Subgroups — C₂×C₃×D₄×C₂²⋊D₅ #14482407

Order 1920.

5072 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4099	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#4086	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#4085	C₂	1	2	yes	maximal, complemented
7	C₃×D₄×C₂²⋊D₅	C₂	1	16	yes	maximal, direct product factor
8	C₂×C₃×#4084	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#4083	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×D₄×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#4076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×C₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×D₄×C₂²⋊D₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂⁵×C₃×C₅	C₂²	1	2	yes	complemented
15	C₂⁴×C₃×D₅	C₂²	1	2	yes	complemented
16	C₂²×C₃×C₅×D₄	—	2	8	no	—
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
19	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃×C₅×D₄	C₂²	1	8	yes	complemented
21	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₃×C₂²⋊D₅	—	2	16	no	—
23	C₂²×C₃×C₂²⋊D₅	C₂²	1	1	yes	characteristic
24	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
25	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
26	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
27	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
28	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
29	C₂²×C₃×C₂²⋊D₅	C₂²	1	16	yes	complemented
30	C₂³×C₃×Dic₅	C₂²	1	2	yes	complemented
31	C₂×C₃×D₄×D₅	—	2	8	no	—
32	C₂×C₃×D₄×D₅	C₂²	1	8	yes	complemented
33	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
35	C₃×#4099	C₂²	1	16	yes	complemented
36	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
38	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	complemented
39	C₃×#4086	C₂²	1	8	yes	complemented
40	C₃×#4085	C₂²	1	16	yes	complemented
41	C₃×#4084	C₂²	1	8	yes	complemented
42	C₃×#4083	C₂²	1	16	yes	complemented
43	C₃×D₄×Dic₅	C₂²	1	8	yes	complemented
44	C₃×#4076	C₂²	1	8	yes	complemented
45	C₃×C₄×C₂²⋊D₅	C₂²	1	8	yes	complemented
46	C₂×C₃×#685	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₃×#685	C₂²	1	2	yes	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×C₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₃×D₄²	—	5	1	no	maximal, Hall
52	C₂³×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂³×C₂²⋊D₅	C₂×C₃	1	2	yes	complemented
54	C₂²×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×#4099	C₂×C₃	1	2	yes	complemented
56	C₂×#4086	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂×#4085	C₂×C₃	1	2	yes	complemented
58	D₄×C₂²⋊D₅	C₂×C₃	1	16	yes	direct product factor
59	C₂×#4084	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂×#4083	C₂×C₃	1	2	yes	complemented
61	C₂×D₄×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
62	C₂×#4076	C₂×C₃	1	1	yes	characteristic, complemented
63	C₂×C₄×C₂²⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂⁴×C₃×C₅	—	2	8	no	—
65	C₂⁴×C₃×C₅	—	2	8	no	—
66	C₂⁴×C₃×C₅	—	4	4	no	—
67	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
68	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
69	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
70	C₂⁴×C₃×C₅	C₂³	1	8	yes	complemented
71	C₂³×C₃×D₅	—	2	8	no	—
72	C₂³×C₃×D₅	—	2	8	no	—
73	C₂³×C₃×D₅	—	4	4	no	—
74	C₂³×C₃×D₅	C₂³	1	2	yes	—
75	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
76	C₂³×C₃×D₅	C₂³	1	8	yes	complemented
77	C₂×C₃×C₅×D₄	—	2	8	no	—
78	C₂×C₃×C₅×D₄	—	2	32	no	—
79	C₂×C₃×C₅×D₄	—	2	4	no	—
80	C₂×C₃×C₅×D₄	D₄	1	8	yes	complemented
81	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
82	C₂×C₃×C₅×D₄	C₂³	1	8	yes	complemented
83	C₂×C₃×C₅×D₄	C₂³	1	4	yes	complemented
84	C₂²×C₃×C₄×C₅	—	2	4	no	—
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	4	yes	complemented
88	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
89	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
90	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
91	C₂×C₃×C₂²⋊D₅	—	2	64	no	—
92	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
93	C₂×C₃×C₂²⋊D₅	—	4	4	no	—
94	C₂×C₃×C₂²⋊D₅	D₄	1	8	yes	direct product factor
95	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
96	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	complemented
97	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	complemented
98	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	complemented
99	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	complemented
100	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	complemented
