Subgroups — C₃×#10617741 #14484148

Order 1920.

2264 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66162	C₂	1	2	yes	maximal, complemented
3	C₃×#65918	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65915	C₂	1	2	yes	maximal, complemented
5	C₃×#65913	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65897	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65892	C₂	1	2	yes	maximal, complemented
8	C₃×#65890	C₂	1	4	yes	maximal, complemented
9	C₃×#65885	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65884	C₂	1	2	yes	maximal, complemented
11	C₃×#65875	C₂	1	2	yes	maximal, complemented
12	C₃×#65862	C₂	1	4	yes	maximal, complemented
13	C₃×D₅×#117	C₂	1	2	yes	maximal, complemented
14	C₃×#65813	C₂	1	2	yes	maximal, complemented
15	C₃×C₄×#709	C₂	1	2	yes	maximal, complemented
16	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×#65804	C₂	1	1	yes	maximal, characteristic, complemented
18	#10617741	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
20	C₂×C₃×#709	C₂²	1	2	yes	—
21	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
23	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
26	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
27	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×#117	C₂²	1	1	yes	characteristic
30	C₃×C₅×#117	C₂²	1	2	yes	complemented
31	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
33	C₃×#4092	C₂²	1	2	yes	complemented
34	C₃×#4092	C₂²	1	2	yes	complemented
35	C₃×#4084	C₂²	1	2	yes	complemented
36	C₃×#4084	C₂²	1	2	yes	complemented
37	C₃×#4083	C₂²	1	4	yes	—
38	C₃×#4081	C₂²	1	4	yes	—
39	C₃×#4076	C₂²	1	2	yes	—
40	C₃×#4075	C₂²	1	4	yes	complemented
41	C₃×C₄×C₂²⋊D₅	C₂²	1	4	yes	complemented
42	C₃×C₄×C₂²⋊D₅	C₂²	1	4	yes	complemented
43	C₃×C₄×C₂²⋊D₅	C₂²	1	4	yes	complemented
44	C₂×C₃×#685	C₂²	1	2	yes	—
45	C₃×#4072	C₂²	1	2	yes	—
46	C₃×#4072	C₂²	1	2	yes	complemented
47	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
48	C₃×#4070	C₂²	1	2	yes	—
49	C₃×#4070	C₂²	1	2	yes	—
50	C₃×#4070	C₂²	1	2	yes	complemented
51	C₃×#4044	C₂²	1	4	yes	complemented
52	C₃×#4042	C₂²	1	4	yes	complemented
53	C₃×#4040	C₂²	1	4	yes	—
54	C₃×#4038	C₂²	1	2	yes	complemented
55	C₃×#4038	C₂²	1	2	yes	complemented
56	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
57	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
58	C₃×#4035	C₂²	1	4	yes	complemented
59	C₃×#4031	C₂²	1	4	yes	complemented
60	C₃×#4030	C₂²	1	4	yes	—
61	C₃×#4029	C₂²	1	4	yes	complemented
62	C₃×D₅×C₂²⋊C₄	C₂²	1	4	yes	—
63	C₃×#4025	C₂²	1	4	yes	complemented
64	C₃×#4023	C₂²	1	4	yes	—
65	C₃×#4022	C₂²	1	4	yes	complemented
66	C₃×#4021	C₂²	1	2	yes	—
67	C₃×C₄×D₂₀	C₂²	1	2	yes	—
68	C₃×C₄×D₂₀	C₂²	1	2	yes	—
69	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
70	C₃×C₄×D₂₀	C₂²	1	2	yes	—
71	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
72	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
73	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
74	C₃×#4018	C₂²	1	4	yes	complemented
75	C₃×#4018	C₂²	1	4	yes	complemented
76	C₃×C₄²×D₅	C₂²	1	4	yes	complemented
77	C₃×#4016	C₂²	1	2	yes	complemented
78	C₃×#4016	C₂²	1	2	yes	complemented
79	C₃×#4015	C₂²	1	1	yes	characteristic, complemented
80	C₃×#4015	C₂²	1	1	yes	characteristic, complemented
81	C₃×C₄×Dic₁₀	C₂²	1	2	yes	complemented
82	C₃×C₄×Dic₁₀	C₂²	1	2	yes	complemented
83	C₃×C₄×Dic₁₀	C₂²	1	2	yes	complemented
84	C₃×#3475	—	5	1	no	maximal, Hall
85	C₄×C₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
86	#66162	C₂×C₃	1	2	yes	complemented
87	#65918	C₂×C₃	1	1	yes	characteristic, complemented
88	#65915	C₂×C₃	1	2	yes	complemented
89	#65913	C₂×C₃	1	1	yes	characteristic, complemented
90	#65897	C₂×C₃	1	1	yes	characteristic, complemented
91	#65892	C₂×C₃	1	2	yes	complemented
92	#65890	C₂×C₃	1	4	yes	complemented
93	#65885	C₂×C₃	1	1	yes	characteristic, complemented
94	#65884	C₂×C₃	1	2	yes	complemented
95	#65875	C₂×C₃	1	2	yes	complemented
96	#65862	C₂×C₃	1	4	yes	complemented
97	D₅×#117	C₂×C₃	1	2	yes	complemented
98	#65813	C₂×C₃	1	2	yes	complemented
99	C₄×#709	C₂×C₃	1	2	yes	complemented
100	C₂×C₄×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
101	#65804	C₂×C₃	1	1	yes	characteristic, complemented
102	C₂³×C₃×D₅	C₂³	1	2	yes	—
103	C₃×C₅×#41	—	2	4	no	—
104	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
106	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
107	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
108	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
109	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
110	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
111	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
