Subgroups — C₃×C₅×#3268 #14276302

Order 1920.

1020 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#550	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#496	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#468	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#466	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#459	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#449	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#447	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#440	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3268	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₃×C₅×AGL(1,ℤ/8)	—	2	4	no	—
22	C₃×C₅×#135	—	2	4	no	—
23	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
33	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₅×#127	—	2	1	no	—
35	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₅×#124	C₂²	1	1	yes	characteristic
37	C₃×C₅×#123	—	2	1	no	—
38	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
39	C₃×C₅×#121	—	2	1	no	—
40	C₃×C₅×#121	—	2	1	no	—
41	C₃×C₅×#121	—	2	1	no	—
42	C₃×C₅×#121	C₂²	1	1	yes	characteristic
43	C₃×C₅×#121	C₂²	1	1	yes	characteristic
44	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×#120	—	2	1	no	—
46	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
47	C₃×C₄×C₅×D₄	—	2	1	no	—
48	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
49	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
50	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
51	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
55	C₃×C₅×#102	C₂²	1	1	yes	characteristic
56	C₃×C₅×#102	C₂²	1	1	yes	characteristic
57	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
58	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
59	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
60	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
62	C₃×#3268	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
63	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#550	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#546	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#496	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#468	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#466	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#464	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#459	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#452	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×#449	C₂×C₃	1	1	yes	characteristic, complemented
74	C₅×#449	C₂×C₃	1	1	yes	characteristic, complemented
75	C₅×#447	C₂×C₃	1	1	yes	characteristic, complemented
76	C₅×#440	C₂×C₃	1	1	yes	characteristic, complemented
77	C₅×#435	C₂×C₃	1	1	yes	characteristic, complemented
78	C₂⁴×C₃×C₅	—	2	1	no	—
79	C₃×C₅×#41	—	2	2	no	—
80	C₃×C₅×#41	—	2	2	no	—
81	C₃×C₅×#41	—	2	2	no	—
82	C₃×C₅×#41	—	4	1	no	—
83	C₃×C₅×#41	—	4	1	no	—
84	C₃×C₅×#41	—	4	1	no	—
85	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
87	C₂×C₃×C₅×D₄	—	2	2	no	—
88	C₂×C₃×C₅×D₄	—	2	1	no	—
89	C₂×C₃×C₅×D₄	—	2	1	no	—
90	C₂×C₃×C₅×D₄	—	2	1	no	—
91	C₂×C₃×C₅×D₄	—	2	1	no	—
92	C₂×C₃×C₅×D₄	—	2	1	no	—
93	C₂×C₃×C₅×D₄	—	2	1	no	—
94	C₂×C₃×C₅×D₄	—	2	1	no	—
95	C₂×C₃×C₅×D₄	—	2	1	no	—
96	C₂×C₃×C₅×D₄	—	2	1	no	—
97	C₂×C₃×C₅×D₄	—	4	1	no	—
98	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
99	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
100	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
102	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
103	C₂²×C₃×C₄×C₅	—	2	1	no	—
104	C₂²×C₃×C₄×C₅	—	2	1	no	—
105	C₂²×C₃×C₄×C₅	—	2	1	no	—
106	C₂²×C₃×C₄×C₅	—	2	1	no	—
107	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
108	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
109	C₃×C₅×Q₁₆	—	2	2	no	—
110	C₃×C₅×SD₁₆	—	2	2	no	—
111	C₃×C₅×SD₁₆	—	2	2	no	—
112	C₃×C₅×SD₁₆	—	4	1	no	—
113	C₃×C₅×SD₁₆	D₄	1	4	yes	complemented
114	C₃×C₅×D₈	—	2	2	no	—
115	C₃×C₅×D₈	—	2	2	no	—
116	C₃×C₅×D₈	—	2	2	no	—
117	C₃×C₅×D₈	—	4	1	no	—
118	C₃×C₅×M₁₆	—	2	2	no	—
119	C₂×C₃×C₅×C₈	—	2	2	no	—
120	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
121	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
122	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
123	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
124	C₃×C₅×C₄⋊C₄	—	2	1	no	—
125	C₃×C₅×C₄⋊C₄	—	2	1	no	—
126	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
127	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
