Subgroups — C₃×C₅×#2720 #14275754

Order 1920.

944 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#399	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#396	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#395	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#395	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic
11	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic
12	C₃×C₅×#387	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic
14	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic
15	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2720	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
19	C₃×C₅×#125	—	2	4	no	—
20	C₃×C₅×C₂²⋊Q₈	—	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×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₄²×C₅	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×#2720	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
55	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
57	C₅×#400	C₂×C₃	1	1	yes	characteristic, complemented
58	C₅×#399	C₂×C₃	1	1	yes	characteristic
59	C₅×#398	C₂×C₃	1	1	yes	characteristic, complemented
60	C₅×#396	C₂×C₃	1	1	yes	characteristic
61	C₅×#395	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#395	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#388	C₂×C₃	1	1	yes	characteristic
65	C₅×#388	C₂×C₃	1	1	yes	characteristic
66	C₅×#387	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#385	C₂×C₃	1	1	yes	characteristic
68	C₅×#385	C₂×C₃	1	1	yes	characteristic
69	C₅×#384	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	—	4	1	no	—
73	C₂×C₃×C₅×Q₈	—	4	1	no	—
74	C₂²×C₃×C₄×C₅	—	2	2	no	—
75	C₂²×C₃×C₄×C₅	—	4	1	no	—
76	C₂²×C₃×C₄×C₅	—	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	—	2	2	no	—
99	C₃×C₅×C₄⋊C₄	—	4	1	no	—
100	C₃×C₅×C₄⋊C₄	—	4	1	no	—
101	C₃×C₅×C₄⋊C₄	—	4	1	no	—
102	C₃×C₅×C₄⋊C₄	—	4	1	no	—
103	C₃×C₅×C₄⋊C₄	—	4	1	no	—
104	C₃×C₅×C₄⋊C₄	—	4	1	no	—
105	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	—
106	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
107	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
108	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
109	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
110	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
111	C₃×C₅×C₂²⋊C₄	Q₈	1	4	yes	complemented
112	C₃×C₄²×C₅	—	2	2	no	—
113	C₃×C₄²×C₅	—	2	2	no	—
114	C₂×C₃×#125	C₂×C₅	1	1	yes	characteristic, complemented
115	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
116	C₃×#400	C₂×C₅	1	1	yes	characteristic, complemented
117	C₃×#399	C₂×C₅	1	1	yes	characteristic
118	C₃×#398	C₂×C₅	1	1	yes	characteristic, complemented
119	C₃×#396	C₂×C₅	1	1	yes	characteristic
120	C₃×#395	C₂×C₅	1	1	yes	characteristic, complemented
121	C₃×#395	C₂×C₅	1	1	yes	characteristic, complemented
122	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
123	C₃×#388	C₂×C₅	1	1	yes	characteristic
124	C₃×#388	C₂×C₅	1	1	yes	characteristic
125	C₃×#387	C₂×C₅	1	1	yes	characteristic, complemented
126	C₃×#385	C₂×C₅	1	1	yes	characteristic
127	C₃×#385	C₂×C₅	1	1	yes	characteristic
128	C₃×#384	C₂×C₅	1	1	yes	characteristic, complemented
129	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
130	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
131	C₅×#125	—	2	4	no	—
132	C₅×C₂²⋊Q₈	—	2	4	no	—
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×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
139	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
145	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
