Subgroups — C₃×C₅×#2716 #14275750

Order 1920.

900 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#126	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#398	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#397	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#396	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#393	C₂	1	1	yes	maximal, characteristic
8	C₃×C₅×#393	C₂	1	1	yes	maximal, characteristic
9	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic
12	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic
13	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2716	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊Q₈	—	2	4	no	—
20	C₃×C₅×#126	—	2	4	no	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
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
35	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
40	C₃×C₅×#95	C₂²	1	1	yes	characteristic
41	C₃×C₅×#95	C₂²	1	1	yes	characteristic
42	C₃×C₅×#95	C₂²	1	1	yes	characteristic
43	C₃×C₅×#95	C₂²	1	1	yes	characteristic
44	C₃×C₅×#95	C₂²	1	1	yes	characteristic
45	C₃×C₅×#95	C₂²	1	1	yes	characteristic
46	C₃×C₅×#95	C₂²	1	1	yes	characteristic
47	C₃×C₅×#95	C₂²	1	1	yes	characteristic
48	C₃×C₅×#95	C₂²	1	1	yes	characteristic
49	C₃×C₅×#95	C₂²	1	1	yes	characteristic
50	C₃×C₅×#95	C₂²	1	1	yes	characteristic
51	C₃×C₅×#95	C₂²	1	1	yes	characteristic
52	C₃×C₅×#95	C₂²	1	1	yes	characteristic
53	C₃×C₅×#95	C₂²	1	1	yes	characteristic
54	C₃×#2716	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
55	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×C₅×#126	C₂×C₃	1	1	yes	characteristic
57	C₅×#400	C₂×C₃	1	1	yes	characteristic, complemented
58	C₅×#398	C₂×C₃	1	1	yes	characteristic, complemented
59	C₅×#397	C₂×C₃	1	1	yes	characteristic
60	C₅×#396	C₂×C₃	1	1	yes	characteristic
61	C₅×#393	C₂×C₃	1	1	yes	characteristic
62	C₅×#393	C₂×C₃	1	1	yes	characteristic
63	C₅×#391	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#391	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#388	C₂×C₃	1	1	yes	characteristic
66	C₅×#388	C₂×C₃	1	1	yes	characteristic
67	C₅×#387	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#387	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#387	C₂×C₃	1	1	yes	characteristic, complemented
70	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₅×Q₈	—	2	2	no	—
72	C₂×C₃×C₅×Q₈	—	2	2	no	—
73	C₂×C₃×C₅×Q₈	—	2	2	no	—
74	C₂×C₃×C₅×Q₈	—	2	2	no	—
75	C₂×C₃×C₅×Q₈	—	4	1	no	—
76	C₂×C₃×C₅×Q₈	—	4	1	no	—
77	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
78	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
81	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
82	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
83	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
85	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
86	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
87	C₂²×C₃×C₄×C₅	C₂³	1	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	C₃×C₅×C₄⋊C₄	—	2	2	no	—
92	C₃×C₅×C₄⋊C₄	—	2	2	no	—
93	C₃×C₅×C₄⋊C₄	—	2	2	no	—
94	C₃×C₅×C₄⋊C₄	—	2	2	no	—
95	C₃×C₅×C₄⋊C₄	—	2	2	no	—
96	C₃×C₅×C₄⋊C₄	—	2	2	no	—
97	C₃×C₅×C₄⋊C₄	—	2	2	no	—
