Subgroups — C₂×C₅×#5655 #14482670

Order 1920.

3264 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#237	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#939	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5655	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₅×#896	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#894	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#888	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#886	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#884	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#883	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#67⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#878	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅×#547	—	3	1	no	maximal, Hall
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
20	C₂²×C₅×#67	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	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
25	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
26	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
27	C₂×C₅×#237	—	2	8	no	—
28	C₂×C₅×#237	C₂²	1	8	yes	complemented
29	C₂×C₅×#235	—	2	8	no	—
30	C₂×C₅×#235	C₂²	1	8	yes	complemented
31	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
32	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
34	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
35	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
36	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
37	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
38	C₃×C₅×#123	C₂²	1	8	yes	complemented
39	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₅×#217	C₂²	1	1	yes	characteristic
45	C₅×#939	C₂²	1	8	yes	complemented
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
50	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
51	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
52	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
53	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
54	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
55	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
56	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
57	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
58	C₂×C₅×Dic₃⋊C₄	C₂²	1	8	yes	complemented
59	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
60	C₅×#896	C₂²	1	8	yes	complemented
61	C₅×#894	C₂²	1	8	yes	complemented
62	C₅×D₃×C₄⋊C₄	C₂²	1	8	yes	complemented
63	C₅×#888	C₂²	1	8	yes	complemented
64	C₅×#886	C₂²	1	8	yes	complemented
65	C₅×#884	C₂²	1	8	yes	complemented
66	C₅×#883	C₂²	1	8	yes	complemented
67	C₅×#67⋊C₄	C₂²	1	8	yes	complemented
68	C₅×#67⋊C₄	C₂²	1	8	yes	complemented
69	C₅×#878	C₂²	1	8	yes	complemented
70	C₂×#5655	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
71	C₂²×C₅×#41	—	3	1	no	—
72	C₂²×C₅×#41	—	3	1	no	—
73	C₅×#547	—	3	16	no	—
74	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
75	C₂×C₅×#123	—	3	1	no	—
76	C₂×C₅×#123	—	3	1	no	—
77	C₂×C₅×#123	—	3	1	no	—
78	C₂×C₅×#123	D₃	1	1	yes	characteristic, complemented
79	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
80	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
81	C₂×C₅×#121	—	3	1	no	—
82	C₂×C₅×#121	—	3	1	no	—
83	C₂×C₄×C₅×D₄	—	3	1	no	—
84	C₂×C₄×C₅×D₄	—	3	1	no	—
85	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
86	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
87	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
88	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
89	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
90	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₅×D₄	—	2	4	no	—
92	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
93	C₂²×C₃×C₄×C₅	—	2	4	no	—
94	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
95	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
96	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
97	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
98	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
99	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
100	C₂×C₅×#67	—	2	4	no	—
101	C₂×C₅×#67	—	2	4	no	—
102	C₂×C₅×#67	—	2	4	no	—
103	C₂×C₅×#67	D₄	1	8	yes	complemented
104	C₂×C₅×#67	C₂³	1	4	yes	—
105	C₂×C₅×#67	C₂³	1	4	yes	—
106	C₂×C₅×#67	C₂³	1	4	yes	—