146	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
149	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
150	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
151	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
152	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
153	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₄²×C₅	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	C₅×#95	C₂²×C₃	1	1	yes	characteristic
163	C₅×#95	C₂²×C₃	1	1	yes	characteristic
164	C₅×#95	C₂²×C₃	1	1	yes	characteristic
165	C₅×#95	C₂²×C₃	1	1	yes	characteristic
166	#2720	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
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	—	2	1	no	—
171	C₂³×C₃×C₅	—	2	1	no	—
172	C₂³×C₃×C₅	—	2	1	no	—
173	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
174	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
175	C₃×C₅×Q₈	—	4	4	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	—	2	1	no	—
211	C₂×C₃×C₄×C₅	—	2	1	no	—
212	C₂×C₃×C₄×C₅	—	4	4	no	—
213	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
214	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
215	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
216	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
217	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
218	C₂×C₃×C₄×C₅	#41	1	2	yes	—
219	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
220	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
221	C₃×#125	—	2	4	no	—
222	C₃×C₂²⋊Q₈	—	2	4	no	—
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×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
229	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
230	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
231	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
233	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
234	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
235	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
236	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
238	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
240	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
241	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
242	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
243	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
245	C₂×C₃×C₄²	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	C₃×#95	C₂²×C₅	1	1	yes	characteristic
253	C₃×#95	C₂²×C₅	1	1	yes	characteristic
254	C₃×#95	C₂²×C₅	1	1	yes	characteristic
255	C₃×#95	C₂²×C₅	1	1	yes	characteristic
256	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
257	C₂×C₅×Q₈	—	2	2	no	—
258	C₂×C₅×Q₈	—	4	1	no	—
259	C₂×C₅×Q₈	—	4	1	no	—
260	C₂²×C₄×C₅	—	2	2	no	—
261	C₂²×C₄×C₅	—	4	1	no	—
262	C₂²×C₄×C₅	—	4	1	no	—
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	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
274	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
275	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
276	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
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	—	2	2	no	—
281	C₅×C₄⋊C₄	—	2	2	no	—
282	C₅×C₄⋊C₄	—	2	2	no	—
283	C₅×C₄⋊C₄	—	2	2	no	—
284	C₅×C₄⋊C₄	—	2	2	no	—
285	C₅×C₄⋊C₄	—	4	1	no	—
286	C₅×C₄⋊C₄	—	4	1	no	—
287	C₅×C₄⋊C₄	—	4	1	no	—
288	C₅×C₄⋊C₄	—	4	1	no	—
289	C₅×C₄⋊C₄	—	4	1	no	—
290	C₅×C₄⋊C₄	—	4	1	no	—
291	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	—
292	C₅×C₂²⋊C₄	—	2	2	no	—
293	C₅×C₂²⋊C₄	—	2	2	no	—
294	C₅×C₂²⋊C₄	—	2	2	no	—
295	C₅×C₂²⋊C₄	—	4	1	no	—
296	C₅×C₂²⋊C₄	—	4	1	no	—
297	C₅×C₂²⋊C₄	C₃×Q₈	1	4	yes	complemented
