Subgroups — C₃×C₅×#2678 #14275712

Order 1920.

1604 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#396	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#392	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#392	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#388	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#386	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#379	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#2678	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
24	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
25	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₅×#123	—	2	4	no	—
27	C₃×C₅×#121	—	2	4	no	—
28	C₃×C₅×#120	—	2	4	no	—
29	C₃×C₅×#120	—	2	4	no	—
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
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×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×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
43	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
44	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
45	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
46	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
55	C₃×C₅×#95	C₂²	1	1	yes	characteristic, complemented
56	C₃×#2678	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
57	C₂×C₅×#123	C₂×C₃	1	1	yes	characteristic, complemented
58	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×C₅×#120	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂×C₅×#120	C₂×C₃	1	1	yes	characteristic, complemented
61	C₅×#397	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#396	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#394	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#394	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#392	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#392	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#390	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#390	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#388	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#386	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#379	C₂×C₃	1	1	yes	characteristic, complemented
72	C₂⁴×C₃×C₅	—	2	2	no	—
73	C₂⁴×C₃×C₅	—	2	2	no	—
74	C₂⁴×C₃×C₅	—	2	2	no	—
75	C₂⁴×C₃×C₅	—	4	1	no	—
76	C₂⁴×C₃×C₅	—	4	1	no	—
77	C₂⁴×C₃×C₅	—	4	1	no	—
78	C₂⁴×C₃×C₅	—	4	1	no	—
79	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
80	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
81	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
82	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
83	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×D₄	—	2	2	no	—
85	C₂×C₃×C₅×D₄	—	2	2	no	—
86	C₂×C₃×C₅×D₄	—	2	2	no	—
87	C₂×C₃×C₅×D₄	—	2	2	no	—
88	C₂×C₃×C₅×D₄	—	2	2	no	—
89	C₂×C₃×C₅×D₄	—	2	2	no	—
90	C₂×C₃×C₅×D₄	—	2	2	no	—
91	C₂×C₃×C₅×D₄	—	2	2	no	—
92	C₂×C₃×C₅×D₄	—	2	2	no	—
93	C₂×C₃×C₅×D₄	—	2	2	no	—
94	C₂×C₃×C₅×D₄	—	4	1	no	—
95	C₂×C₃×C₅×D₄	—	4	1	no	—
96	C₂×C₃×C₅×D₄	—	4	1	no	—
97	C₂×C₃×C₅×D₄	—	4	1	no	—
98	C₂×C₃×C₅×D₄	—	4	1	no	—
99	C₂×C₃×C₅×D₄	—	4	1	no	—
100	C₂×C₃×C₅×D₄	—	4	1	no	—
101	C₂×C₃×C₅×D₄	—	4	1	no	—
102	C₂×C₃×C₅×D₄	—	4	1	no	—
103	C₂×C₃×C₅×D₄	—	4	1	no	—
104	C₂×C₃×C₅×D₄	D₄	1	4	yes	complemented
105	C₂²×C₃×C₄×C₅	—	2	2	no	—
106	C₂²×C₃×C₄×C₅	—	2	2	no	—
107	C₂²×C₃×C₄×C₅	—	4	1	no	—
108	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
109	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
110	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
111	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
112	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
113	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
114	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
115	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
116	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
117	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
118	C₃×C₅×C₄⋊C₄	—	2	2	no	—
119	C₃×C₅×C₄⋊C₄	—	2	2	no	—
120	C₃×C₅×C₄⋊C₄	—	2	2	no	—
121	C₃×C₅×C₄⋊C₄	—	4	1	no	—
122	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
123	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
124	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
125	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
126	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
127	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
128	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
129	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
130	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
131	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
132	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
133	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
134	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
135	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
136	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
137	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
138	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	complemented
139	C₃×C₄²×C₅	—	4	1	no	—