128	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
130	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
131	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
132	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
133	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
134	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
135	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
136	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
137	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
138	C₃×C₄²×C₅	—	2	1	no	—
139	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
140	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
142	C₃×#550	C₂×C₅	1	1	yes	characteristic, complemented
143	C₃×#546	C₂×C₅	1	1	yes	characteristic, complemented
144	C₃×#496	C₂×C₅	1	1	yes	characteristic, complemented
145	C₃×#468	C₂×C₅	1	1	yes	characteristic, complemented
146	C₃×#466	C₂×C₅	1	1	yes	characteristic, complemented
147	C₃×#464	C₂×C₅	1	1	yes	characteristic, complemented
148	C₃×#459	C₂×C₅	1	1	yes	characteristic, complemented
149	C₃×#452	C₂×C₅	1	1	yes	characteristic, complemented
150	C₃×#449	C₂×C₅	1	1	yes	characteristic, complemented
151	C₃×#449	C₂×C₅	1	1	yes	characteristic, complemented
152	C₃×#447	C₂×C₅	1	1	yes	characteristic, complemented
153	C₃×#440	C₂×C₅	1	1	yes	characteristic, complemented
154	C₃×#435	C₂×C₅	1	1	yes	characteristic, complemented
155	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
156	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
157	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic, complemented
158	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
159	C₅×AGL(1,ℤ/8)	—	2	4	no	—
160	C₅×#135	—	2	4	no	—
161	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
162	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
163	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
164	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
165	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
166	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
167	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
168	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
169	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
170	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
171	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₅×#127	—	2	1	no	—
173	C₅×#127	C₂²×C₃	1	1	yes	characteristic, complemented
174	C₅×#124	C₂²×C₃	1	1	yes	characteristic
175	C₅×#123	—	2	1	no	—
176	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
177	C₅×#121	—	2	1	no	—
178	C₅×#121	—	2	1	no	—
179	C₅×#121	—	2	1	no	—
180	C₅×#121	C₂²×C₃	1	1	yes	characteristic
181	C₅×#121	C₂²×C₃	1	1	yes	characteristic
182	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
183	C₅×#120	—	2	1	no	—
184	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
185	C₄×C₅×D₄	—	2	1	no	—
186	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
187	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
188	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
189	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
190	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
191	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
192	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
193	C₅×#102	C₂²×C₃	1	1	yes	characteristic
194	C₅×#102	C₂²×C₃	1	1	yes	characteristic
195	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
196	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
197	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
198	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
199	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
200	#3268	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
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	—	4	2	no	—
206	C₂³×C₃×C₅	—	4	2	no	—
207	C₂³×C₃×C₅	—	8	1	no	—
208	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
209	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
210	C₃×C₅×Q₈	—	2	1	no	—
211	C₃×C₅×Q₈	—	2	1	no	—
212	C₃×C₅×Q₈	—	2	1	no	—
213	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
214	C₃×C₅×D₄	—	2	1	no	—
215	C₃×C₅×D₄	—	2	1	no	—
216	C₃×C₅×D₄	—	2	1	no	—
217	C₃×C₅×D₄	—	2	1	no	—
218	C₃×C₅×D₄	—	2	1	no	—
219	C₃×C₅×D₄	—	2	1	no	—
220	C₃×C₅×D₄	—	2	1	no	—
221	C₃×C₅×D₄	—	4	1	no	—
222	C₃×C₅×D₄	—	4	2	no	—
223	C₃×C₅×D₄	—	4	2	no	—
224	C₃×C₅×D₄	—	4	2	no	—