98	C₃×C₅×C₄⋊C₄	—	4	1	no	—
99	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	—
100	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
101	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
102	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
103	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
104	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
105	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
106	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
107	C₃×C₄²×C₅	—	2	2	no	—
108	C₃×C₄²×C₅	—	2	2	no	—
109	C₃×C₄²×C₅	—	4	1	no	—
110	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂×C₃×#126	C₂×C₅	1	1	yes	characteristic
112	C₃×#400	C₂×C₅	1	1	yes	characteristic, complemented
113	C₃×#398	C₂×C₅	1	1	yes	characteristic, complemented
114	C₃×#397	C₂×C₅	1	1	yes	characteristic
115	C₃×#396	C₂×C₅	1	1	yes	characteristic
116	C₃×#393	C₂×C₅	1	1	yes	characteristic
117	C₃×#393	C₂×C₅	1	1	yes	characteristic
118	C₃×#391	C₂×C₅	1	1	yes	characteristic, complemented
119	C₃×#391	C₂×C₅	1	1	yes	characteristic, complemented
120	C₃×#388	C₂×C₅	1	1	yes	characteristic
121	C₃×#388	C₂×C₅	1	1	yes	characteristic
122	C₃×#387	C₂×C₅	1	1	yes	characteristic, complemented
123	C₃×#387	C₂×C₅	1	1	yes	characteristic, complemented
124	C₃×#387	C₂×C₅	1	1	yes	characteristic, complemented
125	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
126	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
127	C₅×C₄⋊Q₈	—	2	4	no	—
128	C₅×#126	—	2	4	no	—
129	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
130	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
131	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
133	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
136	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
137	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
139	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
145	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
146	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
148	C₅×#95	C₂²×C₃	1	1	yes	characteristic
149	C₅×#95	C₂²×C₃	1	1	yes	characteristic
150	C₅×#95	C₂²×C₃	1	1	yes	characteristic
151	C₅×#95	C₂²×C₃	1	1	yes	characteristic
152	C₅×#95	C₂²×C₃	1	1	yes	characteristic
153	C₅×#95	C₂²×C₃	1	1	yes	characteristic
154	C₅×#95	C₂²×C₃	1	1	yes	characteristic
155	C₅×#95	C₂²×C₃	1	1	yes	characteristic
156	C₅×#95	C₂²×C₃	1	1	yes	characteristic
157	C₅×#95	C₂²×C₃	1	1	yes	characteristic
158	C₅×#95	C₂²×C₃	1	1	yes	characteristic
159	C₅×#95	C₂²×C₃	1	1	yes	characteristic
160	C₅×#95	C₂²×C₃	1	1	yes	characteristic
161	C₅×#95	C₂²×C₃	1	1	yes	characteristic
162	#2716	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
163	C₂³×C₃×C₅	—	2	1	no	—
164	C₂³×C₃×C₅	—	2	1	no	—
165	C₂³×C₃×C₅	—	2	1	no	—
166	C₂³×C₃×C₅	—	2	1	no	—
167	C₂³×C₃×C₅	—	2	1	no	—
168	C₂³×C₃×C₅	—	2	1	no	—
169	C₂³×C₃×C₅	—	2	1	no	—
170	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
171	C₃×C₅×Q₈	—	4	4	no	—
172	C₃×C₅×Q₈	—	4	4	no	—
173	C₂×C₃×C₄×C₅	—	2	1	no	—
174	C₂×C₃×C₄×C₅	—	2	1	no	—
175	C₂×C₃×C₄×C₅	—	2	1	no	—
176	C₂×C₃×C₄×C₅	—	2	1	no	—
177	C₂×C₃×C₄×C₅	—	2	1	no	—
178	C₂×C₃×C₄×C₅	—	2	1	no	—
179	C₂×C₃×C₄×C₅	—	2	1	no	—