101	C₂²×C₃×Dic₅	—	2	8	no	—
102	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
103	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
104	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
105	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
106	C₂²×C₃×Dic₅	C₂³	1	8	yes	complemented
107	C₃×D₄×D₅	—	2	32	no	—
108	C₂×C₃×D₂₀	—	2	4	no	—
109	C₂×C₃×D₂₀	C₂³	1	4	yes	complemented
110	C₂×C₃×C₄×D₅	—	2	4	no	—
111	C₂×C₃×C₄×D₅	C₂³	1	4	yes	complemented
112	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	complemented
113	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	complemented
114	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	complemented
115	C₃×#685	C₂³	1	4	yes	complemented
116	C₃×#685	C₂³	1	8	yes	complemented
117	C₃×C₄⋊Dic₅	C₂³	1	4	yes	complemented
118	C₃×#683	C₂³	1	4	yes	complemented
119	C₃×C₄×Dic₅	C₂³	1	4	yes	complemented
120	C₂³×C₃×D₄	—	5	1	no	—
121	C₂³×C₃×D₄	—	5	2	no	—
122	C₂³×C₃×D₄	D₅	1	1	yes	characteristic, complemented
123	C₃×D₄²	—	5	16	no	—
124	C₂×C₃×#127	—	5	1	no	—
125	C₂×C₃×#121	—	5	1	no	—
126	C₂×C₃×#121	—	5	2	no	—
127	C₂×C₃×#121	—	5	1	no	—
128	C₂×C₃×#120	—	5	2	no	—
129	C₂×C₃×#120	—	5	2	no	—
130	C₂×C₃×C₄×D₄	—	5	1	no	—
131	C₂×C₃×C₄×D₄	—	5	1	no	—
132	C₂⁵×C₅	C₂²×C₃	1	2	yes	complemented
133	C₂⁴×D₅	C₂²×C₃	1	2	yes	complemented
134	C₂²×C₅×D₄	—	2	8	no	—
135	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
136	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	complemented
137	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
138	C₂²×C₅×D₄	C₂²×C₃	1	8	yes	complemented
139	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
140	C₂²×C₂²⋊D₅	—	2	16	no	—
141	C₂²×C₂²⋊D₅	C₂²×C₃	1	1	yes	characteristic
142	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
143	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
144	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
145	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
146	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
147	C₂²×C₂²⋊D₅	C₂²×C₃	1	16	yes	complemented
148	C₂³×Dic₅	C₂²×C₃	1	2	yes	complemented
149	C₂×D₄×D₅	—	2	8	no	—
150	C₂×D₄×D₅	C₂²×C₃	1	8	yes	complemented
151	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
152	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
153	#4099	C₂²×C₃	1	16	yes	complemented
154	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
155	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	complemented
156	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	complemented
157	#4086	C₂²×C₃	1	8	yes	complemented
158	#4085	C₂²×C₃	1	16	yes	complemented
159	#4084	C₂²×C₃	1	8	yes	complemented
160	#4083	C₂²×C₃	1	16	yes	complemented
161	D₄×Dic₅	C₂²×C₃	1	8	yes	complemented
162	#4076	C₂²×C₃	1	8	yes	complemented
163	C₄×C₂²⋊D₅	C₂²×C₃	1	8	yes	complemented
164	C₂×#685	C₂²×C₃	1	1	yes	characteristic, complemented
165	C₂×#685	C₂²×C₃	1	2	yes	complemented
166	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
167	C₂×#683	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₂×D₄²	—	5	1	no	Sylow
170	C₂³×C₃×C₅	—	2	4	no	—
171	C₂³×C₃×C₅	—	2	2	no	—
172	C₂³×C₃×C₅	—	2	4	no	—
173	C₂³×C₃×C₅	—	2	2	no	—
174	C₂³×C₃×C₅	—	2	4	no	—
175	C₂³×C₃×C₅	—	2	4	no	—
176	C₂³×C₃×C₅	—	2	16	no	—
177	C₂³×C₃×C₅	—	2	16	no	—
178	C₂³×C₃×C₅	—	2	4	no	—
179	C₂³×C₃×C₅	—	4	8	no	—
180	C₂³×C₃×C₅	—	4	32	no	—
181	C₂³×C₃×C₅	C₂×D₄	1	4	yes	complemented
182	C₂³×C₃×C₅	C₂×D₄	1	8	yes	complemented
183	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
184	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
185	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
186	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
187	C₂²×C₃×D₅	—	2	2	no	—
188	C₂²×C₃×D₅	—	2	2	no	—
189	C₂²×C₃×D₅	—	2	4	no	—
190	C₂²×C₃×D₅	—	2	4	no	—
191	C₂²×C₃×D₅	—	2	16	no	—
192	C₂²×C₃×D₅	—	2	4	no	—
193	C₂²×C₃×D₅	—	2	16	no	—
194	C₂²×C₃×D₅	—	4	8	no	—
195	C₂²×C₃×D₅	—	4	32	no	—
196	C₂²×C₃×D₅	C₂×D₄	1	4	yes	complemented
197	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
198	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
199	C₃×C₅×D₄	—	2	16	no	—
200	C₃×C₅×D₄	—	2	8	no	—
201	C₃×C₅×D₄	C₂×D₄	1	16	yes	complemented
202	C₂×C₃×C₄×C₅	—	2	2	no	—
203	C₂×C₃×C₄×C₅	—	2	8	no	—
204	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	complemented
205	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
206	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
207	C₃×C₂²⋊D₅	—	2	16	no	—
208	C₃×C₂²⋊D₅	—	2	16	no	—
209	C₃×C₂²⋊D₅	—	2	16	no	—