140	C₂×C₃×#123	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂×C₃×#120	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂×C₃×#120	C₂×C₅	1	1	yes	characteristic, complemented
144	C₃×#397	C₂×C₅	1	1	yes	characteristic, complemented
145	C₃×#396	C₂×C₅	1	1	yes	characteristic, complemented
146	C₃×#394	C₂×C₅	1	1	yes	characteristic, complemented
147	C₃×#394	C₂×C₅	1	1	yes	characteristic, complemented
148	C₃×#392	C₂×C₅	1	1	yes	characteristic, complemented
149	C₃×#392	C₂×C₅	1	1	yes	characteristic, complemented
150	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
151	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
152	C₃×#388	C₂×C₅	1	1	yes	characteristic, complemented
153	C₃×#386	C₂×C₅	1	1	yes	characteristic, complemented
154	C₃×#379	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
156	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
157	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
158	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
159	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
160	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
161	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
162	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
163	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
164	C₅×#123	—	2	4	no	—
165	C₅×#121	—	2	4	no	—
166	C₅×#120	—	2	4	no	—
167	C₅×#120	—	2	4	no	—
168	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
170	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
171	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
173	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
174	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
175	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
176	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
177	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
178	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
179	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
180	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
181	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
182	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
183	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
184	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
185	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
186	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
187	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
188	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
189	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
190	C₅×#95	C₂²×C₃	1	1	yes	characteristic, complemented
191	C₅×#95	C₂²×C₃	1	1	yes	characteristic, complemented
192	C₅×#95	C₂²×C₃	1	1	yes	characteristic, complemented
193	C₅×#95	C₂²×C₃	1	1	yes	characteristic, complemented
194	#2678	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
195	C₂³×C₃×C₅	—	2	1	no	—
196	C₂³×C₃×C₅	—	2	1	no	—
197	C₂³×C₃×C₅	—	2	1	no	—
198	C₂³×C₃×C₅	—	2	1	no	—
199	C₂³×C₃×C₅	—	2	1	no	—
200	C₂³×C₃×C₅	—	2	1	no	—
201	C₂³×C₃×C₅	—	2	1	no	—
202	C₂³×C₃×C₅	—	2	1	no	—
203	C₂³×C₃×C₅	—	2	1	no	—
204	C₂³×C₃×C₅	—	2	1	no	—
205	C₂³×C₃×C₅	—	2	1	no	—
206	C₂³×C₃×C₅	—	2	1	no	—
207	C₂³×C₃×C₅	—	2	1	no	—
208	C₂³×C₃×C₅	—	2	1	no	—
209	C₂³×C₃×C₅	—	2	1	no	—
210	C₂³×C₃×C₅	—	2	1	no	—
211	C₂³×C₃×C₅	—	2	1	no	—
212	C₂³×C₃×C₅	—	2	1	no	—
213	C₂³×C₃×C₅	—	2	1	no	—
214	C₂³×C₃×C₅	—	2	1	no	—
215	C₂³×C₃×C₅	—	2	1	no	—
216	C₂³×C₃×C₅	—	2	1	no	—
217	C₂³×C₃×C₅	—	2	1	no	—
218	C₂³×C₃×C₅	—	2	1	no	—
219	C₂³×C₃×C₅	—	2	1	no	—
220	C₂³×C₃×C₅	—	2	1	no	—
221	C₂³×C₃×C₅	—	2	1	no	—
222	C₂³×C₃×C₅	—	2	1	no	—
223	C₂³×C₃×C₅	—	2	1	no	—
224	C₂³×C₃×C₅	—	2	1	no	—
225	C₂³×C₃×C₅	—	2	1	no	—
226	C₂³×C₃×C₅	—	4	4	no	—
227	C₂³×C₃×C₅	—	4	4	no	—
228	C₂³×C₃×C₅	—	4	4	no	—
229	C₂³×C₃×C₅	—	4	4	no	—
230	C₂³×C₃×C₅	—	4	4	no	—
231	C₂³×C₃×C₅	—	4	4	no	—
232	C₂³×C₃×C₅	—	4	4	no	—
233	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
234	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
235	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
236	C₂³×C₃×C₅	#41	1	2	yes	—
237	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
238	C₃×C₅×D₄	—	4	4	no	—
239	C₃×C₅×D₄	—	4	4	no	—
240	C₃×C₅×D₄	—	4	4	no	—
241	C₃×C₅×D₄	—	4	4	no	—
242	C₃×C₅×D₄	—	4	4	no	—
243	C₃×C₅×D₄	—	4	4	no	—
244	C₃×C₅×D₄	—	4	4	no	—
245	C₂×C₃×C₄×C₅	—	2	1	no	—
246	C₂×C₃×C₄×C₅	—	2	1	no	—
247	C₂×C₃×C₄×C₅	—	2	1	no	—
248	C₂×C₃×C₄×C₅	—	2	1	no	—
249	C₂×C₃×C₄×C₅	—	2	1	no	—
250	C₂×C₃×C₄×C₅	—	2	1	no	—
251	C₂×C₃×C₄×C₅	—	2	1	no	—
252	C₂×C₃×C₄×C₅	—	2	1	no	—
253	C₂×C₃×C₄×C₅	—	2	1	no	—
254	C₂×C₃×C₄×C₅	—	2	1	no	—
255	C₂×C₃×C₄×C₅	—	2	1	no	—
256	C₂×C₃×C₄×C₅	—	2	1	no	—
257	C₂×C₃×C₄×C₅	—	2	1	no	—
258	C₂×C₃×C₄×C₅	—	2	1	no	—
259	C₂×C₃×C₄×C₅	—	2	1	no	—
260	C₂×C₃×C₄×C₅	—	2	1	no	—
261	C₂×C₃×C₄×C₅	—	2	1	no	—
262	C₂×C₃×C₄×C₅	—	2	1	no	—
263	C₂×C₃×C₄×C₅	—	2	1	no	—
264	C₂×C₃×C₄×C₅	—	2	1	no	—
265	C₂×C₃×C₄×C₅	—	2	1	no	—
266	C₂×C₃×C₄×C₅	—	2	1	no	—
267	C₂×C₃×C₄×C₅	—	2	1	no	—
268	C₂×C₃×C₄×C₅	—	2	1	no	—
269	C₂×C₃×C₄×C₅	—	2	1	no	—
270	C₂×C₃×C₄×C₅	—	2	1	no	—
271	C₂×C₃×C₄×C₅	—	2	1	no	—
272	C₂×C₃×C₄×C₅	—	4	4	no	—
273	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
274	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
275	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