180	C₂×C₃×C₄×C₅	—	2	1	no	—
181	C₂×C₃×C₄×C₅	—	2	1	no	—
182	C₂×C₃×C₄×C₅	—	2	1	no	—
183	C₂×C₃×C₄×C₅	—	2	1	no	—
184	C₂×C₃×C₄×C₅	—	2	1	no	—
185	C₂×C₃×C₄×C₅	—	2	1	no	—
186	C₂×C₃×C₄×C₅	—	2	1	no	—
187	C₂×C₃×C₄×C₅	—	2	1	no	—
188	C₂×C₃×C₄×C₅	—	2	1	no	—
189	C₂×C₃×C₄×C₅	—	2	1	no	—
190	C₂×C₃×C₄×C₅	—	2	1	no	—
191	C₂×C₃×C₄×C₅	—	2	1	no	—
192	C₂×C₃×C₄×C₅	—	2	1	no	—
193	C₂×C₃×C₄×C₅	—	2	1	no	—
194	C₂×C₃×C₄×C₅	—	2	1	no	—
195	C₂×C₃×C₄×C₅	—	2	1	no	—
196	C₂×C₃×C₄×C₅	—	2	1	no	—
197	C₂×C₃×C₄×C₅	—	2	1	no	—
198	C₂×C₃×C₄×C₅	—	2	1	no	—
199	C₂×C₃×C₄×C₅	—	2	1	no	—
200	C₂×C₃×C₄×C₅	—	2	1	no	—
201	C₂×C₃×C₄×C₅	—	2	1	no	—
202	C₂×C₃×C₄×C₅	—	2	1	no	—
203	C₂×C₃×C₄×C₅	—	2	1	no	—
204	C₂×C₃×C₄×C₅	—	2	1	no	—
205	C₂×C₃×C₄×C₅	—	2	1	no	—
206	C₂×C₃×C₄×C₅	—	2	1	no	—
207	C₂×C₃×C₄×C₅	—	2	1	no	—
208	C₂×C₃×C₄×C₅	—	2	1	no	—
209	C₂×C₃×C₄×C₅	—	2	1	no	—
210	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
211	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
212	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
213	C₂×C₃×C₄×C₅	#41	1	2	yes	—
214	C₂×C₃×C₄×C₅	#41	1	2	yes	—
215	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
216	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
217	C₃×C₄⋊Q₈	—	2	4	no	—
218	C₃×#126	—	2	4	no	—
219	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
220	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
221	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
222	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
223	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
224	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
225	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
227	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
228	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
229	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
231	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
233	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
236	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
238	C₃×#95	C₂²×C₅	1	1	yes	characteristic
239	C₃×#95	C₂²×C₅	1	1	yes	characteristic
240	C₃×#95	C₂²×C₅	1	1	yes	characteristic
241	C₃×#95	C₂²×C₅	1	1	yes	characteristic
242	C₃×#95	C₂²×C₅	1	1	yes	characteristic
243	C₃×#95	C₂²×C₅	1	1	yes	characteristic
244	C₃×#95	C₂²×C₅	1	1	yes	characteristic
245	C₃×#95	C₂²×C₅	1	1	yes	characteristic
246	C₃×#95	C₂²×C₅	1	1	yes	characteristic
247	C₃×#95	C₂²×C₅	1	1	yes	characteristic
248	C₃×#95	C₂²×C₅	1	1	yes	characteristic
249	C₃×#95	C₂²×C₅	1	1	yes	characteristic
250	C₃×#95	C₂²×C₅	1	1	yes	characteristic
251	C₃×#95	C₂²×C₅	1	1	yes	characteristic
252	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
253	C₂×C₅×Q₈	—	2	2	no	—
254	C₂×C₅×Q₈	—	2	2	no	—
255	C₂×C₅×Q₈	—	2	2	no	—
256	C₂×C₅×Q₈	—	2	2	no	—
257	C₂×C₅×Q₈	—	4	1	no	—
258	C₂×C₅×Q₈	—	4	1	no	—
259	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
260	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
261	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
262	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
263	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
264	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
