Subgroups — C₂×C₅×#5678 #14480755

Order 1920.

2672 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	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×C₅×#939	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#937	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5678	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₅×#886	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#884	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#884	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#883	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#882	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×D₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅×#879	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#876	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅×#538	—	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	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
22	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
23	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
24	C₂²×C₅×#67	C₂²	1	1	yes	characteristic, complemented
25	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
27	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
28	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₅×#124	C₂²	1	8	yes	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, complemented
35	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₅×#217	C₂²	1	1	yes	characteristic
38	C₂×C₅×#217	C₂²	1	1	yes	characteristic
39	C₅×#947	C₂²	1	8	yes	complemented
40	C₅×#946	C₂²	1	8	yes	complemented
41	C₅×#939	C₂²	1	8	yes	complemented
42	C₅×#937	C₂²	1	8	yes	complemented
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	1	yes	characteristic
47	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₅×C₄⋊Dic₃	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×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
58	C₅×#886	C₂²	1	8	yes	complemented
59	C₅×#884	C₂²	1	8	yes	complemented
60	C₅×#884	C₂²	1	8	yes	complemented
61	C₅×#883	C₂²	1	8	yes	complemented
62	C₅×#882	C₂²	1	8	yes	complemented
63	C₅×#67⋊C₄	C₂²	1	8	yes	complemented
64	C₅×D₃×C₂²⋊C₄	C₂²	1	8	yes	complemented
65	C₅×#879	C₂²	1	8	yes	complemented
66	C₅×#876	C₂²	1	8	yes	complemented
67	C₄×C₅×D₁₂	C₂²	1	8	yes	complemented
68	C₂×#5678	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
69	C₅×#538	—	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×#124	D₃	1	1	yes	characteristic, complemented
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×#121	—	3	1	no	—
78	C₂×C₅×#121	—	3	1	no	—
79	C₂×C₅×#121	—	3	1	no	—
80	C₂×C₅×#120	—	3	1	no	—
81	C₂×C₅×#120	—	3	1	no	—
82	C₂×C₄×C₅×D₄	—	3	1	no	—
83	C₂×C₄×C₅×D₄	—	3	1	no	—
84	C₂²×C₅×C₂²⋊C₄	—	3	1	no	—
85	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
86	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
87	C₂³×C₅×D₃	—	2	4	no	—
88	C₂³×C₅×D₃	—	4	2	no	—
89	C₂³×C₅×D₃	—	4	2	no	—
90	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
91	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
92	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
93	C₂³×C₅×D₃	C₂³	1	4	yes	—
94	C₂×C₃×C₅×Q₈	—	4	2	no	—
95	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	complemented
96	C₂×C₃×C₅×D₄	—	4	2	no	—
97	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
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	1	yes	characteristic
103	C₂×C₅×#67	—	2	4	no	—
104	C₂×C₅×#67	—	4	2	no	—
105	C₂×C₅×#67	—	4	2	no	—
106	C₂×C₅×#67	—	4	2	no	—
107	C₂×C₅×#67	C₂³	1	4	yes	—
108	C₂×C₅×#67	C₂³	1	4	yes	—
109	C₂×C₅×#67	C₂³	1	4	yes	—
110	C₂×C₅×#67	C₂³	1	4	yes	complemented
111	C₂²×C₅×Dic₃	—	4	2	no	—
112	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
113	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
114	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
115	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
116	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
117	C₂²×C₅×Dic₃	C₂³	1	4	yes	complemented
118	C₂×C₅×D₁₂	—	2	4	no	—
119	C₂×C₅×D₁₂	—	4	2	no	—
120	C₂×C₅×D₁₂	C₂³	1	4	yes	—
121	C₂×C₅×D₁₂	C₂³	1	4	yes	—
122	C₂×C₄×C₅×D₃	—	4	2	no	—
123	C₂×C₄×C₅×D₃	—	4	2	no	—
124	C₂×C₄×C₅×D₃	—	4	2	no	—
125	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
126	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
127	C₂×C₄×C₅×D₃	C₂³	1	4	yes	complemented
128	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
129	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
131	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
132	C₃×C₄²×C₅	C₂³	1	4	yes	complemented
133	C₅×#217	C₂³	1	4	yes	—
134	C₅×#217	C₂³	1	4	yes	—
135	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