210	C₃×C₂²⋊D₅	—	2	16	no	—
211	C₃×C₂²⋊D₅	—	4	8	no	—
212	C₃×C₂²⋊D₅	C₂×D₄	1	16	yes	direct product factor
213	C₂×C₃×Dic₅	—	2	2	no	—
214	C₂×C₃×Dic₅	—	2	4	no	—
215	C₂×C₃×Dic₅	—	2	2	no	—
216	C₂×C₃×Dic₅	—	2	16	no	—
217	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	complemented
218	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
219	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
220	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
221	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
222	C₃×D₂₀	—	2	8	no	—
223	C₃×C₄×D₅	—	2	8	no	—
224	C₂⁵×C₃	—	5	2	no	—
225	C₂⁵×C₃	C₂×D₅	1	2	yes	complemented
226	C₂²×C₃×D₄	—	2	8	no	—
227	C₂²×C₃×D₄	—	5	1	no	—
228	C₂²×C₃×D₄	—	5	2	no	—
229	C₂²×C₃×D₄	—	5	2	no	—
230	C₂²×C₃×D₄	—	5	2	no	—
231	C₂²×C₃×D₄	—	5	2	no	—
232	C₂²×C₃×D₄	—	5	16	no	—
233	C₂²×C₃×D₄	—	5	2	no	—
234	C₂²×C₃×D₄	—	5	8	no	—
235	C₂²×C₃×D₄	—	5	1	no	—
236	C₂²×C₃×D₄	—	10	16	no	—
237	C₂²×C₃×D₄	—	10	8	no	—
238	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
239	C₂²×C₃×D₄	C₂×D₅	1	2	yes	complemented
240	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic, complemented
241	C₂²×C₃×D₄	C₂×D₅	1	8	yes	complemented
242	C₂³×C₃×C₄	—	5	2	no	—
243	C₂³×C₃×C₄	—	5	1	no	—
244	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic, complemented
245	C₃×#127	—	5	8	no	—
246	C₃×#121	—	5	8	no	—
247	C₃×#121	—	5	16	no	—
248	C₃×#121	—	5	8	no	—
249	C₃×#120	—	5	16	no	—
250	C₃×#120	—	5	16	no	—
251	C₃×C₄×D₄	—	5	8	no	—
252	C₃×C₄×D₄	—	5	8	no	—
253	C₂×C₃×C₄⋊C₄	—	5	1	no	—
254	C₂×C₃×C₄⋊C₄	—	5	1	no	—
255	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
256	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
257	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
258	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
259	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
260	C₂×C₃×C₄²	—	5	1	no	—
261	C₂⁴×C₅	—	2	8	no	—
262	C₂⁴×C₅	—	2	8	no	—
263	C₂⁴×C₅	—	4	4	no	—
264	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
265	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
266	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
267	C₂⁴×C₅	C₂³×C₃	1	8	yes	complemented
268	C₂³×D₅	—	2	8	no	—
269	C₂³×D₅	—	2	8	no	—
270	C₂³×D₅	—	4	4	no	—
271	C₂³×D₅	C₂³×C₃	1	2	yes	—
272	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
273	C₂³×D₅	C₂³×C₃	1	8	yes	complemented
274	C₂×C₅×D₄	—	2	8	no	—
275	C₂×C₅×D₄	—	2	32	no	—
276	C₂×C₅×D₄	—	2	4	no	—
277	C₂×C₅×D₄	C₃×D₄	1	8	yes	complemented
278	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
279	C₂×C₅×D₄	C₂³×C₃	1	8	yes	complemented
280	C₂×C₅×D₄	C₂³×C₃	1	4	yes	complemented
281	C₂²×C₄×C₅	—	2	4	no	—
282	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
283	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
284	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	complemented
285	C₂×C₂²⋊D₅	—	2	8	no	—
286	C₂×C₂²⋊D₅	—	2	8	no	—
287	C₂×C₂²⋊D₅	—	2	8	no	—
288	C₂×C₂²⋊D₅	—	2	64	no	—
289	C₂×C₂²⋊D₅	—	2	8	no	—
290	C₂×C₂²⋊D₅	—	4	4	no	—
291	C₂×C₂²⋊D₅	C₃×D₄	1	8	yes	direct product factor
292	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
293	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	complemented
294	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	complemented
295	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	complemented
296	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	complemented
297	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	complemented
298	C₂²×Dic₅	—	2	8	no	—
299	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
300	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
301	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
302	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
303	C₂²×Dic₅	C₂³×C₃	1	8	yes	complemented
304	D₄×D₅	—	2	32	no	—
305	C₂×D₂₀	—	2	4	no	—
306	C₂×D₂₀	C₂³×C₃	1	4	yes	complemented
307	C₂×C₄×D₅	—	2	4	no	—
308	C₂×C₄×D₅	C₂³×C₃	1	4	yes	complemented
309	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	complemented
310	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	complemented
311	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	complemented
312	#685	C₂³×C₃	1	4	yes	complemented
313	#685	C₂³×C₃	1	8	yes	complemented
314	C₄⋊Dic₅	C₂³×C₃	1	4	yes	complemented
315	#683	C₂³×C₃	1	4	yes	complemented
316	C₄×Dic₅	C₂³×C₃	1	4	yes	complemented
317	C₂³×D₄	—	5	2	no	—
318	C₂³×D₄	—	5	1	no	—
319	C₂³×D₄	C₃×D₅	1	1	yes	characteristic, complemented
320	D₄²	—	5	16	no	—
321	C₂×#127	—	5	1	no	—
