Subgroups — C₂×C₃×#66039 #14483239

Order 1920.

2656 conjugacy classes of subgroups.

The subgroup lattice has 888 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	C₃×#66039	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃×#4043	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4042	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#4040	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#4040	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#4039	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#4038	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#4031	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×#4029	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#4028	C₂	1	1	yes	maximal, characteristic
12	C₂×C₃×D₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₃×D₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₃×#4025	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₃×#4018	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#66039	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
18	C₂⁴×C₃×D₅	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
20	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
21	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
24	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
25	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
26	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
27	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₅×#126	C₂²	1	8	yes	complemented
29	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic
38	C₂×C₃×#685	C₂²	1	1	yes	characteristic
39	C₂×C₃×#685	C₂²	1	1	yes	characteristic
40	C₂×C₃×#685	C₂²	1	1	yes	characteristic
41	C₂×C₃×#685	C₂²	1	1	yes	characteristic
42	C₂×C₃×#685	C₂²	1	1	yes	characteristic
43	C₂×C₃×#685	C₂²	1	1	yes	characteristic
44	C₂×C₃×#685	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₃×#685	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₃×#685	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₃×#683	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₃×#683	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₃×#683	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
54	C₃×#4043	C₂²	1	8	yes	complemented
55	C₃×#4042	C₂²	1	8	yes	complemented
56	C₃×#4040	C₂²	1	8	yes	complemented
57	C₃×#4040	C₂²	1	8	yes	complemented
58	C₃×#4039	C₂²	1	8	yes	complemented
59	C₃×#4038	C₂²	1	8	yes	complemented
60	C₃×#4031	C₂²	1	8	yes	complemented
61	C₃×#4029	C₂²	1	8	yes	complemented
62	C₃×#4028	C₂²	1	8	yes	—
63	C₃×D₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
64	C₃×D₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
65	C₃×#4025	C₂²	1	8	yes	complemented
66	C₃×C₄×D₂₀	C₂²	1	8	yes	complemented
67	C₃×#4018	C₂²	1	8	yes	complemented
68	C₂×C₃×#551	—	5	1	no	maximal, Hall
69	C₂×C₅×#126	C₂×C₃	1	1	yes	characteristic, complemented
70	#66039	C₂×C₃	1	16	yes	direct product factor
71	C₂×#4043	C₂×C₃	1	1	yes	characteristic, complemented
72	C₂×#4042	C₂×C₃	1	1	yes	characteristic, complemented
73	C₂×#4040	C₂×C₃	1	1	yes	characteristic, complemented
74	C₂×#4040	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×#4039	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂×#4038	C₂×C₃	1	1	yes	characteristic, complemented
77	C₂×#4031	C₂×C₃	1	1	yes	characteristic, complemented
78	C₂×#4029	C₂×C₃	1	1	yes	characteristic, complemented
79	C₂×#4028	C₂×C₃	1	1	yes	characteristic
80	C₂×D₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
81	C₂×D₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
82	C₂×#4025	C₂×C₃	1	1	yes	characteristic, complemented
83	C₂×C₄×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
84	C₂×#4018	C₂×C₃	1	1	yes	characteristic, complemented
85	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
86	C₂³×C₃×D₅	—	2	4	no	—
87	C₂³×C₃×D₅	—	2	4	no	—
88	C₂³×C₃×D₅	—	4	2	no	—
89	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
90	C₂³×C₃×D₅	C₂³	1	4	yes	—
91	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
92	C₂³×C₃×D₅	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	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
96	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
97	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
98	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
99	C₂×C₃×C₂²⋊D₅	—	4	2	no	—
100	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
101	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
102	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
