Subgroups — C₅×D₃×#468 #14427885

Order 1920.

1088 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×D₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×D₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₃×#121	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#468	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5174	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5134	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5049	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5042	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4886	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×D₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4812	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×D₃×#103	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#4780	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×D₃×#102	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#468	—	3	1	no	maximal, Hall
17	C₂×C₅×D₃×Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×D₃×D₄	—	2	1	no	—
19	C₂×C₅×D₃×D₄	C₂²	1	1	yes	characteristic
20	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₅×#121	C₂²	1	1	yes	characteristic
25	C₅×#946	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×#215	C₂²	1	1	yes	characteristic, complemented
27	C₅×#939	—	2	1	no	—
28	C₅×#938	C₂²	1	1	yes	characteristic
29	C₂×C₅×#214	C₂²	1	1	yes	characteristic, complemented
30	C₅×#930	C₂²	1	1	yes	characteristic
31	C₅×#924	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₅×#208	C₂²	1	1	yes	characteristic, complemented
33	C₅×D₃×SD₁₆	—	2	4	no	—
34	C₅×D₃×M₁₆	—	2	4	no	—
35	C₂×C₅×#204	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
39	C₂×C₅×D₃×C₈	C₂²	1	1	yes	characteristic
40	C₅×#897	C₂²	1	1	yes	characteristic, complemented
41	C₅×#896	—	2	1	no	—
42	C₅×#895	C₂²	1	1	yes	characteristic
43	C₅×D₃×C₄⋊C₄	—	2	1	no	—
44	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₅×D₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₅×#884	—	2	1	no	—
47	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
48	C₅×D₃×C₂²⋊C₄	—	2	1	no	—
49	C₅×#878	—	2	1	no	—
50	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
51	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
53	C₅×#835	C₂²	1	1	yes	characteristic, complemented
54	C₅×#832	C₂²	1	1	yes	characteristic, complemented
55	C₅×#821	C₂²	1	1	yes	characteristic, complemented
56	C₅×#818	C₂²	1	1	yes	characteristic, complemented
57	C₅×#816	C₂²	1	1	yes	characteristic, complemented
58	C₅×#810	C₂²	1	1	yes	characteristic, complemented
59	C₅×#809	C₂²	1	1	yes	characteristic, complemented
60	C₅×#807	C₂²	1	1	yes	characteristic, complemented
61	C₅×#807	C₂²	1	1	yes	characteristic, complemented
62	D₃×#468	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
63	C₂²×C₅×SD₁₆	—	3	1	no	—
64	C₂²×C₅×M₁₆	—	3	1	no	—
65	C₂×C₅×C₂²⋊Q₈	—	3	1	no	—
66	C₂×C₅×#121	—	3	1	no	—
67	C₅×#468	—	3	1	no	—
68	C₅×#468	—	3	1	no	—
69	C₅×#468	—	3	1	no	—
70	C₅×#468	—	3	1	no	—
71	C₅×#468	—	3	1	no	—
72	C₅×#468	—	3	1	no	—
73	C₅×#468	—	3	1	no	—
74	C₅×#468	D₃	1	1	yes	characteristic, direct product factor
75	C₂×C₅×#107	—	3	1	no	—
76	C₂×C₅×#103	—	3	1	no	—
77	C₂×C₅×#102	—	3	1	no	—
78	C₂³×C₅×D₃	—	2	1	no	—
79	C₂³×C₅×D₃	D₄	1	1	yes	characteristic
80	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₅×D₄	—	2	1	no	—
82	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
83	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
84	C₂×C₅×#67	—	2	1	no	—
85	C₂×C₅×#67	—	2	1	no	—
86	C₂×C₅×#67	—	2	1	no	—
87	C₂²×C₅×Dic₃	D₄	1	1	yes	characteristic
88	C₅×D₃×Q₈	—	2	2	no	—
89	C₅×D₃×Q₈	—	2	2	no	—
90	C₅×D₃×D₄	—	2	2	no	—
91	C₅×D₃×D₄	—	2	2	no	—
92	C₅×D₃×D₄	—	4	4	no	—
93	C₂×C₅×D₁₂	—	2	1	no	—
94	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
95	C₂×C₄×C₅×D₃	—	2	2	no	—
96	C₂×C₄×C₅×D₃	—	2	2	no	—
