Subgroups — C₅×#76429 #14323363

Order 1920.

1616 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#937	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×D₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5220	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4990	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4958	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#4957	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4956	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4955	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4945	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4945	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4940	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2321	—	3	1	no	maximal, Hall
17	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
20	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
21	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₅×#217	C₂²	1	1	yes	characteristic
31	C₂×C₅×#217	C₂²	1	1	yes	characteristic
32	C₂×C₅×#217	C₂²	1	1	yes	characteristic
33	C₂×C₅×#217	C₂²	1	1	yes	characteristic, complemented
34	C₅×#937	C₄	1	8	yes	complemented
35	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
47	C₅×#67⋊C₄	—	2	4	no	—
48	C₅×D₃×C₂²⋊C₄	—	2	4	no	—
49	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
50	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
51	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
52	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
53	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
54	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic, complemented
55	#76429	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
56	C₂×C₅×#120	—	3	1	no	—
57	C₂×C₄×C₅×D₄	—	3	1	no	—
58	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
59	C₅×#390	—	3	1	no	—
60	C₅×#390	D₃	1	1	yes	characteristic, complemented
61	C₅×#388	—	3	1	no	—
62	C₅×#388	—	3	1	no	—
63	C₅×#388	—	3	1	no	—
64	C₅×#388	—	3	1	no	—
65	C₅×#386	—	3	1	no	—
66	C₅×#386	—	3	1	no	—
67	C₅×#386	—	3	1	no	—
68	C₅×#385	—	3	1	no	—
69	C₅×#379	—	3	1	no	—
70	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
71	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
72	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
73	C₂³×C₅×D₃	—	2	2	no	—
74	C₂³×C₅×D₃	—	2	2	no	—
75	C₂³×C₅×D₃	—	4	1	no	—
76	C₂³×C₅×D₃	—	4	1	no	—
77	C₂³×C₅×D₃	—	4	1	no	—
78	C₂³×C₅×D₃	—	4	1	no	—
79	C₂³×C₅×D₃	C₂×C₄	1	4	yes	complemented
80	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
81	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×D₄	—	4	1	no	—
83	C₂×C₃×C₅×D₄	—	4	1	no	—
84	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
85	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
86	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
87	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
89	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₂×C₅×#67	—	2	2	no	—
91	C₂×C₅×#67	—	2	2	no	—
92	C₂×C₅×#67	—	4	1	no	—
93	C₂×C₅×#67	—	4	1	no	—
94	C₂×C₅×#67	C₂×C₄	1	4	yes	—
95	C₂×C₅×#67	C₂×C₄	1	4	yes	complemented
96	C₂²×C₅×Dic₃	—	2	2	no	—
97	C₂²×C₅×Dic₃	—	4	1	no	—
98	C₂²×C₅×Dic₃	—	4	1	no	—
99	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
100	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
101	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
102	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
103	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
104	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
105	C₂×C₄×C₅×D₃	—	2	2	no	—
106	C₂×C₄×C₅×D₃	—	4	1	no	—
107	C₂×C₄×C₅×D₃	—	4	1	no	—
108	C₂×C₄×C₅×D₃	—	4	1	no	—
109	C₂×C₄×C₅×D₃	—	4	1	no	—
110	C₂×C₄×C₅×D₃	D₄	1	4	yes	complemented
111	C₃×C₅×C₄⋊C₄	—	4	1	no	—
112	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
113	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
114	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
115	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
116	C₃×C₄²×C₅	—	4	1	no	—
117	C₅×#217	—	2	2	no	—
118	C₅×#217	—	4	1	no	—
119	C₅×#217	—	4	1	no	—
120	C₅×#217	C₂×C₄	1	4	yes	complemented
121	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
122	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
123	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
124	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
125	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
