Subgroups — C₂×C₅×#5709 #14483616

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#126	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5709	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₅×#898	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#895	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#894	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#889	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#886	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#884	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#884	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#884	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#872	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅×#553	—	3	1	no	maximal, Hall
18	C₂²×C₅×#67	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
22	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
23	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
24	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
25	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
28	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
30	C₃×C₅×#126	C₂²	1	8	yes	complemented
31	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄²×C₅	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×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
46	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
47	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
50	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
51	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
54	C₅×#898	C₂²	1	8	yes	complemented
55	C₅×#895	C₂²	1	8	yes	complemented
56	C₅×#894	C₂²	1	8	yes	complemented
57	C₅×#893	C₂²	1	8	yes	complemented
58	C₅×D₃×C₄⋊C₄	C₂²	1	8	yes	complemented
59	C₅×#889	C₂²	1	8	yes	complemented
60	C₅×#886	C₂²	1	8	yes	complemented
61	C₅×#884	C₂²	1	8	yes	complemented
62	C₅×#884	C₂²	1	8	yes	complemented
63	C₅×#884	C₂²	1	8	yes	complemented
64	C₅×#67⋊C₄	C₂²	1	8	yes	complemented
65	C₅×#67⋊C₄	C₂²	1	8	yes	complemented
66	C₄×C₅×D₁₂	C₂²	1	8	yes	complemented
67	C₅×#872	C₂²	1	8	yes	complemented
68	C₂×#5709	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
69	C₅×#553	—	3	16	no	—
70	C₂×C₅×#126	—	3	1	no	—
71	C₂×C₅×#126	D₃	1	1	yes	characteristic, complemented
72	C₂×C₅×#125	—	3	1	no	—
73	C₂×C₅×#123	—	3	1	no	—
74	C₂×C₅×#123	—	3	1	no	—
75	C₂×C₅×#121	—	3	1	no	—
76	C₂×C₅×#121	—	3	1	no	—
77	C₂×C₅×#121	—	3	1	no	—
78	C₂×C₅×#121	—	3	1	no	—
79	C₂×C₄×C₅×D₄	—	3	1	no	—
80	C₂×C₄×C₅×D₄	—	3	1	no	—
81	C₂×C₄×C₅×D₄	—	3	1	no	—
82	C₂×C₄×C₅×D₄	—	3	1	no	—
83	C₂×C₅×#117	—	3	1	no	—
84	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
85	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
86	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
87	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
88	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
89	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
91	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
92	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
93	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
94	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
95	C₂×C₅×#67	—	2	4	no	—
96	C₂×C₅×#67	—	2	4	no	—
97	C₂×C₅×#67	—	4	2	no	—
98	C₂×C₅×#67	C₂³	1	4	yes	—
99	C₂×C₅×#67	C₂³	1	4	yes	—
100	C₂×C₅×#67	C₂³	1	4	yes	—
101	C₂²×C₅×Dic₃	—	4	2	no	—
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	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
106	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
107	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
108	C₂×C₅×D₁₂	—	2	4	no	—
109	C₂×C₅×D₁₂	—	2	4	no	—
110	C₂×C₅×D₁₂	—	4	2	no	—
111	C₂×C₅×D₁₂	C₂³	1	4	yes	—
112	C₂×C₅×D₁₂	C₂³	1	4	yes	—
113	C₂×C₅×D₁₂	C₂³	1	4	yes	—
114	C₂×C₄×C₅×D₃	—	2	4	no	—
115	C₂×C₄×C₅×D₃	—	2	4	no	—
116	C₂×C₄×C₅×D₃	—	4	2	no	—
117	C₂×C₄×C₅×D₃	—	4	2	no	—
118	C₂×C₄×C₅×D₃	—	4	2	no	—
119	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
120	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
121	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
