Subgroups — C₂×C₅×#5701 #14481190

Order 1920.

2008 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#126	C₂	1	1	yes	maximal, characteristic
2	C₅×#5701	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₅×#890	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#889	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#889	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#889	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#888	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#887	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#879	C₂	1	1	yes	maximal, characteristic
10	C₂×C₅×#879	C₂	1	1	yes	maximal, characteristic
11	C₂×C₅×#879	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×#878	C₂	1	1	yes	maximal, characteristic
13	C₂×C₅×#878	C₂	1	1	yes	maximal, characteristic
14	C₂×C₅×#877	C₂	1	1	yes	maximal, characteristic
15	C₂×C₅×#870	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₅×#541	—	3	1	no	maximal, Hall
18	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
19	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
20	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
21	C₃×C₅×#126	C₂²	1	8	yes	—
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
29	C₂×C₅×#217	C₂²	1	1	yes	characteristic
30	C₂×C₅×#217	C₂²	1	1	yes	characteristic
31	C₂×C₅×#217	C₂²	1	1	yes	characteristic
32	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
33	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
34	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
35	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
36	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
37	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
47	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
48	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
54	C₅×#890	C₂²	1	8	yes	complemented
55	C₅×#889	C₂²	1	8	yes	complemented
56	C₅×#889	C₂²	1	8	yes	complemented
57	C₅×#889	C₂²	1	8	yes	complemented
58	C₅×#888	C₂²	1	8	yes	complemented
59	C₅×#887	C₂²	1	8	yes	complemented
60	C₅×#879	C₂²	1	8	yes	—
61	C₅×#879	C₂²	1	8	yes	—
62	C₅×#879	C₂²	1	8	yes	—
63	C₅×#878	C₂²	1	8	yes	—
64	C₅×#878	C₂²	1	8	yes	—
65	C₅×#877	C₂²	1	8	yes	—
66	C₅×#870	C₂²	1	8	yes	complemented
67	C₄×C₅×Dic₆	C₂²	1	8	yes	complemented
68	C₂×#5701	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
69	C₅×#541	—	3	16	no	—
70	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
71	C₂×C₅×#126	—	3	1	no	—
72	C₂×C₅×#126	—	3	1	no	—
73	C₂×C₅×#126	—	3	1	no	—
74	C₂×C₅×#126	D₃	1	1	yes	characteristic
75	C₂×C₅×#125	—	3	1	no	—
76	C₂×C₅×#125	—	3	1	no	—
77	C₂×C₅×#125	—	3	1	no	—
78	C₂×C₅×#125	—	3	1	no	—
79	C₂×C₅×#125	—	3	1	no	—
80	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
81	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
82	C₂×C₄×C₅×Q₈	—	3	1	no	—
83	C₂×C₄×C₅×Q₈	—	3	1	no	—
84	C₂×C₅×#117	—	3	1	no	—
85	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
86	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
87	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
88	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
89	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
90	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
91	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
92	C₂²×C₅×Dic₃	—	2	4	no	—
93	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
94	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
95	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
96	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
