Subgroups — C₂×C₅×#5637 #14483244

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×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#947	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#946	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5637	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₅×#898	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#898	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#894	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#894	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#892	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#886	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅×#882	C₂	1	1	yes	maximal, characteristic
15	C₂×C₅×D₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#877	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅×#551	—	3	1	no	maximal, Hall
18	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
21	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
22	C₂³×C₅×Dic₃	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, complemented
28	C₃×C₅×C₂²⋊Q₈	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×C₅×#217	C₂²	1	1	yes	characteristic
35	C₅×#947	C₂²	1	8	yes	complemented
36	C₅×#946	C₂²	1	8	yes	complemented
37	C₄×C₅×#67	C₂²	1	8	yes	complemented
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×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
47	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
53	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
58	C₅×#898	C₂²	1	8	yes	complemented
59	C₅×#898	C₂²	1	8	yes	complemented
60	C₅×#894	C₂²	1	8	yes	complemented
61	C₅×#894	C₂²	1	8	yes	complemented
62	C₅×#893	C₂²	1	8	yes	complemented
63	C₅×#892	C₂²	1	8	yes	complemented
64	C₅×#886	C₂²	1	8	yes	complemented
65	C₅×#882	C₂²	1	8	yes	—
66	C₅×D₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
67	C₅×#877	C₂²	1	8	yes	complemented
68	C₂×#5637	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
69	C₅×#551	—	3	16	no	—
70	C₂×C₅×#126	—	3	1	no	—
71	C₂×C₅×#126	—	3	1	no	—
72	C₂×C₅×#124	—	3	1	no	—
73	C₂×C₅×#123	—	3	1	no	—
74	C₂×C₅×#123	—	3	1	no	—
75	C₂×C₅×#123	—	3	1	no	—
76	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
77	C₂×C₅×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
78	C₂×C₅×#120	—	3	1	no	—
79	C₂×C₄×C₅×D₄	—	3	1	no	—
80	C₂×C₄×C₅×D₄	—	3	1	no	—
81	C₂×C₅×#117	—	3	1	no	—
82	C₂×C₅×#117	—	3	1	no	—
83	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
84	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
85	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
86	C₂³×C₅×D₃	—	2	4	no	—
87	C₂³×C₅×D₃	—	2	4	no	—
88	C₂³×C₅×D₃	—	4	2	no	—
89	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
90	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
91	C₂³×C₅×D₃	C₂³	1	4	yes	—
92	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₅×Q₈	—	4	2	no	—
94	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	complemented
95	C₂²×C₃×C₄×C₅	—	4	2	no	—
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	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
100	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
101	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
102	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
103	C₂×C₅×#67	—	2	4	no	—
104	C₂×C₅×#67	C₂³	1	4	yes	—
105	C₂²×C₅×Dic₃	—	2	4	no	—
106	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
107	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
108	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
109	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
110	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
111	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
112	C₂×C₅×D₁₂	—	2	4	no	—
113	C₂×C₅×D₁₂	—	4	2	no	—
114	C₂×C₅×D₁₂	C₂³	1	4	yes	—
115	C₂×C₅×D₁₂	C₂³	1	4	yes	—
116	C₂×C₄×C₅×D₃	—	2	4	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	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	C₅×#217	C₂³	1	4	yes	—
128	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