136	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
137	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
138	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
139	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
140	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
141	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
142	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	complemented
143	C₅×C₄⋊Dic₃	C₂³	1	4	yes	complemented
144	C₅×C₄⋊Dic₃	C₂³	1	4	yes	complemented
145	C₅×Dic₃⋊C₄	C₂³	1	4	yes	complemented
146	C₅×Dic₃⋊C₄	C₂³	1	4	yes	complemented
147	C₅×Dic₃⋊C₄	C₂³	1	4	yes	complemented
148	C₅×Dic₃⋊C₄	C₂³	1	4	yes	complemented
149	C₄×C₅×Dic₃	C₂³	1	4	yes	complemented
150	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic, complemented
151	C₂×#947	C₂×C₅	1	1	yes	characteristic, complemented
152	C₂×#946	C₂×C₅	1	1	yes	characteristic, complemented
153	C₂×#939	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂×#937	C₂×C₅	1	1	yes	characteristic, complemented
155	#5678	C₂×C₅	1	16	yes	direct product factor
156	C₂×#886	C₂×C₅	1	1	yes	characteristic, complemented
157	C₂×#884	C₂×C₅	1	1	yes	characteristic, complemented
158	C₂×#884	C₂×C₅	1	1	yes	characteristic, complemented
159	C₂×#883	C₂×C₅	1	1	yes	characteristic, complemented
160	C₂×#882	C₂×C₅	1	1	yes	characteristic, complemented
161	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
162	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
163	C₂×#879	C₂×C₅	1	1	yes	characteristic, complemented
164	C₂×#876	C₂×C₅	1	1	yes	characteristic, complemented
165	C₂×C₄×D₁₂	C₂×C₅	1	1	yes	characteristic, complemented
166	C₂⁵×C₅	—	3	1	no	—
167	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic, complemented
168	C₂²×C₅×D₄	—	3	1	no	—
169	C₂²×C₅×D₄	—	3	1	no	—
170	C₂²×C₅×D₄	—	3	1	no	—
171	C₂²×C₅×D₄	—	3	1	no	—
172	C₂²×C₅×D₄	—	3	1	no	—
173	C₂²×C₅×D₄	—	3	1	no	—
174	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
175	C₂³×C₄×C₅	—	3	1	no	—
176	C₂³×C₄×C₅	—	3	1	no	—
177	C₂³×C₄×C₅	—	3	1	no	—
178	C₂³×C₄×C₅	—	3	1	no	—
179	C₅×#126	—	3	8	no	—
180	C₅×#126	—	3	8	no	—
181	C₅×#124	—	3	8	no	—
182	C₅×#124	C₂×D₃	1	8	yes	complemented
183	C₅×#123	—	3	8	no	—
184	C₅×#123	—	3	8	no	—
185	C₅×C₂²⋊Q₈	—	3	8	no	—
186	C₅×#121	—	3	8	no	—
187	C₅×#121	—	3	8	no	—
188	C₅×#121	—	3	8	no	—
189	C₅×#120	—	3	8	no	—
190	C₅×#120	—	3	8	no	—
191	C₄×C₅×D₄	—	3	8	no	—
192	C₄×C₅×D₄	—	3	8	no	—
193	C₂×C₅×C₄⋊C₄	—	3	1	no	—
194	C₂×C₅×C₄⋊C₄	—	3	1	no	—
195	C₂×C₅×C₄⋊C₄	—	3	1	no	—
196	C₂×C₅×C₄⋊C₄	—	3	1	no	—
197	C₂×C₅×C₄⋊C₄	—	3	1	no	—
198	C₂×C₅×C₄⋊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	1	no	—
204	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
205	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
206	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
207	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
208	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
209	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
210	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
211	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
212	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
213	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic, complemented
214	C₂×C₄²×C₅	—	3	1	no	—
215	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic, complemented
216	C₂×#538	—	3	1	no	Sylow
217	C₂³×C₃×C₅	—	2	2	no	—
218	C₂³×C₃×C₅	—	2	2	no	—
219	C₂³×C₃×C₅	—	2	2	no	—
220	C₂³×C₃×C₅	—	2	2	no	—
221	C₂³×C₃×C₅	—	2	2	no	—
222	C₂³×C₃×C₅	—	2	2	no	—
223	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
224	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
225	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
226	C₂²×C₅×D₃	—	2	2	no	—
227	C₂²×C₅×D₃	—	2	2	no	—
228	C₂²×C₅×D₃	—	2	2	no	—
229	C₂²×C₅×D₃	—	2	2	no	—
230	C₂²×C₅×D₃	—	2	2	no	—
231	C₂²×C₅×D₃	—	2	2	no	—
232	C₂²×C₅×D₃	—	2	2	no	—
233	C₂²×C₅×D₃	—	2	2	no	—
234	C₂²×C₅×D₃	—	2	8	no	—
235	C₂²×C₅×D₃	—	4	4	no	—
236	C₂²×C₅×D₃	—	4	4	no	—
237	C₂²×C₅×D₃	—	4	16	no	—
238	C₂²×C₅×D₃	#41	1	4	yes	—
239	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
240	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
241	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
242	C₃×C₅×Q₈	—	4	4	no	—
243	C₃×C₅×D₄	—	4	4	no	—
244	C₂×C₃×C₄×C₅	—	2	2	no	—
245	C₂×C₃×C₄×C₅	—	2	2	no	—
246	C₂×C₃×C₄×C₅	—	2	2	no	—
247	C₂×C₃×C₄×C₅	—	2	2	no	—
248	C₂×C₃×C₄×C₅	—	2	2	no	—
249	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
250	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
251	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
252	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
253	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
