Subgroups — C₃×C₅×#3265 #14276299

Order 1920.

1092 conjugacy classes of subgroups.

The subgroup lattice has 876 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	C₂²×C₃×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#548	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×D₄²	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×#463	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#450	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#448	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×#3265	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₃×C₅×D₄	—	2	1	no	—
20	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₃×C₅×AGL(1,ℤ/8)	—	2	4	no	—
23	C₂×C₃×C₅×SD₁₆	—	2	4	no	—
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×SD₁₆	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₅×#127	C₂²	1	1	yes	characteristic
36	C₃×C₅×#124	—	2	1	no	—
37	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
39	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
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×C₅×#120	—	2	1	no	—
47	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₄×C₅×D₄	—	2	1	no	—
49	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
50	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
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, complemented
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, complemented
60	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
62	C₃×#3265	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	C₂²×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#548	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×D₄²	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×#463	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#460	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#450	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×#449	C₂×C₃	1	1	yes	characteristic, complemented
74	C₅×#448	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	C₂⁴×C₃×C₅	—	2	1	no	—
80	C₃×C₅×#41	—	2	2	no	—
81	C₃×C₅×#41	—	4	1	no	—
82	C₂×C₃×C₅×Q₈	—	2	1	no	—
83	C₂×C₃×C₅×Q₈	—	2	2	no	—
84	C₂×C₃×C₅×Q₈	—	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	2	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	—	4	1	no	—
99	C₂×C₃×C₅×D₄	—	4	4	no	—
100	C₂×C₃×C₅×D₄	D₄	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	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
105	C₂²×C₃×C₄×C₅	—	2	1	no	—
106	C₂²×C₃×C₄×C₅	—	2	1	no	—
107	C₂²×C₃×C₄×C₅	—	2	1	no	—
108	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
109	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
110	C₃×C₅×SD₁₆	—	2	2	no	—
111	C₃×C₅×SD₁₆	—	2	2	no	—
112	C₃×C₅×SD₁₆	—	2	2	no	—
113	C₃×C₅×SD₁₆	—	2	2	no	—
114	C₃×C₅×SD₁₆	—	4	1	no	—
115	C₃×C₅×SD₁₆	D₄	1	4	yes	complemented
116	C₃×C₅×D₈	—	2	2	no	—
117	C₃×C₅×D₈	—	2	2	no	—
118	C₃×C₅×D₈	—	4	1	no	—
119	C₃×C₅×M₁₆	—	2	2	no	—
120	C₂×C₃×C₅×C₈	—	2	2	no	—
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	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
125	C₃×C₅×C₄⋊C₄	—	2	1	no	—
126	C₃×C₅×C₄⋊C₄	—	2	1	no	—
127	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
128	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
137	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
138	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
139	C₃×C₄²×C₅	—	2	1	no	—
140	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
141	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂²×C₃×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
143	C₃×#548	C₂×C₅	1	1	yes	characteristic, complemented
144	C₃×D₄²	C₂×C₅	1	1	yes	characteristic, complemented
145	C₃×#496	C₂×C₅	1	1	yes	characteristic, complemented
146	C₃×#468	C₂×C₅	1	1	yes	characteristic, complemented
147	C₃×#466	C₂×C₅	1	1	yes	characteristic, complemented
148	C₃×#463	C₂×C₅	1	1	yes	characteristic, complemented
149	C₃×#460	C₂×C₅	1	1	yes	characteristic, complemented
150	C₃×#450	C₂×C₅	1	1	yes	characteristic, complemented
151	C₃×#449	C₂×C₅	1	1	yes	characteristic, complemented
152	C₃×#448	C₂×C₅	1	1	yes	characteristic, complemented
153	C₃×#447	C₂×C₅	1	1	yes	characteristic, complemented
154	C₃×#440	C₂×C₅	1	1	yes	characteristic, complemented
155	C₃×#435	C₂×C₅	1	1	yes	characteristic, complemented
156	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic, complemented