298	C₄²×C₅	—	2	2	no	—
299	C₄²×C₅	—	2	2	no	—
300	C₂×#125	C₂×C₃×C₅	1	1	yes	characteristic, complemented
301	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
302	#400	C₂×C₃×C₅	1	1	yes	characteristic, complemented
303	#399	C₂×C₃×C₅	1	1	yes	characteristic
304	#398	C₂×C₃×C₅	1	1	yes	characteristic, complemented
305	#396	C₂×C₃×C₅	1	1	yes	characteristic
306	#395	C₂×C₃×C₅	1	1	yes	characteristic, complemented
307	#395	C₂×C₃×C₅	1	1	yes	characteristic, complemented
308	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
309	#388	C₂×C₃×C₅	1	1	yes	characteristic
310	#388	C₂×C₃×C₅	1	1	yes	characteristic
311	#387	C₂×C₃×C₅	1	1	yes	characteristic, complemented
312	#385	C₂×C₃×C₅	1	1	yes	characteristic
313	#385	C₂×C₃×C₅	1	1	yes	characteristic
314	#384	C₂×C₃×C₅	1	1	yes	characteristic, complemented
315	C₂²×C₃×C₅	—	2	2	no	—
316	C₂²×C₃×C₅	—	2	2	no	—
317	C₂²×C₃×C₅	—	2	2	no	—
318	C₂²×C₃×C₅	—	4	1	no	—
319	C₂²×C₃×C₅	—	4	1	no	—
320	C₂²×C₃×C₅	—	4	1	no	—
321	C₂²×C₃×C₅	—	4	1	no	—
322	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
323	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
324	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
325	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
326	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
327	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
328	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
329	C₃×C₄×C₅	—	2	2	no	—
330	C₃×C₄×C₅	—	2	2	no	—
331	C₃×C₄×C₅	—	2	2	no	—
332	C₃×C₄×C₅	—	2	2	no	—
333	C₃×C₄×C₅	—	2	2	no	—
334	C₃×C₄×C₅	—	2	2	no	—
335	C₃×C₄×C₅	—	4	1	no	—
336	C₃×C₄×C₅	—	4	1	no	—
337	C₃×C₄×C₅	—	4	1	no	—
338	C₃×C₄×C₅	—	4	1	no	—
339	C₃×C₄×C₅	—	4	1	no	—
340	C₃×C₄×C₅	—	4	1	no	—
341	C₃×C₄×C₅	—	4	1	no	—
342	C₃×C₄×C₅	—	4	1	no	—
343	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
344	C₂×C₃×Q₈	—	2	2	no	—
345	C₂×C₃×Q₈	—	4	1	no	—
346	C₂×C₃×Q₈	—	4	1	no	—
347	C₂²×C₃×C₄	—	2	2	no	—
348	C₂²×C₃×C₄	—	4	1	no	—
349	C₂²×C₃×C₄	—	4	1	no	—
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	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
357	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
358	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
359	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
360	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
361	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
362	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
363	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
364	C₃×C₄⋊C₄	—	2	2	no	—
365	C₃×C₄⋊C₄	—	2	2	no	—
366	C₃×C₄⋊C₄	—	2	2	no	—
367	C₃×C₄⋊C₄	—	2	2	no	—
368	C₃×C₄⋊C₄	—	2	2	no	—
369	C₃×C₄⋊C₄	—	2	2	no	—
370	C₃×C₄⋊C₄	—	2	2	no	—
371	C₃×C₄⋊C₄	—	2	2	no	—
372	C₃×C₄⋊C₄	—	4	1	no	—
373	C₃×C₄⋊C₄	—	4	1	no	—
374	C₃×C₄⋊C₄	—	4	1	no	—
375	C₃×C₄⋊C₄	—	4	1	no	—
376	C₃×C₄⋊C₄	—	4	1	no	—
377	C₃×C₄⋊C₄	—	4	1	no	—
378	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	—
379	C₃×C₂²⋊C₄	—	2	2	no	—
380	C₃×C₂²⋊C₄	—	2	2	no	—
381	C₃×C₂²⋊C₄	—	2	2	no	—
382	C₃×C₂²⋊C₄	—	4	1	no	—
383	C₃×C₂²⋊C₄	—	4	1	no	—
384	C₃×C₂²⋊C₄	C₅×Q₈	1	4	yes	complemented
385	C₃×C₄²	—	2	2	no	—
386	C₃×C₄²	—	2	2	no	—
387	C₂³×C₅	—	2	1	no	—
388	C₂³×C₅	—	2	1	no	—
389	C₂³×C₅	—	2	1	no	—
390	C₂³×C₅	—	2	1	no	—
391	C₂³×C₅	—	2	1	no	—
392	C₂³×C₅	—	2	1	no	—
393	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
394	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
395	C₅×Q₈	—	4	4	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	—	2	1	no	—
423	C₂×C₄×C₅	—	2	1	no	—
424	C₂×C₄×C₅	—	2	1	no	—
425	C₂×C₄×C₅	—	2	1	no	—
426	C₂×C₄×C₅	—	2	1	no	—
427	C₂×C₄×C₅	—	2	1	no	—