254	C₅×#67	—	2	8	no	—
255	C₅×#67	—	4	4	no	—
256	C₅×#67	—	4	4	no	—
257	C₅×#67	—	4	4	no	—
258	C₂×C₅×Dic₃	—	2	2	no	—
259	C₂×C₅×Dic₃	—	2	2	no	—
260	C₂×C₅×Dic₃	—	2	2	no	—
261	C₂×C₅×Dic₃	—	2	2	no	—
262	C₂×C₅×Dic₃	—	2	2	no	—
263	C₂×C₅×Dic₃	—	4	4	no	—
264	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
265	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
266	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
267	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
268	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
269	C₅×D₁₂	—	2	8	no	—
270	C₅×D₁₂	—	4	4	no	—
271	C₄×C₅×D₃	—	4	4	no	—
272	C₄×C₅×D₃	—	4	4	no	—
273	C₄×C₅×D₃	—	4	4	no	—
274	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
275	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
276	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
277	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
278	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
279	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
280	C₂²×#67	C₂²×C₅	1	1	yes	characteristic, complemented
281	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
282	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
283	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
284	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
285	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
286	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic, complemented
287	C₃×#124	C₂²×C₅	1	8	yes	complemented
288	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
289	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
290	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
291	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
292	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
293	C₂×#217	C₂²×C₅	1	1	yes	characteristic
294	C₂×#217	C₂²×C₅	1	1	yes	characteristic
295	#947	C₂²×C₅	1	8	yes	complemented
296	#946	C₂²×C₅	1	8	yes	complemented
297	#939	C₂²×C₅	1	8	yes	complemented
298	#937	C₂²×C₅	1	8	yes	complemented
299	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
300	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
301	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
302	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
303	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
304	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
305	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
306	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
307	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
308	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
309	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
310	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
311	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
312	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
313	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
314	#886	C₂²×C₅	1	8	yes	complemented
315	#884	C₂²×C₅	1	8	yes	complemented
316	#884	C₂²×C₅	1	8	yes	complemented
317	#883	C₂²×C₅	1	8	yes	complemented
318	#882	C₂²×C₅	1	8	yes	complemented
319	#67⋊C₄	C₂²×C₅	1	8	yes	complemented
320	D₃×C₂²⋊C₄	C₂²×C₅	1	8	yes	complemented
321	#879	C₂²×C₅	1	8	yes	complemented
322	#876	C₂²×C₅	1	8	yes	complemented
323	C₄×D₁₂	C₂²×C₅	1	8	yes	complemented
324	C₂⁴×C₅	—	3	1	no	—
325	C₂⁴×C₅	—	3	1	no	—
326	C₂⁴×C₅	—	3	1	no	—
327	C₂⁴×C₅	—	3	4	no	—
328	C₂⁴×C₅	—	6	4	no	—
329	C₂⁴×C₅	—	12	2	no	—
330	C₂⁴×C₅	—	12	2	no	—
331	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
332	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
333	C₂×C₅×Q₈	—	4	2	no	—
334	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	complemented
335	C₂×C₅×D₄	—	3	4	no	—
336	C₂×C₅×D₄	—	3	4	no	—
337	C₂×C₅×D₄	—	3	4	no	—
338	C₂×C₅×D₄	—	3	4	no	—
339	C₂×C₅×D₄	—	3	4	no	—
340	C₂×C₅×D₄	—	3	4	no	—
341	C₂×C₅×D₄	—	4	2	no	—
342	C₂×C₅×D₄	—	6	4	no	—
343	C₂×C₅×D₄	—	6	4	no	—
344	C₂×C₅×D₄	—	12	2	no	—
345	C₂×C₅×D₄	—	12	2	no	—
346	C₂×C₅×D₄	—	12	2	no	—
347	C₂×C₅×D₄	—	12	2	no	—
348	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
349	C₂²×C₄×C₅	—	3	1	no	—
350	C₂²×C₄×C₅	—	3	1	no	—
351	C₂²×C₄×C₅	—	3	1	no	—
352	C₂²×C₄×C₅	—	3	1	no	—
353	C₂²×C₄×C₅	—	3	1	no	—
354	C₂²×C₄×C₅	—	3	4	no	—
355	C₂²×C₄×C₅	—	3	4	no	—
356	C₂²×C₄×C₅	—	3	4	no	—
357	C₂²×C₄×C₅	—	3	4	no	—
358	C₂²×C₄×C₅	—	12	2	no	—
359	C₂²×C₄×C₅	—	12	2	no	—
360	C₂²×C₄×C₅	—	12	2	no	—
361	C₂²×C₄×C₅	—	12	2	no	—
362	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
363	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
364	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
365	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
366	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