112	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
113	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
114	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
115	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
116	C₃×#709	—	2	8	no	—
117	C₂×C₃×D₂₀	—	2	4	no	—
118	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
119	C₂×C₃×D₂₀	C₂³	1	2	yes	—
120	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
121	C₂×C₃×C₄×D₅	—	2	8	no	—
122	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
123	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
124	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
125	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
126	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
127	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
128	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
129	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
130	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
131	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
133	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
134	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
136	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
138	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
139	C₃×C₄²×C₅	C₂³	1	2	yes	—
140	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
141	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
142	C₃×C₄²×C₅	C₂³	1	2	yes	—
143	C₃×C₄²×C₅	C₂³	1	2	yes	—
144	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
145	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
146	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
147	C₃×#685	C₂³	1	4	yes	—
148	C₃×#685	C₂³	1	4	yes	—
149	C₃×#685	C₂³	1	2	yes	—
150	C₃×#685	C₂³	1	4	yes	—
151	C₃×#685	C₂³	1	4	yes	—
152	C₃×#685	C₂³	1	2	yes	—
153	C₃×#685	C₂³	1	2	yes	—
154	C₃×#685	C₂³	1	2	yes	—
155	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
156	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
157	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
158	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
159	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
160	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
161	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
162	C₃×#683	C₂³	1	4	yes	—
163	C₃×#683	C₂³	1	4	yes	—
164	C₃×#683	C₂³	1	4	yes	—
165	C₃×#683	C₂³	1	4	yes	—
166	C₃×#683	C₂³	1	4	yes	—
167	C₃×#683	C₂³	1	4	yes	—
168	C₃×C₄×Dic₅	C₂³	1	4	yes	—
169	C₃×C₄×Dic₅	C₂³	1	4	yes	—
170	C₃×C₄×Dic₅	C₂³	1	4	yes	—
171	C₃×#556	—	5	1	no	—
172	C₃×#555	—	5	1	no	—
173	C₃×#554	—	5	1	no	—
174	C₃×#553	—	5	2	no	—
175	C₃×#552	—	5	2	no	—
176	C₃×#552	—	5	2	no	—
177	C₃×#551	—	5	4	no	—
178	C₃×#547	—	5	1	no	—
179	C₃×#546	—	5	2	no	—
180	C₃×#533	—	5	1	no	—
181	C₃×#529	—	5	4	no	—
182	C₃×#529	—	5	2	no	—
183	C₃×#525	—	5	2	no	—
184	C₃×C₄×#41	—	5	2	no	—
185	C₃×C₄×#41	D₅	1	1	yes	characteristic, complemented
186	C₂×C₃×C₄×D₄	—	5	1	no	—
187	C₂×C₃×#117	—	5	2	no	—
188	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
189	C₂×#709	C₂²×C₃	1	2	yes	—
190	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
191	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
192	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
193	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
194	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
195	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
196	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
197	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
198	C₅×#117	C₂²×C₃	1	1	yes	characteristic
199	C₅×#117	C₂²×C₃	1	2	yes	complemented
200	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
201	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	complemented
202	#4092	C₂²×C₃	1	2	yes	complemented
203	#4092	C₂²×C₃	1	2	yes	complemented
204	#4084	C₂²×C₃	1	2	yes	complemented
205	#4084	C₂²×C₃	1	2	yes	complemented
206	#4083	C₂²×C₃	1	4	yes	—
207	#4081	C₂²×C₃	1	4	yes	—
208	#4076	C₂²×C₃	1	2	yes	—
209	#4075	C₂²×C₃	1	4	yes	complemented
210	C₄×C₂²⋊D₅	C₂²×C₃	1	4	yes	complemented
211	C₄×C₂²⋊D₅	C₂²×C₃	1	4	yes	complemented
212	C₄×C₂²⋊D₅	C₂²×C₃	1	4	yes	complemented
213	C₂×#685	C₂²×C₃	1	2	yes	—
214	#4072	C₂²×C₃	1	2	yes	—
215	#4072	C₂²×C₃	1	2	yes	complemented
216	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
217	#4070	C₂²×C₃	1	2	yes	—
218	#4070	C₂²×C₃	1	2	yes	—
219	#4070	C₂²×C₃	1	2	yes	complemented
220	#4044	C₂²×C₃	1	4	yes	complemented
221	#4042	C₂²×C₃	1	4	yes	complemented
222	#4040	C₂²×C₃	1	4	yes	—
223	#4038	C₂²×C₃	1	2	yes	complemented
224	#4038	C₂²×C₃	1	2	yes	complemented
225	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