322	C₂×#121	—	5	1	no	—
323	C₂×#121	—	5	2	no	—
324	C₂×#121	—	5	1	no	—
325	C₂×#120	—	5	2	no	—
326	C₂×#120	—	5	2	no	—
327	C₂×C₄×D₄	—	5	1	no	—
328	C₂×C₄×D₄	—	5	1	no	—
329	C₂²×C₃×C₅	—	2	16	no	—
330	C₂²×C₃×C₅	—	2	8	no	—
331	C₂²×C₃×C₅	—	2	4	no	—
332	C₂²×C₃×C₅	—	2	2	no	—
333	C₂²×C₃×C₅	—	2	4	no	—
334	C₂²×C₃×C₅	—	2	2	no	—
335	C₂²×C₃×C₅	—	2	4	no	—
336	C₂²×C₃×C₅	—	2	4	no	—
337	C₂²×C₃×C₅	—	2	4	no	—
338	C₂²×C₃×C₅	—	4	32	no	—
339	C₂²×C₃×C₅	—	4	8	no	—
340	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
341	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
342	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	complemented
343	C₂²×C₃×C₅	C₂²×D₄	1	8	yes	complemented
344	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
345	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
346	C₂×C₃×D₅	—	2	8	no	—
347	C₂×C₃×D₅	—	2	2	no	—
348	C₂×C₃×D₅	—	2	2	no	—
349	C₂×C₃×D₅	—	2	4	no	—
350	C₂×C₃×D₅	—	2	4	no	—
351	C₂×C₃×D₅	—	2	4	no	—
352	C₂×C₃×D₅	—	4	32	no	—
353	C₂×C₃×D₅	—	4	8	no	—
354	C₂×C₃×D₅	C₂²×D₄	1	4	yes	complemented
355	C₃×C₄×C₅	—	2	2	no	—
356	C₃×C₄×C₅	C₂²×D₄	1	4	yes	complemented
357	C₃×Dic₅	—	2	2	no	—
358	C₃×Dic₅	—	2	4	no	—
359	C₃×Dic₅	—	2	2	no	—
360	C₃×Dic₅	C₂²×D₄	1	4	yes	complemented
361	C₂⁴×C₃	—	2	8	no	—
362	C₂⁴×C₃	—	2	8	no	—
363	C₂⁴×C₃	—	4	4	no	—
364	C₂⁴×C₃	—	5	1	no	—
365	C₂⁴×C₃	—	5	2	no	—
366	C₂⁴×C₃	—	5	8	no	—
367	C₂⁴×C₃	—	10	8	no	—
368	C₂⁴×C₃	—	10	8	no	—
369	C₂⁴×C₃	—	20	4	no	—
370	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
371	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
372	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
373	C₂⁴×C₃	C₂²×D₅	1	8	yes	complemented
374	C₂×C₃×D₄	—	2	8	no	—
375	C₂×C₃×D₄	—	2	32	no	—
376	C₂×C₃×D₄	—	2	4	no	—
377	C₂×C₃×D₄	—	5	8	no	—
378	C₂×C₃×D₄	—	5	4	no	—
379	C₂×C₃×D₄	—	5	8	no	—
380	C₂×C₃×D₄	—	5	8	no	—
381	C₂×C₃×D₄	—	5	8	no	—
382	C₂×C₃×D₄	—	5	8	no	—
383	C₂×C₃×D₄	—	5	8	no	—
384	C₂×C₃×D₄	—	5	4	no	—
385	C₂×C₃×D₄	—	10	8	no	—
386	C₂×C₃×D₄	—	10	64	no	—
387	C₂×C₃×D₄	—	10	8	no	—
388	C₂×C₃×D₄	—	10	8	no	—
389	C₂×C₃×D₄	—	10	8	no	—
390	C₂×C₃×D₄	—	10	32	no	—
391	C₂×C₃×D₄	—	10	4	no	—
392	C₂×C₃×D₄	—	20	4	no	—
393	C₂×C₃×D₄	C₂²⋊D₅	1	8	yes	direct product factor
394	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
395	C₂×C₃×D₄	C₂²×D₅	1	8	yes	complemented
396	C₂×C₃×D₄	C₂²×D₅	1	4	yes	complemented
397	C₂²×C₃×C₄	—	2	4	no	—
398	C₂²×C₃×C₄	—	5	1	no	—
399	C₂²×C₃×C₄	—	5	8	no	—
400	C₂²×C₃×C₄	—	5	1	no	—
401	C₂²×C₃×C₄	—	5	2	no	—
402	C₂²×C₃×C₄	—	5	1	no	—
403	C₂²×C₃×C₄	—	5	4	no	—
404	C₂²×C₃×C₄	—	10	8	no	—
405	C₂²×C₃×C₄	—	10	4	no	—
406	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
407	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
408	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	complemented
409	C₃×C₄⋊C₄	—	5	4	no	—
410	C₃×C₄⋊C₄	—	5	4	no	—
411	C₃×C₂²⋊C₄	—	5	4	no	—
412	C₃×C₂²⋊C₄	—	5	8	no	—
413	C₃×C₂²⋊C₄	—	5	8	no	—
414	C₃×C₂²⋊C₄	—	5	4	no	—
415	C₃×C₂²⋊C₄	—	5	8	no	—
416	C₃×C₄²	—	5	4	no	—
417	C₂³×C₅	—	2	4	no	—
418	C₂³×C₅	—	2	2	no	—
419	C₂³×C₅	—	2	4	no	—
420	C₂³×C₅	—	2	2	no	—
421	C₂³×C₅	—	2	4	no	—
422	C₂³×C₅	—	2	4	no	—
423	C₂³×C₅	—	2	16	no	—
424	C₂³×C₅	—	2	16	no	—
425	C₂³×C₅	—	2	4	no	—
426	C₂³×C₅	—	4	8	no	—
427	C₂³×C₅	—	4	32	no	—
428	C₂³×C₅	C₂×C₃×D₄	1	4	yes	complemented
429	C₂³×C₅	C₂×C₃×D₄	1	8	yes	complemented
430	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
431	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
432	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
433	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
434	C₂²×D₅	—	2	2	no	—
435	C₂²×D₅	—	2	2	no	—
436	C₂²×D₅	—	2	4	no	—
437	C₂²×D₅	—	2	4	no	—
438	C₂²×D₅	—	2	16	no	—
439	C₂²×D₅	—	2	4	no	—
440	C₂²×D₅	—	2	16	no	—
441	C₂²×D₅	—	4	8	no	—
442	C₂²×D₅	—	4	32	no	—
443	C₂²×D₅	C₂×C₃×D₄	1	4	yes	complemented
444	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
445	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
446	C₅×D₄	—	2	16	no	—
447	C₅×D₄	—	2	8	no	—
448	C₅×D₄	C₂×C₃×D₄	1	16	yes	complemented
449	C₂×C₄×C₅	—	2	2	no	—
450	C₂×C₄×C₅	—	2	8	no	—
451	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	complemented
452	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
453	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
454	C₂²⋊D₅	—	2	16	no	—
455	C₂²⋊D₅	—	2	16	no	—
456	C₂²⋊D₅	—	2	16	no	—
457	C₂²⋊D₅	—	2	16	no	—
458	C₂²⋊D₅	—	4	8	no	—
459	C₂²⋊D₅	C₂×C₃×D₄	1	16	yes	direct product factor
460	C₂×Dic₅	—	2	2	no	—
461	C₂×Dic₅	—	2	4	no	—
462	C₂×Dic₅	—	2	2	no	—
463	C₂×Dic₅	—	2	16	no	—