157	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
158	C₂²×C₅×D₄	—	2	1	no	—
159	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
160	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
161	C₅×AGL(1,ℤ/8)	—	2	4	no	—
162	C₂×C₅×SD₁₆	—	2	4	no	—
163	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
164	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
165	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
166	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
167	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
170	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
171	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
174	C₅×#127	C₂²×C₃	1	1	yes	characteristic
175	C₅×#124	—	2	1	no	—
176	C₅×#124	C₂²×C₃	1	1	yes	characteristic, complemented
177	C₅×C₂²⋊Q₈	—	2	1	no	—
178	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
179	C₅×#121	—	2	1	no	—
180	C₅×#121	—	2	1	no	—
181	C₅×#121	C₂²×C₃	1	1	yes	characteristic
182	C₅×#121	C₂²×C₃	1	1	yes	characteristic
183	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
184	C₅×#120	—	2	1	no	—
185	C₅×#120	—	2	1	no	—
186	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
187	C₄×C₅×D₄	—	2	1	no	—
188	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
189	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
190	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
191	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
192	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
193	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
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×#102	C₂²×C₃	1	1	yes	characteristic, complemented
198	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
199	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
200	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
201	#3265	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
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	—	4	2	no	—
207	C₂³×C₃×C₅	—	4	2	no	—
208	C₂³×C₃×C₅	—	4	2	no	—
209	C₂³×C₃×C₅	—	4	2	no	—
210	C₂³×C₃×C₅	—	8	1	no	—
211	C₂³×C₃×C₅	—	8	1	no	—
212	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
213	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
214	C₃×C₅×Q₈	—	2	1	no	—
215	C₃×C₅×Q₈	—	2	1	no	—
216	C₃×C₅×Q₈	—	2	1	no	—
217	C₃×C₅×Q₈	—	4	2	no	—
218	C₃×C₅×Q₈	C₂×D₄	1	2	yes	complemented
219	C₃×C₅×D₄	—	2	2	no	—
220	C₃×C₅×D₄	—	2	1	no	—
221	C₃×C₅×D₄	—	2	1	no	—
222	C₃×C₅×D₄	—	2	1	no	—
223	C₃×C₅×D₄	—	2	1	no	—
224	C₃×C₅×D₄	—	2	1	no	—
225	C₃×C₅×D₄	—	2	1	no	—
226	C₃×C₅×D₄	—	2	1	no	—
227	C₃×C₅×D₄	—	4	2	no	—
228	C₃×C₅×D₄	—	4	2	no	—
229	C₃×C₅×D₄	—	4	2	no	—
230	C₃×C₅×D₄	—	4	2	no	—
231	C₃×C₅×D₄	—	4	2	no	—
232	C₃×C₅×D₄	—	4	2	no	—
233	C₃×C₅×D₄	—	4	2	no	—
234	C₃×C₅×D₄	—	8	1	no	—
235	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
241	C₂×C₃×C₄×C₅	—	2	1	no	—
242	C₂×C₃×C₄×C₅	—	2	1	no	—
243	C₂×C₃×C₄×C₅	—	2	1	no	—
244	C₂×C₃×C₄×C₅	—	4	2	no	—
245	C₂×C₃×C₄×C₅	—	4	2	no	—
246	C₂×C₃×C₄×C₅	—	4	2	no	—
247	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
248	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
249	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
250	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
251	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
252	C₃×C₅×C₈	—	2	1	no	—
253	C₃×C₅×C₈	—	2	1	no	—
254	C₃×C₅×C₈	—	2	1	no	—
255	C₃×C₅×C₈	C₂×D₄	1	2	yes	complemented
256	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
257	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
258	C₂²×C₃×D₄	—	2	1	no	—
259	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
260	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
261	C₃×AGL(1,ℤ/8)	—	2	4	no	—
262	C₂×C₃×SD₁₆	—	2	4	no	—
263	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
264	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
265	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
266	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
267	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
268	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
269	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
270	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
271	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
272	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
