Subgroups — C₃×#10618859 #14484127

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×C₅×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66064	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66062	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#66014	C₂	1	4	yes	maximal, complemented
5	C₃×#66013	C₂	1	4	yes	maximal, complemented
6	C₃×#65948	C₂	1	2	yes	maximal, complemented
7	C₃×#65946	C₂	1	2	yes	maximal, complemented
8	C₃×#65940	C₂	1	2	yes	maximal, complemented
9	C₃×#65934	C₂	1	2	yes	maximal, complemented
10	C₃×#65885	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₄×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#65876	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₄×#711	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×#65863	C₂	1	2	yes	maximal, complemented
15	C₃×#65863	C₂	1	2	yes	maximal, complemented
16	C₃×#65856	C₂	1	2	yes	maximal, complemented
17	C₃×D₅×#117	C₂	1	2	yes	maximal, complemented
18	#10618859	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₃×#711	C₂²	1	1	yes	characteristic
20	C₂×C₃×D₄×D₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×#709	C₂²	1	2	yes	—
22	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
23	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₅×#124	C₂²	1	4	yes	complemented
25	C₃×C₅×#121	C₂²	1	2	yes	—
26	C₃×C₅×#121	C₂²	1	2	yes	complemented
27	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
28	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×#117	C₂²	1	2	yes	complemented
30	C₃×C₅×#117	C₂²	1	2	yes	complemented
31	C₃×#4092	C₂²	1	2	yes	—
32	C₃×#4092	C₂²	1	4	yes	complemented
33	C₃×Q₈×Dic₅	C₂²	1	2	yes	complemented
34	C₃×#4084	C₂²	1	4	yes	—
35	C₃×#4084	C₂²	1	2	yes	complemented
36	C₃×#4083	C₂²	1	4	yes	—
37	C₃×#4082	C₂²	1	2	yes	—
38	C₃×#4081	C₂²	1	4	yes	complemented
39	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic
40	C₃×D₄×Dic₅	C₂²	1	1	yes	characteristic, complemented
41	C₃×D₄×Dic₅	C₂²	1	4	yes	complemented
42	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
43	C₃×C₄×C₂²⋊D₅	C₂²	1	2	yes	—
44	C₃×#4072	C₂²	1	2	yes	complemented
45	C₃×#4070	C₂²	1	2	yes	complemented
46	C₃×#4070	C₂²	1	2	yes	complemented
47	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	complemented
48	C₃×#4043	C₂²	1	2	yes	—
49	C₃×#4043	C₂²	1	2	yes	complemented
50	C₃×#4039	C₂²	1	1	yes	characteristic
51	C₃×#4039	C₂²	1	2	yes	—
52	C₃×#4038	C₂²	1	1	yes	characteristic
53	C₃×#4038	C₂²	1	2	yes	—
54	C₃×D₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
55	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
56	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	complemented
57	C₃×#4036	C₂²	1	2	yes	complemented
58	C₃×#4036	C₂²	1	2	yes	complemented
59	C₃×#4033	C₂²	1	2	yes	complemented
60	C₃×#4033	C₂²	1	2	yes	complemented
61	C₃×#4033	C₂²	1	1	yes	characteristic, complemented
62	C₃×#4029	C₂²	1	4	yes	—
63	C₃×#4029	C₂²	1	4	yes	—
64	C₃×#4029	C₂²	1	4	yes	complemented
65	C₃×#4027	C₂²	1	2	yes	—
66	C₃×#4027	C₂²	1	2	yes	—
67	C₃×#4027	C₂²	1	4	yes	complemented
68	C₃×#4027	C₂²	1	4	yes	complemented
69	C₃×D₅×C₂²⋊C₄	C₂²	1	4	yes	—
70	C₃×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
71	C₃×#4025	C₂²	1	4	yes	complemented
72	C₃×#4025	C₂²	1	4	yes	complemented
73	C₃×#4025	C₂²	1	4	yes	complemented
74	C₃×#4023	C₂²	1	4	yes	complemented
75	C₃×#4023	C₂²	1	2	yes	complemented
76	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
77	C₃×#4018	C₂²	1	4	yes	—
78	C₃×#4018	C₂²	1	4	yes	complemented
79	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
80	C₃×C₄²×D₅	C₂²	1	4	yes	complemented
81	C₃×#4016	C₂²	1	4	yes	complemented
82	C₃×#4015	C₂²	1	1	yes	characteristic, complemented
83	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
84	C₃×#3475	—	5	1	no	maximal, Hall
85	C₅×#555	C₂×C₃	1	1	yes	characteristic, complemented
86	#66064	C₂×C₃	1	1	yes	characteristic, complemented
87	#66062	C₂×C₃	1	1	yes	characteristic, complemented
88	#66014	C₂×C₃	1	4	yes	complemented
89	#66013	C₂×C₃	1	4	yes	complemented
90	#65948	C₂×C₃	1	2	yes	complemented
91	#65946	C₂×C₃	1	2	yes	complemented
92	#65940	C₂×C₃	1	2	yes	complemented
93	#65934	C₂×C₃	1	2	yes	complemented
94	#65885	C₂×C₃	1	1	yes	characteristic, complemented
95	C₄×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