97	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
98	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
99	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
100	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
101	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
102	C₂×C₅×Dic₆	—	2	4	no	—
103	C₂×C₅×Dic₆	—	2	4	no	—
104	C₂×C₅×Dic₆	C₂³	1	4	yes	—
105	C₂×C₅×Dic₆	C₂³	1	4	yes	—
106	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
107	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
108	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
109	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₃×C₄²×C₅	C₂³	1	4	yes	—
113	C₅×#217	C₂³	1	4	yes	—
114	C₅×#217	C₂³	1	4	yes	—
115	C₅×#217	C₂³	1	4	yes	—
116	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
117	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
118	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
119	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
120	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
121	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
122	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
123	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
124	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
125	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
126	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
127	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
128	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
129	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
130	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
131	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
132	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
133	C₄×C₅×Dic₃	C₂³	1	4	yes	—
134	C₄×C₅×Dic₃	C₂³	1	4	yes	—
135	C₄×C₅×Dic₃	C₂³	1	4	yes	—
136	C₄×C₅×Dic₃	C₂³	1	4	yes	—
137	C₄×C₅×Dic₃	C₂³	1	4	yes	—
138	C₂×C₃×#126	C₂×C₅	1	1	yes	characteristic
139	#5701	C₂×C₅	1	16	yes	direct product factor
140	C₂×#890	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂×#889	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂×#889	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂×#889	C₂×C₅	1	1	yes	characteristic, complemented
144	C₂×#888	C₂×C₅	1	1	yes	characteristic, complemented
145	C₂×#887	C₂×C₅	1	1	yes	characteristic, complemented
146	C₂×#879	C₂×C₅	1	1	yes	characteristic
147	C₂×#879	C₂×C₅	1	1	yes	characteristic
148	C₂×#879	C₂×C₅	1	1	yes	characteristic
149	C₂×#878	C₂×C₅	1	1	yes	characteristic
150	C₂×#878	C₂×C₅	1	1	yes	characteristic
151	C₂×#877	C₂×C₅	1	1	yes	characteristic
152	C₂×#870	C₂×C₅	1	1	yes	characteristic, complemented
153	C₂×C₄×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
154	C₂²×C₅×Q₈	—	3	1	no	—
155	C₂²×C₅×Q₈	—	3	1	no	—
156	C₂³×C₄×C₅	—	3	1	no	—
157	C₅×C₄⋊Q₈	—	3	8	no	—
158	C₅×#126	—	3	8	no	—
159	C₅×#126	—	3	8	no	—
160	C₅×#126	—	3	8	no	—
161	C₅×#126	C₂×D₃	1	8	yes	—
162	C₅×#125	—	3	8	no	—
163	C₅×#125	—	3	8	no	—
164	C₅×#125	—	3	8	no	—
165	C₅×#125	—	3	8	no	—
166	C₅×#125	—	3	8	no	—
167	C₅×C₂²⋊Q₈	—	3	8	no	—
168	C₅×C₂²⋊Q₈	—	3	8	no	—
169	C₄×C₅×Q₈	—	3	8	no	—
170	C₄×C₅×Q₈	—	3	8	no	—
171	C₅×#117	—	3	8	no	—
172	C₂×C₅×C₄⋊C₄	—	3	1	no	—
173	C₂×C₅×C₄⋊C₄	—	3	1	no	—
174	C₂×C₅×C₄⋊C₄	—	3	1	no	—
175	C₂×C₅×C₄⋊C₄	—	3	1	no	—
176	C₂×C₅×C₄⋊C₄	—	3	1	no	—
177	C₂×C₅×C₄⋊C₄	—	3	1	no	—
178	C₂×C₅×C₄⋊C₄	—	3	1	no	—
179	C₂×C₅×C₄⋊C₄	—	3	1	no	—
180	C₂×C₅×C₄⋊C₄	—	3	1	no	—
181	C₂×C₅×C₄⋊C₄	—	3	1	no	—
182	C₂×C₅×C₄⋊C₄	—	3	1	no	—
183	C₂×C₅×C₄⋊C₄	—	3	1	no	—
184	C₂×C₅×C₄⋊C₄	—	3	1	no	—