97	C₂×C₄×C₅×D₃	—	2	1	no	—
98	C₂×C₄×C₅×D₃	—	2	1	no	—
99	C₂×C₄×C₅×D₃	—	2	1	no	—
100	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
101	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
102	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
103	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
104	C₂×C₅×Dic₆	—	2	1	no	—
105	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
106	C₃×C₅×SD₁₆	—	2	2	no	—
107	C₃×C₅×M₁₆	—	2	2	no	—
108	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
109	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
110	C₃×C₅×C₄⋊C₄	—	2	1	no	—
111	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
114	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
115	C₅×#217	—	2	1	no	—
116	C₅×#217	—	2	1	no	—
117	C₅×#215	—	2	2	no	—
118	C₅×#214	—	2	2	no	—
119	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
120	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
121	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
122	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
123	C₅×C₄⋊Dic₃	—	2	1	no	—
124	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
125	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
126	C₅×Dic₃⋊C₄	—	2	1	no	—
127	C₅×Dic₃⋊C₄	—	2	1	no	—
128	C₅×Dic₃⋊C₄	—	2	1	no	—
129	C₅×Dic₃⋊C₄	—	2	1	no	—
130	C₅×#208	—	2	2	no	—
131	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
132	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
133	C₅×#204	—	2	2	no	—
134	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
135	C₅×ΓL(1,𝔽₂₅)	—	2	2	no	—
136	C₅×D₃×C₈	—	2	2	no	—
137	C₅×D₃×C₈	D₄	1	4	yes	complemented
138	C₂×D₃×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
139	C₂×D₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
140	D₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
141	D₃×#121	C₂×C₅	1	1	yes	characteristic
142	C₃×#468	C₂×C₅	1	1	yes	characteristic, complemented
143	#5174	C₂×C₅	1	1	yes	characteristic, complemented
144	#5134	C₂×C₅	1	1	yes	characteristic, complemented
145	#5049	C₂×C₅	1	1	yes	characteristic, complemented
146	#5042	C₂×C₅	1	1	yes	characteristic, complemented
147	#4886	C₂×C₅	1	1	yes	characteristic, complemented
148	D₃×#107	C₂×C₅	1	1	yes	characteristic, complemented
149	#4812	C₂×C₅	1	1	yes	characteristic, complemented
150	D₃×#103	C₂×C₅	1	1	yes	characteristic, complemented
151	#4780	C₂×C₅	1	1	yes	characteristic, complemented
152	D₃×#102	C₂×C₅	1	1	yes	characteristic, complemented
153	C₂²×C₅×Q₈	—	3	1	no	—
154	C₂²×C₅×D₄	—	3	1	no	—
155	C₂²×C₅×D₄	—	6	1	no	—
156	C₂³×C₄×C₅	—	3	1	no	—
157	C₂×C₅×SD₁₆	—	3	1	no	—
158	C₂×C₅×SD₁₆	—	3	1	no	—
159	C₂×C₅×SD₁₆	—	3	1	no	—
160	C₂×C₅×SD₁₆	—	6	4	no	—
161	C₂×C₅×SD₁₆	C₂×D₃	1	1	yes	characteristic, complemented
162	C₂×C₅×M₁₆	—	3	1	no	—
163	C₂×C₅×M₁₆	—	3	1	no	—
164	C₂×C₅×M₁₆	—	3	1	no	—
165	C₂×C₅×M₁₆	—	6	4	no	—
166	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic, complemented
167	C₂²×C₅×C₈	—	3	1	no	—
168	C₂²×C₅×C₈	—	3	1	no	—
169	C₅×C₂²⋊Q₈	—	3	1	no	—
170	C₅×C₂²⋊Q₈	—	3	1	no	—
171	C₅×C₂²⋊Q₈	—	3	1	no	—
172	C₅×C₂²⋊Q₈	—	6	1	no	—
173	C₅×C₂²⋊Q₈	—	6	1	no	—
174	C₅×C₂²⋊Q₈	C₂×D₃	1	1	yes	characteristic, complemented
175	C₅×#121	—	3	1	no	—
176	C₅×#121	—	3	1	no	—
177	C₅×#121	—	3	1	no	—
178	C₅×#121	—	6	1	no	—
179	C₅×#121	—	6	1	no	—
180	C₅×#121	C₂×D₃	1	1	yes	characteristic
181	C₂×C₅×C₄⋊C₄	—	3	1	no	—
182	C₂×C₅×C₄⋊C₄	—	3	1	no	—
183	C₂×C₅×C₄⋊C₄	—	6	1	no	—
184	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
185	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
186	C₅×#107	—	3	1	no	—
187	C₅×#107	—	3	1	no	—
188	C₅×#107	—	3	1	no	—
189	C₅×#107	C₂×D₃	1	1	yes	characteristic, complemented
190	C₅×#103	—	3	1	no	—
191	C₅×#103	—	3	1	no	—
192	C₅×#103	—	3	1	no	—
193	C₅×#103	C₂×D₃	1	1	yes	characteristic, complemented
194	C₅×#102	—	3	1	no	—
195	C₅×#102	—	3	1	no	—