96	#65876	C₂×C₃	1	1	yes	characteristic, complemented
97	C₄×#711	C₂×C₃	1	1	yes	characteristic, complemented
98	#65863	C₂×C₃	1	2	yes	complemented
99	#65863	C₂×C₃	1	2	yes	complemented
100	#65856	C₂×C₃	1	2	yes	complemented
101	D₅×#117	C₂×C₃	1	2	yes	complemented
102	C₂³×C₃×D₅	C₂³	1	2	yes	—
103	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
104	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
106	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
107	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
108	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
109	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
110	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
111	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
112	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
113	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
114	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
115	C₃×#711	—	2	4	no	—
116	C₃×D₄×D₅	—	2	4	no	—
117	C₃×#709	—	2	8	no	—
118	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
119	C₂×C₃×C₄×D₅	—	2	8	no	—
120	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
121	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
122	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
123	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
124	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
125	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
126	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
127	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
128	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
129	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
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	4	yes	—
135	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
138	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
139	C₃×C₄²×C₅	C₂³	1	4	yes	—
140	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
141	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
142	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
143	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
144	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
145	C₃×#685	C₂³	1	4	yes	—
146	C₃×#685	C₂³	1	4	yes	—
147	C₃×#685	C₂³	1	2	yes	—
148	C₃×#685	C₂³	1	2	yes	—
149	C₃×#685	C₂³	1	2	yes	—
150	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
151	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
152	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
153	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
154	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
155	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
156	C₃×#683	C₂³	1	4	yes	—
157	C₃×#683	C₂³	1	4	yes	—
158	C₃×#683	C₂³	1	2	yes	—
159	C₃×#683	C₂³	1	2	yes	—
160	C₃×#683	C₂³	1	2	yes	—
161	C₃×#683	C₂³	1	4	yes	—
162	C₃×#683	C₂³	1	4	yes	—
163	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
164	C₃×C₄×Dic₅	C₂³	1	4	yes	—
165	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
166	C₃×C₄×Dic₅	C₂³	1	2	yes	—
167	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
168	C₃×C₄×Dic₅	C₂³	1	2	yes	—
169	C₃×C₄×Dic₅	C₂³	1	4	yes	—
170	C₃×C₄×Dic₅	C₂³	1	2	yes	—
171	C₃×#556	—	5	1	no	—
172	C₃×#555	D₅	1	1	yes	characteristic, complemented
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	1	no	—
185	C₃×C₄×#41	—	5	2	no	—
186	C₂×C₃×C₄×D₄	—	5	1	no	—
187	C₂×C₃×#117	—	5	2	no	—
188	C₂×#711	C₂²×C₃	1	1	yes	characteristic
189	C₂×D₄×D₅	C₂²×C₃	1	1	yes	characteristic
190	C₂×#709	C₂²×C₃	1	2	yes	—
191	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
192	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
193	C₅×#124	C₂²×C₃	1	4	yes	complemented
194	C₅×#121	C₂²×C₃	1	2	yes	—
195	C₅×#121	C₂²×C₃	1	2	yes	complemented
196	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
197	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
198	C₅×#117	C₂²×C₃	1	2	yes	complemented
199	C₅×#117	C₂²×C₃	1	2	yes	complemented
200	#4092	C₂²×C₃	1	2	yes	—
201	#4092	C₂²×C₃	1	4	yes	complemented
202	Q₈×Dic₅	C₂²×C₃	1	2	yes	complemented
203	#4084	C₂²×C₃	1	4	yes	—
204	#4084	C₂²×C₃	1	2	yes	complemented
205	#4083	C₂²×C₃	1	4	yes	—
206	#4082	C₂²×C₃	1	2	yes	—
207	#4081	C₂²×C₃	1	4	yes	complemented