273	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
274	C₃×#127	C₂²×C₅	1	1	yes	characteristic
275	C₃×#124	—	2	1	no	—
276	C₃×#124	C₂²×C₅	1	1	yes	characteristic, complemented
277	C₃×C₂²⋊Q₈	—	2	1	no	—
278	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
279	C₃×#121	—	2	1	no	—
280	C₃×#121	—	2	1	no	—
281	C₃×#121	C₂²×C₅	1	1	yes	characteristic
282	C₃×#121	C₂²×C₅	1	1	yes	characteristic
283	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
284	C₃×#120	—	2	1	no	—
285	C₃×#120	—	2	1	no	—
286	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
287	C₃×C₄×D₄	—	2	1	no	—
288	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
289	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
290	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
291	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
292	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
293	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
294	C₃×#102	C₂²×C₅	1	1	yes	characteristic
295	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
296	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
297	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
298	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
299	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
300	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
301	C₂⁴×C₅	—	2	1	no	—
302	C₂⁴×C₅	—	2	1	no	—
303	C₅×#41	—	2	2	no	—
304	C₅×#41	—	4	1	no	—
305	C₂×C₅×Q₈	—	2	1	no	—
306	C₂×C₅×Q₈	—	2	2	no	—
307	C₂×C₅×Q₈	—	4	1	no	—
308	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
309	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
310	C₂×C₅×D₄	—	2	2	no	—
311	C₂×C₅×D₄	—	2	2	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	—	2	1	no	—
318	C₂×C₅×D₄	—	2	1	no	—
319	C₂×C₅×D₄	—	2	1	no	—
320	C₂×C₅×D₄	—	4	1	no	—
321	C₂×C₅×D₄	—	4	1	no	—
322	C₂×C₅×D₄	—	4	4	no	—
323	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
324	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
325	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
326	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
327	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
328	C₂²×C₄×C₅	—	2	1	no	—
329	C₂²×C₄×C₅	—	2	1	no	—
330	C₂²×C₄×C₅	—	2	1	no	—
331	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
332	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
333	C₅×SD₁₆	—	2	2	no	—
334	C₅×SD₁₆	—	2	2	no	—
335	C₅×SD₁₆	—	2	2	no	—
336	C₅×SD₁₆	—	2	2	no	—
337	C₅×SD₁₆	—	4	1	no	—
338	C₅×SD₁₆	C₃×D₄	1	4	yes	complemented
339	C₅×D₈	—	2	2	no	—
340	C₅×D₈	—	2	2	no	—
341	C₅×D₈	—	4	1	no	—
342	C₅×M₁₆	—	2	2	no	—
343	C₂×C₅×C₈	—	2	2	no	—
344	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
345	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
346	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
347	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
348	C₅×C₄⋊C₄	—	2	1	no	—
349	C₅×C₄⋊C₄	—	2	1	no	—
350	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
351	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
352	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	—	2	1	no	—
357	C₅×C₂²⋊C₄	—	2	1	no	—
358	C₅×C₂²⋊C₄	—	2	1	no	—
359	C₅×C₂²⋊C₄	—	2	1	no	—
360	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
361	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
362	C₄²×C₅	—	2	1	no	—
363	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
364	C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	1	1	yes	characteristic, complemented
365	C₂²×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
366	#548	C₂×C₃×C₅	1	1	yes	characteristic, complemented
367	D₄²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
368	#496	C₂×C₃×C₅	1	1	yes	characteristic, complemented
369	#468	C₂×C₃×C₅	1	1	yes	characteristic, complemented
370	#466	C₂×C₃×C₅	1	1	yes	characteristic, complemented
371	#463	C₂×C₃×C₅	1	1	yes	characteristic, complemented
372	#460	C₂×C₃×C₅	1	1	yes	characteristic, complemented
373	#450	C₂×C₃×C₅	1	1	yes	characteristic, complemented
374	#449	C₂×C₃×C₅	1	1	yes	characteristic, complemented
375	#448	C₂×C₃×C₅	1	1	yes	characteristic, complemented
376	#447	C₂×C₃×C₅	1	1	yes	characteristic, complemented
377	#440	C₂×C₃×C₅	1	1	yes	characteristic, complemented
378	#435	C₂×C₃×C₅	1	1	yes	characteristic, complemented
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	—	2	2	no	—