226	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
227	#4035	C₂²×C₃	1	4	yes	complemented
228	#4031	C₂²×C₃	1	4	yes	complemented
229	#4030	C₂²×C₃	1	4	yes	—
230	#4029	C₂²×C₃	1	4	yes	complemented
231	D₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
232	#4025	C₂²×C₃	1	4	yes	complemented
233	#4023	C₂²×C₃	1	4	yes	—
234	#4022	C₂²×C₃	1	4	yes	complemented
235	#4021	C₂²×C₃	1	2	yes	—
236	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
237	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
238	C₄×D₂₀	C₂²×C₃	1	2	yes	—
239	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
240	C₄×D₂₀	C₂²×C₃	1	2	yes	—
241	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
242	C₄×D₂₀	C₂²×C₃	1	2	yes	—
243	#4018	C₂²×C₃	1	4	yes	complemented
244	#4018	C₂²×C₃	1	4	yes	complemented
245	C₄²×D₅	C₂²×C₃	1	4	yes	complemented
246	#4016	C₂²×C₃	1	2	yes	complemented
247	#4016	C₂²×C₃	1	2	yes	complemented
248	#4015	C₂²×C₃	1	1	yes	characteristic, complemented
249	#4015	C₂²×C₃	1	1	yes	characteristic, complemented
250	C₄×Dic₁₀	C₂²×C₃	1	2	yes	complemented
251	C₄×Dic₁₀	C₂²×C₃	1	2	yes	complemented
252	C₄×Dic₁₀	C₂²×C₃	1	2	yes	complemented
253	#3475	—	5	1	no	Sylow
254	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
255	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
256	C₂²×C₃×D₅	—	2	4	no	—
257	C₂²×C₃×D₅	—	2	4	no	—
258	C₂²×C₃×D₅	—	4	2	no	—
259	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
260	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
261	C₃×C₅×Q₈	—	2	2	no	—
262	C₃×C₅×D₄	—	2	4	no	—
263	C₃×C₅×D₄	—	2	2	no	—
264	C₂×C₃×C₄×C₅	—	2	2	no	—
265	C₂×C₃×C₄×C₅	—	2	4	no	—
266	C₂×C₃×C₄×C₅	—	2	4	no	—
267	C₂×C₃×C₄×C₅	—	4	1	no	—
268	C₂×C₃×C₄×C₅	—	4	2	no	—
269	C₂×C₃×C₄×C₅	#41	1	4	yes	complemented
270	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
271	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
272	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
273	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
274	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
275	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
276	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
277	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
278	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
279	C₃×C₂²⋊D₅	—	2	8	no	—
280	C₃×C₂²⋊D₅	—	4	4	no	—
281	C₂×C₃×Dic₅	—	2	4	no	—
282	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
283	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
284	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
285	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
286	C₃×D₂₀	—	2	4	no	—
287	C₃×D₂₀	—	2	2	no	—
288	C₃×D₂₀	#41	1	4	yes	complemented
289	C₃×C₄×D₅	—	2	8	no	—
290	C₃×C₄×D₅	—	2	4	no	—
291	C₃×C₄×D₅	—	2	4	no	—
292	C₃×C₄×D₅	—	2	4	no	—
293	C₃×C₄×D₅	—	2	4	no	—
294	C₃×C₄×D₅	—	4	4	no	—
295	C₃×Dic₁₀	—	2	4	no	—
296	C₃×Dic₁₀	—	4	2	no	—
297	C₂×C₃×#41	—	5	2	no	—
298	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
299	C₂²×C₃×D₄	—	5	1	no	—
300	C₂³×C₃×C₄	—	5	2	no	—
301	C₃×C₄⋊Q₈	—	5	1	no	—
302	C₃×C₄⋊Q₈	—	5	1	no	—
303	C₃×#126	—	5	4	no	—
304	C₃×#126	—	5	4	no	—
305	C₃×#126	—	5	4	no	—
306	C₃×#125	—	5	4	no	—
307	C₃×#125	—	5	2	no	—
308	C₃×#125	—	5	2	no	—
309	C₃×#124	—	5	4	no	—
310	C₃×#124	—	5	2	no	—
311	C₃×#123	—	5	4	no	—
312	C₃×#123	—	5	4	no	—
313	C₃×#123	—	5	4	no	—
314	C₃×#123	—	5	4	no	—
315	C₃×C₂²⋊Q₈	—	5	2	no	—
316	C₃×C₂²⋊Q₈	—	5	2	no	—
317	C₃×C₂²⋊Q₈	—	5	2	no	—
318	C₃×C₂²⋊Q₈	—	5	2	no	—
319	C₃×C₂²⋊Q₈	—	5	2	no	—
320	C₃×C₂²⋊Q₈	—	5	4	no	—
321	C₃×#121	—	5	2	no	—
322	C₃×#121	—	5	2	no	—
323	C₃×#121	—	5	2	no	—
324	C₃×#121	—	5	4	no	—
325	C₃×#120	—	5	4	no	—
326	C₃×C₄×Q₈	—	5	2	no	—
327	C₃×C₄×Q₈	—	5	2	no	—
328	C₃×C₄×Q₈	—	5	2	no	—
329	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
330	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic, complemented
331	C₃×C₄×D₄	—	5	4	no	—
332	C₃×C₄×D₄	—	5	4	no	—
333	C₃×C₄×D₄	—	5	4	no	—
334	C₃×C₄×D₄	—	5	1	no	—
335	C₃×C₄×D₄	—	5	1	no	—
336	C₃×C₄×D₄	—	5	2	no	—
337	C₃×C₄×D₄	—	5	1	no	—
338	C₃×C₄×D₄	—	5	2	no	—
339	C₃×C₄×D₄	—	5	1	no	—
340	C₃×C₄×D₄	—	5	2	no	—
341	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
342	C₃×C₄×D₄	C₂×D₅	1	2	yes	—
343	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
344	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
345	C₃×#117	—	5	2	no	—
346	C₃×#117	—	5	2	no	—
347	C₃×#117	—	5	2	no	—
348	C₃×#117	—	5	2	no	—
349	C₃×#117	—	5	4	no	—
350	C₃×#117	—	5	4	no	—
351	C₃×#117	—	5	4	no	—
352	C₃×#117	C₂×D₅	1	1	yes	characteristic
353	C₃×#117	C₂×D₅	1	2	yes	complemented
354	C₂×C₃×C₄⋊C₄	—	5	1	no	—
355	C₂×C₃×C₄⋊C₄	—	5	2	no	—
356	C₂×C₃×C₄⋊C₄	—	5	2	no	—