129	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
130	C₅×(C₂×D₃)⋊C₄	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	complemented
137	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
138	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
139	C₅×C₄⋊Dic₃	C₂³	1	4	yes	complemented
140	C₅×C₄⋊Dic₃	C₂³	1	4	yes	complemented
141	C₅×Dic₃⋊C₄	C₂³	1	4	yes	complemented
142	C₅×Dic₃⋊C₄	C₂³	1	4	yes	complemented
143	C₅×Dic₃⋊C₄	C₂³	1	4	yes	complemented
144	C₄×C₅×Dic₃	C₂³	1	4	yes	complemented
145	C₄×C₅×Dic₃	C₂³	1	4	yes	complemented
146	C₄×C₅×Dic₃	C₂³	1	4	yes	complemented
147	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
148	C₂×#947	C₂×C₅	1	1	yes	characteristic, complemented
149	C₂×#946	C₂×C₅	1	1	yes	characteristic, complemented
150	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic, complemented
151	C₂²×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
152	#5637	C₂×C₅	1	16	yes	direct product factor
153	C₂×#898	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂×#898	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×#894	C₂×C₅	1	1	yes	characteristic, complemented
156	C₂×#894	C₂×C₅	1	1	yes	characteristic, complemented
157	C₂×#893	C₂×C₅	1	1	yes	characteristic, complemented
158	C₂×#892	C₂×C₅	1	1	yes	characteristic, complemented
159	C₂×#886	C₂×C₅	1	1	yes	characteristic, complemented
160	C₂×#882	C₂×C₅	1	1	yes	characteristic
161	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
162	C₂×#877	C₂×C₅	1	1	yes	characteristic, complemented
163	C₂⁵×C₅	—	3	1	no	—
164	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
165	C₂²×C₅×D₄	—	3	1	no	—
166	C₂²×C₅×D₄	—	3	1	no	—
167	C₂²×C₅×D₄	—	3	1	no	—
168	C₂³×C₄×C₅	—	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	C₂×D₃	1	1	yes	characteristic
173	C₅×#126	—	3	8	no	—
174	C₅×#126	—	3	8	no	—
175	C₅×#124	—	3	8	no	—
176	C₅×#123	—	3	8	no	—
177	C₅×#123	—	3	8	no	—
178	C₅×#123	—	3	8	no	—
179	C₅×C₂²⋊Q₈	—	3	8	no	—
180	C₅×C₂²⋊Q₈	C₂×D₃	1	8	yes	complemented
181	C₅×#120	—	3	8	no	—
182	C₄×C₅×D₄	—	3	8	no	—
183	C₄×C₅×D₄	—	3	8	no	—
184	C₅×#117	—	3	8	no	—
185	C₅×#117	—	3	8	no	—
186	C₂×C₅×C₄⋊C₄	—	3	1	no	—
187	C₂×C₅×C₄⋊C₄	—	3	1	no	—
188	C₂×C₅×C₄⋊C₄	—	3	1	no	—
189	C₂×C₅×C₄⋊C₄	—	3	1	no	—
190	C₂×C₅×C₄⋊C₄	—	3	1	no	—
191	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
192	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
193	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
194	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
195	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
196	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
197	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
198	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
199	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
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	8	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	—	3	8	no	—
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	—	3	1	no	—
213	C₂×#551	—	3	1	no	Sylow
214	C₂³×C₃×C₅	—	2	2	no	—
215	C₂³×C₃×C₅	—	2	2	no	—
216	C₂³×C₃×C₅	#41	1	4	yes	—
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	8	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	—	2	2	no	—
228	C₂²×C₅×D₃	—	2	8	no	—
229	C₂²×C₅×D₃	—	4	4	no	—
230	C₂²×C₅×D₃	—	4	16	no	—
231	C₂²×C₅×D₃	#41	1	4	yes	—
232	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
233	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
234	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
235	C₃×C₅×Q₈	—	4	4	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	—	2	2	no	—
242	C₂×C₃×C₄×C₅	—	4	4	no	—
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	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
248	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
249	C₅×#67	—	2	8	no	—
250	C₂×C₅×Dic₃	—	2	2	no	—
251	C₂×C₅×Dic₃	—	2	8	no	—
252	C₂×C₅×Dic₃	—	2	2	no	—
253	C₂×C₅×Dic₃	—	2	2	no	—
254	C₂×C₅×Dic₃	—	2	2	no	—
255	C₂×C₅×Dic₃	—	2	2	no	—
256	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