208	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
209	D₄×Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
210	D₄×Dic₅	C₂²×C₃	1	4	yes	complemented
211	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
212	C₄×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
213	#4072	C₂²×C₃	1	2	yes	complemented
214	#4070	C₂²×C₃	1	2	yes	complemented
215	#4070	C₂²×C₃	1	2	yes	complemented
216	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	complemented
217	#4043	C₂²×C₃	1	2	yes	—
218	#4043	C₂²×C₃	1	2	yes	complemented
219	#4039	C₂²×C₃	1	2	yes	—
220	#4039	C₂²×C₃	1	1	yes	characteristic
221	#4038	C₂²×C₃	1	2	yes	—
222	#4038	C₂²×C₃	1	1	yes	characteristic
223	D₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
224	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
225	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
226	#4036	C₂²×C₃	1	2	yes	complemented
227	#4036	C₂²×C₃	1	2	yes	complemented
228	#4033	C₂²×C₃	1	2	yes	complemented
229	#4033	C₂²×C₃	1	2	yes	complemented
230	#4033	C₂²×C₃	1	1	yes	characteristic, complemented
231	#4029	C₂²×C₃	1	4	yes	—
232	#4029	C₂²×C₃	1	4	yes	—
233	#4029	C₂²×C₃	1	4	yes	complemented
234	#4027	C₂²×C₃	1	2	yes	—
235	#4027	C₂²×C₃	1	2	yes	—
236	#4027	C₂²×C₃	1	4	yes	complemented
237	#4027	C₂²×C₃	1	4	yes	complemented
238	D₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
239	D₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
240	#4025	C₂²×C₃	1	4	yes	complemented
241	#4025	C₂²×C₃	1	4	yes	complemented
242	#4025	C₂²×C₃	1	4	yes	complemented
243	#4023	C₂²×C₃	1	4	yes	complemented
244	#4023	C₂²×C₃	1	2	yes	complemented
245	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
246	#4018	C₂²×C₃	1	4	yes	—
247	#4018	C₂²×C₃	1	4	yes	complemented
248	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
249	C₄²×D₅	C₂²×C₃	1	4	yes	complemented
250	#4016	C₂²×C₃	1	4	yes	complemented
251	#4015	C₂²×C₃	1	1	yes	characteristic, complemented
252	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
253	#3475	—	5	1	no	Sylow
254	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
255	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
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	1	yes	characteristic
260	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
261	C₃×C₅×Q₈	—	4	2	no	—
262	C₃×C₅×D₄	—	2	2	no	—
263	C₃×C₅×D₄	—	2	2	no	—
264	C₃×C₅×D₄	—	4	4	no	—
265	C₂×C₃×C₄×C₅	—	2	4	no	—
266	C₂×C₃×C₄×C₅	—	2	4	no	—
267	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
268	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
269	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
270	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
271	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
272	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
273	C₃×C₂²⋊D₅	—	2	8	no	—
274	C₃×C₂²⋊D₅	—	2	4	no	—
275	C₃×C₂²⋊D₅	—	2	4	no	—
276	C₂×C₃×Dic₅	—	2	4	no	—
277	C₂×C₃×Dic₅	—	2	4	no	—
278	C₂×C₃×Dic₅	—	4	2	no	—
279	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
280	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
281	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
282	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
283	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
284	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
285	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
286	C₃×D₂₀	#41	1	4	yes	complemented
287	C₃×C₄×D₅	—	2	4	no	—
288	C₃×C₄×D₅	—	2	8	no	—
289	C₃×C₄×D₅	—	2	4	no	—
290	C₃×C₄×D₅	—	2	2	no	—
291	C₃×C₄×D₅	—	2	4	no	—
292	C₃×C₄×D₅	—	4	4	no	—
293	C₃×C₄×D₅	—	4	1	no	—
294	C₃×C₄×D₅	#41	1	4	yes	complemented
295	C₃×Dic₁₀	—	2	4	no	—
296	C₃×Dic₁₀	—	2	2	no	—
297	C₂×C₃×#41	—	5	1	no	—
298	C₂×C₃×#41	—	5	2	no	—
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	C₂×D₅	1	1	yes	characteristic, complemented
303	C₃×#126	—	5	4	no	—
304	C₃×#126	—	5	4	no	—
305	C₃×#126	—	5	4	no	—
306	C₃×#125	—	5	2	no	—
307	C₃×#125	—	5	2	no	—
308	C₃×#125	—	5	4	no	—
309	C₃×#124	—	5	2	no	—
310	C₃×#124	C₂×D₅	1	4	yes	complemented
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	4	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	2	no	—
321	C₃×#121	—	5	4	no	—
322	C₃×#121	—	5	2	no	—
323	C₃×#121	C₂×D₅	1	2	yes	—
324	C₃×#121	C₂×D₅	1	2	yes	complemented