126	C₅×(C₂×D₃)⋊C₄	—	4	1	no	—
127	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	complemented
128	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	complemented
129	C₅×Dic₃⋊C₄	—	2	2	no	—
130	C₅×Dic₃⋊C₄	—	4	1	no	—
131	C₄×C₅×Dic₃	—	2	2	no	—
132	C₄×C₅×Dic₃	—	4	1	no	—
133	C₂×#937	C₂×C₅	1	1	yes	characteristic
134	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
135	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
137	#5220	C₂×C₅	1	1	yes	characteristic, complemented
138	#4990	C₂×C₅	1	1	yes	characteristic, complemented
139	#4989	C₂×C₅	1	1	yes	characteristic, complemented
140	#4958	C₂×C₅	1	1	yes	characteristic, complemented
141	#4957	C₂×C₅	1	1	yes	characteristic, complemented
142	#4956	C₂×C₅	1	1	yes	characteristic, complemented
143	#4955	C₂×C₅	1	1	yes	characteristic, complemented
144	#4945	C₂×C₅	1	1	yes	characteristic, complemented
145	#4945	C₂×C₅	1	1	yes	characteristic, complemented
146	#4940	C₂×C₅	1	1	yes	characteristic, complemented
147	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂⁵×C₅	—	3	1	no	—
149	C₂²×C₅×D₄	—	3	1	no	—
150	C₂²×C₅×D₄	—	3	1	no	—
151	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
152	C₂³×C₄×C₅	—	3	1	no	—
153	C₂³×C₄×C₅	—	3	1	no	—
154	C₂³×C₄×C₅	—	3	1	no	—
155	C₅×#120	—	3	8	no	—
156	C₄×C₅×D₄	—	6	4	no	—
157	C₂×C₅×C₄⋊C₄	—	3	1	no	—
158	C₂×C₅×C₄⋊C₄	—	3	1	no	—
159	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
160	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
161	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
162	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
163	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
164	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
165	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
166	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
167	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
168	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
169	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
170	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
171	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
172	C₂×C₅×C₂²⋊C₄	—	6	4	no	—
173	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
174	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
175	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
176	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
177	C₂×C₄²×C₅	—	3	1	no	—
178	C₂×C₄²×C₅	—	3	1	no	—
179	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic, complemented
180	C₅×#95	—	3	1	no	—
181	C₅×#95	—	3	1	no	—
182	C₅×#95	—	3	1	no	—
183	C₅×#95	—	3	1	no	—
184	C₅×#95	—	3	1	no	—
185	C₅×#95	—	3	1	no	—
186	#2321	—	3	1	no	Sylow
187	C₂³×C₃×C₅	—	2	1	no	—
188	C₂³×C₃×C₅	—	2	1	no	—
189	C₂³×C₃×C₅	—	2	1	no	—
190	C₂³×C₃×C₅	—	2	1	no	—
191	C₂³×C₃×C₅	—	2	1	no	—
192	C₂³×C₃×C₅	—	2	1	no	—
193	C₂³×C₃×C₅	—	2	1	no	—
194	C₂³×C₃×C₅	—	2	1	no	—
195	C₂³×C₃×C₅	—	2	1	no	—
196	C₂³×C₃×C₅	—	2	1	no	—
197	C₂³×C₃×C₅	—	2	1	no	—
198	C₂³×C₃×C₅	—	2	1	no	—
199	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
200	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
201	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
202	C₂²×C₅×D₃	—	2	1	no	—
203	C₂²×C₅×D₃	—	2	1	no	—
204	C₂²×C₅×D₃	—	2	1	no	—
205	C₂²×C₅×D₃	—	2	1	no	—
206	C₂²×C₅×D₃	—	2	1	no	—
207	C₂²×C₅×D₃	—	2	1	no	—
208	C₂²×C₅×D₃	—	2	1	no	—
209	C₂²×C₅×D₃	—	2	1	no	—
210	C₂²×C₅×D₃	—	2	1	no	—
211	C₂²×C₅×D₃	—	2	1	no	—
212	C₂²×C₅×D₃	—	2	8	no	—
213	C₂²×C₅×D₃	—	4	4	no	—
214	C₂²×C₅×D₃	—	4	4	no	—
215	C₂²×C₅×D₃	—	4	4	no	—
216	C₂²×C₅×D₃	—	4	4	no	—
217	C₂²×C₅×D₃	—	4	4	no	—
218	C₂²×C₅×D₃	—	4	4	no	—
219	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
220	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
221	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
222	C₂²×C₅×D₃	#41	1	2	yes	—
223	C₃×C₅×D₄	—	4	4	no	—
224	C₂×C₃×C₄×C₅	—	2	1	no	—
225	C₂×C₃×C₄×C₅	—	2	1	no	—
226	C₂×C₃×C₄×C₅	—	2	1	no	—
227	C₂×C₃×C₄×C₅	—	2	1	no	—
228	C₂×C₃×C₄×C₅	—	2	1	no	—
229	C₂×C₃×C₄×C₅	—	2	1	no	—
230	C₂×C₃×C₄×C₅	—	2	1	no	—
231	C₂×C₃×C₄×C₅	—	2	1	no	—
232	C₂×C₃×C₄×C₅	—	2	1	no	—
233	C₂×C₃×C₄×C₅	—	2	1	no	—
234	C₂×C₃×C₄×C₅	—	2	1	no	—
235	C₂×C₃×C₄×C₅	—	2	1	no	—
236	C₂×C₃×C₄×C₅	—	2	1	no	—
237	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
238	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
239	C₅×#67	—	2	8	no	—
240	C₅×#67	—	4	4	no	—
241	C₂×C₅×Dic₃	—	2	1	no	—
242	C₂×C₅×Dic₃	—	2	1	no	—