196	C₅×#102	—	3	1	no	—
197	C₅×#102	C₂×D₃	1	1	yes	characteristic, complemented
198	C₂×#468	—	3	1	no	Sylow
199	C₂³×C₃×C₅	—	2	1	no	—
200	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₅×D₃	—	2	2	no	—
202	C₂²×C₅×D₃	—	2	2	no	—
203	C₂²×C₅×D₃	—	2	2	no	—
204	C₂²×C₅×D₃	—	2	1	no	—
205	C₂²×C₅×D₃	—	4	2	no	—
206	C₂²×C₅×D₃	—	4	2	no	—
207	C₂²×C₅×D₃	—	4	2	no	—
208	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
210	C₃×C₅×Q₈	—	2	1	no	—
211	C₃×C₅×Q₈	—	2	1	no	—
212	C₃×C₅×D₄	—	2	1	no	—
213	C₃×C₅×D₄	—	2	1	no	—
214	C₃×C₅×D₄	—	4	2	no	—
215	C₂×C₃×C₄×C₅	—	2	1	no	—
216	C₂×C₃×C₄×C₅	—	2	1	no	—
217	C₂×C₃×C₄×C₅	—	2	1	no	—
218	C₂×C₃×C₄×C₅	—	2	1	no	—
219	C₂×C₃×C₄×C₅	—	2	1	no	—
220	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
221	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
222	C₅×#67	—	4	2	no	—
223	C₅×#67	—	4	2	no	—
224	C₅×#67	—	4	2	no	—
225	C₂×C₅×Dic₃	—	2	2	no	—
226	C₂×C₅×Dic₃	—	2	1	no	—
227	C₂×C₅×Dic₃	—	2	1	no	—
228	C₂×C₅×Dic₃	—	2	1	no	—
229	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
230	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
231	C₅×D₁₂	—	2	1	no	—
232	C₅×D₁₂	—	2	1	no	—
233	C₅×D₁₂	—	4	2	no	—
234	C₄×C₅×D₃	—	2	2	no	—
235	C₄×C₅×D₃	—	2	1	no	—
236	C₄×C₅×D₃	—	2	1	no	—
237	C₄×C₅×D₃	—	2	2	no	—
238	C₄×C₅×D₃	—	4	2	no	—
239	C₄×C₅×D₃	—	4	2	no	—
240	C₄×C₅×D₃	—	4	2	no	—
241	C₄×C₅×D₃	C₂×D₄	1	2	yes	—
242	C₄×C₅×D₃	#41	1	2	yes	—
243	C₅×Dic₆	—	2	1	no	—
244	C₅×Dic₆	—	2	1	no	—
245	C₅×Dic₆	—	4	2	no	—
246	C₃×C₅×C₈	—	2	1	no	—
247	C₃×C₅×C₈	C₂×D₄	1	2	yes	complemented
248	C₅×C₃⋊C₈	—	2	1	no	—
249	C₅×C₃⋊C₈	C₂×D₄	1	2	yes	complemented
250	C₂×D₃×Q₈	C₂²×C₅	1	1	yes	characteristic
251	C₂×D₃×D₄	—	2	1	no	—
252	C₂×D₃×D₄	C₂²×C₅	1	1	yes	characteristic
253	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
254	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
255	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
256	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
257	C₃×#121	C₂²×C₅	1	1	yes	characteristic
258	#946	C₂²×C₅	1	1	yes	characteristic, complemented
259	C₂×#215	C₂²×C₅	1	1	yes	characteristic, complemented
260	#939	—	2	1	no	—
261	#938	C₂²×C₅	1	1	yes	characteristic
262	C₂×#214	C₂²×C₅	1	1	yes	characteristic, complemented
263	#930	C₂²×C₅	1	1	yes	characteristic
264	#924	C₂²×C₅	1	1	yes	characteristic, complemented
265	C₂×#208	C₂²×C₅	1	1	yes	characteristic, complemented
266	D₃×SD₁₆	—	2	4	no	—
267	D₃×M₁₆	—	2	4	no	—
268	C₂×#204	C₂²×C₅	1	1	yes	characteristic, complemented
269	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic, complemented
270	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	1	yes	characteristic, complemented
271	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
272	C₂×D₃×C₈	C₂²×C₅	1	1	yes	characteristic
273	#897	C₂²×C₅	1	1	yes	characteristic, complemented
274	#896	—	2	1	no	—
275	#895	C₂²×C₅	1	1	yes	characteristic
276	D₃×C₄⋊C₄	—	2	1	no	—
277	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
278	D₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
279	#884	—	2	1	no	—
280	D₃×C₂²⋊C₄	—	2	1	no	—
281	D₃×C₂²⋊C₄	—	2	1	no	—
282	#878	—	2	1	no	—
283	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
284	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
285	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
286	#835	C₂²×C₅	1	1	yes	characteristic, complemented
287	#832	C₂²×C₅	1	1	yes	characteristic, complemented
288	#821	C₂²×C₅	1	1	yes	characteristic, complemented
289	#818	C₂²×C₅	1	1	yes	characteristic, complemented
290	#816	C₂²×C₅	1	1	yes	characteristic, complemented
291	#810	C₂²×C₅	1	1	yes	characteristic, complemented
292	#809	C₂²×C₅	1	1	yes	characteristic, complemented
293	#807	C₂²×C₅	1	1	yes	characteristic, complemented
294	#807	C₂²×C₅	1	1	yes	characteristic, complemented
295	C₂⁴×C₅	—	3	1	no	—