265	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
266	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
267	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
268	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
269	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
270	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
271	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
272	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
273	C₅×C₄⋊C₄	—	2	2	no	—
274	C₅×C₄⋊C₄	—	2	2	no	—
275	C₅×C₄⋊C₄	—	2	2	no	—
276	C₅×C₄⋊C₄	—	2	2	no	—
277	C₅×C₄⋊C₄	—	2	2	no	—
278	C₅×C₄⋊C₄	—	2	2	no	—
279	C₅×C₄⋊C₄	—	2	2	no	—
280	C₅×C₄⋊C₄	—	4	1	no	—
281	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	—
282	C₅×C₂²⋊C₄	—	2	2	no	—
283	C₅×C₂²⋊C₄	—	2	2	no	—
284	C₅×C₂²⋊C₄	—	2	2	no	—
285	C₅×C₂²⋊C₄	—	2	2	no	—
286	C₅×C₂²⋊C₄	—	2	2	no	—
287	C₅×C₂²⋊C₄	—	4	1	no	—
288	C₅×C₂²⋊C₄	—	4	1	no	—
289	C₄²×C₅	—	2	2	no	—
290	C₄²×C₅	—	2	2	no	—
291	C₄²×C₅	—	4	1	no	—
292	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
293	C₂×#126	C₂×C₃×C₅	1	1	yes	characteristic
294	#400	C₂×C₃×C₅	1	1	yes	characteristic, complemented
295	#398	C₂×C₃×C₅	1	1	yes	characteristic, complemented
296	#397	C₂×C₃×C₅	1	1	yes	characteristic
297	#396	C₂×C₃×C₅	1	1	yes	characteristic
298	#393	C₂×C₃×C₅	1	1	yes	characteristic
299	#393	C₂×C₃×C₅	1	1	yes	characteristic
300	#391	C₂×C₃×C₅	1	1	yes	characteristic, complemented
301	#391	C₂×C₃×C₅	1	1	yes	characteristic, complemented
302	#388	C₂×C₃×C₅	1	1	yes	characteristic
303	#388	C₂×C₃×C₅	1	1	yes	characteristic
304	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
305	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
306	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
307	C₂²×C₃×C₅	—	4	1	no	—
308	C₂²×C₃×C₅	—	4	1	no	—
309	C₂²×C₃×C₅	—	4	1	no	—
310	C₂²×C₃×C₅	—	4	1	no	—
311	C₂²×C₃×C₅	—	4	1	no	—
312	C₂²×C₃×C₅	—	4	1	no	—
313	C₂²×C₃×C₅	—	4	1	no	—
314	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
315	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
316	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
317	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
318	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
319	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
320	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
321	C₃×C₄×C₅	—	2	2	no	—
322	C₃×C₄×C₅	—	2	2	no	—
323	C₃×C₄×C₅	—	2	2	no	—
324	C₃×C₄×C₅	—	2	2	no	—
325	C₃×C₄×C₅	—	2	2	no	—
326	C₃×C₄×C₅	—	4	1	no	—
327	C₃×C₄×C₅	—	4	1	no	—
328	C₃×C₄×C₅	—	4	1	no	—
329	C₃×C₄×C₅	—	4	1	no	—
330	C₃×C₄×C₅	—	4	1	no	—
331	C₃×C₄×C₅	—	4	1	no	—
332	C₃×C₄×C₅	—	4	1	no	—
333	C₃×C₄×C₅	—	4	1	no	—
334	C₃×C₄×C₅	—	4	1	no	—
335	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
336	C₂×C₃×Q₈	—	2	2	no	—
337	C₂×C₃×Q₈	—	2	2	no	—
338	C₂×C₃×Q₈	—	2	2	no	—
339	C₂×C₃×Q₈	—	2	2	no	—
340	C₂×C₃×Q₈	—	4	1	no	—
341	C₂×C₃×Q₈	—	4	1	no	—
342	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
343	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
344	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
345	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
346	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