464	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	complemented
465	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
466	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
467	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
468	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
469	D₂₀	—	2	8	no	—
470	C₄×D₅	—	2	8	no	—
471	C₂⁵	—	5	2	no	—
472	C₂⁵	C₂×C₃×D₅	1	2	yes	complemented
473	C₂²×D₄	—	2	8	no	—
474	C₂²×D₄	—	5	1	no	—
475	C₂²×D₄	—	5	2	no	—
476	C₂²×D₄	—	5	2	no	—
477	C₂²×D₄	—	5	2	no	—
478	C₂²×D₄	—	5	2	no	—
479	C₂²×D₄	—	5	16	no	—
480	C₂²×D₄	—	5	2	no	—
481	C₂²×D₄	—	5	8	no	—
482	C₂²×D₄	—	5	1	no	—
483	C₂²×D₄	—	10	16	no	—
484	C₂²×D₄	—	10	8	no	—
485	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
486	C₂²×D₄	C₂×C₃×D₅	1	2	yes	complemented
487	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
488	C₂²×D₄	C₂×C₃×D₅	1	8	yes	complemented
489	C₂³×C₄	—	5	2	no	—
490	C₂³×C₄	—	5	1	no	—
491	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
492	#127	—	5	8	no	—
493	#121	—	5	8	no	—
494	#121	—	5	16	no	—
495	#121	—	5	8	no	—
496	#120	—	5	16	no	—
497	#120	—	5	16	no	—
498	C₄×D₄	—	5	8	no	—
499	C₄×D₄	—	5	8	no	—
500	C₂×C₄⋊C₄	—	5	1	no	—
501	C₂×C₄⋊C₄	—	5	1	no	—
502	C₂×C₂²⋊C₄	—	5	1	no	—
503	C₂×C₂²⋊C₄	—	5	2	no	—
504	C₂×C₂²⋊C₄	—	5	2	no	—
505	C₂×C₂²⋊C₄	—	5	1	no	—
506	C₂×C₂²⋊C₄	—	5	2	no	—
507	C₂×C₄²	—	5	1	no	—
508	C₂×C₃×C₅	—	2	8	no	—
509	C₂×C₃×C₅	—	2	4	no	—
510	C₂×C₃×C₅	—	4	4	no	—
511	C₂×C₃×C₅	D₄²	1	4	yes	complemented
512	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
513	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
514	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
515	C₃×D₅	—	2	4	no	—
516	C₃×D₅	—	4	4	no	—
517	C₂³×C₃	—	2	4	no	—
518	C₂³×C₃	—	2	2	no	—
519	C₂³×C₃	—	2	4	no	—
520	C₂³×C₃	—	2	2	no	—
521	C₂³×C₃	—	2	4	no	—
522	C₂³×C₃	—	2	16	no	—
523	C₂³×C₃	—	2	4	no	—
524	C₂³×C₃	—	2	4	no	—
525	C₂³×C₃	—	2	16	no	—
526	C₂³×C₃	—	4	8	no	—
527	C₂³×C₃	—	4	32	no	—
528	C₂³×C₃	—	5	4	no	—
529	C₂³×C₃	—	5	2	no	—
530	C₂³×C₃	—	5	4	no	—
531	C₂³×C₃	—	10	16	no	—
532	C₂³×C₃	—	10	2	no	—
533	C₂³×C₃	—	10	2	no	—
534	C₂³×C₃	—	10	4	no	—
535	C₂³×C₃	—	10	4	no	—
536	C₂³×C₃	—	10	4	no	—
537	C₂³×C₃	—	10	16	no	—
538	C₂³×C₃	—	20	8	no	—
539	C₂³×C₃	—	20	32	no	—
540	C₂³×C₃	D₄×D₅	1	4	yes	complemented
541	C₂³×C₃	C₂×C₂²⋊D₅	1	8	yes	complemented
542	C₂³×C₃	C₂³×D₅	1	4	yes	—
543	C₂³×C₃	C₂³×D₅	1	2	yes	—
544	C₂³×C₃	C₂³×D₅	1	4	yes	—
545	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
546	C₃×D₄	—	2	16	no	—
547	C₃×D₄	—	2	8	no	—
548	C₃×D₄	—	5	16	no	—
549	C₃×D₄	—	10	16	no	—
550	C₃×D₄	—	10	16	no	—
551	C₃×D₄	—	10	16	no	—
552	C₃×D₄	—	10	16	no	—
553	C₃×D₄	—	10	8	no	—
554	C₃×D₄	—	20	8	no	—
555	C₃×D₄	C₂×C₂²⋊D₅	1	16	yes	direct product factor
556	C₂×C₃×C₄	—	2	2	no	—
557	C₂×C₃×C₄	—	2	8	no	—
558	C₂×C₃×C₄	—	5	4	no	—
559	C₂×C₃×C₄	—	5	2	no	—
560	C₂×C₃×C₄	—	5	2	no	—
561	C₂×C₃×C₄	—	5	4	no	—
562	C₂×C₃×C₄	—	5	2	no	—
563	C₂×C₃×C₄	—	10	16	no	—
564	C₂×C₃×C₄	—	10	4	no	—
565	C₂×C₃×C₄	—	10	2	no	—
566	C₂×C₃×C₄	—	10	2	no	—
567	C₂×C₃×C₄	—	10	8	no	—
568	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	complemented
569	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
570	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
571	C₂²×C₅	—	2	4	no	—
572	C₂²×C₅	—	2	2	no	—
573	C₂²×C₅	—	2	4	no	—
574	C₂²×C₅	—	2	2	no	—
575	C₂²×C₅	—	2	16	no	—
576	C₂²×C₅	—	2	8	no	—
577	C₂²×C₅	—	2	4	no	—
578	C₂²×C₅	—	2	4	no	—
579	C₂²×C₅	—	2	4	no	—
580	C₂²×C₅	—	4	32	no	—
581	C₂²×C₅	—	4	8	no	—
582	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
583	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
584	C₂²×C₅	C₂²×C₃×D₄	1	4	yes	complemented
585	C₂²×C₅	C₂²×C₃×D₄	1	8	yes	complemented
586	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
587	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
588	C₂×D₅	—	2	2	no	—
589	C₂×D₅	—	2	2	no	—
590	C₂×D₅	—	2	8	no	—
591	C₂×D₅	—	2	4	no	—
592	C₂×D₅	—	2	4	no	—
593	C₂×D₅	—	2	4	no	—
594	C₂×D₅	—	4	32	no	—
595	C₂×D₅	—	4	8	no	—
596	C₂×D₅	C₂²×C₃×D₄	1	4	yes	complemented
597	C₄×C₅	—	2	2	no	—
598	C₄×C₅	C₂²×C₃×D₄	1	4	yes	complemented
599	Dic₅	—	2	2	no	—
600	Dic₅	—	2	4	no	—
601	Dic₅	—	2	2	no	—
602	Dic₅	C₂²×C₃×D₄	1	4	yes	complemented
603	C₂⁴	—	2	8	no	—
604	C₂⁴	—	2	8	no	—
605	C₂⁴	—	4	4	no	—
606	C₂⁴	—	5	1	no	—
607	C₂⁴	—	5	2	no	—
608	C₂⁴	—	5	8	no	—
609	C₂⁴	—	10	8	no	—
610	C₂⁴	—	10	8	no	—
611	C₂⁴	—	20	4	no	—
612	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
613	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