296	C₂⁴×C₅	—	6	1	no	—
297	C₂×C₅×Q₈	—	3	1	no	—
298	C₂×C₅×Q₈	—	6	1	no	—
299	C₂×C₅×Q₈	—	6	2	no	—
300	C₂×C₅×Q₈	—	6	2	no	—
301	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
302	C₂×C₅×D₄	—	2	1	no	—
303	C₂×C₅×D₄	—	3	1	no	—
304	C₂×C₅×D₄	—	6	1	no	—
305	C₂×C₅×D₄	—	6	2	no	—
306	C₂×C₅×D₄	—	6	2	no	—
307	C₂×C₅×D₄	—	6	1	no	—
308	C₂×C₅×D₄	—	6	1	no	—
309	C₂×C₅×D₄	—	6	1	no	—
310	C₂×C₅×D₄	—	12	4	no	—
311	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
312	C₂²×C₄×C₅	—	3	1	no	—
313	C₂²×C₄×C₅	—	3	1	no	—
314	C₂²×C₄×C₅	—	3	1	no	—
315	C₂²×C₄×C₅	—	3	1	no	—
316	C₂²×C₄×C₅	—	3	1	no	—
317	C₂²×C₄×C₅	—	6	2	no	—
318	C₂²×C₄×C₅	—	6	2	no	—
319	C₂²×C₄×C₅	—	6	1	no	—
320	C₂²×C₄×C₅	—	6	1	no	—
321	C₂²×C₄×C₅	—	6	1	no	—
322	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
323	C₅×SD₁₆	—	2	2	no	—
324	C₅×SD₁₆	—	6	2	no	—
325	C₅×SD₁₆	—	6	2	no	—
326	C₅×SD₁₆	—	6	2	no	—
327	C₅×M₁₆	—	2	2	no	—
328	C₅×M₁₆	—	6	2	no	—
329	C₅×M₁₆	—	6	2	no	—
330	C₅×M₁₆	—	6	2	no	—
331	C₂×C₅×C₈	—	3	1	no	—
332	C₂×C₅×C₈	—	3	4	no	—
333	C₂×C₅×C₈	—	3	1	no	—
334	C₂×C₅×C₈	—	6	2	no	—
335	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
336	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
337	C₅×C₄⋊C₄	—	2	1	no	—
338	C₅×C₄⋊C₄	—	3	1	no	—
339	C₅×C₄⋊C₄	—	3	1	no	—
340	C₅×C₄⋊C₄	—	6	1	no	—
341	C₅×C₄⋊C₄	—	6	1	no	—
342	C₅×C₄⋊C₄	—	6	1	no	—
343	C₅×C₄⋊C₄	—	6	1	no	—
344	C₅×C₄⋊C₄	—	6	1	no	—
345	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
346	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
347	C₅×C₂²⋊C₄	—	2	1	no	—
348	C₅×C₂²⋊C₄	—	2	1	no	—
349	C₅×C₂²⋊C₄	—	6	1	no	—
350	C₅×C₂²⋊C₄	—	6	1	no	—
351	C₅×C₂²⋊C₄	—	6	1	no	—
352	C₅×C₂²⋊C₄	—	6	1	no	—
353	C₅×C₂²⋊C₄	—	6	1	no	—
354	C₅×C₂²⋊C₄	—	6	1	no	—
355	C₂²×SD₁₆	—	3	1	no	—
356	C₂²×M₁₆	—	3	1	no	—
357	C₂×C₂²⋊Q₈	—	3	1	no	—
358	C₂×#121	—	3	1	no	—
359	#468	—	3	1	no	—
360	#468	—	3	1	no	—
361	#468	—	3	1	no	—
362	#468	—	3	1	no	—
363	#468	—	3	1	no	—
364	#468	—	3	1	no	—
365	#468	—	3	1	no	—
366	#468	C₅×D₃	1	1	yes	characteristic, direct product factor
367	C₂×#107	—	3	1	no	—
368	C₂×#103	—	3	1	no	—
369	C₂×#102	—	3	1	no	—
370	C₂²×C₃×C₅	—	2	1	no	—
371	C₂²×C₃×C₅	—	2	1	no	—
372	C₂²×C₃×C₅	—	2	1	no	—
373	C₂²×C₃×C₅	—	4	1	no	—
374	C₂²×C₃×C₅	—	4	1	no	—
375	C₂²×C₃×C₅	—	4	1	no	—
376	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₅×D₃	—	2	1	no	—
378	C₂×C₅×D₃	—	2	1	no	—
379	C₂×C₅×D₃	—	2	1	no	—
380	C₂×C₅×D₃	—	4	4	no	—
381	C₂×C₅×D₃	—	4	1	no	—
382	C₂×C₅×D₃	—	4	1	no	—
383	C₂×C₅×D₃	—	4	1	no	—
384	C₂×C₅×D₃	—	8	4	no	—
385	C₂×C₅×D₃	#121	1	2	yes	—
386	C₂×C₅×D₃	AGL(1,ℤ/8)	1	2	yes	—
387	C₂×C₅×D₃	#137	1	2	yes	—
388	C₃×C₄×C₅	—	2	1	no	—
389	C₃×C₄×C₅	—	4	1	no	—
390	C₃×C₄×C₅	—	4	1	no	—
391	C₃×C₄×C₅	—	4	1	no	—
392	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
393	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
394	C₅×Dic₃	—	2	1	no	—
395	C₅×Dic₃	—	4	1	no	—
396	C₅×Dic₃	—	4	1	no	—
397	C₅×Dic₃	—	4	1	no	—
398	C₅×Dic₃	#121	1	2	yes	—
399	C₂³×D₃	—	2	1	no	—
400	C₂³×D₃	C₅×D₄	1	1	yes	characteristic
401	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
402	C₂×C₃×D₄	—	2	1	no	—
403	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
404	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
405	C₂×#67	—	2	1	no	—
406	C₂×#67	—	2	1	no	—
407	C₂×#67	—	2	1	no	—
408	C₂²×Dic₃	C₅×D₄	1	1	yes	characteristic
409	D₃×Q₈	—	2	2	no	—
410	D₃×Q₈	—	2	2	no	—
411	D₃×D₄	—	2	2	no	—
412	D₃×D₄	—	2	2	no	—
413	D₃×D₄	—	4	4	no	—
414	C₂×D₁₂	—	2	1	no	—
415	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
416	C₂×C₄×D₃	—	2	2	no	—
417	C₂×C₄×D₃	—	2	2	no	—
418	C₂×C₄×D₃	—	2	1	no	—
419	C₂×C₄×D₃	—	2	1	no	—
420	C₂×C₄×D₃	—	2	1	no	—
421	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
422	C₂×C₄×D₃	C₅×D₄	1	1	yes	characteristic
423	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
424	C₂×C₄×D₃	C₂³×C₅	1	1	yes	characteristic
425	C₂×Dic₆	—	2	1	no	—