357	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
358	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
359	C₂×C₃×C₄²	—	5	4	no	—
360	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
361	C₂×C₃×C₄²	C₂×D₅	1	2	yes	complemented
362	C₂³×D₅	C₂³×C₃	1	2	yes	—
363	C₅×#41	—	2	4	no	—
364	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
365	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
366	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
367	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
368	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
369	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
370	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
371	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
372	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
373	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
374	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
375	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
376	#709	—	2	8	no	—
377	C₂×D₂₀	—	2	4	no	—
378	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
379	C₂×D₂₀	C₂³×C₃	1	2	yes	—
380	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
381	C₂×C₄×D₅	—	2	8	no	—
382	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
383	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
384	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
385	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
386	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
387	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
388	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
389	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
390	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
391	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
392	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
393	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
394	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
395	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
396	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
397	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
398	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
399	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
400	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
401	C₄²×C₅	C₂³×C₃	1	2	yes	—
402	C₄²×C₅	C₂³×C₃	1	2	yes	—
403	C₄²×C₅	C₂³×C₃	1	2	yes	—
404	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
405	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
406	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
407	#685	C₂³×C₃	1	2	yes	—
408	#685	C₂³×C₃	1	4	yes	—
409	#685	C₂³×C₃	1	4	yes	—
410	#685	C₂³×C₃	1	4	yes	—
411	#685	C₂³×C₃	1	2	yes	—
412	#685	C₂³×C₃	1	2	yes	—
413	#685	C₂³×C₃	1	2	yes	—
414	#685	C₂³×C₃	1	4	yes	—
415	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
416	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
417	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
418	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
419	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
420	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
421	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
422	#683	C₂³×C₃	1	4	yes	—
423	#683	C₂³×C₃	1	4	yes	—
424	#683	C₂³×C₃	1	4	yes	—
425	#683	C₂³×C₃	1	4	yes	—
426	#683	C₂³×C₃	1	4	yes	—
427	#683	C₂³×C₃	1	4	yes	—
428	C₄×Dic₅	C₂³×C₃	1	4	yes	—
429	C₄×Dic₅	C₂³×C₃	1	4	yes	—
430	C₄×Dic₅	C₂³×C₃	1	4	yes	—
431	#556	—	5	1	no	—
432	#555	—	5	1	no	—
433	#554	—	5	1	no	—
434	#553	—	5	2	no	—
435	#552	—	5	2	no	—
436	#552	—	5	2	no	—
437	#551	—	5	4	no	—
438	#547	—	5	1	no	—
439	#546	—	5	2	no	—
440	#533	—	5	1	no	—
441	#529	—	5	4	no	—
442	#529	—	5	2	no	—
443	#525	—	5	2	no	—
444	C₄×#41	—	5	2	no	—
445	C₄×#41	C₃×D₅	1	1	yes	characteristic, complemented
446	C₂×C₄×D₄	—	5	1	no	—
447	C₂×#117	—	5	2	no	—
448	C₂²×C₃×C₅	—	2	1	no	—
449	C₂²×C₃×C₅	—	2	1	no	—
450	C₂²×C₃×C₅	—	2	2	no	—
451	C₂²×C₃×C₅	—	2	2	no	—
452	C₂²×C₃×C₅	—	2	2	no	—
453	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
454	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
455	C₂×C₃×D₅	—	2	2	no	—
456	C₂×C₃×D₅	—	2	2	no	—
457	C₂×C₃×D₅	—	2	2	no	—
458	C₂×C₃×D₅	—	2	2	no	—
459	C₂×C₃×D₅	—	2	2	no	—
460	C₂×C₃×D₅	—	4	8	no	—
461	C₂×C₃×D₅	C₂×#41	1	4	yes	—
462	C₃×C₄×C₅	—	2	2	no	—
463	C₃×C₄×C₅	—	2	1	no	—
464	C₃×C₄×C₅	—	2	2	no	—
465	C₃×C₄×C₅	—	2	1	no	—
466	C₃×C₄×C₅	—	2	2	no	—
467	C₃×C₄×C₅	—	2	1	no	—
468	C₃×C₄×C₅	C₂×#41	1	2	yes	—
469	C₃×C₄×C₅	C₂×#41	1	2	yes	—
470	C₃×C₄×C₅	C₂×#41	1	2	yes	—
471	C₃×Dic₅	—	2	4	no	—
472	C₃×Dic₅	—	2	2	no	—
473	C₃×Dic₅	—	2	2	no	—
474	C₃×Dic₅	—	2	4	no	—
475	C₂⁴×C₃	—	5	2	no	—