383	C₂²×C₃×C₅	—	2	1	no	—
384	C₂²×C₃×C₅	—	2	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	—	4	1	no	—
394	C₂²×C₃×C₅	—	4	1	no	—
395	C₂²×C₃×C₅	—	4	1	no	—
396	C₂²×C₃×C₅	—	8	4	no	—
397	C₂²×C₃×C₅	—	8	4	no	—
398	C₂²×C₃×C₅	AGL(1,ℤ/8)	1	2	yes	complemented
399	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
400	C₃×C₄×C₅	—	2	1	no	—
401	C₃×C₄×C₅	—	2	1	no	—
402	C₃×C₄×C₅	—	2	2	no	—
403	C₃×C₄×C₅	—	2	1	no	—
404	C₃×C₄×C₅	—	2	1	no	—
405	C₃×C₄×C₅	—	4	1	no	—
406	C₃×C₄×C₅	—	4	1	no	—
407	C₃×C₄×C₅	—	4	1	no	—
408	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
409	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
410	C₂⁴×C₃	—	2	1	no	—
411	C₂⁴×C₃	—	2	1	no	—
412	C₃×#41	—	2	2	no	—
413	C₃×#41	—	4	1	no	—
414	C₂×C₃×Q₈	—	2	1	no	—
415	C₂×C₃×Q₈	—	2	2	no	—
416	C₂×C₃×Q₈	—	4	1	no	—
417	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
418	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
419	C₂×C₃×D₄	—	2	2	no	—
420	C₂×C₃×D₄	—	2	2	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	—	2	1	no	—
425	C₂×C₃×D₄	—	2	1	no	—
426	C₂×C₃×D₄	—	2	1	no	—
427	C₂×C₃×D₄	—	2	1	no	—
428	C₂×C₃×D₄	—	2	1	no	—
429	C₂×C₃×D₄	—	4	1	no	—
430	C₂×C₃×D₄	—	4	1	no	—
431	C₂×C₃×D₄	—	4	4	no	—
432	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
433	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
434	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
435	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
436	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
437	C₂²×C₃×C₄	—	2	1	no	—
438	C₂²×C₃×C₄	—	2	1	no	—
439	C₂²×C₃×C₄	—	2	1	no	—
440	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
441	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
442	C₃×SD₁₆	—	2	2	no	—
443	C₃×SD₁₆	—	2	2	no	—
444	C₃×SD₁₆	—	2	2	no	—
445	C₃×SD₁₆	—	2	2	no	—
446	C₃×SD₁₆	—	4	1	no	—
447	C₃×SD₁₆	C₅×D₄	1	4	yes	complemented
448	C₃×D₈	—	2	2	no	—
449	C₃×D₈	—	2	2	no	—
450	C₃×D₈	—	4	1	no	—
451	C₃×M₁₆	—	2	2	no	—
452	C₂×C₃×C₈	—	2	2	no	—
453	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
454	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
455	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
456	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
457	C₃×C₄⋊C₄	—	2	1	no	—
458	C₃×C₄⋊C₄	—	2	1	no	—
459	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
460	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
461	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
462	C₃×C₂²⋊C₄	—	2	1	no	—
463	C₃×C₂²⋊C₄	—	2	1	no	—
464	C₃×C₂²⋊C₄	—	2	1	no	—
465	C₃×C₂²⋊C₄	—	2	1	no	—
466	C₃×C₂²⋊C₄	—	2	1	no	—
467	C₃×C₂²⋊C₄	—	2	1	no	—
468	C₃×C₂²⋊C₄	—	2	1	no	—
469	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
470	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
471	C₃×C₄²	—	2	1	no	—
472	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
473	C₂³×C₅	—	2	1	no	—
474	C₂³×C₅	—	2	1	no	—
475	C₂³×C₅	—	2	1	no	—
476	C₂³×C₅	—	2	1	no	—
477	C₂³×C₅	—	4	2	no	—
478	C₂³×C₅	—	4	2	no	—
479	C₂³×C₅	—	4	2	no	—
480	C₂³×C₅	—	4	2	no	—
481	C₂³×C₅	—	8	1	no	—
482	C₂³×C₅	—	8	1	no	—
483	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
484	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
485	C₅×Q₈	—	2	1	no	—
486	C₅×Q₈	—	2	1	no	—
487	C₅×Q₈	—	2	1	no	—
488	C₅×Q₈	—	4	2	no	—
489	C₅×Q₈	C₂×C₃×D₄	1	2	yes	complemented
490	C₅×D₄	—	2	2	no	—
491	C₅×D₄	—	2	1	no	—
492	C₅×D₄	—	2	1	no	—
493	C₅×D₄	—	2	1	no	—
494	C₅×D₄	—	2	1	no	—
495	C₅×D₄	—	2	1	no	—
496	C₅×D₄	—	2	1	no	—
497	C₅×D₄	—	2	1	no	—
498	C₅×D₄	—	4	2	no	—
499	C₅×D₄	—	4	2	no	—
500	C₅×D₄	—	4	2	no	—
501	C₅×D₄	—	4	2	no	—
502	C₅×D₄	—	4	2	no	—
503	C₅×D₄	—	4	2	no	—
504	C₅×D₄	—	4	2	no	—
505	C₅×D₄	—	8	1	no	—
506	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
507	C₂×C₄×C₅	—	2	1	no	—
508	C₂×C₄×C₅	—	2	1	no	—
509	C₂×C₄×C₅	—	2	1	no	—
510	C₂×C₄×C₅	—	2	1	no	—
511	C₂×C₄×C₅	—	2	1	no	—
512	C₂×C₄×C₅	—	2	1	no	—
513	C₂×C₄×C₅	—	2	1	no	—
514	C₂×C₄×C₅	—	2	1	no	—
515	C₂×C₄×C₅	—	4	2	no	—
516	C₂×C₄×C₅	—	4	2	no	—
517	C₂×C₄×C₅	—	4	2	no	—
518	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
519	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
520	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
521	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
522	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
523	C₅×C₈	—	2	1	no	—
524	C₅×C₈	—	2	1	no	—
525	C₅×C₈	—	2	1	no	—