426	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
427	C₃×SD₁₆	—	2	2	no	—
428	C₃×M₁₆	—	2	2	no	—
429	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
430	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
431	C₃×C₄⋊C₄	—	2	1	no	—
432	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
433	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
434	C₃×C₂²⋊C₄	—	2	1	no	—
435	C₃×C₂²⋊C₄	—	2	1	no	—
436	#217	—	2	1	no	—
437	#217	—	2	1	no	—
438	#215	—	2	2	no	—
439	#214	—	2	2	no	—
440	(C₂×D₃)⋊C₄	—	2	1	no	—
441	(C₂×D₃)⋊C₄	—	2	1	no	—
442	(C₂×D₃)⋊C₄	—	2	1	no	—
443	(C₂×D₃)⋊C₄	—	2	1	no	—
444	C₄⋊Dic₃	—	2	1	no	—
445	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
446	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
447	Dic₃⋊C₄	—	2	1	no	—
448	Dic₃⋊C₄	—	2	1	no	—
449	Dic₃⋊C₄	—	2	1	no	—
450	Dic₃⋊C₄	—	2	1	no	—
451	#208	—	2	2	no	—
452	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
453	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
454	#204	—	2	2	no	—
455	ΓL(1,𝔽₂₅)	—	2	2	no	—
456	ΓL(1,𝔽₂₅)	—	2	2	no	—
457	D₃×C₈	—	2	2	no	—
458	D₃×C₈	C₅×D₄	1	4	yes	complemented
459	C₂³×C₅	—	2	1	no	—
460	C₂³×C₅	—	3	1	no	—
461	C₂³×C₅	—	3	1	no	—
462	C₂³×C₅	—	6	2	no	—
463	C₂³×C₅	—	6	2	no	—
464	C₂³×C₅	—	6	2	no	—
465	C₂³×C₅	—	6	1	no	—
466	C₂³×C₅	—	12	2	no	—
467	C₂³×C₅	—	12	2	no	—
468	C₂³×C₅	—	12	2	no	—
469	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
470	C₅×Q₈	—	2	1	no	—
471	C₅×Q₈	—	2	1	no	—
472	C₅×Q₈	—	6	1	no	—
473	C₅×Q₈	—	6	1	no	—
474	C₅×Q₈	—	12	2	no	—
475	C₅×D₄	—	2	1	no	—
476	C₅×D₄	—	2	1	no	—
477	C₅×D₄	—	4	2	no	—
478	C₅×D₄	—	6	1	no	—
479	C₅×D₄	—	6	1	no	—
480	C₅×D₄	—	12	2	no	—
481	C₅×D₄	—	12	2	no	—
482	C₅×D₄	—	12	2	no	—
483	C₅×D₄	—	12	2	no	—
484	C₂×C₄×C₅	—	2	1	no	—
485	C₂×C₄×C₅	—	2	1	no	—
486	C₂×C₄×C₅	—	2	1	no	—
487	C₂×C₄×C₅	—	2	1	no	—
488	C₂×C₄×C₅	—	2	1	no	—
489	C₂×C₄×C₅	—	3	1	no	—
490	C₂×C₄×C₅	—	3	2	no	—
491	C₂×C₄×C₅	—	3	2	no	—
492	C₂×C₄×C₅	—	3	1	no	—
493	C₂×C₄×C₅	—	6	2	no	—
494	C₂×C₄×C₅	—	6	2	no	—
495	C₂×C₄×C₅	—	6	2	no	—
496	C₂×C₄×C₅	—	6	1	no	—
497	C₂×C₄×C₅	—	6	1	no	—
498	C₂×C₄×C₅	—	6	1	no	—
499	C₂×C₄×C₅	—	6	1	no	—
500	C₂×C₄×C₅	—	6	1	no	—
501	C₂×C₄×C₅	—	12	2	no	—
502	C₂×C₄×C₅	—	12	2	no	—
503	C₂×C₄×C₅	—	12	2	no	—
504	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
505	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
506	C₅×C₈	—	2	1	no	—
507	C₅×C₈	—	3	2	no	—
508	C₅×C₈	—	6	1	no	—
509	C₅×C₈	D₃×D₄	1	2	yes	complemented
510	C₂²×Q₈	—	3	1	no	—
511	C₂²×D₄	—	3	1	no	—
512	C₂²×D₄	—	6	1	no	—
513	C₂³×C₄	—	3	1	no	—
514	C₂×SD₁₆	—	3	1	no	—
515	C₂×SD₁₆	—	3	1	no	—
516	C₂×SD₁₆	—	3	1	no	—
517	C₂×SD₁₆	—	6	4	no	—
518	C₂×SD₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
519	C₂×M₁₆	—	3	1	no	—
520	C₂×M₁₆	—	3	1	no	—
521	C₂×M₁₆	—	3	1	no	—
522	C₂×M₁₆	—	6	4	no	—
523	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic, complemented
524	C₂²×C₈	—	3	1	no	—
525	C₂²×C₈	—	3	1	no	—
526	C₂²⋊Q₈	—	3	1	no	—
527	C₂²⋊Q₈	—	3	1	no	—
528	C₂²⋊Q₈	—	3	1	no	—
529	C₂²⋊Q₈	—	6	1	no	—
530	C₂²⋊Q₈	—	6	1	no	—
531	C₂²⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic, complemented
532	#121	—	3	1	no	—
533	#121	—	3	1	no	—
534	#121	—	3	1	no	—
535	#121	—	6	1	no	—
536	#121	—	6	1	no	—
537	#121	C₂×C₅×D₃	1	1	yes	characteristic
538	C₂×C₄⋊C₄	—	3	1	no	—
539	C₂×C₄⋊C₄	—	3	1	no	—
540	C₂×C₄⋊C₄	—	6	1	no	—
541	C₂×C₂²⋊C₄	—	6	1	no	—
542	C₂×C₂²⋊C₄	—	6	1	no	—
543	#107	—	3	1	no	—
544	#107	—	3	1	no	—
545	#107	—	3	1	no	—
546	#107	C₂×C₅×D₃	1	1	yes	characteristic, complemented
547	#103	—	3	1	no	—
548	#103	—	3	1	no	—
549	#103	—	3	1	no	—
550	#103	C₂×C₅×D₃	1	1	yes	characteristic, complemented
551	#102	—	3	1	no	—
552	#102	—	3	1	no	—
553	#102	—	3	1	no	—
554	#102	C₂×C₅×D₃	1	1	yes	characteristic, complemented
555	C₂×C₃×C₅	—	4	1	no	—
556	C₂×C₃×C₅	—	8	1	no	—
557	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
