Subgroups — C₃×#10617738 #14481503

Order 1920.

2080 conjugacy classes of subgroups.

The subgroup lattice has 812 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×#66166	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66162	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65917	C₂	1	2	yes	maximal, complemented
5	C₃×#65916	C₂	1	2	yes	maximal, complemented
6	C₃×#65898	C₂	1	4	yes	maximal, complemented
7	C₃×#65896	C₂	1	2	yes	maximal, complemented
8	C₃×#65895	C₂	1	2	yes	maximal, complemented
9	C₃×#65894	C₂	1	4	yes	maximal, complemented
10	C₃×#65862	C₂	1	4	yes	maximal, complemented
11	C₃×#65858	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#65851	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×#65813	C₂	1	4	yes	maximal, complemented
14	C₃×C₄×#709	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×#4018	C₂	1	1	yes	maximal, characteristic, complemented
16	#10617738	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂×C₃×#709	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
20	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
21	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
22	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
23	C₃×C₅×#117	C₂²	1	1	yes	characteristic
24	C₃×C₅×#117	C₂²	1	2	yes	complemented
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
27	C₃×#4093	C₂²	1	1	yes	characteristic, complemented
28	C₃×#4092	C₂²	1	2	yes	—
29	C₃×#4090	C₂²	1	1	yes	characteristic, complemented
30	C₃×#4086	C₂²	1	1	yes	characteristic, complemented
31	C₃×#4085	C₂²	1	4	yes	—
32	C₃×#4084	C₂²	1	2	yes	—
33	C₃×#4083	C₂²	1	2	yes	—
34	C₃×#4082	C₂²	1	1	yes	characteristic, complemented
35	C₃×#4081	C₂²	1	2	yes	—
36	C₃×#4076	C₂²	1	4	yes	—
37	C₃×#4075	C₂²	1	4	yes	—
38	C₃×#4075	C₂²	1	4	yes	complemented
39	C₃×C₄×C₂²⋊D₅	C₂²	1	4	yes	—
40	C₃×C₄×C₂²⋊D₅	C₂²	1	4	yes	—
41	C₃×C₄×C₂²⋊D₅	C₂²	1	4	yes	complemented
42	C₂×C₃×#685	C₂²	1	2	yes	—
43	C₃×#4072	C₂²	1	1	yes	characteristic
44	C₃×#4070	C₂²	1	4	yes	complemented
45	C₂×C₃×#683	C₂²	1	2	yes	—
46	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
47	C₃×#4044	C₂²	1	4	yes	—
48	C₃×#4043	C₂²	1	2	yes	—
49	C₃×#4042	C₂²	1	4	yes	complemented
50	C₃×#4041	C₂²	1	2	yes	—
51	C₃×#4040	C₂²	1	4	yes	—
52	C₃×#4036	C₂²	1	2	yes	complemented
53	C₃×#4035	C₂²	1	4	yes	complemented
54	C₃×#4034	C₂²	1	2	yes	complemented
55	C₃×#4032	C₂²	1	2	yes	—
56	C₃×#4031	C₂²	1	4	yes	—
57	C₃×#4030	C₂²	1	4	yes	—
58	C₃×#4029	C₂²	1	4	yes	complemented
59	C₃×#4028	C₂²	1	2	yes	—
60	C₃×#4025	C₂²	1	4	yes	complemented
61	C₃×#4024	C₂²	1	4	yes	—
62	C₃×#4022	C₂²	1	4	yes	—
63	C₃×#4022	C₂²	1	4	yes	complemented
64	C₃×#4021	C₂²	1	4	yes	—
65	C₃×C₄×D₂₀	C₂²	1	4	yes	—
66	C₃×C₄×D₂₀	C₂²	1	2	yes	complemented
67	C₃×#4018	C₂²	1	2	yes	—
68	C₃×#4018	C₂²	1	2	yes	—
69	C₃×#4018	C₂²	1	2	yes	—
70	C₃×#4018	C₂²	1	2	yes	—
71	C₃×#4018	C₂²	1	2	yes	complemented
72	C₃×C₄²×D₅	C₂²	1	2	yes	complemented
73	C₃×#4016	C₂²	1	4	yes	complemented
74	C₃×C₄×Dic₁₀	C₂²	1	4	yes	complemented
75	C₃×C₄×Dic₁₀	C₂²	1	2	yes	complemented
76	C₃×#3455	—	5	1	no	maximal, Hall
77	C₄×C₅×#41	C₂×C₃	1	1	yes	characteristic, complemented
78	#66166	C₂×C₃	1	1	yes	characteristic, complemented