367	C₅×C₄⋊C₄	—	3	4	no	—
368	C₅×C₄⋊C₄	—	3	4	no	—
369	C₅×C₄⋊C₄	—	3	4	no	—
370	C₅×C₄⋊C₄	—	3	4	no	—
371	C₅×C₄⋊C₄	—	3	4	no	—
372	C₅×C₄⋊C₄	—	3	4	no	—
373	C₅×C₂²⋊C₄	—	3	4	no	—
374	C₅×C₂²⋊C₄	—	3	4	no	—
375	C₅×C₂²⋊C₄	—	3	4	no	—
376	C₅×C₂²⋊C₄	—	3	4	no	—
377	C₅×C₂²⋊C₄	—	3	4	no	—
378	C₅×C₂²⋊C₄	—	3	4	no	—
379	C₅×C₂²⋊C₄	—	3	4	no	—
380	C₅×C₂²⋊C₄	—	3	4	no	—
381	C₅×C₂²⋊C₄	—	3	4	no	—
382	C₅×C₂²⋊C₄	—	3	4	no	—
383	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
384	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
385	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	complemented
386	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	complemented
387	C₄²×C₅	—	3	4	no	—
388	C₄²×C₅	C₂²×D₃	1	4	yes	complemented
389	#538	—	3	16	no	—
390	C₂×#126	—	3	1	no	—
391	C₂×#126	—	3	1	no	—
392	C₂×#124	—	3	1	no	—
393	C₂×#124	C₅×D₃	1	1	yes	characteristic, complemented
394	C₂×#123	—	3	1	no	—
395	C₂×#123	—	3	1	no	—
396	C₂×C₂²⋊Q₈	—	3	1	no	—
397	C₂×#121	—	3	1	no	—
398	C₂×#121	—	3	1	no	—
399	C₂×#121	—	3	1	no	—
400	C₂×#120	—	3	1	no	—
401	C₂×#120	—	3	1	no	—
402	C₂×C₄×D₄	—	3	1	no	—
403	C₂×C₄×D₄	—	3	1	no	—
404	C₂²×C₂²⋊C₄	—	3	1	no	—
405	C₂²×C₃×C₅	—	2	2	no	—
406	C₂²×C₃×C₅	—	2	2	no	—
407	C₂²×C₃×C₅	—	2	2	no	—
408	C₂²×C₃×C₅	—	2	2	no	—
409	C₂²×C₃×C₅	—	2	2	no	—
410	C₂²×C₃×C₅	—	2	2	no	—
411	C₂²×C₃×C₅	—	4	4	no	—
412	C₂²×C₃×C₅	—	4	4	no	—
413	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
414	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
415	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
416	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
417	C₂×C₅×D₃	—	2	8	no	—
418	C₂×C₅×D₃	—	2	2	no	—
419	C₂×C₅×D₃	—	2	2	no	—
420	C₂×C₅×D₃	—	2	2	no	—
421	C₂×C₅×D₃	—	2	2	no	—
422	C₂×C₅×D₃	—	2	2	no	—
423	C₂×C₅×D₃	—	2	2	no	—
424	C₂×C₅×D₃	—	2	2	no	—
425	C₂×C₅×D₃	—	2	2	no	—
426	C₂×C₅×D₃	—	4	16	no	—
427	C₂×C₅×D₃	—	4	4	no	—
428	C₂×C₅×D₃	—	4	4	no	—
429	C₂×C₅×D₃	C₂×#41	1	4	yes	—
430	C₃×C₄×C₅	—	2	2	no	—
431	C₃×C₄×C₅	—	2	2	no	—
432	C₃×C₄×C₅	—	2	2	no	—
433	C₃×C₄×C₅	—	2	2	no	—
434	C₃×C₄×C₅	—	2	2	no	—
435	C₅×Dic₃	—	2	2	no	—
436	C₅×Dic₃	—	2	2	no	—
437	C₅×Dic₃	—	2	2	no	—
438	C₅×Dic₃	—	2	2	no	—
439	C₅×Dic₃	—	2	2	no	—
440	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
441	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
442	C₂³×D₃	—	2	4	no	—
443	C₂³×D₃	—	4	2	no	—
444	C₂³×D₃	—	4	2	no	—
445	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
446	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
447	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
448	C₂³×D₃	C₂³×C₅	1	4	yes	—
449	C₂×C₃×Q₈	—	4	2	no	—
450	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	complemented
451	C₂×C₃×D₄	—	4	2	no	—
452	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
453	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
454	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
455	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
456	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
457	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
458	C₂×#67	—	2	4	no	—
459	C₂×#67	—	4	2	no	—
460	C₂×#67	—	4	2	no	—
461	C₂×#67	—	4	2	no	—
462	C₂×#67	C₂³×C₅	1	4	yes	—
463	C₂×#67	C₂³×C₅	1	4	yes	—
464	C₂×#67	C₂³×C₅	1	4	yes	—
465	C₂×#67	C₂³×C₅	1	4	yes	complemented
466	C₂²×Dic₃	—	4	2	no	—
467	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
468	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
469	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
470	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
471	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
472	C₂²×Dic₃	C₂³×C₅	1	4	yes	complemented
473	C₂×D₁₂	—	2	4	no	—
474	C₂×D₁₂	—	4	2	no	—
475	C₂×D₁₂	C₂³×C₅	1	4	yes	—
476	C₂×D₁₂	C₂³×C₅	1	4	yes	—
477	C₂×C₄×D₃	—	4	2	no	—
478	C₂×C₄×D₃	—	4	2	no	—
479	C₂×C₄×D₃	—	4	2	no	—
480	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
481	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
482	C₂×C₄×D₃	C₂³×C₅	1	4	yes	complemented
483	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
484	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
485	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	complemented
486	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	complemented
487	C₃×C₄²	C₂³×C₅	1	4	yes	complemented
488	#217	C₂³×C₅	1	4	yes	—
489	#217	C₂³×C₅	1	4	yes	—
490	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
491	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
492	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
493	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
494	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
495	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