558	C₂×C₃×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
559	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
560	C₅×D₃	—	4	1	no	—
561	C₅×D₃	—	8	1	no	—
562	C₅×D₃	#468	1	4	yes	direct product factor
563	C₂³×C₃	—	2	1	no	—
564	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
565	C₂²×D₃	—	2	2	no	—
566	C₂²×D₃	—	2	2	no	—
567	C₂²×D₃	—	2	2	no	—
568	C₂²×D₃	—	2	1	no	—
569	C₂²×D₃	—	4	2	no	—
570	C₂²×D₃	—	4	2	no	—
571	C₂²×D₃	—	4	2	no	—
572	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
573	C₂²×D₃	C₂×C₅×D₄	1	1	yes	characteristic
574	C₃×Q₈	—	2	1	no	—
575	C₃×Q₈	—	2	1	no	—
576	C₃×D₄	—	2	1	no	—
577	C₃×D₄	—	2	1	no	—
578	C₃×D₄	—	4	2	no	—
579	C₂×C₃×C₄	—	2	1	no	—
580	C₂×C₃×C₄	—	2	1	no	—
581	C₂×C₃×C₄	—	2	1	no	—
582	C₂×C₃×C₄	—	2	1	no	—
583	C₂×C₃×C₄	—	2	1	no	—
584	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
585	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
586	#67	—	4	2	no	—
587	#67	—	4	2	no	—
588	#67	—	4	2	no	—
589	C₂×Dic₃	—	2	2	no	—
590	C₂×Dic₃	—	2	1	no	—
591	C₂×Dic₃	—	2	1	no	—
592	C₂×Dic₃	—	2	1	no	—
593	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
594	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
595	D₁₂	—	2	1	no	—
596	D₁₂	—	2	1	no	—
597	D₁₂	—	4	2	no	—
598	C₄×D₃	—	2	2	no	—
599	C₄×D₃	—	2	1	no	—
600	C₄×D₃	—	2	1	no	—
601	C₄×D₃	—	2	2	no	—
602	C₄×D₃	—	4	2	no	—
603	C₄×D₃	—	4	2	no	—
604	C₄×D₃	—	4	2	no	—
605	C₄×D₃	C₂×C₅×D₄	1	2	yes	—
606	C₄×D₃	C₅×#41	1	2	yes	—
607	Dic₆	—	2	1	no	—
608	Dic₆	—	2	1	no	—
609	Dic₆	—	4	2	no	—
610	C₃×C₈	—	2	1	no	—
611	C₃×C₈	C₂×C₅×D₄	1	2	yes	complemented
612	C₃⋊C₈	—	2	1	no	—
613	C₃⋊C₈	C₂×C₅×D₄	1	2	yes	complemented
614	C₂²×C₅	—	2	1	no	—
615	C₂²×C₅	—	2	1	no	—
616	C₂²×C₅	—	2	1	no	—
617	C₂²×C₅	—	3	2	no	—
618	C₂²×C₅	—	3	2	no	—
619	C₂²×C₅	—	3	2	no	—
620	C₂²×C₅	—	4	1	no	—
621	C₂²×C₅	—	4	1	no	—
622	C₂²×C₅	—	4	1	no	—
623	C₂²×C₅	—	6	1	no	—
624	C₂²×C₅	—	6	1	no	—
625	C₂²×C₅	—	6	1	no	—
626	C₂²×C₅	—	12	4	no	—
627	C₂²×C₅	—	12	1	no	—
628	C₂²×C₅	—	12	1	no	—
629	C₂²×C₅	—	12	1	no	—
630	C₂²×C₅	—	24	4	no	—
631	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
632	C₄×C₅	—	2	1	no	—
633	C₄×C₅	—	3	2	no	—
634	C₄×C₅	—	4	1	no	—
635	C₄×C₅	—	4	1	no	—
636	C₄×C₅	—	4	1	no	—
637	C₄×C₅	—	6	1	no	—
638	C₄×C₅	—	12	1	no	—
639	C₄×C₅	—	12	1	no	—
640	C₄×C₅	—	12	1	no	—
641	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
642	C₄×C₅	D₃×#41	1	1	yes	characteristic
643	C₂⁴	—	3	1	no	—
644	C₂⁴	—	6	1	no	—
645	C₂×Q₈	—	3	1	no	—
646	C₂×Q₈	—	6	1	no	—
647	C₂×Q₈	—	6	2	no	—
648	C₂×Q₈	—	6	2	no	—
649	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
650	C₂×D₄	—	2	1	no	—
651	C₂×D₄	—	3	1	no	—
652	C₂×D₄	—	6	1	no	—
653	C₂×D₄	—	6	2	no	—
654	C₂×D₄	—	6	2	no	—
655	C₂×D₄	—	6	1	no	—
656	C₂×D₄	—	6	1	no	—
657	C₂×D₄	—	6	1	no	—
658	C₂×D₄	—	12	4	no	—
659	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
660	C₂²×C₄	—	3	1	no	—
661	C₂²×C₄	—	3	1	no	—
662	C₂²×C₄	—	3	1	no	—
663	C₂²×C₄	—	3	1	no	—
664	C₂²×C₄	—	3	1	no	—
665	C₂²×C₄	—	6	2	no	—
666	C₂²×C₄	—	6	2	no	—
667	C₂²×C₄	—	6	1	no	—
668	C₂²×C₄	—	6	1	no	—
669	C₂²×C₄	—	6	1	no	—
670	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
671	SD₁₆	—	2	2	no	—
672	SD₁₆	—	6	2	no	—
673	SD₁₆	—	6	2	no	—
674	SD₁₆	—	6	2	no	—
675	M₁₆	—	2	2	no	—
676	M₁₆	—	6	2	no	—
677	M₁₆	—	6	2	no	—
678	M₁₆	—	6	2	no	—
679	C₂×C₈	—	3	1	no	—
680	C₂×C₈	—	3	4	no	—
681	C₂×C₈	—	3	1	no	—
682	C₂×C₈	—	6	2	no	—
683	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
684	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	3	1	no	—
687	C₄⋊C₄	—	3	1	no	—
688	C₄⋊C₄	—	6	1	no	—
689	C₄⋊C₄	—	6	1	no	—
690	C₄⋊C₄	—	6	1	no	—
691	C₄⋊C₄	—	6	1	no	—
692	C₄⋊C₄	—	6	1	no	—
693	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
694	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
695	C₂²⋊C₄	—	2	1	no	—
696	C₂²⋊C₄	—	2	1	no	—
697	C₂²⋊C₄	—	6	1	no	—