257	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
258	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
259	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
260	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
261	C₅×D₁₂	—	2	8	no	—
262	C₅×D₁₂	—	4	4	no	—
263	C₄×C₅×D₃	—	2	8	no	—
264	C₄×C₅×D₃	—	4	4	no	—
265	C₄×C₅×D₃	—	4	4	no	—
266	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
267	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
268	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
269	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
270	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
271	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
272	C₂²×D₁₂	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, complemented
276	C₃×C₂²⋊Q₈	C₂²×C₅	1	8	yes	complemented
277	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
278	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
279	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
280	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
281	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
282	C₂×#217	C₂²×C₅	1	1	yes	characteristic
283	#947	C₂²×C₅	1	8	yes	complemented
284	#946	C₂²×C₅	1	8	yes	complemented
285	C₄×#67	C₂²×C₅	1	8	yes	complemented
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×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
293	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
294	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	8	yes	complemented
295	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
296	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
297	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
298	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
299	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
300	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
301	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
302	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
303	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
304	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
305	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
306	#898	C₂²×C₅	1	8	yes	complemented
307	#898	C₂²×C₅	1	8	yes	complemented
308	#894	C₂²×C₅	1	8	yes	complemented
309	#894	C₂²×C₅	1	8	yes	complemented
310	#893	C₂²×C₅	1	8	yes	complemented
311	#892	C₂²×C₅	1	8	yes	complemented
312	#886	C₂²×C₅	1	8	yes	complemented
313	#882	C₂²×C₅	1	8	yes	—
314	D₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
315	#877	C₂²×C₅	1	8	yes	complemented
316	C₂⁴×C₅	—	3	1	no	—
317	C₂⁴×C₅	—	3	1	no	—
318	C₂⁴×C₅	—	3	1	no	—
319	C₂⁴×C₅	—	3	4	no	—
320	C₂⁴×C₅	—	6	4	no	—
321	C₂⁴×C₅	—	6	4	no	—
322	C₂⁴×C₅	—	12	2	no	—
323	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
324	C₂×C₅×Q₈	—	4	2	no	—
325	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	complemented
326	C₂×C₅×D₄	—	3	4	no	—
327	C₂×C₅×D₄	—	3	4	no	—
328	C₂×C₅×D₄	—	3	4	no	—
329	C₂×C₅×D₄	—	6	4	no	—
330	C₂×C₅×D₄	—	6	4	no	—
331	C₂×C₅×D₄	—	12	2	no	—
332	C₂²×C₄×C₅	—	3	4	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	1	no	—
337	C₂²×C₄×C₅	—	3	1	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	—	4	2	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	C₂²×D₃	1	1	yes	characteristic
347	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
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	4	yes	—
353	C₅×C₄⋊C₄	—	3	4	no	—
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	C₂²×D₃	1	4	yes	complemented
359	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	complemented
360	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	complemented
361	C₅×C₂²⋊C₄	—	3	4	no	—
362	C₅×C₂²⋊C₄	—	3	4	no	—
363	C₅×C₂²⋊C₄	—	3	4	no	—
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	—	3	4	no	—
372	C₅×C₂²⋊C₄	—	3	4	no	—
373	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
374	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
375	C₄²×C₅	—	3	4	no	—
376	C₄²×C₅	—	3	4	no	—