276	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
277	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
278	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
279	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
280	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
281	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
282	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
283	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
284	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
285	C₃×#123	—	2	4	no	—
286	C₃×#121	—	2	4	no	—
287	C₃×#120	—	2	4	no	—
288	C₃×#120	—	2	4	no	—
289	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
290	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
291	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
292	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
293	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
294	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
295	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
296	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
297	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
298	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
299	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
300	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
301	C₂×C₃×C₂²⋊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×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
306	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
307	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
308	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
309	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
310	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
311	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
312	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
313	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
314	C₃×#95	C₂²×C₅	1	1	yes	characteristic, complemented
315	C₂⁴×C₅	—	2	2	no	—
316	C₂⁴×C₅	—	2	2	no	—
317	C₂⁴×C₅	—	2	2	no	—
318	C₂⁴×C₅	—	4	1	no	—
319	C₂⁴×C₅	—	4	1	no	—
320	C₂⁴×C₅	—	4	1	no	—
321	C₂⁴×C₅	—	4	1	no	—
322	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
323	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
324	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
325	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
326	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
327	C₂×C₅×D₄	—	2	2	no	—
328	C₂×C₅×D₄	—	2	2	no	—
329	C₂×C₅×D₄	—	2	2	no	—
330	C₂×C₅×D₄	—	2	2	no	—
331	C₂×C₅×D₄	—	2	2	no	—
332	C₂×C₅×D₄	—	2	2	no	—
333	C₂×C₅×D₄	—	2	2	no	—
334	C₂×C₅×D₄	—	2	2	no	—
335	C₂×C₅×D₄	—	2	2	no	—
336	C₂×C₅×D₄	—	2	2	no	—
337	C₂×C₅×D₄	—	4	1	no	—
338	C₂×C₅×D₄	—	4	1	no	—
339	C₂×C₅×D₄	—	4	1	no	—
340	C₂×C₅×D₄	—	4	1	no	—
341	C₂×C₅×D₄	—	4	1	no	—
342	C₂×C₅×D₄	—	4	1	no	—
343	C₂×C₅×D₄	—	4	1	no	—
344	C₂×C₅×D₄	—	4	1	no	—
345	C₂×C₅×D₄	—	4	1	no	—
346	C₂×C₅×D₄	—	4	1	no	—
347	C₂×C₅×D₄	C₃×D₄	1	4	yes	complemented
348	C₂²×C₄×C₅	—	2	2	no	—
349	C₂²×C₄×C₅	—	2	2	no	—
350	C₂²×C₄×C₅	—	4	1	no	—
351	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
352	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
353	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
354	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
355	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
356	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
357	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
358	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
359	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
360	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
361	C₅×C₄⋊C₄	—	2	2	no	—
362	C₅×C₄⋊C₄	—	2	2	no	—
363	C₅×C₄⋊C₄	—	2	2	no	—
364	C₅×C₄⋊C₄	—	4	1	no	—
365	C₅×C₂²⋊C₄	—	2	2	no	—
366	C₅×C₂²⋊C₄	—	2	2	no	—
367	C₅×C₂²⋊C₄	—	2	2	no	—
368	C₅×C₂²⋊C₄	—	2	2	no	—
369	C₅×C₂²⋊C₄	—	2	2	no	—
370	C₅×C₂²⋊C₄	—	2	2	no	—
371	C₅×C₂²⋊C₄	—	2	2	no	—
372	C₅×C₂²⋊C₄	—	2	2	no	—
373	C₅×C₂²⋊C₄	—	2	2	no	—
374	C₅×C₂²⋊C₄	—	4	1	no	—
375	C₅×C₂²⋊C₄	—	4	1	no	—
376	C₅×C₂²⋊C₄	—	4	1	no	—
377	C₅×C₂²⋊C₄	—	4	1	no	—
378	C₅×C₂²⋊C₄	—	4	1	no	—
379	C₅×C₂²⋊C₄	—	4	1	no	—
380	C₅×C₂²⋊C₄	—	4	1	no	—
381	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	complemented
382	C₄²×C₅	—	4	1	no	—
383	C₂×#123	C₂×C₃×C₅	1	1	yes	characteristic, complemented
384	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic, complemented
385	C₂×#120	C₂×C₃×C₅	1	1	yes	characteristic, complemented
386	C₂×#120	C₂×C₃×C₅	1	1	yes	characteristic, complemented
387	#397	C₂×C₃×C₅	1	1	yes	characteristic, complemented
388	#396	C₂×C₃×C₅	1	1	yes	characteristic, complemented
389	#394	C₂×C₃×C₅	1	1	yes	characteristic, complemented
390	#394	C₂×C₃×C₅	1	1	yes	characteristic, complemented
391	#392	C₂×C₃×C₅	1	1	yes	characteristic, complemented
392	#392	C₂×C₃×C₅	1	1	yes	characteristic, complemented
393	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
394	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
395	#388	C₂×C₃×C₅	1	1	yes	characteristic, complemented
396	#386	C₂×C₃×C₅	1	1	yes	characteristic, complemented
397	#379	C₂×C₃×C₅	1	1	yes	characteristic, complemented
398	C₂²×C₃×C₅	—	2	2	no	—