103	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
104	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
105	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
106	C₂×C₃×D₂₀	—	2	4	no	—
107	C₂×C₃×D₂₀	—	2	4	no	—
108	C₂×C₃×D₂₀	C₂³	1	4	yes	—
109	C₂×C₃×D₂₀	C₂³	1	4	yes	—
110	C₂×C₃×C₄×D₅	—	2	4	no	—
111	C₂×C₃×C₄×D₅	—	2	4	no	—
112	C₂×C₃×C₄×D₅	—	4	2	no	—
113	C₂×C₃×C₄×D₅	—	4	2	no	—
114	C₂×C₃×C₄×D₅	—	4	2	no	—
115	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
116	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
117	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
118	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
119	C₂×C₃×C₄×D₅	C₂³	1	4	yes	complemented
120	C₂×C₃×Dic₁₀	—	4	2	no	—
121	C₂×C₃×Dic₁₀	C₂³	1	4	yes	complemented
122	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
123	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
124	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
125	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
127	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
128	C₃×C₄²×C₅	C₂³	1	4	yes	complemented
129	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
130	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
131	C₃×#685	C₂³	1	4	yes	—
132	C₃×#685	C₂³	1	4	yes	—
133	C₃×#685	C₂³	1	4	yes	—
134	C₃×#685	C₂³	1	4	yes	—
135	C₃×#685	C₂³	1	4	yes	—
136	C₃×#685	C₂³	1	4	yes	—
137	C₃×#685	C₂³	1	4	yes	complemented
138	C₃×#685	C₂³	1	4	yes	complemented
139	C₃×#685	C₂³	1	4	yes	complemented
140	C₃×C₄⋊Dic₅	C₂³	1	4	yes	complemented
141	C₃×C₄⋊Dic₅	C₂³	1	4	yes	complemented
142	C₃×#683	C₂³	1	4	yes	complemented
143	C₃×#683	C₂³	1	4	yes	complemented
144	C₃×#683	C₂³	1	4	yes	complemented
145	C₃×C₄×Dic₅	C₂³	1	4	yes	complemented
146	C₃×C₄×Dic₅	C₂³	1	4	yes	complemented
147	C₃×#551	—	5	16	no	—
148	C₂×C₃×#126	—	5	1	no	—
149	C₂×C₃×#126	D₅	1	1	yes	characteristic, complemented
150	C₂×C₃×#124	—	5	1	no	—
151	C₂×C₃×#123	—	5	1	no	—
152	C₂×C₃×#123	—	5	1	no	—
153	C₂×C₃×#123	—	5	1	no	—
154	C₂×C₃×C₂²⋊Q₈	—	5	1	no	—
155	C₂×C₃×C₂²⋊Q₈	—	5	1	no	—
156	C₂×C₃×#120	—	5	1	no	—
157	C₂×C₃×C₄×D₄	—	5	1	no	—
158	C₂×C₃×C₄×D₄	—	5	1	no	—
159	C₂×C₃×#117	—	5	1	no	—
160	C₂×C₃×#117	—	5	1	no	—
161	C₂²×C₃×C₂²⋊C₄	—	5	1	no	—
162	C₂²×C₃×C₂²⋊C₄	—	5	1	no	—
163	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic
164	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
165	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
166	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
167	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
168	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
169	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
170	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
171	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₅×#126	C₂²×C₃	1	8	yes	complemented
174	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
175	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
176	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
177	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
178	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
179	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
180	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
181	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
182	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
183	C₂×#685	C₂²×C₃	1	1	yes	characteristic
184	C₂×#685	C₂²×C₃	1	1	yes	characteristic
185	C₂×#685	C₂²×C₃	1	1	yes	characteristic
186	C₂×#685	C₂²×C₃	1	1	yes	characteristic
187	C₂×#685	C₂²×C₃	1	1	yes	characteristic
188	C₂×#685	C₂²×C₃	1	1	yes	characteristic
189	C₂×#685	C₂²×C₃	1	1	yes	characteristic, complemented
190	C₂×#685	C₂²×C₃	1	1	yes	characteristic, complemented
191	C₂×#685	C₂²×C₃	1	1	yes	characteristic, complemented
192	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
193	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
194	C₂×#683	C₂²×C₃	1	1	yes	characteristic, complemented
195	C₂×#683	C₂²×C₃	1	1	yes	characteristic, complemented
196	C₂×#683	C₂²×C₃	1	1	yes	characteristic, complemented
197	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
198	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
199	#4043	C₂²×C₃	1	8	yes	complemented
200	#4042	C₂²×C₃	1	8	yes	complemented
201	#4040	C₂²×C₃	1	8	yes	complemented
202	#4040	C₂²×C₃	1	8	yes	complemented
203	#4039	C₂²×C₃	1	8	yes	complemented
204	#4038	C₂²×C₃	1	8	yes	complemented
205	#4031	C₂²×C₃	1	8	yes	complemented
206	#4029	C₂²×C₃	1	8	yes	complemented
207	#4028	C₂²×C₃	1	8	yes	—