225	C₃×C₅×D₄	—	4	2	no	—
226	C₃×C₅×D₄	—	4	2	no	—
227	C₃×C₅×D₄	—	8	1	no	—
228	C₃×C₅×D₄	—	8	1	no	—
229	C₃×C₅×D₄	—	8	1	no	—
230	C₃×C₅×D₄	—	8	1	no	—
231	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
232	C₂×C₃×C₄×C₅	—	2	1	no	—
233	C₂×C₃×C₄×C₅	—	2	1	no	—
234	C₂×C₃×C₄×C₅	—	2	1	no	—
235	C₂×C₃×C₄×C₅	—	2	1	no	—
236	C₂×C₃×C₄×C₅	—	2	1	no	—
237	C₂×C₃×C₄×C₅	—	2	1	no	—
238	C₂×C₃×C₄×C₅	—	2	1	no	—
239	C₂×C₃×C₄×C₅	—	2	1	no	—
240	C₂×C₃×C₄×C₅	—	4	2	no	—
241	C₂×C₃×C₄×C₅	—	4	2	no	—
242	C₂×C₃×C₄×C₅	—	4	2	no	—
243	C₂×C₃×C₄×C₅	—	8	1	no	—
244	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
245	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
246	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
247	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
248	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
249	C₃×C₅×C₈	—	2	1	no	—
250	C₃×C₅×C₈	—	2	1	no	—
251	C₃×C₅×C₈	—	2	1	no	—
252	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
253	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
254	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
255	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
256	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
257	C₃×AGL(1,ℤ/8)	—	2	4	no	—
258	C₃×#135	—	2	4	no	—
259	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
260	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
261	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
262	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
264	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
265	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
266	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
267	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
268	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
269	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
270	C₃×#127	—	2	1	no	—
271	C₃×#127	C₂²×C₅	1	1	yes	characteristic, complemented
272	C₃×#124	C₂²×C₅	1	1	yes	characteristic
273	C₃×#123	—	2	1	no	—
274	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
275	C₃×#121	—	2	1	no	—
276	C₃×#121	—	2	1	no	—
277	C₃×#121	—	2	1	no	—
278	C₃×#121	C₂²×C₅	1	1	yes	characteristic
279	C₃×#121	C₂²×C₅	1	1	yes	characteristic
280	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
281	C₃×#120	—	2	1	no	—
282	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
283	C₃×C₄×D₄	—	2	1	no	—
284	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
285	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
286	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
287	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
288	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
289	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
290	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
291	C₃×#102	C₂²×C₅	1	1	yes	characteristic
292	C₃×#102	C₂²×C₅	1	1	yes	characteristic
293	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
294	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
295	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
296	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
297	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
298	C₂⁴×C₅	—	2	1	no	—
299	C₅×#41	—	2	2	no	—
300	C₅×#41	—	2	2	no	—
301	C₅×#41	—	2	2	no	—
302	C₅×#41	—	4	1	no	—
303	C₅×#41	—	4	1	no	—
304	C₅×#41	—	4	1	no	—
305	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
306	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
307	C₂×C₅×D₄	—	2	2	no	—
308	C₂×C₅×D₄	—	2	1	no	—
309	C₂×C₅×D₄	—	2	1	no	—
310	C₂×C₅×D₄	—	2	1	no	—
311	C₂×C₅×D₄	—	2	1	no	—
312	C₂×C₅×D₄	—	2	1	no	—
313	C₂×C₅×D₄	—	2	1	no	—
314	C₂×C₅×D₄	—	2	1	no	—
315	C₂×C₅×D₄	—	2	1	no	—
316	C₂×C₅×D₄	—	2	1	no	—
317	C₂×C₅×D₄	—	4	1	no	—
318	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
319	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
320	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
321	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
322	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
323	C₂²×C₄×C₅	—	2	1	no	—
324	C₂²×C₄×C₅	—	2	1	no	—
325	C₂²×C₄×C₅	—	2	1	no	—
326	C₂²×C₄×C₅	—	2	1	no	—
327	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
328	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
329	C₅×Q₁₆	—	2	2	no	—
330	C₅×SD₁₆	—	2	2	no	—
331	C₅×SD₁₆	—	2	2	no	—
332	C₅×SD₁₆	—	4	1	no	—
333	C₅×SD₁₆	C₃×D₄	1	4	yes	complemented
334	C₅×D₈	—	2	2	no	—