476	C₃×#41	—	2	4	no	—
477	C₃×#41	—	10	8	no	—
478	C₂×C₃×Q₈	—	5	2	no	—
479	C₂×C₃×Q₈	—	5	2	no	—
480	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
481	C₂×C₃×D₄	—	5	4	no	—
482	C₂×C₃×D₄	—	5	4	no	—
483	C₂×C₃×D₄	—	5	1	no	—
484	C₂×C₃×D₄	—	5	2	no	—
485	C₂×C₃×D₄	—	5	1	no	—
486	C₂×C₃×D₄	—	10	4	no	—
487	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
488	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
489	C₂²×C₃×C₄	—	5	2	no	—
490	C₂²×C₃×C₄	—	5	4	no	—
491	C₂²×C₃×C₄	—	5	2	no	—
492	C₂²×C₃×C₄	—	5	2	no	—
493	C₂²×C₃×C₄	—	5	2	no	—
494	C₂²×C₃×C₄	—	5	2	no	—
495	C₂²×C₃×C₄	—	5	4	no	—
496	C₂²×C₃×C₄	—	10	8	no	—
497	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
498	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
499	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
500	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
501	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
502	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
503	C₃×C₄⋊C₄	—	5	4	no	—
504	C₃×C₄⋊C₄	—	5	4	no	—
505	C₃×C₄⋊C₄	—	5	4	no	—
506	C₃×C₄⋊C₄	—	5	4	no	—
507	C₃×C₄⋊C₄	—	5	4	no	—
508	C₃×C₄⋊C₄	—	5	4	no	—
509	C₃×C₄⋊C₄	—	5	1	no	—
510	C₃×C₄⋊C₄	—	5	2	no	—
511	C₃×C₄⋊C₄	—	5	2	no	—
512	C₃×C₄⋊C₄	—	5	1	no	—
513	C₃×C₄⋊C₄	—	5	2	no	—
514	C₃×C₄⋊C₄	—	5	2	no	—
515	C₃×C₄⋊C₄	—	5	2	no	—
516	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
517	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
518	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
519	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
520	C₃×C₂²⋊C₄	—	5	4	no	—
521	C₃×C₂²⋊C₄	—	5	4	no	—
522	C₃×C₂²⋊C₄	—	5	4	no	—
523	C₃×C₂²⋊C₄	—	5	2	no	—
524	C₃×C₂²⋊C₄	—	5	4	no	—
525	C₃×C₂²⋊C₄	—	5	4	no	—
526	C₃×C₂²⋊C₄	—	5	2	no	—
527	C₃×C₂²⋊C₄	—	5	2	no	—
528	C₃×C₂²⋊C₄	—	5	2	no	—
529	C₃×C₂²⋊C₄	—	5	4	no	—
530	C₃×C₂²⋊C₄	—	5	4	no	—
531	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
532	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
533	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
534	C₃×C₄²	—	5	4	no	—
535	C₃×C₄²	—	5	4	no	—
536	C₃×C₄²	—	5	4	no	—
537	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
538	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
539	C₃×C₄²	C₂²×D₅	1	2	yes	—
540	C₃×C₄²	C₂²×D₅	1	2	yes	—
541	C₃×C₄²	C₂²×D₅	1	2	yes	—
542	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
543	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
544	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
545	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
546	C₂²×D₅	—	2	4	no	—
547	C₂²×D₅	—	2	4	no	—
548	C₂²×D₅	—	4	2	no	—
549	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
550	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
551	C₅×Q₈	—	2	2	no	—
552	C₅×D₄	—	2	4	no	—
553	C₅×D₄	—	2	2	no	—
554	C₂×C₄×C₅	—	2	2	no	—
555	C₂×C₄×C₅	—	2	4	no	—
556	C₂×C₄×C₅	—	2	4	no	—
557	C₂×C₄×C₅	—	4	1	no	—
558	C₂×C₄×C₅	—	4	2	no	—
559	C₂×C₄×C₅	C₃×#41	1	4	yes	complemented
560	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
561	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
562	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
563	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
564	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
565	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
566	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
567	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
568	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
569	C₂²⋊D₅	—	2	8	no	—
570	C₂²⋊D₅	—	4	4	no	—
571	C₂×Dic₅	—	2	4	no	—
572	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
573	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
574	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
575	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
576	D₂₀	—	2	4	no	—
577	D₂₀	—	2	2	no	—
578	D₂₀	C₃×#41	1	4	yes	complemented
579	C₄×D₅	—	2	8	no	—
580	C₄×D₅	—	2	4	no	—
581	C₄×D₅	—	2	4	no	—
582	C₄×D₅	—	2	4	no	—
583	C₄×D₅	—	2	4	no	—
584	C₄×D₅	—	4	4	no	—
585	Dic₁₀	—	2	4	no	—
586	Dic₁₀	—	4	2	no	—
587	C₂×#41	—	5	2	no	—
588	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
589	C₂²×D₄	—	5	1	no	—
590	C₂³×C₄	—	5	2	no	—
591	C₄⋊Q₈	—	5	1	no	—
592	C₄⋊Q₈	—	5	1	no	—
593	#126	—	5	4	no	—
594	#126	—	5	4	no	—
595	#126	—	5	4	no	—
596	#125	—	5	4	no	—
597	#125	—	5	2	no	—
598	#125	—	5	2	no	—
599	#124	—	5	4	no	—
600	#124	—	5	2	no	—
601	#123	—	5	4	no	—
602	#123	—	5	4	no	—
603	#123	—	5	4	no	—
604	#123	—	5	4	no	—
605	C₂²⋊Q₈	—	5	2	no	—
606	C₂²⋊Q₈	—	5	2	no	—
607	C₂²⋊Q₈	—	5	2	no	—
608	C₂²⋊Q₈	—	5	2	no	—
609	C₂²⋊Q₈	—	5	2	no	—
610	C₂²⋊Q₈	—	5	4	no	—
611	#121	—	5	2	no	—
612	#121	—	5	2	no	—
613	#121	—	5	2	no	—
614	#121	—	5	4	no	—
