Subgroups — C₃×D₅×#932 #72229613

Order 2880.

1428 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#91821	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#932	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#91491	C₂	1	2	yes	maximal, complemented
6	C₃×#91489	C₂	1	2	yes	maximal, complemented
7	C₃×D₅×#214	C₂	1	2	yes	maximal, complemented
8	C₃×D₅×#213	C₂	1	2	yes	maximal, complemented
9	C₃×#91312	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#91298	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×D₅×AGL(1,ℤ/8)	—	3	1	no	maximal
13	D₅×#932	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂³×C₃²×D₅	—	2	1	no	—
15	C₂×C₃²×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
16	C₃×#6817	C₂²	1	1	yes	characteristic, complemented
17	C₃×C₅×#235	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₃²×C₂²⋊D₅	—	2	1	no	—
19	C₃²×D₄×D₅	—	2	1	no	—
20	C₃²×D₄×D₅	—	2	1	no	—
21	C₃²×D₄×D₅	C₂²	1	2	yes	—
22	C₃²×D₄×D₅	C₂²	1	2	yes	complemented
23	C₂×C₃²×D₂₀	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃²×C₄×D₅	C₂²	1	1	yes	characteristic
25	C₃×D₅×#67	—	2	1	no	—
26	C₃×#6782	—	2	1	no	—
27	C₃×D₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₄×D₃×D₅	—	2	1	no	—
29	C₃×#6773	C₂²	1	1	yes	characteristic, complemented
30	C₃×#6772	C₂²	1	1	yes	characteristic, complemented
31	C₃×#6771	—	2	1	no	—
32	C₃×D₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
33	C₃×#6716	C₂²	1	2	yes	complemented
34	C₃×#6715	C₂²	1	2	yes	complemented
35	C₃×#6710	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₅×#214	C₂²	1	2	yes	complemented
37	C₃×C₅×#213	C₂²	1	2	yes	complemented
38	C₃×C₅×#208	C₂²	1	1	yes	characteristic, complemented
39	C₃×#6657	C₂²	1	2	yes	complemented
40	C₃×#6655	C₂²	1	2	yes	complemented
41	C₃×#6653	C₂²	1	2	yes	complemented
42	C₃×#6652	C₂²	1	2	yes	complemented
43	C₃×#6649	C₂²	1	2	yes	complemented
44	C₃×D₅×C₃⋊C₈	C₂²	1	2	yes	complemented
45	C₂×C₃×#932	—	5	1	no	maximal, Hall
46	C₃×D₅×#41	—	3	1	no	—
47	C₂×C₃×D₄×D₅	—	2	1	no	—
48	C₂×C₃×D₄×D₅	D₃	1	1	yes	characteristic, complemented
49	C₂×C₃×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
50	D₅×#235	C₂×C₃	1	1	yes	characteristic, complemented
51	C₃×C₅×AGL(1,ℤ/8)	—	3	1	no	—
52	#91821	C₂×C₃	1	1	yes	characteristic, complemented
53	C₅×#932	C₂×C₃	1	1	yes	characteristic, complemented
54	C₃×#4095	—	3	1	no	—
55	C₃×#4078	—	3	1	no	—
56	C₃×#4060	—	3	2	no	—
57	C₃×D₅×SD₁₆	—	3	2	no	—
58	C₃×#4057	—	3	2	no	—
59	C₃×D₅×D₈	—	3	2	no	—
60	C₃×#4054	—	3	1	no	—
61	C₃×D₅×M₁₆	—	3	1	no	—
62	#91491	C₂×C₃	1	2	yes	complemented
63	#91489	C₂×C₃	1	2	yes	complemented
64	D₅×#214	C₂×C₃	1	2	yes	complemented
65	D₅×#213	C₂×C₃	1	2	yes	complemented
66	#91312	C₂×C₃	1	1	yes	characteristic, complemented
67	#91298	C₂×C₃	1	1	yes	characteristic, complemented
68	D₅×#208	C₂×C₃	1	1	yes	characteristic, complemented
69	C₂³×C₃²×C₅	—	2	1	no	—
70	C₂²×C₃²×D₅	—	2	1	no	—
71	C₂²×C₃²×D₅	—	2	2	no	—
72	C₂²×C₃²×D₅	—	2	2	no	—
73	C₂²×C₃²×D₅	—	4	4	no	—
74	C₂²×C₃²×D₅	D₄	1	1	yes	characteristic
75	C₂×C₃×D₃×D₅	—	2	1	no	—
76	C₃²×C₅×D₄	—	2	1	no	—
77	C₃²×C₅×D₄	C₂³	1	2	yes	—
78	C₂×C₃²×C₄×C₅	C₂³	1	1	yes	characteristic
79	C₃×#1220	—	2	1	no	—
80	C₃×D₆₀	C₂³	1	1	yes	characteristic, complemented
81	C₃×C₄×D₁₅	—	2	1	no	—
82	C₃×Dic₃₀	C₂³	1	1	yes	characteristic, complemented
83	C₃×C₅×#67	—	2	1	no	—
84	C₃×C₅×D₁₂	C₂³	1	1	yes	characteristic, complemented
85	C₃×C₄×C₅×D₃	—	2	1	no	—
86	C₃×C₅×Dic₆	C₂³	1	1	yes	characteristic, complemented
87	C₃²×C₂²⋊D₅	—	2	2	no	—
88	C₃²×C₂²⋊D₅	—	2	2	no	—
89	C₂×C₃²×Dic₅	D₄	1	1	yes	characteristic
90	C₃²×D₂₀	—	2	1	no	—
91	C₃²×D₂₀	C₂³	1	2	yes	—
92	C₃²×C₄×D₅	D₄	1	1	yes	characteristic
93	C₃²×C₄×D₅	D₄	1	1	yes	characteristic
94	C₃²×C₄×D₅	C₂³	1	1	yes	characteristic
95	C₃²×C₄×D₅	C₂³	1	1	yes	characteristic
96	C₃×#1204	—	2	1	no	—
97	C₃×#1203	—	2	1	no	—
98	C₃×#1202	—	2	1	no	—
99	C₃×#1201	—	2	1	no	—
100	C₃×#1200	—	2	1	no	—
101	C₃×D₃×Dic₅	—	2	1	no	—
102	C₃×D₅×Dic₃	—	2	1	no	—
103	C₃×C₃⋊#168	C₂³	1	2	yes	complemented