377	C₄²×C₅	—	3	4	no	—
378	#551	—	3	16	no	—
379	C₂×#126	—	3	1	no	—
380	C₂×#126	—	3	1	no	—
381	C₂×#124	—	3	1	no	—
382	C₂×#123	—	3	1	no	—
383	C₂×#123	—	3	1	no	—
384	C₂×#123	—	3	1	no	—
385	C₂×C₂²⋊Q₈	—	3	1	no	—
386	C₂×C₂²⋊Q₈	C₅×D₃	1	1	yes	characteristic, complemented
387	C₂×#120	—	3	1	no	—
388	C₂×C₄×D₄	—	3	1	no	—
389	C₂×C₄×D₄	—	3	1	no	—
390	C₂×#117	—	3	1	no	—
391	C₂×#117	—	3	1	no	—
392	C₂²×C₂²⋊C₄	—	3	1	no	—
393	C₂²×C₂²⋊C₄	—	3	1	no	—
394	C₂²×C₃×C₅	—	2	8	no	—
395	C₂²×C₃×C₅	—	2	2	no	—
396	C₂²×C₃×C₅	—	2	2	no	—
397	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
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×C₅×D₃	—	2	8	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	—	2	2	no	—
411	C₂×C₅×D₃	—	4	16	no	—
412	C₂×C₅×D₃	—	4	4	no	—
413	C₂×C₅×D₃	—	4	4	no	—
414	C₂×C₅×D₃	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	C₅×Dic₃	—	2	2	no	—
422	C₅×Dic₃	—	2	2	no	—
423	C₅×Dic₃	—	2	2	no	—
424	C₅×Dic₃	—	2	2	no	—
425	C₅×Dic₃	—	2	2	no	—
426	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
427	C₂³×D₃	—	2	4	no	—
428	C₂³×D₃	—	2	4	no	—
429	C₂³×D₃	—	4	2	no	—
430	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
431	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
432	C₂³×D₃	C₂³×C₅	1	4	yes	—
433	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
434	C₂×C₃×Q₈	—	4	2	no	—
435	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	complemented
436	C₂²×C₃×C₄	—	4	2	no	—
437	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
438	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
439	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
440	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
441	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
442	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
443	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
444	C₂×#67	—	2	4	no	—
445	C₂×#67	C₂³×C₅	1	4	yes	—
446	C₂²×Dic₃	—	2	4	no	—
447	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
448	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
449	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
450	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
451	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
452	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
453	C₂×D₁₂	—	2	4	no	—
454	C₂×D₁₂	—	4	2	no	—
455	C₂×D₁₂	C₂³×C₅	1	4	yes	—
456	C₂×D₁₂	C₂³×C₅	1	4	yes	—
457	C₂×C₄×D₃	—	2	4	no	—
458	C₂×C₄×D₃	—	4	2	no	—
459	C₂×C₄×D₃	—	4	2	no	—
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	complemented
463	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	complemented
464	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	complemented
465	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	complemented
466	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
467	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
468	#217	C₂³×C₅	1	4	yes	—
469	(C₂×D₃)⋊C₄	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	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	complemented
478	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	complemented
479	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	complemented
480	C₄⋊Dic₃	C₂³×C₅	1	4	yes	complemented
481	C₄⋊Dic₃	C₂³×C₅	1	4	yes	complemented
482	Dic₃⋊C₄	C₂³×C₅	1	4	yes	complemented
483	Dic₃⋊C₄	C₂³×C₅	1	4	yes	complemented
484	Dic₃⋊C₄	C₂³×C₅	1	4	yes	complemented
485	C₄×Dic₃	C₂³×C₅	1	4	yes	complemented
486	C₄×Dic₃	C₂³×C₅	1	4	yes	complemented
487	C₄×Dic₃	C₂³×C₅	1	4	yes	complemented
488	C₂³×C₅	—	2	2	no	—
489	C₂³×C₅	—	2	2	no	—
490	C₂³×C₅	—	3	4	no	—
491	C₂³×C₅	—	3	2	no	—
492	C₂³×C₅	—	3	2	no	—
493	C₂³×C₅	—	3	2	no	—
494	C₂³×C₅	—	6	8	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	8	no	—
501	C₂³×C₅	—	6	2	no	—
502	C₂³×C₅	—	6	2	no	—
503	C₂³×C₅	—	6	2	no	—
504	C₂³×C₅	—	12	4	no	—
505	C₂³×C₅	—	12	16	no	—
506	C₂³×C₅	#239	1	4	yes	—
507	C₂³×C₅	C₂³×D₃	1	2	yes	—
508	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
509	C₅×Q₈	—	4	4	no	—
510	C₅×D₄	—	6	8	no	—
511	C₅×D₄	—	6	8	no	—
512	C₅×D₄	—	12	4	no	—