122	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
123	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
124	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
125	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
126	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
127	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
128	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₃×C₄²×C₅	C₂³	1	4	yes	—
131	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
132	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
133	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
134	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
135	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
136	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
137	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
138	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
139	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
140	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
141	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
142	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
143	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
144	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
145	C₄×C₅×Dic₃	C₂³	1	4	yes	—
146	C₄×C₅×Dic₃	C₂³	1	4	yes	—
147	C₂×C₃×#126	C₂×C₅	1	1	yes	characteristic, complemented
148	#5709	C₂×C₅	1	16	yes	direct product factor
149	C₂×#898	C₂×C₅	1	1	yes	characteristic, complemented
150	C₂×#895	C₂×C₅	1	1	yes	characteristic, complemented
151	C₂×#894	C₂×C₅	1	1	yes	characteristic, complemented
152	C₂×#893	C₂×C₅	1	1	yes	characteristic, complemented
153	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂×#889	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×#886	C₂×C₅	1	1	yes	characteristic, complemented
156	C₂×#884	C₂×C₅	1	1	yes	characteristic, complemented
157	C₂×#884	C₂×C₅	1	1	yes	characteristic, complemented
158	C₂×#884	C₂×C₅	1	1	yes	characteristic, complemented
159	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
160	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
161	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
162	C₂×#872	C₂×C₅	1	1	yes	characteristic, complemented
163	C₂²×C₅×D₄	—	3	1	no	—
164	C₂²×C₅×D₄	—	3	1	no	—
165	C₂²×C₅×D₄	—	3	1	no	—
166	C₂²×C₅×D₄	—	3	1	no	—
167	C₂²×C₅×D₄	—	3	1	no	—
168	C₂²×C₅×D₄	—	3	1	no	—
169	C₂³×C₄×C₅	—	3	1	no	—
170	C₂³×C₄×C₅	—	3	1	no	—
171	C₂³×C₄×C₅	—	3	1	no	—
172	C₂³×C₄×C₅	—	3	1	no	—
173	C₂³×C₄×C₅	—	3	1	no	—
174	C₂³×C₄×C₅	—	3	1	no	—
175	C₅×#126	—	3	8	no	—
176	C₅×#126	C₂×D₃	1	8	yes	complemented
177	C₅×#125	—	3	8	no	—
178	C₅×#123	—	3	8	no	—
179	C₅×#123	—	3	8	no	—
180	C₅×#121	—	3	8	no	—
181	C₅×#121	—	3	8	no	—
182	C₅×#121	—	3	8	no	—
183	C₅×#121	—	3	8	no	—
184	C₄×C₅×D₄	—	3	8	no	—
185	C₄×C₅×D₄	—	3	8	no	—
186	C₄×C₅×D₄	—	3	8	no	—
187	C₄×C₅×D₄	—	3	8	no	—
188	C₅×#117	—	3	8	no	—
189	C₂×C₅×C₄⋊C₄	—	3	1	no	—
190	C₂×C₅×C₄⋊C₄	—	3	1	no	—
191	C₂×C₅×C₄⋊C₄	—	3	1	no	—
192	C₂×C₅×C₄⋊C₄	—	3	1	no	—
193	C₂×C₅×C₄⋊C₄	—	3	1	no	—
194	C₂×C₅×C₄⋊C₄	—	3	1	no	—
195	C₂×C₅×C₄⋊C₄	—	3	1	no	—
196	C₂×C₅×C₄⋊C₄	—	3	8	no	—
197	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
198	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
199	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
200	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
201	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
202	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
203	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
204	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
205	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
206	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
207	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
208	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
209	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
210	C₂×C₄²×C₅	—	3	1	no	—
211	C₂×C₄²×C₅	—	3	1	no	—
212	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
213	C₂×#553	—	3	1	no	Sylow
214	C₂³×C₃×C₅	—	2	2	no	—
215	C₂³×C₃×C₅	—	2	2	no	—
216	C₂³×C₃×C₅	—	2	2	no	—