335	C₅×D₈	—	2	2	no	—
336	C₅×D₈	—	2	2	no	—
337	C₅×D₈	—	4	1	no	—
338	C₅×M₁₆	—	2	2	no	—
339	C₂×C₅×C₈	—	2	2	no	—
340	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
341	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
342	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
343	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
344	C₅×C₄⋊C₄	—	2	1	no	—
345	C₅×C₄⋊C₄	—	2	1	no	—
346	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
347	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
348	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
349	C₅×C₂²⋊C₄	—	2	1	no	—
350	C₅×C₂²⋊C₄	—	2	1	no	—
351	C₅×C₂²⋊C₄	—	2	1	no	—
352	C₅×C₂²⋊C₄	—	2	1	no	—
353	C₅×C₂²⋊C₄	—	2	1	no	—
354	C₅×C₂²⋊C₄	—	2	1	no	—
355	C₅×C₂²⋊C₄	—	2	1	no	—
356	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
357	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
358	C₄²×C₅	—	2	1	no	—
359	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
360	C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	1	1	yes	characteristic, complemented
361	C₂×#135	C₂×C₃×C₅	1	1	yes	characteristic, complemented
362	#550	C₂×C₃×C₅	1	1	yes	characteristic, complemented
363	#546	C₂×C₃×C₅	1	1	yes	characteristic, complemented
364	#496	C₂×C₃×C₅	1	1	yes	characteristic, complemented
365	#468	C₂×C₃×C₅	1	1	yes	characteristic, complemented
366	#466	C₂×C₃×C₅	1	1	yes	characteristic, complemented
367	#464	C₂×C₃×C₅	1	1	yes	characteristic, complemented
368	#459	C₂×C₃×C₅	1	1	yes	characteristic, complemented
369	#452	C₂×C₃×C₅	1	1	yes	characteristic, complemented
370	#449	C₂×C₃×C₅	1	1	yes	characteristic, complemented
371	#449	C₂×C₃×C₅	1	1	yes	characteristic, complemented
372	#447	C₂×C₃×C₅	1	1	yes	characteristic, complemented
373	#440	C₂×C₃×C₅	1	1	yes	characteristic, complemented
374	#435	C₂×C₃×C₅	1	1	yes	characteristic, complemented
375	C₂²×C₃×C₅	—	2	1	no	—
376	C₂²×C₃×C₅	—	2	1	no	—
377	C₂²×C₃×C₅	—	2	2	no	—
378	C₂²×C₃×C₅	—	2	1	no	—
379	C₂²×C₃×C₅	—	2	1	no	—
380	C₂²×C₃×C₅	—	2	1	no	—
381	C₂²×C₃×C₅	—	2	1	no	—
382	C₂²×C₃×C₅	—	4	1	no	—
383	C₂²×C₃×C₅	—	4	1	no	—
384	C₂²×C₃×C₅	—	4	1	no	—
385	C₂²×C₃×C₅	—	4	1	no	—
386	C₂²×C₃×C₅	—	4	1	no	—
387	C₂²×C₃×C₅	—	4	1	no	—
388	C₂²×C₃×C₅	—	4	1	no	—
389	C₂²×C₃×C₅	—	4	1	no	—
390	C₂²×C₃×C₅	—	4	1	no	—
391	C₂²×C₃×C₅	—	4	1	no	—
392	C₂²×C₃×C₅	—	4	1	no	—
393	C₂²×C₃×C₅	—	8	4	no	—
394	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
395	C₃×C₄×C₅	—	2	1	no	—
396	C₃×C₄×C₅	—	2	1	no	—
397	C₃×C₄×C₅	—	2	2	no	—
398	C₃×C₄×C₅	—	2	1	no	—
399	C₃×C₄×C₅	—	2	1	no	—
400	C₃×C₄×C₅	—	4	1	no	—
401	C₃×C₄×C₅	—	4	1	no	—
402	C₃×C₄×C₅	—	4	1	no	—
403	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
404	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
405	C₂⁴×C₃	—	2	1	no	—
406	C₃×#41	—	2	2	no	—
407	C₃×#41	—	2	2	no	—
408	C₃×#41	—	2	2	no	—
409	C₃×#41	—	4	1	no	—
410	C₃×#41	—	4	1	no	—
411	C₃×#41	—	4	1	no	—
412	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
413	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
414	C₂×C₃×D₄	—	2	2	no	—
415	C₂×C₃×D₄	—	2	1	no	—
416	C₂×C₃×D₄	—	2	1	no	—
417	C₂×C₃×D₄	—	2	1	no	—
418	C₂×C₃×D₄	—	2	1	no	—
419	C₂×C₃×D₄	—	2	1	no	—
420	C₂×C₃×D₄	—	2	1	no	—
421	C₂×C₃×D₄	—	2	1	no	—
422	C₂×C₃×D₄	—	2	1	no	—
423	C₂×C₃×D₄	—	2	1	no	—
424	C₂×C₃×D₄	—	4	1	no	—
425	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
426	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
427	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
428	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
429	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
430	C₂²×C₃×C₄	—	2	1	no	—
431	C₂²×C₃×C₄	—	2	1	no	—
432	C₂²×C₃×C₄	—	2	1	no	—
433	C₂²×C₃×C₄	—	2	1	no	—
434	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
435	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
436	C₃×Q₁₆	—	2	2	no	—
437	C₃×SD₁₆	—	2	2	no	—
438	C₃×SD₁₆	—	2	2	no	—
439	C₃×SD₁₆	—	4	1	no	—
440	C₃×SD₁₆	C₅×D₄	1	4	yes	complemented
441	C₃×D₈	—	2	2	no	—
442	C₃×D₈	—	2	2	no	—
443	C₃×D₈	—	2	2	no	—
444	C₃×D₈	—	4	1	no	—
445	C₃×M₁₆	—	2	2	no	—
446	C₂×C₃×C₈	—	2	2	no	—
447	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
448	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
449	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
450	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
451	C₃×C₄⋊C₄	—	2	1	no	—
452	C₃×C₄⋊C₄	—	2	1	no	—
453	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
454	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