185	C₂×C₅×C₄⋊C₄	—	3	1	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	C₂×D₃	1	1	yes	characteristic
190	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
191	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
192	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
193	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
194	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
195	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
196	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
197	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
198	C₂×C₄²×C₅	—	3	1	no	—
199	C₂×C₄²×C₅	—	3	1	no	—
200	C₂×C₄²×C₅	—	3	1	no	—
201	C₂×C₄²×C₅	—	3	1	no	—
202	C₂×C₄²×C₅	—	3	1	no	—
203	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
204	C₂×#541	—	3	1	no	Sylow
205	C₂³×C₃×C₅	—	2	2	no	—
206	C₂³×C₃×C₅	—	2	2	no	—
207	C₂³×C₃×C₅	—	2	2	no	—
208	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
209	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
210	C₂×C₃×C₄×C₅	—	2	2	no	—
211	C₂×C₃×C₄×C₅	—	2	2	no	—
212	C₂×C₃×C₄×C₅	—	2	2	no	—
213	C₂×C₃×C₄×C₅	—	2	2	no	—
214	C₂×C₃×C₄×C₅	—	2	2	no	—
215	C₂×C₃×C₄×C₅	—	2	2	no	—
216	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
217	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
218	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
219	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
220	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
221	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
222	C₂×C₅×Dic₃	—	2	2	no	—
223	C₂×C₅×Dic₃	—	2	2	no	—
224	C₂×C₅×Dic₃	—	2	2	no	—
225	C₂×C₅×Dic₃	—	2	2	no	—
226	C₂×C₅×Dic₃	—	2	2	no	—
227	C₂×C₅×Dic₃	—	2	2	no	—
228	C₂×C₅×Dic₃	—	2	2	no	—
229	C₂×C₅×Dic₃	—	2	8	no	—
230	C₂×C₅×Dic₃	#41	1	4	yes	—
231	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
232	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
233	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
234	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
235	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
236	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
237	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
238	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
239	C₅×Dic₆	—	2	8	no	—
240	C₅×Dic₆	—	2	8	no	—
241	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
242	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
243	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
244	C₃×#126	C₂²×C₅	1	8	yes	—
245	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
246	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
248	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
249	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
250	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
251	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
252	C₂×#217	C₂²×C₅	1	1	yes	characteristic
253	C₂×#217	C₂²×C₅	1	1	yes	characteristic
254	C₂×#217	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
256	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
257	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
258	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
260	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
261	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
262	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
263	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
264	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
265	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
266	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