107	C₂×C₅×#67	C₂³	1	4	yes	—
108	C₂²×C₅×Dic₃	—	2	4	no	—
109	C₂²×C₅×Dic₃	—	2	4	no	—
110	C₂²×C₅×Dic₃	—	2	4	no	—
111	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
112	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
113	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
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	1	yes	characteristic
118	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
119	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
120	C₅×#237	—	2	32	no	—
121	C₅×#235	—	2	32	no	—
122	C₂×C₅×D₁₂	—	2	4	no	—
123	C₂×C₅×D₁₂	C₂³	1	4	yes	—
124	C₂×C₄×C₅×D₃	—	2	4	no	—
125	C₂×C₄×C₅×D₃	—	2	4	no	—
126	C₂×C₄×C₅×D₃	—	2	4	no	—
127	C₂×C₄×C₅×D₃	—	2	4	no	—
128	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
129	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
130	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
131	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
132	C₂×C₅×Dic₆	—	2	4	no	—
133	C₂×C₅×Dic₆	—	2	4	no	—
134	C₂×C₅×Dic₆	C₂³	1	4	yes	—
135	C₂×C₅×Dic₆	C₂³	1	4	yes	—
136	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
137	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
138	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
140	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
141	C₅×#217	C₂³	1	4	yes	—
142	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
143	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
144	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
145	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
146	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
147	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
148	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
149	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
150	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
151	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
152	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
153	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
154	C₄×C₅×Dic₃	C₂³	1	4	yes	—
155	C₂²×#237	C₂×C₅	1	1	yes	characteristic, complemented
156	C₂²×#235	C₂×C₅	1	1	yes	characteristic, complemented
157	C₂×C₃×#123	C₂×C₅	1	1	yes	characteristic, complemented
158	C₂×#939	C₂×C₅	1	1	yes	characteristic, complemented
159	C₂²×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
160	#5655	C₂×C₅	1	16	yes	direct product factor
161	C₂×#896	C₂×C₅	1	1	yes	characteristic, complemented
162	C₂×#894	C₂×C₅	1	1	yes	characteristic, complemented
163	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
164	C₂×#888	C₂×C₅	1	1	yes	characteristic, complemented
165	C₂×#886	C₂×C₅	1	1	yes	characteristic, complemented
166	C₂×#884	C₂×C₅	1	1	yes	characteristic, complemented
167	C₂×#883	C₂×C₅	1	1	yes	characteristic, complemented
168	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
169	C₂×#67⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
170	C₂×#878	C₂×C₅	1	1	yes	characteristic, complemented
171	C₂×C₅×#41	—	3	8	no	—
172	C₂×C₅×#41	—	3	8	no	—
173	C₂×C₅×#41	—	6	8	no	—
174	C₂×C₅×#41	—	6	8	no	—
175	C₂²×C₅×Q₈	—	3	1	no	—
176	C₂²×C₅×Q₈	—	3	1	no	—
177	C₂²×C₅×D₄	—	3	1	no	—
178	C₂²×C₅×D₄	—	3	1	no	—
179	C₂²×C₅×D₄	—	3	1	no	—
180	C₂²×C₅×D₄	—	3	1	no	—
181	C₂²×C₅×D₄	—	3	1	no	—
182	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
183	C₂³×C₄×C₅	—	3	1	no	—
184	C₂³×C₄×C₅	—	3	1	no	—
185	C₂³×C₄×C₅	—	3	1	no	—
186	C₂³×C₄×C₅	—	3	1	no	—
187	C₂³×C₄×C₅	—	3	1	no	—
188	C₂³×C₄×C₅	—	3	1	no	—
189	C₂³×C₄×C₅	—	3	1	no	—
190	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
191	C₅×C₄⋊Q₈	—	3	8	no	—
192	C₅×#123	—	3	8	no	—
193	C₅×#123	—	3	8	no	—
194	C₅×#123	—	3	8	no	—
195	C₅×#123	C₂×D₃	1	8	yes	complemented
196	C₅×C₂²⋊Q₈	—	3	8	no	—
197	C₅×C₂²⋊Q₈	—	3	8	no	—
198	C₅×#121	—	3	8	no	—
199	C₅×#121	—	3	8	no	—
200	C₄×C₅×D₄	—	3	8	no	—
201	C₄×C₅×D₄	—	3	8	no	—
202	C₂×C₅×C₄⋊C₄	—	3	1	no	—
203	C₂×C₅×C₄⋊C₄	—	3	1	no	—
204	C₂×C₅×C₄⋊C₄	—	3	1	no	—
205	C₂×C₅×C₄⋊C₄	—	3	1	no	—
206	C₂×C₅×C₄⋊C₄	—	3	1	no	—
207	C₂×C₅×C₄⋊C₄	—	3	1	no	—
208	C₂×C₅×C₄⋊C₄	—	3	8	no	—
209	C₂×C₅×C₄⋊C₄	—	3	1	no	—
210	C₂×C₅×C₄⋊C₄	—	3	1	no	—
211	C₂×C₅×C₄⋊C₄	—	3	8	no	—
212	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
213	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
214	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