208	D₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
209	D₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
210	#4025	C₂²×C₃	1	8	yes	complemented
211	C₄×D₂₀	C₂²×C₃	1	8	yes	complemented
212	#4018	C₂²×C₃	1	8	yes	complemented
213	C₂×#551	—	5	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×C₃×D₅	—	2	2	no	—
220	C₂²×C₃×D₅	—	2	2	no	—
221	C₂²×C₃×D₅	—	2	2	no	—
222	C₂²×C₃×D₅	—	2	2	no	—
223	C₂²×C₃×D₅	—	2	2	no	—
224	C₂²×C₃×D₅	—	2	2	no	—
225	C₂²×C₃×D₅	—	2	2	no	—
226	C₂²×C₃×D₅	—	2	8	no	—
227	C₂²×C₃×D₅	—	2	8	no	—
228	C₂²×C₃×D₅	—	4	4	no	—
229	C₂²×C₃×D₅	—	4	16	no	—
230	C₂²×C₃×D₅	#41	1	4	yes	—
231	C₂²×C₃×D₅	#41	1	4	yes	—
232	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
233	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
234	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
235	C₂×C₃×C₄×C₅	—	2	2	no	—
236	C₂×C₃×C₄×C₅	—	2	2	no	—
237	C₂×C₃×C₄×C₅	—	2	2	no	—
238	C₂×C₃×C₄×C₅	—	2	2	no	—
239	C₂×C₃×C₄×C₅	—	2	2	no	—
240	C₂×C₃×C₄×C₅	—	2	2	no	—
241	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
242	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
243	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
244	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
245	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
246	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
247	C₃×C₂²⋊D₅	—	4	4	no	—
248	C₂×C₃×Dic₅	—	2	2	no	—
249	C₂×C₃×Dic₅	—	2	2	no	—
250	C₂×C₃×Dic₅	—	2	2	no	—
251	C₂×C₃×Dic₅	—	2	2	no	—
252	C₂×C₃×Dic₅	—	2	2	no	—
253	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
254	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
255	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
256	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
257	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
258	C₃×D₂₀	—	2	8	no	—
259	C₃×D₂₀	—	2	8	no	—
260	C₃×C₄×D₅	—	2	8	no	—
261	C₃×C₄×D₅	—	2	8	no	—
262	C₃×C₄×D₅	—	4	4	no	—
263	C₃×C₄×D₅	—	4	4	no	—
264	C₃×C₄×D₅	—	4	4	no	—
265	C₃×Dic₁₀	—	4	4	no	—
266	C₂⁵×C₃	—	5	1	no	—
267	C₂²×C₃×Q₈	—	5	1	no	—
268	C₂²×C₃×D₄	—	5	1	no	—
269	C₂²×C₃×D₄	—	5	1	no	—
270	C₂²×C₃×D₄	—	5	1	no	—
271	C₂³×C₃×C₄	—	5	1	no	—
272	C₂³×C₃×C₄	—	5	1	no	—
273	C₂³×C₃×C₄	—	5	1	no	—
274	C₂³×C₃×C₄	—	5	1	no	—
275	C₂³×C₃×C₄	—	5	1	no	—
276	C₃×#126	—	5	8	no	—
277	C₃×#126	C₂×D₅	1	8	yes	complemented
278	C₃×#124	—	5	8	no	—
279	C₃×#123	—	5	8	no	—
280	C₃×#123	—	5	8	no	—
281	C₃×#123	—	5	8	no	—
282	C₃×C₂²⋊Q₈	—	5	8	no	—
283	C₃×C₂²⋊Q₈	—	5	8	no	—
284	C₃×#120	—	5	8	no	—
285	C₃×C₄×D₄	—	5	8	no	—
286	C₃×C₄×D₄	—	5	8	no	—
287	C₃×#117	—	5	8	no	—
288	C₃×#117	—	5	8	no	—
289	C₂×C₃×C₄⋊C₄	—	5	1	no	—
290	C₂×C₃×C₄⋊C₄	—	5	1	no	—
291	C₂×C₃×C₄⋊C₄	—	5	1	no	—
292	C₂×C₃×C₄⋊C₄	—	5	1	no	—
293	C₂×C₃×C₄⋊C₄	—	5	1	no	—
294	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
295	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
296	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
297	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
298	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
299	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
300	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
301	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
302	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
303	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
304	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
305	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
306	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
307	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
308	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
309	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
310	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
311	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
312	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic
313	C₂×C₃×C₄²	—	5	1	no	—
314	C₂×C₃×C₄²	—	5	1	no	—
315	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
316	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
317	C₂³×D₅	—	2	4	no	—
318	C₂³×D₅	—	2	4	no	—
319	C₂³×D₅	—	4	2	no	—
320	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
321	C₂³×D₅	C₂³×C₃	1	4	yes	—
322	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
323	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
324	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
325	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
326	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
327	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
328	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