217	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
218	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
219	C₂²×C₅×D₃	—	2	2	no	—
220	C₂²×C₅×D₃	—	2	2	no	—
221	C₂²×C₅×D₃	—	2	2	no	—
222	C₂²×C₅×D₃	—	2	2	no	—
223	C₂²×C₅×D₃	—	2	2	no	—
224	C₂²×C₅×D₃	—	2	2	no	—
225	C₂²×C₅×D₃	—	2	2	no	—
226	C₂²×C₅×D₃	—	2	2	no	—
227	C₂²×C₅×D₃	#41	1	4	yes	—
228	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
229	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
230	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
231	C₂×C₃×C₄×C₅	—	2	2	no	—
232	C₂×C₃×C₄×C₅	—	2	2	no	—
233	C₂×C₃×C₄×C₅	—	2	2	no	—
234	C₂×C₃×C₄×C₅	—	2	2	no	—
235	C₂×C₃×C₄×C₅	—	2	2	no	—
236	C₂×C₃×C₄×C₅	—	2	2	no	—
237	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
238	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
239	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
240	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
241	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
242	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
243	C₅×#67	—	2	8	no	—
244	C₅×#67	—	2	8	no	—
245	C₅×#67	—	4	4	no	—
246	C₂×C₅×Dic₃	—	2	2	no	—
247	C₂×C₅×Dic₃	—	2	2	no	—
248	C₂×C₅×Dic₃	—	2	2	no	—
249	C₂×C₅×Dic₃	—	2	2	no	—
250	C₂×C₅×Dic₃	—	4	4	no	—
251	C₂×C₅×Dic₃	#41	1	4	yes	—
252	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
253	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
254	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
255	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
256	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
257	C₅×D₁₂	—	2	8	no	—
258	C₅×D₁₂	—	2	8	no	—
259	C₅×D₁₂	—	4	4	no	—
260	C₄×C₅×D₃	—	2	8	no	—
261	C₄×C₅×D₃	—	2	8	no	—
262	C₄×C₅×D₃	—	4	4	no	—
263	C₄×C₅×D₃	—	4	4	no	—
264	C₄×C₅×D₃	—	4	4	no	—
265	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
266	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
267	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
268	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
269	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
270	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
271	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
272	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
273	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
274	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
275	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
276	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
277	C₃×#126	C₂²×C₅	1	8	yes	complemented
278	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
279	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
280	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
281	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
282	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
283	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
284	C₂×C₃×C₄²	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×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
289	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
290	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
291	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
292	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
293	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
294	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
295	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
296	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
297	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
298	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
299	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
300	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
301	#898	C₂²×C₅	1	8	yes	complemented
302	#895	C₂²×C₅	1	8	yes	complemented
303	#894	C₂²×C₅	1	8	yes	complemented
304	#893	C₂²×C₅	1	8	yes	complemented
305	D₃×C₄⋊C₄	C₂²×C₅	1	8	yes	complemented
306	#889	C₂²×C₅	1	8	yes	complemented
307	#886	C₂²×C₅	1	8	yes	complemented
308	#884	C₂²×C₅	1	8	yes	complemented
309	#884	C₂²×C₅	1	8	yes	complemented
310	#884	C₂²×C₅	1	8	yes	complemented