104	C₃×C₅×C₃⋊C₈	C₂³	1	2	yes	complemented
105	D₅×AGL(1,ℤ/8)	—	3	1	no	Hall
106	C₂²×C₃²×D₄	—	5	1	no	—
107	C₂×C₃×#235	—	5	1	no	—
108	C₂×C₃×#214	—	5	2	no	—
109	C₃×#932	—	5	1	no	—
110	C₃×#932	—	5	1	no	—
111	C₃×#932	—	5	2	no	—
112	C₃×#932	—	5	2	no	—
113	C₃×#932	—	5	1	no	—
114	C₃×#932	D₅	1	1	yes	characteristic, direct product factor
115	C₂×C₃×#213	—	5	2	no	—
116	C₂×C₃×#208	—	5	1	no	—
117	C₂³×C₃×D₅	—	2	2	no	—
118	C₂³×C₃×D₅	—	2	1	no	—
119	C₂³×C₃×D₅	—	2	1	no	—
120	C₃×C₅×#41	—	3	1	no	—
121	C₂×C₃×C₅×D₄	—	2	1	no	—
122	C₂×C₃×C₅×D₄	C₂×D₃	1	1	yes	characteristic, complemented
123	C₂×C₃×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
124	#6817	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₅×#235	C₂²×C₃	1	1	yes	characteristic, complemented
126	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
127	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
128	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
129	C₃×#713	—	3	1	no	—
130	C₃×Q₈×D₅	—	3	1	no	—
131	C₃×#711	—	3	1	no	—
132	C₃×#711	—	6	1	no	—
133	C₃×D₄×D₅	—	2	2	no	—
134	C₃×D₄×D₅	—	2	2	no	—
135	C₃×D₄×D₅	—	2	2	no	—
136	C₃×D₄×D₅	—	2	2	no	—
137	C₃×D₄×D₅	—	2	1	no	—
138	C₃×D₄×D₅	—	2	1	no	—
139	C₃×D₄×D₅	—	2	1	no	—
140	C₃×D₄×D₅	—	2	1	no	—
141	C₃×D₄×D₅	—	3	1	no	—
142	C₃×D₄×D₅	—	6	1	no	—
143	C₃×D₄×D₅	C₂×D₃	1	2	yes	—
144	C₃×D₄×D₅	C₂×D₃	1	2	yes	complemented
145	C₃×D₄×D₅	C₂²×C₃	1	2	yes	—
146	C₃×D₄×D₅	C₂²×C₃	1	2	yes	complemented
147	C₃×#709	—	3	1	no	—
148	C₃×#709	—	6	1	no	—
149	C₂×C₃×D₂₀	—	2	1	no	—
150	C₂×C₃×D₂₀	C₂×D₃	1	1	yes	characteristic, complemented
151	C₂×C₃×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
152	C₂×C₃×C₄×D₅	—	2	1	no	—
153	C₂×C₃×C₄×D₅	—	6	1	no	—
154	C₂×C₃×C₄×D₅	C₂×D₃	1	1	yes	characteristic
155	C₂×C₃×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
156	D₅×#67	—	2	1	no	—
157	#6782	—	2	1	no	—
158	D₅×D₁₂	C₂²×C₃	1	1	yes	characteristic, complemented
159	C₄×D₃×D₅	—	2	1	no	—
160	#6773	C₂²×C₃	1	1	yes	characteristic, complemented
161	#6772	C₂²×C₃	1	1	yes	characteristic, complemented
162	#6771	—	2	1	no	—
163	D₅×Dic₆	C₂²×C₃	1	1	yes	characteristic, complemented
164	C₃×C₅×SD₁₆	—	3	2	no	—
165	C₃×C₅×D₈	—	3	2	no	—
166	C₃×C₅×M₁₆	—	3	1	no	—
167	#6716	C₂²×C₃	1	2	yes	complemented
168	#6715	C₂²×C₃	1	2	yes	complemented
169	#6710	C₂²×C₃	1	1	yes	characteristic, complemented
170	C₅×#214	C₂²×C₃	1	2	yes	complemented
171	C₅×#213	C₂²×C₃	1	2	yes	complemented
172	C₅×#208	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₃×#688	—	3	2	no	—
174	C₃×#687	—	3	2	no	—
175	C₃×#686	—	3	2	no	—
176	C₃×#686	—	3	2	no	—
177	C₃×#681	—	3	1	no	—
178	C₃×D₄₀	—	3	2	no	—
179	C₃×#677	—	3	2	no	—
180	C₃×#676	—	3	2	no	—
181	C₃×C₈×D₅	—	3	2	no	—
182	#6657	C₂²×C₃	1	2	yes	complemented
183	#6655	C₂²×C₃	1	2	yes	complemented
184	#6653	C₂²×C₃	1	2	yes	complemented
185	#6652	C₂²×C₃	1	2	yes	complemented
186	#6649	C₂²×C₃	1	2	yes	complemented
187	D₅×C₃⋊C₈	C₂²×C₃	1	2	yes	complemented
188	C₂×C₃×AGL(1,ℤ/8)	—	15	1	no	—
189	C₂×#932	—	5	1	no	—
190	C₂²×C₃²×C₅	—	2	2	no	—
191	C₂²×C₃²×C₅	—	4	2	no	—
192	C₂²×C₃²×C₅	C₂×D₄	1	1	yes	characteristic
193	C₂×C₃×D₁₅	—	2	1	no	—
194	C₂×C₃×C₅×D₃	—	2	1	no	—
195	C₂×C₃²×D₅	—	2	2	no	—
196	C₂×C₃²×D₅	—	2	2	no	—
197	C₂×C₃²×D₅	—	4	4	no	—
198	C₂×C₃²×D₅	—	4	2	no	—
199	C₂×C₃²×D₅	—	4	4	no	—
200	C₂×C₃²×D₅	C₂×D₄	1	1	yes	characteristic
201	C₂×C₃²×D₅	C₂×D₄	1	1	yes	characteristic
202	C₃×D₃×D₅	—	4	2	no	—
203	C₃²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
204	C₃²×C₄×C₅	C₂⁴	1	1	yes	characteristic
205	C₃×Dic₁₅	—	2	1	no	—
206	C₃×C₅×Dic₃	—	2	1	no	—
207	C₃²×Dic₅	C₂×D₄	1	1	yes	characteristic
208	C₃²×Dic₅	C₂×D₄	1	1	yes	characteristic
209	D₅×#41	—	3	1	no	—
210	C₂×D₄×D₅	C₃×D₃	1	1	yes	characteristic, complemented
211	C₅×AGL(1,ℤ/8)	—	3	1	no	—
212	#4095	—	3	1	no	—
213	#4078	—	3	1	no	—
214	#4060	—	3	2	no	—
215	D₅×SD₁₆	—	3	2	no	—
216	#4057	—	3	2	no	—
217	D₅×D₈	—	3	2	no	—
218	#4054	—	3	1	no	—
219	D₅×M₁₆	—	3	1	no	—
220	C₂⁴×C₃²	—	10	1	no	—
221	C₂×C₃²×D₄	—	5	2	no	—
222	C₂×C₃²×D₄	—	5	2	no	—
223	C₂×C₃²×D₄	—	5	1	no	—
224	C₂×C₃²×D₄	—	10	1	no	—