329	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
330	C₂×C₂²⋊D₅	—	4	2	no	—
331	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
332	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
333	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
334	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
335	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
336	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
337	C₂×D₂₀	—	2	4	no	—
338	C₂×D₂₀	—	2	4	no	—
339	C₂×D₂₀	C₂³×C₃	1	4	yes	—
340	C₂×D₂₀	C₂³×C₃	1	4	yes	—
341	C₂×C₄×D₅	—	2	4	no	—
342	C₂×C₄×D₅	—	2	4	no	—
343	C₂×C₄×D₅	—	4	2	no	—
344	C₂×C₄×D₅	—	4	2	no	—
345	C₂×C₄×D₅	—	4	2	no	—
346	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
347	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
348	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
349	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
350	C₂×C₄×D₅	C₂³×C₃	1	4	yes	complemented
351	C₂×Dic₁₀	—	4	2	no	—
352	C₂×Dic₁₀	C₂³×C₃	1	4	yes	complemented
353	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
354	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
355	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
356	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
357	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
358	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
359	C₄²×C₅	C₂³×C₃	1	4	yes	complemented
360	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
361	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
362	#685	C₂³×C₃	1	4	yes	—
363	#685	C₂³×C₃	1	4	yes	—
364	#685	C₂³×C₃	1	4	yes	—
365	#685	C₂³×C₃	1	4	yes	—
366	#685	C₂³×C₃	1	4	yes	—
367	#685	C₂³×C₃	1	4	yes	—
368	#685	C₂³×C₃	1	4	yes	complemented
369	#685	C₂³×C₃	1	4	yes	complemented
370	#685	C₂³×C₃	1	4	yes	complemented
371	C₄⋊Dic₅	C₂³×C₃	1	4	yes	complemented
372	C₄⋊Dic₅	C₂³×C₃	1	4	yes	complemented
373	#683	C₂³×C₃	1	4	yes	complemented
374	#683	C₂³×C₃	1	4	yes	complemented
375	#683	C₂³×C₃	1	4	yes	complemented
376	C₄×Dic₅	C₂³×C₃	1	4	yes	complemented
377	C₄×Dic₅	C₂³×C₃	1	4	yes	complemented
378	#551	—	5	16	no	—
379	C₂×#126	—	5	1	no	—
380	C₂×#126	C₃×D₅	1	1	yes	characteristic, complemented
381	C₂×#124	—	5	1	no	—
382	C₂×#123	—	5	1	no	—
383	C₂×#123	—	5	1	no	—
384	C₂×#123	—	5	1	no	—
385	C₂×C₂²⋊Q₈	—	5	1	no	—
386	C₂×C₂²⋊Q₈	—	5	1	no	—
387	C₂×#120	—	5	1	no	—
388	C₂×C₄×D₄	—	5	1	no	—
389	C₂×C₄×D₄	—	5	1	no	—
390	C₂×#117	—	5	1	no	—
391	C₂×#117	—	5	1	no	—
392	C₂²×C₂²⋊C₄	—	5	1	no	—
393	C₂²×C₂²⋊C₄	—	5	1	no	—
394	C₂²×C₃×C₅	—	2	2	no	—
395	C₂²×C₃×C₅	—	2	2	no	—
396	C₂²×C₃×C₅	—	2	2	no	—
397	C₂²×C₃×C₅	—	4	4	no	—
398	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
399	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
400	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
401	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
402	C₂×C₃×D₅	—	2	8	no	—
403	C₂×C₃×D₅	—	2	8	no	—
404	C₂×C₃×D₅	—	2	2	no	—
405	C₂×C₃×D₅	—	2	2	no	—
406	C₂×C₃×D₅	—	2	2	no	—
407	C₂×C₃×D₅	—	2	2	no	—
408	C₂×C₃×D₅	—	2	2	no	—
409	C₂×C₃×D₅	—	2	2	no	—
410	C₂×C₃×D₅	—	2	2	no	—
411	C₂×C₃×D₅	—	4	16	no	—
412	C₂×C₃×D₅	—	4	4	no	—
413	C₂×C₃×D₅	C₂×#41	1	4	yes	—
414	C₂×C₃×D₅	C₂×#41	1	4	yes	—
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	C₃×C₄×C₅	—	2	2	no	—
420	C₃×C₄×C₅	—	2	2	no	—
421	C₃×Dic₅	—	2	2	no	—
422	C₃×Dic₅	—	2	2	no	—
423	C₃×Dic₅	—	2	2	no	—
424	C₃×Dic₅	—	2	2	no	—
425	C₃×Dic₅	—	2	2	no	—
426	C₂⁴×C₃	—	5	1	no	—
427	C₂⁴×C₃	—	5	1	no	—
428	C₂⁴×C₃	—	5	1	no	—
429	C₂⁴×C₃	—	5	4	no	—
430	C₂⁴×C₃	—	10	4	no	—
431	C₂⁴×C₃	—	10	4	no	—
432	C₂⁴×C₃	—	20	2	no	—
433	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
434	C₂×C₃×Q₈	—	5	4	no	—
435	C₂×C₃×Q₈	—	20	2	no	—
436	C₂×C₃×D₄	—	5	4	no	—
437	C₂×C₃×D₄	—	5	4	no	—
438	C₂×C₃×D₄	—	5	4	no	—
439	C₂×C₃×D₄	—	10	4	no	—
440	C₂×C₃×D₄	—	10	4	no	—
441	C₂×C₃×D₄	—	20	2	no	—
442	C₂²×C₃×C₄	—	5	1	no	—
443	C₂²×C₃×C₄	—	5	1	no	—
444	C₂²×C₃×C₄	—	5	1	no	—
445	C₂²×C₃×C₄	—	5	1	no	—
446	C₂²×C₃×C₄	—	5	1	no	—
447	C₂²×C₃×C₄	—	5	4	no	—
448	C₂²×C₃×C₄	—	5	4	no	—
449	C₂²×C₃×C₄	—	5	4	no	—
450	C₂²×C₃×C₄	—	5	4	no	—
451	C₂²×C₃×C₄	—	5	4	no	—
452	C₂²×C₃×C₄	—	10	4	no	—
453	C₂²×C₃×C₄	—	10	4	no	—
454	C₂²×C₃×C₄	—	20	2	no	—
455	C₂²×C₃×C₄	—	20	2	no	—
456	C₂²×C₃×C₄	—	20	2	no	—
457	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
458	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
459	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
460	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
461	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