311	#67⋊C₄	C₂²×C₅	1	8	yes	complemented
312	#67⋊C₄	C₂²×C₅	1	8	yes	complemented
313	C₄×D₁₂	C₂²×C₅	1	8	yes	complemented
314	#872	C₂²×C₅	1	8	yes	complemented
315	C₂⁴×C₅	—	3	1	no	—
316	C₂⁴×C₅	—	3	1	no	—
317	C₂⁴×C₅	—	3	1	no	—
318	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
319	C₂×C₅×D₄	—	3	4	no	—
320	C₂×C₅×D₄	—	3	4	no	—
321	C₂×C₅×D₄	—	3	4	no	—
322	C₂×C₅×D₄	—	3	4	no	—
323	C₂×C₅×D₄	—	3	4	no	—
324	C₂×C₅×D₄	—	3	4	no	—
325	C₂×C₅×D₄	—	6	4	no	—
326	C₂×C₅×D₄	—	6	4	no	—
327	C₂×C₅×D₄	—	6	4	no	—
328	C₂×C₅×D₄	—	6	4	no	—
329	C₂×C₅×D₄	—	12	2	no	—
330	C₂×C₅×D₄	—	12	2	no	—
331	C₂²×C₄×C₅	—	3	1	no	—
332	C₂²×C₄×C₅	—	3	1	no	—
333	C₂²×C₄×C₅	—	3	1	no	—
334	C₂²×C₄×C₅	—	3	1	no	—
335	C₂²×C₄×C₅	—	3	1	no	—
336	C₂²×C₄×C₅	—	3	4	no	—
337	C₂²×C₄×C₅	—	3	4	no	—
338	C₂²×C₄×C₅	—	3	4	no	—
339	C₂²×C₄×C₅	—	3	4	no	—
340	C₂²×C₄×C₅	—	3	4	no	—
341	C₂²×C₄×C₅	—	3	4	no	—
342	C₂²×C₄×C₅	—	6	4	no	—
343	C₂²×C₄×C₅	—	6	4	no	—
344	C₂²×C₄×C₅	—	12	2	no	—
345	C₂²×C₄×C₅	—	12	2	no	—
346	C₂²×C₄×C₅	—	12	2	no	—
347	C₂²×C₄×C₅	—	12	2	no	—
348	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
349	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
350	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
351	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
352	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
353	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
354	C₅×C₄⋊C₄	—	3	4	no	—
355	C₅×C₄⋊C₄	—	3	4	no	—
356	C₅×C₄⋊C₄	—	3	4	no	—
357	C₅×C₄⋊C₄	—	3	4	no	—
358	C₅×C₄⋊C₄	—	3	4	no	—
359	C₅×C₄⋊C₄	—	3	4	no	—
360	C₅×C₄⋊C₄	—	3	4	no	—
361	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
362	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
363	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
364	C₅×C₂²⋊C₄	—	3	4	no	—
365	C₅×C₂²⋊C₄	—	3	4	no	—
366	C₅×C₂²⋊C₄	—	3	4	no	—
367	C₅×C₂²⋊C₄	—	3	4	no	—
368	C₅×C₂²⋊C₄	—	3	4	no	—
369	C₅×C₂²⋊C₄	—	3	4	no	—
370	C₅×C₂²⋊C₄	—	3	4	no	—
371	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
372	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
373	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
374	C₄²×C₅	—	3	4	no	—
375	C₄²×C₅	—	3	4	no	—
376	C₄²×C₅	C₂²×D₃	1	4	yes	—
377	#553	—	3	16	no	—
378	C₂×#126	—	3	1	no	—
379	C₂×#126	C₅×D₃	1	1	yes	characteristic, complemented
380	C₂×#125	—	3	1	no	—
381	C₂×#123	—	3	1	no	—
382	C₂×#123	—	3	1	no	—
383	C₂×#121	—	3	1	no	—
384	C₂×#121	—	3	1	no	—
385	C₂×#121	—	3	1	no	—
386	C₂×#121	—	3	1	no	—
387	C₂×C₄×D₄	—	3	1	no	—
388	C₂×C₄×D₄	—	3	1	no	—
389	C₂×C₄×D₄	—	3	1	no	—
390	C₂×C₄×D₄	—	3	1	no	—
391	C₂×#117	—	3	1	no	—
392	C₂²×C₄⋊C₄	—	3	1	no	—
393	C₂²×C₃×C₅	—	2	2	no	—
394	C₂²×C₃×C₅	—	2	2	no	—
395	C₂²×C₃×C₅	—	2	2	no	—
396	C₂²×C₃×C₅	—	4	4	no	—
397	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
398	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
399	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
400	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
401	C₂×C₅×D₃	—	2	8	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	—	2	2	no	—
408	C₂×C₅×D₃	—	2	2	no	—
409	C₂×C₅×D₃	—	2	2	no	—
410	C₂×C₅×D₃	—	4	4	no	—
411	C₂×C₅×D₃	—	4	4	no	—
412	C₂×C₅×D₃	C₂×#41	1	4	yes	—
413	C₃×C₄×C₅	—	2	2	no	—
414	C₃×C₄×C₅	—	2	2	no	—
415	C₃×C₄×C₅	—	2	2	no	—
416	C₃×C₄×C₅	—	2	2	no	—
417	C₃×C₄×C₅	—	2	2	no	—
418	C₃×C₄×C₅	—	2	2	no	—
419	C₅×Dic₃	—	2	2	no	—
420	C₅×Dic₃	—	2	2	no	—
421	C₅×Dic₃	—	2	2	no	—
422	C₅×Dic₃	—	2	2	no	—
423	C₅×Dic₃	C₂×#41	1	4	yes	—
424	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
425	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
426	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
427	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
428	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
429	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
430	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
431	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
432	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
433	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
434	C₂×#67	—	2	4	no	—
435	C₂×#67	—	2	4	no	—
436	C₂×#67	—	4	2	no	—