243	C₂×C₅×Dic₃	—	2	1	no	—
244	C₂×C₅×Dic₃	—	2	1	no	—
245	C₂×C₅×Dic₃	—	2	1	no	—
246	C₂×C₅×Dic₃	—	2	1	no	—
247	C₂×C₅×Dic₃	—	2	1	no	—
248	C₂×C₅×Dic₃	—	2	1	no	—
249	C₂×C₅×Dic₃	—	2	1	no	—
250	C₂×C₅×Dic₃	—	2	1	no	—
251	C₂×C₅×Dic₃	—	2	1	no	—
252	C₂×C₅×Dic₃	—	2	1	no	—
253	C₂×C₅×Dic₃	—	2	1	no	—
254	C₂×C₅×Dic₃	—	2	1	no	—
255	C₂×C₅×Dic₃	—	2	1	no	—
256	C₂×C₅×Dic₃	—	4	4	no	—
257	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
258	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
259	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
260	C₄×C₅×D₃	—	4	4	no	—
261	C₄×C₅×D₃	—	4	4	no	—
262	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
263	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
264	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
265	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
266	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
267	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
268	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
269	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
270	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
271	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
272	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
273	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
274	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
275	C₂×#217	C₂²×C₅	1	1	yes	characteristic
276	C₂×#217	C₂²×C₅	1	1	yes	characteristic
277	C₂×#217	C₂²×C₅	1	1	yes	characteristic
278	C₂×#217	C₂²×C₅	1	1	yes	characteristic, complemented
279	#937	C₄×C₅	1	8	yes	complemented
280	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
281	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
282	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
283	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
284	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
285	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
286	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
287	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
288	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
289	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
290	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
291	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
292	#67⋊C₄	—	2	4	no	—
293	D₃×C₂²⋊C₄	—	2	4	no	—
294	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
295	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
296	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
297	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
298	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
299	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic, complemented
300	C₂⁴×C₅	—	3	1	no	—
301	C₂⁴×C₅	—	3	1	no	—
302	C₂⁴×C₅	—	3	4	no	—
303	C₂⁴×C₅	—	6	2	no	—
304	C₂⁴×C₅	—	6	2	no	—
305	C₂⁴×C₅	—	12	1	no	—
306	C₂⁴×C₅	—	12	1	no	—
307	C₂⁴×C₅	—	12	1	no	—
308	C₂⁴×C₅	—	12	1	no	—
309	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
310	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
311	C₂×C₅×D₄	—	3	4	no	—
312	C₂×C₅×D₄	—	3	4	no	—
313	C₂×C₅×D₄	—	4	1	no	—
314	C₂×C₅×D₄	—	4	1	no	—
315	C₂×C₅×D₄	—	6	2	no	—
316	C₂×C₅×D₄	—	6	2	no	—
317	C₂×C₅×D₄	—	12	1	no	—
318	C₂×C₅×D₄	—	12	1	no	—
319	C₂×C₅×D₄	C₄×D₃	1	4	yes	complemented
320	C₂²×C₄×C₅	—	3	1	no	—
321	C₂²×C₄×C₅	—	3	1	no	—
322	C₂²×C₄×C₅	—	3	1	no	—
323	C₂²×C₄×C₅	—	3	4	no	—
324	C₂²×C₄×C₅	—	3	1	no	—
325	C₂²×C₄×C₅	—	3	1	no	—
326	C₂²×C₄×C₅	—	3	1	no	—
327	C₂²×C₄×C₅	—	6	2	no	—
328	C₂²×C₄×C₅	—	6	2	no	—
329	C₂²×C₄×C₅	—	12	1	no	—
330	C₂²×C₄×C₅	—	12	1	no	—
331	C₂²×C₄×C₅	—	12	1	no	—
332	C₂²×C₄×C₅	—	12	1	no	—
333	C₂²×C₄×C₅	—	12	1	no	—
334	C₂²×C₄×C₅	—	12	1	no	—
335	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
336	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
337	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
338	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
339	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
340	C₅×C₄⋊C₄	—	4	1	no	—
341	C₅×C₄⋊C₄	—	6	2	no	—
342	C₅×C₄⋊C₄	—	12	1	no	—
343	C₅×C₂²⋊C₄	—	2	2	no	—
344	C₅×C₂²⋊C₄	—	2	2	no	—
345	C₅×C₂²⋊C₄	—	3	4	no	—
346	C₅×C₂²⋊C₄	—	3	4	no	—
347	C₅×C₂²⋊C₄	—	3	4	no	—
348	C₅×C₂²⋊C₄	—	4	1	no	—
349	C₅×C₂²⋊C₄	—	4	1	no	—
350	C₅×C₂²⋊C₄	—	6	2	no	—
351	C₅×C₂²⋊C₄	—	6	2	no	—
352	C₅×C₂²⋊C₄	—	6	2	no	—
353	C₅×C₂²⋊C₄	—	6	2	no	—
354	C₅×C₂²⋊C₄	—	6	2	no	—
355	C₅×C₂²⋊C₄	—	12	1	no	—