513	C₂×C₄×C₅	—	2	2	no	—
514	C₂×C₄×C₅	—	2	2	no	—
515	C₂×C₄×C₅	—	2	2	no	—
516	C₂×C₄×C₅	—	2	2	no	—
517	C₂×C₄×C₅	—	2	2	no	—
518	C₂×C₄×C₅	—	2	2	no	—
519	C₂×C₄×C₅	—	3	2	no	—
520	C₂×C₄×C₅	—	3	2	no	—
521	C₂×C₄×C₅	—	3	2	no	—
522	C₂×C₄×C₅	—	3	2	no	—
523	C₂×C₄×C₅	—	3	2	no	—
524	C₂×C₄×C₅	—	4	4	no	—
525	C₂×C₄×C₅	—	6	8	no	—
526	C₂×C₄×C₅	—	6	2	no	—
527	C₂×C₄×C₅	—	6	8	no	—
528	C₂×C₄×C₅	—	6	2	no	—
529	C₂×C₄×C₅	—	6	2	no	—
530	C₂×C₄×C₅	—	6	2	no	—
531	C₂×C₄×C₅	—	6	2	no	—
532	C₂×C₄×C₅	—	12	4	no	—
533	C₂×C₄×C₅	—	12	4	no	—
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	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
538	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
539	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
540	C₂⁵	—	3	1	no	—
541	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
542	C₂²×D₄	—	3	1	no	—
543	C₂²×D₄	—	3	1	no	—
544	C₂²×D₄	—	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	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
550	#126	—	3	8	no	—
551	#126	—	3	8	no	—
552	#124	—	3	8	no	—
553	#123	—	3	8	no	—
554	#123	—	3	8	no	—
555	#123	—	3	8	no	—
556	C₂²⋊Q₈	—	3	8	no	—
557	C₂²⋊Q₈	C₂×C₅×D₃	1	8	yes	complemented
558	#120	—	3	8	no	—
559	C₄×D₄	—	3	8	no	—
560	C₄×D₄	—	3	8	no	—
561	#117	—	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	C₂×C₅×D₃	1	1	yes	characteristic, complemented
569	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
570	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
571	C₂×C₂²⋊C₄	—	3	1	no	—
572	C₂×C₂²⋊C₄	—	3	1	no	—
573	C₂×C₂²⋊C₄	—	3	1	no	—
574	C₂×C₂²⋊C₄	—	3	1	no	—
575	C₂×C₂²⋊C₄	—	3	1	no	—
576	C₂×C₂²⋊C₄	—	3	1	no	—
577	C₂×C₂²⋊C₄	—	3	1	no	—
578	C₂×C₂²⋊C₄	—	3	8	no	—
579	C₂×C₂²⋊C₄	—	3	1	no	—
580	C₂×C₂²⋊C₄	—	3	1	no	—
581	C₂×C₂²⋊C₄	—	3	1	no	—
582	C₂×C₂²⋊C₄	—	3	1	no	—
583	C₂×C₂²⋊C₄	—	3	1	no	—
584	C₂×C₂²⋊C₄	—	3	8	no	—
585	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
586	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
587	C₂×C₄²	—	3	1	no	—
588	C₂×C₄²	—	3	1	no	—
589	C₂×C₄²	—	3	1	no	—
590	C₂×C₃×C₅	—	2	4	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	C₅×D₃	—	2	4	no	—
596	C₅×D₃	—	4	2	no	—
597	C₅×D₃	—	4	2	no	—
598	C₂³×C₃	—	2	2	no	—
599	C₂³×C₃	—	2	2	no	—
600	C₂³×C₃	C₅×#41	1	4	yes	—
601	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
602	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
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	8	no	—
608	C₂²×D₃	—	2	2	no	—
609	C₂²×D₃	—	2	2	no	—
610	C₂²×D₃	—	2	2	no	—
611	C₂²×D₃	—	2	2	no	—
612	C₂²×D₃	—	2	8	no	—
613	C₂²×D₃	—	4	4	no	—
614	C₂²×D₃	—	4	16	no	—
615	C₂²×D₃	C₅×#41	1	4	yes	—
616	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
617	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
618	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
619	C₃×Q₈	—	4	4	no	—
620	C₂×C₃×C₄	—	2	2	no	—
621	C₂×C₃×C₄	—	2	2	no	—
622	C₂×C₃×C₄	—	2	2	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	—	4	4	no	—
627	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
628	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
629	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
630	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
631	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
632	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
633	#67	—	2	8	no	—
634	C₂×Dic₃	—	2	2	no	—
635	C₂×Dic₃	—	2	8	no	—
636	C₂×Dic₃	—	2	2	no	—
637	C₂×Dic₃	—	2	2	no	—
638	C₂×Dic₃	—	2	2	no	—
639	C₂×Dic₃	—	2	2	no	—
640	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
641	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
642	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
643	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
644	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
645	D₁₂	—	2	8	no	—
646	D₁₂	—	4	4	no	—
647	C₄×D₃	—	2	8	no	—
648	C₄×D₃	—	4	4	no	—
649	C₄×D₃	—	4	4	no	—
650	C₂²×C₅	—	2	8	no	—
651	C₂²×C₅	—	2	2	no	—
652	C₂²×C₅	—	2	2	no	—
653	C₂²×C₅	—	3	4	no	—
654	C₂²×C₅	—	6	8	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	—	6	2	no	—