428	C₂×C₄×C₅	—	2	1	no	—
429	C₂×C₄×C₅	—	2	1	no	—
430	C₂×C₄×C₅	—	2	1	no	—
431	C₂×C₄×C₅	—	2	1	no	—
432	C₂×C₄×C₅	—	4	4	no	—
433	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
434	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
435	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
436	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
437	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
438	C₂×C₄×C₅	C₃×#41	1	2	yes	—
439	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
440	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
441	#125	—	2	4	no	—
442	C₂²⋊Q₈	—	2	4	no	—
443	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
444	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
445	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
446	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
452	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
453	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
458	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
459	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
460	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
461	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
462	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
463	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
464	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
465	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
466	#95	C₂²×C₃×C₅	1	1	yes	characteristic
467	#95	C₂²×C₃×C₅	1	1	yes	characteristic
468	#95	C₂²×C₃×C₅	1	1	yes	characteristic
469	#95	C₂²×C₃×C₅	1	1	yes	characteristic
470	#95	C₂²×C₃×C₅	1	1	yes	characteristic
471	#95	C₂²×C₃×C₅	1	1	yes	characteristic
472	#95	C₂²×C₃×C₅	1	1	yes	characteristic
473	#95	C₂²×C₃×C₅	1	1	yes	characteristic
474	#95	C₂²×C₃×C₅	1	1	yes	characteristic
475	#95	C₂²×C₃×C₅	1	1	yes	characteristic
476	C₂×C₃×C₅	—	4	2	no	—
477	C₂×C₃×C₅	#535	1	1	yes	characteristic
478	C₂×C₃×C₅	#539	1	1	yes	characteristic
479	C₂×C₃×C₅	#544	1	1	yes	characteristic
480	C₂×C₃×C₅	#547	1	1	yes	characteristic
481	C₂×C₃×C₅	D₄×Q₈	1	1	yes	characteristic
482	C₂×C₃×C₅	#554	1	1	yes	characteristic
483	C₂×C₃×C₅	#563	1	1	yes	characteristic
484	C₂³×C₃	—	2	1	no	—
485	C₂³×C₃	—	2	1	no	—
486	C₂³×C₃	—	2	1	no	—
487	C₂³×C₃	—	2	1	no	—
488	C₂³×C₃	—	2	1	no	—
489	C₂³×C₃	—	2	1	no	—
490	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
491	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
492	C₃×Q₈	—	4	4	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	—	2	1	no	—
520	C₂×C₃×C₄	—	2	1	no	—
521	C₂×C₃×C₄	—	2	1	no	—
522	C₂×C₃×C₄	—	2	1	no	—
523	C₂×C₃×C₄	—	2	1	no	—
524	C₂×C₃×C₄	—	2	1	no	—
525	C₂×C₃×C₄	—	2	1	no	—
526	C₂×C₃×C₄	—	2	1	no	—
527	C₂×C₃×C₄	—	2	1	no	—
528	C₂×C₃×C₄	—	2	1	no	—
529	C₂×C₃×C₄	—	4	4	no	—
530	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
531	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
532	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
533	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
534	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
535	C₂×C₃×C₄	C₅×#41	1	2	yes	—
536	C₂²×C₅	—	2	2	no	—
537	C₂²×C₅	—	2	2	no	—
538	C₂²×C₅	—	2	2	no	—
539	C₂²×C₅	—	4	1	no	—
540	C₂²×C₅	—	4	1	no	—
541	C₂²×C₅	—	4	1	no	—
542	C₂²×C₅	—	4	1	no	—
543	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
544	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
545	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
546	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
547	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
548	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