356	C₅×C₂²⋊C₄	—	12	1	no	—
357	C₅×C₂²⋊C₄	—	12	1	no	—
358	C₅×C₂²⋊C₄	—	12	1	no	—
359	C₄²×C₅	—	4	1	no	—
360	C₄²×C₅	—	6	2	no	—
361	C₄²×C₅	—	12	1	no	—
362	C₂×#120	—	3	1	no	—
363	C₂×C₄×D₄	—	3	1	no	—
364	C₂²×C₂²⋊C₄	—	3	1	no	—
365	#390	—	3	1	no	—
366	#390	C₅×D₃	1	1	yes	characteristic, complemented
367	#388	—	3	1	no	—
368	#388	—	3	1	no	—
369	#388	—	3	1	no	—
370	#388	—	3	1	no	—
371	#386	—	3	1	no	—
372	#386	—	3	1	no	—
373	#386	—	3	1	no	—
374	#385	—	3	1	no	—
375	#379	—	3	1	no	—
376	C₄×C₂²⋊C₄	—	3	1	no	—
377	C₂²×C₃×C₅	—	2	2	no	—
378	C₂²×C₃×C₅	—	2	2	no	—
379	C₂²×C₃×C₅	—	2	2	no	—
380	C₂²×C₃×C₅	—	2	2	no	—
381	C₂²×C₃×C₅	—	2	2	no	—
382	C₂²×C₃×C₅	—	2	2	no	—
383	C₂²×C₃×C₅	—	4	1	no	—
384	C₂²×C₃×C₅	—	4	1	no	—
385	C₂²×C₃×C₅	—	4	1	no	—
386	C₂²×C₃×C₅	—	4	1	no	—
387	C₂²×C₃×C₅	—	4	1	no	—
388	C₂²×C₃×C₅	—	4	1	no	—
389	C₂²×C₃×C₅	—	4	1	no	—
390	C₂²×C₃×C₅	—	4	1	no	—
391	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
392	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
393	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
394	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
395	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
396	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
397	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
398	C₂×C₅×D₃	—	2	2	no	—
399	C₂×C₅×D₃	—	2	2	no	—
400	C₂×C₅×D₃	—	2	2	no	—
401	C₂×C₅×D₃	—	2	2	no	—
402	C₂×C₅×D₃	—	2	2	no	—
403	C₂×C₅×D₃	—	2	2	no	—
404	C₂×C₅×D₃	—	2	2	no	—
405	C₂×C₅×D₃	—	2	2	no	—
406	C₂×C₅×D₃	—	2	2	no	—
407	C₂×C₅×D₃	—	4	16	no	—
408	C₂×C₅×D₃	—	4	1	no	—
409	C₂×C₅×D₃	—	4	1	no	—
410	C₂×C₅×D₃	—	4	1	no	—
411	C₂×C₅×D₃	—	4	1	no	—
412	C₂×C₅×D₃	C₄×D₄	1	4	yes	—
413	C₃×C₄×C₅	—	2	2	no	—
414	C₃×C₄×C₅	—	2	2	no	—
415	C₃×C₄×C₅	—	4	1	no	—
416	C₃×C₄×C₅	—	4	1	no	—
417	C₃×C₄×C₅	—	4	1	no	—
418	C₅×Dic₃	—	2	2	no	—
419	C₅×Dic₃	—	2	2	no	—
420	C₅×Dic₃	—	2	2	no	—
421	C₅×Dic₃	—	4	1	no	—
422	C₅×Dic₃	—	4	1	no	—
423	C₅×Dic₃	—	4	1	no	—
424	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
425	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
426	C₂³×D₃	—	2	2	no	—
427	C₂³×D₃	—	2	2	no	—
428	C₂³×D₃	—	4	1	no	—
429	C₂³×D₃	—	4	1	no	—
430	C₂³×D₃	—	4	1	no	—
431	C₂³×D₃	—	4	1	no	—
432	C₂³×D₃	C₂×C₄×C₅	1	4	yes	complemented
433	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
434	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
435	C₂×C₃×D₄	—	4	1	no	—
436	C₂×C₃×D₄	—	4	1	no	—
437	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
438	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
439	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
440	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
441	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
442	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
443	C₂×#67	—	2	2	no	—
444	C₂×#67	—	2	2	no	—
445	C₂×#67	—	4	1	no	—
446	C₂×#67	—	4	1	no	—
447	C₂×#67	C₂×C₄×C₅	1	4	yes	—
448	C₂×#67	C₂×C₄×C₅	1	4	yes	complemented
449	C₂²×Dic₃	—	2	2	no	—
450	C₂²×Dic₃	—	4	1	no	—
451	C₂²×Dic₃	—	4	1	no	—
452	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
453	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
454	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
455	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
456	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
457	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
458	C₂×C₄×D₃	—	2	2	no	—
459	C₂×C₄×D₃	—	4	1	no	—
460	C₂×C₄×D₃	—	4	1	no	—
461	C₂×C₄×D₃	—	4	1	no	—
462	C₂×C₄×D₃	—	4	1	no	—
463	C₂×C₄×D₃	C₅×D₄	1	4	yes	complemented
464	C₃×C₄⋊C₄	—	4	1	no	—
465	C₃×C₂²⋊C₄	—	2	2	no	—
466	C₃×C₂²⋊C₄	—	2	2	no	—
467	C₃×C₂²⋊C₄	—	4	1	no	—
468	C₃×C₂²⋊C₄	—	4	1	no	—
469	C₃×C₄²	—	4	1	no	—
470	#217	—	2	2	no	—
471	#217	—	4	1	no	—
472	#217	—	4	1	no	—
473	#217	C₂×C₄×C₅	1	4	yes	complemented
474	(C₂×D₃)⋊C₄	—	2	2	no	—
475	(C₂×D₃)⋊C₄	—	2	2	no	—
476	(C₂×D₃)⋊C₄	—	2	2	no	—
477	(C₂×D₃)⋊C₄	—	2	2	no	—
478	(C₂×D₃)⋊C₄	—	4	1	no	—
479	(C₂×D₃)⋊C₄	—	4	1	no	—
480	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
481	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
482	Dic₃⋊C₄	—	2	2	no	—
483	Dic₃⋊C₄	—	4	1	no	—
484	C₄×Dic₃	—	2	2	no	—
485	C₄×Dic₃	—	4	1	no	—
486	C₂³×C₅	—	2	1	no	—
487	C₂³×C₅	—	2	1	no	—
488	C₂³×C₅	—	2	1	no	—
489	C₂³×C₅	—	2	1	no	—
490	C₂³×C₅	—	2	1	no	—
491	C₂³×C₅	—	2	1	no	—
492	C₂³×C₅	—	2	1	no	—
493	C₂³×C₅	—	2	1	no	—
494	C₂³×C₅	—	2	1	no	—
495	C₂³×C₅	—	2	1	no	—
496	C₂³×C₅	—	2	1	no	—
497	C₂³×C₅	—	2	1	no	—
498	C₂³×C₅	—	3	2	no	—