661	C₂²×C₅	—	6	2	no	—
662	C₂²×C₅	—	6	2	no	—
663	C₂²×C₅	—	12	16	no	—
664	C₂²×C₅	—	12	4	no	—
665	C₂²×C₅	—	12	4	no	—
666	C₂²×C₅	#1004	1	2	yes	—
667	C₂²×C₅	C₂×#239	1	4	yes	—
668	C₂²×C₅	C₂×#239	1	2	yes	—
669	C₂²×C₅	D₃×#41	1	2	yes	—
670	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
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	C₄×C₅	—	6	2	no	—
678	C₄×C₅	—	6	2	no	—
679	C₄×C₅	—	6	2	no	—
680	C₄×C₅	—	6	2	no	—
681	C₄×C₅	—	6	2	no	—
682	C₂⁴	—	3	1	no	—
683	C₂⁴	—	3	1	no	—
684	C₂⁴	—	3	1	no	—
685	C₂⁴	—	3	4	no	—
686	C₂⁴	—	6	4	no	—
687	C₂⁴	—	6	4	no	—
688	C₂⁴	—	12	2	no	—
689	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
690	C₂×Q₈	—	4	2	no	—
691	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	complemented
692	C₂×D₄	—	3	4	no	—
693	C₂×D₄	—	3	4	no	—
694	C₂×D₄	—	3	4	no	—
695	C₂×D₄	—	6	4	no	—
696	C₂×D₄	—	6	4	no	—
697	C₂×D₄	—	12	2	no	—
698	C₂²×C₄	—	3	1	no	—
699	C₂²×C₄	—	3	1	no	—
700	C₂²×C₄	—	3	1	no	—
701	C₂²×C₄	—	3	1	no	—
702	C₂²×C₄	—	3	1	no	—
703	C₂²×C₄	—	3	4	no	—
704	C₂²×C₄	—	3	4	no	—
705	C₂²×C₄	—	3	4	no	—
706	C₂²×C₄	—	3	4	no	—
707	C₂²×C₄	—	4	2	no	—
708	C₂²×C₄	—	6	4	no	—
709	C₂²×C₄	—	6	4	no	—
710	C₂²×C₄	—	12	2	no	—
711	C₂²×C₄	—	12	2	no	—
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	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
717	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
718	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
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	—	3	4	no	—
724	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
725	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
726	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
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	—	3	4	no	—
734	C₂²⋊C₄	—	3	4	no	—
735	C₂²⋊C₄	—	3	4	no	—
736	C₂²⋊C₄	—	3	4	no	—
737	C₂²⋊C₄	—	3	4	no	—
738	C₂²⋊C₄	—	3	4	no	—
739	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
740	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
741	C₄²	—	3	4	no	—
742	C₄²	—	3	4	no	—
743	C₄²	—	3	4	no	—
744	C₃×C₅	C₂×#551	1	1	yes	characteristic, complemented, Hall
745	C₂²×C₃	—	2	8	no	—
746	C₂²×C₃	—	2	2	no	—
747	C₂²×C₃	—	2	2	no	—
748	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
749	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
750	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
751	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
752	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
753	C₂×D₃	—	2	8	no	—
754	C₂×D₃	—	2	2	no	—
755	C₂×D₃	—	2	2	no	—
756	C₂×D₃	—	2	2	no	—
757	C₂×D₃	—	2	2	no	—
758	C₂×D₃	—	2	2	no	—
759	C₂×D₃	—	2	2	no	—
760	C₂×D₃	—	2	2	no	—
761	C₂×D₃	—	2	2	no	—
762	C₂×D₃	—	4	16	no	—
763	C₂×D₃	—	4	4	no	—
764	C₂×D₃	—	4	4	no	—
765	C₂×D₃	C₂×C₅×#41	1	4	yes	—
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	Dic₃	—	2	2	no	—
773	Dic₃	—	2	2	no	—
774	Dic₃	—	2	2	no	—
775	Dic₃	—	2	2	no	—
776	Dic₃	—	2	2	no	—
777	C₂×C₅	—	2	4	no	—
778	C₂×C₅	—	6	4	no	—
779	C₂×C₅	—	12	2	no	—
780	C₂×C₅	—	12	2	no	—
781	C₂×C₅	#5637	1	4	yes	direct product factor
782	C₂×C₅	C₂×#1004	1	1	yes	characteristic
783	C₂×C₅	C₂²×#239	1	1	yes	characteristic
784	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
785	C₂³	—	2	2	no	—
786	C₂³	—	2	2	no	—
787	C₂³	—	3	4	no	—
788	C₂³	—	3	2	no	—
789	C₂³	—	3	2	no	—
790	C₂³	—	3	2	no	—
791	C₂³	—	6	8	no	—
792	C₂³	—	6	2	no	—
793	C₂³	—	6	2	no	—
794	C₂³	—	6	2	no	—
795	C₂³	—	6	2	no	—
796	C₂³	—	6	2	no	—
797	C₂³	—	6	8	no	—
798	C₂³	—	6	2	no	—
799	C₂³	—	6	2	no	—
800	C₂³	—	6	2	no	—
801	C₂³	—	12	4	no	—
802	C₂³	—	12	16	no	—
803	C₂³	C₅×#239	1	4	yes	—
804	C₂³	C₂³×C₅×D₃	1	2	yes	—
805	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
806	Q₈	—	4	4	no	—
807	D₄	—	6	8	no	—
808	D₄	—	6	8	no	—
809	D₄	—	12	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	—	3	2	no	—
817	C₂×C₄	—	3	2	no	—
818	C₂×C₄	—	3	2	no	—
819	C₂×C₄	—	3	2	no	—
820	C₂×C₄	—	3	2	no	—
821	C₂×C₄	—	4	4	no	—
822	C₂×C₄	—	6	8	no	—
823	C₂×C₄	—	6	2	no	—
824	C₂×C₄	—	6	8	no	—
825	C₂×C₄	—	6	2	no	—
826	C₂×C₄	—	6	2	no	—