215	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
216	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
217	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
218	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
219	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
220	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
221	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
222	C₂×C₄²×C₅	—	3	1	no	—
223	C₂×#547	—	3	1	no	Sylow
224	C₂³×C₃×C₅	—	2	2	no	—
225	C₂³×C₃×C₅	—	2	2	no	—
226	C₂³×C₃×C₅	—	2	2	no	—
227	C₂³×C₃×C₅	—	2	2	no	—
228	C₂³×C₃×C₅	—	2	2	no	—
229	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
230	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
231	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
232	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
233	C₂²×C₅×D₃	—	2	2	no	—
234	C₂²×C₅×D₃	—	2	2	no	—
235	C₂²×C₅×D₃	—	2	2	no	—
236	C₂²×C₅×D₃	—	2	2	no	—
237	C₂²×C₅×D₃	—	2	2	no	—
238	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
239	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
240	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
241	C₃×C₅×D₄	—	2	8	no	—
242	C₂×C₃×C₄×C₅	—	2	2	no	—
243	C₂×C₃×C₄×C₅	—	2	2	no	—
244	C₂×C₃×C₄×C₅	—	2	2	no	—
245	C₂×C₃×C₄×C₅	—	2	8	no	—
246	C₂×C₃×C₄×C₅	—	2	2	no	—
247	C₂×C₃×C₄×C₅	—	2	2	no	—
248	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
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	C₅×#67	—	2	8	no	—
254	C₅×#67	—	2	8	no	—
255	C₅×#67	—	2	8	no	—
256	C₅×#67	C₂×D₄	1	16	yes	complemented
257	C₂×C₅×Dic₃	—	2	2	no	—
258	C₂×C₅×Dic₃	—	2	2	no	—
259	C₂×C₅×Dic₃	—	2	2	no	—
260	C₂×C₅×Dic₃	—	2	8	no	—
261	C₂×C₅×Dic₃	—	2	2	no	—
262	C₂×C₅×Dic₃	—	2	8	no	—
263	C₂×C₅×Dic₃	—	2	8	no	—
264	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
265	C₂×C₅×Dic₃	#41	1	4	yes	complemented
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	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
270	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
271	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
272	C₅×D₁₂	—	2	8	no	—
273	C₄×C₅×D₃	—	2	8	no	—
274	C₄×C₅×D₃	—	2	8	no	—
275	C₄×C₅×D₃	—	2	8	no	—
276	C₄×C₅×D₃	—	2	8	no	—
277	C₅×Dic₆	—	2	8	no	—
278	C₅×Dic₆	—	2	8	no	—
279	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
280	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
281	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
282	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
283	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
284	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
285	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
286	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
287	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
288	C₂×#237	—	2	8	no	—
289	C₂×#237	C₂²×C₅	1	8	yes	complemented
290	C₂×#235	—	2	8	no	—
291	C₂×#235	C₂²×C₅	1	8	yes	complemented
292	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
293	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
294	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
295	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
296	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
297	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
298	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
299	C₃×#123	C₂²×C₅	1	8	yes	complemented
300	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
301	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
302	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
303	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
304	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
305	C₂×#217	C₂²×C₅	1	1	yes	characteristic
306	#939	C₂²×C₅	1	8	yes	complemented
307	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
308	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
309	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
310	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
311	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
312	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
313	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
314	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
315	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