437	C₂×#67	C₂³×C₅	1	4	yes	—
438	C₂×#67	C₂³×C₅	1	4	yes	—
439	C₂×#67	C₂³×C₅	1	4	yes	—
440	C₂²×Dic₃	—	4	2	no	—
441	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
442	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
443	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
444	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
445	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
446	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
447	C₂×D₁₂	—	2	4	no	—
448	C₂×D₁₂	—	2	4	no	—
449	C₂×D₁₂	—	4	2	no	—
450	C₂×D₁₂	C₂³×C₅	1	4	yes	—
451	C₂×D₁₂	C₂³×C₅	1	4	yes	—
452	C₂×D₁₂	C₂³×C₅	1	4	yes	—
453	C₂×C₄×D₃	—	2	4	no	—
454	C₂×C₄×D₃	—	2	4	no	—
455	C₂×C₄×D₃	—	4	2	no	—
456	C₂×C₄×D₃	—	4	2	no	—
457	C₂×C₄×D₃	—	4	2	no	—
458	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
459	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
460	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
461	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
462	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
463	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
464	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
465	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
466	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
467	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
468	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
469	C₃×C₄²	C₂³×C₅	1	4	yes	—
470	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
471	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
472	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
473	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
474	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
475	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
476	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
477	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
478	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
479	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
480	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
481	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
482	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
483	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
484	C₄×Dic₃	C₂³×C₅	1	4	yes	—
485	C₄×Dic₃	C₂³×C₅	1	4	yes	—
486	C₂³×C₅	—	2	2	no	—
487	C₂³×C₅	—	2	2	no	—
488	C₂³×C₅	—	2	2	no	—
489	C₂³×C₅	—	3	4	no	—
490	C₂³×C₅	—	3	2	no	—
491	C₂³×C₅	—	3	2	no	—
492	C₂³×C₅	—	3	2	no	—
493	C₂³×C₅	—	6	2	no	—
494	C₂³×C₅	—	6	2	no	—
495	C₂³×C₅	—	6	2	no	—
496	C₂³×C₅	—	6	2	no	—
497	C₂³×C₅	—	6	2	no	—
498	C₂³×C₅	—	6	2	no	—
499	C₂³×C₅	—	6	2	no	—
500	C₂³×C₅	—	6	2	no	—
501	C₂³×C₅	C₂³×D₃	1	2	yes	—
502	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
503	C₅×D₄	—	6	8	no	—
504	C₅×D₄	—	6	8	no	—
505	C₅×D₄	—	6	8	no	—
506	C₅×D₄	—	6	8	no	—
507	C₅×D₄	—	12	4	no	—
508	C₅×D₄	—	12	4	no	—
509	C₂×C₄×C₅	—	2	2	no	—
510	C₂×C₄×C₅	—	2	2	no	—
511	C₂×C₄×C₅	—	2	2	no	—
512	C₂×C₄×C₅	—	2	2	no	—
513	C₂×C₄×C₅	—	2	2	no	—
514	C₂×C₄×C₅	—	2	2	no	—
515	C₂×C₄×C₅	—	3	4	no	—
516	C₂×C₄×C₅	—	3	2	no	—
517	C₂×C₄×C₅	—	3	2	no	—
518	C₂×C₄×C₅	—	3	2	no	—
519	C₂×C₄×C₅	—	3	2	no	—
520	C₂×C₄×C₅	—	3	2	no	—
521	C₂×C₄×C₅	—	6	8	no	—
522	C₂×C₄×C₅	—	6	8	no	—
523	C₂×C₄×C₅	—	6	2	no	—
524	C₂×C₄×C₅	—	6	2	no	—
525	C₂×C₄×C₅	—	6	2	no	—
526	C₂×C₄×C₅	—	6	2	no	—
527	C₂×C₄×C₅	—	12	4	no	—
528	C₂×C₄×C₅	—	12	4	no	—
529	C₂×C₄×C₅	—	12	4	no	—
530	C₂×C₄×C₅	—	12	4	no	—
531	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
532	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
533	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
534	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
535	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
536	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
537	C₂²×D₄	—	3	1	no	—
538	C₂²×D₄	—	3	1	no	—
539	C₂²×D₄	—	3	1	no	—
540	C₂²×D₄	—	3	1	no	—
541	C₂²×D₄	—	3	1	no	—
542	C₂²×D₄	—	3	1	no	—
543	C₂³×C₄	—	3	1	no	—
544	C₂³×C₄	—	3	1	no	—
545	C₂³×C₄	—	3	1	no	—
546	C₂³×C₄	—	3	1	no	—
547	C₂³×C₄	—	3	1	no	—
548	C₂³×C₄	—	3	1	no	—
549	#126	—	3	8	no	—
550	#126	C₂×C₅×D₃	1	8	yes	complemented