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	1	no	—
329	C₃×C₄×Q₈	—	5	2	no	—
330	C₃×C₄×Q₈	—	5	1	no	—
331	C₃×C₄×D₄	—	5	1	no	—
332	C₃×C₄×D₄	—	5	1	no	—
333	C₃×C₄×D₄	—	5	4	no	—
334	C₃×C₄×D₄	—	5	2	no	—
335	C₃×C₄×D₄	—	5	2	no	—
336	C₃×C₄×D₄	—	5	1	no	—
337	C₃×C₄×D₄	—	5	2	no	—
338	C₃×C₄×D₄	—	5	2	no	—
339	C₃×C₄×D₄	—	5	2	no	—
340	C₃×C₄×D₄	—	5	4	no	—
341	C₃×C₄×D₄	—	5	4	no	—
342	C₃×C₄×D₄	—	5	1	no	—
343	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
344	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic, complemented
345	C₃×#117	—	5	2	no	—
346	C₃×#117	—	5	1	no	—
347	C₃×#117	—	5	2	no	—
348	C₃×#117	—	5	4	no	—
349	C₃×#117	—	5	2	no	—
350	C₃×#117	—	5	4	no	—
351	C₃×#117	—	5	4	no	—
352	C₃×#117	C₂×D₅	1	2	yes	complemented
353	C₃×#117	C₂×D₅	1	2	yes	complemented
354	C₂×C₃×C₄⋊C₄	—	5	2	no	—
355	C₂×C₃×C₄⋊C₄	—	5	2	no	—
356	C₂×C₃×C₄⋊C₄	—	5	1	no	—
357	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
358	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
359	C₂×C₃×C₄²	—	5	2	no	—
360	C₂×C₃×C₄²	—	5	1	no	—
361	C₂×C₃×C₄²	—	5	4	no	—
362	C₂³×D₅	C₂³×C₃	1	2	yes	—
363	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
364	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
365	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
366	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
367	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
368	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
369	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
370	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
371	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
372	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
373	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
374	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
375	#711	—	2	4	no	—
376	D₄×D₅	—	2	4	no	—
377	#709	—	2	8	no	—
378	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
379	C₂×C₄×D₅	—	2	8	no	—
380	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
381	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
382	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
383	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
384	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
385	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
386	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
387	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
388	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
389	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
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	4	yes	—
395	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
396	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
397	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
398	C₄²×C₅	C₂³×C₃	1	4	yes	—
399	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
400	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
401	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
402	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
403	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
404	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
405	#685	C₂³×C₃	1	2	yes	—
406	#685	C₂³×C₃	1	4	yes	—
407	#685	C₂³×C₃	1	2	yes	—
408	#685	C₂³×C₃	1	4	yes	—
409	#685	C₂³×C₃	1	2	yes	—
410	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
411	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
412	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
413	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
414	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
415	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
416	#683	C₂³×C₃	1	2	yes	—
417	#683	C₂³×C₃	1	2	yes	—
418	#683	C₂³×C₃	1	2	yes	—
419	#683	C₂³×C₃	1	4	yes	—
420	#683	C₂³×C₃	1	4	yes	—
421	#683	C₂³×C₃	1	4	yes	—
422	#683	C₂³×C₃	1	4	yes	—
423	C₄×Dic₅	C₂³×C₃	1	2	yes	—
424	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
425	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
426	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
427	C₄×Dic₅	C₂³×C₃	1	2	yes	—
428	C₄×Dic₅	C₂³×C₃	1	4	yes	—
429	C₄×Dic₅	C₂³×C₃	1	4	yes	—
430	C₄×Dic₅	C₂³×C₃	1	2	yes	—
431	#556	—	5	1	no	—
432	#555	C₃×D₅	1	1	yes	characteristic, complemented
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	1	no	—