316	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
317	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
318	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
319	C₂×Dic₃⋊C₄	C₂²×C₅	1	8	yes	complemented
320	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
321	#896	C₂²×C₅	1	8	yes	complemented
322	#894	C₂²×C₅	1	8	yes	complemented
323	D₃×C₄⋊C₄	C₂²×C₅	1	8	yes	complemented
324	#888	C₂²×C₅	1	8	yes	complemented
325	#886	C₂²×C₅	1	8	yes	complemented
326	#884	C₂²×C₅	1	8	yes	complemented
327	#883	C₂²×C₅	1	8	yes	complemented
328	#67⋊C₄	C₂²×C₅	1	8	yes	complemented
329	#67⋊C₄	C₂²×C₅	1	8	yes	complemented
330	#878	C₂²×C₅	1	8	yes	complemented
331	C₂⁴×C₅	—	3	1	no	—
332	C₂⁴×C₅	—	3	1	no	—
333	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
334	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
335	C₅×#41	—	6	32	no	—
336	C₅×#41	—	6	32	no	—
337	C₂×C₅×Q₈	—	3	4	no	—
338	C₂×C₅×Q₈	—	3	4	no	—
339	C₂×C₅×Q₈	—	6	4	no	—
340	C₂×C₅×Q₈	—	6	4	no	—
341	C₂×C₅×D₄	—	2	4	no	—
342	C₂×C₅×D₄	—	3	8	no	—
343	C₂×C₅×D₄	—	3	4	no	—
344	C₂×C₅×D₄	—	3	4	no	—
345	C₂×C₅×D₄	—	3	4	no	—
346	C₂×C₅×D₄	—	3	4	no	—
347	C₂×C₅×D₄	—	3	4	no	—
348	C₂×C₅×D₄	—	6	4	no	—
349	C₂×C₅×D₄	—	6	4	no	—
350	C₂×C₅×D₄	—	6	4	no	—
351	C₂×C₅×D₄	—	6	4	no	—
352	C₂×C₅×D₄	C₂²×D₃	1	4	yes	—
353	C₂²×C₄×C₅	—	2	4	no	—
354	C₂²×C₄×C₅	—	3	1	no	—
355	C₂²×C₄×C₅	—	3	1	no	—
356	C₂²×C₄×C₅	—	3	4	no	—
357	C₂²×C₄×C₅	—	3	4	no	—
358	C₂²×C₄×C₅	—	3	4	no	—
359	C₂²×C₄×C₅	—	3	1	no	—
360	C₂²×C₄×C₅	—	3	1	no	—
361	C₂²×C₄×C₅	—	3	1	no	—
362	C₂²×C₄×C₅	—	3	1	no	—
363	C₂²×C₄×C₅	—	3	4	no	—
364	C₂²×C₄×C₅	—	3	4	no	—
365	C₂²×C₄×C₅	—	3	4	no	—
366	C₂²×C₄×C₅	—	3	4	no	—
367	C₂²×C₄×C₅	—	6	4	no	—
368	C₂²×C₄×C₅	—	6	4	no	—
369	C₂²×C₄×C₅	—	6	4	no	—
370	C₂²×C₄×C₅	—	6	4	no	—
371	C₂²×C₄×C₅	—	6	4	no	—
372	C₂²×C₄×C₅	—	6	4	no	—
373	C₂²×C₄×C₅	—	6	4	no	—
374	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
375	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
376	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
377	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
378	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
379	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
380	C₅×C₄⋊C₄	—	3	4	no	—
381	C₅×C₄⋊C₄	—	3	4	no	—
382	C₅×C₄⋊C₄	—	3	4	no	—
383	C₅×C₄⋊C₄	—	3	4	no	—
384	C₅×C₄⋊C₄	—	3	4	no	—
385	C₅×C₄⋊C₄	—	3	4	no	—
386	C₅×C₄⋊C₄	—	3	4	no	—
387	C₅×C₄⋊C₄	—	3	4	no	—
388	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
389	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
390	C₅×C₂²⋊C₄	—	3	4	no	—
391	C₅×C₂²⋊C₄	—	3	4	no	—
392	C₅×C₂²⋊C₄	—	3	4	no	—
393	C₅×C₂²⋊C₄	—	3	4	no	—
394	C₅×C₂²⋊C₄	—	3	4	no	—
395	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
396	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
397	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
398	C₄²×C₅	—	3	4	no	—
399	C₂²×#41	—	3	1	no	—
400	C₂²×#41	—	3	1	no	—
401	#547	—	3	16	no	—
402	C₂×C₄⋊Q₈	—	3	1	no	—
403	C₂×#123	—	3	1	no	—
404	C₂×#123	—	3	1	no	—
405	C₂×#123	—	3	1	no	—
406	C₂×#123	C₅×D₃	1	1	yes	characteristic, complemented
407	C₂×C₂²⋊Q₈	—	3	1	no	—
408	C₂×C₂²⋊Q₈	—	3	1	no	—
409	C₂×#121	—	3	1	no	—
410	C₂×#121	—	3	1	no	—
411	C₂×C₄×D₄	—	3	1	no	—
412	C₂×C₄×D₄	—	3	1	no	—
413	C₂²×C₄⋊C₄	—	3	1	no	—
414	C₂²×C₄⋊C₄	—	3	1	no	—
415	C₂²×C₃×C₅	—	2	8	no	—
416	C₂²×C₃×C₅	—	2	2	no	—
417	C₂²×C₃×C₅	—	2	2	no	—
418	C₂²×C₃×C₅	—	2	2	no	—
419	C₂²×C₃×C₅	—	2	2	no	—
420	C₂²×C₃×C₅	—	2	2	no	—
421	C₂²×C₃×C₅	—	4	4	no	—
422	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
423	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
424	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
425	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
426	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
427	C₂×C₅×D₃	—	2	8	no	—
428	C₂×C₅×D₃	—	2	2	no	—
429	C₂×C₅×D₃	—	2	2	no	—
430	C₂×C₅×D₃	—	2	2	no	—
431	C₂×C₅×D₃	—	2	2	no	—
432	C₂×C₅×D₃	—	2	2	no	—
433	C₂×C₅×D₃	—	4	4	no	—
434	C₂×C₅×D₃	C₂²×D₄	1	4	yes	—
435	C₃×C₄×C₅	—	2	2	no	—
436	C₃×C₄×C₅	—	2	2	no	—
437	C₃×C₄×C₅	—	2	2	no	—
438	C₃×C₄×C₅	—	2	2	no	—
439	C₃×C₄×C₅	—	2	2	no	—
440	C₅×Dic₃	—	2	2	no	—
441	C₅×Dic₃	—	2	2	no	—
442	C₅×Dic₃	—	2	2	no	—
443	C₅×Dic₃	—	2	2	no	—
444	C₅×Dic₃	C₂²×D₄	1	4	yes	—
445	C₅×Dic₃	C₂×#41	1	4	yes	complemented
446	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
