Subgroups — C₅×#73462 #14327492

Order 1920.

1176 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5213	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×C₃⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4958	C₂	1	1	yes	maximal, characteristic
6	C₅×#4942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×Dic₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4940	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4933	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4932	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4669	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4664	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4652	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#4651	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2353	—	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	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
20	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₂×C₅×#217	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×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₅×(C₂×D₃)⋊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×#67⋊C₄	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	#73462	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
54	C₂×C₄×C₅×D₄	—	3	1	no	—
55	C₅×#388	—	3	1	no	—
56	C₅×#388	—	3	1	no	—
57	C₅×#387	—	3	1	no	—
58	C₅×#387	—	3	1	no	—
59	C₅×#386	—	3	1	no	—
60	C₅×#386	—	3	1	no	—
61	C₅×#383	—	3	1	no	—
62	C₅×#381	—	3	1	no	—
63	C₅×#380	—	3	1	no	—
64	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
65	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
66	C₄×C₅×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
67	C₅×#376	—	3	1	no	—
68	C₂×C₅×#95	—	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	—	2	2	no	—
72	C₂²×C₃×C₄×C₅	—	2	2	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	—	2	2	no	—
81	C₂×C₅×#67	—	2	2	no	—
82	C₂×C₅×#67	C₂×C₄	1	4	yes	—
83	C₂²×C₅×Dic₃	—	2	2	no	—
84	C₂²×C₅×Dic₃	—	2	2	no	—
85	C₂²×C₅×Dic₃	—	4	1	no	—
86	C₂²×C₅×Dic₃	—	4	1	no	—
87	C₂²×C₅×Dic₃	—	4	1	no	—
88	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	—
89	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
90	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
91	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
92	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
93	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
94	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
95	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
96	C₂×C₄×C₅×D₃	—	4	1	no	—
97	C₂×C₄×C₅×D₃	—	4	1	no	—
98	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	complemented
99	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
100	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	4	yes	—
101	C₃×C₄²×C₅	—	2	2	no	—
102	C₃×C₄²×C₅	—	4	1	no	—
103	C₅×#217	—	2	2	no	—
104	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
105	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
106	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
107	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
108	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	complemented
109	C₅×Dic₃⋊C₄	—	4	1	no	—
110	C₅×Dic₃⋊C₄	—	4	1	no	—
111	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	complemented
112	C₄×C₅×Dic₃	—	2	2	no	—
113	C₄×C₅×Dic₃	—	4	1	no	—
114	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
115	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic
116	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
117	#5213	C₂×C₅	1	1	yes	characteristic