79	#66162	C₂×C₃	1	1	yes	characteristic, complemented
80	#65917	C₂×C₃	1	2	yes	complemented
81	#65916	C₂×C₃	1	2	yes	complemented
82	#65898	C₂×C₃	1	4	yes	complemented
83	#65896	C₂×C₃	1	2	yes	complemented
84	#65895	C₂×C₃	1	2	yes	complemented
85	#65894	C₂×C₃	1	4	yes	complemented
86	#65862	C₂×C₃	1	4	yes	complemented
87	#65858	C₂×C₃	1	1	yes	characteristic, complemented
88	#65851	C₂×C₃	1	1	yes	characteristic, complemented
89	#65813	C₂×C₃	1	4	yes	complemented
90	C₄×#709	C₂×C₃	1	1	yes	characteristic, complemented
91	C₂×#4018	C₂×C₃	1	1	yes	characteristic, complemented
92	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
93	C₃×C₅×#41	—	2	4	no	—
94	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
96	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
97	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
98	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
99	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
100	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₂²⋊D₅	C₂³	1	2	yes	—
102	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
103	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
104	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
105	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
106	C₃×#709	—	2	4	no	—
107	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
108	C₂×C₃×D₂₀	C₂³	1	4	yes	—
109	C₂×C₃×C₄×D₅	—	2	4	no	—
110	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
111	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
112	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
113	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
114	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
115	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
116	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
117	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
118	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
119	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₃×C₄²×C₅	C₂³	1	2	yes	—
121	C₃×C₄²×C₅	C₂³	1	2	yes	—
122	C₃×C₄²×C₅	C₂³	1	4	yes	—
123	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
124	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
125	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
126	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
127	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
128	C₃×#685	C₂³	1	4	yes	—
129	C₃×#685	C₂³	1	4	yes	—
130	C₃×#685	C₂³	1	2	yes	—
131	C₃×#685	C₂³	1	2	yes	—
132	C₃×#685	C₂³	1	2	yes	—
133	C₃×#685	C₂³	1	2	yes	—
134	C₃×#685	C₂³	1	4	yes	—
135	C₃×#685	C₂³	1	4	yes	—
136	C₃×#685	C₂³	1	4	yes	—
137	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
138	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
139	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
140	C₃×#683	C₂³	1	4	yes	—
141	C₃×#683	C₂³	1	4	yes	—
142	C₃×#683	C₂³	1	4	yes	—
143	C₃×#683	C₂³	1	4	yes	—
144	C₃×#683	C₂³	1	4	yes	—
145	C₃×#683	C₂³	1	2	yes	—
146	C₃×#683	C₂³	1	2	yes	—
147	C₃×#683	C₂³	1	2	yes	—
148	C₃×#683	C₂³	1	2	yes	—
149	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
150	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
151	C₃×C₄×Dic₅	C₂³	1	2	yes	—