225	C₂×C₃²×D₄	—	10	1	no	—
226	C₂×C₃²×D₄	—	10	1	no	—
227	C₂×C₃²×D₄	C₂×D₅	1	1	yes	characteristic, complemented
228	C₂²×C₃²×C₄	—	5	1	no	—
229	C₂×C₃×#67	—	10	1	no	—
230	C₃×#235	—	5	1	no	—
231	C₃×#235	—	5	1	no	—
232	C₃×#235	—	5	1	no	—
233	C₃×#235	—	10	1	no	—
234	C₃×#235	—	10	1	no	—
235	C₃×#235	C₂×D₅	1	1	yes	characteristic, complemented
236	C₂×C₃×D₁₂	—	5	1	no	—
237	C₂×C₃×C₄×D₃	—	10	1	no	—
238	C₂×C₃×Dic₆	—	5	1	no	—
239	C₃×#214	—	5	2	no	—
240	C₃×#214	—	5	2	no	—
241	C₃×#214	—	5	2	no	—
242	C₃×#214	C₂×D₅	1	2	yes	complemented
243	C₃×#213	—	5	2	no	—
244	C₃×#213	—	5	2	no	—
245	C₃×#213	—	5	2	no	—
246	C₃×#213	C₂×D₅	1	2	yes	complemented
247	C₃×#208	—	5	1	no	—
248	C₃×#208	—	5	2	no	—
249	C₃×#208	C₂×D₅	1	1	yes	characteristic, complemented
250	C₂×C₃×C₃⋊C₈	—	5	2	no	—
251	C₂³×C₃×C₅	—	2	2	no	—
252	C₂³×C₃×C₅	—	2	1	no	—
253	C₂³×C₃×C₅	—	2	1	no	—
254	C₂²×C₃×D₅	—	2	1	no	—
255	C₂²×C₃×D₅	—	2	2	no	—
256	C₂²×C₃×D₅	—	2	4	no	—
257	C₂²×C₃×D₅	—	2	4	no	—
258	C₂²×C₃×D₅	—	2	1	no	—
259	C₂²×C₃×D₅	—	2	1	no	—
260	C₂²×C₃×D₅	—	2	2	no	—
261	C₂²×C₃×D₅	—	2	2	no	—
262	C₂²×C₃×D₅	—	2	2	no	—
263	C₂²×C₃×D₅	—	2	2	no	—
264	C₂²×C₃×D₅	—	4	8	no	—
265	C₂²×C₃×D₅	—	4	4	no	—
266	C₂²×C₃×D₅	—	4	4	no	—
267	C₂²×C₃×D₅	—	6	1	no	—
268	C₂²×C₃×D₅	#67	1	1	yes	characteristic
269	C₂²×C₃×D₅	C₃×D₄	1	1	yes	characteristic
270	C₂×D₃×D₅	—	2	1	no	—
271	C₃×C₅×Q₈	—	3	1	no	—
272	C₃×C₅×D₄	—	2	2	no	—
273	C₃×C₅×D₄	—	2	2	no	—
274	C₃×C₅×D₄	—	2	1	no	—
275	C₃×C₅×D₄	—	2	1	no	—
276	C₃×C₅×D₄	—	3	1	no	—
277	C₃×C₅×D₄	—	6	1	no	—
278	C₃×C₅×D₄	C₂²×D₃	1	2	yes	—
279	C₃×C₅×D₄	C₂³×C₃	1	2	yes	—
280	C₂×C₃×C₄×C₅	—	2	1	no	—
281	C₂×C₃×C₄×C₅	—	6	1	no	—
282	C₂×C₃×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
283	C₂×C₃×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
284	#1220	—	2	1	no	—
285	D₆₀	C₂³×C₃	1	1	yes	characteristic, complemented
286	C₄×D₁₅	—	2	1	no	—
287	Dic₃₀	C₂³×C₃	1	1	yes	characteristic, complemented
288	C₅×#67	—	2	1	no	—
289	C₅×D₁₂	C₂³×C₃	1	1	yes	characteristic, complemented
290	C₄×C₅×D₃	—	2	1	no	—
291	C₅×Dic₆	C₂³×C₃	1	1	yes	characteristic, complemented
292	C₃×C₂²⋊D₅	—	2	4	no	—
293	C₃×C₂²⋊D₅	—	2	4	no	—
294	C₃×C₂²⋊D₅	—	2	2	no	—
295	C₃×C₂²⋊D₅	—	2	2	no	—
296	C₃×C₂²⋊D₅	—	2	2	no	—
297	C₃×C₂²⋊D₅	—	2	2	no	—
298	C₃×C₂²⋊D₅	—	6	1	no	—
299	C₃×C₂²⋊D₅	—	6	1	no	—
300	C₃×C₂²⋊D₅	—	6	1	no	—
301	C₂×C₃×Dic₅	—	2	1	no	—
302	C₂×C₃×Dic₅	—	6	1	no	—
303	C₂×C₃×Dic₅	#67	1	1	yes	characteristic
304	C₂×C₃×Dic₅	C₃×D₄	1	1	yes	characteristic
305	C₃×D₂₀	—	2	2	no	—
306	C₃×D₂₀	—	2	2	no	—
307	C₃×D₂₀	—	2	1	no	—
308	C₃×D₂₀	—	2	1	no	—
309	C₃×D₂₀	—	3	1	no	—
310	C₃×D₂₀	—	6	1	no	—
311	C₃×D₂₀	C₂²×D₃	1	2	yes	—
312	C₃×D₂₀	C₂³×C₃	1	2	yes	—
313	C₃×C₄×D₅	—	2	1	no	—
314	C₃×C₄×D₅	—	2	1	no	—
315	C₃×C₄×D₅	—	2	1	no	—
316	C₃×C₄×D₅	—	2	1	no	—
317	C₃×C₄×D₅	—	6	1	no	—
318	C₃×C₄×D₅	—	6	1	no	—
319	C₃×C₄×D₅	—	6	1	no	—
320	C₃×C₄×D₅	#67	1	1	yes	characteristic
321	C₃×C₄×D₅	#67	1	1	yes	characteristic
322	C₃×C₄×D₅	C₃×D₄	1	1	yes	characteristic
323	C₃×C₄×D₅	C₃×D₄	1	1	yes	characteristic
324	C₃×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
325	C₃×C₄×D₅	C₂²×D₃	1	1	yes	characteristic
326	C₃×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
327	C₃×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
328	C₃×Dic₁₀	—	3	1	no	—
329	C₃×Dic₁₀	—	6	1	no	—
330	#1204	—	2	1	no	—
331	#1203	—	2	1	no	—
332	#1202	—	2	1	no	—
333	#1201	—	2	1	no	—
334	#1200	—	2	1	no	—
335	D₃×Dic₅	—	2	1	no	—
336	D₅×Dic₃	—	2	1	no	—
337	C₃×C₅×C₈	—	3	2	no	—
338	C₃⋊#168	C₂³×C₃	1	2	yes	complemented
339	C₃×#168	—	3	2	no	—
340	C₅×C₃⋊C₈	C₂³×C₃	1	2	yes	complemented
341	C₂×C₃×#41	—	15	1	no	—
342	C₂²×C₃×D₄	—	5	1	no	—
343	C₂²×C₃×D₄	—	5	1	no	—
344	C₂²×C₃×D₄	—	10	1	no	—
345	C₂×#235	—	5	1	no	—
346	C₃×AGL(1,ℤ/8)	—	3	1	no	—
347	C₃×AGL(1,ℤ/8)	—	15	1	no	—
348	C₃×AGL(1,ℤ/8)	—	15	2	no	—
349	C₃×AGL(1,ℤ/8)	—	15	2	no	—
350	C₃×AGL(1,ℤ/8)	—	15	1	no	—
351	C₃×AGL(1,ℤ/8)	—	15	1	no	—
352	C₂×C₃×SD₁₆	—	15	2	no	—
353	C₂×C₃×D₈	—	15	2	no	—
354	C₂×C₃×M₁₆	—	15	1	no	—
355	C₂×#214	—	5	2	no	—
356	#932	—	5	1	no	—
357	#932	—	5	1	no	—