549	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
550	C₄×C₅	—	2	2	no	—
551	C₄×C₅	—	2	2	no	—
552	C₄×C₅	—	2	2	no	—
553	C₄×C₅	—	2	2	no	—
554	C₄×C₅	—	2	2	no	—
555	C₄×C₅	—	2	2	no	—
556	C₄×C₅	—	4	1	no	—
557	C₄×C₅	—	4	1	no	—
558	C₄×C₅	—	4	1	no	—
559	C₄×C₅	—	4	1	no	—
560	C₄×C₅	—	4	1	no	—
561	C₄×C₅	—	4	1	no	—
562	C₄×C₅	—	4	1	no	—
563	C₄×C₅	—	4	1	no	—
564	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	—	4	1	no	—
567	C₂×Q₈	—	4	1	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	4	1	no	—
570	C₂²×C₄	—	4	1	no	—
571	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
572	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
573	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
574	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
575	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
576	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
577	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
578	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
579	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
580	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
581	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
582	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
583	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
584	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
585	C₄⋊C₄	—	2	2	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	—	2	2	no	—
589	C₄⋊C₄	—	2	2	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	4	1	no	—
594	C₄⋊C₄	—	4	1	no	—
595	C₄⋊C₄	—	4	1	no	—
596	C₄⋊C₄	—	4	1	no	—
597	C₄⋊C₄	—	4	1	no	—
598	C₄⋊C₄	—	4	1	no	—
599	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	—
600	C₂²⋊C₄	—	2	2	no	—
601	C₂²⋊C₄	—	2	2	no	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	4	1	no	—
604	C₂²⋊C₄	—	4	1	no	—
605	C₂²⋊C₄	C₃×C₅×Q₈	1	4	yes	complemented
606	C₄²	—	2	2	no	—
607	C₄²	—	2	2	no	—
608	C₃×C₅	#2720	1	1	yes	characteristic, direct product factor, Hall
609	C₂²×C₃	—	2	2	no	—
610	C₂²×C₃	—	2	2	no	—
611	C₂²×C₃	—	2	2	no	—
612	C₂²×C₃	—	4	1	no	—
613	C₂²×C₃	—	4	1	no	—
614	C₂²×C₃	—	4	1	no	—
615	C₂²×C₃	—	4	1	no	—
616	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
617	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
618	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
619	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
620	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
621	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
622	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
623	C₃×C₄	—	2	2	no	—
624	C₃×C₄	—	2	2	no	—
625	C₃×C₄	—	2	2	no	—
626	C₃×C₄	—	2	2	no	—
627	C₃×C₄	—	2	2	no	—
628	C₃×C₄	—	2	2	no	—
629	C₃×C₄	—	4	1	no	—
630	C₃×C₄	—	4	1	no	—
631	C₃×C₄	—	4	1	no	—
632	C₃×C₄	—	4	1	no	—
633	C₃×C₄	—	4	1	no	—
634	C₃×C₄	—	4	1	no	—
635	C₃×C₄	—	4	1	no	—
636	C₃×C₄	—	4	1	no	—
637	C₂×C₅	—	4	2	no	—
638	C₂×C₅	C₃×#535	1	1	yes	characteristic
639	C₂×C₅	C₃×#539	1	1	yes	characteristic
640	C₂×C₅	C₃×#544	1	1	yes	characteristic
641	C₂×C₅	C₃×#547	1	1	yes	characteristic
642	C₂×C₅	C₃×D₄×Q₈	1	1	yes	characteristic
643	C₂×C₅	C₃×#554	1	1	yes	characteristic
644	C₂×C₅	C₃×#563	1	1	yes	characteristic
645	C₂³	—	2	1	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	2	1	no	—
650	C₂³	—	2	1	no	—
651	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
652	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
653	Q₈	—	4	4	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	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	4	4	no	—
691	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