399	C₂²×C₃×C₅	—	2	2	no	—
400	C₂²×C₃×C₅	—	2	2	no	—
401	C₂²×C₃×C₅	—	2	2	no	—
402	C₂²×C₃×C₅	—	2	2	no	—
403	C₂²×C₃×C₅	—	2	2	no	—
404	C₂²×C₃×C₅	—	2	2	no	—
405	C₂²×C₃×C₅	—	2	2	no	—
406	C₂²×C₃×C₅	—	2	2	no	—
407	C₂²×C₃×C₅	—	2	2	no	—
408	C₂²×C₃×C₅	—	2	2	no	—
409	C₂²×C₃×C₅	—	2	2	no	—
410	C₂²×C₃×C₅	—	4	16	no	—
411	C₂²×C₃×C₅	—	4	1	no	—
412	C₂²×C₃×C₅	—	4	1	no	—
413	C₂²×C₃×C₅	—	4	1	no	—
414	C₂²×C₃×C₅	—	4	1	no	—
415	C₂²×C₃×C₅	—	4	1	no	—
416	C₂²×C₃×C₅	—	4	1	no	—
417	C₂²×C₃×C₅	—	4	1	no	—
418	C₂²×C₃×C₅	—	4	1	no	—
419	C₂²×C₃×C₅	—	4	1	no	—
420	C₂²×C₃×C₅	—	4	1	no	—
421	C₂²×C₃×C₅	—	4	1	no	—
422	C₂²×C₃×C₅	—	4	1	no	—
423	C₂²×C₃×C₅	—	4	1	no	—
424	C₂²×C₃×C₅	—	4	1	no	—
425	C₂²×C₃×C₅	—	4	1	no	—
426	C₂²×C₃×C₅	—	4	1	no	—
427	C₂²×C₃×C₅	—	4	1	no	—
428	C₂²×C₃×C₅	—	4	1	no	—
429	C₂²×C₃×C₅	—	4	1	no	—
430	C₂²×C₃×C₅	—	4	1	no	—
431	C₂²×C₃×C₅	—	4	1	no	—
432	C₂²×C₃×C₅	—	4	1	no	—
433	C₂²×C₃×C₅	—	4	1	no	—
434	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
435	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
436	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
437	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
438	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
439	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
440	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
441	C₃×C₄×C₅	—	2	2	no	—
442	C₃×C₄×C₅	—	2	2	no	—
443	C₃×C₄×C₅	—	2	2	no	—
444	C₃×C₄×C₅	—	4	1	no	—
445	C₃×C₄×C₅	—	4	1	no	—
446	C₃×C₄×C₅	—	4	1	no	—
447	C₃×C₄×C₅	—	4	1	no	—
448	C₃×C₄×C₅	—	4	1	no	—
449	C₃×C₄×C₅	—	4	1	no	—
450	C₃×C₄×C₅	—	4	1	no	—
451	C₂⁴×C₃	—	2	2	no	—
452	C₂⁴×C₃	—	2	2	no	—
453	C₂⁴×C₃	—	2	2	no	—
454	C₂⁴×C₃	—	4	1	no	—
455	C₂⁴×C₃	—	4	1	no	—
456	C₂⁴×C₃	—	4	1	no	—
457	C₂⁴×C₃	—	4	1	no	—
458	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
459	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
460	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
461	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
462	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
463	C₂×C₃×D₄	—	2	2	no	—
464	C₂×C₃×D₄	—	2	2	no	—
465	C₂×C₃×D₄	—	2	2	no	—
466	C₂×C₃×D₄	—	2	2	no	—
467	C₂×C₃×D₄	—	2	2	no	—
468	C₂×C₃×D₄	—	2	2	no	—
469	C₂×C₃×D₄	—	2	2	no	—
470	C₂×C₃×D₄	—	2	2	no	—
471	C₂×C₃×D₄	—	2	2	no	—
472	C₂×C₃×D₄	—	2	2	no	—
473	C₂×C₃×D₄	—	4	1	no	—
474	C₂×C₃×D₄	—	4	1	no	—
475	C₂×C₃×D₄	—	4	1	no	—
476	C₂×C₃×D₄	—	4	1	no	—
477	C₂×C₃×D₄	—	4	1	no	—
478	C₂×C₃×D₄	—	4	1	no	—
479	C₂×C₃×D₄	—	4	1	no	—
480	C₂×C₃×D₄	—	4	1	no	—
481	C₂×C₃×D₄	—	4	1	no	—
482	C₂×C₃×D₄	—	4	1	no	—
483	C₂×C₃×D₄	C₅×D₄	1	4	yes	complemented
484	C₂²×C₃×C₄	—	2	2	no	—
485	C₂²×C₃×C₄	—	2	2	no	—
486	C₂²×C₃×C₄	—	4	1	no	—
487	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
488	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
489	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
490	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
491	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
492	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
493	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
494	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
495	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
496	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
497	C₃×C₄⋊C₄	—	2	2	no	—
498	C₃×C₄⋊C₄	—	2	2	no	—
499	C₃×C₄⋊C₄	—	2	2	no	—
500	C₃×C₄⋊C₄	—	4	1	no	—
501	C₃×C₂²⋊C₄	—	2	2	no	—
502	C₃×C₂²⋊C₄	—	2	2	no	—
503	C₃×C₂²⋊C₄	—	2	2	no	—
504	C₃×C₂²⋊C₄	—	2	2	no	—
505	C₃×C₂²⋊C₄	—	2	2	no	—
506	C₃×C₂²⋊C₄	—	2	2	no	—
507	C₃×C₂²⋊C₄	—	2	2	no	—
508	C₃×C₂²⋊C₄	—	2	2	no	—
509	C₃×C₂²⋊C₄	—	2	2	no	—
510	C₃×C₂²⋊C₄	—	4	1	no	—
511	C₃×C₂²⋊C₄	—	4	1	no	—
512	C₃×C₂²⋊C₄	—	4	1	no	—
513	C₃×C₂²⋊C₄	—	4	1	no	—
514	C₃×C₂²⋊C₄	—	4	1	no	—
515	C₃×C₂²⋊C₄	—	4	1	no	—
516	C₃×C₂²⋊C₄	—	4	1	no	—
517	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	complemented
518	C₃×C₄²	—	4	1	no	—
519	C₂³×C₅	—	2	1	no	—
520	C₂³×C₅	—	2	1	no	—
521	C₂³×C₅	—	2	1	no	—
522	C₂³×C₅	—	2	1	no	—
523	C₂³×C₅	—	2	1	no	—
524	C₂³×C₅	—	2	1	no	—
525	C₂³×C₅	—	2	1	no	—
526	C₂³×C₅	—	2	1	no	—
527	C₂³×C₅	—	2	1	no	—
528	C₂³×C₅	—	2	1	no	—
529	C₂³×C₅	—	2	1	no	—
530	C₂³×C₅	—	2	1	no	—
531	C₂³×C₅	—	2	1	no	—
532	C₂³×C₅	—	2	1	no	—
533	C₂³×C₅	—	2	1	no	—
534	C₂³×C₅	—	2	1	no	—
535	C₂³×C₅	—	2	1	no	—
536	C₂³×C₅	—	2	1	no	—
537	C₂³×C₅	—	2	1	no	—
538	C₂³×C₅	—	2	1	no	—
539	C₂³×C₅	—	2	1	no	—
540	C₂³×C₅	—	2	1	no	—
541	C₂³×C₅	—	2	1	no	—
542	C₂³×C₅	—	2	1	no	—
543	C₂³×C₅	—	2	1	no	—
544	C₂³×C₅	—	2	1	no	—
545	C₂³×C₅	—	2	1	no	—
546	C₂³×C₅	—	2	1	no	—
547	C₂³×C₅	—	2	1	no	—
548	C₂³×C₅	—	2	1	no	—
549	C₂³×C₅	—	2	1	no	—
550	C₂³×C₅	—	4	4	no	—
551	C₂³×C₅	—	4	4	no	—
552	C₂³×C₅	—	4	4	no	—
553	C₂³×C₅	—	4	4	no	—
554	C₂³×C₅	—	4	4	no	—
555	C₂³×C₅	—	4	4	no	—
556	C₂³×C₅	—	4	4	no	—
557	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
558	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
559	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
560	C₂³×C₅	C₃×#41	1	2	yes	—
561	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
562	C₅×D₄	—	4	4	no	—
563	C₅×D₄	—	4	4	no	—
564	C₅×D₄	—	4	4	no	—
565	C₅×D₄	—	4	4	no	—
566	C₅×D₄	—	4	4	no	—
567	C₅×D₄	—	4	4	no	—
568	C₅×D₄	—	4	4	no	—
569	C₂×C₄×C₅	—	2	1	no	—
570	C₂×C₄×C₅	—	2	1	no	—