347	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
348	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
349	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
350	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
351	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
352	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
353	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
354	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
355	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
356	C₃×C₄⋊C₄	—	2	2	no	—
357	C₃×C₄⋊C₄	—	2	2	no	—
358	C₃×C₄⋊C₄	—	2	2	no	—
359	C₃×C₄⋊C₄	—	2	2	no	—
360	C₃×C₄⋊C₄	—	2	2	no	—
361	C₃×C₄⋊C₄	—	2	2	no	—
362	C₃×C₄⋊C₄	—	2	2	no	—
363	C₃×C₄⋊C₄	—	4	1	no	—
364	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	—
365	C₃×C₂²⋊C₄	—	2	2	no	—
366	C₃×C₂²⋊C₄	—	2	2	no	—
367	C₃×C₂²⋊C₄	—	2	2	no	—
368	C₃×C₂²⋊C₄	—	2	2	no	—
369	C₃×C₂²⋊C₄	—	2	2	no	—
370	C₃×C₂²⋊C₄	—	4	1	no	—
371	C₃×C₂²⋊C₄	—	4	1	no	—
372	C₃×C₄²	—	2	2	no	—
373	C₃×C₄²	—	2	2	no	—
374	C₃×C₄²	—	4	1	no	—
375	C₂³×C₅	—	2	1	no	—
376	C₂³×C₅	—	2	1	no	—
377	C₂³×C₅	—	2	1	no	—
378	C₂³×C₅	—	2	1	no	—
379	C₂³×C₅	—	2	1	no	—
380	C₂³×C₅	—	2	1	no	—
381	C₂³×C₅	—	2	1	no	—
382	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
383	C₅×Q₈	—	4	4	no	—
384	C₅×Q₈	—	4	4	no	—
385	C₂×C₄×C₅	—	2	1	no	—
386	C₂×C₄×C₅	—	2	1	no	—
387	C₂×C₄×C₅	—	2	1	no	—
388	C₂×C₄×C₅	—	2	1	no	—
389	C₂×C₄×C₅	—	2	1	no	—
390	C₂×C₄×C₅	—	2	1	no	—
391	C₂×C₄×C₅	—	2	1	no	—
392	C₂×C₄×C₅	—	2	1	no	—
393	C₂×C₄×C₅	—	2	1	no	—
394	C₂×C₄×C₅	—	2	1	no	—
395	C₂×C₄×C₅	—	2	1	no	—
396	C₂×C₄×C₅	—	2	1	no	—
397	C₂×C₄×C₅	—	2	1	no	—
398	C₂×C₄×C₅	—	2	1	no	—
399	C₂×C₄×C₅	—	2	1	no	—
400	C₂×C₄×C₅	—	2	1	no	—
401	C₂×C₄×C₅	—	2	1	no	—
402	C₂×C₄×C₅	—	2	1	no	—
403	C₂×C₄×C₅	—	2	1	no	—
404	C₂×C₄×C₅	—	2	1	no	—
405	C₂×C₄×C₅	—	2	1	no	—
406	C₂×C₄×C₅	—	2	1	no	—
407	C₂×C₄×C₅	—	2	1	no	—
408	C₂×C₄×C₅	—	2	1	no	—
409	C₂×C₄×C₅	—	2	1	no	—
410	C₂×C₄×C₅	—	2	1	no	—
411	C₂×C₄×C₅	—	2	1	no	—
412	C₂×C₄×C₅	—	2	1	no	—
413	C₂×C₄×C₅	—	2	1	no	—
414	C₂×C₄×C₅	—	2	1	no	—
415	C₂×C₄×C₅	—	2	1	no	—
416	C₂×C₄×C₅	—	2	1	no	—
417	C₂×C₄×C₅	—	2	1	no	—
418	C₂×C₄×C₅	—	2	1	no	—
419	C₂×C₄×C₅	—	2	1	no	—
420	C₂×C₄×C₅	—	2	1	no	—
421	C₂×C₄×C₅	—	2	1	no	—
422	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
423	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
424	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
425	C₂×C₄×C₅	C₃×#41	1	2	yes	—
426	C₂×C₄×C₅	C₃×#41	1	2	yes	—
427	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
428	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
429	C₄⋊Q₈	—	2	4	no	—
430	#126	—	2	4	no	—
431	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
440	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
441	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
442	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
443	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
444	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
445	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
446	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
447	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