692	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
693	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
694	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
695	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
696	C₂×C₄	C₃×C₅×#41	1	2	yes	—
697	C₂×C₃	—	4	2	no	—
698	C₂×C₃	C₅×#535	1	1	yes	characteristic
699	C₂×C₃	C₅×#539	1	1	yes	characteristic
700	C₂×C₃	C₅×#544	1	1	yes	characteristic
701	C₂×C₃	C₅×#547	1	1	yes	characteristic
702	C₂×C₃	C₅×D₄×Q₈	1	1	yes	characteristic
703	C₂×C₃	C₅×#554	1	1	yes	characteristic
704	C₂×C₃	C₅×#563	1	1	yes	characteristic
705	C₅	C₃×#2720	1	1	yes	characteristic, direct product factor, Sylow
706	C₂²	—	2	2	no	—
707	C₂²	—	2	2	no	—
708	C₂²	—	2	2	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	4	1	no	—
711	C₂²	—	4	1	no	—
712	C₂²	—	4	1	no	—
713	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
714	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
715	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
716	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
717	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
718	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
719	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
720	C₄	—	2	2	no	—
721	C₄	—	2	2	no	—
722	C₄	—	2	2	no	—
723	C₄	—	2	2	no	—
724	C₄	—	2	2	no	—
725	C₄	—	2	2	no	—
726	C₄	—	4	1	no	—
727	C₄	—	4	1	no	—
728	C₄	—	4	1	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	1	no	—
731	C₄	—	4	1	no	—
732	C₄	—	4	1	no	—
733	C₄	—	4	1	no	—
734	C₃	C₅×#2720	1	1	yes	characteristic, direct product factor, Sylow
735	C₂	—	4	2	no	—
736	C₂	C₃×C₅×#535	1	1	yes	characteristic
737	C₂	C₃×C₅×#539	1	1	yes	characteristic
738	C₂	C₃×C₅×#544	1	1	yes	characteristic
739	C₂	C₃×C₅×#547	1	1	yes	characteristic
740	C₂	C₃×C₅×D₄×Q₈	1	1	yes	characteristic
741	C₂	C₃×C₅×#554	1	1	yes	characteristic
742	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×#125	C₂	semidirect
3. C₃×C₅×#400	C₂	semidirect
5. C₃×C₅×#398	C₂	semidirect
7. C₃×C₅×#395	C₂	semidirect
8. C₃×C₅×#395	C₂	semidirect
9. C₃×C₅×#389	C₂	semidirect
12. C₃×C₅×#387	C₂	semidirect
15. C₃×C₅×#384	C₂	semidirect
16. C₅×#2720	C₃	direct (N × H)
54. C₃×#2720	C₅	direct (N × H)
55. C₂×C₅×#125	C₂×C₃	semidirect
57. C₅×#400	C₂×C₃	semidirect
59. C₅×#398	C₂×C₃	semidirect
61. C₅×#395	C₂×C₃	semidirect
62. C₅×#395	C₂×C₃	semidirect
63. C₅×#389	C₂×C₃	semidirect
66. C₅×#387	C₂×C₃	semidirect
69. C₅×#384	C₂×C₃	semidirect
111. C₃×C₅×C₂²⋊C₄	Q₈	semidirect
114. C₂×C₃×#125	C₂×C₅	semidirect
116. C₃×#400	C₂×C₅	semidirect
118. C₃×#398	C₂×C₅	semidirect
120. C₃×#395	C₂×C₅	semidirect
121. C₃×#395	C₂×C₅	semidirect
122. C₃×#389	C₂×C₅	semidirect
125. C₃×#387	C₂×C₅	semidirect
128. C₃×#384	C₂×C₅	semidirect
166. #2720	C₃×C₅	direct (N × H)
297. C₅×C₂²⋊C₄	C₃×Q₈	semidirect
300. C₂×#125	C₂×C₃×C₅	semidirect
302. #400	C₂×C₃×C₅	semidirect
304. #398	C₂×C₃×C₅	semidirect
306. #395	C₂×C₃×C₅	semidirect
307. #395	C₂×C₃×C₅	semidirect
308. #389	C₂×C₃×C₅	semidirect
311. #387	C₂×C₃×C₅	semidirect
314. #384	C₂×C₃×C₅	semidirect
384. C₃×C₂²⋊C₄	C₅×Q₈	semidirect
605. C₂²⋊C₄	C₃×C₅×Q₈	semidirect
608. C₃×C₅	#2720	direct (N × H)
705. C₅	C₃×#2720	direct (N × H)
734. C₃	C₅×#2720	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×#125	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₃×C₅×#400	2
C₃×C₅×#399	2
C₃×C₅×#398	2
C₃×C₅×#396	2
C₃×C₅×#395	2
C₃×C₅×#389	2
C₃×C₅×#388	2
C₃×C₅×#387	2
C₃×C₅×#385	2
C₃×C₅×#384	2
C₅×#2720	3
C₃×#2720	5

Subgroups — C3×C5×#2720 #14275754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2720 #14275754