455	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
456	C₃×C₂²⋊C₄	—	2	1	no	—
457	C₃×C₂²⋊C₄	—	2	1	no	—
458	C₃×C₂²⋊C₄	—	2	1	no	—
459	C₃×C₂²⋊C₄	—	2	1	no	—
460	C₃×C₂²⋊C₄	—	2	1	no	—
461	C₃×C₂²⋊C₄	—	2	1	no	—
462	C₃×C₂²⋊C₄	—	2	1	no	—
463	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
464	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
465	C₃×C₄²	—	2	1	no	—
466	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
467	C₂³×C₅	—	2	1	no	—
468	C₂³×C₅	—	2	1	no	—
469	C₂³×C₅	—	2	1	no	—
470	C₂³×C₅	—	2	1	no	—
471	C₂³×C₅	—	4	2	no	—
472	C₂³×C₅	—	4	2	no	—
473	C₂³×C₅	—	8	1	no	—
474	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
475	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
476	C₅×Q₈	—	2	1	no	—
477	C₅×Q₈	—	2	1	no	—
478	C₅×Q₈	—	2	1	no	—
479	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
480	C₅×D₄	—	2	1	no	—
481	C₅×D₄	—	2	1	no	—
482	C₅×D₄	—	2	1	no	—
483	C₅×D₄	—	2	1	no	—
484	C₅×D₄	—	2	1	no	—
485	C₅×D₄	—	2	1	no	—
486	C₅×D₄	—	2	1	no	—
487	C₅×D₄	—	4	1	no	—
488	C₅×D₄	—	4	2	no	—
489	C₅×D₄	—	4	2	no	—
490	C₅×D₄	—	4	2	no	—
491	C₅×D₄	—	4	2	no	—
492	C₅×D₄	—	4	2	no	—
493	C₅×D₄	—	8	1	no	—
494	C₅×D₄	—	8	1	no	—
495	C₅×D₄	—	8	1	no	—
496	C₅×D₄	—	8	1	no	—
497	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
498	C₂×C₄×C₅	—	2	1	no	—
499	C₂×C₄×C₅	—	2	1	no	—
500	C₂×C₄×C₅	—	2	1	no	—
501	C₂×C₄×C₅	—	2	1	no	—
502	C₂×C₄×C₅	—	2	1	no	—
503	C₂×C₄×C₅	—	2	1	no	—
504	C₂×C₄×C₅	—	2	1	no	—
505	C₂×C₄×C₅	—	2	1	no	—
506	C₂×C₄×C₅	—	4	2	no	—
507	C₂×C₄×C₅	—	4	2	no	—
508	C₂×C₄×C₅	—	4	2	no	—
509	C₂×C₄×C₅	—	8	1	no	—
510	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
511	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
512	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
513	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
514	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
515	C₅×C₈	—	2	1	no	—
516	C₅×C₈	—	2	1	no	—
517	C₅×C₈	—	2	1	no	—
518	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
519	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
520	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
521	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
522	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
523	AGL(1,ℤ/8)	—	2	4	no	—
524	#135	—	2	4	no	—
525	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
526	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
527	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
528	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
529	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
530	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
531	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
532	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
533	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
534	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
535	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
536	#127	—	2	1	no	—
537	#127	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
538	#124	C₂²×C₃×C₅	1	1	yes	characteristic
539	#123	—	2	1	no	—
540	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
541	#121	—	2	1	no	—
542	#121	—	2	1	no	—
543	#121	—	2	1	no	—
544	#121	C₂²×C₃×C₅	1	1	yes	characteristic
545	#121	C₂²×C₃×C₅	1	1	yes	characteristic
546	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
547	#120	—	2	1	no	—
548	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
549	C₄×D₄	—	2	1	no	—
550	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
551	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
552	C₂×C₂²⋊C₄	—	2	1	no	—
553	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
554	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
555	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
556	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
557	#102	C₂²×C₃×C₅	1	1	yes	characteristic
558	#102	C₂²×C₃×C₅	1	1	yes	characteristic
559	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
560	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
561	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
562	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
563	#97	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
564	C₂×C₃×C₅	—	4	1	no	—
565	C₂×C₃×C₅	—	4	1	no	—
566	C₂×C₃×C₅	—	4	2	no	—
567	C₂×C₃×C₅	—	8	1	no	—
568	C₂×C₃×C₅	—	8	1	no	—
569	C₂×C₃×C₅	—	8	1	no	—
570	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