152	C₃×C₄×Dic₅	C₂³	1	2	yes	—
153	C₃×C₄×Dic₅	C₂³	1	4	yes	—
154	C₃×#542	—	5	2	no	—
155	C₃×#542	—	5	2	no	—
156	C₃×#541	—	5	2	no	—
157	C₃×#540	—	5	2	no	—
158	C₃×#539	—	5	4	no	—
159	C₃×#538	—	5	4	no	—
160	C₃×#533	—	5	1	no	—
161	C₃×#532	—	5	1	no	—
162	C₃×#529	—	5	4	no	—
163	C₃×#529	—	5	4	no	—
164	C₃×#525	—	5	1	no	—
165	C₃×#525	—	5	1	no	—
166	C₃×C₄×#41	—	5	1	no	—
167	C₃×C₄×#41	D₅	1	1	yes	characteristic, complemented
168	C₂×C₃×#117	—	5	1	no	—
169	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
170	C₂×#709	C₂²×C₃	1	1	yes	characteristic
171	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
172	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
173	C₄×C₅×D₄	C₂²×C₃	1	4	yes	—
174	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
175	C₅×#117	C₂²×C₃	1	1	yes	characteristic
176	C₅×#117	C₂²×C₃	1	2	yes	complemented
177	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
178	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	complemented
179	#4093	C₂²×C₃	1	1	yes	characteristic, complemented
180	#4092	C₂²×C₃	1	2	yes	—
181	#4090	C₂²×C₃	1	1	yes	characteristic, complemented
182	#4086	C₂²×C₃	1	1	yes	characteristic, complemented
183	#4085	C₂²×C₃	1	4	yes	—
184	#4084	C₂²×C₃	1	2	yes	—
185	#4083	C₂²×C₃	1	2	yes	—
186	#4082	C₂²×C₃	1	1	yes	characteristic, complemented
187	#4081	C₂²×C₃	1	2	yes	—
188	#4076	C₂²×C₃	1	4	yes	—
189	#4075	C₂²×C₃	1	4	yes	—
190	#4075	C₂²×C₃	1	4	yes	complemented
191	C₄×C₂²⋊D₅	C₂²×C₃	1	4	yes	—
192	C₄×C₂²⋊D₅	C₂²×C₃	1	4	yes	—
193	C₄×C₂²⋊D₅	C₂²×C₃	1	4	yes	complemented
194	C₂×#685	C₂²×C₃	1	2	yes	—
195	#4072	C₂²×C₃	1	1	yes	characteristic
196	#4070	C₂²×C₃	1	4	yes	complemented
197	C₂×#683	C₂²×C₃	1	2	yes	—
198	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
199	#4044	C₂²×C₃	1	4	yes	—
200	#4043	C₂²×C₃	1	2	yes	—
201	#4042	C₂²×C₃	1	4	yes	complemented
202	#4041	C₂²×C₃	1	2	yes	—
203	#4040	C₂²×C₃	1	4	yes	—
204	#4036	C₂²×C₃	1	2	yes	complemented
205	#4035	C₂²×C₃	1	4	yes	complemented
206	#4034	C₂²×C₃	1	2	yes	complemented
207	#4032	C₂²×C₃	1	2	yes	—
208	#4031	C₂²×C₃	1	4	yes	—
209	#4030	C₂²×C₃	1	4	yes	—
210	#4029	C₂²×C₃	1	4	yes	complemented
211	#4028	C₂²×C₃	1	2	yes	—
212	#4025	C₂²×C₃	1	4	yes	complemented
213	#4024	C₂²×C₃	1	4	yes	—
214	#4022	C₂²×C₃	1	4	yes	—
215	#4022	C₂²×C₃	1	4	yes	complemented
216	#4021	C₂²×C₃	1	4	yes	—
217	C₄×D₂₀	C₂²×C₃	1	4	yes	—
218	C₄×D₂₀	C₂²×C₃	1	2	yes	complemented
219	#4018	C₂²×C₃	1	2	yes	—
220	#4018	C₂²×C₃	1	2	yes	—
221	#4018	C₂²×C₃	1	2	yes	—
222	#4018	C₂²×C₃	1	2	yes	—
223	#4018	C₂²×C₃	1	2	yes	complemented
224	C₄²×D₅	C₂²×C₃	1	2	yes	complemented
225	#4016	C₂²×C₃	1	4	yes	complemented
226	C₄×Dic₁₀	C₂²×C₃	1	2	yes	complemented
227	C₄×Dic₁₀	C₂²×C₃	1	4	yes	complemented
228	#3455	—	5	1	no	Sylow
229	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
230	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
231	C₂²×C₃×D₅	—	2	2	no	—
232	C₂²×C₃×D₅	—	4	2	no	—
233	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
234	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
235	C₃×C₅×Q₈	—	2	2	no	—
236	C₃×C₅×D₄	—	2	4	no	—
237	C₃×C₅×D₄	—	2	2	no	—
238	C₂×C₃×C₄×C₅	—	2	4	no	—
239	C₂×C₃×C₄×C₅	—	4	4	no	—
240	C₂×C₃×C₄×C₅	—	4	2	no	—