447	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
448	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
449	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
450	C₂×C₃×D₄	—	2	4	no	—
451	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
452	C₂²×C₃×C₄	—	2	4	no	—
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	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
459	C₂×#67	—	2	4	no	—
460	C₂×#67	—	2	4	no	—
461	C₂×#67	—	2	4	no	—
462	C₂×#67	C₅×D₄	1	8	yes	complemented
463	C₂×#67	C₂³×C₅	1	4	yes	—
464	C₂×#67	C₂³×C₅	1	4	yes	—
465	C₂×#67	C₂³×C₅	1	4	yes	—
466	C₂×#67	C₂³×C₅	1	4	yes	—
467	C₂²×Dic₃	—	2	4	no	—
468	C₂²×Dic₃	—	2	4	no	—
469	C₂²×Dic₃	—	2	4	no	—
470	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
471	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
472	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
473	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
474	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
475	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
476	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
477	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
478	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
479	#237	—	2	32	no	—
480	#235	—	2	32	no	—
481	C₂×D₁₂	—	2	4	no	—
482	C₂×D₁₂	C₂³×C₅	1	4	yes	—
483	C₂×C₄×D₃	—	2	4	no	—
484	C₂×C₄×D₃	—	2	4	no	—
485	C₂×C₄×D₃	—	2	4	no	—
486	C₂×C₄×D₃	—	2	4	no	—
487	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
488	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
489	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
490	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
491	C₂×Dic₆	—	2	4	no	—
492	C₂×Dic₆	—	2	4	no	—
493	C₂×Dic₆	C₂³×C₅	1	4	yes	—
494	C₂×Dic₆	C₂³×C₅	1	4	yes	—
495	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
496	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
497	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
498	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
499	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
500	#217	C₂³×C₅	1	4	yes	—
501	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
502	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
503	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
504	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
505	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
506	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
507	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
508	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
509	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
510	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
511	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
512	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
513	C₄×Dic₃	C₂³×C₅	1	4	yes	—
514	C₂³×C₅	—	2	2	no	—
515	C₂³×C₅	—	2	2	no	—
516	C₂³×C₅	—	2	2	no	—
517	C₂³×C₅	—	2	2	no	—
518	C₂³×C₅	—	2	2	no	—
519	C₂³×C₅	—	3	4	no	—
520	C₂³×C₅	—	3	2	no	—
521	C₂³×C₅	—	3	2	no	—
522	C₂³×C₅	—	6	2	no	—
523	C₂³×C₅	—	6	2	no	—
524	C₂³×C₅	—	6	2	no	—
525	C₂³×C₅	—	6	2	no	—
526	C₂³×C₅	—	6	2	no	—
527	C₂³×C₅	D₃×D₄	1	4	yes	—
528	C₂³×C₅	C₂³×D₃	1	2	yes	—
529	C₂³×C₅	C₂³×D₃	1	2	yes	—
530	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
531	C₅×Q₈	—	6	8	no	—
532	C₅×Q₈	—	6	8	no	—
533	C₅×D₄	—	2	8	no	—
534	C₅×D₄	—	3	16	no	—
535	C₅×D₄	—	6	8	no	—
536	C₅×D₄	—	6	8	no	—
537	C₅×D₄	—	6	8	no	—
538	C₅×D₄	—	6	8	no	—
539	C₂×C₄×C₅	—	2	2	no	—
540	C₂×C₄×C₅	—	2	2	no	—
541	C₂×C₄×C₅	—	2	8	no	—
542	C₂×C₄×C₅	—	2	2	no	—
543	C₂×C₄×C₅	—	2	2	no	—
544	C₂×C₄×C₅	—	2	2	no	—
545	C₂×C₄×C₅	—	3	4	no	—
546	C₂×C₄×C₅	—	3	4	no	—
547	C₂×C₄×C₅	—	3	2	no	—
548	C₂×C₄×C₅	—	3	2	no	—
549	C₂×C₄×C₅	—	3	2	no	—
550	C₂×C₄×C₅	—	3	2	no	—
551	C₂×C₄×C₅	—	3	2	no	—
552	C₂×C₄×C₅	—	3	2	no	—
553	C₂×C₄×C₅	—	6	8	no	—
554	C₂×C₄×C₅	—	6	8	no	—
555	C₂×C₄×C₅	—	6	8	no	—
556	C₂×C₄×C₅	—	6	8	no	—
557	C₂×C₄×C₅	—	6	8	no	—
558	C₂×C₄×C₅	—	6	8	no	—
559	C₂×C₄×C₅	—	6	2	no	—
560	C₂×C₄×C₅	—	6	2	no	—
561	C₂×C₄×C₅	—	6	2	no	—
562	C₂×C₄×C₅	—	6	8	no	—
563	C₂×C₄×C₅	—	6	2	no	—
564	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
565	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
566	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
567	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