614	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
615	C₂⁴	C₂²×C₃×D₅	1	8	yes	complemented
616	C₂×D₄	—	2	8	no	—
617	C₂×D₄	—	2	32	no	—
618	C₂×D₄	—	2	4	no	—
619	C₂×D₄	—	5	8	no	—
620	C₂×D₄	—	5	4	no	—
621	C₂×D₄	—	5	8	no	—
622	C₂×D₄	—	5	8	no	—
623	C₂×D₄	—	5	8	no	—
624	C₂×D₄	—	5	8	no	—
625	C₂×D₄	—	5	8	no	—
626	C₂×D₄	—	5	4	no	—
627	C₂×D₄	—	10	8	no	—
628	C₂×D₄	—	10	64	no	—
629	C₂×D₄	—	10	8	no	—
630	C₂×D₄	—	10	8	no	—
631	C₂×D₄	—	10	8	no	—
632	C₂×D₄	—	10	32	no	—
633	C₂×D₄	—	10	4	no	—
634	C₂×D₄	—	20	4	no	—
635	C₂×D₄	C₃×C₂²⋊D₅	1	8	yes	direct product factor
636	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
637	C₂×D₄	C₂²×C₃×D₅	1	8	yes	complemented
638	C₂×D₄	C₂²×C₃×D₅	1	4	yes	complemented
639	C₂²×C₄	—	2	4	no	—
640	C₂²×C₄	—	5	1	no	—
641	C₂²×C₄	—	5	1	no	—
642	C₂²×C₄	—	5	2	no	—
643	C₂²×C₄	—	5	1	no	—
644	C₂²×C₄	—	5	8	no	—
645	C₂²×C₄	—	5	4	no	—
646	C₂²×C₄	—	10	8	no	—
647	C₂²×C₄	—	10	4	no	—
648	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
649	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
650	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	complemented
651	C₄⋊C₄	—	5	4	no	—
652	C₄⋊C₄	—	5	4	no	—
653	C₂²⋊C₄	—	5	4	no	—
654	C₂²⋊C₄	—	5	8	no	—
655	C₂²⋊C₄	—	5	8	no	—
656	C₂²⋊C₄	—	5	4	no	—
657	C₂²⋊C₄	—	5	8	no	—
658	C₄²	—	5	4	no	—
659	C₃×C₅	C₂×D₄²	1	1	yes	characteristic, complemented, Hall
660	C₂²×C₃	—	2	8	no	—
661	C₂²×C₃	—	2	16	no	—
662	C₂²×C₃	—	2	4	no	—
663	C₂²×C₃	—	2	2	no	—
664	C₂²×C₃	—	2	4	no	—
665	C₂²×C₃	—	2	2	no	—
666	C₂²×C₃	—	2	4	no	—
667	C₂²×C₃	—	2	4	no	—
668	C₂²×C₃	—	2	4	no	—
669	C₂²×C₃	—	4	32	no	—
670	C₂²×C₃	—	4	8	no	—
671	C₂²×C₃	—	5	4	no	—
672	C₂²×C₃	—	10	8	no	—
673	C₂²×C₃	—	10	2	no	—
674	C₂²×C₃	—	10	2	no	—
675	C₂²×C₃	—	10	4	no	—
676	C₂²×C₃	—	10	4	no	—
677	C₂²×C₃	—	10	4	no	—
678	C₂²×C₃	—	20	32	no	—
679	C₂²×C₃	—	20	8	no	—
680	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
681	C₂²×C₃	C₂×D₄×D₅	1	4	yes	complemented
682	C₂²×C₃	#4144	1	2	yes	—
683	C₂²×C₃	C₂²×C₂²⋊D₅	1	2	yes	—
684	C₂²×C₃	C₂²×C₂²⋊D₅	1	8	yes	complemented
685	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
686	C₃×C₄	—	2	2	no	—
687	C₃×C₄	—	5	4	no	—
688	C₃×C₄	—	10	4	no	—
689	C₃×C₄	—	10	2	no	—
690	C₃×C₄	—	10	2	no	—
691	C₃×C₄	C₂²×C₂²⋊D₅	1	4	yes	complemented
692	C₂×C₅	—	2	8	no	—
693	C₂×C₅	—	2	4	no	—
694	C₂×C₅	—	4	4	no	—
695	C₂×C₅	C₃×D₄²	1	4	yes	complemented
696	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
697	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
698	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
699	D₅	—	2	4	no	—
700	D₅	—	4	4	no	—
701	C₂³	—	2	4	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	4	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	2	4	no	—
706	C₂³	—	2	16	no	—
707	C₂³	—	2	4	no	—
708	C₂³	—	2	4	no	—
709	C₂³	—	2	16	no	—
710	C₂³	—	4	8	no	—
711	C₂³	—	4	32	no	—
712	C₂³	—	5	4	no	—
713	C₂³	—	5	2	no	—
714	C₂³	—	5	4	no	—
715	C₂³	—	10	16	no	—
716	C₂³	—	10	2	no	—
717	C₂³	—	10	2	no	—
718	C₂³	—	10	4	no	—
719	C₂³	—	10	4	no	—
720	C₂³	—	10	4	no	—
721	C₂³	—	10	16	no	—
722	C₂³	—	20	8	no	—
723	C₂³	—	20	32	no	—
724	C₂³	C₃×D₄×D₅	1	4	yes	complemented
725	C₂³	C₂×C₃×C₂²⋊D₅	1	8	yes	complemented
726	C₂³	C₂³×C₃×D₅	1	4	yes	—
727	C₂³	C₂³×C₃×D₅	1	2	yes	—
728	C₂³	C₂³×C₃×D₅	1	4	yes	—
729	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
730	D₄	—	2	16	no	—
731	D₄	—	2	8	no	—
732	D₄	—	5	16	no	—
733	D₄	—	10	16	no	—
734	D₄	—	10	16	no	—
735	D₄	—	10	16	no	—
736	D₄	—	10	16	no	—
737	D₄	—	10	8	no	—
738	D₄	—	20	8	no	—
739	D₄	C₂×C₃×C₂²⋊D₅	1	16	yes	direct product factor
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	8	no	—
742	C₂×C₄	—	5	4	no	—
743	C₂×C₄	—	5	2	no	—
744	C₂×C₄	—	5	2	no	—
745	C₂×C₄	—	5	4	no	—
746	C₂×C₄	—	5	2	no	—
747	C₂×C₄	—	10	16	no	—
748	C₂×C₄	—	10	4	no	—
749	C₂×C₄	—	10	2	no	—
750	C₂×C₄	—	10	2	no	—
751	C₂×C₄	—	10	8	no	—
752	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	complemented
753	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
754	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
755	C₂×C₃	—	2	4	no	—
756	C₂×C₃	—	2	8	no	—
757	C₂×C₃	—	4	4	no	—
758	C₂×C₃	—	10	4	no	—
759	C₂×C₃	—	20	4	no	—
760	C₂×C₃	D₄×C₂²⋊D₅	1	4	yes	direct product factor
761	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
762	C₂×C₃	C₂×#4144	1	1	yes	characteristic
763	C₂×C₃	C₂³×C₂²⋊D₅	1	1	yes	characteristic
764	C₅	C₂×C₃×D₄²	1	1	yes	characteristic, complemented, Sylow
765	C₂²	—	2	8	no	—
766	C₂²	—	2	16	no	—
767	C₂²	—	2	4	no	—
768	C₂²	—	2	2	no	—
769	C₂²	—	2	4	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	4	no	—