571	C₂×C₄×C₅	—	2	1	no	—
572	C₂×C₄×C₅	—	2	1	no	—
573	C₂×C₄×C₅	—	2	1	no	—
574	C₂×C₄×C₅	—	2	1	no	—
575	C₂×C₄×C₅	—	2	1	no	—
576	C₂×C₄×C₅	—	2	1	no	—
577	C₂×C₄×C₅	—	2	1	no	—
578	C₂×C₄×C₅	—	2	1	no	—
579	C₂×C₄×C₅	—	2	1	no	—
580	C₂×C₄×C₅	—	2	1	no	—
581	C₂×C₄×C₅	—	2	1	no	—
582	C₂×C₄×C₅	—	2	1	no	—
583	C₂×C₄×C₅	—	2	1	no	—
584	C₂×C₄×C₅	—	2	1	no	—
585	C₂×C₄×C₅	—	2	1	no	—
586	C₂×C₄×C₅	—	2	1	no	—
587	C₂×C₄×C₅	—	2	1	no	—
588	C₂×C₄×C₅	—	2	1	no	—
589	C₂×C₄×C₅	—	2	1	no	—
590	C₂×C₄×C₅	—	2	1	no	—
591	C₂×C₄×C₅	—	2	1	no	—
592	C₂×C₄×C₅	—	2	1	no	—
593	C₂×C₄×C₅	—	2	1	no	—
594	C₂×C₄×C₅	—	2	1	no	—
595	C₂×C₄×C₅	—	2	1	no	—
596	C₂×C₄×C₅	—	4	4	no	—
597	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
598	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
599	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
600	C₂⁵	C₂²×C₃×C₅	1	1	yes	characteristic
601	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
602	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
603	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
604	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
605	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
606	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
607	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
608	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
609	#123	—	2	4	no	—
610	#121	—	2	4	no	—
611	#120	—	2	4	no	—
612	#120	—	2	4	no	—
613	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
614	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
615	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
616	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
617	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
618	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
619	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
620	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
621	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
622	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
623	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
625	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
626	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
627	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
628	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
629	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
630	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
631	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
632	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
633	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
634	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
635	#95	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
636	#95	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
637	#95	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
638	#95	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
639	C₂×C₃×C₅	—	4	2	no	—
640	C₂×C₃×C₅	—	4	2	no	—
641	C₂×C₃×C₅	—	4	2	no	—
642	C₂×C₃×C₅	—	4	2	no	—
643	C₂×C₃×C₅	—	8	1	no	—
644	C₂×C₃×C₅	#534	1	1	yes	characteristic
645	C₂×C₃×C₅	#535	1	1	yes	characteristic
646	C₂×C₃×C₅	#538	1	1	yes	characteristic
647	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
648	C₂×C₃×C₅	#546	1	1	yes	characteristic
649	C₂×C₃×C₅	#546	1	1	yes	characteristic
650	C₂×C₃×C₅	#560	1	1	yes	characteristic
651	C₂³×C₃	—	2	1	no	—
652	C₂³×C₃	—	2	1	no	—
653	C₂³×C₃	—	2	1	no	—
654	C₂³×C₃	—	2	1	no	—
655	C₂³×C₃	—	2	1	no	—
656	C₂³×C₃	—	2	1	no	—
657	C₂³×C₃	—	2	1	no	—
658	C₂³×C₃	—	2	1	no	—
659	C₂³×C₃	—	2	1	no	—
660	C₂³×C₃	—	2	1	no	—
661	C₂³×C₃	—	2	1	no	—
662	C₂³×C₃	—	2	1	no	—
663	C₂³×C₃	—	2	1	no	—
664	C₂³×C₃	—	2	1	no	—
665	C₂³×C₃	—	2	1	no	—
666	C₂³×C₃	—	2	1	no	—
667	C₂³×C₃	—	2	1	no	—
668	C₂³×C₃	—	2	1	no	—
669	C₂³×C₃	—	2	1	no	—
670	C₂³×C₃	—	2	1	no	—
671	C₂³×C₃	—	2	1	no	—
672	C₂³×C₃	—	2	1	no	—
673	C₂³×C₃	—	2	1	no	—
674	C₂³×C₃	—	2	1	no	—
675	C₂³×C₃	—	2	1	no	—
676	C₂³×C₃	—	2	1	no	—
677	C₂³×C₃	—	2	1	no	—
678	C₂³×C₃	—	2	1	no	—
679	C₂³×C₃	—	2	1	no	—
680	C₂³×C₃	—	2	1	no	—
681	C₂³×C₃	—	2	1	no	—
682	C₂³×C₃	—	4	4	no	—
683	C₂³×C₃	—	4	4	no	—
684	C₂³×C₃	—	4	4	no	—
685	C₂³×C₃	—	4	4	no	—
686	C₂³×C₃	—	4	4	no	—
687	C₂³×C₃	—	4	4	no	—
688	C₂³×C₃	—	4	4	no	—
689	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
690	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
691	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
692	C₂³×C₃	C₅×#41	1	2	yes	—
693	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
694	C₃×D₄	—	4	4	no	—
695	C₃×D₄	—	4	4	no	—
696	C₃×D₄	—	4	4	no	—
697	C₃×D₄	—	4	4	no	—
698	C₃×D₄	—	4	4	no	—
699	C₃×D₄	—	4	4	no	—
700	C₃×D₄	—	4	4	no	—
701	C₂×C₃×C₄	—	2	1	no	—
702	C₂×C₃×C₄	—	2	1	no	—
703	C₂×C₃×C₄	—	2	1	no	—
704	C₂×C₃×C₄	—	2	1	no	—
705	C₂×C₃×C₄	—	2	1	no	—
706	C₂×C₃×C₄	—	2	1	no	—
707	C₂×C₃×C₄	—	2	1	no	—
708	C₂×C₃×C₄	—	2	1	no	—
709	C₂×C₃×C₄	—	2	1	no	—
710	C₂×C₃×C₄	—	2	1	no	—
711	C₂×C₃×C₄	—	2	1	no	—
712	C₂×C₃×C₄	—	2	1	no	—
713	C₂×C₃×C₄	—	2	1	no	—
714	C₂×C₃×C₄	—	2	1	no	—
715	C₂×C₃×C₄	—	2	1	no	—
716	C₂×C₃×C₄	—	2	1	no	—
717	C₂×C₃×C₄	—	2	1	no	—
718	C₂×C₃×C₄	—	2	1	no	—
719	C₂×C₃×C₄	—	2	1	no	—
720	C₂×C₃×C₄	—	2	1	no	—
721	C₂×C₃×C₄	—	2	1	no	—