571	C₂×C₃×C₅	#575	1	1	yes	characteristic
572	C₂×C₃×C₅	#576	1	1	yes	characteristic
573	C₂³×C₃	—	2	1	no	—
574	C₂³×C₃	—	2	1	no	—
575	C₂³×C₃	—	2	1	no	—
576	C₂³×C₃	—	2	1	no	—
577	C₂³×C₃	—	4	2	no	—
578	C₂³×C₃	—	4	2	no	—
579	C₂³×C₃	—	8	1	no	—
580	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
581	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
582	C₃×Q₈	—	2	1	no	—
583	C₃×Q₈	—	2	1	no	—
584	C₃×Q₈	—	2	1	no	—
585	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
586	C₃×D₄	—	2	1	no	—
587	C₃×D₄	—	2	1	no	—
588	C₃×D₄	—	2	1	no	—
589	C₃×D₄	—	2	1	no	—
590	C₃×D₄	—	2	1	no	—
591	C₃×D₄	—	2	1	no	—
592	C₃×D₄	—	2	1	no	—
593	C₃×D₄	—	4	1	no	—
594	C₃×D₄	—	4	2	no	—
595	C₃×D₄	—	4	2	no	—
596	C₃×D₄	—	4	2	no	—
597	C₃×D₄	—	4	2	no	—
598	C₃×D₄	—	4	2	no	—
599	C₃×D₄	—	8	1	no	—
600	C₃×D₄	—	8	1	no	—
601	C₃×D₄	—	8	1	no	—
602	C₃×D₄	—	8	1	no	—
603	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
604	C₂×C₃×C₄	—	2	1	no	—
605	C₂×C₃×C₄	—	2	1	no	—
606	C₂×C₃×C₄	—	2	1	no	—
607	C₂×C₃×C₄	—	2	1	no	—
608	C₂×C₃×C₄	—	2	1	no	—
609	C₂×C₃×C₄	—	2	1	no	—
610	C₂×C₃×C₄	—	2	1	no	—
611	C₂×C₃×C₄	—	2	1	no	—
612	C₂×C₃×C₄	—	4	2	no	—
613	C₂×C₃×C₄	—	4	2	no	—
614	C₂×C₃×C₄	—	4	2	no	—
615	C₂×C₃×C₄	—	8	1	no	—
616	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
617	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
618	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
619	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
620	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
621	C₃×C₈	—	2	1	no	—
622	C₃×C₈	—	2	1	no	—
623	C₃×C₈	—	2	1	no	—
624	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
625	C₂²×C₅	—	2	1	no	—
626	C₂²×C₅	—	2	1	no	—
627	C₂²×C₅	—	2	1	no	—
628	C₂²×C₅	—	2	1	no	—
629	C₂²×C₅	—	2	1	no	—
630	C₂²×C₅	—	2	1	no	—
631	C₂²×C₅	—	2	2	no	—
632	C₂²×C₅	—	4	1	no	—
633	C₂²×C₅	—	4	1	no	—
634	C₂²×C₅	—	4	1	no	—
635	C₂²×C₅	—	4	1	no	—
636	C₂²×C₅	—	4	1	no	—
637	C₂²×C₅	—	4	1	no	—
638	C₂²×C₅	—	4	1	no	—
639	C₂²×C₅	—	4	1	no	—
640	C₂²×C₅	—	4	1	no	—
641	C₂²×C₅	—	4	1	no	—
642	C₂²×C₅	—	4	1	no	—
643	C₂²×C₅	—	8	4	no	—
644	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
645	C₄×C₅	—	2	1	no	—
646	C₄×C₅	—	2	1	no	—
647	C₄×C₅	—	2	1	no	—
648	C₄×C₅	—	2	1	no	—
649	C₄×C₅	—	2	2	no	—
650	C₄×C₅	—	4	1	no	—
651	C₄×C₅	—	4	1	no	—
652	C₄×C₅	—	4	1	no	—
653	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
654	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
655	C₂⁴	—	2	1	no	—
656	#41	—	2	2	no	—
657	#41	—	2	2	no	—
658	#41	—	2	2	no	—
659	#41	—	4	1	no	—
660	#41	—	4	1	no	—
661	#41	—	4	1	no	—
662	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
663	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
664	C₂×D₄	—	2	2	no	—
665	C₂×D₄	—	2	1	no	—
666	C₂×D₄	—	2	1	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	1	no	—
669	C₂×D₄	—	2	1	no	—
670	C₂×D₄	—	2	1	no	—
671	C₂×D₄	—	2	1	no	—
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	1	no	—
674	C₂×D₄	—	4	1	no	—
675	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
676	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
677	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
678	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
679	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
680	C₂²×C₄	—	2	1	no	—
681	C₂²×C₄	—	2	1	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
685	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
686	Q₁₆	—	2	2	no	—
687	SD₁₆	—	2	2	no	—
688	SD₁₆	—	2	2	no	—
689	SD₁₆	—	4	1	no	—
690	SD₁₆	C₃×C₅×D₄	1	4	yes	complemented
691	D₈	—	2	2	no	—
692	D₈	—	2	2	no	—
693	D₈	—	2	2	no	—
694	D₈	—	4	1	no	—
695	M₁₆	—	2	2	no	—
696	C₂×C₈	—	2	2	no	—
697	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
698	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
699	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
700	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
704	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
705	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
706	C₂²⋊C₄	—	2	1	no	—
707	C₂²⋊C₄	—	2	1	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	1	no	—
710	C₂²⋊C₄	—	2	1	no	—
711	C₂²⋊C₄	—	2	1	no	—
712	C₂²⋊C₄	—	2	1	no	—
713	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
714	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
715	C₄²	—	2	1	no	—
716	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
717	C₃×C₅	#3268	1	1	yes	characteristic, direct product factor, Hall