827	C₂×C₄	—	6	2	no	—
828	C₂×C₄	—	6	2	no	—
829	C₂×C₄	—	12	4	no	—
830	C₂×C₄	—	12	4	no	—
831	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
832	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
833	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
834	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
835	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
836	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
837	C₂×C₃	—	2	4	no	—
838	C₂×C₃	C₅×#551	1	4	yes	complemented
839	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
840	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
841	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
842	D₃	—	2	4	no	—
843	D₃	—	4	2	no	—
844	D₃	—	4	2	no	—
845	C₅	C₂×#5637	1	1	yes	characteristic, direct product factor, Sylow
846	C₂²	—	2	2	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	8	no	—
849	C₂²	—	3	4	no	—
850	C₂²	—	6	2	no	—
851	C₂²	—	6	2	no	—
852	C₂²	—	6	8	no	—
853	C₂²	—	6	2	no	—
854	C₂²	—	6	2	no	—
855	C₂²	—	6	2	no	—
856	C₂²	—	6	2	no	—
857	C₂²	—	6	2	no	—
858	C₂²	—	6	2	no	—
859	C₂²	—	12	16	no	—
860	C₂²	—	12	4	no	—
861	C₂²	—	12	4	no	—
862	C₂²	C₅×#1004	1	2	yes	—
863	C₂²	C₂×C₅×#239	1	4	yes	—
864	C₂²	C₂×C₅×#239	1	2	yes	—
865	C₂²	C₅×D₃×#41	1	2	yes	—
866	C₂²	C₂⁴×C₅×D₃	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	—	6	2	no	—
874	C₄	—	6	2	no	—
875	C₄	—	6	2	no	—
876	C₄	—	6	2	no	—
877	C₄	—	6	2	no	—
878	C₃	C₂×C₅×#551	1	1	yes	characteristic, complemented, Sylow
879	C₂	—	2	4	no	—
880	C₂	—	6	4	no	—
881	C₂	—	12	2	no	—
882	C₂	—	12	2	no	—
883	C₂	C₅×#5637	1	4	yes	direct product factor
884	C₂	C₂×C₅×#1004	1	1	yes	characteristic
885	C₂	C₂²×C₅×#239	1	1	yes	characteristic
886	C₂	C₂×C₅×D₃×#41	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×C₂²⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₅×#882	C₂
hypercenter	C₂×C₅×C₂²⋊Q₈	D₃
hypocenter	C₃	C₂×C₅×#551
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₂²⋊Q₈	C₂	semidirect
2. C₂×C₅×#947	C₂	semidirect
3. C₂×C₅×#946	C₂	semidirect
4. C₂×C₄×C₅×#67	C₂	semidirect
5. C₂²×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₅×#5637	C₂	direct (N × H)
7. C₂×C₅×#898	C₂	semidirect
8. C₂×C₅×#898	C₂	semidirect
9. C₂×C₅×#894	C₂	semidirect
10. C₂×C₅×#894	C₂	semidirect
11. C₂×C₅×#893	C₂	semidirect
12. C₂×C₅×#892	C₂	semidirect
13. C₂×C₅×#886	C₂	semidirect
15. C₂×C₅×D₃×C₂²⋊C₄	C₂	semidirect
16. C₂×C₅×#877	C₂	semidirect
19. C₂²×C₃×C₅×Q₈	C₂²	semidirect
27. C₂²×C₄×C₅×D₃	C₂²	semidirect
28. C₃×C₅×C₂²⋊Q₈	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. C₅×#947	C₂²	semidirect
36. C₅×#946	C₂²	semidirect
37. C₄×C₅×#67	C₂²	semidirect
46. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
47. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
48. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
49. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
50. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
51. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
52. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
53. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
54. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
55. C₂×C₄×C₅×Dic₃	C₂²	semidirect
56. C₂×C₄×C₅×Dic₃	C₂²	semidirect
57. C₂×C₄×C₅×Dic₃	C₂²	semidirect
58. C₅×#898	C₂²	semidirect
59. C₅×#898	C₂²	semidirect
60. C₅×#894	C₂²	semidirect
61. C₅×#894	C₂²	semidirect
62. C₅×#893	C₂²	semidirect
63. C₅×#892	C₂²	semidirect
64. C₅×#886	C₂²	semidirect
66. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
67. C₅×#877	C₂²	semidirect
68. C₂×#5637	C₅	direct (N × H)
77. C₂×C₅×C₂²⋊Q₈	D₃	semidirect
94. C₂×C₃×C₅×Q₈	C₂³	semidirect
121. C₂×C₄×C₅×D₃	C₂³	semidirect
122. C₃×C₅×C₄⋊C₄	C₂³	semidirect
123. C₃×C₅×C₄⋊C₄	C₂³	semidirect
124. C₃×C₅×C₄⋊C₄	C₂³	semidirect
136. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
137. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
138. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
139. C₅×C₄⋊Dic₃	C₂³	semidirect
140. C₅×C₄⋊Dic₃	C₂³	semidirect
141. C₅×Dic₃⋊C₄	C₂³	semidirect