118	C₂×C₃⋊#95	C₂×C₅	1	1	yes	characteristic, complemented
119	#4958	C₂×C₅	1	1	yes	characteristic
120	#4942	C₂×C₅	1	1	yes	characteristic, complemented
121	Dic₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
122	#4940	C₂×C₅	1	1	yes	characteristic, complemented
123	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
124	#4933	C₂×C₅	1	1	yes	characteristic, complemented
125	#4932	C₂×C₅	1	1	yes	characteristic, complemented
126	#4669	C₂×C₅	1	1	yes	characteristic, complemented
127	#4664	C₂×C₅	1	1	yes	characteristic, complemented
128	#4652	C₂×C₅	1	1	yes	characteristic, complemented
129	#4651	C₂×C₅	1	1	yes	characteristic, complemented
130	C₂²×C₅×D₄	—	3	1	no	—
131	C₂³×C₄×C₅	—	3	1	no	—
132	C₂³×C₄×C₅	—	3	1	no	—
133	C₂³×C₄×C₅	—	3	1	no	—
134	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
135	C₄×C₅×D₄	—	3	8	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×C₂²⋊C₄	—	3	1	no	—
140	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
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	C₂×D₃	1	1	yes	characteristic
146	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
147	C₂×C₄²×C₅	—	3	1	no	—
148	C₂×C₄²×C₅	—	3	1	no	—
149	C₂×C₄²×C₅	—	3	1	no	—
150	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
151	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
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	—	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	#2353	—	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	C₂²×C₄	1	2	yes	—
172	C₂³×C₃×C₅	#41	1	2	yes	—
173	C₂³×C₃×C₅	#41	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	—	4	4	no	—
198	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
199	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
200	C₂×C₃×C₄×C₅	#41	1	2	yes	—
201	C₅×#67	—	2	8	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	—	4	4	no	—
220	C₂×C₅×Dic₃	—	4	4	no	—
221	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
222	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
223	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
224	C₂×C₅×Dic₃	#41	1	2	yes	—
225	C₄×C₅×D₃	—	4	4	no	—
226	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
227	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
228	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
229	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
230	C₂²×C₄×D₃	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×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₃×C₄²	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×Dic₃⋊C₄	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×C₄×Dic₃	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	#67⋊C₄	C₄×C₅	1	8	yes	complemented
248	C₃×#95	C₂²×C₅	1	1	yes	characteristic
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	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
262	C₂⁴×C₅	—	3	1	no	—
263	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
264	C₂×C₅×D₄	—	3	4	no	—
265	C₂×C₅×D₄	—	6	2	no	—
266	C₂×C₅×D₄	—	6	2	no	—
267	C₂²×C₄×C₅	—	2	2	no	—
268	C₂²×C₄×C₅	—	2	2	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	4	no	—
274	C₂²×C₄×C₅	—	3	4	no	—
275	C₂²×C₄×C₅	—	3	1	no	—
276	C₂²×C₄×C₅	—	3	1	no	—
277	C₂²×C₄×C₅	—	3	1	no	—
278	C₂²×C₄×C₅	—	4	1	no	—
279	C₂²×C₄×C₅	—	6	2	no	—
280	C₂²×C₄×C₅	—	6	2	no	—
281	C₂²×C₄×C₅	—	12	1	no	—
282	C₂²×C₄×C₅	—	12	1	no	—
283	C₂²×C₄×C₅	—	12	1	no	—
284	C₂²×C₄×C₅	—	12	1	no	—
285	C₂²×C₄×C₅	—	12	1	no	—
286	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
287	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
288	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