718	C₂²×C₃	—	2	1	no	—
719	C₂²×C₃	—	2	1	no	—
720	C₂²×C₃	—	2	2	no	—
721	C₂²×C₃	—	2	1	no	—
722	C₂²×C₃	—	2	1	no	—
723	C₂²×C₃	—	2	1	no	—
724	C₂²×C₃	—	2	1	no	—
725	C₂²×C₃	—	4	1	no	—
726	C₂²×C₃	—	4	1	no	—
727	C₂²×C₃	—	4	1	no	—
728	C₂²×C₃	—	4	1	no	—
729	C₂²×C₃	—	4	1	no	—
730	C₂²×C₃	—	4	1	no	—
731	C₂²×C₃	—	4	1	no	—
732	C₂²×C₃	—	4	1	no	—
733	C₂²×C₃	—	4	1	no	—
734	C₂²×C₃	—	4	1	no	—
735	C₂²×C₃	—	4	1	no	—
736	C₂²×C₃	—	8	4	no	—
737	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
738	C₃×C₄	—	2	1	no	—
739	C₃×C₄	—	2	1	no	—
740	C₃×C₄	—	2	2	no	—
741	C₃×C₄	—	2	1	no	—
742	C₃×C₄	—	2	1	no	—
743	C₃×C₄	—	4	1	no	—
744	C₃×C₄	—	4	1	no	—
745	C₃×C₄	—	4	1	no	—
746	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
747	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
748	C₂×C₅	—	4	1	no	—
749	C₂×C₅	—	4	1	no	—
750	C₂×C₅	—	4	2	no	—
751	C₂×C₅	—	8	1	no	—
752	C₂×C₅	—	8	1	no	—
753	C₂×C₅	—	8	1	no	—
754	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
755	C₂×C₅	C₃×#575	1	1	yes	characteristic
756	C₂×C₅	C₃×#576	1	1	yes	characteristic
757	C₂³	—	2	1	no	—
758	C₂³	—	2	1	no	—
759	C₂³	—	2	1	no	—
760	C₂³	—	2	1	no	—
761	C₂³	—	4	2	no	—
762	C₂³	—	4	2	no	—
763	C₂³	—	8	1	no	—
764	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
765	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
766	Q₈	—	2	1	no	—
767	Q₈	—	2	1	no	—
768	Q₈	—	2	1	no	—
769	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
770	D₄	—	2	1	no	—
771	D₄	—	2	1	no	—
772	D₄	—	2	1	no	—
773	D₄	—	2	1	no	—
774	D₄	—	2	1	no	—
775	D₄	—	2	1	no	—
776	D₄	—	2	1	no	—
777	D₄	—	4	1	no	—
778	D₄	—	4	2	no	—
779	D₄	—	4	2	no	—
780	D₄	—	4	2	no	—
781	D₄	—	4	2	no	—
782	D₄	—	4	2	no	—
783	D₄	—	8	1	no	—
784	D₄	—	8	1	no	—
785	D₄	—	8	1	no	—
786	D₄	—	8	1	no	—
787	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
788	C₂×C₄	—	2	1	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	1	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	4	2	no	—
797	C₂×C₄	—	4	2	no	—
798	C₂×C₄	—	4	2	no	—
799	C₂×C₄	—	8	1	no	—
800	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
801	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
802	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
803	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
804	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
805	C₈	—	2	1	no	—
806	C₈	—	2	1	no	—
807	C₈	—	2	1	no	—
808	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
809	C₂×C₃	—	4	1	no	—
810	C₂×C₃	—	4	1	no	—
811	C₂×C₃	—	4	2	no	—
812	C₂×C₃	—	8	1	no	—
813	C₂×C₃	—	8	1	no	—
814	C₂×C₃	—	8	1	no	—
815	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
816	C₂×C₃	C₅×#575	1	1	yes	characteristic
817	C₂×C₃	C₅×#576	1	1	yes	characteristic
818	C₅	C₃×#3268	1	1	yes	characteristic, direct product factor, Sylow
819	C₂²	—	2	1	no	—
820	C₂²	—	2	1	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	1	no	—
823	C₂²	—	2	1	no	—
824	C₂²	—	2	1	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	1	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	1	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	8	4	no	—
838	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
839	C₄	—	2	1	no	—
840	C₄	—	2	1	no	—
841	C₄	—	2	2	no	—
842	C₄	—	2	1	no	—
843	C₄	—	2	1	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	1	no	—
846	C₄	—	4	1	no	—
847	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
848	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
849	C₃	C₅×#3268	1	1	yes	characteristic, direct product factor, Sylow
850	C₂	—	4	1	no	—
851	C₂	—	4	1	no	—
852	C₂	—	4	2	no	—
853	C₂	—	8	1	no	—
854	C₂	—	8	1	no	—
855	C₂	—	8	1	no	—
856	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
857	C₂	C₃×C₅×#575	1	1	yes	characteristic
858	C₂	C₃×C₅×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄×C₅×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₃×C₅×#135	C₂	semidirect
3. C₃×C₅×#550	C₂	semidirect
4. C₃×C₅×#546	C₂	semidirect
5. C₃×C₅×#496	C₂	semidirect
6. C₃×C₅×#468	C₂	semidirect
7. C₃×C₅×#466	C₂	semidirect
8. C₃×C₅×#464	C₂	semidirect
9. C₃×C₅×#459	C₂	semidirect
10. C₃×C₅×#452	C₂	semidirect
11. C₃×C₅×#449	C₂	semidirect
12. C₃×C₅×#449	C₂	semidirect
13. C₃×C₅×#447	C₂	semidirect
14. C₃×C₅×#440	C₂	semidirect
15. C₃×C₅×#435	C₂	semidirect
16. C₅×#3268	C₃	direct (N × H)
19. C₂×C₃×C₅×#41	C₂²	semidirect
23. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
26. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
27. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
33. C₂²×C₃×C₅×C₈	C₂²	semidirect
35. C₃×C₅×#127	C₂²	semidirect
44. C₃×C₅×#121	C₂²	semidirect
46. C₃×C₄×C₅×Q₈	C₂²	semidirect
51. C₃×C₅×#107	C₂²	semidirect
52. C₃×C₅×C₄⋊C₈	C₂²	semidirect
53. C₃×C₅×#103	C₂²	semidirect
54. C₃×C₅×#103	C₂²	semidirect
57. C₃×C₅×#102	C₂²	semidirect
58. C₃×C₅×#102	C₂²	semidirect
60. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
61. C₃×C₅×#97	C₂²	semidirect
62. C₃×#3268	C₅	direct (N × H)
63. C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
64. C₂×C₅×#135	C₂×C₃	semidirect
65. C₅×#550	C₂×C₃	semidirect
66. C₅×#546	C₂×C₃	semidirect
67. C₅×#496	C₂×C₃	semidirect
68. C₅×#468	C₂×C₃	semidirect
69. C₅×#466	C₂×C₃	semidirect
70. C₅×#464	C₂×C₃	semidirect
71. C₅×#459	C₂×C₃	semidirect
72. C₅×#452	C₂×C₃	semidirect
73. C₅×#449	C₂×C₃	semidirect
74. C₅×#449	C₂×C₃	semidirect
75. C₅×#447	C₂×C₃	semidirect
76. C₅×#440	C₂×C₃	semidirect
77. C₅×#435	C₂×C₃	semidirect
113. C₃×C₅×SD₁₆	D₄	semidirect
140. C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
141. C₂×C₃×#135	C₂×C₅	semidirect
142. C₃×#550	C₂×C₅	semidirect
143. C₃×#546	C₂×C₅	semidirect
144. C₃×#496	C₂×C₅	semidirect
145. C₃×#468	C₂×C₅	semidirect
146. C₃×#466	C₂×C₅	semidirect
147. C₃×#464	C₂×C₅	semidirect
148. C₃×#459	C₂×C₅	semidirect
149. C₃×#452	C₂×C₅	semidirect
150. C₃×#449	C₂×C₅	semidirect
151. C₃×#449	C₂×C₅	semidirect
152. C₃×#447	C₂×C₅	semidirect
153. C₃×#440	C₂×C₅	semidirect
154. C₃×#435	C₂×C₅	semidirect
157. C₂×C₅×#41	C₂²×C₃	semidirect
161. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
164. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
165. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
171. C₂²×C₅×C₈	C₂²×C₃	semidirect
173. C₅×#127	C₂²×C₃	semidirect
182. C₅×#121	C₂²×C₃	semidirect
184. C₄×C₅×Q₈	C₂²×C₃	semidirect
189. C₅×#107	C₂²×C₃	semidirect
190. C₅×C₄⋊C₈	C₂²×C₃	semidirect
191. C₅×#103	C₂²×C₃	semidirect
192. C₅×#103	C₂²×C₃	semidirect
195. C₅×#102	C₂²×C₃	semidirect
196. C₅×#102	C₂²×C₃	semidirect
198. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
199. C₅×#97	C₂²×C₃	semidirect
200. #3268	C₃×C₅	direct (N × H)
255. C₂×C₃×#41	C₂²×C₅	semidirect
259. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
262. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
263. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
269. C₂²×C₃×C₈	C₂²×C₅	semidirect
271. C₃×#127	C₂²×C₅	semidirect
280. C₃×#121	C₂²×C₅	semidirect
282. C₃×C₄×Q₈	C₂²×C₅	semidirect
287. C₃×#107	C₂²×C₅	semidirect
288. C₃×C₄⋊C₈	C₂²×C₅	semidirect
289. C₃×#103	C₂²×C₅	semidirect
290. C₃×#103	C₂²×C₅	semidirect
293. C₃×#102	C₂²×C₅	semidirect
294. C₃×#102	C₂²×C₅	semidirect
296. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
297. C₃×#97	C₂²×C₅	semidirect
333. C₅×SD₁₆	C₃×D₄	semidirect
360. C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	semidirect
361. C₂×#135	C₂×C₃×C₅	semidirect
362. #550	C₂×C₃×C₅	semidirect
363. #546	C₂×C₃×C₅	semidirect
364. #496	C₂×C₃×C₅	semidirect
365. #468	C₂×C₃×C₅	semidirect
366. #466	C₂×C₃×C₅	semidirect
367. #464	C₂×C₃×C₅	semidirect
368. #459	C₂×C₃×C₅	semidirect
369. #452	C₂×C₃×C₅	semidirect
370. #449	C₂×C₃×C₅	semidirect
371. #449	C₂×C₃×C₅	semidirect
372. #447	C₂×C₃×C₅	semidirect
373. #440	C₂×C₃×C₅	semidirect
374. #435	C₂×C₃×C₅	semidirect
440. C₃×SD₁₆	C₅×D₄	semidirect
521. C₂×#41	C₂²×C₃×C₅	semidirect
525. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
528. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
529. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
535. C₂²×C₈	C₂²×C₃×C₅	semidirect
537. #127	C₂²×C₃×C₅	semidirect
546. #121	C₂²×C₃×C₅	semidirect
548. C₄×Q₈	C₂²×C₃×C₅	semidirect
553. #107	C₂²×C₃×C₅	semidirect
554. C₄⋊C₈	C₂²×C₃×C₅	semidirect
555. #103	C₂²×C₃×C₅	semidirect
556. #103	C₂²×C₃×C₅	semidirect
559. #102	C₂²×C₃×C₅	semidirect
560. #102	C₂²×C₃×C₅	semidirect
562. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
563. #97	C₂²×C₃×C₅	semidirect
690. SD₁₆	C₃×C₅×D₄	semidirect
717. C₃×C₅	#3268	direct (N × H)
818. C₅	C₃×#3268	direct (N × H)
849. C₃	C₅×#3268	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×AGL(1,ℤ/8)	2
C₂×C₃×C₅×#135	2
C₃×C₅×#550	2
C₃×C₅×#546	2
C₃×C₅×#496	2
C₃×C₅×#468	2
C₃×C₅×#466	2
C₃×C₅×#464	2
C₃×C₅×#459	2
C₃×C₅×#452	2
C₃×C₅×#449	2
C₃×C₅×#447	2
C₃×C₅×#440	2
C₃×C₅×#435	2
C₅×#3268	3
C₃×#3268	5

Subgroups — C3×C5×#3268 #14276302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3268 #14276302