526	C₅×C₈	C₂×C₃×D₄	1	2	yes	complemented
527	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
528	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
529	C₂²×D₄	—	2	1	no	—
530	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
531	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
532	AGL(1,ℤ/8)	—	2	4	no	—
533	C₂×SD₁₆	—	2	4	no	—
534	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
535	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
536	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
537	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
538	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
539	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
540	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
541	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
542	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
543	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
544	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
545	#127	C₂²×C₃×C₅	1	1	yes	characteristic
546	#124	—	2	1	no	—
547	#124	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
548	C₂²⋊Q₈	—	2	1	no	—
549	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
550	#121	—	2	1	no	—
551	#121	—	2	1	no	—
552	#121	C₂²×C₃×C₅	1	1	yes	characteristic
553	#121	C₂²×C₃×C₅	1	1	yes	characteristic
554	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
555	#120	—	2	1	no	—
556	#120	—	2	1	no	—
557	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
558	C₄×D₄	—	2	1	no	—
559	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
560	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
561	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
562	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
563	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
564	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
565	#102	C₂²×C₃×C₅	1	1	yes	characteristic
566	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
567	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
568	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
569	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
570	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
571	#97	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
572	C₂×C₃×C₅	—	2	2	no	—
573	C₂×C₃×C₅	—	4	1	no	—
574	C₂×C₃×C₅	—	4	2	no	—
575	C₂×C₃×C₅	—	8	1	no	—
576	C₂×C₃×C₅	—	8	1	no	—
577	C₂×C₃×C₅	—	8	1	no	—
578	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
579	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
580	C₂×C₃×C₅	#577	1	1	yes	characteristic
581	C₂³×C₃	—	2	1	no	—
582	C₂³×C₃	—	2	1	no	—
583	C₂³×C₃	—	2	1	no	—
584	C₂³×C₃	—	2	1	no	—
585	C₂³×C₃	—	4	2	no	—
586	C₂³×C₃	—	4	2	no	—
587	C₂³×C₃	—	4	2	no	—
588	C₂³×C₃	—	4	2	no	—
589	C₂³×C₃	—	8	1	no	—
590	C₂³×C₃	—	8	1	no	—
591	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
592	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
593	C₃×Q₈	—	2	1	no	—
594	C₃×Q₈	—	2	1	no	—
595	C₃×Q₈	—	2	1	no	—
596	C₃×Q₈	—	4	2	no	—
597	C₃×Q₈	C₂×C₅×D₄	1	2	yes	complemented
598	C₃×D₄	—	2	2	no	—
599	C₃×D₄	—	2	1	no	—
600	C₃×D₄	—	2	1	no	—
601	C₃×D₄	—	2	1	no	—
602	C₃×D₄	—	2	1	no	—
603	C₃×D₄	—	2	1	no	—
604	C₃×D₄	—	2	1	no	—
605	C₃×D₄	—	2	1	no	—
606	C₃×D₄	—	4	2	no	—
607	C₃×D₄	—	4	2	no	—
608	C₃×D₄	—	4	2	no	—
609	C₃×D₄	—	4	2	no	—
610	C₃×D₄	—	4	2	no	—
611	C₃×D₄	—	4	2	no	—
612	C₃×D₄	—	4	2	no	—
613	C₃×D₄	—	8	1	no	—
614	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
615	C₂×C₃×C₄	—	2	1	no	—
616	C₂×C₃×C₄	—	2	1	no	—
617	C₂×C₃×C₄	—	2	1	no	—
618	C₂×C₃×C₄	—	2	1	no	—
619	C₂×C₃×C₄	—	2	1	no	—
620	C₂×C₃×C₄	—	2	1	no	—
621	C₂×C₃×C₄	—	2	1	no	—
622	C₂×C₃×C₄	—	2	1	no	—
623	C₂×C₃×C₄	—	4	2	no	—
624	C₂×C₃×C₄	—	4	2	no	—
625	C₂×C₃×C₄	—	4	2	no	—
626	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
627	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
628	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
629	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
630	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
631	C₃×C₈	—	2	1	no	—
632	C₃×C₈	—	2	1	no	—
633	C₃×C₈	—	2	1	no	—
634	C₃×C₈	C₂×C₅×D₄	1	2	yes	complemented
635	C₂²×C₅	—	2	1	no	—
636	C₂²×C₅	—	2	1	no	—
637	C₂²×C₅	—	2	1	no	—
638	C₂²×C₅	—	2	1	no	—
639	C₂²×C₅	—	2	1	no	—
640	C₂²×C₅	—	2	2	no	—
641	C₂²×C₅	—	4	1	no	—
642	C₂²×C₅	—	4	1	no	—
643	C₂²×C₅	—	4	1	no	—