358	#932	—	5	2	no	—
359	#932	—	5	2	no	—
360	#932	—	5	1	no	—
361	#932	C₃×D₅	1	1	yes	characteristic, direct product factor
362	C₂×#213	—	5	2	no	—
363	C₂×#208	—	5	1	no	—
364	C₂×C₃²×C₅	—	2	1	no	—
365	C₂×C₃²×C₅	—	4	2	no	—
366	C₂×C₃²×C₅	C₂²×D₄	1	1	yes	characteristic
367	C₃×D₁₅	—	4	1	no	—
368	C₃×C₅×D₃	—	4	1	no	—
369	C₃²×D₅	—	2	1	no	—
370	C₃²×D₅	—	4	2	no	—
371	C₃²×D₅	AGL(1,ℤ/8)	1	2	yes	complemented
372	C₂³×D₅	—	2	1	no	—
373	C₅×#41	—	3	1	no	—
374	C₂×C₅×D₄	C₂×C₃×D₃	1	1	yes	characteristic, complemented
375	C₂×C₂²⋊D₅	—	2	1	no	—
376	#713	—	3	1	no	—
377	Q₈×D₅	—	3	1	no	—
378	#711	—	3	1	no	—
379	#711	—	6	1	no	—
380	D₄×D₅	—	2	1	no	—
381	D₄×D₅	—	2	1	no	—
382	D₄×D₅	—	3	1	no	—
383	D₄×D₅	—	6	1	no	—
384	D₄×D₅	C₂×C₃×D₃	1	2	yes	—
385	D₄×D₅	C₂×C₃×D₃	1	2	yes	complemented
386	#709	—	3	1	no	—
387	#709	—	6	1	no	—
388	C₂×D₂₀	C₂×C₃×D₃	1	1	yes	characteristic, complemented
389	C₂×C₄×D₅	—	6	1	no	—
390	C₂×C₄×D₅	C₂×C₃×D₃	1	1	yes	characteristic
391	C₅×SD₁₆	—	3	2	no	—
392	C₅×D₈	—	3	2	no	—
393	C₅×M₁₆	—	3	1	no	—
394	#688	—	3	2	no	—
395	#687	—	3	2	no	—
396	#686	—	3	2	no	—
397	#686	—	3	2	no	—
398	#681	—	3	1	no	—
399	D₄₀	—	3	2	no	—
400	#677	—	3	2	no	—
401	#676	—	3	2	no	—
402	C₈×D₅	—	3	2	no	—
403	C₂³×C₃²	—	2	1	no	—
404	C₂³×C₃²	—	5	1	no	—
405	C₂³×C₃²	—	10	2	no	—
406	C₂³×C₃²	—	10	2	no	—
407	C₂³×C₃²	—	10	1	no	—
408	C₂³×C₃²	—	20	4	no	—
409	C₂²×C₃×D₃	—	10	1	no	—
410	C₃²×D₄	—	2	1	no	—
411	C₃²×D₄	—	5	2	no	—
412	C₃²×D₄	—	10	2	no	—
413	C₃²×D₄	—	10	2	no	—
414	C₃²×D₄	—	10	1	no	—
415	C₃²×D₄	C₂²×D₅	1	2	yes	—
416	C₂×C₃²×C₄	—	5	1	no	—
417	C₂×C₃²×C₄	—	5	1	no	—
418	C₂×C₃²×C₄	—	5	1	no	—
419	C₂×C₃²×C₄	—	5	1	no	—
420	C₂×C₃²×C₄	—	5	1	no	—
421	C₂×C₃²×C₄	C₂²×D₅	1	1	yes	characteristic
422	C₃×#67	—	2	1	no	—
423	C₃×#67	—	10	1	no	—
424	C₃×#67	—	10	1	no	—
425	C₃×#67	—	10	1	no	—
426	C₂×C₃×Dic₃	—	10	1	no	—
427	C₃×D₁₂	—	5	1	no	—
428	C₃×D₁₂	—	10	1	no	—
429	C₃×D₁₂	C₂²×D₅	1	1	yes	characteristic, complemented
430	C₃×C₄×D₃	—	2	1	no	—
431	C₃×C₄×D₃	—	10	1	no	—
432	C₃×C₄×D₃	—	10	1	no	—
433	C₃×C₄×D₃	—	10	1	no	—
434	C₃×Dic₆	—	5	1	no	—
435	C₃×Dic₆	—	10	1	no	—
436	C₃×Dic₆	C₂²×D₅	1	1	yes	characteristic, complemented
437	C₃×C₃⋊C₈	—	5	2	no	—
438	C₃×C₃⋊C₈	C₂²×D₅	1	2	yes	complemented
439	C₂×AGL(1,ℤ/8)	—	15	1	no	Sylow
440	C₂²×C₃×C₅	—	2	4	no	—
441	C₂²×C₃×C₅	—	2	2	no	—
442	C₂²×C₃×C₅	—	2	2	no	—
443	C₂²×C₃×C₅	—	2	1	no	—
444	C₂²×C₃×C₅	—	4	4	no	—
445	C₂²×C₃×C₅	—	4	2	no	—
446	C₂²×C₃×C₅	—	4	2	no	—
447	C₂²×C₃×C₅	—	6	1	no	—
448	C₂²×C₃×C₅	C₂×#67	1	1	yes	characteristic
449	C₂²×C₃×C₅	C₂×C₃×D₄	1	1	yes	characteristic
450	C₂×D₁₅	—	2	1	no	—
451	C₂×C₅×D₃	—	2	1	no	—
452	C₂×C₃×D₅	—	2	4	no	—
453	C₂×C₃×D₅	—	2	2	no	—
454	C₂×C₃×D₅	—	2	2	no	—
455	C₂×C₃×D₅	—	2	4	no	—
456	C₂×C₃×D₅	—	2	2	no	—
457	C₂×C₃×D₅	—	2	2	no	—
458	C₂×C₃×D₅	—	2	1	no	—
459	C₂×C₃×D₅	—	2	1	no	—
460	C₂×C₃×D₅	—	4	8	no	—
461	C₂×C₃×D₅	—	4	4	no	—
462	C₂×C₃×D₅	—	4	4	no	—
463	C₂×C₃×D₅	—	4	8	no	—
464	C₂×C₃×D₅	—	4	4	no	—
465	C₂×C₃×D₅	—	4	2	no	—
466	C₂×C₃×D₅	—	4	2	no	—
467	C₂×C₃×D₅	—	4	4	no	—
468	C₂×C₃×D₅	—	4	4	no	—
469	C₂×C₃×D₅	—	6	1	no	—
470	C₂×C₃×D₅	—	12	2	no	—
471	C₂×C₃×D₅	C₂×#67	1	1	yes	characteristic
472	C₂×C₃×D₅	C₂×#67	1	1	yes	characteristic
473	C₂×C₃×D₅	C₂×C₃×D₄	1	1	yes	characteristic
474	C₂×C₃×D₅	C₂×C₃×D₄	1	1	yes	characteristic
475	D₃×D₅	—	4	2	no	—
476	C₃×C₄×C₅	—	2	1	no	—
477	C₃×C₄×C₅	—	2	1	no	—
478	C₃×C₄×C₅	—	6	1	no	—
479	C₃×C₄×C₅	C₂×#67	1	1	yes	characteristic
480	C₃×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
481	C₃×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
482	C₃×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
483	Dic₁₅	—	2	1	no	—
484	C₃×Dic₅	—	2	1	no	—
485	C₃×Dic₅	—	2	1	no	—
486	C₃×Dic₅	—	6	1	no	—
487	C₃×Dic₅	C₂×#67	1	1	yes	characteristic
488	C₃×Dic₅	C₂×#67	1	1	yes	characteristic
489	C₃×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
490	C₃×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
491	C₅×Dic₃	—	2	1	no	—
492	C₂⁴×C₃	—	10	1	no	—
493	C₂⁴×C₃	—	10	1	no	—
494	C₂⁴×C₃	—	10	2	no	—
495	C₃×#41	—	3	1	no	—
496	C₃×#41	—	15	1	no	—