551	#125	—	3	8	no	—
552	#123	—	3	8	no	—
553	#123	—	3	8	no	—
554	#121	—	3	8	no	—
555	#121	—	3	8	no	—
556	#121	—	3	8	no	—
557	#121	—	3	8	no	—
558	C₄×D₄	—	3	8	no	—
559	C₄×D₄	—	3	8	no	—
560	C₄×D₄	—	3	8	no	—
561	C₄×D₄	—	3	8	no	—
562	#117	—	3	8	no	—
563	C₂×C₄⋊C₄	—	3	1	no	—
564	C₂×C₄⋊C₄	—	3	1	no	—
565	C₂×C₄⋊C₄	—	3	1	no	—
566	C₂×C₄⋊C₄	—	3	1	no	—
567	C₂×C₄⋊C₄	—	3	1	no	—
568	C₂×C₄⋊C₄	—	3	1	no	—
569	C₂×C₄⋊C₄	—	3	1	no	—
570	C₂×C₄⋊C₄	—	3	8	no	—
571	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
572	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
573	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
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	C₂×C₅×D₃	1	1	yes	characteristic
582	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
583	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
584	C₂×C₄²	—	3	1	no	—
585	C₂×C₄²	—	3	1	no	—
586	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
587	C₂×C₃×C₅	—	4	2	no	—
588	C₂×C₃×C₅	#553	1	4	yes	complemented
589	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
590	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
591	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
592	C₅×D₃	—	2	4	no	—
593	C₅×D₃	—	4	2	no	—
594	C₅×D₃	—	4	2	no	—
595	C₂³×C₃	—	2	2	no	—
596	C₂³×C₃	—	2	2	no	—
597	C₂³×C₃	—	2	2	no	—
598	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
599	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
600	C₂²×D₃	—	2	2	no	—
601	C₂²×D₃	—	2	2	no	—
602	C₂²×D₃	—	2	2	no	—
603	C₂²×D₃	—	2	2	no	—
604	C₂²×D₃	—	2	2	no	—
605	C₂²×D₃	—	2	2	no	—
606	C₂²×D₃	—	2	2	no	—
607	C₂²×D₃	—	2	2	no	—
608	C₂²×D₃	C₅×#41	1	4	yes	—
609	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
610	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
611	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
612	C₂×C₃×C₄	—	2	2	no	—
613	C₂×C₃×C₄	—	2	2	no	—
614	C₂×C₃×C₄	—	2	2	no	—
615	C₂×C₃×C₄	—	2	2	no	—
616	C₂×C₃×C₄	—	2	2	no	—
617	C₂×C₃×C₄	—	2	2	no	—
618	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
619	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
620	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
621	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
622	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
623	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
624	#67	—	2	8	no	—
625	#67	—	2	8	no	—
626	#67	—	4	4	no	—
627	C₂×Dic₃	—	2	2	no	—
628	C₂×Dic₃	—	2	2	no	—
629	C₂×Dic₃	—	2	2	no	—
630	C₂×Dic₃	—	2	2	no	—
631	C₂×Dic₃	—	4	4	no	—
632	C₂×Dic₃	C₅×#41	1	4	yes	—
633	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
634	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
635	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
636	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
637	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
638	D₁₂	—	2	8	no	—
639	D₁₂	—	2	8	no	—
640	D₁₂	—	4	4	no	—
641	C₄×D₃	—	2	8	no	—
642	C₄×D₃	—	2	8	no	—
643	C₄×D₃	—	4	4	no	—
644	C₄×D₃	—	4	4	no	—
645	C₄×D₃	—	4	4	no	—
646	C₂²×C₅	—	2	2	no	—
647	C₂²×C₅	—	2	2	no	—
648	C₂²×C₅	—	2	2	no	—
649	C₂²×C₅	—	3	4	no	—
650	C₂²×C₅	—	4	4	no	—
651	C₂²×C₅	—	6	2	no	—
652	C₂²×C₅	—	6	2	no	—
653	C₂²×C₅	—	6	8	no	—
654	C₂²×C₅	—	6	2	no	—
655	C₂²×C₅	—	6	2	no	—
656	C₂²×C₅	—	6	2	no	—
657	C₂²×C₅	—	6	2	no	—
658	C₂²×C₅	—	6	2	no	—
659	C₂²×C₅	—	6	2	no	—
660	C₂²×C₅	—	12	4	no	—
661	C₂²×C₅	—	12	4	no	—
662	C₂²×C₅	D₃×#41	1	2	yes	—
663	C₂²×C₅	D₃×#41	1	2	yes	—
664	C₂²×C₅	#1009	1	2	yes	—
665	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
666	C₄×C₅	—	2	2	no	—
667	C₄×C₅	—	2	2	no	—
668	C₄×C₅	—	2	2	no	—
669	C₄×C₅	—	2	2	no	—
670	C₄×C₅	—	2	2	no	—
671	C₄×C₅	—	2	2	no	—
672	C₄×C₅	—	3	4	no	—
673	C₄×C₅	—	6	2	no	—
674	C₄×C₅	—	6	2	no	—
675	C₄×C₅	—	6	2	no	—
676	C₄×C₅	—	6	2	no	—
677	C₂⁴	—	3	1	no	—
678	C₂⁴	—	3	1	no	—
679	C₂⁴	—	3	1	no	—
680	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
681	C₂×D₄	—	3	4	no	—
682	C₂×D₄	—	3	4	no	—
683	C₂×D₄	—	3	4	no	—
684	C₂×D₄	—	3	4	no	—
685	C₂×D₄	—	3	4	no	—
686	C₂×D₄	—	3	4	no	—
687	C₂×D₄	—	6	4	no	—
688	C₂×D₄	—	6	4	no	—
689	C₂×D₄	—	6	4	no	—
690	C₂×D₄	—	6	4	no	—