499	C₂³×C₅	—	3	2	no	—
500	C₂³×C₅	—	3	2	no	—
501	C₂³×C₅	—	3	2	no	—
502	C₂³×C₅	—	6	8	no	—
503	C₂³×C₅	—	6	1	no	—
504	C₂³×C₅	—	6	1	no	—
505	C₂³×C₅	—	6	1	no	—
506	C₂³×C₅	—	6	1	no	—
507	C₂³×C₅	—	6	1	no	—
508	C₂³×C₅	—	6	1	no	—
509	C₂³×C₅	—	6	1	no	—
510	C₂³×C₅	—	6	1	no	—
511	C₂³×C₅	—	6	1	no	—
512	C₂³×C₅	—	6	1	no	—
513	C₂³×C₅	—	12	4	no	—
514	C₂³×C₅	—	12	4	no	—
515	C₂³×C₅	—	12	4	no	—
516	C₂³×C₅	—	12	4	no	—
517	C₂³×C₅	—	12	4	no	—
518	C₂³×C₅	—	12	4	no	—
519	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
520	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
521	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
522	C₅×D₄	—	4	4	no	—
523	C₅×D₄	—	6	8	no	—
524	C₅×D₄	—	12	4	no	—
525	C₂×C₄×C₅	—	2	1	no	—
526	C₂×C₄×C₅	—	2	1	no	—
527	C₂×C₄×C₅	—	2	1	no	—
528	C₂×C₄×C₅	—	2	1	no	—
529	C₂×C₄×C₅	—	2	1	no	—
530	C₂×C₄×C₅	—	2	1	no	—
531	C₂×C₄×C₅	—	2	1	no	—
532	C₂×C₄×C₅	—	2	1	no	—
533	C₂×C₄×C₅	—	2	1	no	—
534	C₂×C₄×C₅	—	2	1	no	—
535	C₂×C₄×C₅	—	2	1	no	—
536	C₂×C₄×C₅	—	2	1	no	—
537	C₂×C₄×C₅	—	2	1	no	—
538	C₂×C₄×C₅	—	3	2	no	—
539	C₂×C₄×C₅	—	3	2	no	—
540	C₂×C₄×C₅	—	3	2	no	—
541	C₂×C₄×C₅	—	6	1	no	—
542	C₂×C₄×C₅	—	6	1	no	—
543	C₂×C₄×C₅	—	6	1	no	—
544	C₂×C₄×C₅	—	6	1	no	—
545	C₂×C₄×C₅	—	6	1	no	—
546	C₂×C₄×C₅	—	6	1	no	—
547	C₂×C₄×C₅	—	6	1	no	—
548	C₂×C₄×C₅	—	6	1	no	—
549	C₂×C₄×C₅	—	6	1	no	—
550	C₂×C₄×C₅	—	6	1	no	—
551	C₂×C₄×C₅	—	6	1	no	—
552	C₂×C₄×C₅	—	6	1	no	—
553	C₂×C₄×C₅	—	6	1	no	—
554	C₂×C₄×C₅	—	6	1	no	—
555	C₂×C₄×C₅	—	6	1	no	—
556	C₂×C₄×C₅	—	12	4	no	—
557	C₂×C₄×C₅	—	12	4	no	—
558	C₂×C₄×C₅	—	12	4	no	—
559	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
560	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
561	C₂⁵	—	3	1	no	—
562	C₂²×D₄	—	3	1	no	—
563	C₂²×D₄	—	3	1	no	—
564	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
565	C₂³×C₄	—	3	1	no	—
566	C₂³×C₄	—	3	1	no	—
567	C₂³×C₄	—	3	1	no	—
568	#120	—	3	8	no	—
569	C₄×D₄	—	6	4	no	—
570	C₂×C₄⋊C₄	—	3	1	no	—
571	C₂×C₄⋊C₄	—	3	1	no	—
572	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
573	C₂×C₂²⋊C₄	—	3	1	no	—
574	C₂×C₂²⋊C₄	—	3	1	no	—
575	C₂×C₂²⋊C₄	—	3	1	no	—
576	C₂×C₂²⋊C₄	—	3	1	no	—
577	C₂×C₂²⋊C₄	—	3	1	no	—
578	C₂×C₂²⋊C₄	—	3	1	no	—
579	C₂×C₂²⋊C₄	—	3	1	no	—
580	C₂×C₂²⋊C₄	—	3	1	no	—
581	C₂×C₂²⋊C₄	—	3	1	no	—
582	C₂×C₂²⋊C₄	—	3	1	no	—
583	C₂×C₂²⋊C₄	—	3	1	no	—
584	C₂×C₂²⋊C₄	—	3	1	no	—
585	C₂×C₂²⋊C₄	—	6	4	no	—
586	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
587	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
588	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
589	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
590	C₂×C₄²	—	3	1	no	—
591	C₂×C₄²	—	3	1	no	—
592	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic, complemented
593	#95	—	3	1	no	—
594	#95	—	3	1	no	—
595	#95	—	3	1	no	—
596	#95	—	3	1	no	—
597	#95	—	3	1	no	—
598	#95	—	3	1	no	—
599	C₂×C₃×C₅	—	4	2	no	—
600	C₂×C₃×C₅	—	4	2	no	—
601	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
602	C₂×C₃×C₅	#518	1	1	yes	characteristic
603	C₂×C₃×C₅	#518	1	1	yes	characteristic
604	C₂×C₃×C₅	#534	1	1	yes	characteristic
605	C₂×C₃×C₅	#535	1	1	yes	characteristic
606	C₂×C₃×C₅	#538	1	1	yes	characteristic
607	C₂×C₃×C₅	#538	1	1	yes	characteristic
608	C₅×D₃	—	2	4	no	—
609	C₅×D₃	—	4	2	no	—
610	C₂³×C₃	—	2	1	no	—
611	C₂³×C₃	—	2	1	no	—
612	C₂³×C₃	—	2	1	no	—
613	C₂³×C₃	—	2	1	no	—
614	C₂³×C₃	—	2	1	no	—
615	C₂³×C₃	—	2	1	no	—
616	C₂³×C₃	—	2	1	no	—
617	C₂³×C₃	—	2	1	no	—
618	C₂³×C₃	—	2	1	no	—
619	C₂³×C₃	—	2	1	no	—
620	C₂³×C₃	—	2	1	no	—
621	C₂³×C₃	—	2	1	no	—
622	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
623	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
624	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
625	C₂²×D₃	—	2	1	no	—
626	C₂²×D₃	—	2	1	no	—
627	C₂²×D₃	—	2	1	no	—
628	C₂²×D₃	—	2	1	no	—
629	C₂²×D₃	—	2	1	no	—
630	C₂²×D₃	—	2	1	no	—
631	C₂²×D₃	—	2	1	no	—
632	C₂²×D₃	—	2	1	no	—
633	C₂²×D₃	—	2	1	no	—
634	C₂²×D₃	—	2	1	no	—
635	C₂²×D₃	—	2	8	no	—
636	C₂²×D₃	—	4	4	no	—
637	C₂²×D₃	—	4	4	no	—
638	C₂²×D₃	—	4	4	no	—
639	C₂²×D₃	—	4	4	no	—
640	C₂²×D₃	—	4	4	no	—
641	C₂²×D₃	—	4	4	no	—
642	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
643	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
644	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
645	C₂²×D₃	C₅×#41	1	2	yes	—
646	C₃×D₄	—	4	4	no	—
647	C₂×C₃×C₄	—	2	1	no	—
648	C₂×C₃×C₄	—	2	1	no	—
649	C₂×C₃×C₄	—	2	1	no	—
650	C₂×C₃×C₄	—	2	1	no	—
651	C₂×C₃×C₄	—	2	1	no	—