267	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
268	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
269	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
270	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
271	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
272	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
273	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
274	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
275	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
276	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
277	#890	C₂²×C₅	1	8	yes	complemented
278	#889	C₂²×C₅	1	8	yes	complemented
279	#889	C₂²×C₅	1	8	yes	complemented
280	#889	C₂²×C₅	1	8	yes	complemented
281	#888	C₂²×C₅	1	8	yes	complemented
282	#887	C₂²×C₅	1	8	yes	complemented
283	#879	C₂²×C₅	1	8	yes	—
284	#879	C₂²×C₅	1	8	yes	—
285	#879	C₂²×C₅	1	8	yes	—
286	#878	C₂²×C₅	1	8	yes	—
287	#878	C₂²×C₅	1	8	yes	—
288	#877	C₂²×C₅	1	8	yes	—
289	#870	C₂²×C₅	1	8	yes	complemented
290	C₄×Dic₆	C₂²×C₅	1	8	yes	complemented
291	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
292	C₂×C₅×Q₈	—	3	4	no	—
293	C₂×C₅×Q₈	—	3	4	no	—
294	C₂×C₅×Q₈	—	6	4	no	—
295	C₂×C₅×Q₈	—	6	4	no	—
296	C₂²×C₄×C₅	—	3	1	no	—
297	C₂²×C₄×C₅	—	3	4	no	—
298	C₂²×C₄×C₅	—	3	1	no	—
299	C₂²×C₄×C₅	—	3	1	no	—
300	C₂²×C₄×C₅	—	3	1	no	—
301	C₂²×C₄×C₅	—	3	1	no	—
302	C₂²×C₄×C₅	—	3	1	no	—
303	C₂²×C₄×C₅	—	3	1	no	—
304	C₂²×C₄×C₅	—	3	1	no	—
305	C₂²×C₄×C₅	—	6	4	no	—
306	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
307	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
308	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
309	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
310	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
311	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
312	C₅×C₄⋊C₄	—	3	4	no	—
313	C₅×C₄⋊C₄	—	3	4	no	—
314	C₅×C₄⋊C₄	—	3	4	no	—
315	C₅×C₄⋊C₄	—	3	4	no	—
316	C₅×C₄⋊C₄	—	3	4	no	—
317	C₅×C₄⋊C₄	—	3	4	no	—
318	C₅×C₄⋊C₄	—	3	4	no	—
319	C₅×C₄⋊C₄	—	3	4	no	—
320	C₅×C₄⋊C₄	—	3	4	no	—
321	C₅×C₄⋊C₄	—	3	4	no	—
322	C₅×C₄⋊C₄	—	3	4	no	—
323	C₅×C₄⋊C₄	—	3	4	no	—
324	C₅×C₄⋊C₄	—	3	4	no	—
325	C₅×C₄⋊C₄	—	3	4	no	—
326	C₅×C₄⋊C₄	—	3	4	no	—
327	C₅×C₄⋊C₄	—	3	4	no	—
328	C₅×C₄⋊C₄	—	3	4	no	—
329	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
330	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
331	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
332	C₅×C₂²⋊C₄	—	3	4	no	—
333	C₅×C₂²⋊C₄	—	3	4	no	—
334	C₅×C₂²⋊C₄	—	3	4	no	—
335	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
336	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
337	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
338	C₄²×C₅	—	3	4	no	—
339	C₄²×C₅	—	3	4	no	—
340	C₄²×C₅	—	3	4	no	—
341	C₄²×C₅	—	3	4	no	—
342	C₄²×C₅	—	3	4	no	—
343	C₄²×C₅	C₂²×D₃	1	4	yes	—
344	#541	—	3	16	no	—
345	C₂×C₄⋊Q₈	—	3	1	no	—
346	C₂×#126	—	3	1	no	—
347	C₂×#126	—	3	1	no	—
348	C₂×#126	—	3	1	no	—
349	C₂×#126	C₅×D₃	1	1	yes	characteristic
350	C₂×#125	—	3	1	no	—
351	C₂×#125	—	3	1	no	—
352	C₂×#125	—	3	1	no	—
353	C₂×#125	—	3	1	no	—
354	C₂×#125	—	3	1	no	—
355	C₂×C₂²⋊Q₈	—	3	1	no	—
356	C₂×C₂²⋊Q₈	—	3	1	no	—
357	C₂×C₄×Q₈	—	3	1	no	—
358	C₂×C₄×Q₈	—	3	1	no	—
359	C₂×#117	—	3	1	no	—
360	C₂²×C₃×C₅	—	2	2	no	—
361	C₂²×C₃×C₅	—	2	2	no	—
362	C₂²×C₃×C₅	—	2	2	no	—
363	C₂²×C₃×C₅	—	4	4	no	—
364	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
365	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
366	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