497	C₃×#41	—	15	1	no	—
498	C₃×#41	—	15	1	no	—
499	C₃×#41	—	30	1	no	—
500	C₃×#41	—	30	1	no	—
501	C₂×C₃×Q₈	—	15	1	no	—
502	C₂×C₃×D₄	—	2	1	no	—
503	C₂×C₃×D₄	—	5	2	no	—
504	C₂×C₃×D₄	—	5	2	no	—
505	C₂×C₃×D₄	—	5	2	no	—
506	C₂×C₃×D₄	—	5	2	no	—
507	C₂×C₃×D₄	—	5	1	no	—
508	C₂×C₃×D₄	—	5	1	no	—
509	C₂×C₃×D₄	—	10	1	no	—
510	C₂×C₃×D₄	—	10	2	no	—
511	C₂×C₃×D₄	—	10	2	no	—
512	C₂×C₃×D₄	—	10	1	no	—
513	C₂×C₃×D₄	—	10	1	no	—
514	C₂×C₃×D₄	—	10	1	no	—
515	C₂×C₃×D₄	—	10	1	no	—
516	C₂×C₃×D₄	—	10	1	no	—
517	C₂×C₃×D₄	—	10	1	no	—
518	C₂×C₃×D₄	—	10	2	no	—
519	C₂×C₃×D₄	—	10	2	no	—
520	C₂×C₃×D₄	—	10	2	no	—
521	C₂×C₃×D₄	—	15	1	no	—
522	C₂×C₃×D₄	—	30	1	no	—
523	C₂×C₃×D₄	D₃×D₅	1	1	yes	characteristic, complemented
524	C₂×C₃×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
525	C₂²×C₃×C₄	—	5	1	no	—
526	C₂²×C₃×C₄	—	5	1	no	—
527	C₂²×C₃×C₄	—	10	1	no	—
528	C₂²×C₃×C₄	—	30	1	no	—
529	C₂×#67	—	10	1	no	—
530	#235	—	5	1	no	—
531	#235	—	5	1	no	—
532	#235	—	5	1	no	—
533	#235	—	10	1	no	—
534	#235	—	10	1	no	—
535	#235	C₂×C₃×D₅	1	1	yes	characteristic, complemented
536	C₂×D₁₂	—	5	1	no	—
537	C₂×C₄×D₃	—	10	1	no	—
538	C₂×Dic₆	—	5	1	no	—
539	C₃×SD₁₆	—	3	2	no	—
540	C₃×SD₁₆	—	15	2	no	—
541	C₃×SD₁₆	—	15	2	no	—
542	C₃×SD₁₆	—	15	2	no	—
543	C₃×D₈	—	3	2	no	—
544	C₃×D₈	—	15	2	no	—
545	C₃×D₈	—	15	2	no	—
546	C₃×D₈	—	15	2	no	—
547	C₃×M₁₆	—	3	1	no	—
548	C₃×M₁₆	—	15	2	no	—
549	C₃×M₁₆	—	15	1	no	—
550	C₂×C₃×C₈	—	15	2	no	—
551	#214	—	5	2	no	—
552	#214	—	5	2	no	—
553	#214	—	5	2	no	—
554	#214	C₂×C₃×D₅	1	2	yes	complemented
555	#213	—	5	2	no	—
556	#213	—	5	2	no	—
557	#213	—	5	2	no	—
558	#213	C₂×C₃×D₅	1	2	yes	complemented
559	#208	—	5	1	no	—
560	#208	—	5	2	no	—
561	#208	C₂×C₃×D₅	1	1	yes	characteristic, complemented
562	C₂×C₃⋊C₈	—	5	2	no	—
563	C₃²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Hall
564	C₂³×C₅	—	2	1	no	—
565	C₂²×D₅	—	2	1	no	—
566	C₂²×D₅	—	2	2	no	—
567	C₂²×D₅	—	2	2	no	—
568	C₂²×D₅	—	4	4	no	—
569	C₂²×D₅	—	6	1	no	—
570	C₂²×D₅	C₃×#67	1	1	yes	characteristic
571	C₅×Q₈	—	3	1	no	—
572	C₅×D₄	—	2	1	no	—
573	C₅×D₄	—	3	1	no	—
574	C₅×D₄	—	6	1	no	—
575	C₅×D₄	C₂²×C₃×D₃	1	2	yes	—
576	C₂×C₄×C₅	—	6	1	no	—
577	C₂×C₄×C₅	C₂²×C₃×D₃	1	1	yes	characteristic
578	C₂²⋊D₅	—	2	2	no	—
579	C₂²⋊D₅	—	2	2	no	—
580	C₂²⋊D₅	—	6	1	no	—
581	C₂²⋊D₅	—	6	1	no	—
582	C₂²⋊D₅	—	6	1	no	—
583	C₂×Dic₅	—	6	1	no	—
584	C₂×Dic₅	C₃×#67	1	1	yes	characteristic
585	D₂₀	—	2	1	no	—
586	D₂₀	—	3	1	no	—
587	D₂₀	—	6	1	no	—
588	D₂₀	C₂²×C₃×D₃	1	2	yes	—
589	C₄×D₅	—	6	1	no	—
590	C₄×D₅	—	6	1	no	—
591	C₄×D₅	—	6	1	no	—
592	C₄×D₅	C₃×#67	1	1	yes	characteristic
593	C₄×D₅	C₃×#67	1	1	yes	characteristic
594	C₄×D₅	C₂²×C₃×D₃	1	1	yes	characteristic
595	C₄×D₅	C₂²×C₃×D₃	1	1	yes	characteristic
596	Dic₁₀	—	3	1	no	—
597	Dic₁₀	—	6	1	no	—
598	C₅×C₈	—	3	2	no	—
599	#168	—	3	2	no	—
600	C₂²×C₃²	—	2	2	no	—
601	C₂²×C₃²	—	4	2	no	—
602	C₂²×C₃²	—	5	1	no	—
603	C₂²×C₃²	—	5	1	no	—
604	C₂²×C₃²	—	10	2	no	—
605	C₂²×C₃²	—	10	2	no	—
606	C₂²×C₃²	—	20	2	no	—
607	C₂²×C₃²	—	20	4	no	—
608	C₂²×C₃²	—	20	4	no	—
609	C₂²×C₃²	D₄×D₅	1	1	yes	characteristic
610	C₂×C₃×D₃	—	2	1	no	—
611	C₂×C₃×D₃	—	10	1	no	—
612	C₂×C₃×D₃	—	20	2	no	—
613	C₃²×C₄	—	5	1	no	—
614	C₃²×C₄	—	5	1	no	—
615	C₃²×C₄	D₄×D₅	1	1	yes	characteristic
616	C₃²×C₄	C₂³×D₅	1	1	yes	characteristic
617	C₃×Dic₃	—	2	1	no	—
618	C₃×Dic₃	—	10	1	no	—
619	C₂×#41	—	15	1	no	—
620	C₂²×D₄	—	5	1	no	—
621	AGL(1,ℤ/8)	—	3	1	no	—
622	AGL(1,ℤ/8)	—	15	1	no	—
623	AGL(1,ℤ/8)	—	15	2	no	—
624	AGL(1,ℤ/8)	—	15	2	no	—
625	AGL(1,ℤ/8)	—	15	1	no	—
626	AGL(1,ℤ/8)	—	15	1	no	—
627	C₂×SD₁₆	—	15	2	no	—
628	C₂×D₈	—	15	2	no	—
629	C₂×M₁₆	—	15	1	no	—
630	C₂×C₃×C₅	—	2	2	no	—
631	C₂×C₃×C₅	—	2	1	no	—
632	C₂×C₃×C₅	—	2	1	no	—
633	C₂×C₃×C₅	—	2	1	no	—
634	C₂×C₃×C₅	—	4	4	no	—
635	C₂×C₃×C₅	—	4	2	no	—
636	C₂×C₃×C₅	—	4	2	no	—
637	C₂×C₃×C₅	—	12	1	no	—
638	C₂×C₃×C₅	C₂²×#67	1	1	yes	characteristic
639	C₂×C₃×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
640	D₁₅	—	4	1	no	—
641	C₃×D₅	—	2	2	no	—
642	C₃×D₅	—	2	1	no	—
643	C₃×D₅	—	2	1	no	—
644	C₃×D₅	—	2	2	no	—