241	C₂×C₃×C₄×C₅	#41	1	4	yes	—
242	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
243	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
244	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
245	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
246	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
247	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
248	C₃×C₂²⋊D₅	—	2	4	no	—
249	C₃×C₂²⋊D₅	—	4	4	no	—
250	C₃×C₂²⋊D₅	—	4	4	no	—
251	C₂×C₃×Dic₅	—	2	2	no	—
252	C₂×C₃×Dic₅	—	4	2	no	—
253	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
254	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
255	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
256	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
257	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
258	C₃×D₂₀	—	2	2	no	—
259	C₃×D₂₀	—	4	4	no	—
260	C₃×C₄×D₅	—	2	4	no	—
261	C₃×C₄×D₅	—	2	4	no	—
262	C₃×C₄×D₅	—	2	4	no	—
263	C₃×C₄×D₅	—	4	4	no	—
264	C₃×Dic₁₀	—	2	2	no	—
265	C₃×Dic₁₀	—	4	4	no	—
266	C₂×C₃×#41	—	5	1	no	—
267	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
268	C₂³×C₃×C₄	—	5	1	no	—
269	C₃×C₄⋊Q₈	—	5	1	no	—
270	C₃×C₄⋊Q₈	—	5	2	no	—
271	C₃×#127	—	5	1	no	—
272	C₃×#126	—	5	4	no	—
273	C₃×#126	—	5	4	no	—
274	C₃×#126	—	5	4	no	—
275	C₃×#126	—	5	4	no	—
276	C₃×#125	—	5	4	no	—
277	C₃×#125	—	5	2	no	—
278	C₃×#125	—	5	4	no	—
279	C₃×#124	—	5	1	no	—
280	C₃×#124	—	5	1	no	—
281	C₃×#124	—	5	4	no	—
282	C₃×#124	—	5	4	no	—
283	C₃×#123	—	5	2	no	—
284	C₃×#123	—	5	4	no	—
285	C₃×#123	—	5	4	no	—
286	C₃×#123	—	5	4	no	—
287	C₃×#123	—	5	4	no	—
288	C₃×#123	—	5	2	no	—
289	C₃×C₂²⋊Q₈	—	5	2	no	—
290	C₃×C₂²⋊Q₈	—	5	4	no	—
291	C₃×C₂²⋊Q₈	—	5	4	no	—
292	C₃×C₂²⋊Q₈	—	5	2	no	—
293	C₃×C₂²⋊Q₈	—	5	4	no	—
294	C₃×#121	—	5	2	no	—
295	C₃×#121	—	5	4	no	—
296	C₃×#121	—	5	4	no	—
297	C₃×#121	—	5	2	no	—
298	C₃×#121	—	5	4	no	—
299	C₃×#120	—	5	2	no	—
300	C₃×#120	—	5	2	no	—
301	C₃×C₄×Q₈	—	5	2	no	—
302	C₃×C₄×Q₈	—	5	4	no	—
303	C₃×C₄×Q₈	C₂×D₅	1	2	yes	complemented
304	C₃×C₄×D₄	—	5	4	no	—
305	C₃×C₄×D₄	—	5	4	no	—
306	C₃×C₄×D₄	—	5	4	no	—
307	C₃×C₄×D₄	—	5	4	no	—
308	C₃×C₄×D₄	—	5	2	no	—
309	C₃×C₄×D₄	C₂×D₅	1	4	yes	—
310	C₃×C₄×D₄	C₂×D₅	1	2	yes	complemented
311	C₃×#117	—	5	1	no	—
312	C₃×#117	—	5	2	no	—
313	C₃×#117	—	5	2	no	—
314	C₃×#117	—	5	2	no	—
315	C₃×#117	—	5	2	no	—
316	C₃×#117	—	5	2	no	—
317	C₃×#117	C₂×D₅	1	1	yes	characteristic
318	C₃×#117	C₂×D₅	1	2	yes	complemented
319	C₂×C₃×C₄⋊C₄	—	5	2	no	—
320	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
321	C₂×C₃×C₄²	—	5	1	no	—
322	C₂×C₃×C₄²	—	5	2	no	—
323	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
324	C₂×C₃×C₄²	C₂×D₅	1	2	yes	complemented
325	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
326	C₅×#41	—	2	4	no	—
327	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
328	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
329	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
330	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
331	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
332	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
333	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
334	C₂×C₂²⋊D₅	C₂³×C₃	1	2	yes	—