691	C₂×D₄	—	12	2	no	—
692	C₂×D₄	—	12	2	no	—
693	C₂²×C₄	—	3	1	no	—
694	C₂²×C₄	—	3	1	no	—
695	C₂²×C₄	—	3	1	no	—
696	C₂²×C₄	—	3	1	no	—
697	C₂²×C₄	—	3	1	no	—
698	C₂²×C₄	—	3	4	no	—
699	C₂²×C₄	—	3	4	no	—
700	C₂²×C₄	—	3	4	no	—
701	C₂²×C₄	—	3	4	no	—
702	C₂²×C₄	—	3	4	no	—
703	C₂²×C₄	—	3	4	no	—
704	C₂²×C₄	—	6	4	no	—
705	C₂²×C₄	—	6	4	no	—
706	C₂²×C₄	—	12	2	no	—
707	C₂²×C₄	—	12	2	no	—
708	C₂²×C₄	—	12	2	no	—
709	C₂²×C₄	—	12	2	no	—
710	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
711	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
712	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
713	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
714	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
715	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
716	C₄⋊C₄	—	3	4	no	—
717	C₄⋊C₄	—	3	4	no	—
718	C₄⋊C₄	—	3	4	no	—
719	C₄⋊C₄	—	3	4	no	—
720	C₄⋊C₄	—	3	4	no	—
721	C₄⋊C₄	—	3	4	no	—
722	C₄⋊C₄	—	3	4	no	—
723	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
724	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
725	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
726	C₂²⋊C₄	—	3	4	no	—
727	C₂²⋊C₄	—	3	4	no	—
728	C₂²⋊C₄	—	3	4	no	—
729	C₂²⋊C₄	—	3	4	no	—
730	C₂²⋊C₄	—	3	4	no	—
731	C₂²⋊C₄	—	3	4	no	—
732	C₂²⋊C₄	—	3	4	no	—
733	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
734	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
735	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
736	C₄²	—	3	4	no	—
737	C₄²	—	3	4	no	—
738	C₄²	C₂²×C₅×D₃	1	4	yes	—
739	C₃×C₅	C₂×#553	1	1	yes	characteristic, complemented, Hall
740	C₂²×C₃	—	2	2	no	—
741	C₂²×C₃	—	2	2	no	—
742	C₂²×C₃	—	2	2	no	—
743	C₂²×C₃	—	4	4	no	—
744	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
745	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
746	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
747	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
748	C₂×D₃	—	2	8	no	—
749	C₂×D₃	—	2	2	no	—
750	C₂×D₃	—	2	2	no	—
751	C₂×D₃	—	2	2	no	—
752	C₂×D₃	—	2	2	no	—
753	C₂×D₃	—	2	2	no	—
754	C₂×D₃	—	2	2	no	—
755	C₂×D₃	—	2	2	no	—
756	C₂×D₃	—	2	2	no	—
757	C₂×D₃	—	4	4	no	—
758	C₂×D₃	—	4	4	no	—
759	C₂×D₃	C₂×C₅×#41	1	4	yes	—
760	C₃×C₄	—	2	2	no	—
761	C₃×C₄	—	2	2	no	—
762	C₃×C₄	—	2	2	no	—
763	C₃×C₄	—	2	2	no	—
764	C₃×C₄	—	2	2	no	—
765	C₃×C₄	—	2	2	no	—
766	Dic₃	—	2	2	no	—
767	Dic₃	—	2	2	no	—
768	Dic₃	—	2	2	no	—
769	Dic₃	—	2	2	no	—
770	Dic₃	C₂×C₅×#41	1	4	yes	—
771	C₂×C₅	—	4	2	no	—
772	C₂×C₅	—	6	4	no	—
773	C₂×C₅	—	12	2	no	—
774	C₂×C₅	—	12	2	no	—
775	C₂×C₅	#5709	1	4	yes	direct product factor
776	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
777	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
778	C₂×C₅	C₂×#1009	1	1	yes	characteristic
779	C₂³	—	2	2	no	—
780	C₂³	—	2	2	no	—
781	C₂³	—	2	2	no	—
782	C₂³	—	3	4	no	—
783	C₂³	—	3	2	no	—
784	C₂³	—	3	2	no	—
785	C₂³	—	3	2	no	—
786	C₂³	—	6	2	no	—
787	C₂³	—	6	2	no	—
788	C₂³	—	6	2	no	—
789	C₂³	—	6	2	no	—
790	C₂³	—	6	2	no	—
791	C₂³	—	6	2	no	—
792	C₂³	—	6	2	no	—
793	C₂³	—	6	2	no	—
794	C₂³	C₂³×C₅×D₃	1	2	yes	—
795	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
796	D₄	—	6	8	no	—
797	D₄	—	6	8	no	—
798	D₄	—	6	8	no	—
799	D₄	—	6	8	no	—
800	D₄	—	12	4	no	—
801	D₄	—	12	4	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	3	4	no	—
809	C₂×C₄	—	3	2	no	—
810	C₂×C₄	—	3	2	no	—
811	C₂×C₄	—	3	2	no	—
812	C₂×C₄	—	3	2	no	—
813	C₂×C₄	—	3	2	no	—
814	C₂×C₄	—	6	8	no	—
815	C₂×C₄	—	6	8	no	—
816	C₂×C₄	—	6	2	no	—
817	C₂×C₄	—	6	2	no	—
818	C₂×C₄	—	6	2	no	—
819	C₂×C₄	—	6	2	no	—
820	C₂×C₄	—	12	4	no	—
821	C₂×C₄	—	12	4	no	—
822	C₂×C₄	—	12	4	no	—
823	C₂×C₄	—	12	4	no	—
824	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
825	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
826	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
827	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
828	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
829	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
830	C₂×C₃	—	4	2	no	—
831	C₂×C₃	C₅×#553	1	4	yes	complemented
832	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