448	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
449	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
450	#95	C₂²×C₃×C₅	1	1	yes	characteristic
451	#95	C₂²×C₃×C₅	1	1	yes	characteristic
452	#95	C₂²×C₃×C₅	1	1	yes	characteristic
453	#95	C₂²×C₃×C₅	1	1	yes	characteristic
454	#95	C₂²×C₃×C₅	1	1	yes	characteristic
455	#95	C₂²×C₃×C₅	1	1	yes	characteristic
456	#95	C₂²×C₃×C₅	1	1	yes	characteristic
457	#95	C₂²×C₃×C₅	1	1	yes	characteristic
458	#95	C₂²×C₃×C₅	1	1	yes	characteristic
459	#95	C₂²×C₃×C₅	1	1	yes	characteristic
460	#95	C₂²×C₃×C₅	1	1	yes	characteristic
461	#95	C₂²×C₃×C₅	1	1	yes	characteristic
462	#95	C₂²×C₃×C₅	1	1	yes	characteristic
463	#95	C₂²×C₃×C₅	1	1	yes	characteristic
464	C₂×C₃×C₅	—	8	1	no	—
465	C₂×C₃×C₅	#536	1	1	yes	characteristic
466	C₂×C₃×C₅	#541	1	1	yes	characteristic
467	C₂×C₃×C₅	#542	1	1	yes	characteristic
468	C₂×C₃×C₅	#546	1	1	yes	characteristic
469	C₂×C₃×C₅	#548	1	1	yes	characteristic
470	C₂×C₃×C₅	#556	1	1	yes	characteristic
471	C₂×C₃×C₅	#563	1	1	yes	characteristic
472	C₂³×C₃	—	2	1	no	—
473	C₂³×C₃	—	2	1	no	—
474	C₂³×C₃	—	2	1	no	—
475	C₂³×C₃	—	2	1	no	—
476	C₂³×C₃	—	2	1	no	—
477	C₂³×C₃	—	2	1	no	—
478	C₂³×C₃	—	2	1	no	—
479	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
480	C₃×Q₈	—	4	4	no	—
481	C₃×Q₈	—	4	4	no	—
482	C₂×C₃×C₄	—	2	1	no	—
483	C₂×C₃×C₄	—	2	1	no	—
484	C₂×C₃×C₄	—	2	1	no	—
485	C₂×C₃×C₄	—	2	1	no	—
486	C₂×C₃×C₄	—	2	1	no	—
487	C₂×C₃×C₄	—	2	1	no	—
488	C₂×C₃×C₄	—	2	1	no	—
489	C₂×C₃×C₄	—	2	1	no	—
490	C₂×C₃×C₄	—	2	1	no	—
491	C₂×C₃×C₄	—	2	1	no	—
492	C₂×C₃×C₄	—	2	1	no	—
493	C₂×C₃×C₄	—	2	1	no	—
494	C₂×C₃×C₄	—	2	1	no	—
495	C₂×C₃×C₄	—	2	1	no	—
496	C₂×C₃×C₄	—	2	1	no	—
497	C₂×C₃×C₄	—	2	1	no	—
498	C₂×C₃×C₄	—	2	1	no	—
499	C₂×C₃×C₄	—	2	1	no	—
500	C₂×C₃×C₄	—	2	1	no	—
501	C₂×C₃×C₄	—	2	1	no	—
502	C₂×C₃×C₄	—	2	1	no	—
503	C₂×C₃×C₄	—	2	1	no	—
504	C₂×C₃×C₄	—	2	1	no	—
505	C₂×C₃×C₄	—	2	1	no	—
506	C₂×C₃×C₄	—	2	1	no	—
507	C₂×C₃×C₄	—	2	1	no	—
508	C₂×C₃×C₄	—	2	1	no	—
509	C₂×C₃×C₄	—	2	1	no	—
510	C₂×C₃×C₄	—	2	1	no	—
511	C₂×C₃×C₄	—	2	1	no	—
512	C₂×C₃×C₄	—	2	1	no	—
513	C₂×C₃×C₄	—	2	1	no	—
514	C₂×C₃×C₄	—	2	1	no	—
515	C₂×C₃×C₄	—	2	1	no	—
516	C₂×C₃×C₄	—	2	1	no	—
517	C₂×C₃×C₄	—	2	1	no	—
518	C₂×C₃×C₄	—	2	1	no	—
519	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
520	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
521	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
522	C₂×C₃×C₄	C₅×#41	1	2	yes	—
523	C₂×C₃×C₄	C₅×#41	1	2	yes	—
524	C₂²×C₅	—	4	1	no	—
525	C₂²×C₅	—	4	1	no	—
526	C₂²×C₅	—	4	1	no	—
527	C₂²×C₅	—	4	1	no	—
528	C₂²×C₅	—	4	1	no	—
529	C₂²×C₅	—	4	1	no	—
530	C₂²×C₅	—	4	1	no	—
531	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
532	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
533	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
534	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
535	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
536	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
537	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
538	C₄×C₅	—	2	2	no	—
539	C₄×C₅	—	2	2	no	—
540	C₄×C₅	—	2	2	no	—
541	C₄×C₅	—	2	2	no	—
542	C₄×C₅	—	2	2	no	—
543	C₄×C₅	—	4	1	no	—