289	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
290	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
291	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
292	C₅×C₄⋊C₄	—	3	4	no	—
293	C₅×C₄⋊C₄	—	12	1	no	—
294	C₅×C₄⋊C₄	—	12	1	no	—
295	C₅×C₂²⋊C₄	—	2	2	no	—
296	C₅×C₂²⋊C₄	—	3	4	no	—
297	C₅×C₂²⋊C₄	—	6	2	no	—
298	C₅×C₂²⋊C₄	—	6	2	no	—
299	C₅×C₂²⋊C₄	—	6	2	no	—
300	C₅×C₂²⋊C₄	—	12	1	no	—
301	C₅×C₂²⋊C₄	—	12	1	no	—
302	C₅×C₂²⋊C₄	C₄×D₃	1	4	yes	—
303	C₄²×C₅	—	2	2	no	—
304	C₄²×C₅	—	3	4	no	—
305	C₄²×C₅	—	4	1	no	—
306	C₄²×C₅	—	6	2	no	—
307	C₄²×C₅	—	12	1	no	—
308	C₂×C₄×D₄	—	3	1	no	—
309	#388	—	3	1	no	—
310	#388	—	3	1	no	—
311	#387	—	3	1	no	—
312	#387	—	3	1	no	—
313	#386	—	3	1	no	—
314	#386	—	3	1	no	—
315	#383	—	3	1	no	—
316	#381	—	3	1	no	—
317	#380	—	3	1	no	—
318	C₄×C₂²⋊C₄	—	3	1	no	—
319	C₄×C₂²⋊C₄	—	3	1	no	—
320	C₄×C₂²⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
321	#376	—	3	1	no	—
322	C₂×#95	—	3	1	no	—
323	C₂²×C₃×C₅	—	2	2	no	—
324	C₂²×C₃×C₅	—	2	2	no	—
325	C₂²×C₃×C₅	—	2	2	no	—
326	C₂²×C₃×C₅	—	2	2	no	—
327	C₂²×C₃×C₅	—	2	2	no	—
328	C₂²×C₃×C₅	—	2	2	no	—
329	C₂²×C₃×C₅	#117	1	4	yes	—
330	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
331	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
332	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
333	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
334	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
335	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
336	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
337	C₂×C₅×D₃	—	2	2	no	—
338	C₂×C₅×D₃	—	2	2	no	—
339	C₂×C₅×D₃	—	2	2	no	—
340	C₂×C₅×D₃	—	4	1	no	—
341	C₂×C₅×D₃	—	4	1	no	—
342	C₂×C₅×D₃	—	4	1	no	—
343	C₂×C₅×D₃	—	4	1	no	—
344	C₃×C₄×C₅	—	2	2	no	—
345	C₃×C₄×C₅	—	2	2	no	—
346	C₃×C₄×C₅	—	2	2	no	—
347	C₃×C₄×C₅	—	4	1	no	—
348	C₃×C₄×C₅	—	4	1	no	—
349	C₃×C₄×C₅	—	4	1	no	—
350	C₅×Dic₃	—	2	2	no	—
351	C₅×Dic₃	—	2	2	no	—
352	C₅×Dic₃	—	2	2	no	—
353	C₅×Dic₃	—	2	2	no	—
354	C₅×Dic₃	—	4	1	no	—
355	C₅×Dic₃	—	4	1	no	—
356	C₅×Dic₃	—	4	1	no	—
357	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
358	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
359	C₂²×C₃×C₄	—	2	2	no	—
360	C₂²×C₃×C₄	—	2	2	no	—
361	C₂²×C₃×C₄	—	4	1	no	—
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	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
368	C₂×#67	—	2	2	no	—
369	C₂×#67	—	2	2	no	—
370	C₂×#67	C₂×C₄×C₅	1	4	yes	—
371	C₂²×Dic₃	—	2	2	no	—
372	C₂²×Dic₃	—	2	2	no	—
373	C₂²×Dic₃	—	4	1	no	—
374	C₂²×Dic₃	—	4	1	no	—
375	C₂²×Dic₃	—	4	1	no	—
376	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	—
377	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
378	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
379	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
380	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
381	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
382	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
383	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
384	C₂×C₄×D₃	—	4	1	no	—
385	C₂×C₄×D₃	—	4	1	no	—
386	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	complemented
387	C₃×C₂²⋊C₄	—	2	2	no	—
388	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	4	yes	—
389	C₃×C₄²	—	2	2	no	—
390	C₃×C₄²	—	4	1	no	—
391	#217	—	2	2	no	—
392	(C₂×D₃)⋊C₄	—	2	2	no	—
393	(C₂×D₃)⋊C₄	—	2	2	no	—
394	(C₂×D₃)⋊C₄	—	4	1	no	—
395	(C₂×D₃)⋊C₄	—	4	1	no	—
396	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
397	Dic₃⋊C₄	—	4	1	no	—
398	Dic₃⋊C₄	—	4	1	no	—
399	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
400	C₄×Dic₃	—	2	2	no	—
401	C₄×Dic₃	—	4	1	no	—