722	C₂×C₃×C₄	—	2	1	no	—
723	C₂×C₃×C₄	—	2	1	no	—
724	C₂×C₃×C₄	—	2	1	no	—
725	C₂×C₃×C₄	—	2	1	no	—
726	C₂×C₃×C₄	—	2	1	no	—
727	C₂×C₃×C₄	—	2	1	no	—
728	C₂×C₃×C₄	—	4	4	no	—
729	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
730	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
731	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
732	C₂²×C₅	—	2	2	no	—
733	C₂²×C₅	—	2	2	no	—
734	C₂²×C₅	—	2	2	no	—
735	C₂²×C₅	—	2	2	no	—
736	C₂²×C₅	—	2	2	no	—
737	C₂²×C₅	—	2	2	no	—
738	C₂²×C₅	—	2	2	no	—
739	C₂²×C₅	—	2	2	no	—
740	C₂²×C₅	—	2	2	no	—
741	C₂²×C₅	—	2	2	no	—
742	C₂²×C₅	—	2	2	no	—
743	C₂²×C₅	—	2	2	no	—
744	C₂²×C₅	—	4	16	no	—
745	C₂²×C₅	—	4	1	no	—
746	C₂²×C₅	—	4	1	no	—
747	C₂²×C₅	—	4	1	no	—
748	C₂²×C₅	—	4	1	no	—
749	C₂²×C₅	—	4	1	no	—
750	C₂²×C₅	—	4	1	no	—
751	C₂²×C₅	—	4	1	no	—
752	C₂²×C₅	—	4	1	no	—
753	C₂²×C₅	—	4	1	no	—
754	C₂²×C₅	—	4	1	no	—
755	C₂²×C₅	—	4	1	no	—
756	C₂²×C₅	—	4	1	no	—
757	C₂²×C₅	—	4	1	no	—
758	C₂²×C₅	—	4	1	no	—
759	C₂²×C₅	—	4	1	no	—
760	C₂²×C₅	—	4	1	no	—
761	C₂²×C₅	—	4	1	no	—
762	C₂²×C₅	—	4	1	no	—
763	C₂²×C₅	—	4	1	no	—
764	C₂²×C₅	—	4	1	no	—
765	C₂²×C₅	—	4	1	no	—
766	C₂²×C₅	—	4	1	no	—
767	C₂²×C₅	—	4	1	no	—
768	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
769	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
770	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
771	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
772	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
773	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
774	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
775	C₄×C₅	—	2	2	no	—
776	C₄×C₅	—	2	2	no	—
777	C₄×C₅	—	2	2	no	—
778	C₄×C₅	—	4	1	no	—
779	C₄×C₅	—	4	1	no	—
780	C₄×C₅	—	4	1	no	—
781	C₄×C₅	—	4	1	no	—
782	C₄×C₅	—	4	1	no	—
783	C₄×C₅	—	4	1	no	—
784	C₄×C₅	—	4	1	no	—
785	C₂⁴	—	2	2	no	—
786	C₂⁴	—	2	2	no	—
787	C₂⁴	—	2	2	no	—
788	C₂⁴	—	4	1	no	—
789	C₂⁴	—	4	1	no	—
790	C₂⁴	—	4	1	no	—
791	C₂⁴	—	4	1	no	—
792	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
793	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
794	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
795	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
796	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	2	2	no	—
799	C₂×D₄	—	2	2	no	—
800	C₂×D₄	—	2	2	no	—
801	C₂×D₄	—	2	2	no	—
802	C₂×D₄	—	2	2	no	—
803	C₂×D₄	—	2	2	no	—
804	C₂×D₄	—	2	2	no	—
805	C₂×D₄	—	2	2	no	—
806	C₂×D₄	—	2	2	no	—
807	C₂×D₄	—	4	1	no	—
808	C₂×D₄	—	4	1	no	—
809	C₂×D₄	—	4	1	no	—
810	C₂×D₄	—	4	1	no	—
811	C₂×D₄	—	4	1	no	—
812	C₂×D₄	—	4	1	no	—
813	C₂×D₄	—	4	1	no	—
814	C₂×D₄	—	4	1	no	—
815	C₂×D₄	—	4	1	no	—
816	C₂×D₄	—	4	1	no	—
817	C₂×D₄	C₃×C₅×D₄	1	4	yes	complemented
818	C₂²×C₄	—	2	2	no	—
819	C₂²×C₄	—	2	2	no	—
820	C₂²×C₄	—	4	1	no	—
821	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
822	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
823	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
824	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
825	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
826	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
827	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
828	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
829	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
830	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	4	1	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	4	1	no	—
845	C₂²⋊C₄	—	4	1	no	—
846	C₂²⋊C₄	—	4	1	no	—
847	C₂²⋊C₄	—	4	1	no	—
848	C₂²⋊C₄	—	4	1	no	—
849	C₂²⋊C₄	—	4	1	no	—
850	C₂²⋊C₄	—	4	1	no	—
851	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	complemented
852	C₄²	—	4	1	no	—
853	C₃×C₅	#2678	1	1	yes	characteristic, direct product factor, Hall
854	C₂²×C₃	—	2	2	no	—
855	C₂²×C₃	—	2	2	no	—
856	C₂²×C₃	—	2	2	no	—
857	C₂²×C₃	—	2	2	no	—
858	C₂²×C₃	—	2	2	no	—
859	C₂²×C₃	—	2	2	no	—
860	C₂²×C₃	—	2	2	no	—
861	C₂²×C₃	—	2	2	no	—
862	C₂²×C₃	—	2	2	no	—
863	C₂²×C₃	—	2	2	no	—
864	C₂²×C₃	—	2	2	no	—
865	C₂²×C₃	—	2	2	no	—
866	C₂²×C₃	—	4	16	no	—
867	C₂²×C₃	—	4	1	no	—
868	C₂²×C₃	—	4	1	no	—
869	C₂²×C₃	—	4	1	no	—
870	C₂²×C₃	—	4	1	no	—
871	C₂²×C₃	—	4	1	no	—
872	C₂²×C₃	—	4	1	no	—
873	C₂²×C₃	—	4	1	no	—
874	C₂²×C₃	—	4	1	no	—
875	C₂²×C₃	—	4	1	no	—
876	C₂²×C₃	—	4	1	no	—
877	C₂²×C₃	—	4	1	no	—
878	C₂²×C₃	—	4	1	no	—
879	C₂²×C₃	—	4	1	no	—
880	C₂²×C₃	—	4	1	no	—
881	C₂²×C₃	—	4	1	no	—
882	C₂²×C₃	—	4	1	no	—
883	C₂²×C₃	—	4	1	no	—
884	C₂²×C₃	—	4	1	no	—
885	C₂²×C₃	—	4	1	no	—
886	C₂²×C₃	—	4	1	no	—
887	C₂²×C₃	—	4	1	no	—
888	C₂²×C₃	—	4	1	no	—
889	C₂²×C₃	—	4	1	no	—
890	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
891	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
892	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
893	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
894	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
895	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
896	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
897	C₃×C₄	—	2	2	no	—
898	C₃×C₄	—	2	2	no	—
899	C₃×C₄	—	2	2	no	—
900	C₃×C₄	—	4	1	no	—
901	C₃×C₄	—	4	1	no	—
902	C₃×C₄	—	4	1	no	—
903	C₃×C₄	—	4	1	no	—
904	C₃×C₄	—	4	1	no	—
905	C₃×C₄	—	4	1	no	—
906	C₃×C₄	—	4	1	no	—
907	C₂×C₅	—	4	2	no	—