544	C₄×C₅	—	4	1	no	—
545	C₄×C₅	—	4	1	no	—
546	C₄×C₅	—	4	1	no	—
547	C₄×C₅	—	4	1	no	—
548	C₄×C₅	—	4	1	no	—
549	C₄×C₅	—	4	1	no	—
550	C₄×C₅	—	4	1	no	—
551	C₄×C₅	—	4	1	no	—
552	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
553	C₂×Q₈	—	2	2	no	—
554	C₂×Q₈	—	2	2	no	—
555	C₂×Q₈	—	2	2	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	4	1	no	—
558	C₂×Q₈	—	4	1	no	—
559	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
560	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
561	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
562	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
563	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
564	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
565	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
566	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
567	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
568	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
569	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
570	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
571	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
572	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
573	C₄⋊C₄	—	2	2	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	4	1	no	—
581	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	—
582	C₂²⋊C₄	—	2	2	no	—
583	C₂²⋊C₄	—	2	2	no	—
584	C₂²⋊C₄	—	2	2	no	—
585	C₂²⋊C₄	—	2	2	no	—
586	C₂²⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	4	1	no	—
588	C₂²⋊C₄	—	4	1	no	—
589	C₄²	—	2	2	no	—
590	C₄²	—	2	2	no	—
591	C₄²	—	4	1	no	—
592	C₃×C₅	#2716	1	1	yes	characteristic, direct product factor, Hall
593	C₂²×C₃	—	4	1	no	—
594	C₂²×C₃	—	4	1	no	—
595	C₂²×C₃	—	4	1	no	—
596	C₂²×C₃	—	4	1	no	—
597	C₂²×C₃	—	4	1	no	—
598	C₂²×C₃	—	4	1	no	—
599	C₂²×C₃	—	4	1	no	—
600	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
601	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
602	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
603	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
604	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
605	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
606	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
607	C₃×C₄	—	2	2	no	—
608	C₃×C₄	—	2	2	no	—
609	C₃×C₄	—	2	2	no	—
610	C₃×C₄	—	2	2	no	—
611	C₃×C₄	—	2	2	no	—
612	C₃×C₄	—	4	1	no	—
613	C₃×C₄	—	4	1	no	—
614	C₃×C₄	—	4	1	no	—
615	C₃×C₄	—	4	1	no	—
616	C₃×C₄	—	4	1	no	—
617	C₃×C₄	—	4	1	no	—
618	C₃×C₄	—	4	1	no	—
619	C₃×C₄	—	4	1	no	—
620	C₃×C₄	—	4	1	no	—
621	C₂×C₅	—	8	1	no	—
622	C₂×C₅	C₃×#536	1	1	yes	characteristic
623	C₂×C₅	C₃×#541	1	1	yes	characteristic
624	C₂×C₅	C₃×#542	1	1	yes	characteristic
625	C₂×C₅	C₃×#546	1	1	yes	characteristic
626	C₂×C₅	C₃×#548	1	1	yes	characteristic
627	C₂×C₅	C₃×#556	1	1	yes	characteristic
628	C₂×C₅	C₃×#563	1	1	yes	characteristic
629	C₂³	—	2	1	no	—
630	C₂³	—	2	1	no	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
637	Q₈	—	4	4	no	—
638	Q₈	—	4	4	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
677	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
678	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