644	C₂²×C₅	—	4	1	no	—
645	C₂²×C₅	—	4	1	no	—
646	C₂²×C₅	—	4	1	no	—
647	C₂²×C₅	—	4	1	no	—
648	C₂²×C₅	—	4	1	no	—
649	C₂²×C₅	—	4	1	no	—
650	C₂²×C₅	—	4	1	no	—
651	C₂²×C₅	—	4	1	no	—
652	C₂²×C₅	—	8	4	no	—
653	C₂²×C₅	—	8	4	no	—
654	C₂²×C₅	C₃×AGL(1,ℤ/8)	1	2	yes	complemented
655	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
656	C₄×C₅	—	2	1	no	—
657	C₄×C₅	—	2	1	no	—
658	C₄×C₅	—	2	1	no	—
659	C₄×C₅	—	2	1	no	—
660	C₄×C₅	—	2	2	no	—
661	C₄×C₅	—	4	1	no	—
662	C₄×C₅	—	4	1	no	—
663	C₄×C₅	—	4	1	no	—
664	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
665	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
666	C₂⁴	—	2	1	no	—
667	C₂⁴	—	2	1	no	—
668	#41	—	2	2	no	—
669	#41	—	4	1	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	4	1	no	—
673	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
674	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	1	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	4	1	no	—
686	C₂×D₄	—	4	1	no	—
687	C₂×D₄	—	4	4	no	—
688	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
689	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
690	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
691	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
692	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
693	C₂²×C₄	—	2	1	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	1	no	—
696	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
697	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
698	SD₁₆	—	2	2	no	—
699	SD₁₆	—	2	2	no	—
700	SD₁₆	—	2	2	no	—
701	SD₁₆	—	2	2	no	—
702	SD₁₆	—	4	1	no	—
703	SD₁₆	C₃×C₅×D₄	1	4	yes	complemented
704	D₈	—	2	2	no	—
705	D₈	—	2	2	no	—
706	D₈	—	4	1	no	—
707	M₁₆	—	2	2	no	—
708	C₂×C₈	—	2	2	no	—
709	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
710	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
711	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
712	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
716	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
717	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
718	C₂²⋊C₄	—	2	1	no	—
719	C₂²⋊C₄	—	2	1	no	—
720	C₂²⋊C₄	—	2	1	no	—
721	C₂²⋊C₄	—	2	1	no	—
722	C₂²⋊C₄	—	2	1	no	—
723	C₂²⋊C₄	—	2	1	no	—
724	C₂²⋊C₄	—	2	1	no	—
725	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
726	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
727	C₄²	—	2	1	no	—
728	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
729	C₃×C₅	#3265	1	1	yes	characteristic, direct product factor, Hall
730	C₂²×C₃	—	2	1	no	—
731	C₂²×C₃	—	2	1	no	—
732	C₂²×C₃	—	2	1	no	—
733	C₂²×C₃	—	2	2	no	—
734	C₂²×C₃	—	2	1	no	—
735	C₂²×C₃	—	2	1	no	—
736	C₂²×C₃	—	4	1	no	—
737	C₂²×C₃	—	4	1	no	—
738	C₂²×C₃	—	4	1	no	—
739	C₂²×C₃	—	4	1	no	—
740	C₂²×C₃	—	4	1	no	—
741	C₂²×C₃	—	4	1	no	—
742	C₂²×C₃	—	4	1	no	—
743	C₂²×C₃	—	4	1	no	—
744	C₂²×C₃	—	4	1	no	—
745	C₂²×C₃	—	4	1	no	—
746	C₂²×C₃	—	4	1	no	—
747	C₂²×C₃	—	8	4	no	—
748	C₂²×C₃	—	8	4	no	—
749	C₂²×C₃	C₅×AGL(1,ℤ/8)	1	2	yes	complemented
750	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
751	C₃×C₄	—	2	1	no	—
752	C₃×C₄	—	2	1	no	—
753	C₃×C₄	—	2	2	no	—
754	C₃×C₄	—	2	1	no	—
755	C₃×C₄	—	2	1	no	—
756	C₃×C₄	—	4	1	no	—
757	C₃×C₄	—	4	1	no	—
758	C₃×C₄	—	4	1	no	—
759	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
760	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
761	C₂×C₅	—	2	2	no	—
762	C₂×C₅	—	4	1	no	—
763	C₂×C₅	—	4	2	no	—
764	C₂×C₅	—	8	1	no	—
765	C₂×C₅	—	8	1	no	—
766	C₂×C₅	—	8	1	no	—
767	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
768	C₂×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
769	C₂×C₅	C₃×#577	1	1	yes	characteristic
770	C₂³	—	2	1	no	—
771	C₂³	—	2	1	no	—
772	C₂³	—	2	1	no	—
773	C₂³	—	2	1	no	—
774	C₂³	—	4	2	no	—
775	C₂³	—	4	2	no	—
776	C₂³	—	4	2	no	—
777	C₂³	—	4	2	no	—
778	C₂³	—	8	1	no	—
779	C₂³	—	8	1	no	—
780	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
781	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
782	Q₈	—	2	1	no	—
783	Q₈	—	2	1	no	—
784	Q₈	—	2	1	no	—
785	Q₈	—	4	2	no	—
786	Q₈	C₂×C₃×C₅×D₄	1	2	yes	complemented
787	D₄	—	2	2	no	—
788	D₄	—	2	1	no	—
789	D₄	—	2	1	no	—
790	D₄	—	2	1	no	—
791	D₄	—	2	1	no	—
792	D₄	—	2	1	no	—
793	D₄	—	2	1	no	—
794	D₄	—	2	1	no	—
795	D₄	—	4	2	no	—
796	D₄	—	4	2	no	—
797	D₄	—	4	2	no	—
798	D₄	—	4	2	no	—
799	D₄	—	4	2	no	—
800	D₄	—	4	2	no	—
801	D₄	—	4	2	no	—
802	D₄	—	8	1	no	—