445	C₄×#41	—	5	2	no	—
446	C₂×C₄×D₄	—	5	1	no	—
447	C₂×#117	—	5	2	no	—
448	C₂²×C₃×C₅	—	2	2	no	—
449	C₂²×C₃×C₅	—	2	2	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	—	2	2	no	—
454	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
455	C₂×C₃×D₅	—	2	2	no	—
456	C₂×C₃×D₅	—	2	1	no	—
457	C₂×C₃×D₅	—	2	2	no	—
458	C₂×C₃×D₅	—	2	1	no	—
459	C₂×C₃×D₅	—	4	8	no	—
460	C₂×C₃×D₅	C₂×#41	1	2	yes	—
461	C₂×C₃×D₅	C₂×#41	1	4	yes	—
462	C₃×C₄×C₅	—	2	2	no	—
463	C₃×C₄×C₅	—	2	2	no	—
464	C₃×C₄×C₅	—	2	4	no	—
465	C₃×C₄×C₅	—	2	1	no	—
466	C₃×C₄×C₅	C₂×#41	1	2	yes	—
467	C₃×C₄×C₅	C₂×#41	1	2	yes	—
468	C₃×Dic₅	—	2	4	no	—
469	C₃×Dic₅	—	2	2	no	—
470	C₃×Dic₅	—	2	2	no	—
471	C₃×Dic₅	—	2	1	no	—
472	C₃×Dic₅	—	2	2	no	—
473	C₃×Dic₅	—	2	1	no	—
474	C₃×Dic₅	C₂×#41	1	2	yes	—
475	C₂⁴×C₃	—	5	2	no	—
476	C₃×#41	—	10	8	no	—
477	C₃×#41	—	10	4	no	—
478	C₂×C₃×Q₈	—	5	1	no	—
479	C₂×C₃×Q₈	—	5	2	no	—
480	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
481	C₂×C₃×D₄	—	5	2	no	—
482	C₂×C₃×D₄	—	5	4	no	—
483	C₂×C₃×D₄	—	5	2	no	—
484	C₂×C₃×D₄	—	5	1	no	—
485	C₂×C₃×D₄	—	10	4	no	—
486	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
487	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
488	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
489	C₂²×C₃×C₄	—	5	1	no	—
490	C₂²×C₃×C₄	—	5	2	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	4	no	—
495	C₂²×C₃×C₄	—	5	1	no	—
496	C₂²×C₃×C₄	—	5	2	no	—
497	C₂²×C₃×C₄	—	5	2	no	—
498	C₂²×C₃×C₄	—	5	1	no	—
499	C₂²×C₃×C₄	—	5	4	no	—
500	C₂²×C₃×C₄	—	10	8	no	—
501	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
502	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
503	C₃×C₄⋊C₄	—	5	4	no	—
504	C₃×C₄⋊C₄	—	5	4	no	—
505	C₃×C₄⋊C₄	—	5	2	no	—
506	C₃×C₄⋊C₄	—	5	2	no	—
507	C₃×C₄⋊C₄	—	5	4	no	—
508	C₃×C₄⋊C₄	—	5	4	no	—
509	C₃×C₄⋊C₄	—	5	2	no	—
510	C₃×C₄⋊C₄	—	5	1	no	—
511	C₃×C₄⋊C₄	—	5	2	no	—
512	C₃×C₄⋊C₄	—	5	1	no	—
513	C₃×C₄⋊C₄	—	5	4	no	—
514	C₃×C₄⋊C₄	—	5	4	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	2	yes	—
518	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
519	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
520	C₃×C₂²⋊C₄	—	5	4	no	—
521	C₃×C₂²⋊C₄	—	5	2	no	—
522	C₃×C₂²⋊C₄	—	5	2	no	—
523	C₃×C₂²⋊C₄	—	5	4	no	—
524	C₃×C₂²⋊C₄	—	5	4	no	—
525	C₃×C₂²⋊C₄	—	5	2	no	—
526	C₃×C₂²⋊C₄	—	5	2	no	—
527	C₃×C₂²⋊C₄	—	5	4	no	—
528	C₃×C₂²⋊C₄	—	5	2	no	—
529	C₃×C₂²⋊C₄	—	5	4	no	—
530	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
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	4	yes	—
534	C₃×C₄²	—	5	2	no	—
535	C₃×C₄²	—	5	1	no	—
536	C₃×C₄²	—	5	4	no	—
537	C₃×C₄²	—	5	1	no	—
538	C₃×C₄²	—	5	4	no	—
539	C₃×C₄²	—	5	2	no	—
540	C₃×C₄²	—	5	1	no	—
541	C₃×C₄²	—	5	2	no	—
542	C₃×C₄²	C₂²×D₅	1	4	yes	—
543	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
544	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
545	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
546	C₂²×D₅	—	2	4	no	—
547	C₂²×D₅	—	2	4	no	—
548	C₂²×D₅	—	4	2	no	—
549	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
550	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
551	C₅×Q₈	—	4	2	no	—
552	C₅×D₄	—	2	2	no	—
553	C₅×D₄	—	2	2	no	—
554	C₅×D₄	—	4	4	no	—
555	C₂×C₄×C₅	—	2	4	no	—
556	C₂×C₄×C₅	—	2	4	no	—
557	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
558	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
559	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
560	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
561	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
562	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
563	C₂²⋊D₅	—	2	8	no	—
564	C₂²⋊D₅	—	2	4	no	—
565	C₂²⋊D₅	—	2	4	no	—
566	C₂×Dic₅	—	2	4	no	—
567	C₂×Dic₅	—	2	4	no	—
568	C₂×Dic₅	—	4	2	no	—
569	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
570	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
571	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
572	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
573	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
574	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
575	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
576	D₂₀	C₃×#41	1	4	yes	complemented
577	C₄×D₅	—	2	4	no	—
578	C₄×D₅	—	2	8	no	—
579	C₄×D₅	—	2	4	no	—
580	C₄×D₅	—	2	2	no	—
581	C₄×D₅	—	2	4	no	—