615	#120	—	5	4	no	—
616	C₄×Q₈	—	5	2	no	—
617	C₄×Q₈	—	5	2	no	—
618	C₄×Q₈	—	5	2	no	—
619	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
620	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
621	C₄×D₄	—	5	4	no	—
622	C₄×D₄	—	5	4	no	—
623	C₄×D₄	—	5	4	no	—
624	C₄×D₄	—	5	1	no	—
625	C₄×D₄	—	5	1	no	—
626	C₄×D₄	—	5	2	no	—
627	C₄×D₄	—	5	1	no	—
628	C₄×D₄	—	5	2	no	—
629	C₄×D₄	—	5	1	no	—
630	C₄×D₄	—	5	2	no	—
631	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
632	C₄×D₄	C₂×C₃×D₅	1	2	yes	—
633	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
634	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
635	#117	—	5	2	no	—
636	#117	—	5	2	no	—
637	#117	—	5	2	no	—
638	#117	—	5	2	no	—
639	#117	—	5	4	no	—
640	#117	—	5	4	no	—
641	#117	—	5	4	no	—
642	#117	C₂×C₃×D₅	1	1	yes	characteristic
643	#117	C₂×C₃×D₅	1	2	yes	complemented
644	C₂×C₄⋊C₄	—	5	1	no	—
645	C₂×C₄⋊C₄	—	5	2	no	—
646	C₂×C₄⋊C₄	—	5	2	no	—
647	C₂×C₂²⋊C₄	—	5	2	no	—
648	C₂×C₂²⋊C₄	—	5	4	no	—
649	C₂×C₄²	—	5	4	no	—
650	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
651	C₂×C₄²	C₂×C₃×D₅	1	2	yes	complemented
652	C₂×C₃×C₅	—	2	2	no	—
653	C₂×C₃×C₅	—	4	2	no	—
654	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
655	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
656	C₂×C₃×C₅	#585	1	1	yes	characteristic
657	C₃×D₅	—	2	4	no	—
658	C₃×D₅	—	4	2	no	—
659	C₂³×C₃	—	5	2	no	—
660	C₂³×C₃	—	5	2	no	—
661	C₂³×C₃	—	10	4	no	—
662	C₂³×C₃	—	10	4	no	—
663	C₂³×C₃	—	20	2	no	—
664	C₂³×C₃	C₂³×D₅	1	2	yes	—
665	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
666	C₃×Q₈	—	2	2	no	—
667	C₃×Q₈	—	10	4	no	—
668	C₃×Q₈	—	20	2	no	—
669	C₃×D₄	—	2	4	no	—
670	C₃×D₄	—	2	2	no	—
671	C₃×D₄	—	5	4	no	—
672	C₃×D₄	—	10	4	no	—
673	C₃×D₄	—	10	8	no	—
674	C₃×D₄	—	10	2	no	—
675	C₃×D₄	—	20	4	no	—
676	C₂×C₃×C₄	—	2	4	no	—
677	C₂×C₃×C₄	—	2	2	no	—
678	C₂×C₃×C₄	—	2	4	no	—
679	C₂×C₃×C₄	—	4	2	no	—
680	C₂×C₃×C₄	—	4	1	no	—
681	C₂×C₃×C₄	—	5	2	no	—
682	C₂×C₃×C₄	—	5	4	no	—
683	C₂×C₃×C₄	—	5	4	no	—
684	C₂×C₃×C₄	—	5	2	no	—
685	C₂×C₃×C₄	—	10	8	no	—
686	C₂×C₃×C₄	—	10	4	no	—
687	C₂×C₃×C₄	—	10	4	no	—
688	C₂×C₃×C₄	—	10	4	no	—
689	C₂×C₃×C₄	—	10	4	no	—
690	C₂×C₃×C₄	—	10	4	no	—
691	C₂×C₃×C₄	—	20	4	no	—
692	C₂×C₃×C₄	#709	1	4	yes	complemented
693	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
694	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
695	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
696	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
697	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
698	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
699	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
700	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
701	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
702	C₂²×C₅	—	2	1	no	—
703	C₂²×C₅	—	2	1	no	—
704	C₂²×C₅	—	2	2	no	—
705	C₂²×C₅	—	2	2	no	—
706	C₂²×C₅	—	2	2	no	—
707	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
708	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
709	C₂×D₅	—	2	2	no	—
710	C₂×D₅	—	2	2	no	—
711	C₂×D₅	—	2	2	no	—
712	C₂×D₅	—	2	2	no	—
713	C₂×D₅	—	2	2	no	—
714	C₂×D₅	—	4	8	no	—
715	C₂×D₅	C₂×C₃×#41	1	4	yes	—
716	C₄×C₅	—	2	2	no	—
717	C₄×C₅	—	2	1	no	—
718	C₄×C₅	—	2	2	no	—
719	C₄×C₅	—	2	1	no	—
720	C₄×C₅	—	2	2	no	—
721	C₄×C₅	—	2	1	no	—
722	C₄×C₅	C₂×C₃×#41	1	2	yes	—
723	C₄×C₅	C₂×C₃×#41	1	2	yes	—
724	C₄×C₅	C₂×C₃×#41	1	2	yes	—
725	Dic₅	—	2	4	no	—
726	Dic₅	—	2	2	no	—
727	Dic₅	—	2	2	no	—
728	Dic₅	—	2	4	no	—
729	C₂⁴	—	5	2	no	—
730	#41	—	2	4	no	—
731	#41	—	10	8	no	—
732	C₂×Q₈	—	5	2	no	—
733	C₂×Q₈	—	5	2	no	—
734	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
735	C₂×D₄	—	5	4	no	—
736	C₂×D₄	—	5	4	no	—
737	C₂×D₄	—	5	1	no	—
738	C₂×D₄	—	5	2	no	—
739	C₂×D₄	—	5	1	no	—
740	C₂×D₄	—	10	4	no	—
741	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
742	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
743	C₂²×C₄	—	5	2	no	—
744	C₂²×C₄	—	5	2	no	—
745	C₂²×C₄	—	5	4	no	—
746	C₂²×C₄	—	5	2	no	—
747	C₂²×C₄	—	5	2	no	—
748	C₂²×C₄	—	5	2	no	—
749	C₂²×C₄	—	5	4	no	—
750	C₂²×C₄	—	10	8	no	—
751	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
752	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
753	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
754	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
755	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
756	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
757	C₄⋊C₄	—	5	1	no	—
758	C₄⋊C₄	—	5	2	no	—
759	C₄⋊C₄	—	5	2	no	—
760	C₄⋊C₄	—	5	4	no	—
761	C₄⋊C₄	—	5	4	no	—
762	C₄⋊C₄	—	5	1	no	—
763	C₄⋊C₄	—	5	2	no	—
764	C₄⋊C₄	—	5	2	no	—
765	C₄⋊C₄	—	5	4	no	—
766	C₄⋊C₄	—	5	4	no	—
767	C₄⋊C₄	—	5	4	no	—
768	C₄⋊C₄	—	5	4	no	—