367	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
368	C₃×C₄×C₅	—	2	2	no	—
369	C₃×C₄×C₅	—	2	2	no	—
370	C₃×C₄×C₅	—	2	2	no	—
371	C₃×C₄×C₅	—	2	2	no	—
372	C₃×C₄×C₅	—	2	2	no	—
373	C₃×C₄×C₅	—	2	2	no	—
374	C₅×Dic₃	—	2	2	no	—
375	C₅×Dic₃	—	2	2	no	—
376	C₅×Dic₃	—	2	2	no	—
377	C₅×Dic₃	—	2	2	no	—
378	C₅×Dic₃	—	2	2	no	—
379	C₅×Dic₃	—	2	2	no	—
380	C₅×Dic₃	—	2	2	no	—
381	C₅×Dic₃	C₂×#41	1	4	yes	—
382	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
383	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
384	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
385	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
386	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
387	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
388	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
389	C₂²×Dic₃	—	2	4	no	—
390	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
391	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
392	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
393	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
394	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
395	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
396	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
397	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
398	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
399	C₂×Dic₆	—	2	4	no	—
400	C₂×Dic₆	—	2	4	no	—
401	C₂×Dic₆	C₂³×C₅	1	4	yes	—
402	C₂×Dic₆	C₂³×C₅	1	4	yes	—
403	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
404	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
405	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
406	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
407	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
408	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
409	C₃×C₄²	C₂³×C₅	1	4	yes	—
410	#217	C₂³×C₅	1	4	yes	—
411	#217	C₂³×C₅	1	4	yes	—
412	#217	C₂³×C₅	1	4	yes	—
413	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
414	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
415	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
416	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
417	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
418	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
419	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
420	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
421	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
422	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
423	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
424	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
425	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
426	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
427	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
428	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
429	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
430	C₄×Dic₃	C₂³×C₅	1	4	yes	—
431	C₄×Dic₃	C₂³×C₅	1	4	yes	—
432	C₄×Dic₃	C₂³×C₅	1	4	yes	—
433	C₄×Dic₃	C₂³×C₅	1	4	yes	—
434	C₄×Dic₃	C₂³×C₅	1	4	yes	—
435	C₂³×C₅	—	2	2	no	—
436	C₂³×C₅	—	2	2	no	—
437	C₂³×C₅	—	2	2	no	—
438	C₂³×C₅	C₂³×D₃	1	2	yes	—
439	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
440	C₅×Q₈	—	6	8	no	—
441	C₅×Q₈	—	6	8	no	—
442	C₂×C₄×C₅	—	2	2	no	—
443	C₂×C₄×C₅	—	2	2	no	—
444	C₂×C₄×C₅	—	2	2	no	—
445	C₂×C₄×C₅	—	2	2	no	—
446	C₂×C₄×C₅	—	2	2	no	—
447	C₂×C₄×C₅	—	2	2	no	—
448	C₂×C₄×C₅	—	3	4	no	—
449	C₂×C₄×C₅	—	3	2	no	—
450	C₂×C₄×C₅	—	3	2	no	—
451	C₂×C₄×C₅	—	3	2	no	—
452	C₂×C₄×C₅	—	3	2	no	—