142. C₅×Dic₃⋊C₄	C₂³	semidirect
143. C₅×Dic₃⋊C₄	C₂³	semidirect
144. C₄×C₅×Dic₃	C₂³	semidirect
145. C₄×C₅×Dic₃	C₂³	semidirect
146. C₄×C₅×Dic₃	C₂³	semidirect
147. C₂×C₃×C₂²⋊Q₈	C₂×C₅	semidirect
148. C₂×#947	C₂×C₅	semidirect
149. C₂×#946	C₂×C₅	semidirect
150. C₂×C₄×#67	C₂×C₅	semidirect
151. C₂²×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
152. #5637	C₂×C₅	direct (N × H)
153. C₂×#898	C₂×C₅	semidirect
154. C₂×#898	C₂×C₅	semidirect
155. C₂×#894	C₂×C₅	semidirect
156. C₂×#894	C₂×C₅	semidirect
157. C₂×#893	C₂×C₅	semidirect
158. C₂×#892	C₂×C₅	semidirect
159. C₂×#886	C₂×C₅	semidirect
161. C₂×D₃×C₂²⋊C₄	C₂×C₅	semidirect
162. C₂×#877	C₂×C₅	semidirect
164. C₂²×C₅×Q₈	C₂×D₃	semidirect
180. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
191. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
192. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
193. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
267. C₂²×C₃×Q₈	C₂²×C₅	semidirect
275. C₂²×C₄×D₃	C₂²×C₅	semidirect
276. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
277. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
278. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
279. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
283. #947	C₂²×C₅	semidirect
284. #946	C₂²×C₅	semidirect
285. C₄×#67	C₂²×C₅	semidirect
294. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
295. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
296. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
297. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
298. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
299. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
300. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
301. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
302. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
303. C₂×C₄×Dic₃	C₂²×C₅	semidirect
304. C₂×C₄×Dic₃	C₂²×C₅	semidirect
305. C₂×C₄×Dic₃	C₂²×C₅	semidirect
306. #898	C₂²×C₅	semidirect
307. #898	C₂²×C₅	semidirect
308. #894	C₂²×C₅	semidirect
309. #894	C₂²×C₅	semidirect
310. #893	C₂²×C₅	semidirect
311. #892	C₂²×C₅	semidirect
312. #886	C₂²×C₅	semidirect
314. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
315. #877	C₂²×C₅	semidirect
325. C₂×C₅×Q₈	C₂²×D₃	semidirect
358. C₅×C₄⋊C₄	C₂²×D₃	semidirect
359. C₅×C₄⋊C₄	C₂²×D₃	semidirect
360. C₅×C₄⋊C₄	C₂²×D₃	semidirect
386. C₂×C₂²⋊Q₈	C₅×D₃	semidirect
435. C₂×C₃×Q₈	C₂³×C₅	semidirect
462. C₂×C₄×D₃	C₂³×C₅	semidirect
463. C₃×C₄⋊C₄	C₂³×C₅	semidirect
464. C₃×C₄⋊C₄	C₂³×C₅	semidirect
465. C₃×C₄⋊C₄	C₂³×C₅	semidirect
477. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
478. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
479. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
480. C₄⋊Dic₃	C₂³×C₅	semidirect
481. C₄⋊Dic₃	C₂³×C₅	semidirect
482. Dic₃⋊C₄	C₂³×C₅	semidirect
483. Dic₃⋊C₄	C₂³×C₅	semidirect
484. Dic₃⋊C₄	C₂³×C₅	semidirect
485. C₄×Dic₃	C₂³×C₅	semidirect
486. C₄×Dic₃	C₂³×C₅	semidirect
487. C₄×Dic₃	C₂³×C₅	semidirect
541. C₂²×Q₈	C₂×C₅×D₃	semidirect
557. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
568. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
569. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
570. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
591. C₂×C₃×C₅	#551	semidirect
691. C₂×Q₈	C₂²×C₅×D₃	semidirect
724. C₄⋊C₄	C₂²×C₅×D₃	semidirect
725. C₄⋊C₄	C₂²×C₅×D₃	semidirect
726. C₄⋊C₄	C₂²×C₅×D₃	semidirect
744. C₃×C₅	C₂×#551	semidirect
781. C₂×C₅	#5637	direct (N × H)
838. C₂×C₃	C₅×#551	semidirect
845. C₅	C₂×#5637	direct (N × H)
878. C₃	C₂×C₅×#551	semidirect
883. C₂	C₅×#5637	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×C₂²⋊Q₈	2
C₂×C₅×#947	2
C₂×C₅×#946	2
C₂×C₄×C₅×#67	2
C₂²×C₅×(C₂×D₃)⋊C₄	2
C₅×#5637	2
C₂×C₅×#898	2
C₂×C₅×#894	2
C₂×C₅×#893	2
C₂×C₅×#892	2
C₂×C₅×#886	2
C₂×C₅×#882	2
C₂×C₅×D₃×C₂²⋊C₄	2
C₂×C₅×#877	2
C₂×C₅×#551	3
C₂×#5637	5

Subgroups — C2×C5×#5637 #14483244

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5637 #14483244