772	C₂²	—	2	4	no	—
773	C₂²	—	2	4	no	—
774	C₂²	—	4	32	no	—
775	C₂²	—	4	8	no	—
776	C₂²	—	5	4	no	—
777	C₂²	—	10	8	no	—
778	C₂²	—	10	2	no	—
779	C₂²	—	10	2	no	—
780	C₂²	—	10	4	no	—
781	C₂²	—	10	4	no	—
782	C₂²	—	10	4	no	—
783	C₂²	—	20	32	no	—
784	C₂²	—	20	8	no	—
785	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
786	C₂²	C₂×C₃×D₄×D₅	1	4	yes	complemented
787	C₂²	C₃×#4144	1	2	yes	—
788	C₂²	C₂²×C₃×C₂²⋊D₅	1	2	yes	—
789	C₂²	C₂²×C₃×C₂²⋊D₅	1	8	yes	complemented
790	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
791	C₄	—	2	2	no	—
792	C₄	—	5	4	no	—
793	C₄	—	10	4	no	—
794	C₄	—	10	2	no	—
795	C₄	—	10	2	no	—
796	C₄	C₂²×C₃×C₂²⋊D₅	1	4	yes	complemented
797	C₃	C₂×D₄×C₂²⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
798	C₂	—	2	4	no	—
799	C₂	—	2	8	no	—
800	C₂	—	4	4	no	—
801	C₂	—	10	4	no	—
802	C₂	—	20	4	no	—
803	C₂	C₃×D₄×C₂²⋊D₅	1	4	yes	direct product factor
804	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
805	C₂	C₂×C₃×#4144	1	1	yes	characteristic
806	C₂	C₂³×C₃×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂³×C₃×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂³×C₃×D₄	D₅
hypocenter	C₅	C₂×C₃×D₄²
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₅×D₄	C₂	semidirect
2. C₂³×C₃×C₂²⋊D₅	C₂	semidirect
3. C₂²×C₃×D₄×D₅	C₂	semidirect
4. C₂×C₃×#4099	C₂	semidirect
5. C₂×C₃×#4086	C₂	semidirect
6. C₂×C₃×#4085	C₂	semidirect
7. C₃×D₄×C₂²⋊D₅	C₂	direct (N × H)
8. C₂×C₃×#4084	C₂	semidirect
9. C₂×C₃×#4083	C₂	semidirect
10. C₂×C₃×D₄×Dic₅	C₂	semidirect
11. C₂×C₃×#4076	C₂	semidirect
12. C₂×C₃×C₄×C₂²⋊D₅	C₂	semidirect
13. C₂×D₄×C₂²⋊D₅	C₃	direct (N × H)
14. C₂⁵×C₃×C₅	C₂²	semidirect
15. C₂⁴×C₃×D₅	C₂²	semidirect
18. C₂²×C₃×C₅×D₄	C₂²	semidirect
19. C₂²×C₃×C₅×D₄	C₂²	semidirect
20. C₂²×C₃×C₅×D₄	C₂²	semidirect
21. C₂³×C₃×C₄×C₅	C₂²	semidirect
24. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
25. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
26. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
27. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
28. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
29. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
30. C₂³×C₃×Dic₅	C₂²	semidirect
32. C₂×C₃×D₄×D₅	C₂²	semidirect
33. C₂²×C₃×D₂₀	C₂²	semidirect
34. C₂²×C₃×C₄×D₅	C₂²	semidirect
35. C₃×#4099	C₂²	semidirect
36. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
37. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
38. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
39. C₃×#4086	C₂²	semidirect
40. C₃×#4085	C₂²	semidirect
41. C₃×#4084	C₂²	semidirect
42. C₃×#4083	C₂²	semidirect
43. C₃×D₄×Dic₅	C₂²	semidirect
44. C₃×#4076	C₂²	semidirect
45. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
46. C₂×C₃×#685	C₂²	semidirect
47. C₂×C₃×#685	C₂²	semidirect
48. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
49. C₂×C₃×#683	C₂²	semidirect
50. C₂×C₃×C₄×Dic₅	C₂²	semidirect
52. C₂³×C₅×D₄	C₂×C₃	semidirect
53. C₂³×C₂²⋊D₅	C₂×C₃	semidirect
54. C₂²×D₄×D₅	C₂×C₃	semidirect
55. C₂×#4099	C₂×C₃	semidirect
56. C₂×#4086	C₂×C₃	semidirect
57. C₂×#4085	C₂×C₃	semidirect
58. D₄×C₂²⋊D₅	C₂×C₃	direct (N × H)
59. C₂×#4084	C₂×C₃	semidirect
60. C₂×#4083	C₂×C₃	semidirect
61. C₂×D₄×Dic₅	C₂×C₃	semidirect
62. C₂×#4076	C₂×C₃	semidirect
63. C₂×C₄×C₂²⋊D₅	C₂×C₃	semidirect
70. C₂⁴×C₃×C₅	C₂³	semidirect
76. C₂³×C₃×D₅	C₂³	semidirect
80. C₂×C₃×C₅×D₄	D₄	semidirect
82. C₂×C₃×C₅×D₄	C₂³	semidirect
83. C₂×C₃×C₅×D₄	C₂³	semidirect
87. C₂²×C₃×C₄×C₅	C₂³	semidirect
94. C₂×C₃×C₂²⋊D₅	D₄	direct (N × H)
96. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
97. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
98. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
99. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
100. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
106. C₂²×C₃×Dic₅	C₂³	semidirect
109. C₂×C₃×D₂₀	C₂³	semidirect
111. C₂×C₃×C₄×D₅	C₂³	semidirect
112. C₃×C₂²⋊Dic₅	C₂³	semidirect
113. C₃×C₂²⋊Dic₅	C₂³	semidirect
114. C₃×C₂²⋊Dic₅	C₂³	semidirect
115. C₃×#685	C₂³	semidirect
116. C₃×#685	C₂³	semidirect
117. C₃×C₄⋊Dic₅	C₂³	semidirect
118. C₃×#683	C₂³	semidirect
119. C₃×C₄×Dic₅	C₂³	semidirect
122. C₂³×C₃×D₄	D₅	semidirect
132. C₂⁵×C₅	C₂²×C₃	semidirect
133. C₂⁴×D₅	C₂²×C₃	semidirect
136. C₂²×C₅×D₄	C₂²×C₃	semidirect
137. C₂²×C₅×D₄	C₂²×C₃	semidirect
138. C₂²×C₅×D₄	C₂²×C₃	semidirect
139. C₂³×C₄×C₅	C₂²×C₃	semidirect
142. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
143. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
144. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
145. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
146. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
147. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
148. C₂³×Dic₅	C₂²×C₃	semidirect
150. C₂×D₄×D₅	C₂²×C₃	semidirect
151. C₂²×D₂₀	C₂²×C₃	semidirect
152. C₂²×C₄×D₅	C₂²×C₃	semidirect
153. #4099	C₂²×C₃	semidirect
154. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
155. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
156. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
157. #4086	C₂²×C₃	semidirect
158. #4085	C₂²×C₃	semidirect
159. #4084	C₂²×C₃	semidirect
160. #4083	C₂²×C₃	semidirect
161. D₄×Dic₅	C₂²×C₃	semidirect
162. #4076	C₂²×C₃	semidirect
163. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
164. C₂×#685	C₂²×C₃	semidirect
165. C₂×#685	C₂²×C₃	semidirect
166. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
167. C₂×#683	C₂²×C₃	semidirect
168. C₂×C₄×Dic₅	C₂²×C₃	semidirect
181. C₂³×C₃×C₅	C₂×D₄	semidirect
182. C₂³×C₃×C₅	C₂×D₄	semidirect
196. C₂²×C₃×D₅	C₂×D₄	semidirect
201. C₃×C₅×D₄	C₂×D₄	semidirect
204. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
212. C₃×C₂²⋊D₅	C₂×D₄	direct (N × H)
217. C₂×C₃×Dic₅	C₂×D₄	semidirect
225. C₂⁵×C₃	C₂×D₅	semidirect
239. C₂²×C₃×D₄	C₂×D₅	semidirect
240. C₂²×C₃×D₄	C₂×D₅	semidirect
241. C₂²×C₃×D₄	C₂×D₅	semidirect
244. C₂³×C₃×C₄	C₂×D₅	semidirect
267. C₂⁴×C₅	C₂³×C₃	semidirect
273. C₂³×D₅	C₂³×C₃	semidirect
277. C₂×C₅×D₄	C₃×D₄	semidirect
279. C₂×C₅×D₄	C₂³×C₃	semidirect
280. C₂×C₅×D₄	C₂³×C₃	semidirect
284. C₂²×C₄×C₅	C₂³×C₃	semidirect
291. C₂×C₂²⋊D₅	C₃×D₄	direct (N × H)
293. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
294. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
295. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
296. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
297. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
303. C₂²×Dic₅	C₂³×C₃	semidirect
306. C₂×D₂₀	C₂³×C₃	semidirect
308. C₂×C₄×D₅	C₂³×C₃	semidirect
309. C₂²⋊Dic₅	C₂³×C₃	semidirect
310. C₂²⋊Dic₅	C₂³×C₃	semidirect
311. C₂²⋊Dic₅	C₂³×C₃	semidirect
312. #685	C₂³×C₃	semidirect
313. #685	C₂³×C₃	semidirect
314. C₄⋊Dic₅	C₂³×C₃	semidirect
315. #683	C₂³×C₃	semidirect
316. C₄×Dic₅	C₂³×C₃	semidirect
319. C₂³×D₄	C₃×D₅	semidirect
342. C₂²×C₃×C₅	C₂²×D₄	semidirect
343. C₂²×C₃×C₅	C₂²×D₄	semidirect
354. C₂×C₃×D₅	C₂²×D₄	semidirect
356. C₃×C₄×C₅	C₂²×D₄	semidirect
360. C₃×Dic₅	C₂²×D₄	semidirect
373. C₂⁴×C₃	C₂²×D₅	semidirect
393. C₂×C₃×D₄	C₂²⋊D₅	direct (N × H)
395. C₂×C₃×D₄	C₂²×D₅	semidirect
396. C₂×C₃×D₄	C₂²×D₅	semidirect
408. C₂²×C₃×C₄	C₂²×D₅	semidirect
428. C₂³×C₅	C₂×C₃×D₄	semidirect
429. C₂³×C₅	C₂×C₃×D₄	semidirect
443. C₂²×D₅	C₂×C₃×D₄	semidirect
448. C₅×D₄	C₂×C₃×D₄	semidirect
451. C₂×C₄×C₅	C₂×C₃×D₄	semidirect
459. C₂²⋊D₅	C₂×C₃×D₄	direct (N × H)
464. C₂×Dic₅	C₂×C₃×D₄	semidirect
472. C₂⁵	C₂×C₃×D₅	semidirect
486. C₂²×D₄	C₂×C₃×D₅	semidirect
487. C₂²×D₄	C₂×C₃×D₅	semidirect
488. C₂²×D₄	C₂×C₃×D₅	semidirect
491. C₂³×C₄	C₂×C₃×D₅	semidirect
511. C₂×C₃×C₅	D₄²	semidirect
540. C₂³×C₃	D₄×D₅	semidirect
541. C₂³×C₃	C₂×C₂²⋊D₅	semidirect
555. C₃×D₄	C₂×C₂²⋊D₅	direct (N × H)
568. C₂×C₃×C₄	C₂×C₂²⋊D₅	semidirect
584. C₂²×C₅	C₂²×C₃×D₄	semidirect
585. C₂²×C₅	C₂²×C₃×D₄	semidirect
596. C₂×D₅	C₂²×C₃×D₄	semidirect
598. C₄×C₅	C₂²×C₃×D₄	semidirect
602. Dic₅	C₂²×C₃×D₄	semidirect
615. C₂⁴	C₂²×C₃×D₅	semidirect
635. C₂×D₄	C₃×C₂²⋊D₅	direct (N × H)
637. C₂×D₄	C₂²×C₃×D₅	semidirect
638. C₂×D₄	C₂²×C₃×D₅	semidirect
650. C₂²×C₄	C₂²×C₃×D₅	semidirect
659. C₃×C₅	C₂×D₄²	semidirect
681. C₂²×C₃	C₂×D₄×D₅	semidirect
684. C₂²×C₃	C₂²×C₂²⋊D₅	semidirect
691. C₃×C₄	C₂²×C₂²⋊D₅	semidirect
695. C₂×C₅	C₃×D₄²	semidirect
724. C₂³	C₃×D₄×D₅	semidirect
725. C₂³	C₂×C₃×C₂²⋊D₅	semidirect
739. D₄	C₂×C₃×C₂²⋊D₅	direct (N × H)
752. C₂×C₄	C₂×C₃×C₂²⋊D₅	semidirect
760. C₂×C₃	D₄×C₂²⋊D₅	direct (N × H)
764. C₅	C₂×C₃×D₄²	semidirect
786. C₂²	C₂×C₃×D₄×D₅	semidirect
789. C₂²	C₂²×C₃×C₂²⋊D₅	semidirect
796. C₄	C₂²×C₃×C₂²⋊D₅	semidirect
797. C₃	C₂×D₄×C₂²⋊D₅	direct (N × H)
803. C₂	C₃×D₄×C₂²⋊D₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₅×D₄	2
C₂³×C₃×C₂²⋊D₅	2
C₂²×C₃×D₄×D₅	2
C₂×C₃×#4099	2
C₂×C₃×#4086	2
C₂×C₃×#4085	2
C₃×D₄×C₂²⋊D₅	2
C₂×C₃×#4084	2
C₂×C₃×#4083	2
C₂×C₃×D₄×Dic₅	2
C₂×C₃×#4076	2
C₂×C₃×C₄×C₂²⋊D₅	2
C₂×D₄×C₂²⋊D₅	3
C₂×C₃×D₄²	5

Subgroups — C2×C3×D4×C22⋊D5 #14482407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₄×C₂²⋊D₅ #14482407