453	C₂×C₄×C₅	—	3	2	no	—
454	C₂×C₄×C₅	—	3	2	no	—
455	C₂×C₄×C₅	—	3	2	no	—
456	C₂×C₄×C₅	—	3	2	no	—
457	C₂×C₄×C₅	—	6	8	no	—
458	C₂×C₄×C₅	—	6	2	no	—
459	C₂×C₄×C₅	—	6	2	no	—
460	C₂×C₄×C₅	—	6	2	no	—
461	C₂×C₄×C₅	—	6	2	no	—
462	C₂×C₄×C₅	—	6	2	no	—
463	C₂×C₄×C₅	—	6	2	no	—
464	C₂×C₄×C₅	—	6	2	no	—
465	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
466	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
467	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
468	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
469	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
470	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
471	C₂²×Q₈	—	3	1	no	—
472	C₂²×Q₈	—	3	1	no	—
473	C₂³×C₄	—	3	1	no	—
474	C₄⋊Q₈	—	3	8	no	—
475	#126	—	3	8	no	—
476	#126	—	3	8	no	—
477	#126	—	3	8	no	—
478	#126	C₂×C₅×D₃	1	8	yes	—
479	#125	—	3	8	no	—
480	#125	—	3	8	no	—
481	#125	—	3	8	no	—
482	#125	—	3	8	no	—
483	#125	—	3	8	no	—
484	C₂²⋊Q₈	—	3	8	no	—
485	C₂²⋊Q₈	—	3	8	no	—
486	C₄×Q₈	—	3	8	no	—
487	C₄×Q₈	—	3	8	no	—
488	#117	—	3	8	no	—
489	C₂×C₄⋊C₄	—	3	1	no	—
490	C₂×C₄⋊C₄	—	3	1	no	—
491	C₂×C₄⋊C₄	—	3	1	no	—
492	C₂×C₄⋊C₄	—	3	1	no	—
493	C₂×C₄⋊C₄	—	3	1	no	—
494	C₂×C₄⋊C₄	—	3	1	no	—
495	C₂×C₄⋊C₄	—	3	1	no	—
496	C₂×C₄⋊C₄	—	3	1	no	—
497	C₂×C₄⋊C₄	—	3	1	no	—
498	C₂×C₄⋊C₄	—	3	1	no	—
499	C₂×C₄⋊C₄	—	3	1	no	—
500	C₂×C₄⋊C₄	—	3	1	no	—
501	C₂×C₄⋊C₄	—	3	1	no	—
502	C₂×C₄⋊C₄	—	3	1	no	—
503	C₂×C₄⋊C₄	—	3	1	no	—
504	C₂×C₄⋊C₄	—	3	1	no	—
505	C₂×C₄⋊C₄	—	3	1	no	—
506	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
508	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
509	C₂×C₂²⋊C₄	—	3	1	no	—
510	C₂×C₂²⋊C₄	—	3	1	no	—
511	C₂×C₂²⋊C₄	—	3	1	no	—
512	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
513	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
514	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
515	C₂×C₄²	—	3	1	no	—
516	C₂×C₄²	—	3	1	no	—
517	C₂×C₄²	—	3	1	no	—
518	C₂×C₄²	—	3	1	no	—
519	C₂×C₄²	—	3	1	no	—
520	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
521	C₂×C₃×C₅	—	4	2	no	—
522	C₂×C₃×C₅	#541	1	4	yes	complemented
523	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
524	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
525	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
526	C₂³×C₃	—	2	2	no	—
527	C₂³×C₃	—	2	2	no	—
528	C₂³×C₃	—	2	2	no	—
529	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
530	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
531	C₂×C₃×C₄	—	2	2	no	—
532	C₂×C₃×C₄	—	2	2	no	—
533	C₂×C₃×C₄	—	2	2	no	—
534	C₂×C₃×C₄	—	2	2	no	—
535	C₂×C₃×C₄	—	2	2	no	—
536	C₂×C₃×C₄	—	2	2	no	—
537	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
538	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
539	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
540	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
541	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
542	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
543	C₂×Dic₃	—	2	2	no	—
544	C₂×Dic₃	—	2	2	no	—
545	C₂×Dic₃	—	2	2	no	—
546	C₂×Dic₃	—	2	2	no	—
547	C₂×Dic₃	—	2	2	no	—
548	C₂×Dic₃	—	2	2	no	—
549	C₂×Dic₃	—	2	2	no	—
550	C₂×Dic₃	—	2	8	no	—
551	C₂×Dic₃	C₅×#41	1	4	yes	—
552	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
553	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
554	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
555	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
556	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
557	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