462	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
463	C₃×C₄⋊C₄	—	5	4	no	—
464	C₃×C₄⋊C₄	—	5	4	no	—
465	C₃×C₄⋊C₄	—	5	4	no	—
466	C₃×C₄⋊C₄	—	5	4	no	—
467	C₃×C₄⋊C₄	—	5	4	no	—
468	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	complemented
469	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	complemented
470	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	complemented
471	C₃×C₂²⋊C₄	—	5	4	no	—
472	C₃×C₂²⋊C₄	—	5	4	no	—
473	C₃×C₂²⋊C₄	—	5	4	no	—
474	C₃×C₂²⋊C₄	—	5	4	no	—
475	C₃×C₂²⋊C₄	—	5	4	no	—
476	C₃×C₂²⋊C₄	—	5	4	no	—
477	C₃×C₂²⋊C₄	—	5	4	no	—
478	C₃×C₂²⋊C₄	—	5	4	no	—
479	C₃×C₂²⋊C₄	—	5	4	no	—
480	C₃×C₂²⋊C₄	—	5	4	no	—
481	C₃×C₂²⋊C₄	—	5	4	no	—
482	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
483	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
484	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
485	C₃×C₄²	—	5	4	no	—
486	C₃×C₄²	—	5	4	no	—
487	C₃×C₄²	C₂²×D₅	1	4	yes	complemented
488	C₂³×C₅	—	2	2	no	—
489	C₂³×C₅	—	2	2	no	—
490	C₂³×C₅	—	2	2	no	—
491	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
492	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
493	C₂²×D₅	—	2	2	no	—
494	C₂²×D₅	—	2	2	no	—
495	C₂²×D₅	—	2	2	no	—
496	C₂²×D₅	—	2	2	no	—
497	C₂²×D₅	—	2	2	no	—
498	C₂²×D₅	—	2	2	no	—
499	C₂²×D₅	—	2	2	no	—
500	C₂²×D₅	—	2	8	no	—
501	C₂²×D₅	—	2	8	no	—
502	C₂²×D₅	—	4	4	no	—
503	C₂²×D₅	—	4	16	no	—
504	C₂²×D₅	C₃×#41	1	4	yes	—
505	C₂²×D₅	C₃×#41	1	4	yes	—
506	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
507	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
508	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
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	C₂⁴×C₃	1	2	yes	—
516	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
517	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
518	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
519	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
520	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
521	C₂²⋊D₅	—	4	4	no	—
522	C₂×Dic₅	—	2	2	no	—
523	C₂×Dic₅	—	2	2	no	—
524	C₂×Dic₅	—	2	2	no	—
525	C₂×Dic₅	—	2	2	no	—
526	C₂×Dic₅	—	2	2	no	—
527	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
528	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
529	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
530	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
531	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
532	D₂₀	—	2	8	no	—
533	D₂₀	—	2	8	no	—
534	C₄×D₅	—	2	8	no	—
535	C₄×D₅	—	2	8	no	—
536	C₄×D₅	—	4	4	no	—
537	C₄×D₅	—	4	4	no	—
538	C₄×D₅	—	4	4	no	—
539	Dic₁₀	—	4	4	no	—
540	C₂⁵	—	5	1	no	—
541	C₂²×Q₈	—	5	1	no	—
542	C₂²×D₄	—	5	1	no	—
543	C₂²×D₄	—	5	1	no	—
544	C₂²×D₄	—	5	1	no	—
545	C₂³×C₄	—	5	1	no	—
546	C₂³×C₄	—	5	1	no	—
547	C₂³×C₄	—	5	1	no	—
548	C₂³×C₄	—	5	1	no	—
549	C₂³×C₄	—	5	1	no	—
550	#126	—	5	8	no	—
551	#126	C₂×C₃×D₅	1	8	yes	complemented
552	#124	—	5	8	no	—
553	#123	—	5	8	no	—
554	#123	—	5	8	no	—
555	#123	—	5	8	no	—
556	C₂²⋊Q₈	—	5	8	no	—
557	C₂²⋊Q₈	—	5	8	no	—
558	#120	—	5	8	no	—
559	C₄×D₄	—	5	8	no	—
560	C₄×D₄	—	5	8	no	—
561	#117	—	5	8	no	—
562	#117	—	5	8	no	—
563	C₂×C₄⋊C₄	—	5	1	no	—
564	C₂×C₄⋊C₄	—	5	1	no	—
565	C₂×C₄⋊C₄	—	5	1	no	—
566	C₂×C₄⋊C₄	—	5	1	no	—
567	C₂×C₄⋊C₄	—	5	1	no	—
568	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
569	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
570	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
571	C₂×C₂²⋊C₄	—	5	1	no	—
572	C₂×C₂²⋊C₄	—	5	1	no	—
573	C₂×C₂²⋊C₄	—	5	1	no	—
574	C₂×C₂²⋊C₄	—	5	1	no	—
575	C₂×C₂²⋊C₄	—	5	1	no	—
576	C₂×C₂²⋊C₄	—	5	1	no	—
577	C₂×C₂²⋊C₄	—	5	1	no	—
578	C₂×C₂²⋊C₄	—	5	1	no	—
579	C₂×C₂²⋊C₄	—	5	1	no	—
580	C₂×C₂²⋊C₄	—	5	1	no	—
581	C₂×C₂²⋊C₄	—	5	1	no	—
582	C₂×C₂²⋊C₄	—	5	8	no	—
583	C₂×C₂²⋊C₄	—	5	8	no	—
584	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
585	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
586	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
587	C₂×C₄²	—	5	1	no	—
588	C₂×C₄²	—	5	1	no	—
589	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic, complemented
590	C₂×C₃×C₅	—	4	2	no	—
591	C₂×C₃×C₅	#551	1	4	yes	complemented
592	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
593	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
594	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
595	C₃×D₅	—	2	4	no	—
596	C₃×D₅	—	2	4	no	—
597	C₃×D₅	—	4	2	no	—
598	C₂³×C₃	—	2	2	no	—
599	C₂³×C₃	—	2	2	no	—
600	C₂³×C₃	—	2	2	no	—
601	C₂³×C₃	—	5	4	no	—
602	C₂³×C₃	—	5	4	no	—
603	C₂³×C₃	—	5	2	no	—
604	C₂³×C₃	—	5	2	no	—
605	C₂³×C₃	—	5	2	no	—
606	C₂³×C₃	—	10	8	no	—