652	C₂×C₃×C₄	—	2	1	no	—
653	C₂×C₃×C₄	—	2	1	no	—
654	C₂×C₃×C₄	—	2	1	no	—
655	C₂×C₃×C₄	—	2	1	no	—
656	C₂×C₃×C₄	—	2	1	no	—
657	C₂×C₃×C₄	—	2	1	no	—
658	C₂×C₃×C₄	—	2	1	no	—
659	C₂×C₃×C₄	—	2	1	no	—
660	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
661	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
662	#67	—	2	8	no	—
663	#67	—	4	4	no	—
664	C₂×Dic₃	—	2	1	no	—
665	C₂×Dic₃	—	2	1	no	—
666	C₂×Dic₃	—	2	1	no	—
667	C₂×Dic₃	—	2	1	no	—
668	C₂×Dic₃	—	2	1	no	—
669	C₂×Dic₃	—	2	1	no	—
670	C₂×Dic₃	—	2	1	no	—
671	C₂×Dic₃	—	2	1	no	—
672	C₂×Dic₃	—	2	1	no	—
673	C₂×Dic₃	—	2	1	no	—
674	C₂×Dic₃	—	2	1	no	—
675	C₂×Dic₃	—	2	1	no	—
676	C₂×Dic₃	—	2	1	no	—
677	C₂×Dic₃	—	2	1	no	—
678	C₂×Dic₃	—	2	1	no	—
679	C₂×Dic₃	—	4	4	no	—
680	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
681	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
682	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
683	C₄×D₃	—	4	4	no	—
684	C₄×D₃	—	4	4	no	—
685	C₂²×C₅	—	2	2	no	—
686	C₂²×C₅	—	2	2	no	—
687	C₂²×C₅	—	2	2	no	—
688	C₂²×C₅	—	2	2	no	—
689	C₂²×C₅	—	2	2	no	—
690	C₂²×C₅	—	2	2	no	—
691	C₂²×C₅	—	3	4	no	—
692	C₂²×C₅	—	4	1	no	—
693	C₂²×C₅	—	4	1	no	—
694	C₂²×C₅	—	4	1	no	—
695	C₂²×C₅	—	4	1	no	—
696	C₂²×C₅	—	4	1	no	—
697	C₂²×C₅	—	4	1	no	—
698	C₂²×C₅	—	4	1	no	—
699	C₂²×C₅	—	4	1	no	—
700	C₂²×C₅	—	6	2	no	—
701	C₂²×C₅	—	6	2	no	—
702	C₂²×C₅	—	6	2	no	—
703	C₂²×C₅	—	6	2	no	—
704	C₂²×C₅	—	6	2	no	—
705	C₂²×C₅	—	6	2	no	—
706	C₂²×C₅	—	6	2	no	—
707	C₂²×C₅	—	6	2	no	—
708	C₂²×C₅	—	6	2	no	—
709	C₂²×C₅	—	12	16	no	—
710	C₂²×C₅	—	12	1	no	—
711	C₂²×C₅	—	12	1	no	—
712	C₂²×C₅	—	12	1	no	—
713	C₂²×C₅	—	12	1	no	—
714	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
715	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
716	C₂²×C₅	#1004	1	1	yes	characteristic
717	C₂²×C₅	#1004	1	1	yes	characteristic
718	C₂²×C₅	#1004	1	1	yes	characteristic
719	C₂²×C₅	D₃×#41	1	1	yes	characteristic
720	C₂²×C₅	#1009	1	1	yes	characteristic
721	C₄×C₅	—	2	2	no	—
722	C₄×C₅	—	2	2	no	—
723	C₄×C₅	—	4	1	no	—
724	C₄×C₅	—	4	1	no	—
725	C₄×C₅	—	4	1	no	—
726	C₄×C₅	—	6	2	no	—
727	C₄×C₅	—	6	2	no	—
728	C₄×C₅	—	6	2	no	—
729	C₄×C₅	—	12	1	no	—
730	C₄×C₅	—	12	1	no	—
731	C₄×C₅	—	12	1	no	—
732	C₂⁴	—	3	1	no	—
733	C₂⁴	—	3	1	no	—
734	C₂⁴	—	3	4	no	—
735	C₂⁴	—	6	2	no	—
736	C₂⁴	—	6	2	no	—
737	C₂⁴	—	12	1	no	—
738	C₂⁴	—	12	1	no	—
739	C₂⁴	—	12	1	no	—
740	C₂⁴	—	12	1	no	—
741	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
742	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
743	C₂×D₄	—	3	4	no	—
744	C₂×D₄	—	3	4	no	—
745	C₂×D₄	—	4	1	no	—
746	C₂×D₄	—	4	1	no	—
747	C₂×D₄	—	6	2	no	—
748	C₂×D₄	—	6	2	no	—
749	C₂×D₄	—	12	1	no	—
750	C₂×D₄	—	12	1	no	—
751	C₂×D₄	C₄×C₅×D₃	1	4	yes	complemented
752	C₂²×C₄	—	3	1	no	—
753	C₂²×C₄	—	3	1	no	—
754	C₂²×C₄	—	3	1	no	—
755	C₂²×C₄	—	3	4	no	—
756	C₂²×C₄	—	3	1	no	—
757	C₂²×C₄	—	3	1	no	—
758	C₂²×C₄	—	3	1	no	—
759	C₂²×C₄	—	6	2	no	—
760	C₂²×C₄	—	6	2	no	—
761	C₂²×C₄	—	12	1	no	—
762	C₂²×C₄	—	12	1	no	—
763	C₂²×C₄	—	12	1	no	—
764	C₂²×C₄	—	12	1	no	—
765	C₂²×C₄	—	12	1	no	—
766	C₂²×C₄	—	12	1	no	—
767	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
768	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
769	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
770	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
771	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
772	C₄⋊C₄	—	4	1	no	—
773	C₄⋊C₄	—	6	2	no	—
774	C₄⋊C₄	—	12	1	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	2	no	—
777	C₂²⋊C₄	—	3	4	no	—
778	C₂²⋊C₄	—	3	4	no	—
779	C₂²⋊C₄	—	3	4	no	—
780	C₂²⋊C₄	—	4	1	no	—
781	C₂²⋊C₄	—	4	1	no	—
782	C₂²⋊C₄	—	6	2	no	—
783	C₂²⋊C₄	—	6	2	no	—
784	C₂²⋊C₄	—	6	2	no	—
785	C₂²⋊C₄	—	6	2	no	—
786	C₂²⋊C₄	—	6	2	no	—
787	C₂²⋊C₄	—	12	1	no	—
788	C₂²⋊C₄	—	12	1	no	—
789	C₂²⋊C₄	—	12	1	no	—
790	C₂²⋊C₄	—	12	1	no	—
791	C₄²	—	4	1	no	—
792	C₄²	—	6	2	no	—
793	C₄²	—	12	1	no	—
794	C₃×C₅	#2321	1	1	yes	characteristic, complemented, Hall
795	C₂²×C₃	—	2	2	no	—
796	C₂²×C₃	—	2	2	no	—
797	C₂²×C₃	—	2	2	no	—
798	C₂²×C₃	—	2	2	no	—
799	C₂²×C₃	—	2	2	no	—
800	C₂²×C₃	—	2	2	no	—
801	C₂²×C₃	—	4	1	no	—
802	C₂²×C₃	—	4	1	no	—
803	C₂²×C₃	—	4	1	no	—
804	C₂²×C₃	—	4	1	no	—
805	C₂²×C₃	—	4	1	no	—
806	C₂²×C₃	—	4	1	no	—
807	C₂²×C₃	—	4	1	no	—
808	C₂²×C₃	—	4	1	no	—
809	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
810	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
811	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