558	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
559	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
560	Dic₆	—	2	8	no	—
561	Dic₆	—	2	8	no	—
562	C₂²×C₅	—	2	2	no	—
563	C₂²×C₅	—	2	2	no	—
564	C₂²×C₅	—	2	2	no	—
565	C₂²×C₅	—	4	4	no	—
566	C₂²×C₅	D₃×#41	1	2	yes	—
567	C₂²×C₅	#1010	1	2	yes	—
568	C₂²×C₅	#1010	1	2	yes	—
569	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
570	C₄×C₅	—	2	2	no	—
571	C₄×C₅	—	2	2	no	—
572	C₄×C₅	—	2	2	no	—
573	C₄×C₅	—	2	2	no	—
574	C₄×C₅	—	2	2	no	—
575	C₄×C₅	—	2	2	no	—
576	C₄×C₅	—	3	4	no	—
577	C₄×C₅	—	6	2	no	—
578	C₄×C₅	—	6	2	no	—
579	C₄×C₅	—	6	2	no	—
580	C₄×C₅	—	6	2	no	—
581	C₄×C₅	—	6	2	no	—
582	C₄×C₅	—	6	2	no	—
583	C₄×C₅	—	6	2	no	—
584	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
585	C₂×Q₈	—	3	4	no	—
586	C₂×Q₈	—	3	4	no	—
587	C₂×Q₈	—	6	4	no	—
588	C₂×Q₈	—	6	4	no	—
589	C₂²×C₄	—	3	1	no	—
590	C₂²×C₄	—	3	1	no	—
591	C₂²×C₄	—	3	1	no	—
592	C₂²×C₄	—	3	1	no	—
593	C₂²×C₄	—	3	1	no	—
594	C₂²×C₄	—	3	1	no	—
595	C₂²×C₄	—	3	1	no	—
596	C₂²×C₄	—	3	1	no	—
597	C₂²×C₄	—	3	4	no	—
598	C₂²×C₄	—	6	4	no	—
599	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
600	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
601	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
602	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
603	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
604	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
605	C₄⋊C₄	—	3	4	no	—
606	C₄⋊C₄	—	3	4	no	—
607	C₄⋊C₄	—	3	4	no	—
608	C₄⋊C₄	—	3	4	no	—
609	C₄⋊C₄	—	3	4	no	—
610	C₄⋊C₄	—	3	4	no	—
611	C₄⋊C₄	—	3	4	no	—
612	C₄⋊C₄	—	3	4	no	—
613	C₄⋊C₄	—	3	4	no	—
614	C₄⋊C₄	—	3	4	no	—
615	C₄⋊C₄	—	3	4	no	—
616	C₄⋊C₄	—	3	4	no	—
617	C₄⋊C₄	—	3	4	no	—
618	C₄⋊C₄	—	3	4	no	—
619	C₄⋊C₄	—	3	4	no	—
620	C₄⋊C₄	—	3	4	no	—
621	C₄⋊C₄	—	3	4	no	—
622	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
623	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
624	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
625	C₂²⋊C₄	—	3	4	no	—
626	C₂²⋊C₄	—	3	4	no	—
627	C₂²⋊C₄	—	3	4	no	—
628	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
629	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
630	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
631	C₄²	—	3	4	no	—
632	C₄²	—	3	4	no	—
633	C₄²	—	3	4	no	—
634	C₄²	—	3	4	no	—
635	C₄²	—	3	4	no	—
636	C₄²	C₂²×C₅×D₃	1	4	yes	—
637	C₃×C₅	C₂×#541	1	1	yes	characteristic, complemented, Hall
638	C₂²×C₃	—	2	2	no	—
639	C₂²×C₃	—	2	2	no	—
640	C₂²×C₃	—	2	2	no	—
641	C₂²×C₃	—	4	4	no	—
642	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
643	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
644	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
645	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
646	C₃×C₄	—	2	2	no	—
647	C₃×C₄	—	2	2	no	—
648	C₃×C₄	—	2	2	no	—
649	C₃×C₄	—	2	2	no	—
650	C₃×C₄	—	2	2	no	—
651	C₃×C₄	—	2	2	no	—
652	Dic₃	—	2	2	no	—
653	Dic₃	—	2	2	no	—
654	Dic₃	—	2	2	no	—
655	Dic₃	—	2	2	no	—
656	Dic₃	—	2	2	no	—
657	Dic₃	—	2	2	no	—
658	Dic₃	—	2	2	no	—
659	Dic₃	C₂×C₅×#41	1	4	yes	—
660	C₂×C₅	—	4	2	no	—
661	C₂×C₅	#5701	1	4	yes	direct product factor
662	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
663	C₂×C₅	C₂×#1010	1	1	yes	characteristic
664	C₂×C₅	C₂×#1010	1	1	yes	characteristic
665	C₂³	—	2	2	no	—
666	C₂³	—	2	2	no	—
667	C₂³	—	2	2	no	—
668	C₂³	C₂³×C₅×D₃	1	2	yes	—
669	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
670	Q₈	—	6	8	no	—
671	Q₈	—	6	8	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	3	4	no	—
679	C₂×C₄	—	3	2	no	—
680	C₂×C₄	—	3	2	no	—
681	C₂×C₄	—	3	2	no	—
682	C₂×C₄	—	3	2	no	—