803	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	1	no	—
806	C₂×C₄	—	2	1	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	1	no	—
812	C₂×C₄	—	4	2	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
816	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
817	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
818	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
819	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
820	C₈	—	2	1	no	—
821	C₈	—	2	1	no	—
822	C₈	—	2	1	no	—
823	C₈	C₂×C₃×C₅×D₄	1	2	yes	complemented
824	C₂×C₃	—	2	2	no	—
825	C₂×C₃	—	4	1	no	—
826	C₂×C₃	—	4	2	no	—
827	C₂×C₃	—	8	1	no	—
828	C₂×C₃	—	8	1	no	—
829	C₂×C₃	—	8	1	no	—
830	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
831	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
832	C₂×C₃	C₅×#577	1	1	yes	characteristic
833	C₅	C₃×#3265	1	1	yes	characteristic, direct product factor, Sylow
834	C₂²	—	2	1	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	1	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	1	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	4	1	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	1	no	—
849	C₂²	—	4	1	no	—
850	C₂²	—	4	1	no	—
851	C₂²	—	8	4	no	—
852	C₂²	—	8	4	no	—
853	C₂²	C₃×C₅×AGL(1,ℤ/8)	1	2	yes	complemented
854	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	2	no	—
858	C₄	—	2	1	no	—
859	C₄	—	2	1	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	1	no	—
863	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
864	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
865	C₃	C₅×#3265	1	1	yes	characteristic, direct product factor, Sylow
866	C₂	—	2	2	no	—
867	C₂	—	4	1	no	—
868	C₂	—	4	2	no	—
869	C₂	—	8	1	no	—
870	C₂	—	8	1	no	—
871	C₂	—	8	1	no	—
872	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
873	C₂	C₂×C₃×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
874	C₂	C₃×C₅×#577	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. C₂²×C₃×C₅×SD₁₆	C₂	semidirect
3. C₃×C₅×#548	C₂	semidirect
4. C₃×C₅×D₄²	C₂	semidirect
5. C₃×C₅×#496	C₂	semidirect
6. C₃×C₅×#468	C₂	semidirect
7. C₃×C₅×#466	C₂	semidirect
8. C₃×C₅×#463	C₂	semidirect
9. C₃×C₅×#460	C₂	semidirect
10. C₃×C₅×#450	C₂	semidirect
11. C₃×C₅×#449	C₂	semidirect
12. C₃×C₅×#448	C₂	semidirect
13. C₃×C₅×#447	C₂	semidirect
14. C₃×C₅×#440	C₂	semidirect
15. C₃×C₅×#435	C₂	semidirect
16. C₅×#3265	C₃	direct (N × H)
17. C₂×C₃×C₅×#41	C₂²	semidirect
18. C₂²×C₃×C₅×Q₈	C₂²	semidirect
26. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
27. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
28. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
29. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
31. C₂×C₃×C₅×D₈	C₂²	semidirect
32. C₂×C₃×C₅×D₈	C₂²	semidirect
33. C₂×C₃×C₅×M₁₆	C₂²	semidirect
34. C₂²×C₃×C₅×C₈	C₂²	semidirect
37. C₃×C₅×#124	C₂²	semidirect
39. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
44. C₃×C₅×#121	C₂²	semidirect
47. 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
56. C₃×C₅×#102	C₂²	semidirect
57. C₃×C₅×#102	C₂²	semidirect
58. C₃×C₅×#102	C₂²	semidirect
59. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
60. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
61. C₃×C₅×#97	C₂²	semidirect
62. C₃×#3265	C₅	direct (N × H)
63. C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
64. C₂²×C₅×SD₁₆	C₂×C₃	semidirect
65. C₅×#548	C₂×C₃	semidirect
66. C₅×D₄²	C₂×C₃	semidirect
67. C₅×#496	C₂×C₃	semidirect
68. C₅×#468	C₂×C₃	semidirect
69. C₅×#466	C₂×C₃	semidirect
70. C₅×#463	C₂×C₃	semidirect
71. C₅×#460	C₂×C₃	semidirect
72. C₅×#450	C₂×C₃	semidirect
73. C₅×#449	C₂×C₃	semidirect
74. C₅×#448	C₂×C₃	semidirect
75. C₅×#447	C₂×C₃	semidirect
76. C₅×#440	C₂×C₃	semidirect
77. C₅×#435	C₂×C₃	semidirect
115. C₃×C₅×SD₁₆	D₄	semidirect
141. C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
142. C₂²×C₃×SD₁₆	C₂×C₅	semidirect
143. C₃×#548	C₂×C₅	semidirect
144. C₃×D₄²	C₂×C₅	semidirect
145. C₃×#496	C₂×C₅	semidirect
146. C₃×#468	C₂×C₅	semidirect
147. C₃×#466	C₂×C₅	semidirect
148. C₃×#463	C₂×C₅	semidirect
149. C₃×#460	C₂×C₅	semidirect
150. C₃×#450	C₂×C₅	semidirect
151. C₃×#449	C₂×C₅	semidirect
152. C₃×#448	C₂×C₅	semidirect
153. C₃×#447	C₂×C₅	semidirect
154. C₃×#440	C₂×C₅	semidirect
155. C₃×#435	C₂×C₅	semidirect
156. C₂×C₅×#41	C₂²×C₃	semidirect
157. C₂²×C₅×Q₈	C₂²×C₃	semidirect
165. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
166. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
167. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
168. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
170. C₂×C₅×D₈	C₂²×C₃	semidirect
171. C₂×C₅×D₈	C₂²×C₃	semidirect
172. C₂×C₅×M₁₆	C₂²×C₃	semidirect
173. C₂²×C₅×C₈	C₂²×C₃	semidirect
176. C₅×#124	C₂²×C₃	semidirect
178. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
183. C₅×#121	C₂²×C₃	semidirect
186. C₄×C₅×Q₈	C₂²×C₃	semidirect
190. C₅×#107	C₂²×C₃	semidirect
191. C₅×C₄⋊C₈	C₂²×C₃	semidirect
192. C₅×#103	C₂²×C₃	semidirect
193. C₅×#103	C₂²×C₃	semidirect
195. C₅×#102	C₂²×C₃	semidirect
196. C₅×#102	C₂²×C₃	semidirect
197. C₅×#102	C₂²×C₃	semidirect
198. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
199. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
200. C₅×#97	C₂²×C₃	semidirect
201. #3265	C₃×C₅	direct (N × H)
218. C₃×C₅×Q₈	C₂×D₄	semidirect
255. C₃×C₅×C₈	C₂×D₄	semidirect
256. C₂×C₃×#41	C₂²×C₅	semidirect
257. C₂²×C₃×Q₈	C₂²×C₅	semidirect
265. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
266. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
267. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
268. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
270. C₂×C₃×D₈	C₂²×C₅	semidirect
271. C₂×C₃×D₈	C₂²×C₅	semidirect
272. C₂×C₃×M₁₆	C₂²×C₅	semidirect
273. C₂²×C₃×C₈	C₂²×C₅	semidirect
276. C₃×#124	C₂²×C₅	semidirect
278. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
283. C₃×#121	C₂²×C₅	semidirect
286. C₃×C₄×Q₈	C₂²×C₅	semidirect
290. C₃×#107	C₂²×C₅	semidirect
291. C₃×C₄⋊C₈	C₂²×C₅	semidirect
292. C₃×#103	C₂²×C₅	semidirect
293. C₃×#103	C₂²×C₅	semidirect
295. C₃×#102	C₂²×C₅	semidirect
296. C₃×#102	C₂²×C₅	semidirect
297. C₃×#102	C₂²×C₅	semidirect
298. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
299. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
300. C₃×#97	C₂²×C₅	semidirect
338. C₅×SD₁₆	C₃×D₄	semidirect
364. C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	semidirect
365. C₂²×SD₁₆	C₂×C₃×C₅	semidirect
366. #548	C₂×C₃×C₅	semidirect
367. D₄²	C₂×C₃×C₅	semidirect
368. #496	C₂×C₃×C₅	semidirect
369. #468	C₂×C₃×C₅	semidirect
370. #466	C₂×C₃×C₅	semidirect
371. #463	C₂×C₃×C₅	semidirect
372. #460	C₂×C₃×C₅	semidirect
373. #450	C₂×C₃×C₅	semidirect
374. #449	C₂×C₃×C₅	semidirect
375. #448	C₂×C₃×C₅	semidirect
376. #447	C₂×C₃×C₅	semidirect
377. #440	C₂×C₃×C₅	semidirect
378. #435	C₂×C₃×C₅	semidirect
398. C₂²×C₃×C₅	AGL(1,ℤ/8)	semidirect
447. C₃×SD₁₆	C₅×D₄	semidirect
489. C₅×Q₈	C₂×C₃×D₄	semidirect
526. C₅×C₈	C₂×C₃×D₄	semidirect
527. C₂×#41	C₂²×C₃×C₅	semidirect
528. C₂²×Q₈	C₂²×C₃×C₅	semidirect
536. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
537. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
538. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
539. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
541. C₂×D₈	C₂²×C₃×C₅	semidirect
542. C₂×D₈	C₂²×C₃×C₅	semidirect
543. C₂×M₁₆	C₂²×C₃×C₅	semidirect
544. C₂²×C₈	C₂²×C₃×C₅	semidirect
547. #124	C₂²×C₃×C₅	semidirect
549. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
554. #121	C₂²×C₃×C₅	semidirect
557. C₄×Q₈	C₂²×C₃×C₅	semidirect
561. #107	C₂²×C₃×C₅	semidirect
562. C₄⋊C₈	C₂²×C₃×C₅	semidirect
563. #103	C₂²×C₃×C₅	semidirect
564. #103	C₂²×C₃×C₅	semidirect
566. #102	C₂²×C₃×C₅	semidirect
567. #102	C₂²×C₃×C₅	semidirect
568. #102	C₂²×C₃×C₅	semidirect
569. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
570. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
571. #97	C₂²×C₃×C₅	semidirect
597. C₃×Q₈	C₂×C₅×D₄	semidirect
634. C₃×C₈	C₂×C₅×D₄	semidirect
654. C₂²×C₅	C₃×AGL(1,ℤ/8)	semidirect
703. SD₁₆	C₃×C₅×D₄	semidirect
729. C₃×C₅	#3265	direct (N × H)
749. C₂²×C₃	C₅×AGL(1,ℤ/8)	semidirect
786. Q₈	C₂×C₃×C₅×D₄	semidirect
823. C₈	C₂×C₃×C₅×D₄	semidirect
833. C₅	C₃×#3265	direct (N × H)
853. C₂²	C₃×C₅×AGL(1,ℤ/8)	semidirect
865. C₃	C₅×#3265	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
C₂²×C₃×C₅×SD₁₆	2
C₃×C₅×#548	2
C₃×C₅×D₄²	2
C₃×C₅×#496	2
C₃×C₅×#468	2
C₃×C₅×#466	2
C₃×C₅×#463	2
C₃×C₅×#460	2
C₃×C₅×#450	2
C₃×C₅×#449	2
C₃×C₅×#448	2
C₃×C₅×#447	2
C₃×C₅×#440	2
C₃×C₅×#435	2
C₅×#3265	3
C₃×#3265	5

Subgroups — C3×C5×#3265 #14276299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3265 #14276299