769	C₄⋊C₄	—	5	2	no	—
770	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
771	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
772	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
773	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
774	C₂²⋊C₄	—	5	4	no	—
775	C₂²⋊C₄	—	5	4	no	—
776	C₂²⋊C₄	—	5	4	no	—
777	C₂²⋊C₄	—	5	2	no	—
778	C₂²⋊C₄	—	5	4	no	—
779	C₂²⋊C₄	—	5	4	no	—
780	C₂²⋊C₄	—	5	2	no	—
781	C₂²⋊C₄	—	5	2	no	—
782	C₂²⋊C₄	—	5	2	no	—
783	C₂²⋊C₄	—	5	4	no	—
784	C₂²⋊C₄	—	5	4	no	—
785	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
786	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
787	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
788	C₄²	—	5	4	no	—
789	C₄²	—	5	4	no	—
790	C₄²	—	5	4	no	—
791	C₄²	C₂²×C₃×D₅	1	2	yes	—
792	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
793	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
794	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
795	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
796	C₄²	C₂²×C₃×D₅	1	2	yes	—
797	C₄²	C₂²×C₃×D₅	1	2	yes	—
798	C₃×C₅	#3475	1	1	yes	characteristic, complemented, Hall
799	C₂²×C₃	—	2	1	no	—
800	C₂²×C₃	—	2	1	no	—
801	C₂²×C₃	—	2	2	no	—
802	C₂²×C₃	—	2	2	no	—
803	C₂²×C₃	—	2	2	no	—
804	C₂²×C₃	—	5	4	no	—
805	C₂²×C₃	—	10	2	no	—
806	C₂²×C₃	—	10	2	no	—
807	C₂²×C₃	—	10	2	no	—
808	C₂²×C₃	—	10	2	no	—
809	C₂²×C₃	—	10	2	no	—
810	C₂²×C₃	—	20	8	no	—
811	C₂²×C₃	C₂×#709	1	2	yes	—
812	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
813	C₃×C₄	—	2	2	no	—
814	C₃×C₄	—	2	2	no	—
815	C₃×C₄	—	2	1	no	—
816	C₃×C₄	—	2	1	no	—
817	C₃×C₄	—	2	2	no	—
818	C₃×C₄	—	2	1	no	—
819	C₃×C₄	—	10	2	no	—
820	C₃×C₄	—	10	2	no	—
821	C₃×C₄	—	10	4	no	—
822	C₃×C₄	—	10	4	no	—
823	C₃×C₄	C₂×#709	1	2	yes	—
824	C₃×C₄	C₂×#709	1	2	yes	—
825	C₃×C₄	D₅×#41	1	2	yes	—
826	C₂×C₅	—	2	2	no	—
827	C₂×C₅	—	4	2	no	—
828	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
829	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
830	C₂×C₅	C₃×#585	1	1	yes	characteristic
831	D₅	—	2	4	no	—
832	D₅	—	4	2	no	—
833	C₂³	—	5	2	no	—
834	C₂³	—	5	2	no	—
835	C₂³	—	10	4	no	—
836	C₂³	—	10	4	no	—
837	C₂³	—	20	2	no	—
838	C₂³	C₂³×C₃×D₅	1	2	yes	—
839	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
840	Q₈	—	2	2	no	—
841	Q₈	—	10	4	no	—
842	Q₈	—	20	2	no	—
843	D₄	—	2	4	no	—
844	D₄	—	2	2	no	—
845	D₄	—	5	4	no	—
846	D₄	—	10	4	no	—
847	D₄	—	10	8	no	—
848	D₄	—	10	2	no	—
849	D₄	—	20	4	no	—
850	C₂×C₄	—	2	4	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	4	no	—
853	C₂×C₄	—	4	2	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	5	2	no	—
856	C₂×C₄	—	5	4	no	—
857	C₂×C₄	—	5	4	no	—
858	C₂×C₄	—	5	2	no	—
859	C₂×C₄	—	10	8	no	—
860	C₂×C₄	—	10	4	no	—
861	C₂×C₄	—	10	4	no	—
862	C₂×C₄	—	10	4	no	—
863	C₂×C₄	—	10	4	no	—
864	C₂×C₄	—	10	4	no	—
865	C₂×C₄	—	20	4	no	—
866	C₂×C₄	C₃×#709	1	4	yes	complemented
867	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
868	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
869	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
870	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
871	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
872	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
873	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
874	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
875	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
876	C₂×C₃	—	2	2	no	—
877	C₂×C₃	—	4	2	no	—
878	C₂×C₃	—	10	4	no	—
879	C₂×C₃	—	20	2	no	—
880	C₂×C₃	C₂²×#709	1	1	yes	characteristic
881	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
882	C₂×C₃	#66283	1	1	yes	characteristic
883	C₅	C₃×#3475	1	1	yes	characteristic, complemented, Sylow
884	C₂²	—	2	1	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	5	4	no	—
890	C₂²	—	10	2	no	—
891	C₂²	—	10	2	no	—
892	C₂²	—	10	2	no	—
893	C₂²	—	10	2	no	—
894	C₂²	—	10	2	no	—
895	C₂²	—	20	8	no	—
896	C₂²	C₂×C₃×#709	1	2	yes	—
897	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
898	C₄	—	2	2	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	1	no	—
901	C₄	—	2	1	no	—
902	C₄	—	2	2	no	—
903	C₄	—	2	1	no	—
904	C₄	—	10	2	no	—
905	C₄	—	10	2	no	—
906	C₄	—	10	4	no	—
907	C₄	—	10	4	no	—
908	C₄	C₂×C₃×#709	1	2	yes	—
909	C₄	C₂×C₃×#709	1	2	yes	—
910	C₄	C₃×D₅×#41	1	2	yes	—
911	C₃	#10617741	1	1	yes	characteristic, direct product factor, Sylow
912	C₂	—	2	2	no	—
913	C₂	—	4	2	no	—
914	C₂	—	10	4	no	—
915	C₂	—	20	2	no	—
916	C₂	C₂²×C₃×#709	1	1	yes	characteristic
917	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
918	C₂	C₃×#66283	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₄×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×C₄×#41	D₅