402	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
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	—	3	2	no	—
408	C₂³×C₅	—	6	1	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	C₂×C₄×D₃	1	2	yes	—
415	C₂³×C₅	#235	1	2	yes	—
416	C₂³×C₅	#235	1	2	yes	—
417	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
418	C₅×D₄	—	6	8	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	—	3	2	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	—	12	4	no	—
457	C₂×C₄×C₅	—	12	4	no	—
458	C₂×C₄×C₅	—	12	4	no	—
459	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
460	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
461	C₂×C₄×C₅	#237	1	2	yes	—
462	C₂²×D₄	—	3	1	no	—
463	C₂³×C₄	—	3	1	no	—
464	C₂³×C₄	—	3	1	no	—
465	C₂³×C₄	—	3	1	no	—
466	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
467	C₄×D₄	—	3	8	no	—
468	C₂×C₄⋊C₄	—	3	1	no	—
469	C₂×C₄⋊C₄	—	3	1	no	—
470	C₂×C₄⋊C₄	—	3	1	no	—
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	C₂×C₅×D₃	1	1	yes	characteristic
478	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
479	C₂×C₄²	—	3	1	no	—
480	C₂×C₄²	—	3	1	no	—
481	C₂×C₄²	—	3	1	no	—
482	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
483	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
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	—	3	1	no	—
495	#95	—	3	1	no	—
496	#95	C₂×C₅×D₃	1	1	yes	characteristic
497	#95	C₂×C₅×D₃	1	1	yes	characteristic
498	C₂×C₃×C₅	—	2	4	no	—
499	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
500	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
501	C₂×C₃×C₅	#518	1	1	yes	characteristic
502	C₂×C₃×C₅	#551	1	1	yes	characteristic
503	C₂×C₃×C₅	#551	1	1	yes	characteristic
504	C₂×C₃×C₅	#553	1	1	yes	characteristic
505	C₂×C₃×C₅	#553	1	1	yes	characteristic
506	C₅×D₃	—	4	2	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	C₅×#41	1	2	yes	—
513	C₂³×C₃	C₅×#41	1	2	yes	—
514	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
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	—	2	1	no	—
520	C₂²×D₃	—	2	1	no	—
521	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
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	—	2	1	no	—
537	C₂×C₃×C₄	—	4	4	no	—
538	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
539	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
540	C₂×C₃×C₄	C₅×#41	1	2	yes	—
541	#67	—	2	8	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	—	2	1	no	—
559	C₂×Dic₃	—	4	4	no	—
560	C₂×Dic₃	—	4	4	no	—
561	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
562	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
563	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
564	C₂×Dic₃	C₅×#41	1	2	yes	—
565	C₄×D₃	—	4	4	no	—
566	C₂²×C₅	—	2	2	no	—
567	C₂²×C₅	—	2	2	no	—
568	C₂²×C₅	—	2	2	no	—
569	C₂²×C₅	—	2	2	no	—
570	C₂²×C₅	—	2	2	no	—
571	C₂²×C₅	—	2	2	no	—
572	C₂²×C₅	—	6	2	no	—
573	C₂²×C₅	—	6	2	no	—
574	C₂²×C₅	—	6	2	no	—
575	C₂²×C₅	—	12	1	no	—
576	C₂²×C₅	—	12	1	no	—
577	C₂²×C₅	—	12	1	no	—
578	C₂²×C₅	—	12	1	no	—
579	C₂²×C₅	#872	1	4	yes	—
580	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
581	C₂²×C₅	C₂×#235	1	1	yes	characteristic
582	C₂²×C₅	C₂×#235	1	1	yes	characteristic
583	C₂²×C₅	C₂×#237	1	1	yes	characteristic
584	C₂²×C₅	#1004	1	1	yes	characteristic
585	C₂²×C₅	D₃×#41	1	1	yes	characteristic
586	C₂²×C₅	#1009	1	1	yes	characteristic
587	C₄×C₅	—	2	2	no	—
588	C₄×C₅	—	2	2	no	—
589	C₄×C₅	—	2	2	no	—
590	C₄×C₅	—	4	1	no	—
591	C₄×C₅	—	4	1	no	—
592	C₄×C₅	—	4	1	no	—
593	C₄×C₅	—	6	2	no	—
594	C₄×C₅	—	6	2	no	—
595	C₄×C₅	—	6	2	no	—
596	C₄×C₅	—	6	2	no	—
597	C₄×C₅	—	12	1	no	—
598	C₄×C₅	—	12	1	no	—
599	C₄×C₅	—	12	1	no	—