683	C₂×C₄	—	3	2	no	—
684	C₂×C₄	—	3	2	no	—
685	C₂×C₄	—	3	2	no	—
686	C₂×C₄	—	3	2	no	—
687	C₂×C₄	—	6	8	no	—
688	C₂×C₄	—	6	2	no	—
689	C₂×C₄	—	6	2	no	—
690	C₂×C₄	—	6	2	no	—
691	C₂×C₄	—	6	2	no	—
692	C₂×C₄	—	6	2	no	—
693	C₂×C₄	—	6	2	no	—
694	C₂×C₄	—	6	2	no	—
695	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
696	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
697	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
698	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
699	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
700	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
701	C₂×C₃	—	4	2	no	—
702	C₂×C₃	C₅×#541	1	4	yes	complemented
703	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
704	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
705	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
706	C₅	C₂×#5701	1	1	yes	characteristic, direct product factor, Sylow
707	C₂²	—	2	2	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	2	2	no	—
710	C₂²	—	4	4	no	—
711	C₂²	C₅×D₃×#41	1	2	yes	—
712	C₂²	C₅×#1010	1	2	yes	—
713	C₂²	C₅×#1010	1	2	yes	—
714	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
715	C₄	—	2	2	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	2	no	—
719	C₄	—	2	2	no	—
720	C₄	—	2	2	no	—
721	C₄	—	3	4	no	—
722	C₄	—	6	2	no	—
723	C₄	—	6	2	no	—
724	C₄	—	6	2	no	—
725	C₄	—	6	2	no	—
726	C₄	—	6	2	no	—
727	C₄	—	6	2	no	—
728	C₄	—	6	2	no	—
729	C₃	C₂×C₅×#541	1	1	yes	characteristic, complemented, Sylow
730	C₂	—	4	2	no	—
731	C₂	C₅×#5701	1	4	yes	direct product factor
732	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
733	C₂	C₂×C₅×#1010	1	1	yes	characteristic
734	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×#126	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×C₅	C₂³
hypercenter	C₂×C₅×#126	D₃
hypocenter	C₃	C₂×C₅×#541
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#126

Complements

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

N	H ≅ G/N	type
2. C₅×#5701	C₂	direct (N × H)
3. C₂×C₅×#890	C₂	semidirect
4. C₂×C₅×#889	C₂	semidirect
5. C₂×C₅×#889	C₂	semidirect
6. C₂×C₅×#889	C₂	semidirect
7. C₂×C₅×#888	C₂	semidirect
8. C₂×C₅×#887	C₂	semidirect
15. C₂×C₅×#870	C₂	semidirect
16. C₂×C₄×C₅×Dic₆	C₂	semidirect
54. C₅×#890	C₂²	semidirect
55. C₅×#889	C₂²	semidirect
56. C₅×#889	C₂²	semidirect
57. C₅×#889	C₂²	semidirect
58. C₅×#888	C₂²	semidirect
59. C₅×#887	C₂²	semidirect
66. C₅×#870	C₂²	semidirect
67. C₄×C₅×Dic₆	C₂²	semidirect
68. C₂×#5701	C₅	direct (N × H)
139. #5701	C₂×C₅	direct (N × H)
140. C₂×#890	C₂×C₅	semidirect
141. C₂×#889	C₂×C₅	semidirect
142. C₂×#889	C₂×C₅	semidirect
143. C₂×#889	C₂×C₅	semidirect
144. C₂×#888	C₂×C₅	semidirect
145. C₂×#887	C₂×C₅	semidirect
152. C₂×#870	C₂×C₅	semidirect
153. C₂×C₄×Dic₆	C₂×C₅	semidirect
277. #890	C₂²×C₅	semidirect
278. #889	C₂²×C₅	semidirect
279. #889	C₂²×C₅	semidirect
280. #889	C₂²×C₅	semidirect
281. #888	C₂²×C₅	semidirect
282. #887	C₂²×C₅	semidirect
289. #870	C₂²×C₅	semidirect
290. C₄×Dic₆	C₂²×C₅	semidirect
522. C₂×C₃×C₅	#541	semidirect
637. C₃×C₅	C₂×#541	semidirect
661. C₂×C₅	#5701	direct (N × H)
702. C₂×C₃	C₅×#541	semidirect
706. C₅	C₂×#5701	direct (N × H)
729. C₃	C₂×C₅×#541	semidirect
731. C₂	C₅×#5701	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#126	2
C₅×#5701	2
C₂×C₅×#890	2
C₂×C₅×#889	2
C₂×C₅×#888	2
C₂×C₅×#887	2
C₂×C₅×#879	2
C₂×C₅×#878	2
C₂×C₅×#877	2
C₂×C₅×#870	2
C₂×C₄×C₅×Dic₆	2
C₂×C₅×#541	3
C₂×#5701	5

Subgroups — C2×C5×#5701 #14481190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5701 #14481190