908	C₂×C₅	—	4	2	no	—
909	C₂×C₅	—	4	2	no	—
910	C₂×C₅	—	4	2	no	—
911	C₂×C₅	—	8	1	no	—
912	C₂×C₅	C₃×#534	1	1	yes	characteristic
913	C₂×C₅	C₃×#535	1	1	yes	characteristic
914	C₂×C₅	C₃×#538	1	1	yes	characteristic
915	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
916	C₂×C₅	C₃×#546	1	1	yes	characteristic
917	C₂×C₅	C₃×#546	1	1	yes	characteristic
918	C₂×C₅	C₃×#560	1	1	yes	characteristic
919	C₂³	—	2	1	no	—
920	C₂³	—	2	1	no	—
921	C₂³	—	2	1	no	—
922	C₂³	—	2	1	no	—
923	C₂³	—	2	1	no	—
924	C₂³	—	2	1	no	—
925	C₂³	—	2	1	no	—
926	C₂³	—	2	1	no	—
927	C₂³	—	2	1	no	—
928	C₂³	—	2	1	no	—
929	C₂³	—	2	1	no	—
930	C₂³	—	2	1	no	—
931	C₂³	—	2	1	no	—
932	C₂³	—	2	1	no	—
933	C₂³	—	2	1	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	2	1	no	—
937	C₂³	—	2	1	no	—
938	C₂³	—	2	1	no	—
939	C₂³	—	2	1	no	—
940	C₂³	—	2	1	no	—
941	C₂³	—	2	1	no	—
942	C₂³	—	2	1	no	—
943	C₂³	—	2	1	no	—
944	C₂³	—	2	1	no	—
945	C₂³	—	2	1	no	—
946	C₂³	—	2	1	no	—
947	C₂³	—	2	1	no	—
948	C₂³	—	2	1	no	—
949	C₂³	—	2	1	no	—
950	C₂³	—	4	4	no	—
951	C₂³	—	4	4	no	—
952	C₂³	—	4	4	no	—
953	C₂³	—	4	4	no	—
954	C₂³	—	4	4	no	—
955	C₂³	—	4	4	no	—
956	C₂³	—	4	4	no	—
957	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
958	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
959	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
960	C₂³	C₃×C₅×#41	1	2	yes	—
961	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
962	D₄	—	4	4	no	—
963	D₄	—	4	4	no	—
964	D₄	—	4	4	no	—
965	D₄	—	4	4	no	—
966	D₄	—	4	4	no	—
967	D₄	—	4	4	no	—
968	D₄	—	4	4	no	—
969	C₂×C₄	—	2	1	no	—
970	C₂×C₄	—	2	1	no	—
971	C₂×C₄	—	2	1	no	—
972	C₂×C₄	—	2	1	no	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	1	no	—
975	C₂×C₄	—	2	1	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	1	no	—
979	C₂×C₄	—	2	1	no	—
980	C₂×C₄	—	2	1	no	—
981	C₂×C₄	—	2	1	no	—
982	C₂×C₄	—	2	1	no	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	1	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	1	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	4	4	no	—
997	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
998	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
999	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
1000	C₂×C₃	—	4	2	no	—
1001	C₂×C₃	—	4	2	no	—
1002	C₂×C₃	—	4	2	no	—
1003	C₂×C₃	—	4	2	no	—
1004	C₂×C₃	—	8	1	no	—
1005	C₂×C₃	C₅×#534	1	1	yes	characteristic
1006	C₂×C₃	C₅×#535	1	1	yes	characteristic
1007	C₂×C₃	C₅×#538	1	1	yes	characteristic
1008	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
1009	C₂×C₃	C₅×#546	1	1	yes	characteristic
1010	C₂×C₃	C₅×#546	1	1	yes	characteristic
1011	C₂×C₃	C₅×#560	1	1	yes	characteristic
1012	C₅	C₃×#2678	1	1	yes	characteristic, direct product factor, Sylow
1013	C₂²	—	2	2	no	—
1014	C₂²	—	2	2	no	—
1015	C₂²	—	2	2	no	—
1016	C₂²	—	2	2	no	—
1017	C₂²	—	2	2	no	—
1018	C₂²	—	2	2	no	—
1019	C₂²	—	2	2	no	—
1020	C₂²	—	2	2	no	—
1021	C₂²	—	2	2	no	—
1022	C₂²	—	2	2	no	—
1023	C₂²	—	2	2	no	—
1024	C₂²	—	2	2	no	—
1025	C₂²	—	4	16	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	1	no	—
1028	C₂²	—	4	1	no	—
1029	C₂²	—	4	1	no	—
1030	C₂²	—	4	1	no	—
1031	C₂²	—	4	1	no	—
1032	C₂²	—	4	1	no	—
1033	C₂²	—	4	1	no	—
1034	C₂²	—	4	1	no	—
1035	C₂²	—	4	1	no	—
1036	C₂²	—	4	1	no	—
1037	C₂²	—	4	1	no	—
1038	C₂²	—	4	1	no	—
1039	C₂²	—	4	1	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	—	4	1	no	—
1043	C₂²	—	4	1	no	—
1044	C₂²	—	4	1	no	—
1045	C₂²	—	4	1	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	4	1	no	—
1049	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
1050	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
1051	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
1052	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1053	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1054	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1055	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1056	C₄	—	2	2	no	—
1057	C₄	—	2	2	no	—
1058	C₄	—	2	2	no	—
1059	C₄	—	4	1	no	—
1060	C₄	—	4	1	no	—
1061	C₄	—	4	1	no	—
1062	C₄	—	4	1	no	—
1063	C₄	—	4	1	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	1	no	—
1066	C₃	C₅×#2678	1	1	yes	characteristic, direct product factor, Sylow
1067	C₂	—	4	2	no	—
1068	C₂	—	4	2	no	—
1069	C₂	—	4	2	no	—
1070	C₂	—	4	2	no	—
1071	C₂	—	8	1	no	—
1072	C₂	C₃×C₅×#534	1	1	yes	characteristic
1073	C₂	C₃×C₅×#535	1	1	yes	characteristic
1074	C₂	C₃×C₅×#538	1	1	yes	characteristic
1075	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
1076	C₂	C₃×C₅×#546	1	1	yes	characteristic
1077	C₂	C₃×C₅×#546	1	1	yes	characteristic
1078	C₂	C₃×C₅×#560	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
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×#123	C₂	semidirect
2. C₂×C₃×C₅×#121	C₂	semidirect
3. C₂×C₃×C₅×#120	C₂	semidirect
4. C₂×C₃×C₅×#120	C₂	semidirect
5. C₃×C₅×#397	C₂	semidirect
6. C₃×C₅×#396	C₂	semidirect
7. C₃×C₅×#394	C₂	semidirect
8. C₃×C₅×#394	C₂	semidirect
9. C₃×C₅×#392	C₂	semidirect
10. C₃×C₅×#392	C₂	semidirect
11. C₃×C₅×#390	C₂	semidirect
12. C₃×C₅×#390	C₂	semidirect
13. C₃×C₅×#388	C₂	semidirect
14. C₃×C₅×#386	C₂	semidirect
15. C₃×C₅×#379	C₂	semidirect
16. C₅×#2678	C₃	direct (N × H)
24. C₂²×C₃×C₅×D₄	C₂²	semidirect