812	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
813	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
814	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
815	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
816	C₂×D₃	—	2	2	no	—
817	C₂×D₃	—	2	2	no	—
818	C₂×D₃	—	2	2	no	—
819	C₂×D₃	—	2	2	no	—
820	C₂×D₃	—	2	2	no	—
821	C₂×D₃	—	2	2	no	—
822	C₂×D₃	—	2	2	no	—
823	C₂×D₃	—	2	2	no	—
824	C₂×D₃	—	2	2	no	—
825	C₂×D₃	—	4	16	no	—
826	C₂×D₃	—	4	1	no	—
827	C₂×D₃	—	4	1	no	—
828	C₂×D₃	—	4	1	no	—
829	C₂×D₃	—	4	1	no	—
830	C₂×D₃	C₄×C₅×D₄	1	4	yes	—
831	C₃×C₄	—	2	2	no	—
832	C₃×C₄	—	2	2	no	—
833	C₃×C₄	—	4	1	no	—
834	C₃×C₄	—	4	1	no	—
835	C₃×C₄	—	4	1	no	—
836	Dic₃	—	2	2	no	—
837	Dic₃	—	2	2	no	—
838	Dic₃	—	2	2	no	—
839	Dic₃	—	4	1	no	—
840	Dic₃	—	4	1	no	—
841	Dic₃	—	4	1	no	—
842	C₂×C₅	—	4	2	no	—
843	C₂×C₅	—	4	2	no	—
844	C₂×C₅	—	6	4	no	—
845	C₂×C₅	—	12	2	no	—
846	C₂×C₅	#5486	1	1	yes	characteristic
847	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
848	C₂×C₅	#5545	1	1	yes	characteristic
849	C₂×C₅	#5605	1	1	yes	characteristic
850	C₂×C₅	#5613	1	1	yes	characteristic
851	C₂×C₅	#5678	1	1	yes	characteristic
852	C₂×C₅	#5715	1	1	yes	characteristic
853	C₂³	—	2	1	no	—
854	C₂³	—	2	1	no	—
855	C₂³	—	2	1	no	—
856	C₂³	—	2	1	no	—
857	C₂³	—	2	1	no	—
858	C₂³	—	2	1	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	1	no	—
863	C₂³	—	2	1	no	—
864	C₂³	—	2	1	no	—
865	C₂³	—	3	2	no	—
866	C₂³	—	3	2	no	—
867	C₂³	—	3	2	no	—
868	C₂³	—	3	2	no	—
869	C₂³	—	6	8	no	—
870	C₂³	—	6	1	no	—
871	C₂³	—	6	1	no	—
872	C₂³	—	6	1	no	—
873	C₂³	—	6	1	no	—
874	C₂³	—	6	1	no	—
875	C₂³	—	6	1	no	—
876	C₂³	—	6	1	no	—
877	C₂³	—	6	1	no	—
878	C₂³	—	6	1	no	—
879	C₂³	—	6	1	no	—
880	C₂³	—	12	4	no	—
881	C₂³	—	12	4	no	—
882	C₂³	—	12	4	no	—
883	C₂³	—	12	4	no	—
884	C₂³	—	12	4	no	—
885	C₂³	—	12	4	no	—
886	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
887	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
888	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
889	D₄	—	4	4	no	—
890	D₄	—	6	8	no	—
891	D₄	—	12	4	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	1	no	—
905	C₂×C₄	—	3	2	no	—
906	C₂×C₄	—	3	2	no	—
907	C₂×C₄	—	3	2	no	—
908	C₂×C₄	—	6	1	no	—
909	C₂×C₄	—	6	1	no	—
910	C₂×C₄	—	6	1	no	—
911	C₂×C₄	—	6	1	no	—
912	C₂×C₄	—	6	1	no	—
913	C₂×C₄	—	6	1	no	—
914	C₂×C₄	—	6	1	no	—
915	C₂×C₄	—	6	1	no	—
916	C₂×C₄	—	6	1	no	—
917	C₂×C₄	—	6	1	no	—
918	C₂×C₄	—	6	1	no	—
919	C₂×C₄	—	6	1	no	—
920	C₂×C₄	—	6	1	no	—
921	C₂×C₄	—	6	1	no	—
922	C₂×C₄	—	6	1	no	—
923	C₂×C₄	—	12	4	no	—
924	C₂×C₄	—	12	4	no	—
925	C₂×C₄	—	12	4	no	—
926	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
927	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
928	C₂×C₃	—	4	2	no	—
929	C₂×C₃	—	4	2	no	—
930	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
931	C₂×C₃	C₅×#518	1	1	yes	characteristic
932	C₂×C₃	C₅×#518	1	1	yes	characteristic
933	C₂×C₃	C₅×#534	1	1	yes	characteristic
934	C₂×C₃	C₅×#535	1	1	yes	characteristic
935	C₂×C₃	C₅×#538	1	1	yes	characteristic
936	C₂×C₃	C₅×#538	1	1	yes	characteristic
937	D₃	—	2	4	no	—
938	D₃	—	4	2	no	—
939	C₅	#76429	1	1	yes	characteristic, direct product factor, Sylow
940	C₂²	—	2	2	no	—
941	C₂²	—	2	2	no	—
942	C₂²	—	2	2	no	—
943	C₂²	—	2	2	no	—
944	C₂²	—	2	2	no	—
945	C₂²	—	2	2	no	—
946	C₂²	—	3	4	no	—
947	C₂²	—	4	1	no	—
948	C₂²	—	4	1	no	—
949	C₂²	—	4	1	no	—
950	C₂²	—	4	1	no	—
951	C₂²	—	4	1	no	—
952	C₂²	—	4	1	no	—
953	C₂²	—	4	1	no	—
954	C₂²	—	4	1	no	—
955	C₂²	—	6	2	no	—
956	C₂²	—	6	2	no	—
957	C₂²	—	6	2	no	—
958	C₂²	—	6	2	no	—
959	C₂²	—	6	2	no	—
960	C₂²	—	6	2	no	—
961	C₂²	—	6	2	no	—
962	C₂²	—	6	2	no	—
963	C₂²	—	6	2	no	—
964	C₂²	—	12	16	no	—
965	C₂²	—	12	1	no	—
966	C₂²	—	12	1	no	—
967	C₂²	—	12	1	no	—
968	C₂²	—	12	1	no	—
969	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
970	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
971	C₂²	C₅×#1004	1	1	yes	characteristic
972	C₂²	C₅×#1004	1	1	yes	characteristic
973	C₂²	C₅×#1004	1	1	yes	characteristic
974	C₂²	C₅×D₃×#41	1	1	yes	characteristic
975	C₂²	C₅×#1009	1	1	yes	characteristic
976	C₄	—	2	2	no	—
977	C₄	—	2	2	no	—
978	C₄	—	4	1	no	—
979	C₄	—	4	1	no	—
980	C₄	—	4	1	no	—
981	C₄	—	6	2	no	—
982	C₄	—	6	2	no	—
983	C₄	—	6	2	no	—
984	C₄	—	12	1	no	—
985	C₄	—	12	1	no	—
986	C₄	—	12	1	no	—
987	C₃	C₅×#2321	1	1	yes	characteristic, complemented, Sylow
988	C₂	—	4	2	no	—
989	C₂	—	4	2	no	—
990	C₂	—	6	4	no	—
991	C₂	—	12	2	no	—
992	C₂	C₅×#5486	1	1	yes	characteristic