645	C₃×D₅	—	4	4	no	—
646	C₃×D₅	—	4	2	no	—
647	C₃×D₅	—	4	2	no	—
648	C₃×D₅	—	12	1	no	—
649	C₃×D₅	#932	1	2	yes	direct product factor
650	C₃×D₅	C₃×AGL(1,ℤ/8)	1	2	yes	complemented
651	C₅×D₃	—	4	1	no	—
652	C₂³×C₃	—	2	2	no	—
653	C₂³×C₃	—	2	1	no	—
654	C₂³×C₃	—	2	1	no	—
655	C₂³×C₃	—	5	1	no	—
656	C₂³×C₃	—	5	1	no	—
657	C₂³×C₃	—	10	1	no	—
658	C₂³×C₃	—	10	2	no	—
659	C₂³×C₃	—	10	2	no	—
660	C₂³×C₃	—	10	2	no	—
661	C₂³×C₃	—	10	2	no	—
662	C₂³×C₃	—	10	4	no	—
663	C₂³×C₃	—	10	4	no	—
664	C₂³×C₃	—	10	2	no	—
665	C₂³×C₃	—	10	1	no	—
666	C₂³×C₃	—	10	1	no	—
667	C₂³×C₃	—	20	4	no	—
668	C₂³×C₃	—	20	4	no	—
669	C₂³×C₃	—	20	8	no	—
670	C₂³×C₃	—	30	1	no	—
671	C₂²×D₃	—	10	1	no	—
672	C₃×Q₈	—	3	1	no	—
673	C₃×Q₈	—	15	1	no	—
674	C₃×Q₈	—	30	1	no	—
675	C₃×D₄	—	2	2	no	—
676	C₃×D₄	—	2	1	no	—
677	C₃×D₄	—	2	1	no	—
678	C₃×D₄	—	2	2	no	—
679	C₃×D₄	—	3	1	no	—
680	C₃×D₄	—	5	2	no	—
681	C₃×D₄	—	5	2	no	—
682	C₃×D₄	—	6	1	no	—
683	C₃×D₄	—	10	2	no	—
684	C₃×D₄	—	10	2	no	—
685	C₃×D₄	—	10	2	no	—
686	C₃×D₄	—	10	2	no	—
687	C₃×D₄	—	10	2	no	—
688	C₃×D₄	—	10	2	no	—
689	C₃×D₄	—	10	4	no	—
690	C₃×D₄	—	10	4	no	—
691	C₃×D₄	—	10	1	no	—
692	C₃×D₄	—	10	1	no	—
693	C₃×D₄	—	15	1	no	—
694	C₃×D₄	—	30	1	no	—
695	C₃×D₄	—	30	1	no	—
696	C₃×D₄	—	30	1	no	—
697	C₃×D₄	—	30	1	no	—
698	C₃×D₄	C₂×D₃×D₅	1	2	yes	—
699	C₃×D₄	C₂²×C₃×D₅	1	2	yes	—
700	C₂×C₃×C₄	—	2	1	no	—
701	C₂×C₃×C₄	—	5	1	no	—
702	C₂×C₃×C₄	—	5	1	no	—
703	C₂×C₃×C₄	—	5	1	no	—
704	C₂×C₃×C₄	—	5	1	no	—
705	C₂×C₃×C₄	—	5	1	no	—
706	C₂×C₃×C₄	—	5	1	no	—
707	C₂×C₃×C₄	—	5	1	no	—
708	C₂×C₃×C₄	—	5	1	no	—
709	C₂×C₃×C₄	—	5	1	no	—
710	C₂×C₃×C₄	—	5	1	no	—
711	C₂×C₃×C₄	—	6	1	no	—
712	C₂×C₃×C₄	—	10	1	no	—
713	C₂×C₃×C₄	—	10	1	no	—
714	C₂×C₃×C₄	—	10	1	no	—
715	C₂×C₃×C₄	—	10	1	no	—
716	C₂×C₃×C₄	—	10	1	no	—
717	C₂×C₃×C₄	—	30	1	no	—
718	C₂×C₃×C₄	—	30	1	no	—
719	C₂×C₃×C₄	—	30	1	no	—
720	C₂×C₃×C₄	—	30	1	no	—
721	C₂×C₃×C₄	C₂×D₃×D₅	1	1	yes	characteristic
722	C₂×C₃×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
723	#67	—	2	1	no	—
724	#67	—	10	1	no	—
725	#67	—	10	1	no	—
726	#67	—	10	1	no	—
727	C₂×Dic₃	—	10	1	no	—
728	D₁₂	—	5	1	no	—
729	D₁₂	—	10	1	no	—
730	D₁₂	C₂²×C₃×D₅	1	1	yes	characteristic, complemented
731	C₄×D₃	—	2	1	no	—
732	C₄×D₃	—	10	1	no	—
733	C₄×D₃	—	10	1	no	—
734	C₄×D₃	—	10	1	no	—
735	Dic₆	—	5	1	no	—
736	Dic₆	—	10	1	no	—
737	Dic₆	C₂²×C₃×D₅	1	1	yes	characteristic, complemented
738	C₃×C₈	—	3	2	no	—
739	C₃×C₈	—	15	2	no	—
740	C₃⋊C₈	—	5	2	no	—
741	C₃⋊C₈	C₂²×C₃×D₅	1	2	yes	complemented
742	C₂²×C₅	—	2	2	no	—
743	C₂²×C₅	—	4	2	no	—
744	C₂²×C₅	—	6	1	no	—
745	C₂²×C₅	C₂×C₃×#67	1	1	yes	characteristic
746	C₂×D₅	—	2	2	no	—
747	C₂×D₅	—	2	2	no	—
748	C₂×D₅	—	4	4	no	—
749	C₂×D₅	—	4	2	no	—
750	C₂×D₅	—	4	4	no	—
751	C₂×D₅	—	6	1	no	—
752	C₂×D₅	—	12	2	no	—
753	C₂×D₅	C₂×C₃×#67	1	1	yes	characteristic
754	C₂×D₅	C₂×C₃×#67	1	1	yes	characteristic
755	C₄×C₅	—	6	1	no	—
756	C₄×C₅	C₂×C₃×#67	1	1	yes	characteristic
757	C₄×C₅	C₂³×C₃×D₃	1	1	yes	characteristic
758	Dic₅	—	6	1	no	—
759	Dic₅	C₂×C₃×#67	1	1	yes	characteristic
760	Dic₅	C₂×C₃×#67	1	1	yes	characteristic
761	C₂×C₃²	—	2	1	no	—
762	C₂×C₃²	—	4	2	no	—
763	C₂×C₃²	—	5	2	no	—
764	C₂×C₃²	—	10	1	no	—
765	C₂×C₃²	—	20	2	no	—
766	C₂×C₃²	C₂×D₄×D₅	1	1	yes	characteristic
767	C₃×D₃	—	4	1	no	—
768	C₃×D₃	—	20	1	no	—
769	C₂⁴	—	10	1	no	—
770	#41	—	3	1	no	—
771	#41	—	15	1	no	—
772	#41	—	15	1	no	—
773	#41	—	15	1	no	—
774	#41	—	30	1	no	—
775	#41	—	30	1	no	—
776	C₂×Q₈	—	15	1	no	—
777	C₂×D₄	—	5	2	no	—
778	C₂×D₄	—	5	2	no	—
779	C₂×D₄	—	5	1	no	—
780	C₂×D₄	—	10	1	no	—
781	C₂×D₄	—	10	1	no	—
782	C₂×D₄	—	10	1	no	—
783	C₂×D₄	—	15	1	no	—
784	C₂×D₄	—	30	1	no	—
785	C₂×D₄	C₃×D₃×D₅	1	1	yes	characteristic, complemented
786	C₂²×C₄	—	5	1	no	—
787	C₂²×C₄	—	30	1	no	—
788	SD₁₆	—	3	2	no	—
789	SD₁₆	—	15	2	no	—
790	SD₁₆	—	15	2	no	—
791	SD₁₆	—	15	2	no	—
792	D₈	—	3	2	no	—
793	D₈	—	15	2	no	—
794	D₈	—	15	2	no	—
795	D₈	—	15	2	no	—
796	M₁₆	—	3	1	no	—
797	M₁₆	—	15	2	no	—
798	M₁₆	—	15	1	no	—
799	C₂×C₈	—	15	2	no	—
800	C₃×C₅	—	2	1	no	—
801	C₃×C₅	C₂×#932	1	1	yes	characteristic, complemented