679	C₂×C₄	C₃×C₅×#41	1	2	yes	—
680	C₂×C₄	C₃×C₅×#41	1	2	yes	—
681	C₂×C₃	—	8	1	no	—
682	C₂×C₃	C₅×#536	1	1	yes	characteristic
683	C₂×C₃	C₅×#541	1	1	yes	characteristic
684	C₂×C₃	C₅×#542	1	1	yes	characteristic
685	C₂×C₃	C₅×#546	1	1	yes	characteristic
686	C₂×C₃	C₅×#548	1	1	yes	characteristic
687	C₂×C₃	C₅×#556	1	1	yes	characteristic
688	C₂×C₃	C₅×#563	1	1	yes	characteristic
689	C₅	C₃×#2716	1	1	yes	characteristic, direct product factor, Sylow
690	C₂²	—	4	1	no	—
691	C₂²	—	4	1	no	—
692	C₂²	—	4	1	no	—
693	C₂²	—	4	1	no	—
694	C₂²	—	4	1	no	—
695	C₂²	—	4	1	no	—
696	C₂²	—	4	1	no	—
697	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
698	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
699	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
700	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
701	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
702	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
703	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	2	2	no	—
707	C₄	—	2	2	no	—
708	C₄	—	2	2	no	—
709	C₄	—	4	1	no	—
710	C₄	—	4	1	no	—
711	C₄	—	4	1	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	1	no	—
714	C₄	—	4	1	no	—
715	C₄	—	4	1	no	—
716	C₄	—	4	1	no	—
717	C₄	—	4	1	no	—
718	C₃	C₅×#2716	1	1	yes	characteristic, direct product factor, Sylow
719	C₂	—	8	1	no	—
720	C₂	C₃×C₅×#536	1	1	yes	characteristic
721	C₂	C₃×C₅×#541	1	1	yes	characteristic
722	C₂	C₃×C₅×#542	1	1	yes	characteristic
723	C₂	C₃×C₅×#546	1	1	yes	characteristic
724	C₂	C₃×C₅×#548	1	1	yes	characteristic
725	C₂	C₃×C₅×#556	1	1	yes	characteristic
726	C₂	C₃×C₅×#563	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
3. C₃×C₅×#400	C₂	semidirect
4. C₃×C₅×#398	C₂	semidirect
9. C₃×C₅×#391	C₂	semidirect
10. C₃×C₅×#391	C₂	semidirect
13. C₃×C₅×#387	C₂	semidirect
14. C₃×C₅×#387	C₂	semidirect
15. C₃×C₅×#387	C₂	semidirect
16. C₅×#2716	C₃	direct (N × H)
54. C₃×#2716	C₅	direct (N × H)
55. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
57. C₅×#400	C₂×C₃	semidirect
58. C₅×#398	C₂×C₃	semidirect
63. C₅×#391	C₂×C₃	semidirect
64. C₅×#391	C₂×C₃	semidirect
67. C₅×#387	C₂×C₃	semidirect
68. C₅×#387	C₂×C₃	semidirect
69. C₅×#387	C₂×C₃	semidirect
110. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
112. C₃×#400	C₂×C₅	semidirect
113. C₃×#398	C₂×C₅	semidirect
118. C₃×#391	C₂×C₅	semidirect
119. C₃×#391	C₂×C₅	semidirect
122. C₃×#387	C₂×C₅	semidirect
123. C₃×#387	C₂×C₅	semidirect
124. C₃×#387	C₂×C₅	semidirect
162. #2716	C₃×C₅	direct (N × H)
292. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
294. #400	C₂×C₃×C₅	semidirect
295. #398	C₂×C₃×C₅	semidirect
300. #391	C₂×C₃×C₅	semidirect
301. #391	C₂×C₃×C₅	semidirect
304. #387	C₂×C₃×C₅	semidirect
305. #387	C₂×C₃×C₅	semidirect
306. #387	C₂×C₃×C₅	semidirect
592. C₃×C₅	#2716	direct (N × H)
689. C₅	C₃×#2716	direct (N × H)
718. C₃	C₅×#2716	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×C₄⋊Q₈	2
C₂×C₃×C₅×#126	2
C₃×C₅×#400	2
C₃×C₅×#398	2
C₃×C₅×#397	2
C₃×C₅×#396	2
C₃×C₅×#393	2
C₃×C₅×#391	2
C₃×C₅×#388	2
C₃×C₅×#387	2
C₅×#2716	3
C₃×#2716	5

Subgroups — C3×C5×#2716 #14275750

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2716 #14275750