335	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
336	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
337	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
338	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
339	#709	—	2	4	no	—
340	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
341	C₂×D₂₀	C₂³×C₃	1	4	yes	—
342	C₂×C₄×D₅	—	2	4	no	—
343	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
344	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
345	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
346	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
347	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
348	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
349	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
350	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
351	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
352	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
353	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
354	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
355	C₄²×C₅	C₂³×C₃	1	2	yes	—
356	C₄²×C₅	C₂³×C₃	1	2	yes	—
357	C₄²×C₅	C₂³×C₃	1	4	yes	—
358	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
359	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
360	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
361	#685	C₂³×C₃	1	2	yes	—
362	#685	C₂³×C₃	1	2	yes	—
363	#685	C₂³×C₃	1	2	yes	—
364	#685	C₂³×C₃	1	2	yes	—
365	#685	C₂³×C₃	1	4	yes	—
366	#685	C₂³×C₃	1	4	yes	—
367	#685	C₂³×C₃	1	4	yes	—
368	#685	C₂³×C₃	1	4	yes	—
369	#685	C₂³×C₃	1	4	yes	—
370	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
371	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
372	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
373	#683	C₂³×C₃	1	4	yes	—
374	#683	C₂³×C₃	1	4	yes	—
375	#683	C₂³×C₃	1	4	yes	—
376	#683	C₂³×C₃	1	2	yes	—
377	#683	C₂³×C₃	1	4	yes	—
378	#683	C₂³×C₃	1	4	yes	—
379	#683	C₂³×C₃	1	2	yes	—
380	#683	C₂³×C₃	1	2	yes	—
381	#683	C₂³×C₃	1	2	yes	—
382	C₄×Dic₅	C₂³×C₃	1	2	yes	—
383	C₄×Dic₅	C₂³×C₃	1	2	yes	—
384	C₄×Dic₅	C₂³×C₃	1	4	yes	—
385	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
386	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
387	#542	—	5	2	no	—
388	#542	—	5	2	no	—
389	#541	—	5	2	no	—
390	#540	—	5	2	no	—
391	#539	—	5	4	no	—
392	#538	—	5	4	no	—
393	#533	—	5	1	no	—
394	#532	—	5	1	no	—
395	#529	—	5	4	no	—
396	#529	—	5	4	no	—
397	#525	—	5	1	no	—
398	#525	—	5	1	no	—
399	C₄×#41	—	5	1	no	—
400	C₄×#41	C₃×D₅	1	1	yes	characteristic, complemented
401	C₂×#117	—	5	1	no	—
402	C₂²×C₃×C₅	—	2	2	no	—
403	C₂²×C₃×C₅	—	2	2	no	—
404	C₂²×C₃×C₅	—	2	4	no	—
405	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
406	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
407	C₂×C₃×D₅	—	2	2	no	—
408	C₂×C₃×D₅	—	2	2	no	—
409	C₂×C₃×D₅	—	2	4	no	—
410	C₂×C₃×D₅	—	2	2	no	—
411	C₂×C₃×D₅	—	2	2	no	—
412	C₂×C₃×D₅	—	4	4	no	—
413	C₃×C₄×C₅	—	2	2	no	—
414	C₃×C₄×C₅	—	2	4	no	—
415	C₃×C₄×C₅	—	2	2	no	—
416	C₃×C₄×C₅	—	2	2	no	—
417	C₃×C₄×C₅	C₂×#41	1	2	yes	—
418	C₃×C₄×C₅	C₂×#41	1	2	yes	—
419	C₃×Dic₅	—	2	2	no	—
420	C₃×Dic₅	—	2	2	no	—
421	C₃×Dic₅	—	2	2	no	—
422	C₃×Dic₅	—	2	4	no	—
423	C₃×Dic₅	—	2	2	no	—