hypocenter	C₅	C₃×#3475
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×#41

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×C₅×#41	C₂	semidirect
2. C₃×#66162	C₂	semidirect
3. C₃×#65918	C₂	semidirect
4. C₃×#65915	C₂	semidirect
5. C₃×#65913	C₂	semidirect
6. C₃×#65897	C₂	semidirect
7. C₃×#65892	C₂	semidirect
8. C₃×#65890	C₂	semidirect
9. C₃×#65885	C₂	semidirect
10. C₃×#65884	C₂	semidirect
11. C₃×#65875	C₂	semidirect
12. C₃×#65862	C₂	semidirect
13. C₃×D₅×#117	C₂	semidirect
14. C₃×#65813	C₂	semidirect
15. C₃×C₄×#709	C₂	semidirect
16. C₂×C₃×C₄×D₂₀	C₂	semidirect
17. C₃×#65804	C₂	semidirect
18. #10617741	C₃	direct (N × H)
23. C₃×C₄×C₅×Q₈	C₂²	semidirect
24. C₃×C₄×C₅×Q₈	C₂²	semidirect
27. C₃×C₄×C₅×D₄	C₂²	semidirect
28. C₃×C₄×C₅×D₄	C₂²	semidirect
30. C₃×C₅×#117	C₂²	semidirect
32. C₂×C₃×C₄²×C₅	C₂²	semidirect
33. C₃×#4092	C₂²	semidirect
34. C₃×#4092	C₂²	semidirect
35. C₃×#4084	C₂²	semidirect
36. C₃×#4084	C₂²	semidirect
40. C₃×#4075	C₂²	semidirect
41. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
42. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
43. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
46. C₃×#4072	C₂²	semidirect
50. C₃×#4070	C₂²	semidirect
51. C₃×#4044	C₂²	semidirect
52. C₃×#4042	C₂²	semidirect
54. C₃×#4038	C₂²	semidirect
55. C₃×#4038	C₂²	semidirect
56. C₃×D₅×C₄⋊C₄	C₂²	semidirect
57. C₃×D₅×C₄⋊C₄	C₂²	semidirect
58. C₃×#4035	C₂²	semidirect
59. C₃×#4031	C₂²	semidirect
61. C₃×#4029	C₂²	semidirect
63. C₃×#4025	C₂²	semidirect
65. C₃×#4022	C₂²	semidirect
74. C₃×#4018	C₂²	semidirect
75. C₃×#4018	C₂²	semidirect
76. C₃×C₄²×D₅	C₂²	semidirect
77. C₃×#4016	C₂²	semidirect
78. C₃×#4016	C₂²	semidirect
79. C₃×#4015	C₂²	semidirect
80. C₃×#4015	C₂²	semidirect
81. C₃×C₄×Dic₁₀	C₂²	semidirect
82. C₃×C₄×Dic₁₀	C₂²	semidirect
83. C₃×C₄×Dic₁₀	C₂²	semidirect
85. C₄×C₅×#41	C₂×C₃	semidirect
86. #66162	C₂×C₃	semidirect
87. #65918	C₂×C₃	semidirect
88. #65915	C₂×C₃	semidirect
89. #65913	C₂×C₃	semidirect
90. #65897	C₂×C₃	semidirect
91. #65892	C₂×C₃	semidirect
92. #65890	C₂×C₃	semidirect
93. #65885	C₂×C₃	semidirect
94. #65884	C₂×C₃	semidirect
95. #65875	C₂×C₃	semidirect
96. #65862	C₂×C₃	semidirect
97. D₅×#117	C₂×C₃	semidirect
98. #65813	C₂×C₃	semidirect
99. C₄×#709	C₂×C₃	semidirect
100. C₂×C₄×D₂₀	C₂×C₃	semidirect
101. #65804	C₂×C₃	semidirect
185. C₃×C₄×#41	D₅	semidirect
192. C₄×C₅×Q₈	C₂²×C₃	semidirect
193. C₄×C₅×Q₈	C₂²×C₃	semidirect
196. C₄×C₅×D₄	C₂²×C₃	semidirect
197. C₄×C₅×D₄	C₂²×C₃	semidirect
199. C₅×#117	C₂²×C₃	semidirect
201. C₂×C₄²×C₅	C₂²×C₃	semidirect
202. #4092	C₂²×C₃	semidirect
203. #4092	C₂²×C₃	semidirect
204. #4084	C₂²×C₃	semidirect
205. #4084	C₂²×C₃	semidirect
209. #4075	C₂²×C₃	semidirect
210. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
211. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
212. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
215. #4072	C₂²×C₃	semidirect
219. #4070	C₂²×C₃	semidirect
220. #4044	C₂²×C₃	semidirect
221. #4042	C₂²×C₃	semidirect
223. #4038	C₂²×C₃	semidirect
224. #4038	C₂²×C₃	semidirect
225. D₅×C₄⋊C₄	C₂²×C₃	semidirect
226. D₅×C₄⋊C₄	C₂²×C₃	semidirect
227. #4035	C₂²×C₃	semidirect
228. #4031	C₂²×C₃	semidirect
230. #4029	C₂²×C₃	semidirect
232. #4025	C₂²×C₃	semidirect
234. #4022	C₂²×C₃	semidirect
243. #4018	C₂²×C₃	semidirect
244. #4018	C₂²×C₃	semidirect
245. C₄²×D₅	C₂²×C₃	semidirect
246. #4016	C₂²×C₃	semidirect
247. #4016	C₂²×C₃	semidirect
248. #4015	C₂²×C₃	semidirect
249. #4015	C₂²×C₃	semidirect
250. C₄×Dic₁₀	C₂²×C₃	semidirect
251. C₄×Dic₁₀	C₂²×C₃	semidirect
252. C₄×Dic₁₀	C₂²×C₃	semidirect
269. C₂×C₃×C₄×C₅	#41	semidirect
288. C₃×D₂₀	#41	semidirect
329. C₃×C₄×Q₈	C₂×D₅	semidirect
330. C₃×C₄×Q₈	C₂×D₅	semidirect
343. C₃×C₄×D₄	C₂×D₅	semidirect
344. C₃×C₄×D₄	C₂×D₅	semidirect
353. C₃×#117	C₂×D₅	semidirect
361. C₂×C₃×C₄²	C₂×D₅	semidirect
445. C₄×#41	C₃×D₅	semidirect
559. C₂×C₄×C₅	C₃×#41	semidirect
578. D₂₀	C₃×#41	semidirect
619. C₄×Q₈	C₂×C₃×D₅	semidirect
620. C₄×Q₈	C₂×C₃×D₅	semidirect
633. C₄×D₄	C₂×C₃×D₅	semidirect
634. C₄×D₄	C₂×C₃×D₅	semidirect
643. #117	C₂×C₃×D₅	semidirect
651. C₂×C₄²	C₂×C₃×D₅	semidirect
692. C₂×C₃×C₄	#709	semidirect
798. C₃×C₅	#3475	semidirect
866. C₂×C₄	C₃×#709	semidirect
883. C₅	C₃×#3475	semidirect
911. C₃	#10617741	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄×C₅×#41	2
C₃×#66162	2
C₃×#65918	2
C₃×#65915	2
C₃×#65913	2
C₃×#65897	2
C₃×#65892	2
C₃×#65890	2
C₃×#65885	2
C₃×#65884	2
C₃×#65875	2
C₃×#65862	2
C₃×D₅×#117	2
C₃×#65813	2
C₃×C₄×#709	2
C₂×C₃×C₄×D₂₀	2
C₃×#65804	2
#10617741	3
C₃×#3475	5

Subgroups — C3×#10617741 #14484148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617741 #14484148