600	C₂⁴	—	3	1	no	—
601	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
602	C₂×D₄	—	3	4	no	—
603	C₂×D₄	—	6	2	no	—
604	C₂×D₄	—	6	2	no	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	2	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	4	no	—
612	C₂²×C₄	—	3	4	no	—
613	C₂²×C₄	—	3	1	no	—
614	C₂²×C₄	—	3	1	no	—
615	C₂²×C₄	—	3	1	no	—
616	C₂²×C₄	—	4	1	no	—
617	C₂²×C₄	—	6	2	no	—
618	C₂²×C₄	—	6	2	no	—
619	C₂²×C₄	—	12	1	no	—
620	C₂²×C₄	—	12	1	no	—
621	C₂²×C₄	—	12	1	no	—
622	C₂²×C₄	—	12	1	no	—
623	C₂²×C₄	—	12	1	no	—
624	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
625	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
626	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
627	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
628	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
629	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
630	C₄⋊C₄	—	3	4	no	—
631	C₄⋊C₄	—	12	1	no	—
632	C₄⋊C₄	—	12	1	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	3	4	no	—
635	C₂²⋊C₄	—	6	2	no	—
636	C₂²⋊C₄	—	6	2	no	—
637	C₂²⋊C₄	—	6	2	no	—
638	C₂²⋊C₄	—	12	1	no	—
639	C₂²⋊C₄	—	12	1	no	—
640	C₂²⋊C₄	C₄×C₅×D₃	1	4	yes	—
641	C₄²	—	2	2	no	—
642	C₄²	—	3	4	no	—
643	C₄²	—	4	1	no	—
644	C₄²	—	6	2	no	—
645	C₄²	—	12	1	no	—
646	C₃×C₅	#2353	1	1	yes	characteristic, complemented, Hall
647	C₂²×C₃	—	2	2	no	—
648	C₂²×C₃	—	2	2	no	—
649	C₂²×C₃	—	2	2	no	—
650	C₂²×C₃	—	2	2	no	—
651	C₂²×C₃	—	2	2	no	—
652	C₂²×C₃	—	2	2	no	—
653	C₂²×C₃	C₅×#117	1	4	yes	—
654	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
655	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
656	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
657	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
658	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
659	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
660	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
661	C₂×D₃	—	2	2	no	—
662	C₂×D₃	—	2	2	no	—
663	C₂×D₃	—	2	2	no	—
664	C₂×D₃	—	4	1	no	—
665	C₂×D₃	—	4	1	no	—
666	C₂×D₃	—	4	1	no	—
667	C₂×D₃	—	4	1	no	—
668	C₃×C₄	—	2	2	no	—
669	C₃×C₄	—	2	2	no	—
670	C₃×C₄	—	2	2	no	—
671	C₃×C₄	—	4	1	no	—
672	C₃×C₄	—	4	1	no	—
673	C₃×C₄	—	4	1	no	—
674	Dic₃	—	2	2	no	—
675	Dic₃	—	2	2	no	—
676	Dic₃	—	2	2	no	—
677	Dic₃	—	2	2	no	—
678	Dic₃	—	4	1	no	—
679	Dic₃	—	4	1	no	—
680	Dic₃	—	4	1	no	—
681	C₂×C₅	—	2	4	no	—
682	C₂×C₅	—	12	2	no	—
683	C₂×C₅	C₂×#872	1	1	yes	characteristic
684	C₂×C₅	#5495	1	1	yes	characteristic
685	C₂×C₅	#5527	1	1	yes	characteristic
686	C₂×C₅	C₄×#237	1	1	yes	characteristic
687	C₂×C₅	#5540	1	1	yes	characteristic
688	C₂×C₅	#5545	1	1	yes	characteristic
689	C₂×C₅	#5565	1	1	yes	characteristic
690	C₂³	—	2	1	no	—
691	C₂³	—	2	1	no	—
692	C₂³	—	2	1	no	—
693	C₂³	—	2	1	no	—
694	C₂³	—	3	2	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	—	6	1	no	—
701	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
702	C₂³	C₅×#235	1	2	yes	—
703	C₂³	C₅×#235	1	2	yes	—
704	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
705	D₄	—	6	8	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	—	2	1	no	—
721	C₂×C₄	—	3	2	no	—
722	C₂×C₄	—	3	2	no	—
723	C₂×C₄	—	3	2	no	—
724	C₂×C₄	—	3	2	no	—
725	C₂×C₄	—	4	4	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	—	6	1	no	—
743	C₂×C₄	—	12	4	no	—
744	C₂×C₄	—	12	4	no	—
745	C₂×C₄	—	12	4	no	—
746	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
747	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
748	C₂×C₄	C₅×#237	1	2	yes	—
749	C₂×C₃	—	2	4	no	—
750	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
751	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