993	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
994	C₂	C₅×#5545	1	1	yes	characteristic
995	C₂	C₅×#5605	1	1	yes	characteristic
996	C₂	C₅×#5613	1	1	yes	characteristic
997	C₂	C₅×#5678	1	1	yes	characteristic
998	C₂	C₅×#5715	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×#390	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₅×#937	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#390	D₃
hypocenter	C₃	C₅×#2321
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#390

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#67⋊C₄	C₂	semidirect
3. C₂×C₅×D₃×C₂²⋊C₄	C₂	semidirect
4. C₃×C₅×#390	C₂	semidirect
5. C₅×#5220	C₂	semidirect
6. C₅×#4990	C₂	semidirect
7. C₅×#4989	C₂	semidirect
8. C₅×#4958	C₂	semidirect
9. C₅×#4957	C₂	semidirect
10. C₅×#4956	C₂	semidirect
11. C₅×#4955	C₂	semidirect
12. C₅×#4945	C₂	semidirect
13. C₅×#4945	C₂	semidirect
14. C₅×#4940	C₂	semidirect
15. C₄×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
21. C₂³×C₅×Dic₃	C₂²	semidirect
24. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
27. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
28. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
29. C₂×C₃×C₄²×C₅	C₂²	semidirect
33. C₂×C₅×#217	C₂²	semidirect
34. C₅×#937	C₄	semidirect
43. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
44. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
45. C₂×C₄×C₅×Dic₃	C₂²	semidirect
46. C₂×C₄×C₅×Dic₃	C₂²	semidirect
49. C₅×C₃⋊#95	C₂²	semidirect
50. C₅×C₃⋊#95	C₂²	semidirect
51. C₅×C₃⋊#95	C₂²	semidirect
52. C₅×C₃⋊#95	C₂²	semidirect
53. C₅×C₃⋊#95	C₂²	semidirect
54. C₅×C₃⋊#95	C₂²	semidirect
55. #76429	C₅	direct (N × H)
60. C₅×#390	D₃	semidirect
79. C₂³×C₅×D₃	C₂×C₄	semidirect
84. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
95. C₂×C₅×#67	C₂×C₄	semidirect
110. C₂×C₄×C₅×D₃	D₄	semidirect
120. C₅×#217	C₂×C₄	semidirect
127. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
128. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
134. C₂×#67⋊C₄	C₂×C₅	semidirect
135. C₂×D₃×C₂²⋊C₄	C₂×C₅	semidirect
136. C₃×#390	C₂×C₅	semidirect
137. #5220	C₂×C₅	semidirect
138. #4990	C₂×C₅	semidirect
139. #4989	C₂×C₅	semidirect
140. #4958	C₂×C₅	semidirect
141. #4957	C₂×C₅	semidirect
142. #4956	C₂×C₅	semidirect
143. #4955	C₂×C₅	semidirect
144. #4945	C₂×C₅	semidirect
145. #4945	C₂×C₅	semidirect
146. #4940	C₂×C₅	semidirect
147. C₄×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
159. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
175. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
176. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
179. C₂×C₄²×C₅	C₂×D₃	semidirect
266. C₂³×Dic₃	C₂²×C₅	semidirect
269. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
272. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
273. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
274. C₂×C₃×C₄²	C₂²×C₅	semidirect
278. C₂×#217	C₂²×C₅	semidirect
279. #937	C₄×C₅	semidirect
288. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
289. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
290. C₂×C₄×Dic₃	C₂²×C₅	semidirect
291. C₂×C₄×Dic₃	C₂²×C₅	semidirect
294. C₃⋊#95	C₂²×C₅	semidirect
295. C₃⋊#95	C₂²×C₅	semidirect
296. C₃⋊#95	C₂²×C₅	semidirect
297. C₃⋊#95	C₂²×C₅	semidirect
298. C₃⋊#95	C₂²×C₅	semidirect
299. C₃⋊#95	C₂²×C₅	semidirect
319. C₂×C₅×D₄	C₄×D₃	semidirect
366. #390	C₅×D₃	semidirect
432. C₂³×D₃	C₂×C₄×C₅	semidirect
437. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
448. C₂×#67	C₂×C₄×C₅	semidirect
463. C₂×C₄×D₃	C₅×D₄	semidirect
473. #217	C₂×C₄×C₅	semidirect
480. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
481. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
572. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
588. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
589. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
592. C₂×C₄²	C₂×C₅×D₃	semidirect
751. C₂×D₄	C₄×C₅×D₃	semidirect
794. C₃×C₅	#2321	semidirect
939. C₅	#76429	direct (N × H)
987. C₃	C₅×#2321	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#937	2
C₂×C₅×#67⋊C₄	2
C₂×C₅×D₃×C₂²⋊C₄	2
C₃×C₅×#390	2
C₅×#5220	2
C₅×#4990	2
C₅×#4989	2
C₅×#4958	2
C₅×#4957	2
C₅×#4956	2
C₅×#4955	2
C₅×#4945	2
C₅×#4940	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₅×#2321	3
#76429	5

Subgroups — C5×#76429 #14323363

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#76429 #14323363