698	C₂²⋊C₄	—	6	1	no	—
699	C₂²⋊C₄	—	6	1	no	—
700	C₂²⋊C₄	—	6	1	no	—
701	C₂²⋊C₄	—	6	1	no	—
702	C₂²⋊C₄	—	6	1	no	—
703	C₃×C₅	C₂×#468	1	1	yes	characteristic, complemented, Hall
704	C₂²×C₃	—	2	1	no	—
705	C₂²×C₃	—	2	1	no	—
706	C₂²×C₃	—	2	1	no	—
707	C₂²×C₃	—	4	1	no	—
708	C₂²×C₃	—	4	1	no	—
709	C₂²×C₃	—	4	1	no	—
710	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
711	C₂×D₃	—	2	1	no	—
712	C₂×D₃	—	2	1	no	—
713	C₂×D₃	—	2	1	no	—
714	C₂×D₃	—	4	4	no	—
715	C₂×D₃	—	4	1	no	—
716	C₂×D₃	—	4	1	no	—
717	C₂×D₃	—	4	1	no	—
718	C₂×D₃	—	8	4	no	—
719	C₂×D₃	C₅×#121	1	2	yes	—
720	C₂×D₃	C₅×AGL(1,ℤ/8)	1	2	yes	—
721	C₂×D₃	C₅×#137	1	2	yes	—
722	C₃×C₄	—	2	1	no	—
723	C₃×C₄	—	4	1	no	—
724	C₃×C₄	—	4	1	no	—
725	C₃×C₄	—	4	1	no	—
726	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
727	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
728	Dic₃	—	2	1	no	—
729	Dic₃	—	4	1	no	—
730	Dic₃	—	4	1	no	—
731	Dic₃	—	4	1	no	—
732	Dic₃	C₅×#121	1	2	yes	—
733	C₂×C₅	—	3	4	no	—
734	C₂×C₅	—	4	1	no	—
735	C₂×C₅	—	8	1	no	—
736	C₂×C₅	—	12	1	no	—
737	C₂×C₅	—	24	1	no	—
738	C₂×C₅	D₃×#121	1	1	yes	characteristic
739	C₂×C₅	D₃×AGL(1,ℤ/8)	1	1	yes	characteristic
740	C₂×C₅	D₃×#137	1	1	yes	characteristic
741	C₂³	—	2	1	no	—
742	C₂³	—	3	1	no	—
743	C₂³	—	3	1	no	—
744	C₂³	—	6	2	no	—
745	C₂³	—	6	2	no	—
746	C₂³	—	6	2	no	—
747	C₂³	—	6	1	no	—
748	C₂³	—	12	2	no	—
749	C₂³	—	12	2	no	—
750	C₂³	—	12	2	no	—
751	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
752	Q₈	—	2	1	no	—
753	Q₈	—	2	1	no	—
754	Q₈	—	6	1	no	—
755	Q₈	—	6	1	no	—
756	Q₈	—	12	2	no	—
757	D₄	—	2	1	no	—
758	D₄	—	2	1	no	—
759	D₄	—	4	2	no	—
760	D₄	—	6	1	no	—
761	D₄	—	6	1	no	—
762	D₄	—	12	2	no	—
763	D₄	—	12	2	no	—
764	D₄	—	12	2	no	—
765	D₄	—	12	2	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	3	1	no	—
772	C₂×C₄	—	3	2	no	—
773	C₂×C₄	—	3	2	no	—
774	C₂×C₄	—	3	1	no	—
775	C₂×C₄	—	6	2	no	—
776	C₂×C₄	—	6	2	no	—
777	C₂×C₄	—	6	2	no	—
778	C₂×C₄	—	6	1	no	—
779	C₂×C₄	—	6	1	no	—
780	C₂×C₄	—	6	1	no	—
781	C₂×C₄	—	6	1	no	—
782	C₂×C₄	—	6	1	no	—
783	C₂×C₄	—	12	2	no	—
784	C₂×C₄	—	12	2	no	—
785	C₂×C₄	—	12	2	no	—
786	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
787	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
788	C₈	—	2	1	no	—
789	C₈	—	3	2	no	—
790	C₈	—	6	1	no	—
791	C₈	C₅×D₃×D₄	1	2	yes	complemented
792	C₂×C₃	—	4	1	no	—
793	C₂×C₃	—	8	1	no	—
794	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
795	C₂×C₃	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
796	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
797	D₃	—	4	1	no	—
798	D₃	—	8	1	no	—
799	D₃	C₅×#468	1	4	yes	direct product factor
800	C₅	D₃×#468	1	1	yes	characteristic, direct product factor, Sylow
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	3	2	no	—
805	C₂²	—	3	2	no	—
806	C₂²	—	3	2	no	—
807	C₂²	—	4	1	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	4	1	no	—
810	C₂²	—	6	1	no	—
811	C₂²	—	6	1	no	—
812	C₂²	—	6	1	no	—
813	C₂²	—	12	4	no	—
814	C₂²	—	12	1	no	—
815	C₂²	—	12	1	no	—
816	C₂²	—	12	1	no	—
817	C₂²	—	24	4	no	—
818	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
819	C₄	—	2	1	no	—
820	C₄	—	3	2	no	—
821	C₄	—	4	1	no	—
822	C₄	—	4	1	no	—
823	C₄	—	4	1	no	—
824	C₄	—	6	1	no	—
825	C₄	—	12	1	no	—
826	C₄	—	12	1	no	—
827	C₄	—	12	1	no	—
828	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
829	C₄	C₅×D₃×#41	1	1	yes	characteristic
830	C₃	C₂×C₅×#468	1	1	yes	characteristic, complemented, Sylow
831	C₂	—	3	4	no	—
832	C₂	—	4	1	no	—
833	C₂	—	8	1	no	—
834	C₂	—	12	1	no	—
835	C₂	—	24	1	no	—
836	C₂	C₅×D₃×#121	1	1	yes	characteristic
837	C₂	C₅×D₃×AGL(1,ℤ/8)	1	1	yes	characteristic
838	C₂	C₅×D₃×#137	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#468	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₅×D₃×#121	C₂
hypercenter	C₅×#468	D₃
hypocenter	C₃	C₂×C₅×#468
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#468