568	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
569	C₂×#41	—	3	8	no	—
570	C₂×#41	—	3	8	no	—
571	C₂×#41	—	6	8	no	—
572	C₂×#41	—	6	8	no	—
573	C₂²×Q₈	—	3	1	no	—
574	C₂²×Q₈	—	3	1	no	—
575	C₂²×D₄	—	3	1	no	—
576	C₂²×D₄	—	3	1	no	—
577	C₂²×D₄	—	3	1	no	—
578	C₂²×D₄	—	3	1	no	—
579	C₂²×D₄	—	3	1	no	—
580	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
581	C₂³×C₄	—	3	1	no	—
582	C₂³×C₄	—	3	1	no	—
583	C₂³×C₄	—	3	1	no	—
584	C₂³×C₄	—	3	1	no	—
585	C₂³×C₄	—	3	1	no	—
586	C₂³×C₄	—	3	1	no	—
587	C₂³×C₄	—	3	1	no	—
588	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
589	C₄⋊Q₈	—	3	8	no	—
590	#123	—	3	8	no	—
591	#123	—	3	8	no	—
592	#123	—	3	8	no	—
593	#123	C₂×C₅×D₃	1	8	yes	complemented
594	C₂²⋊Q₈	—	3	8	no	—
595	C₂²⋊Q₈	—	3	8	no	—
596	#121	—	3	8	no	—
597	#121	—	3	8	no	—
598	C₄×D₄	—	3	8	no	—
599	C₄×D₄	—	3	8	no	—
600	C₂×C₄⋊C₄	—	3	1	no	—
601	C₂×C₄⋊C₄	—	3	1	no	—
602	C₂×C₄⋊C₄	—	3	1	no	—
603	C₂×C₄⋊C₄	—	3	1	no	—
604	C₂×C₄⋊C₄	—	3	1	no	—
605	C₂×C₄⋊C₄	—	3	1	no	—
606	C₂×C₄⋊C₄	—	3	8	no	—
607	C₂×C₄⋊C₄	—	3	1	no	—
608	C₂×C₄⋊C₄	—	3	1	no	—
609	C₂×C₄⋊C₄	—	3	8	no	—
610	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
612	C₂×C₂²⋊C₄	—	3	1	no	—
613	C₂×C₂²⋊C₄	—	3	1	no	—
614	C₂×C₂²⋊C₄	—	3	1	no	—
615	C₂×C₂²⋊C₄	—	3	1	no	—
616	C₂×C₂²⋊C₄	—	3	1	no	—
617	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
618	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
619	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
620	C₂×C₄²	—	3	1	no	—
621	C₂×C₃×C₅	—	2	4	no	—
622	C₂×C₃×C₅	—	4	2	no	—
623	C₂×C₃×C₅	#547	1	4	yes	complemented
624	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
625	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
626	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
627	C₅×D₃	—	2	4	no	—
628	C₅×D₃	—	4	2	no	—
629	C₂³×C₃	—	2	2	no	—
630	C₂³×C₃	—	2	2	no	—
631	C₂³×C₃	—	2	2	no	—
632	C₂³×C₃	—	2	2	no	—
633	C₂³×C₃	—	2	2	no	—
634	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
635	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
636	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
637	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
638	C₂²×D₃	—	2	2	no	—
639	C₂²×D₃	—	2	2	no	—
640	C₂²×D₃	—	2	2	no	—
641	C₂²×D₃	—	2	2	no	—
642	C₂²×D₃	—	2	2	no	—
643	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
644	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
645	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
646	C₃×D₄	—	2	8	no	—
647	C₂×C₃×C₄	—	2	2	no	—
648	C₂×C₃×C₄	—	2	2	no	—
649	C₂×C₃×C₄	—	2	2	no	—
650	C₂×C₃×C₄	—	2	8	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	—	2	8	no	—
660	#67	—	2	8	no	—
661	#67	C₂×C₅×D₄	1	16	yes	complemented
662	C₂×Dic₃	—	2	2	no	—
663	C₂×Dic₃	—	2	2	no	—
664	C₂×Dic₃	—	2	2	no	—
665	C₂×Dic₃	—	2	8	no	—
666	C₂×Dic₃	—	2	2	no	—
667	C₂×Dic₃	—	2	8	no	—
668	C₂×Dic₃	—	2	8	no	—
669	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
670	C₂×Dic₃	C₅×#41	1	4	yes	complemented
671	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
672	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
673	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
674	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
675	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
676	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
677	D₁₂	—	2	8	no	—
678	C₄×D₃	—	2	8	no	—
679	C₄×D₃	—	2	8	no	—
680	C₄×D₃	—	2	8	no	—
681	C₄×D₃	—	2	8	no	—
682	Dic₆	—	2	8	no	—
683	Dic₆	—	2	8	no	—
684	C₂²×C₅	—	2	8	no	—
685	C₂²×C₅	—	2	2	no	—
686	C₂²×C₅	—	2	2	no	—
687	C₂²×C₅	—	2	2	no	—
688	C₂²×C₅	—	2	2	no	—
689	C₂²×C₅	—	2	2	no	—
690	C₂²×C₅	—	3	4	no	—
691	C₂²×C₅	—	4	4	no	—
692	C₂²×C₅	—	6	8	no	—
693	C₂²×C₅	—	6	2	no	—
694	C₂²×C₅	—	6	2	no	—
695	C₂²×C₅	—	6	2	no	—
696	C₂²×C₅	—	6	2	no	—
697	C₂²×C₅	—	6	2	no	—
698	C₂²×C₅	—	12	4	no	—
699	C₂²×C₅	C₂×D₃×D₄	1	4	yes	—
700	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
701	C₂²×C₅	D₃×#41	1	2	yes	—
702	C₂²×C₅	#1010	1	2	yes	—
703	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
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	—	2	2	no	—
709	C₄×C₅	—	3	4	no	—
710	C₄×C₅	—	3	4	no	—
711	C₄×C₅	—	6	2	no	—
712	C₄×C₅	—	6	2	no	—
713	C₄×C₅	—	6	2	no	—
714	C₄×C₅	—	6	2	no	—
715	C₂⁴	—	3	1	no	—
716	C₂⁴	—	3	1	no	—
717	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
718	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