496	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	complemented
497	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	complemented
498	C₄⋊Dic₃	C₂³×C₅	1	4	yes	complemented
499	C₄⋊Dic₃	C₂³×C₅	1	4	yes	complemented
500	Dic₃⋊C₄	C₂³×C₅	1	4	yes	complemented
501	Dic₃⋊C₄	C₂³×C₅	1	4	yes	complemented
502	Dic₃⋊C₄	C₂³×C₅	1	4	yes	complemented
503	Dic₃⋊C₄	C₂³×C₅	1	4	yes	complemented
504	C₄×Dic₃	C₂³×C₅	1	4	yes	complemented
505	C₂³×C₅	—	2	2	no	—
506	C₂³×C₅	—	2	2	no	—
507	C₂³×C₅	—	2	2	no	—
508	C₂³×C₅	—	2	2	no	—
509	C₂³×C₅	—	2	2	no	—
510	C₂³×C₅	—	2	2	no	—
511	C₂³×C₅	—	3	4	no	—
512	C₂³×C₅	—	3	2	no	—
513	C₂³×C₅	—	3	2	no	—
514	C₂³×C₅	—	3	2	no	—
515	C₂³×C₅	—	6	8	no	—
516	C₂³×C₅	—	6	2	no	—
517	C₂³×C₅	—	6	2	no	—
518	C₂³×C₅	—	6	2	no	—
519	C₂³×C₅	—	6	2	no	—
520	C₂³×C₅	—	6	2	no	—
521	C₂³×C₅	—	6	2	no	—
522	C₂³×C₅	—	6	2	no	—
523	C₂³×C₅	—	6	2	no	—
524	C₂³×C₅	—	12	4	no	—
525	C₂³×C₅	—	12	4	no	—
526	C₂³×C₅	—	12	16	no	—
527	C₂³×C₅	C₂³×D₃	1	2	yes	—
528	C₂³×C₅	C₂³×D₃	1	2	yes	—
529	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
530	C₅×Q₈	—	4	4	no	—
531	C₅×D₄	—	4	4	no	—
532	C₅×D₄	—	6	8	no	—
533	C₅×D₄	—	6	8	no	—
534	C₅×D₄	—	12	4	no	—
535	C₅×D₄	—	12	4	no	—
536	C₅×D₄	—	12	4	no	—
537	C₅×D₄	—	12	4	no	—
538	C₂×C₄×C₅	—	2	2	no	—
539	C₂×C₄×C₅	—	2	2	no	—
540	C₂×C₄×C₅	—	2	2	no	—
541	C₂×C₄×C₅	—	2	2	no	—
542	C₂×C₄×C₅	—	2	2	no	—
543	C₂×C₄×C₅	—	3	2	no	—
544	C₂×C₄×C₅	—	3	2	no	—
545	C₂×C₄×C₅	—	3	2	no	—
546	C₂×C₄×C₅	—	3	2	no	—
547	C₂×C₄×C₅	—	3	2	no	—
548	C₂×C₄×C₅	—	6	2	no	—
549	C₂×C₄×C₅	—	6	2	no	—
550	C₂×C₄×C₅	—	6	2	no	—
551	C₂×C₄×C₅	—	6	2	no	—
552	C₂×C₄×C₅	—	6	2	no	—
553	C₂×C₄×C₅	—	12	4	no	—
554	C₂×C₄×C₅	—	12	4	no	—
555	C₂×C₄×C₅	—	12	4	no	—
556	C₂×C₄×C₅	—	12	4	no	—
557	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
558	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
559	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
560	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
561	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
562	C₂⁵	—	3	1	no	—
563	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
564	C₂²×D₄	—	3	1	no	—
565	C₂²×D₄	—	3	1	no	—
566	C₂²×D₄	—	3	1	no	—
567	C₂²×D₄	—	3	1	no	—
568	C₂²×D₄	—	3	1	no	—
569	C₂²×D₄	—	3	1	no	—
570	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
571	C₂³×C₄	—	3	1	no	—
572	C₂³×C₄	—	3	1	no	—
573	C₂³×C₄	—	3	1	no	—
574	C₂³×C₄	—	3	1	no	—
575	#126	—	3	8	no	—
576	#126	—	3	8	no	—
577	#124	—	3	8	no	—
578	#124	C₂×C₅×D₃	1	8	yes	complemented
579	#123	—	3	8	no	—
580	#123	—	3	8	no	—
581	C₂²⋊Q₈	—	3	8	no	—
582	#121	—	3	8	no	—
583	#121	—	3	8	no	—
584	#121	—	3	8	no	—
585	#120	—	3	8	no	—
586	#120	—	3	8	no	—
587	C₄×D₄	—	3	8	no	—
588	C₄×D₄	—	3	8	no	—
589	C₂×C₄⋊C₄	—	3	1	no	—
590	C₂×C₄⋊C₄	—	3	1	no	—
591	C₂×C₄⋊C₄	—	3	1	no	—
592	C₂×C₄⋊C₄	—	3	1	no	—
593	C₂×C₄⋊C₄	—	3	1	no	—
594	C₂×C₄⋊C₄	—	3	1	no	—
595	C₂×C₂²⋊C₄	—	3	1	no	—
596	C₂×C₂²⋊C₄	—	3	1	no	—
597	C₂×C₂²⋊C₄	—	3	1	no	—
598	C₂×C₂²⋊C₄	—	3	1	no	—
599	C₂×C₂²⋊C₄	—	3	1	no	—
600	C₂×C₂²⋊C₄	—	3	1	no	—
601	C₂×C₂²⋊C₄	—	3	1	no	—
602	C₂×C₂²⋊C₄	—	3	1	no	—
603	C₂×C₂²⋊C₄	—	3	1	no	—
604	C₂×C₂²⋊C₄	—	3	1	no	—
605	C₂×C₂²⋊C₄	—	3	8	no	—
606	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
607	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
608	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
609	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic, complemented
610	C₂×C₄²	—	3	1	no	—
611	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic, complemented
612	C₂×C₃×C₅	—	4	2	no	—
613	C₂×C₃×C₅	—	4	2	no	—
614	C₂×C₃×C₅	#538	1	4	yes	complemented
615	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
616	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
617	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
618	C₅×D₃	—	2	4	no	—
619	C₅×D₃	—	4	2	no	—
620	C₅×D₃	—	4	2	no	—
621	C₂³×C₃	—	2	2	no	—
622	C₂³×C₃	—	2	2	no	—
623	C₂³×C₃	—	2	2	no	—
624	C₂³×C₃	—	2	2	no	—
625	C₂³×C₃	—	2	2	no	—
626	C₂³×C₃	—	2	2	no	—
627	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
628	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
629	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
630	C₂²×D₃	—	2	2	no	—
631	C₂²×D₃	—	2	2	no	—
632	C₂²×D₃	—	2	2	no	—
633	C₂²×D₃	—	2	2	no	—
634	C₂²×D₃	—	2	2	no	—
635	C₂²×D₃	—	2	2	no	—
636	C₂²×D₃	—	2	2	no	—
637	C₂²×D₃	—	2	2	no	—
638	C₂²×D₃	—	2	8	no	—
639	C₂²×D₃	—	4	4	no	—
640	C₂²×D₃	—	4	4	no	—
641	C₂²×D₃	—	4	16	no	—
642	C₂²×D₃	C₅×#41	1	4	yes	—
643	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
644	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
645	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
646	C₃×Q₈	—	4	4	no	—
647	C₃×D₄	—	4	4	no	—
648	C₂×C₃×C₄	—	2	2	no	—
649	C₂×C₃×C₄	—	2	2	no	—
650	C₂×C₃×C₄	—	2	2	no	—