752	C₂×C₃	C₅×#518	1	1	yes	characteristic
753	C₂×C₃	C₅×#551	1	1	yes	characteristic
754	C₂×C₃	C₅×#551	1	1	yes	characteristic
755	C₂×C₃	C₅×#553	1	1	yes	characteristic
756	C₂×C₃	C₅×#553	1	1	yes	characteristic
757	D₃	—	4	2	no	—
758	C₅	#73462	1	1	yes	characteristic, direct product factor, Sylow
759	C₂²	—	2	2	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	2	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	6	2	no	—
766	C₂²	—	6	2	no	—
767	C₂²	—	6	2	no	—
768	C₂²	—	12	1	no	—
769	C₂²	—	12	1	no	—
770	C₂²	—	12	1	no	—
771	C₂²	—	12	1	no	—
772	C₂²	C₅×#872	1	4	yes	—
773	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
774	C₂²	C₂×C₅×#235	1	1	yes	characteristic
775	C₂²	C₂×C₅×#235	1	1	yes	characteristic
776	C₂²	C₂×C₅×#237	1	1	yes	characteristic
777	C₂²	C₅×#1004	1	1	yes	characteristic
778	C₂²	C₅×D₃×#41	1	1	yes	characteristic
779	C₂²	C₅×#1009	1	1	yes	characteristic
780	C₄	—	2	2	no	—
781	C₄	—	2	2	no	—
782	C₄	—	2	2	no	—
783	C₄	—	4	1	no	—
784	C₄	—	4	1	no	—
785	C₄	—	4	1	no	—
786	C₄	—	6	2	no	—
787	C₄	—	6	2	no	—
788	C₄	—	6	2	no	—
789	C₄	—	6	2	no	—
790	C₄	—	12	1	no	—
791	C₄	—	12	1	no	—
792	C₄	—	12	1	no	—
793	C₃	C₅×#2353	1	1	yes	characteristic, complemented, Sylow
794	C₂	—	2	4	no	—
795	C₂	—	12	2	no	—
796	C₂	C₂×C₅×#872	1	1	yes	characteristic
797	C₂	C₅×#5495	1	1	yes	characteristic
798	C₂	C₅×#5527	1	1	yes	characteristic
799	C₂	C₄×C₅×#237	1	1	yes	characteristic
800	C₂	C₅×#5540	1	1	yes	characteristic
801	C₂	C₅×#5545	1	1	yes	characteristic
802	C₂	C₅×#5565	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×C₄×C₅×C₂²⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×#67	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₄×C₅×C₂²⋊C₄	D₃
hypocenter	C₃	C₅×#2353
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. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
4. C₂×C₅×C₃⋊#95	C₂	semidirect
6. C₅×#4942	C₂	semidirect
7. C₅×Dic₃×C₂²⋊C₄	C₂	semidirect
8. C₅×#4940	C₂	semidirect
9. C₄×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
10. C₅×#4933	C₂	semidirect
11. C₅×#4932	C₂	semidirect
12. C₅×#4669	C₂	semidirect
13. C₅×#4664	C₂	semidirect
14. C₅×#4652	C₂	semidirect
15. C₅×#4651	C₂	semidirect
38. C₅×#67⋊C₄	C₄	semidirect
53. #73462	C₅	direct (N × H)
66. C₄×C₅×C₂²⋊C₄	D₃	semidirect
98. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
108. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
111. C₅×Dic₃⋊C₄	C₂×C₄	semidirect
114. C₄×C₅×Dic₃	C₂×C₄	semidirect
116. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
118. C₂×C₃⋊#95	C₂×C₅	semidirect
120. #4942	C₂×C₅	semidirect
121. Dic₃×C₂²⋊C₄	C₂×C₅	semidirect
122. #4940	C₂×C₅	semidirect
123. C₄×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
124. #4933	C₂×C₅	semidirect
125. #4932	C₂×C₅	semidirect
126. #4669	C₂×C₅	semidirect
127. #4664	C₂×C₅	semidirect
128. #4652	C₂×C₅	semidirect
129. #4651	C₂×C₅	semidirect
247. #67⋊C₄	C₄×C₅	semidirect
320. C₄×C₂²⋊C₄	C₅×D₃	semidirect
386. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
396. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
399. Dic₃⋊C₄	C₂×C₄×C₅	semidirect
402. C₄×Dic₃	C₂×C₄×C₅	semidirect
646. C₃×C₅	#2353	semidirect
758. C₅	#73462	direct (N × H)
793. C₃	C₅×#2353	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#67⋊C₄	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#5213	2
C₂×C₅×C₃⋊#95	2
C₅×#4958	2
C₅×#4942	2
C₅×Dic₃×C₂²⋊C₄	2
C₅×#4940	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₅×#4933	2
C₅×#4932	2
C₅×#4669	2
C₅×#4664	2
C₅×#4652	2
C₅×#4651	2
C₅×#2353	3
#73462	5

Subgroups — C5×#73462 #14327492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73462 #14327492