582	C₄×D₅	—	4	4	no	—
583	C₄×D₅	—	4	1	no	—
584	C₄×D₅	C₃×#41	1	4	yes	complemented
585	Dic₁₀	—	2	4	no	—
586	Dic₁₀	—	2	2	no	—
587	C₂×#41	—	5	1	no	—
588	C₂×#41	—	5	2	no	—
589	C₂²×D₄	—	5	1	no	—
590	C₂³×C₄	—	5	2	no	—
591	C₄⋊Q₈	—	5	1	no	—
592	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
593	#126	—	5	4	no	—
594	#126	—	5	4	no	—
595	#126	—	5	4	no	—
596	#125	—	5	2	no	—
597	#125	—	5	2	no	—
598	#125	—	5	4	no	—
599	#124	—	5	2	no	—
600	#124	C₂×C₃×D₅	1	4	yes	complemented
601	#123	—	5	4	no	—
602	#123	—	5	4	no	—
603	#123	—	5	4	no	—
604	#123	—	5	4	no	—
605	C₂²⋊Q₈	—	5	4	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	2	no	—
611	#121	—	5	2	no	—
612	#121	—	5	4	no	—
613	#121	C₂×C₃×D₅	1	2	yes	—
614	#121	C₂×C₃×D₅	1	2	yes	complemented
615	#120	—	5	4	no	—
616	C₄×Q₈	—	5	2	no	—
617	C₄×Q₈	—	5	2	no	—
618	C₄×Q₈	—	5	1	no	—
619	C₄×Q₈	—	5	2	no	—
620	C₄×Q₈	—	5	1	no	—
621	C₄×D₄	—	5	1	no	—
622	C₄×D₄	—	5	1	no	—
623	C₄×D₄	—	5	4	no	—
624	C₄×D₄	—	5	2	no	—
625	C₄×D₄	—	5	2	no	—
626	C₄×D₄	—	5	1	no	—
627	C₄×D₄	—	5	2	no	—
628	C₄×D₄	—	5	2	no	—
629	C₄×D₄	—	5	4	no	—
630	C₄×D₄	—	5	2	no	—
631	C₄×D₄	—	5	4	no	—
632	C₄×D₄	—	5	1	no	—
633	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
634	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
635	#117	—	5	2	no	—
636	#117	—	5	1	no	—
637	#117	—	5	2	no	—
638	#117	—	5	4	no	—
639	#117	—	5	2	no	—
640	#117	—	5	4	no	—
641	#117	—	5	4	no	—
642	#117	C₂×C₃×D₅	1	2	yes	complemented
643	#117	C₂×C₃×D₅	1	2	yes	complemented
644	C₂×C₄⋊C₄	—	5	2	no	—
645	C₂×C₄⋊C₄	—	5	2	no	—
646	C₂×C₄⋊C₄	—	5	1	no	—
647	C₂×C₂²⋊C₄	—	5	4	no	—
648	C₂×C₂²⋊C₄	—	5	2	no	—
649	C₂×C₄²	—	5	2	no	—
650	C₂×C₄²	—	5	4	no	—
651	C₂×C₄²	—	5	1	no	—
652	C₂×C₃×C₅	—	4	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	2	no	—
658	C₃×D₅	—	2	4	no	—
659	C₂³×C₃	—	5	1	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	2	yes	—
666	C₃×Q₈	—	4	2	no	—
667	C₃×Q₈	—	10	2	no	—
668	C₃×Q₈	—	10	4	no	—
669	C₃×D₄	—	2	2	no	—
670	C₃×D₄	—	2	2	no	—
671	C₃×D₄	—	4	4	no	—
672	C₃×D₄	—	5	4	no	—
673	C₃×D₄	—	10	4	no	—
674	C₃×D₄	—	10	8	no	—
675	C₃×D₄	—	10	4	no	—
676	C₂×C₃×C₄	—	2	4	no	—
677	C₂×C₃×C₄	—	2	4	no	—
678	C₂×C₃×C₄	—	5	1	no	—
679	C₂×C₃×C₄	—	5	4	no	—
680	C₂×C₃×C₄	—	5	1	no	—
681	C₂×C₃×C₄	—	5	2	no	—
682	C₂×C₃×C₄	—	5	2	no	—
683	C₂×C₃×C₄	—	5	4	no	—
684	C₂×C₃×C₄	—	5	1	no	—
685	C₂×C₃×C₄	—	5	2	no	—
686	C₂×C₃×C₄	—	10	4	no	—
687	C₂×C₃×C₄	—	10	4	no	—
688	C₂×C₃×C₄	—	10	8	no	—
689	C₂×C₃×C₄	—	10	4	no	—
690	C₂×C₃×C₄	—	10	4	no	—
691	C₂×C₃×C₄	—	10	4	no	—
692	C₂×C₃×C₄	—	10	2	no	—
693	C₂×C₃×C₄	—	20	4	no	—
694	C₂×C₃×C₄	—	20	1	no	—
695	C₂×C₃×C₄	—	20	2	no	—
696	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
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	4	yes	—
700	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
701	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
702	C₂²×C₅	—	2	2	no	—
703	C₂²×C₅	—	2	2	no	—
704	C₂²×C₅	—	2	2	no	—
705	C₂²×C₅	—	2	2	no	—
706	C₂²×C₅	—	2	2	no	—
707	C₂²×C₅	—	2	2	no	—
708	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
709	C₂×D₅	—	2	2	no	—
710	C₂×D₅	—	2	1	no	—
711	C₂×D₅	—	2	2	no	—
712	C₂×D₅	—	2	1	no	—
713	C₂×D₅	—	4	8	no	—
714	C₂×D₅	C₂×C₃×#41	1	2	yes	—
715	C₂×D₅	C₂×C₃×#41	1	4	yes	—
716	C₄×C₅	—	2	2	no	—
717	C₄×C₅	—	2	2	no	—
718	C₄×C₅	—	2	4	no	—
719	C₄×C₅	—	2	1	no	—
720	C₄×C₅	C₂×C₃×#41	1	2	yes	—
721	C₄×C₅	C₂×C₃×#41	1	2	yes	—
722	Dic₅	—	2	4	no	—
723	Dic₅	—	2	2	no	—
724	Dic₅	—	2	2	no	—
725	Dic₅	—	2	1	no	—
726	Dic₅	—	2	2	no	—
727	Dic₅	—	2	1	no	—
728	Dic₅	C₂×C₃×#41	1	2	yes	—
729	C₂⁴	—	5	2	no	—
730	#41	—	10	8	no	—
731	#41	—	10	4	no	—
732	C₂×Q₈	—	5	1	no	—
733	C₂×Q₈	—	5	2	no	—
734	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
735	C₂×D₄	—	5	2	no	—
736	C₂×D₄	—	5	4	no	—
737	C₂×D₄	—	5	2	no	—
738	C₂×D₄	—	5	1	no	—
739	C₂×D₄	—	10	4	no	—
740	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
741	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
742	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
743	C₂²×C₄	—	5	1	no	—
744	C₂²×C₄	—	5	2	no	—
745	C₂²×C₄	—	5	2	no	—
746	C₂²×C₄	—	5	2	no	—
747	C₂²×C₄	—	5	2	no	—
748	C₂²×C₄	—	5	4	no	—
749	C₂²×C₄	—	5	1	no	—
750	C₂²×C₄	—	5	2	no	—
751	C₂²×C₄	—	5	2	no	—
752	C₂²×C₄	—	5	1	no	—
753	C₂²×C₄	—	5	4	no	—
754	C₂²×C₄	—	10	8	no	—
755	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