651	C₂×C₃×C₄	—	2	2	no	—
652	C₂×C₃×C₄	—	2	2	no	—
653	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
654	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
655	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
656	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
657	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
658	#67	—	2	8	no	—
659	#67	—	4	4	no	—
660	#67	—	4	4	no	—
661	#67	—	4	4	no	—
662	C₂×Dic₃	—	2	2	no	—
663	C₂×Dic₃	—	2	2	no	—
664	C₂×Dic₃	—	2	2	no	—
665	C₂×Dic₃	—	2	2	no	—
666	C₂×Dic₃	—	2	2	no	—
667	C₂×Dic₃	—	4	4	no	—
668	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
669	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
670	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
671	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
672	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
673	D₁₂	—	2	8	no	—
674	D₁₂	—	4	4	no	—
675	C₄×D₃	—	4	4	no	—
676	C₄×D₃	—	4	4	no	—
677	C₄×D₃	—	4	4	no	—
678	C₂²×C₅	—	2	2	no	—
679	C₂²×C₅	—	2	2	no	—
680	C₂²×C₅	—	2	2	no	—
681	C₂²×C₅	—	2	2	no	—
682	C₂²×C₅	—	2	2	no	—
683	C₂²×C₅	—	2	2	no	—
684	C₂²×C₅	—	3	4	no	—
685	C₂²×C₅	—	4	4	no	—
686	C₂²×C₅	—	4	4	no	—
687	C₂²×C₅	—	6	8	no	—
688	C₂²×C₅	—	6	2	no	—
689	C₂²×C₅	—	6	2	no	—
690	C₂²×C₅	—	6	2	no	—
691	C₂²×C₅	—	6	2	no	—
692	C₂²×C₅	—	6	2	no	—
693	C₂²×C₅	—	6	2	no	—
694	C₂²×C₅	—	6	2	no	—
695	C₂²×C₅	—	6	2	no	—
696	C₂²×C₅	—	12	16	no	—
697	C₂²×C₅	—	12	4	no	—
698	C₂²×C₅	—	12	4	no	—
699	C₂²×C₅	#1004	1	2	yes	—
700	C₂²×C₅	D₃×#41	1	2	yes	—
701	C₂²×C₅	#1009	1	2	yes	—
702	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
703	C₄×C₅	—	2	2	no	—
704	C₄×C₅	—	2	2	no	—
705	C₄×C₅	—	2	2	no	—
706	C₄×C₅	—	2	2	no	—
707	C₄×C₅	—	2	2	no	—
708	C₄×C₅	—	6	2	no	—
709	C₄×C₅	—	6	2	no	—
710	C₄×C₅	—	6	2	no	—
711	C₄×C₅	—	6	2	no	—
712	C₄×C₅	—	6	2	no	—
713	C₂⁴	—	3	1	no	—
714	C₂⁴	—	3	1	no	—
715	C₂⁴	—	3	1	no	—
716	C₂⁴	—	3	4	no	—
717	C₂⁴	—	6	4	no	—
718	C₂⁴	—	12	2	no	—
719	C₂⁴	—	12	2	no	—
720	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
721	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
722	C₂×Q₈	—	4	2	no	—
723	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	complemented
724	C₂×D₄	—	3	4	no	—
725	C₂×D₄	—	3	4	no	—
726	C₂×D₄	—	3	4	no	—
727	C₂×D₄	—	3	4	no	—
728	C₂×D₄	—	3	4	no	—
729	C₂×D₄	—	3	4	no	—
730	C₂×D₄	—	4	2	no	—
731	C₂×D₄	—	6	4	no	—
732	C₂×D₄	—	6	4	no	—
733	C₂×D₄	—	12	2	no	—
734	C₂×D₄	—	12	2	no	—
735	C₂×D₄	—	12	2	no	—
736	C₂×D₄	—	12	2	no	—
737	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
738	C₂²×C₄	—	3	1	no	—
739	C₂²×C₄	—	3	1	no	—
740	C₂²×C₄	—	3	1	no	—
741	C₂²×C₄	—	3	1	no	—
742	C₂²×C₄	—	3	1	no	—
743	C₂²×C₄	—	3	4	no	—
744	C₂²×C₄	—	3	4	no	—
745	C₂²×C₄	—	3	4	no	—
746	C₂²×C₄	—	3	4	no	—
747	C₂²×C₄	—	12	2	no	—
748	C₂²×C₄	—	12	2	no	—
749	C₂²×C₄	—	12	2	no	—
750	C₂²×C₄	—	12	2	no	—
751	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
752	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
753	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
754	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
755	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
756	C₄⋊C₄	—	3	4	no	—
757	C₄⋊C₄	—	3	4	no	—
758	C₄⋊C₄	—	3	4	no	—
759	C₄⋊C₄	—	3	4	no	—
760	C₄⋊C₄	—	3	4	no	—
761	C₄⋊C₄	—	3	4	no	—
762	C₂²⋊C₄	—	3	4	no	—
763	C₂²⋊C₄	—	3	4	no	—
764	C₂²⋊C₄	—	3	4	no	—
765	C₂²⋊C₄	—	3	4	no	—
766	C₂²⋊C₄	—	3	4	no	—
767	C₂²⋊C₄	—	3	4	no	—
768	C₂²⋊C₄	—	3	4	no	—
769	C₂²⋊C₄	—	3	4	no	—
770	C₂²⋊C₄	—	3	4	no	—
771	C₂²⋊C₄	—	3	4	no	—
772	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
773	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
774	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
775	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	complemented
776	C₄²	—	3	4	no	—
777	C₄²	C₂²×C₅×D₃	1	4	yes	complemented
778	C₃×C₅	C₂×#538	1	1	yes	characteristic, complemented, Hall
779	C₂²×C₃	—	2	2	no	—
780	C₂²×C₃	—	2	2	no	—
781	C₂²×C₃	—	2	2	no	—
782	C₂²×C₃	—	2	2	no	—
783	C₂²×C₃	—	2	2	no	—
784	C₂²×C₃	—	2	2	no	—
785	C₂²×C₃	—	4	4	no	—
786	C₂²×C₃	—	4	4	no	—
787	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
788	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
789	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
790	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
791	C₂×D₃	—	2	8	no	—
792	C₂×D₃	—	2	2	no	—
793	C₂×D₃	—	2	2	no	—
794	C₂×D₃	—	2	2	no	—
795	C₂×D₃	—	2	2	no	—
796	C₂×D₃	—	2	2	no	—
797	C₂×D₃	—	2	2	no	—
798	C₂×D₃	—	2	2	no	—
799	C₂×D₃	—	2	2	no	—
800	C₂×D₃	—	4	16	no	—
801	C₂×D₃	—	4	4	no	—
802	C₂×D₃	—	4	4	no	—
803	C₂×D₃	C₂×C₅×#41	1	4	yes	—
804	C₃×C₄	—	2	2	no	—
805	C₃×C₄	—	2	2	no	—
806	C₃×C₄	—	2	2	no	—
807	C₃×C₄	—	2	2	no	—
808	C₃×C₄	—	2	2	no	—
809	Dic₃	—	2	2	no	—
810	Dic₃	—	2	2	no	—