719	#41	—	6	32	no	—
720	#41	—	6	32	no	—
721	C₂×Q₈	—	3	4	no	—
722	C₂×Q₈	—	3	4	no	—
723	C₂×Q₈	—	6	4	no	—
724	C₂×Q₈	—	6	4	no	—
725	C₂×D₄	—	2	4	no	—
726	C₂×D₄	—	3	8	no	—
727	C₂×D₄	—	3	4	no	—
728	C₂×D₄	—	3	4	no	—
729	C₂×D₄	—	3	4	no	—
730	C₂×D₄	—	3	4	no	—
731	C₂×D₄	—	3	4	no	—
732	C₂×D₄	—	6	4	no	—
733	C₂×D₄	—	6	4	no	—
734	C₂×D₄	—	6	4	no	—
735	C₂×D₄	—	6	4	no	—
736	C₂×D₄	C₂²×C₅×D₃	1	4	yes	—
737	C₂²×C₄	—	2	4	no	—
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	1	no	—
744	C₂²×C₄	—	3	4	no	—
745	C₂²×C₄	—	3	4	no	—
746	C₂²×C₄	—	3	4	no	—
747	C₂²×C₄	—	3	4	no	—
748	C₂²×C₄	—	3	4	no	—
749	C₂²×C₄	—	3	4	no	—
750	C₂²×C₄	—	3	4	no	—
751	C₂²×C₄	—	6	4	no	—
752	C₂²×C₄	—	6	4	no	—
753	C₂²×C₄	—	6	4	no	—
754	C₂²×C₄	—	6	4	no	—
755	C₂²×C₄	—	6	4	no	—
756	C₂²×C₄	—	6	4	no	—
757	C₂²×C₄	—	6	4	no	—
758	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
759	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
760	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
761	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
762	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
763	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
764	C₄⋊C₄	—	3	4	no	—
765	C₄⋊C₄	—	3	4	no	—
766	C₄⋊C₄	—	3	4	no	—
767	C₄⋊C₄	—	3	4	no	—
768	C₄⋊C₄	—	3	4	no	—
769	C₄⋊C₄	—	3	4	no	—
770	C₄⋊C₄	—	3	4	no	—
771	C₄⋊C₄	—	3	4	no	—
772	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
773	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
774	C₂²⋊C₄	—	3	4	no	—
775	C₂²⋊C₄	—	3	4	no	—
776	C₂²⋊C₄	—	3	4	no	—
777	C₂²⋊C₄	—	3	4	no	—
778	C₂²⋊C₄	—	3	4	no	—
779	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
780	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
781	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
782	C₄²	—	3	4	no	—
783	C₃×C₅	C₂×#547	1	1	yes	characteristic, complemented, Hall
784	C₂²×C₃	—	2	8	no	—
785	C₂²×C₃	—	2	2	no	—
786	C₂²×C₃	—	2	2	no	—
787	C₂²×C₃	—	2	2	no	—
788	C₂²×C₃	—	2	2	no	—
789	C₂²×C₃	—	2	2	no	—
790	C₂²×C₃	—	4	4	no	—
791	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
792	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
793	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
794	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
795	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
796	C₂×D₃	—	2	8	no	—
797	C₂×D₃	—	2	2	no	—
798	C₂×D₃	—	2	2	no	—
799	C₂×D₃	—	2	2	no	—
800	C₂×D₃	—	2	2	no	—
801	C₂×D₃	—	2	2	no	—
802	C₂×D₃	—	4	4	no	—
803	C₂×D₃	C₂²×C₅×D₄	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	C₂²×C₅×D₄	1	4	yes	—
814	Dic₃	C₂×C₅×#41	1	4	yes	complemented
815	C₂×C₅	—	2	4	no	—
816	C₂×C₅	—	4	2	no	—
817	C₂×C₅	—	6	4	no	—
818	C₂×C₅	—	12	2	no	—
819	C₂×C₅	#5655	1	4	yes	direct product factor
820	C₂×C₅	C₂²×D₃×D₄	1	1	yes	characteristic
821	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
822	C₂×C₅	C₂×#1010	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	—	3	4	no	—
829	C₂³	—	3	2	no	—
830	C₂³	—	3	2	no	—
831	C₂³	—	6	2	no	—
832	C₂³	—	6	2	no	—
833	C₂³	—	6	2	no	—
834	C₂³	—	6	2	no	—
835	C₂³	—	6	2	no	—
836	C₂³	C₅×D₃×D₄	1	4	yes	—
837	C₂³	C₂³×C₅×D₃	1	2	yes	—
838	C₂³	C₂³×C₅×D₃	1	2	yes	—
839	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
840	Q₈	—	6	8	no	—
841	Q₈	—	6	8	no	—
842	D₄	—	2	8	no	—
843	D₄	—	3	16	no	—
844	D₄	—	6	8	no	—
845	D₄	—	6	8	no	—
846	D₄	—	6	8	no	—
847	D₄	—	6	8	no	—
848	C₂×C₄	—	2	2	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	8	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	3	4	no	—
855	C₂×C₄	—	3	4	no	—
856	C₂×C₄	—	3	2	no	—
857	C₂×C₄	—	3	2	no	—
858	C₂×C₄	—	3	2	no	—
859	C₂×C₄	—	3	2	no	—
860	C₂×C₄	—	3	2	no	—
861	C₂×C₄	—	3	2	no	—
862	C₂×C₄	—	6	8	no	—
863	C₂×C₄	—	6	8	no	—
864	C₂×C₄	—	6	8	no	—
865	C₂×C₄	—	6	8	no	—
866	C₂×C₄	—	6	8	no	—
867	C₂×C₄	—	6	8	no	—
868	C₂×C₄	—	6	2	no	—
869	C₂×C₄	—	6	2	no	—
870	C₂×C₄	—	6	2	no	—
871	C₂×C₄	—	6	8	no	—
872	C₂×C₄	—	6	2	no	—
873	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
874	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
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×C₃	—	2	4	no	—
879	C₂×C₃	—	4	2	no	—
880	C₂×C₃	C₅×#547	1	4	yes	complemented
881	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
882	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
883	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