756	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
757	C₄⋊C₄	—	5	1	no	—
758	C₄⋊C₄	—	5	2	no	—
759	C₄⋊C₄	—	5	4	no	—
760	C₄⋊C₄	—	5	4	no	—
761	C₄⋊C₄	—	5	1	no	—
762	C₄⋊C₄	—	5	2	no	—
763	C₄⋊C₄	—	5	2	no	—
764	C₄⋊C₄	—	5	4	no	—
765	C₄⋊C₄	—	5	4	no	—
766	C₄⋊C₄	—	5	2	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	2	yes	—
772	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
773	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
774	C₂²⋊C₄	—	5	4	no	—
775	C₂²⋊C₄	—	5	2	no	—
776	C₂²⋊C₄	—	5	2	no	—
777	C₂²⋊C₄	—	5	4	no	—
778	C₂²⋊C₄	—	5	4	no	—
779	C₂²⋊C₄	—	5	2	no	—
780	C₂²⋊C₄	—	5	2	no	—
781	C₂²⋊C₄	—	5	4	no	—
782	C₂²⋊C₄	—	5	2	no	—
783	C₂²⋊C₄	—	5	4	no	—
784	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
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	4	yes	—
788	C₄²	—	5	2	no	—
789	C₄²	—	5	1	no	—
790	C₄²	—	5	4	no	—
791	C₄²	—	5	1	no	—
792	C₄²	—	5	2	no	—
793	C₄²	—	5	4	no	—
794	C₄²	—	5	1	no	—
795	C₄²	—	5	2	no	—
796	C₄²	C₂²×C₃×D₅	1	4	yes	—
797	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
798	C₃×C₅	#3475	1	1	yes	characteristic, complemented, Hall
799	C₂²×C₃	—	2	2	no	—
800	C₂²×C₃	—	2	2	no	—
801	C₂²×C₃	—	2	2	no	—
802	C₂²×C₃	—	2	2	no	—
803	C₂²×C₃	—	2	2	no	—
804	C₂²×C₃	—	2	2	no	—
805	C₂²×C₃	—	5	2	no	—
806	C₂²×C₃	—	5	4	no	—
807	C₂²×C₃	—	10	2	no	—
808	C₂²×C₃	—	10	1	no	—
809	C₂²×C₃	—	10	2	no	—
810	C₂²×C₃	—	10	1	no	—
811	C₂²×C₃	—	20	8	no	—
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	4	no	—
816	C₃×C₄	—	2	1	no	—
817	C₃×C₄	—	5	2	no	—
818	C₃×C₄	—	10	2	no	—
819	C₃×C₄	—	10	1	no	—
820	C₃×C₄	—	10	2	no	—
821	C₃×C₄	—	10	4	no	—
822	C₃×C₄	—	10	2	no	—
823	C₃×C₄	—	10	1	no	—
824	C₃×C₄	D₅×#41	1	2	yes	—
825	C₃×C₄	D₅×#41	1	2	yes	—
826	C₂×C₅	—	4	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	2	no	—
832	D₅	—	2	4	no	—
833	C₂³	—	5	1	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	2	yes	—
840	Q₈	—	4	2	no	—
841	Q₈	—	10	2	no	—
842	Q₈	—	10	4	no	—
843	D₄	—	2	2	no	—
844	D₄	—	2	2	no	—
845	D₄	—	4	4	no	—
846	D₄	—	5	4	no	—
847	D₄	—	10	4	no	—
848	D₄	—	10	8	no	—
849	D₄	—	10	4	no	—
850	C₂×C₄	—	2	4	no	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	5	1	no	—
853	C₂×C₄	—	5	4	no	—
854	C₂×C₄	—	5	2	no	—
855	C₂×C₄	—	5	1	no	—
856	C₂×C₄	—	5	4	no	—
857	C₂×C₄	—	5	2	no	—
858	C₂×C₄	—	5	1	no	—
859	C₂×C₄	—	5	2	no	—
860	C₂×C₄	—	10	4	no	—
861	C₂×C₄	—	10	4	no	—
862	C₂×C₄	—	10	8	no	—
863	C₂×C₄	—	10	4	no	—
864	C₂×C₄	—	10	4	no	—
865	C₂×C₄	—	10	4	no	—
866	C₂×C₄	—	10	2	no	—
867	C₂×C₄	—	20	4	no	—
868	C₂×C₄	—	20	1	no	—
869	C₂×C₄	—	20	2	no	—
870	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
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	4	yes	—
874	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
875	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
876	C₂×C₃	—	4	2	no	—
877	C₂×C₃	—	4	2	no	—
878	C₂×C₃	—	10	2	no	—
879	C₂×C₃	—	10	4	no	—
880	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
881	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
882	C₂×C₃	#66285	1	1	yes	characteristic
883	C₅	C₃×#3475	1	1	yes	characteristic, complemented, Sylow
884	C₂²	—	2	2	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	2	2	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	2	no	—
890	C₂²	—	5	2	no	—
891	C₂²	—	5	4	no	—
892	C₂²	—	10	2	no	—
893	C₂²	—	10	1	no	—
894	C₂²	—	10	2	no	—
895	C₂²	—	10	1	no	—
896	C₂²	—	20	8	no	—
897	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
898	C₄	—	2	2	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	4	no	—
901	C₄	—	2	1	no	—
902	C₄	—	5	2	no	—
903	C₄	—	10	2	no	—
904	C₄	—	10	1	no	—
905	C₄	—	10	2	no	—
906	C₄	—	10	4	no	—
907	C₄	—	10	2	no	—
908	C₄	—	10	1	no	—
909	C₄	C₃×D₅×#41	1	2	yes	—
910	C₄	C₃×D₅×#41	1	2	yes	—
911	C₃	#10618859	1	1	yes	characteristic, direct product factor, Sylow
912	C₂	—	4	2	no	—
913	C₂	—	4	2	no	—
914	C₂	—	10	2	no	—
915	C₂	—	10	4	no	—
916	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
917	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
918	C₂	C₃×#66285	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₅×#555	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×#555	D₅
hypocenter	C₅	C₃×#3475
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#555

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#555	C₂	semidirect