802	C₃×C₅	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented
803	C₂²×C₃	—	2	4	no	—
804	C₂²×C₃	—	2	2	no	—
805	C₂²×C₃	—	2	2	no	—
806	C₂²×C₃	—	2	1	no	—
807	C₂²×C₃	—	4	4	no	—
808	C₂²×C₃	—	4	2	no	—
809	C₂²×C₃	—	4	2	no	—
810	C₂²×C₃	—	5	1	no	—
811	C₂²×C₃	—	5	1	no	—
812	C₂²×C₃	—	5	1	no	—
813	C₂²×C₃	—	5	1	no	—
814	C₂²×C₃	—	6	1	no	—
815	C₂²×C₃	—	10	1	no	—
816	C₂²×C₃	—	10	1	no	—
817	C₂²×C₃	—	10	2	no	—
818	C₂²×C₃	—	10	2	no	—
819	C₂²×C₃	—	10	4	no	—
820	C₂²×C₃	—	10	4	no	—
821	C₂²×C₃	—	10	2	no	—
822	C₂²×C₃	—	10	2	no	—
823	C₂²×C₃	—	20	4	no	—
824	C₂²×C₃	—	20	2	no	—
825	C₂²×C₃	—	20	2	no	—
826	C₂²×C₃	—	20	4	no	—
827	C₂²×C₃	—	20	4	no	—
828	C₂²×C₃	—	20	8	no	—
829	C₂²×C₃	—	20	8	no	—
830	C₂²×C₃	—	20	4	no	—
831	C₂²×C₃	—	20	4	no	—
832	C₂²×C₃	—	30	1	no	—
833	C₂²×C₃	—	60	2	no	—
834	C₂²×C₃	D₅×#67	1	1	yes	characteristic
835	C₂²×C₃	C₃×D₄×D₅	1	1	yes	characteristic
836	C₂×D₃	—	2	1	no	—
837	C₂×D₃	—	10	1	no	—
838	C₂×D₃	—	20	2	no	—
839	C₃×C₄	—	2	1	no	—
840	C₃×C₄	—	2	1	no	—
841	C₃×C₄	—	5	1	no	—
842	C₃×C₄	—	5	1	no	—
843	C₃×C₄	—	5	1	no	—
844	C₃×C₄	—	5	1	no	—
845	C₃×C₄	—	6	1	no	—
846	C₃×C₄	—	10	1	no	—
847	C₃×C₄	—	10	1	no	—
848	C₃×C₄	—	30	1	no	—
849	C₃×C₄	D₅×#67	1	1	yes	characteristic
850	C₃×C₄	C₃×D₄×D₅	1	1	yes	characteristic
851	C₃×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
852	C₃×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
853	Dic₃	—	2	1	no	—
854	Dic₃	—	10	1	no	—
855	C₂×C₅	—	2	1	no	—
856	C₂×C₅	—	4	2	no	—
857	C₂×C₅	—	12	1	no	—
858	C₂×C₅	C₂²×C₃×#67	1	1	yes	characteristic
859	D₅	—	2	1	no	—
860	D₅	—	4	2	no	—
861	D₅	—	12	1	no	—
862	D₅	C₃×#932	1	2	yes	direct product factor
863	C₃²	D₅×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
864	C₂³	—	2	1	no	—
865	C₂³	—	5	1	no	—
866	C₂³	—	10	2	no	—
867	C₂³	—	10	2	no	—
868	C₂³	—	10	1	no	—
869	C₂³	—	20	4	no	—
870	C₂³	—	30	1	no	—
871	Q₈	—	3	1	no	—
872	Q₈	—	15	1	no	—
873	Q₈	—	30	1	no	—
874	D₄	—	2	1	no	—
875	D₄	—	3	1	no	—
876	D₄	—	5	2	no	—
877	D₄	—	6	1	no	—
878	D₄	—	10	2	no	—
879	D₄	—	10	2	no	—
880	D₄	—	10	1	no	—
881	D₄	—	15	1	no	—
882	D₄	—	30	1	no	—
883	D₄	—	30	1	no	—
884	D₄	—	30	1	no	—
885	D₄	—	30	1	no	—
886	D₄	C₂×C₃×D₃×D₅	1	2	yes	—
887	C₂×C₄	—	5	1	no	—
888	C₂×C₄	—	5	1	no	—
889	C₂×C₄	—	5	1	no	—
890	C₂×C₄	—	5	1	no	—
891	C₂×C₄	—	5	1	no	—
892	C₂×C₄	—	6	1	no	—
893	C₂×C₄	—	30	1	no	—
894	C₂×C₄	—	30	1	no	—
895	C₂×C₄	—	30	1	no	—
896	C₂×C₄	—	30	1	no	—
897	C₂×C₄	C₂×C₃×D₃×D₅	1	1	yes	characteristic
898	C₈	—	3	2	no	—
899	C₈	—	15	2	no	—
900	C₂×C₃	—	2	2	no	—
901	C₂×C₃	—	2	1	no	—
902	C₂×C₃	—	2	1	no	—
903	C₂×C₃	—	2	1	no	—
904	C₂×C₃	—	4	4	no	—
905	C₂×C₃	—	4	2	no	—
906	C₂×C₃	—	4	2	no	—
907	C₂×C₃	—	5	2	no	—
908	C₂×C₃	—	5	2	no	—
909	C₂×C₃	—	10	2	no	—
910	C₂×C₃	—	10	2	no	—
911	C₂×C₃	—	10	1	no	—
912	C₂×C₃	—	10	1	no	—
913	C₂×C₃	—	12	1	no	—
914	C₂×C₃	—	20	4	no	—
915	C₂×C₃	—	20	2	no	—
916	C₂×C₃	—	20	2	no	—
917	C₂×C₃	—	60	1	no	—
918	C₂×C₃	C₂×D₅×#67	1	1	yes	characteristic
919	C₂×C₃	C₂×C₃×D₄×D₅	1	1	yes	characteristic
920	D₃	—	4	1	no	—
921	D₃	—	20	1	no	—
922	C₅	C₂×C₃×#932	1	1	yes	characteristic, complemented, Sylow
923	C₂²	—	2	2	no	—
924	C₂²	—	4	2	no	—
925	C₂²	—	5	1	no	—
926	C₂²	—	5	1	no	—
927	C₂²	—	6	1	no	—
928	C₂²	—	10	2	no	—
929	C₂²	—	10	2	no	—
930	C₂²	—	20	2	no	—
931	C₂²	—	20	4	no	—
932	C₂²	—	20	4	no	—
933	C₂²	—	30	1	no	—
934	C₂²	—	60	2	no	—
935	C₂²	C₃×D₅×#67	1	1	yes	characteristic
936	C₄	—	5	1	no	—
937	C₄	—	5	1	no	—
938	C₄	—	6	1	no	—
939	C₄	—	30	1	no	—
940	C₄	C₃×D₅×#67	1	1	yes	characteristic
941	C₄	C₂²×C₃×D₃×D₅	1	1	yes	characteristic
942	C₃	—	2	1	no	—
943	C₃	D₅×#932	1	1	yes	characteristic, direct product factor
944	C₃	C₃×D₅×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented
945	C₂	—	2	1	no	—
946	C₂	—	4	2	no	—
947	C₂	—	5	2	no	—
948	C₂	—	10	1	no	—
949	C₂	—	12	1	no	—
950	C₂	—	20	2	no	—
951	C₂	—	60	1	no	—
952	C₂	C₂×C₃×D₅×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₅×#67
commutator, cosocle	C₃×C₄×C₅	C₂⁴×C₃
Frattini	C₄	C₂²×C₃×D₃×D₅
Fitting	C₂×C₃²×C₅×D₄	C₂²
socle	C₂×C₃²×C₅	C₂²×D₄
hypercenter	C₂×C₃×D₄	D₃×D₅