424	C₂⁴×C₃	—	5	1	no	—
425	C₃×#41	—	2	4	no	—
426	C₃×#41	—	10	4	no	—
427	C₂×C₃×Q₈	—	5	1	no	—
428	C₂×C₃×Q₈	—	5	4	no	—
429	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
430	C₂×C₃×D₄	—	5	2	no	—
431	C₂×C₃×D₄	—	5	4	no	—
432	C₂×C₃×D₄	—	5	4	no	—
433	C₂×C₃×D₄	—	5	1	no	—
434	C₂×C₃×D₄	—	5	4	no	—
435	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
436	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
437	C₂²×C₃×C₄	—	5	1	no	—
438	C₂²×C₃×C₄	—	5	2	no	—
439	C₂²×C₃×C₄	—	5	2	no	—
440	C₂²×C₃×C₄	—	5	2	no	—
441	C₂²×C₃×C₄	—	5	2	no	—
442	C₂²×C₃×C₄	—	5	4	no	—
443	C₂²×C₃×C₄	—	10	4	no	—
444	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
445	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
446	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
447	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
448	C₃×C₄⋊C₄	—	5	2	no	—
449	C₃×C₄⋊C₄	—	5	2	no	—
450	C₃×C₄⋊C₄	—	5	2	no	—
451	C₃×C₄⋊C₄	—	5	2	no	—
452	C₃×C₄⋊C₄	—	5	4	no	—
453	C₃×C₄⋊C₄	—	5	4	no	—
454	C₃×C₄⋊C₄	—	5	4	no	—
455	C₃×C₄⋊C₄	—	5	4	no	—
456	C₃×C₄⋊C₄	—	5	4	no	—
457	C₃×C₄⋊C₄	—	5	2	no	—
458	C₃×C₄⋊C₄	—	5	4	no	—
459	C₃×C₄⋊C₄	—	5	4	no	—
460	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
461	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
462	C₃×C₂²⋊C₄	—	5	2	no	—
463	C₃×C₂²⋊C₄	—	5	4	no	—
464	C₃×C₂²⋊C₄	—	5	4	no	—
465	C₃×C₂²⋊C₄	—	5	2	no	—
466	C₃×C₂²⋊C₄	—	5	2	no	—
467	C₃×C₂²⋊C₄	—	5	2	no	—
468	C₃×C₂²⋊C₄	—	5	2	no	—
469	C₃×C₂²⋊C₄	—	5	4	no	—
470	C₃×C₂²⋊C₄	—	5	4	no	—
471	C₃×C₂²⋊C₄	—	5	4	no	—
472	C₃×C₂²⋊C₄	—	5	4	no	—
473	C₃×C₂²⋊C₄	—	5	4	no	—
474	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
475	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
476	C₃×C₄²	—	5	1	no	—
477	C₃×C₄²	—	5	1	no	—
478	C₃×C₄²	—	5	4	no	—
479	C₃×C₄²	—	5	2	no	—
480	C₃×C₄²	—	5	2	no	—
481	C₃×C₄²	C₂²×D₅	1	2	yes	—
482	C₃×C₄²	C₂²×D₅	1	4	yes	—
483	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
484	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
485	C₃×C₄²	C₂²×D₅	1	2	yes	—
486	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
487	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
488	C₂²×D₅	—	2	2	no	—
489	C₂²×D₅	—	4	2	no	—
490	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
491	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
492	C₅×Q₈	—	2	2	no	—
493	C₅×D₄	—	2	4	no	—
494	C₅×D₄	—	2	2	no	—
495	C₂×C₄×C₅	—	2	4	no	—
496	C₂×C₄×C₅	—	4	4	no	—
497	C₂×C₄×C₅	—	4	2	no	—
498	C₂×C₄×C₅	C₃×#41	1	4	yes	—
499	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
500	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
501	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
502	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
503	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
504	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
505	C₂²⋊D₅	—	2	4	no	—
506	C₂²⋊D₅	—	4	4	no	—
507	C₂²⋊D₅	—	4	4	no	—
508	C₂×Dic₅	—	2	2	no	—
509	C₂×Dic₅	—	4	2	no	—
510	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
511	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
512	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
513	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