607	C₂³×C₃	—	10	8	no	—
608	C₂³×C₃	—	10	2	no	—
609	C₂³×C₃	—	10	2	no	—
610	C₂³×C₃	—	10	2	no	—
611	C₂³×C₃	—	10	2	no	—
612	C₂³×C₃	—	10	2	no	—
613	C₂³×C₃	—	10	2	no	—
614	C₂³×C₃	—	10	2	no	—
615	C₂³×C₃	—	20	4	no	—
616	C₂³×C₃	—	20	16	no	—
617	C₂³×C₃	C₂³×D₅	1	2	yes	—
618	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
619	C₃×Q₈	—	20	4	no	—
620	C₃×D₄	—	10	8	no	—
621	C₃×D₄	—	10	8	no	—
622	C₃×D₄	—	20	4	no	—
623	C₂×C₃×C₄	—	2	2	no	—
624	C₂×C₃×C₄	—	2	2	no	—
625	C₂×C₃×C₄	—	2	2	no	—
626	C₂×C₃×C₄	—	2	2	no	—
627	C₂×C₃×C₄	—	2	2	no	—
628	C₂×C₃×C₄	—	2	2	no	—
629	C₂×C₃×C₄	—	5	2	no	—
630	C₂×C₃×C₄	—	5	2	no	—
631	C₂×C₃×C₄	—	5	2	no	—
632	C₂×C₃×C₄	—	5	2	no	—
633	C₂×C₃×C₄	—	5	2	no	—
634	C₂×C₃×C₄	—	10	8	no	—
635	C₂×C₃×C₄	—	10	8	no	—
636	C₂×C₃×C₄	—	10	2	no	—
637	C₂×C₃×C₄	—	10	2	no	—
638	C₂×C₃×C₄	—	10	2	no	—
639	C₂×C₃×C₄	—	10	2	no	—
640	C₂×C₃×C₄	—	10	2	no	—
641	C₂×C₃×C₄	—	20	4	no	—
642	C₂×C₃×C₄	—	20	4	no	—
643	C₂×C₃×C₄	—	20	4	no	—
644	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
645	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
646	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
647	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
648	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
649	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
650	C₂²×C₅	—	2	2	no	—
651	C₂²×C₅	—	2	2	no	—
652	C₂²×C₅	—	2	2	no	—
653	C₂²×C₅	—	4	4	no	—
654	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
655	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
656	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
657	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
658	C₂×D₅	—	2	2	no	—
659	C₂×D₅	—	2	2	no	—
660	C₂×D₅	—	2	2	no	—
661	C₂×D₅	—	2	2	no	—
662	C₂×D₅	—	2	8	no	—
663	C₂×D₅	—	2	8	no	—
664	C₂×D₅	—	2	2	no	—
665	C₂×D₅	—	2	2	no	—
666	C₂×D₅	—	2	2	no	—
667	C₂×D₅	—	4	16	no	—
668	C₂×D₅	—	4	4	no	—
669	C₂×D₅	C₂×C₃×#41	1	4	yes	—
670	C₂×D₅	C₂×C₃×#41	1	4	yes	—
671	C₄×C₅	—	2	2	no	—
672	C₄×C₅	—	2	2	no	—
673	C₄×C₅	—	2	2	no	—
674	C₄×C₅	—	2	2	no	—
675	C₄×C₅	—	2	2	no	—
676	C₄×C₅	—	2	2	no	—
677	Dic₅	—	2	2	no	—
678	Dic₅	—	2	2	no	—
679	Dic₅	—	2	2	no	—
680	Dic₅	—	2	2	no	—
681	Dic₅	—	2	2	no	—
682	C₂⁴	—	5	1	no	—
683	C₂⁴	—	5	1	no	—
684	C₂⁴	—	5	1	no	—
685	C₂⁴	—	5	4	no	—
686	C₂⁴	—	10	4	no	—
687	C₂⁴	—	10	4	no	—
688	C₂⁴	—	20	2	no	—
689	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
690	C₂×Q₈	—	5	4	no	—
691	C₂×Q₈	—	20	2	no	—
692	C₂×D₄	—	5	4	no	—
693	C₂×D₄	—	5	4	no	—
694	C₂×D₄	—	5	4	no	—
695	C₂×D₄	—	10	4	no	—
696	C₂×D₄	—	10	4	no	—
697	C₂×D₄	—	20	2	no	—
698	C₂²×C₄	—	5	1	no	—
699	C₂²×C₄	—	5	1	no	—
700	C₂²×C₄	—	5	1	no	—
701	C₂²×C₄	—	5	1	no	—
702	C₂²×C₄	—	5	1	no	—
703	C₂²×C₄	—	5	4	no	—
704	C₂²×C₄	—	5	4	no	—
705	C₂²×C₄	—	5	4	no	—
706	C₂²×C₄	—	5	4	no	—
707	C₂²×C₄	—	5	4	no	—
708	C₂²×C₄	—	10	4	no	—
709	C₂²×C₄	—	10	4	no	—
710	C₂²×C₄	—	20	2	no	—
711	C₂²×C₄	—	20	2	no	—
712	C₂²×C₄	—	20	2	no	—
713	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
714	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
715	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
716	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
717	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
718	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
719	C₄⋊C₄	—	5	4	no	—
720	C₄⋊C₄	—	5	4	no	—
721	C₄⋊C₄	—	5	4	no	—
722	C₄⋊C₄	—	5	4	no	—
723	C₄⋊C₄	—	5	4	no	—
724	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	complemented
725	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	complemented
726	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	complemented
727	C₂²⋊C₄	—	5	4	no	—
728	C₂²⋊C₄	—	5	4	no	—
729	C₂²⋊C₄	—	5	4	no	—
730	C₂²⋊C₄	—	5	4	no	—
731	C₂²⋊C₄	—	5	4	no	—
732	C₂²⋊C₄	—	5	4	no	—
733	C₂²⋊C₄	—	5	4	no	—
734	C₂²⋊C₄	—	5	4	no	—
735	C₂²⋊C₄	—	5	4	no	—
736	C₂²⋊C₄	—	5	4	no	—
737	C₂²⋊C₄	—	5	4	no	—
738	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
739	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
740	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
741	C₄²	—	5	4	no	—
742	C₄²	—	5	4	no	—
743	C₄²	C₂²×C₃×D₅	1	4	yes	complemented
744	C₃×C₅	C₂×#551	1	1	yes	characteristic, complemented, Hall
745	C₂²×C₃	—	2	2	no	—
746	C₂²×C₃	—	2	2	no	—
747	C₂²×C₃	—	2	2	no	—
748	C₂²×C₃	—	4	4	no	—
749	C₂²×C₃	—	5	4	no	—
750	C₂²×C₃	—	5	4	no	—
751	C₂²×C₃	—	10	2	no	—
752	C₂²×C₃	—	10	2	no	—
753	C₂²×C₃	—	10	2	no	—
754	C₂²×C₃	—	10	2	no	—
755	C₂²×C₃	—	10	8	no	—
756	C₂²×C₃	—	10	8	no	—
757	C₂²×C₃	—	10	2	no	—
758	C₂²×C₃	—	10	2	no	—
759	C₂²×C₃	—	10	2	no	—
760	C₂²×C₃	—	20	16	no	—
761	C₂²×C₃	—	20	4	no	—
762	C₂²×C₃	D₅×#41	1	2	yes	—