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×D₃×SD₁₆	C₂	semidirect
2. C₂×C₅×D₃×M₁₆	C₂	semidirect
3. C₅×D₃×C₂²⋊Q₈	C₂	semidirect
5. C₃×C₅×#468	C₂	semidirect
6. C₅×#5174	C₂	semidirect
7. C₅×#5134	C₂	semidirect
8. C₅×#5049	C₂	semidirect
9. C₅×#5042	C₂	semidirect
10. C₅×#4886	C₂	semidirect
11. C₅×D₃×#107	C₂	semidirect
12. C₅×#4812	C₂	semidirect
13. C₅×D₃×#103	C₂	semidirect
14. C₅×#4780	C₂	semidirect
15. C₅×D₃×#102	C₂	semidirect
21. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
22. C₂×C₃×C₅×M₁₆	C₂²	semidirect
23. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
25. C₅×#946	C₂²	semidirect
26. C₂×C₅×#215	C₂²	semidirect
29. C₂×C₅×#214	C₂²	semidirect
31. C₅×#924	C₂²	semidirect
32. C₂×C₅×#208	C₂²	semidirect
35. C₂×C₅×#204	C₂²	semidirect
36. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
37. C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	semidirect
40. C₅×#897	C₂²	semidirect
50. C₃×C₅×#107	C₂²	semidirect
51. C₃×C₅×#103	C₂²	semidirect
52. C₃×C₅×#102	C₂²	semidirect
53. C₅×#835	C₂²	semidirect
54. C₅×#832	C₂²	semidirect
55. C₅×#821	C₂²	semidirect
56. C₅×#818	C₂²	semidirect
57. C₅×#816	C₂²	semidirect
58. C₅×#810	C₂²	semidirect
59. C₅×#809	C₂²	semidirect
60. C₅×#807	C₂²	semidirect
61. C₅×#807	C₂²	semidirect
62. D₃×#468	C₅	direct (N × H)
74. C₅×#468	D₃	direct (N × H)
137. C₅×D₃×C₈	D₄	semidirect
138. C₂×D₃×SD₁₆	C₂×C₅	semidirect
139. C₂×D₃×M₁₆	C₂×C₅	semidirect
140. D₃×C₂²⋊Q₈	C₂×C₅	semidirect
142. C₃×#468	C₂×C₅	semidirect
143. #5174	C₂×C₅	semidirect
144. #5134	C₂×C₅	semidirect
145. #5049	C₂×C₅	semidirect
146. #5042	C₂×C₅	semidirect
147. #4886	C₂×C₅	semidirect
148. D₃×#107	C₂×C₅	semidirect
149. #4812	C₂×C₅	semidirect
150. D₃×#103	C₂×C₅	semidirect
151. #4780	C₂×C₅	semidirect
152. D₃×#102	C₂×C₅	semidirect
161. C₂×C₅×SD₁₆	C₂×D₃	semidirect
166. C₂×C₅×M₁₆	C₂×D₃	semidirect
174. C₅×C₂²⋊Q₈	C₂×D₃	semidirect
189. C₅×#107	C₂×D₃	semidirect
193. C₅×#103	C₂×D₃	semidirect
197. C₅×#102	C₂×D₃	semidirect
247. C₃×C₅×C₈	C₂×D₄	semidirect
249. C₅×C₃⋊C₈	C₂×D₄	semidirect
254. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
255. C₂×C₃×M₁₆	C₂²×C₅	semidirect
256. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
258. #946	C₂²×C₅	semidirect
259. C₂×#215	C₂²×C₅	semidirect
262. C₂×#214	C₂²×C₅	semidirect
264. #924	C₂²×C₅	semidirect
265. C₂×#208	C₂²×C₅	semidirect
268. C₂×#204	C₂²×C₅	semidirect
269. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
270. C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	semidirect
273. #897	C₂²×C₅	semidirect
283. C₃×#107	C₂²×C₅	semidirect
284. C₃×#103	C₂²×C₅	semidirect
285. C₃×#102	C₂²×C₅	semidirect
286. #835	C₂²×C₅	semidirect
287. #832	C₂²×C₅	semidirect
288. #821	C₂²×C₅	semidirect
289. #818	C₂²×C₅	semidirect
290. #816	C₂²×C₅	semidirect
291. #810	C₂²×C₅	semidirect
292. #809	C₂²×C₅	semidirect
293. #807	C₂²×C₅	semidirect
294. #807	C₂²×C₅	semidirect
366. #468	C₅×D₃	direct (N × H)
458. D₃×C₈	C₅×D₄	semidirect
509. C₅×C₈	D₃×D₄	semidirect
518. C₂×SD₁₆	C₂×C₅×D₃	semidirect
523. C₂×M₁₆	C₂×C₅×D₃	semidirect
531. C₂²⋊Q₈	C₂×C₅×D₃	semidirect
546. #107	C₂×C₅×D₃	semidirect
550. #103	C₂×C₅×D₃	semidirect
554. #102	C₂×C₅×D₃	semidirect
562. C₅×D₃	#468	direct (N × H)
611. C₃×C₈	C₂×C₅×D₄	semidirect
613. C₃⋊C₈	C₂×C₅×D₄	semidirect
703. C₃×C₅	C₂×#468	semidirect
791. C₈	C₅×D₃×D₄	semidirect
799. D₃	C₅×#468	direct (N × H)
800. C₅	D₃×#468	direct (N × H)
830. C₃	C₂×C₅×#468	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×D₃×SD₁₆	2
C₂×C₅×D₃×M₁₆	2
C₅×D₃×C₂²⋊Q₈	2
C₅×D₃×#121	2
C₃×C₅×#468	2
C₅×#5174	2
C₅×#5134	2
C₅×#5049	2
C₅×#5042	2
C₅×#4886	2
C₅×D₃×#107	2
C₅×#4812	2
C₅×D₃×#103	2
C₅×#4780	2
C₅×D₃×#102	2
C₂×C₅×#468	3
D₃×#468	5

Subgroups — C5×D3×#468 #14427885

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#468 #14427885