514	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
515	D₂₀	—	2	2	no	—
516	D₂₀	—	4	4	no	—
517	C₄×D₅	—	2	4	no	—
518	C₄×D₅	—	2	4	no	—
519	C₄×D₅	—	2	4	no	—
520	C₄×D₅	—	4	4	no	—
521	Dic₁₀	—	2	2	no	—
522	Dic₁₀	—	4	4	no	—
523	C₂×#41	—	5	1	no	—
524	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
525	C₂³×C₄	—	5	1	no	—
526	C₄⋊Q₈	—	5	1	no	—
527	C₄⋊Q₈	—	5	2	no	—
528	#127	—	5	1	no	—
529	#126	—	5	4	no	—
530	#126	—	5	4	no	—
531	#126	—	5	4	no	—
532	#126	—	5	4	no	—
533	#125	—	5	4	no	—
534	#125	—	5	2	no	—
535	#125	—	5	4	no	—
536	#124	—	5	1	no	—
537	#124	—	5	1	no	—
538	#124	—	5	4	no	—
539	#124	—	5	4	no	—
540	#123	—	5	2	no	—
541	#123	—	5	4	no	—
542	#123	—	5	4	no	—
543	#123	—	5	4	no	—
544	#123	—	5	2	no	—
545	#123	—	5	4	no	—
546	C₂²⋊Q₈	—	5	2	no	—
547	C₂²⋊Q₈	—	5	4	no	—
548	C₂²⋊Q₈	—	5	2	no	—
549	C₂²⋊Q₈	—	5	4	no	—
550	C₂²⋊Q₈	—	5	4	no	—
551	#121	—	5	2	no	—
552	#121	—	5	4	no	—
553	#121	—	5	4	no	—
554	#121	—	5	2	no	—
555	#121	—	5	4	no	—
556	#120	—	5	2	no	—
557	#120	—	5	2	no	—
558	C₄×Q₈	—	5	2	no	—
559	C₄×Q₈	—	5	4	no	—
560	C₄×Q₈	C₂×C₃×D₅	1	2	yes	complemented
561	C₄×D₄	—	5	4	no	—
562	C₄×D₄	—	5	4	no	—
563	C₄×D₄	—	5	4	no	—
564	C₄×D₄	—	5	2	no	—
565	C₄×D₄	—	5	4	no	—
566	C₄×D₄	C₂×C₃×D₅	1	4	yes	—
567	C₄×D₄	C₂×C₃×D₅	1	2	yes	complemented
568	#117	—	5	1	no	—
569	#117	—	5	2	no	—
570	#117	—	5	2	no	—
571	#117	—	5	2	no	—
572	#117	—	5	2	no	—
573	#117	—	5	2	no	—
574	#117	C₂×C₃×D₅	1	1	yes	characteristic
575	#117	C₂×C₃×D₅	1	2	yes	complemented
576	C₂×C₄⋊C₄	—	5	2	no	—
577	C₂×C₂²⋊C₄	—	5	2	no	—
578	C₂×C₄²	—	5	1	no	—
579	C₂×C₄²	—	5	2	no	—
580	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
581	C₂×C₄²	C₂×C₃×D₅	1	2	yes	complemented
582	C₂×C₃×C₅	—	2	2	no	—
583	C₂×C₃×C₅	—	4	2	no	—
584	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
585	C₂×C₃×C₅	#585	1	2	yes	—
586	C₃×D₅	—	4	2	no	—
587	C₃×D₅	—	4	2	no	—
588	C₂³×C₃	—	5	2	no	—
589	C₂³×C₃	—	5	2	no	—
590	C₂³×C₃	—	10	2	no	—
591	C₂³×C₃	—	20	2	no	—
592	C₂³×C₃	C₂³×D₅	1	2	yes	—
593	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
594	C₃×Q₈	—	2	2	no	—
595	C₃×Q₈	—	10	2	no	—
596	C₃×Q₈	—	20	4	no	—
597	C₃×D₄	—	2	4	no	—
598	C₃×D₄	—	2	2	no	—
599	C₃×D₄	—	10	4	no	—
600	C₃×D₄	—	10	2	no	—
601	C₃×D₄	—	20	4	no	—
602	C₃×D₄	—	20	4	no	—
603	C₃×D₄	—	20	4	no	—
604	C₂×C₃×C₄	—	2	4	no	—
605	C₂×C₃×C₄	—	4	2	no	—
606	C₂×C₃×C₄	—	4	4	no	—
607	C₂×C₃×C₄	—	5	2	no	—
608	C₂×C₃×C₄	—	5	2	no	—
609	C₂×C₃×C₄	—	5	4	no	—
610	C₂×C₃×C₄	—	5	2	no	—
611	C₂×C₃×C₄	—	5	2	no	—
612	C₂×C₃×C₄	—	10	2	no	—
613	C₂×C₃×C₄	—	10	4	no	—
614	C₂×C₃×C₄	—	10	4	no	—
615	C₂×C₃×C₄	—	10	4	no	—
616	C₂×C₃×C₄	—	20	4	no	—
617	C₂×C₃×C₄	—	20	2	no	—
618	C₂×C₃×C₄	#709	1	4	yes	—
619	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
620	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
621	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
622	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
623	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
624	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
625	C₂²×C₅	—	2	2	no	—
626	C₂²×C₅	—	2	2	no	—
627	C₂²×C₅	—	2	4	no	—
628	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
629	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
630	C₂×D₅	—	2	2	no	—