811	Dic₃	—	2	2	no	—
812	Dic₃	—	2	2	no	—
813	Dic₃	—	2	2	no	—
814	C₂×C₅	—	4	2	no	—
815	C₂×C₅	—	4	2	no	—
816	C₂×C₅	—	6	4	no	—
817	C₂×C₅	—	12	2	no	—
818	C₂×C₅	—	12	2	no	—
819	C₂×C₅	#5678	1	4	yes	direct product factor
820	C₂×C₅	C₂×#1004	1	1	yes	characteristic
821	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
822	C₂×C₅	C₂×#1009	1	1	yes	characteristic
823	C₂³	—	2	2	no	—
824	C₂³	—	2	2	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	2	no	—
827	C₂³	—	2	2	no	—
828	C₂³	—	2	2	no	—
829	C₂³	—	3	4	no	—
830	C₂³	—	3	2	no	—
831	C₂³	—	3	2	no	—
832	C₂³	—	3	2	no	—
833	C₂³	—	6	8	no	—
834	C₂³	—	6	2	no	—
835	C₂³	—	6	2	no	—
836	C₂³	—	6	2	no	—
837	C₂³	—	6	2	no	—
838	C₂³	—	6	2	no	—
839	C₂³	—	6	2	no	—
840	C₂³	—	6	2	no	—
841	C₂³	—	6	2	no	—
842	C₂³	—	12	4	no	—
843	C₂³	—	12	4	no	—
844	C₂³	—	12	16	no	—
845	C₂³	C₂³×C₅×D₃	1	2	yes	—
846	C₂³	C₂³×C₅×D₃	1	2	yes	—
847	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
848	Q₈	—	4	4	no	—
849	D₄	—	4	4	no	—
850	D₄	—	6	8	no	—
851	D₄	—	6	8	no	—
852	D₄	—	12	4	no	—
853	D₄	—	12	4	no	—
854	D₄	—	12	4	no	—
855	D₄	—	12	4	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	3	2	no	—
862	C₂×C₄	—	3	2	no	—
863	C₂×C₄	—	3	2	no	—
864	C₂×C₄	—	3	2	no	—
865	C₂×C₄	—	3	2	no	—
866	C₂×C₄	—	6	2	no	—
867	C₂×C₄	—	6	2	no	—
868	C₂×C₄	—	6	2	no	—
869	C₂×C₄	—	6	2	no	—
870	C₂×C₄	—	6	2	no	—
871	C₂×C₄	—	12	4	no	—
872	C₂×C₄	—	12	4	no	—
873	C₂×C₄	—	12	4	no	—
874	C₂×C₄	—	12	4	no	—
875	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
876	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
877	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
878	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
879	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
880	C₂×C₃	—	4	2	no	—
881	C₂×C₃	—	4	2	no	—
882	C₂×C₃	C₅×#538	1	4	yes	complemented
883	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
884	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
885	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
886	D₃	—	2	4	no	—
887	D₃	—	4	2	no	—
888	D₃	—	4	2	no	—
889	C₅	C₂×#5678	1	1	yes	characteristic, direct product factor, Sylow
890	C₂²	—	2	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	2	2	no	—
894	C₂²	—	2	2	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	3	4	no	—
897	C₂²	—	4	4	no	—
898	C₂²	—	4	4	no	—
899	C₂²	—	6	8	no	—
900	C₂²	—	6	2	no	—
901	C₂²	—	6	2	no	—
902	C₂²	—	6	2	no	—
903	C₂²	—	6	2	no	—
904	C₂²	—	6	2	no	—
905	C₂²	—	6	2	no	—
906	C₂²	—	6	2	no	—
907	C₂²	—	6	2	no	—
908	C₂²	—	12	16	no	—
909	C₂²	—	12	4	no	—
910	C₂²	—	12	4	no	—
911	C₂²	C₅×#1004	1	2	yes	—
912	C₂²	C₅×D₃×#41	1	2	yes	—
913	C₂²	C₅×#1009	1	2	yes	—
914	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
915	C₄	—	2	2	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	2	2	no	—
920	C₄	—	6	2	no	—
921	C₄	—	6	2	no	—
922	C₄	—	6	2	no	—
923	C₄	—	6	2	no	—
924	C₄	—	6	2	no	—
925	C₃	C₂×C₅×#538	1	1	yes	characteristic, complemented, Sylow
926	C₂	—	4	2	no	—
927	C₂	—	4	2	no	—
928	C₂	—	6	4	no	—
929	C₂	—	12	2	no	—
930	C₂	—	12	2	no	—
931	C₂	C₅×#5678	1	4	yes	direct product factor
932	C₂	C₂×C₅×#1004	1	1	yes	characteristic
933	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
934	C₂	C₂×C₅×#1009	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂×C₃×C₅×#124	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#124	D₃
hypocenter	C₃	C₂×C₅×#538
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#124	C₂	semidirect
2. C₂×C₅×#947	C₂	semidirect
3. C₂×C₅×#946	C₂	semidirect
4. C₂×C₅×#939	C₂	semidirect
5. C₂×C₅×#937	C₂	semidirect
6. C₅×#5678	C₂	direct (N × H)
7. C₂×C₅×#886	C₂	semidirect
8. C₂×C₅×#884	C₂	semidirect
9. C₂×C₅×#884	C₂	semidirect
10. C₂×C₅×#883	C₂	semidirect
11. C₂×C₅×#882	C₂	semidirect
12. C₂×C₅×#67⋊C₄	C₂	semidirect
13. C₂×C₅×D₃×C₂²⋊C₄	C₂	semidirect
14. C₂×C₅×#879	C₂	semidirect
15. C₂×C₅×#876	C₂	semidirect
16. C₂×C₄×C₅×D₁₂	C₂	semidirect
19. C₂²×C₃×C₅×Q₈	C₂²	semidirect
24. C₂²×C₅×#67	C₂²	semidirect
25. C₂³×C₅×Dic₃	C₂²	semidirect
30. C₂²×C₄×C₅×D₃	C₂²	semidirect
31. C₃×C₅×#124	C₂²	semidirect
34. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
35. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
36. C₂×C₃×C₄²×C₅	C₂²	semidirect
39. C₅×#947	C₂²	semidirect
40. C₅×#946	C₂²	semidirect
41. C₅×#939	C₂²	semidirect
42. C₅×#937	C₂²	semidirect
49. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
50. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
51. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
52. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
53. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
54. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
55. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
56. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
57. C₂×C₄×C₅×Dic₃	C₂²	semidirect
58. C₅×#886	C₂²	semidirect
59. C₅×#884	C₂²	semidirect
60. C₅×#884	C₂²	semidirect
61. C₅×#883	C₂²	semidirect
62. C₅×#882	C₂²	semidirect
63. C₅×#67⋊C₄	C₂²	semidirect
64. C₅×D₃×C₂²⋊C₄	C₂²	semidirect
65. C₅×#879	C₂²	semidirect
66. C₅×#876	C₂²	semidirect
67. C₄×C₅×D₁₂	C₂²	semidirect
68. C₂×#5678	C₅	direct (N × H)
73. C₂×C₅×#124	D₃	semidirect
95. C₂×C₃×C₅×Q₈	C₂³	semidirect
110. C₂×C₅×#67	C₂³	semidirect
117. C₂²×C₅×Dic₃	C₂³	semidirect
127. C₂×C₄×C₅×D₃	C₂³	semidirect
130. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
131. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
132. C₃×C₄²×C₅	C₂³	semidirect
141. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
142. C₅×(C₂×D₃)⋊C₄	C₂³	semidirect
143. C₅×C₄⋊Dic₃	C₂³	semidirect
144. C₅×C₄⋊Dic₃	C₂³	semidirect
145. C₅×Dic₃⋊C₄	C₂³	semidirect
146. C₅×Dic₃⋊C₄	C₂³	semidirect
147. C₅×Dic₃⋊C₄	C₂³	semidirect
148. C₅×Dic₃⋊C₄	C₂³	semidirect
149. C₄×C₅×Dic₃	C₂³	semidirect
150. C₂×C₃×#124	C₂×C₅	semidirect
151. C₂×#947	C₂×C₅	semidirect
152. C₂×#946	C₂×C₅	semidirect
153. C₂×#939	C₂×C₅	semidirect
154. C₂×#937	C₂×C₅	semidirect
155. #5678	C₂×C₅	direct (N × H)
156. C₂×#886	C₂×C₅	semidirect
157. C₂×#884	C₂×C₅	semidirect
158. C₂×#884	C₂×C₅	semidirect
159. C₂×#883	C₂×C₅	semidirect
160. C₂×#882	C₂×C₅	semidirect
161. C₂×#67⋊C₄	C₂×C₅	semidirect
162. C₂×D₃×C₂²⋊C₄	C₂×C₅	semidirect
163. C₂×#879	C₂×C₅	semidirect
164. C₂×#876	C₂×C₅	semidirect
165. C₂×C₄×D₁₂	C₂×C₅	semidirect
167. C₂²×C₅×Q₈	C₂×D₃	semidirect
182. C₅×#124	C₂×D₃	semidirect
212. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
213. C₂×C₅×C₂²⋊C₄	C₂×D₃	semidirect
215. C₂×C₄²×C₅	C₂×D₃	semidirect
275. C₂²×C₃×Q₈	C₂²×C₅	semidirect
280. C₂²×#67	C₂²×C₅	semidirect
281. C₂³×Dic₃	C₂²×C₅	semidirect
286. C₂²×C₄×D₃	C₂²×C₅	semidirect
287. C₃×#124	C₂²×C₅	semidirect
290. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
291. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
292. C₂×C₃×C₄²	C₂²×C₅	semidirect
295. #947	C₂²×C₅	semidirect
296. #946	C₂²×C₅	semidirect
297. #939	C₂²×C₅	semidirect
298. #937	C₂²×C₅	semidirect
305. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
306. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
307. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
308. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
309. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
310. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
311. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
312. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
313. C₂×C₄×Dic₃	C₂²×C₅	semidirect
314. #886	C₂²×C₅	semidirect
315. #884	C₂²×C₅	semidirect
316. #884	C₂²×C₅	semidirect
317. #883	C₂²×C₅	semidirect
318. #882	C₂²×C₅	semidirect
319. #67⋊C₄	C₂²×C₅	semidirect
320. D₃×C₂²⋊C₄	C₂²×C₅	semidirect
321. #879	C₂²×C₅	semidirect
322. #876	C₂²×C₅	semidirect
323. C₄×D₁₂	C₂²×C₅	semidirect
334. C₂×C₅×Q₈	C₂²×D₃	semidirect
385. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
386. C₅×C₂²⋊C₄	C₂²×D₃	semidirect
388. C₄²×C₅	C₂²×D₃	semidirect
393. C₂×#124	C₅×D₃	semidirect
450. C₂×C₃×Q₈	C₂³×C₅	semidirect
465. C₂×#67	C₂³×C₅	semidirect
472. C₂²×Dic₃	C₂³×C₅	semidirect
482. C₂×C₄×D₃	C₂³×C₅	semidirect
485. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
486. C₃×C₂²⋊C₄	C₂³×C₅	semidirect
487. C₃×C₄²	C₂³×C₅	semidirect
496. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
497. (C₂×D₃)⋊C₄	C₂³×C₅	semidirect
498. C₄⋊Dic₃	C₂³×C₅	semidirect
499. C₄⋊Dic₃	C₂³×C₅	semidirect
500. Dic₃⋊C₄	C₂³×C₅	semidirect
501. Dic₃⋊C₄	C₂³×C₅	semidirect
502. Dic₃⋊C₄	C₂³×C₅	semidirect
503. Dic₃⋊C₄	C₂³×C₅	semidirect
504. C₄×Dic₃	C₂³×C₅	semidirect
563. C₂²×Q₈	C₂×C₅×D₃	semidirect
578. #124	C₂×C₅×D₃	semidirect
608. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
609. C₂×C₂²⋊C₄	C₂×C₅×D₃	semidirect
611. C₂×C₄²	C₂×C₅×D₃	semidirect
614. C₂×C₃×C₅	#538	semidirect
723. C₂×Q₈	C₂²×C₅×D₃	semidirect
774. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
775. C₂²⋊C₄	C₂²×C₅×D₃	semidirect
777. C₄²	C₂²×C₅×D₃	semidirect
778. C₃×C₅	C₂×#538	semidirect
819. C₂×C₅	#5678	direct (N × H)
882. C₂×C₃	C₅×#538	semidirect
889. C₅	C₂×#5678	direct (N × H)
925. C₃	C₂×C₅×#538	semidirect
931. C₂	C₅×#5678	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×#124	2
C₂×C₅×#947	2
C₂×C₅×#946	2
C₂×C₅×#939	2
C₂×C₅×#937	2
C₅×#5678	2
C₂×C₅×#886	2
C₂×C₅×#884	2
C₂×C₅×#883	2
C₂×C₅×#882	2
C₂×C₅×#67⋊C₄	2
C₂×C₅×D₃×C₂²⋊C₄	2
C₂×C₅×#879	2
C₂×C₅×#876	2
C₂×C₄×C₅×D₁₂	2
C₂×C₅×#538	3
C₂×#5678	5

Subgroups — C2×C5×#5678 #14480755

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5678 #14480755