylow
755	C₂²	—	2	2	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	6	2	no	—
763	C₂²	—	6	2	no	—
764	C₂²	—	6	2	no	—
765	C₂²	—	12	1	no	—
766	C₂²	—	12	1	no	—
767	C₂²	—	12	1	no	—
768	C₂²	—	12	1	no	—
769	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
770	C₂²	C₅×#1004	1	1	yes	characteristic
771	C₂²	C₅×#1004	1	1	yes	characteristic
772	C₂²	C₅×#1004	1	1	yes	characteristic
773	C₂²	C₅×#1007	1	1	yes	characteristic
774	C₂²	C₅×#1009	1	1	yes	characteristic
775	C₂²	C₅×#1010	1	1	yes	characteristic
776	C₄	—	2	2	no	—
777	C₄	—	2	2	no	—
778	C₄	—	4	1	no	—
779	C₄	—	4	1	no	—
780	C₄	—	4	1	no	—
781	C₄	—	4	1	no	—
782	C₄	—	6	2	no	—
783	C₄	—	6	2	no	—
784	C₄	—	6	2	no	—
785	C₄	—	12	1	no	—
786	C₄	—	12	1	no	—
787	C₄	—	12	1	no	—
788	C₄	—	12	1	no	—
789	C₃	C₅×#2379	1	1	yes	characteristic, complemented, Sylow
790	C₂	—	4	2	no	—
791	C₂	—	12	2	no	—
792	C₂	C₅×#5504	1	1	yes	characteristic
793	C₂	C₅×#5545	1	1	yes	characteristic
794	C₂	C₅×#5546	1	1	yes	characteristic
795	C₂	C₅×#5594	1	1	yes	characteristic
796	C₂	C₅×#5646	1	1	yes	characteristic
797	C₂	C₅×#5647	1	1	yes	characteristic
798	C₂	C₅×#5667	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×#385	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×#67	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#385	D₃
hypocenter	C₃	C₅×#2379
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#385

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#385	C₂	semidirect
4. C₅×#5210	C₂	semidirect
5. C₅×#4989	C₂	semidirect
6. C₅×#4989	C₂	semidirect
7. C₅×#4977	C₂	semidirect
8. C₅×#4973	C₂	semidirect
10. C₅×#4951	C₂	semidirect
11. C₅×#4945	C₂	semidirect
12. C₅×#4670	C₂	semidirect
13. C₅×#4669	C₂	semidirect
14. C₅×#4650	C₂	semidirect
15. C₅×#4646	C₂	semidirect
40. C₅×#885	C₄	semidirect
53. #74402	C₅	direct (N × H)
66. C₅×#385	D₃	semidirect
95. C₂×C₅×Dic₆	C₂×C₄	semidirect
99. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
102. C₅×#217	C₂×C₄	semidirect
106. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
107. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
114. C₄×C₅×Dic₃	C₂×C₄	semidirect
116. C₃×#385	C₂×C₅	semidirect
118. #5210	C₂×C₅	semidirect
119. #4989	C₂×C₅	semidirect
120. #4989	C₂×C₅	semidirect
121. #4977	C₂×C₅	semidirect
122. #4973	C₂×C₅	semidirect
124. #4951	C₂×C₅	semidirect
125. #4945	C₂×C₅	semidirect
126. #4670	C₂×C₅	semidirect
127. #4669	C₂×C₅	semidirect
128. #4650	C₂×C₅	semidirect
129. #4646	C₂×C₅	semidirect
248. #885	C₄×C₅	semidirect
303. C₅×C₂²⋊C₄	C₄×D₃	semidirect
319. #385	C₅×D₃	semidirect
382. C₂×Dic₆	C₂×C₄×C₅	semidirect
386. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
389. #217	C₂×C₄×C₅	semidirect
393. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
394. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
401. C₄×Dic₃	C₂×C₄×C₅	semidirect
639. C₂²⋊C₄	C₄×C₅×D₃	semidirect
643. C₃×C₅	#2379	semidirect
754. C₅	#74402	direct (N × H)
789. C₃	C₅×#2379	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#885	2
C₃×C₅×#385	2
C₅×#5213	2
C₅×#5210	2
C₅×#4989	2
C₅×#4977	2
C₅×#4973	2
C₅×#4956	2
C₅×#4951	2
C₅×#4945	2
C₅×#4670	2
C₅×#4669	2
C₅×#4650	2
C₅×#4646	2
C₅×#2379	3
#74402	5

Subgroups — C5×#74402 #14331133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#74402 #14331133