833	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
834	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
835	D₃	—	2	4	no	—
836	D₃	—	4	2	no	—
837	D₃	—	4	2	no	—
838	C₅	C₂×#5709	1	1	yes	characteristic, direct product factor, Sylow
839	C₂²	—	2	2	no	—
840	C₂²	—	2	2	no	—
841	C₂²	—	2	2	no	—
842	C₂²	—	3	4	no	—
843	C₂²	—	4	4	no	—
844	C₂²	—	6	8	no	—
845	C₂²	—	6	2	no	—
846	C₂²	—	6	2	no	—
847	C₂²	—	6	2	no	—
848	C₂²	—	6	2	no	—
849	C₂²	—	6	2	no	—
850	C₂²	—	6	2	no	—
851	C₂²	—	6	2	no	—
852	C₂²	—	6	2	no	—
853	C₂²	—	12	4	no	—
854	C₂²	—	12	4	no	—
855	C₂²	C₅×D₃×#41	1	2	yes	—
856	C₂²	C₅×D₃×#41	1	2	yes	—
857	C₂²	C₅×#1009	1	2	yes	—
858	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
859	C₄	—	2	2	no	—
860	C₄	—	2	2	no	—
861	C₄	—	2	2	no	—
862	C₄	—	2	2	no	—
863	C₄	—	2	2	no	—
864	C₄	—	2	2	no	—
865	C₄	—	3	4	no	—
866	C₄	—	6	2	no	—
867	C₄	—	6	2	no	—
868	C₄	—	6	2	no	—
869	C₄	—	6	2	no	—
870	C₃	C₂×C₅×#553	1	1	yes	characteristic, complemented, Sylow
871	C₂	—	4	2	no	—
872	C₂	—	6	4	no	—
873	C₂	—	12	2	no	—
874	C₂	—	12	2	no	—
875	C₂	C₅×#5709	1	4	yes	direct product factor
876	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
877	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
878	C₂	C₂×C₅×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#126	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#126	D₃
hypocenter	C₃	C₂×C₅×#553
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#126

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#126	C₂	semidirect
2. C₅×#5709	C₂	direct (N × H)
3. C₂×C₅×#898	C₂	semidirect
4. C₂×C₅×#895	C₂	semidirect
5. C₂×C₅×#894	C₂	semidirect
6. C₂×C₅×#893	C₂	semidirect
7. C₂×C₅×D₃×C₄⋊C₄	C₂	semidirect
8. C₂×C₅×#889	C₂	semidirect
9. C₂×C₅×#886	C₂	semidirect
10. C₂×C₅×#884	C₂	semidirect
11. C₂×C₅×#884	C₂	semidirect
12. C₂×C₅×#884	C₂	semidirect
13. C₂×C₅×#67⋊C₄	C₂	semidirect
14. C₂×C₅×#67⋊C₄	C₂	semidirect
15. C₂×C₄×C₅×D₁₂	C₂	semidirect
16. C₂×C₅×#872	C₂	semidirect
30. C₃×C₅×#126	C₂²	semidirect
54. C₅×#898	C₂²	semidirect
55. C₅×#895	C₂²	semidirect
56. C₅×#894	C₂²	semidirect
57. C₅×#893	C₂²	semidirect
58. C₅×D₃×C₄⋊C₄	C₂²	semidirect
59. C₅×#889	C₂²	semidirect
60. C₅×#886	C₂²	semidirect
61. C₅×#884	C₂²	semidirect
62. C₅×#884	C₂²	semidirect
63. C₅×#884	C₂²	semidirect
64. C₅×#67⋊C₄	C₂²	semidirect
65. C₅×#67⋊C₄	C₂²	semidirect
66. C₄×C₅×D₁₂	C₂²	semidirect
67. C₅×#872	C₂²	semidirect
68. C₂×#5709	C₅	direct (N × H)
71. C₂×C₅×#126	D₃	semidirect
147. C₂×C₃×#126	C₂×C₅	semidirect
148. #5709	C₂×C₅	direct (N × H)
149. C₂×#898	C₂×C₅	semidirect
150. C₂×#895	C₂×C₅	semidirect
151. C₂×#894	C₂×C₅	semidirect
152. C₂×#893	C₂×C₅	semidirect
153. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
154. C₂×#889	C₂×C₅	semidirect
155. C₂×#886	C₂×C₅	semidirect
156. C₂×#884	C₂×C₅	semidirect
157. C₂×#884	C₂×C₅	semidirect
158. C₂×#884	C₂×C₅	semidirect
159. C₂×#67⋊C₄	C₂×C₅	semidirect
160. C₂×#67⋊C₄	C₂×C₅	semidirect
161. C₂×C₄×D₁₂	C₂×C₅	semidirect
162. C₂×#872	C₂×C₅	semidirect
176. C₅×#126	C₂×D₃	semidirect
277. C₃×#126	C₂²×C₅	semidirect
301. #898	C₂²×C₅	semidirect
302. #895	C₂²×C₅	semidirect
303. #894	C₂²×C₅	semidirect
304. #893	C₂²×C₅	semidirect
305. D₃×C₄⋊C₄	C₂²×C₅	semidirect
306. #889	C₂²×C₅	semidirect
307. #886	C₂²×C₅	semidirect
308. #884	C₂²×C₅	semidirect
309. #884	C₂²×C₅	semidirect
310. #884	C₂²×C₅	semidirect
311. #67⋊C₄	C₂²×C₅	semidirect
312. #67⋊C₄	C₂²×C₅	semidirect
313. C₄×D₁₂	C₂²×C₅	semidirect
314. #872	C₂²×C₅	semidirect
379. C₂×#126	C₅×D₃	semidirect
550. #126	C₂×C₅×D₃	semidirect
588. C₂×C₃×C₅	#553	semidirect
739. C₃×C₅	C₂×#553	semidirect
775. C₂×C₅	#5709	direct (N × H)
831. C₂×C₃	C₅×#553	semidirect
838. C₅	C₂×#5709	direct (N × H)
870. C₃	C₂×C₅×#553	semidirect
875. C₂	C₅×#5709	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#126	2
C₅×#5709	2
C₂×C₅×#898	2
C₂×C₅×#895	2
C₂×C₅×#894	2
C₂×C₅×#893	2
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₅×#889	2
C₂×C₅×#886	2
C₂×C₅×#884	2
C₂×C₅×#67⋊C₄	2
C₂×C₄×C₅×D₁₂	2
C₂×C₅×#872	2
C₂×C₅×#553	3
C₂×#5709	5

Subgroups — C2×C5×#5709 #14483616

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5709 #14483616