763	C₂²×C₃	D₅×#41	1	2	yes	—
764	C₂²×C₃	#4149	1	2	yes	—
765	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
766	C₃×C₄	—	2	2	no	—
767	C₃×C₄	—	2	2	no	—
768	C₃×C₄	—	2	2	no	—
769	C₃×C₄	—	2	2	no	—
770	C₃×C₄	—	2	2	no	—
771	C₃×C₄	—	2	2	no	—
772	C₃×C₄	—	10	2	no	—
773	C₃×C₄	—	10	2	no	—
774	C₃×C₄	—	10	2	no	—
775	C₃×C₄	—	10	2	no	—
776	C₃×C₄	—	10	2	no	—
777	C₂×C₅	—	4	2	no	—
778	C₂×C₅	C₃×#551	1	4	yes	complemented
779	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
780	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
781	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
782	D₅	—	2	4	no	—
783	D₅	—	2	4	no	—
784	D₅	—	4	2	no	—
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	5	4	no	—
789	C₂³	—	5	4	no	—
790	C₂³	—	5	2	no	—
791	C₂³	—	5	2	no	—
792	C₂³	—	5	2	no	—
793	C₂³	—	10	8	no	—
794	C₂³	—	10	8	no	—
795	C₂³	—	10	2	no	—
796	C₂³	—	10	2	no	—
797	C₂³	—	10	2	no	—
798	C₂³	—	10	2	no	—
799	C₂³	—	10	2	no	—
800	C₂³	—	10	2	no	—
801	C₂³	—	10	2	no	—
802	C₂³	—	20	4	no	—
803	C₂³	—	20	16	no	—
804	C₂³	C₂³×C₃×D₅	1	2	yes	—
805	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
806	Q₈	—	20	4	no	—
807	D₄	—	10	8	no	—
808	D₄	—	10	8	no	—
809	D₄	—	20	4	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	5	2	no	—
817	C₂×C₄	—	5	2	no	—
818	C₂×C₄	—	5	2	no	—
819	C₂×C₄	—	5	2	no	—
820	C₂×C₄	—	5	2	no	—
821	C₂×C₄	—	10	8	no	—
822	C₂×C₄	—	10	8	no	—
823	C₂×C₄	—	10	2	no	—
824	C₂×C₄	—	10	2	no	—
825	C₂×C₄	—	10	2	no	—
826	C₂×C₄	—	10	2	no	—
827	C₂×C₄	—	10	2	no	—
828	C₂×C₄	—	20	4	no	—
829	C₂×C₄	—	20	4	no	—
830	C₂×C₄	—	20	4	no	—
831	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
832	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
833	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
834	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
835	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
836	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
837	C₂×C₃	—	4	2	no	—
838	C₂×C₃	—	10	4	no	—
839	C₂×C₃	—	10	4	no	—
840	C₂×C₃	—	20	2	no	—
841	C₂×C₃	#66039	1	4	yes	direct product factor
842	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
843	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
844	C₂×C₃	C₂×#4149	1	1	yes	characteristic
845	C₅	C₂×C₃×#551	1	1	yes	characteristic, complemented, Sylow
846	C₂²	—	2	2	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	4	4	no	—
850	C₂²	—	5	4	no	—
851	C₂²	—	5	4	no	—
852	C₂²	—	10	2	no	—
853	C₂²	—	10	2	no	—
854	C₂²	—	10	2	no	—
855	C₂²	—	10	2	no	—
856	C₂²	—	10	8	no	—
857	C₂²	—	10	8	no	—
858	C₂²	—	10	2	no	—
859	C₂²	—	10	2	no	—
860	C₂²	—	10	2	no	—
861	C₂²	—	20	16	no	—
862	C₂²	—	20	4	no	—
863	C₂²	C₃×D₅×#41	1	2	yes	—
864	C₂²	C₃×D₅×#41	1	2	yes	—
865	C₂²	C₃×#4149	1	2	yes	—
866	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
867	C₄	—	2	2	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	2	no	—
870	C₄	—	2	2	no	—
871	C₄	—	2	2	no	—
872	C₄	—	2	2	no	—
873	C₄	—	10	2	no	—
874	C₄	—	10	2	no	—
875	C₄	—	10	2	no	—
876	C₄	—	10	2	no	—
877	C₄	—	10	2	no	—
878	C₃	C₂×#66039	1	1	yes	characteristic, direct product factor, Sylow
879	C₂	—	4	2	no	—
880	C₂	—	10	4	no	—
881	C₂	—	10	4	no	—
882	C₂	—	20	2	no	—
883	C₂	C₃×#66039	1	4	yes	direct product factor
884	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
885	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
886	C₂	C₂×C₃×#4149	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₅×#126	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₃×#4028	C₂
hypercenter	C₂×C₃×#126	D₅
hypocenter	C₅	C₂×C₃×#551
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#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. C₃×#66039	C₂	direct (N × H)
3. C₂×C₃×#4043	C₂	semidirect
4. C₂×C₃×#4042	C₂	semidirect
5. C₂×C₃×#4040	C₂	semidirect
6. C₂×C₃×#4040	C₂	semidirect
7. C₂×C₃×#4039	C₂	semidirect
8. C₂×C₃×#4038	C₂	semidirect
9. C₂×C₃×#4031	C₂	semidirect
10. C₂×C₃×#4029	C₂	semidirect
12. C₂×C₃×D₅×C₂²⋊C₄	C₂	semidirect
13. C₂×C₃×D₅×C₂²⋊C₄	C₂	semidirect
14. C₂×C₃×#4025	C₂	semidirect
15. C₂×C₃×C₄×D₂₀	C₂	semidirect
16. C₂×C₃×#4018	C₂	semidirect
17. C₂×#66039	C₃	direct (N × H)
26. C₂²×C₃×C₄×D₅	C₂²	semidirect
27. C₂²×C₃×Dic₁₀	C₂²	semidirect
28. C₃×C₅×#126	C₂²	semidirect
29. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
30. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
31. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
35. C₂×C₃×C₄²×C₅	C₂²	semidirect
44. C₂×C₃×#685	C₂²	semidirect
45. C₂×C₃×#685	C₂²	semidirect
46. C₂×C₃×#685	C₂²	semidirect
47. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
48. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
49. C₂×C₃×#683	C₂²	semidirect
50. C₂×C₃×#683	C₂²	semidirect
51. C₂×C₃×#683	C₂²	semidirect
52. C₂×C₃×C₄×Dic₅	C₂²	semidirect
53. C₂×C₃×C₄×Dic₅	C₂²	semidirect
54. C₃×#4043	C₂²	semidirect
55. C₃×#4042	C₂²	semidirect
56. C₃×#4040	C₂²	semidirect
57. C₃×#4040	C₂²	semidirect
58. C₃×#4039	C₂²	semidirect
59. C₃×#4038	C₂²	semidirect
60. C₃×#4031	C₂²	semidirect
61. C₃×#4029	C₂²	semidirect
63. C₃×D₅×C₂²⋊C₄	C₂²	semidirect
64. C₃×D₅×C₂²⋊C₄	C₂²	semidirect
65. C₃×#4025	C₂²	semidirect
66. C₃×C₄×D₂₀	C₂²	semidirect
67. C₃×#4018	C₂²	semidirect
69. C₂×C₅×#126	C₂×C₃	semidirect
70. #66039	C₂×C₃	direct (N × H)
71. C₂×#4043	C₂×C₃	semidirect
72. C₂×#4042	C₂×C₃	semidirect
73. C₂×#4040	C₂×C₃	semidirect
74. C₂×#4040	C₂×C₃	semidirect
75. C₂×#4039	C₂×C₃	semidirect
76. C₂×#4038	C₂×C₃	semidirect
77. C₂×#4031	C₂×C₃	semidirect
78. C₂×#4029	C₂×C₃	semidirect
80. C₂×D₅×C₂²⋊C₄	C₂×C₃	semidirect
81. C₂×D₅×C₂²⋊C₄	C₂×C₃	semidirect
82. C₂×#4025	C₂×C₃	semidirect
83. C₂×C₄×D₂₀	C₂×C₃	semidirect
84. C₂×#4018	C₂×C₃	semidirect
119. C₂×C₃×C₄×D₅	C₂³	semidirect
121. C₂×C₃×Dic₁₀	C₂³	semidirect
122. C₃×C₅×C₄⋊C₄	C₂³	semidirect
123. C₃×C₅×C₄⋊C₄	C₂³	semidirect
124. C₃×C₅×C₄⋊C₄	C₂³	semidirect
128. C₃×C₄²×C₅	C₂³	semidirect
137. C₃×#685	C₂³	semidirect
138. C₃×#685	C₂³	semidirect
139. C₃×#685	C₂³	semidirect
140. C₃×C₄⋊Dic₅	C₂³	semidirect
141. C₃×C₄⋊Dic₅	C₂³	semidirect
142. C₃×#683	C₂³	semidirect
143. C₃×#683	C₂³	semidirect
144. C₃×#683	C₂³	semidirect
145. C₃×C₄×Dic₅	C₂³	semidirect
146. C₃×C₄×Dic₅	C₂³	semidirect
149. C₂×C₃×#126	D₅	semidirect
171. C₂²×C₄×D₅	C₂²×C₃	semidirect
172. C₂²×Dic₁₀	C₂²×C₃	semidirect
173. C₅×#126	C₂²×C₃	semidirect
174. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
175. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
176. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
180. C₂×C₄²×C₅	C₂²×C₃	semidirect
189. C₂×#685	C₂²×C₃	semidirect
190. C₂×#685	C₂²×C₃	semidirect
191. C₂×#685	C₂²×C₃	semidirect
192. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
193. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
194. C₂×#683	C₂²×C₃	semidirect
195. C₂×#683	C₂²×C₃	semidirect
196. C₂×#683	C₂²×C₃	semidirect
197. C₂×C₄×Dic₅	C₂²×C₃	semidirect
198. C₂×C₄×Dic₅	C₂²×C₃	semidirect
199. #4043	C₂²×C₃	semidirect
200. #4042	C₂²×C₃	semidirect
201. #4040	C₂²×C₃	semidirect
202. #4040	C₂²×C₃	semidirect
203. #4039	C₂²×C₃	semidirect
204. #4038	C₂²×C₃	semidirect
205. #4031	C₂²×C₃	semidirect
206. #4029	C₂²×C₃	semidirect
208. D₅×C₂²⋊C₄	C₂²×C₃	semidirect
209. D₅×C₂²⋊C₄	C₂²×C₃	semidirect
210. #4025	C₂²×C₃	semidirect
211. C₄×D₂₀	C₂²×C₃	semidirect
212. #4018	C₂²×C₃	semidirect
277. C₃×#126	C₂×D₅	semidirect
294. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
295. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
296. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
315. C₂×C₃×C₄²	C₂×D₅	semidirect
350. C₂×C₄×D₅	C₂³×C₃	semidirect
352. C₂×Dic₁₀	C₂³×C₃	semidirect
353. C₅×C₄⋊C₄	C₂³×C₃	semidirect
354. C₅×C₄⋊C₄	C₂³×C₃	semidirect
355. C₅×C₄⋊C₄	C₂³×C₃	semidirect
359. C₄²×C₅	C₂³×C₃	semidirect
368. #685	C₂³×C₃	semidirect
369. #685	C₂³×C₃	semidirect
370. #685	C₂³×C₃	semidirect
371. C₄⋊Dic₅	C₂³×C₃	semidirect
372. C₄⋊Dic₅	C₂³×C₃	semidirect
373. #683	C₂³×C₃	semidirect
374. #683	C₂³×C₃	semidirect
375. #683	C₂³×C₃	semidirect
376. C₄×Dic₅	C₂³×C₃	semidirect
377. C₄×Dic₅	C₂³×C₃	semidirect
380. C₂×#126	C₃×D₅	semidirect
468. C₃×C₄⋊C₄	C₂²×D₅	semidirect
469. C₃×C₄⋊C₄	C₂²×D₅	semidirect
470. C₃×C₄⋊C₄	C₂²×D₅	semidirect
487. C₃×C₄²	C₂²×D₅	semidirect
551. #126	C₂×C₃×D₅	semidirect
568. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
569. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
570. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
589. C₂×C₄²	C₂×C₃×D₅	semidirect
591. C₂×C₃×C₅	#551	semidirect
724. C₄⋊C₄	C₂²×C₃×D₅	semidirect
725. C₄⋊C₄	C₂²×C₃×D₅	semidirect
726. C₄⋊C₄	C₂²×C₃×D₅	semidirect
743. C₄²	C₂²×C₃×D₅	semidirect
744. C₃×C₅	C₂×#551	semidirect
778. C₂×C₅	C₃×#551	semidirect
841. C₂×C₃	#66039	direct (N × H)
845. C₅	C₂×C₃×#551	semidirect
878. C₃	C₂×#66039	direct (N × H)
883. C₂	C₃×#66039	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
C₃×#66039	2
C₂×C₃×#4043	2
C₂×C₃×#4042	2
C₂×C₃×#4040	2
C₂×C₃×#4039	2
C₂×C₃×#4038	2
C₂×C₃×#4031	2
C₂×C₃×#4029	2
C₂×C₃×#4028	2
C₂×C₃×D₅×C₂²⋊C₄	2
C₂×C₃×#4025	2
C₂×C₃×C₄×D₂₀	2
C₂×C₃×#4018	2
C₂×#66039	3
C₂×C₃×#551	5

Subgroups — C2×C3×#66039 #14483239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66039 #14483239