2. C₃×#66064	C₂	semidirect
3. C₃×#66062	C₂	semidirect
4. C₃×#66014	C₂	semidirect
5. C₃×#66013	C₂	semidirect
6. C₃×#65948	C₂	semidirect
7. C₃×#65946	C₂	semidirect
8. C₃×#65940	C₂	semidirect
9. C₃×#65934	C₂	semidirect
10. C₃×#65885	C₂	semidirect
11. C₃×C₄×D₄×D₅	C₂	semidirect
12. C₃×#65876	C₂	semidirect
13. C₃×C₄×#711	C₂	semidirect
14. C₃×#65863	C₂	semidirect
15. C₃×#65863	C₂	semidirect
16. C₃×#65856	C₂	semidirect
17. C₃×D₅×#117	C₂	semidirect
18. #10618859	C₃	direct (N × H)
23. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
24. C₃×C₅×#124	C₂²	semidirect
26. C₃×C₅×#121	C₂²	semidirect
28. C₃×C₄×C₅×D₄	C₂²	semidirect
29. C₃×C₅×#117	C₂²	semidirect
30. C₃×C₅×#117	C₂²	semidirect
32. C₃×#4092	C₂²	semidirect
33. C₃×Q₈×Dic₅	C₂²	semidirect
35. C₃×#4084	C₂²	semidirect
38. C₃×#4081	C₂²	semidirect
40. C₃×D₄×Dic₅	C₂²	semidirect
41. C₃×D₄×Dic₅	C₂²	semidirect
44. C₃×#4072	C₂²	semidirect
45. C₃×#4070	C₂²	semidirect
46. C₃×#4070	C₂²	semidirect
47. C₂×C₃×C₄×Dic₅	C₂²	semidirect
49. C₃×#4043	C₂²	semidirect
55. C₃×D₅×C₄⋊C₄	C₂²	semidirect
56. C₃×D₅×C₄⋊C₄	C₂²	semidirect
57. C₃×#4036	C₂²	semidirect
58. C₃×#4036	C₂²	semidirect
59. C₃×#4033	C₂²	semidirect
60. C₃×#4033	C₂²	semidirect
61. C₃×#4033	C₂²	semidirect
64. C₃×#4029	C₂²	semidirect
67. C₃×#4027	C₂²	semidirect
68. C₃×#4027	C₂²	semidirect
71. C₃×#4025	C₂²	semidirect
72. C₃×#4025	C₂²	semidirect
73. C₃×#4025	C₂²	semidirect
74. C₃×#4023	C₂²	semidirect
75. C₃×#4023	C₂²	semidirect
78. C₃×#4018	C₂²	semidirect
80. C₃×C₄²×D₅	C₂²	semidirect
81. C₃×#4016	C₂²	semidirect
82. C₃×#4015	C₂²	semidirect
83. C₃×C₄×Dic₁₀	C₂²	semidirect
85. C₅×#555	C₂×C₃	semidirect
86. #66064	C₂×C₃	semidirect
87. #66062	C₂×C₃	semidirect
88. #66014	C₂×C₃	semidirect
89. #66013	C₂×C₃	semidirect
90. #65948	C₂×C₃	semidirect
91. #65946	C₂×C₃	semidirect
92. #65940	C₂×C₃	semidirect
93. #65934	C₂×C₃	semidirect
94. #65885	C₂×C₃	semidirect
95. C₄×D₄×D₅	C₂×C₃	semidirect
96. #65876	C₂×C₃	semidirect
97. C₄×#711	C₂×C₃	semidirect
98. #65863	C₂×C₃	semidirect
99. #65863	C₂×C₃	semidirect
100. #65856	C₂×C₃	semidirect
101. D₅×#117	C₂×C₃	semidirect
172. C₃×#555	D₅	semidirect
192. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
193. C₅×#124	C₂²×C₃	semidirect
195. C₅×#121	C₂²×C₃	semidirect
197. C₄×C₅×D₄	C₂²×C₃	semidirect
198. C₅×#117	C₂²×C₃	semidirect
199. C₅×#117	C₂²×C₃	semidirect
201. #4092	C₂²×C₃	semidirect
202. Q₈×Dic₅	C₂²×C₃	semidirect
204. #4084	C₂²×C₃	semidirect
207. #4081	C₂²×C₃	semidirect
209. D₄×Dic₅	C₂²×C₃	semidirect
210. D₄×Dic₅	C₂²×C₃	semidirect
213. #4072	C₂²×C₃	semidirect
214. #4070	C₂²×C₃	semidirect
215. #4070	C₂²×C₃	semidirect
216. C₂×C₄×Dic₅	C₂²×C₃	semidirect
218. #4043	C₂²×C₃	semidirect
224. D₅×C₄⋊C₄	C₂²×C₃	semidirect
225. D₅×C₄⋊C₄	C₂²×C₃	semidirect
226. #4036	C₂²×C₃	semidirect
227. #4036	C₂²×C₃	semidirect
228. #4033	C₂²×C₃	semidirect
229. #4033	C₂²×C₃	semidirect
230. #4033	C₂²×C₃	semidirect
233. #4029	C₂²×C₃	semidirect
236. #4027	C₂²×C₃	semidirect
237. #4027	C₂²×C₃	semidirect
240. #4025	C₂²×C₃	semidirect
241. #4025	C₂²×C₃	semidirect
242. #4025	C₂²×C₃	semidirect
243. #4023	C₂²×C₃	semidirect
244. #4023	C₂²×C₃	semidirect
247. #4018	C₂²×C₃	semidirect
249. C₄²×D₅	C₂²×C₃	semidirect
250. #4016	C₂²×C₃	semidirect
251. #4015	C₂²×C₃	semidirect
252. C₄×Dic₁₀	C₂²×C₃	semidirect
286. C₃×D₂₀	#41	semidirect
294. C₃×C₄×D₅	#41	semidirect
302. C₃×C₄⋊Q₈	C₂×D₅	semidirect
310. C₃×#124	C₂×D₅	semidirect
324. C₃×#121	C₂×D₅	semidirect
344. C₃×C₄×D₄	C₂×D₅	semidirect
352. C₃×#117	C₂×D₅	semidirect
353. C₃×#117	C₂×D₅	semidirect
432. #555	C₃×D₅	semidirect
576. D₂₀	C₃×#41	semidirect
584. C₄×D₅	C₃×#41	semidirect
592. C₄⋊Q₈	C₂×C₃×D₅	semidirect
600. #124	C₂×C₃×D₅	semidirect
614. #121	C₂×C₃×D₅	semidirect
634. C₄×D₄	C₂×C₃×D₅	semidirect
642. #117	C₂×C₃×D₅	semidirect
643. #117	C₂×C₃×D₅	semidirect
798. C₃×C₅	#3475	semidirect
883. C₅	C₃×#3475	semidirect
911. C₃	#10618859	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×C₅×#555	2
C₃×#66064	2
C₃×#66062	2
C₃×#66014	2
C₃×#66013	2
C₃×#65948	2
C₃×#65946	2
C₃×#65940	2
C₃×#65934	2
C₃×#65885	2
C₃×C₄×D₄×D₅	2
C₃×#65876	2
C₃×C₄×#711	2
C₃×#65863	2
C₃×#65856	2
C₃×D₅×#117	2
#10618859	3
C₃×#3475	5

Subgroups — C3×#10618859 #14484127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10618859 #14484127