884	D₃	—	2	4	no	—
885	D₃	—	4	2	no	—
886	C₅	C₂×#5655	1	1	yes	characteristic, direct product factor, Sylow
887	C₂²	—	2	8	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	2	2	no	—
892	C₂²	—	2	2	no	—
893	C₂²	—	3	4	no	—
894	C₂²	—	4	4	no	—
895	C₂²	—	6	8	no	—
896	C₂²	—	6	2	no	—
897	C₂²	—	6	2	no	—
898	C₂²	—	6	2	no	—
899	C₂²	—	6	2	no	—
900	C₂²	—	6	2	no	—
901	C₂²	—	12	4	no	—
902	C₂²	C₂×C₅×D₃×D₄	1	4	yes	—
903	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
904	C₂²	C₅×D₃×#41	1	2	yes	—
905	C₂²	C₅×#1010	1	2	yes	—
906	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
907	C₄	—	2	2	no	—
908	C₄	—	2	2	no	—
909	C₄	—	2	2	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	2	no	—
912	C₄	—	3	4	no	—
913	C₄	—	3	4	no	—
914	C₄	—	6	2	no	—
915	C₄	—	6	2	no	—
916	C₄	—	6	2	no	—
917	C₄	—	6	2	no	—
918	C₃	C₂×C₅×#547	1	1	yes	characteristic, complemented, Sylow
919	C₂	—	2	4	no	—
920	C₂	—	4	2	no	—
921	C₂	—	6	4	no	—
922	C₂	—	12	2	no	—
923	C₂	C₅×#5655	1	4	yes	direct product factor
924	C₂	C₂²×C₅×D₃×D₄	1	1	yes	characteristic
925	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
926	C₂	C₂×C₅×#1010	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×#123	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₅×#123	D₃
hypocenter	C₃	C₂×C₅×#547
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#123

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#237	C₂	semidirect
2. C₂²×C₅×#235	C₂	semidirect
3. C₂×C₃×C₅×#123	C₂	semidirect
4. C₂×C₅×#939	C₂	semidirect
5. C₂²×C₅×Dic₃⋊C₄	C₂	semidirect
6. C₅×#5655	C₂	direct (N × H)
7. C₂×C₅×#896	C₂	semidirect
8. C₂×C₅×#894	C₂	semidirect
9. C₂×C₅×D₃×C₄⋊C₄	C₂	semidirect
10. C₂×C₅×#888	C₂	semidirect
11. C₂×C₅×#886	C₂	semidirect
12. C₂×C₅×#884	C₂	semidirect
13. C₂×C₅×#883	C₂	semidirect
14. C₂×C₅×#67⋊C₄	C₂	semidirect
15. C₂×C₅×#67⋊C₄	C₂	semidirect
16. C₂×C₅×#878	C₂	semidirect
28. C₂×C₅×#237	C₂²	semidirect
30. C₂×C₅×#235	C₂²	semidirect
38. C₃×C₅×#123	C₂²	semidirect
45. C₅×#939	C₂²	semidirect
58. C₂×C₅×Dic₃⋊C₄	C₂²	semidirect
60. C₅×#896	C₂²	semidirect
61. C₅×#894	C₂²	semidirect
62. C₅×D₃×C₄⋊C₄	C₂²	semidirect
63. C₅×#888	C₂²	semidirect
64. C₅×#886	C₂²	semidirect
65. C₅×#884	C₂²	semidirect
66. C₅×#883	C₂²	semidirect
67. C₅×#67⋊C₄	C₂²	semidirect
68. C₅×#67⋊C₄	C₂²	semidirect
69. C₅×#878	C₂²	semidirect
70. C₂×#5655	C₅	direct (N × H)
78. C₂×C₅×#123	D₃	semidirect
103. C₂×C₅×#67	D₄	semidirect
155. C₂²×#237	C₂×C₅	semidirect
156. C₂²×#235	C₂×C₅	semidirect
157. C₂×C₃×#123	C₂×C₅	semidirect
158. C₂×#939	C₂×C₅	semidirect
159. C₂²×Dic₃⋊C₄	C₂×C₅	semidirect
160. #5655	C₂×C₅	direct (N × H)
161. C₂×#896	C₂×C₅	semidirect
162. C₂×#894	C₂×C₅	semidirect
163. C₂×D₃×C₄⋊C₄	C₂×C₅	semidirect
164. C₂×#888	C₂×C₅	semidirect
165. C₂×#886	C₂×C₅	semidirect
166. C₂×#884	C₂×C₅	semidirect
167. C₂×#883	C₂×C₅	semidirect
168. C₂×#67⋊C₄	C₂×C₅	semidirect
169. C₂×#67⋊C₄	C₂×C₅	semidirect
170. C₂×#878	C₂×C₅	semidirect
195. C₅×#123	C₂×D₃	semidirect
256. C₅×#67	C₂×D₄	semidirect
265. C₂×C₅×Dic₃	#41	semidirect
289. C₂×#237	C₂²×C₅	semidirect
291. C₂×#235	C₂²×C₅	semidirect
299. C₃×#123	C₂²×C₅	semidirect
306. #939	C₂²×C₅	semidirect
319. C₂×Dic₃⋊C₄	C₂²×C₅	semidirect
321. #896	C₂²×C₅	semidirect
322. #894	C₂²×C₅	semidirect
323. D₃×C₄⋊C₄	C₂²×C₅	semidirect
324. #888	C₂²×C₅	semidirect
325. #886	C₂²×C₅	semidirect
326. #884	C₂²×C₅	semidirect
327. #883	C₂²×C₅	semidirect
328. #67⋊C₄	C₂²×C₅	semidirect
329. #67⋊C₄	C₂²×C₅	semidirect
330. #878	C₂²×C₅	semidirect
406. C₂×#123	C₅×D₃	semidirect
445. C₅×Dic₃	C₂×#41	semidirect
462. C₂×#67	C₅×D₄	semidirect
593. #123	C₂×C₅×D₃	semidirect
623. C₂×C₃×C₅	#547	semidirect
661. #67	C₂×C₅×D₄	semidirect
670. C₂×Dic₃	C₅×#41	semidirect
783. C₃×C₅	C₂×#547	semidirect
814. Dic₃	C₂×C₅×#41	semidirect
819. C₂×C₅	#5655	direct (N × H)
880. C₂×C₃	C₅×#547	semidirect
886. C₅	C₂×#5655	direct (N × H)
918. C₃	C₂×C₅×#547	semidirect
923. C₂	C₅×#5655	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#237	2
C₂²×C₅×#235	2
C₂×C₃×C₅×#123	2
C₂×C₅×#939	2
C₂²×C₅×Dic₃⋊C₄	2
C₅×#5655	2
C₂×C₅×#896	2
C₂×C₅×#894	2
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₅×#888	2
C₂×C₅×#886	2
C₂×C₅×#884	2
C₂×C₅×#883	2
C₂×C₅×#67⋊C₄	2
C₂×C₅×#878	2
C₂×C₅×#547	3
C₂×#5655	5

Subgroups — C2×C5×#5655 #14482670

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5655 #14482670