hypocenter	C₃×C₅	C₂×C₃×AGL(1,ℤ/8)
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×D₄×D₅	C₂	semidirect
2. C₃×D₅×#235	C₂	semidirect
3. C₃×#91821	C₂	semidirect
4. C₃×C₅×#932	C₂	semidirect
5. C₃×#91491	C₂	semidirect
6. C₃×#91489	C₂	semidirect
7. C₃×D₅×#214	C₂	semidirect
8. C₃×D₅×#213	C₂	semidirect
9. C₃×#91312	C₂	semidirect
10. C₃×#91298	C₂	semidirect
11. C₃×D₅×#208	C₂	semidirect
13. D₅×#932	C₃	direct (N × H)
15. C₂×C₃²×C₅×D₄	C₂²	semidirect
16. C₃×#6817	C₂²	semidirect
17. C₃×C₅×#235	C₂²	semidirect
22. C₃²×D₄×D₅	C₂²	semidirect
23. C₂×C₃²×D₂₀	C₂²	semidirect
27. C₃×D₅×D₁₂	C₂²	semidirect
29. C₃×#6773	C₂²	semidirect
30. C₃×#6772	C₂²	semidirect
32. C₃×D₅×Dic₆	C₂²	semidirect
33. C₃×#6716	C₂²	semidirect
34. C₃×#6715	C₂²	semidirect
35. C₃×#6710	C₂²	semidirect
36. C₃×C₅×#214	C₂²	semidirect
37. C₃×C₅×#213	C₂²	semidirect
38. C₃×C₅×#208	C₂²	semidirect
39. C₃×#6657	C₂²	semidirect
40. C₃×#6655	C₂²	semidirect
41. C₃×#6653	C₂²	semidirect
42. C₃×#6652	C₂²	semidirect
43. C₃×#6649	C₂²	semidirect
44. C₃×D₅×C₃⋊C₈	C₂²	semidirect
48. C₂×C₃×D₄×D₅	D₃	semidirect
49. C₂×C₃×D₄×D₅	C₂×C₃	semidirect
50. D₅×#235	C₂×C₃	semidirect
52. #91821	C₂×C₃	semidirect
53. C₅×#932	C₂×C₃	semidirect
62. #91491	C₂×C₃	semidirect
63. #91489	C₂×C₃	semidirect
64. D₅×#214	C₂×C₃	semidirect
65. D₅×#213	C₂×C₃	semidirect
66. #91312	C₂×C₃	semidirect
67. #91298	C₂×C₃	semidirect
68. D₅×#208	C₂×C₃	semidirect
80. C₃×D₆₀	C₂³	semidirect
82. C₃×Dic₃₀	C₂³	semidirect
84. C₃×C₅×D₁₂	C₂³	semidirect
86. C₃×C₅×Dic₆	C₂³	semidirect
103. C₃×C₃⋊#168	C₂³	semidirect
104. C₃×C₅×C₃⋊C₈	C₂³	semidirect
114. C₃×#932	D₅	direct (N × H)
122. C₂×C₃×C₅×D₄	C₂×D₃	semidirect
123. C₂×C₃×C₅×D₄	C₂²×C₃	semidirect
124. #6817	C₂²×C₃	semidirect
125. C₅×#235	C₂²×C₃	semidirect
144. C₃×D₄×D₅	C₂×D₃	semidirect
146. C₃×D₄×D₅	C₂²×C₃	semidirect
150. C₂×C₃×D₂₀	C₂×D₃	semidirect
151. C₂×C₃×D₂₀	C₂²×C₃	semidirect
158. D₅×D₁₂	C₂²×C₃	semidirect
160. #6773	C₂²×C₃	semidirect
161. #6772	C₂²×C₃	semidirect
163. D₅×Dic₆	C₂²×C₃	semidirect
167. #6716	C₂²×C₃	semidirect
168. #6715	C₂²×C₃	semidirect
169. #6710	C₂²×C₃	semidirect
170. C₅×#214	C₂²×C₃	semidirect
171. C₅×#213	C₂²×C₃	semidirect
172. C₅×#208	C₂²×C₃	semidirect
182. #6657	C₂²×C₃	semidirect
183. #6655	C₂²×C₃	semidirect
184. #6653	C₂²×C₃	semidirect
185. #6652	C₂²×C₃	semidirect
186. #6649	C₂²×C₃	semidirect
187. D₅×C₃⋊C₈	C₂²×C₃	semidirect
210. C₂×D₄×D₅	C₃×D₃	semidirect
227. C₂×C₃²×D₄	C₂×D₅	semidirect
235. C₃×#235	C₂×D₅	semidirect
242. C₃×#214	C₂×D₅	semidirect
246. C₃×#213	C₂×D₅	semidirect
249. C₃×#208	C₂×D₅	semidirect
285. D₆₀	C₂³×C₃	semidirect
287. Dic₃₀	C₂³×C₃	semidirect
289. C₅×D₁₂	C₂³×C₃	semidirect
291. C₅×Dic₆	C₂³×C₃	semidirect
338. C₃⋊#168	C₂³×C₃	semidirect
340. C₅×C₃⋊C₈	C₂³×C₃	semidirect
361. #932	C₃×D₅	direct (N × H)
371. C₃²×D₅	AGL(1,ℤ/8)	semidirect
374. C₂×C₅×D₄	C₂×C₃×D₃	semidirect
385. D₄×D₅	C₂×C₃×D₃	semidirect
388. C₂×D₂₀	C₂×C₃×D₃	semidirect
429. C₃×D₁₂	C₂²×D₅	semidirect
436. C₃×Dic₆	C₂²×D₅	semidirect
438. C₃×C₃⋊C₈	C₂²×D₅	semidirect
523. C₂×C₃×D₄	D₃×D₅	semidirect
524. C₂×C₃×D₄	C₂×C₃×D₅	semidirect
535. #235	C₂×C₃×D₅	semidirect
554. #214	C₂×C₃×D₅	semidirect
558. #213	C₂×C₃×D₅	semidirect
561. #208	C₂×C₃×D₅	semidirect
563. C₃²×C₅	C₂×AGL(1,ℤ/8)	semidirect
649. C₃×D₅	#932	direct (N × H)
650. C₃×D₅	C₃×AGL(1,ℤ/8)	semidirect
730. D₁₂	C₂²×C₃×D₅	semidirect
737. Dic₆	C₂²×C₃×D₅	semidirect
741. C₃⋊C₈	C₂²×C₃×D₅	semidirect
785. C₂×D₄	C₃×D₃×D₅	semidirect
801. C₃×C₅	C₂×#932	semidirect
802. C₃×C₅	C₂×C₃×AGL(1,ℤ/8)	semidirect
862. D₅	C₃×#932	direct (N × H)
863. C₃²	D₅×AGL(1,ℤ/8)	semidirect
922. C₅	C₂×C₃×#932	semidirect
943. C₃	D₅×#932	direct (N × H)
944. C₃	C₃×D₅×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×D₄×D₅	2
C₃×D₅×#235	2
C₃×#91821	2
C₃×C₅×#932	2
C₃×#91491	2
C₃×#91489	2
C₃×D₅×#214	2
C₃×D₅×#213	2
C₃×#91312	2
C₃×#91298	2
C₃×D₅×#208	2
C₃×D₅×AGL(1,ℤ/8)	3
D₅×#932	3
C₂×C₃×#932	5

Subgroups — C3×D5×#932 #72229613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#932 #72229613