25. C₂³×C₃×C₄×C₅	C₂²	semidirect
30. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
31. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
32. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
33. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
46. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
47. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
48. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
49. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
50. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
51. C₂×C₃×C₄²×C₅	C₂²	semidirect
52. C₃×C₅×#95	C₂²	semidirect
53. C₃×C₅×#95	C₂²	semidirect
54. C₃×C₅×#95	C₂²	semidirect
55. C₃×C₅×#95	C₂²	semidirect
56. C₃×#2678	C₅	direct (N × H)
57. C₂×C₅×#123	C₂×C₃	semidirect
58. C₂×C₅×#121	C₂×C₃	semidirect
59. C₂×C₅×#120	C₂×C₃	semidirect
60. C₂×C₅×#120	C₂×C₃	semidirect
61. C₅×#397	C₂×C₃	semidirect
62. C₅×#396	C₂×C₃	semidirect
63. C₅×#394	C₂×C₃	semidirect
64. C₅×#394	C₂×C₃	semidirect
65. C₅×#392	C₂×C₃	semidirect
66. C₅×#392	C₂×C₃	semidirect
67. C₅×#390	C₂×C₃	semidirect
68. C₅×#390	C₂×C₃	semidirect
69. C₅×#388	C₂×C₃	semidirect
70. C₅×#386	C₂×C₃	semidirect
71. C₅×#379	C₂×C₃	semidirect
104. C₂×C₃×C₅×D₄	D₄	semidirect
138. C₃×C₅×C₂²⋊C₄	D₄	semidirect
140. C₂×C₃×#123	C₂×C₅	semidirect
141. C₂×C₃×#121	C₂×C₅	semidirect
142. C₂×C₃×#120	C₂×C₅	semidirect
143. C₂×C₃×#120	C₂×C₅	semidirect
144. C₃×#397	C₂×C₅	semidirect
145. C₃×#396	C₂×C₅	semidirect
146. C₃×#394	C₂×C₅	semidirect
147. C₃×#394	C₂×C₅	semidirect
148. C₃×#392	C₂×C₅	semidirect
149. C₃×#392	C₂×C₅	semidirect
150. C₃×#390	C₂×C₅	semidirect
151. C₃×#390	C₂×C₅	semidirect
152. C₃×#388	C₂×C₅	semidirect
153. C₃×#386	C₂×C₅	semidirect
154. C₃×#379	C₂×C₅	semidirect
162. C₂²×C₅×D₄	C₂²×C₃	semidirect
163. C₂³×C₄×C₅	C₂²×C₃	semidirect
168. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
169. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
170. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
171. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
184. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
185. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
186. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
187. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
188. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
189. C₂×C₄²×C₅	C₂²×C₃	semidirect
190. C₅×#95	C₂²×C₃	semidirect
191. C₅×#95	C₂²×C₃	semidirect
192. C₅×#95	C₂²×C₃	semidirect
193. C₅×#95	C₂²×C₃	semidirect
194. #2678	C₃×C₅	direct (N × H)
283. C₂²×C₃×D₄	C₂²×C₅	semidirect
284. C₂³×C₃×C₄	C₂²×C₅	semidirect
289. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
290. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
291. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
292. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
305. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
306. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
307. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
308. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
309. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
310. C₂×C₃×C₄²	C₂²×C₅	semidirect
311. C₃×#95	C₂²×C₅	semidirect
312. C₃×#95	C₂²×C₅	semidirect
313. C₃×#95	C₂²×C₅	semidirect
314. C₃×#95	C₂²×C₅	semidirect
347. C₂×C₅×D₄	C₃×D₄	semidirect
381. C₅×C₂²⋊C₄	C₃×D₄	semidirect
383. C₂×#123	C₂×C₃×C₅	semidirect
384. C₂×#121	C₂×C₃×C₅	semidirect
385. C₂×#120	C₂×C₃×C₅	semidirect
386. C₂×#120	C₂×C₃×C₅	semidirect
387. #397	C₂×C₃×C₅	semidirect
388. #396	C₂×C₃×C₅	semidirect
389. #394	C₂×C₃×C₅	semidirect
390. #394	C₂×C₃×C₅	semidirect
391. #392	C₂×C₃×C₅	semidirect
392. #392	C₂×C₃×C₅	semidirect
393. #390	C₂×C₃×C₅	semidirect
394. #390	C₂×C₃×C₅	semidirect
395. #388	C₂×C₃×C₅	semidirect
396. #386	C₂×C₃×C₅	semidirect
397. #379	C₂×C₃×C₅	semidirect
483. C₂×C₃×D₄	C₅×D₄	semidirect
517. C₃×C₂²⋊C₄	C₅×D₄	semidirect
607. C₂²×D₄	C₂²×C₃×C₅	semidirect
608. C₂³×C₄	C₂²×C₃×C₅	semidirect
613. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
614. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
615. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
616. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
629. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
630. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
631. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
632. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
633. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
634. C₂×C₄²	C₂²×C₃×C₅	semidirect
635. #95	C₂²×C₃×C₅	semidirect
636. #95	C₂²×C₃×C₅	semidirect
637. #95	C₂²×C₃×C₅	semidirect
638. #95	C₂²×C₃×C₅	semidirect
817. C₂×D₄	C₃×C₅×D₄	semidirect
851. C₂²⋊C₄	C₃×C₅×D₄	semidirect
853. C₃×C₅	#2678	direct (N × H)
1012. C₅	C₃×#2678	direct (N × H)
1066. C₃	C₅×#2678	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×#123	2
C₂×C₃×C₅×#121	2
C₂×C₃×C₅×#120	2
C₃×C₅×#397	2
C₃×C₅×#396	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₅×#390	2
C₃×C₅×#388	2
C₃×C₅×#386	2
C₃×C₅×#379	2
C₅×#2678	3
C₃×#2678	5

Subgroups — C3×C5×#2678 #14275712

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2678 #14275712