631	C₂×D₅	—	2	2	no	—
632	C₂×D₅	—	2	4	no	—
633	C₂×D₅	—	2	2	no	—
634	C₂×D₅	—	2	2	no	—
635	C₂×D₅	—	4	4	no	—
636	C₄×C₅	—	2	2	no	—
637	C₄×C₅	—	2	4	no	—
638	C₄×C₅	—	2	2	no	—
639	C₄×C₅	—	2	2	no	—
640	C₄×C₅	C₂×C₃×#41	1	2	yes	—
641	C₄×C₅	C₂×C₃×#41	1	2	yes	—
642	Dic₅	—	2	2	no	—
643	Dic₅	—	2	2	no	—
644	Dic₅	—	2	2	no	—
645	Dic₅	—	2	4	no	—
646	Dic₅	—	2	2	no	—
647	C₂⁴	—	5	1	no	—
648	#41	—	2	4	no	—
649	#41	—	10	4	no	—
650	C₂×Q₈	—	5	1	no	—
651	C₂×Q₈	—	5	4	no	—
652	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
653	C₂×D₄	—	5	2	no	—
654	C₂×D₄	—	5	4	no	—
655	C₂×D₄	—	5	4	no	—
656	C₂×D₄	—	5	1	no	—
657	C₂×D₄	—	5	4	no	—
658	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
659	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
660	C₂²×C₄	—	5	1	no	—
661	C₂²×C₄	—	5	2	no	—
662	C₂²×C₄	—	5	2	no	—
663	C₂²×C₄	—	5	2	no	—
664	C₂²×C₄	—	5	2	no	—
665	C₂²×C₄	—	5	4	no	—
666	C₂²×C₄	—	10	4	no	—
667	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
668	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
669	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
670	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
671	C₄⋊C₄	—	5	2	no	—
672	C₄⋊C₄	—	5	2	no	—
673	C₄⋊C₄	—	5	2	no	—
674	C₄⋊C₄	—	5	2	no	—
675	C₄⋊C₄	—	5	2	no	—
676	C₄⋊C₄	—	5	4	no	—
677	C₄⋊C₄	—	5	4	no	—
678	C₄⋊C₄	—	5	4	no	—
679	C₄⋊C₄	—	5	4	no	—
680	C₄⋊C₄	—	5	4	no	—
681	C₄⋊C₄	—	5	4	no	—
682	C₄⋊C₄	—	5	4	no	—
683	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
684	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
685	C₂²⋊C₄	—	5	2	no	—
686	C₂²⋊C₄	—	5	4	no	—
687	C₂²⋊C₄	—	5	4	no	—
688	C₂²⋊C₄	—	5	2	no	—
689	C₂²⋊C₄	—	5	2	no	—
690	C₂²⋊C₄	—	5	2	no	—
691	C₂²⋊C₄	—	5	2	no	—
692	C₂²⋊C₄	—	5	4	no	—
693	C₂²⋊C₄	—	5	4	no	—
694	C₂²⋊C₄	—	5	4	no	—
695	C₂²⋊C₄	—	5	4	no	—
696	C₂²⋊C₄	—	5	4	no	—
697	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
698	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
699	C₄²	—	5	2	no	—
700	C₄²	—	5	2	no	—
701	C₄²	—	5	1	no	—
702	C₄²	—	5	1	no	—
703	C₄²	—	5	4	no	—
704	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
705	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
706	C₄²	C₂²×C₃×D₅	1	2	yes	—
707	C₄²	C₂²×C₃×D₅	1	2	yes	—
708	C₄²	C₂²×C₃×D₅	1	4	yes	—
709	C₃×C₅	#3455	1	1	yes	characteristic, complemented, Hall
710	C₂²×C₃	—	2	2	no	—
711	C₂²×C₃	—	2	2	no	—
712	C₂²×C₃	—	2	4	no	—
713	C₂²×C₃	—	10	2	no	—
714	C₂²×C₃	—	10	2	no	—
715	C₂²×C₃	—	10	4	no	—
716	C₂²×C₃	—	10	2	no	—
717	C₂²×C₃	—	10	2	no	—
718	C₂²×C₃	—	20	4	no	—
719	C₂²×C₃	C₂×#709	1	2	yes	—
720	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
721	C₃×C₄	—	2	2	no	—
722	C₃×C₄	—	2	2	no	—
723	C₃×C₄	—	2	2	no	—
724	C₃×C₄	—	2	4	no	—
725	C₃×C₄	—	10	2	no	—
726	C₃×C₄	—	10	2	no	—
727	C₃×C₄	—	10	2	no	—
728	C₃×C₄	—	10	4	no	—
729	C₃×C₄	—	10	2	no	—
730	C₃×C₄	C₂×#709	1	2	yes	—
731	C₃×C₄	C₂×#709	1	2	yes	—
732	C₂×C₅	—	2	2	no	—
733	C₂×C₅	—	4	2	no	—
734	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
735	C₂×C₅	C₃×#585	1	2	yes	—
736	D₅	—	4	2	no	—
737	D₅	—	4	2	no	—
738	C₂³	—	5	2	no	—
739	C₂³	—	5	2	no	—
740	C₂³	—	10	2	no	—
741	C₂³	—	20	2	no	—
742	C₂³	C₂³×C₃×D₅	1	2	yes	—
743	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
744	Q₈	—	2	2	no	—
745	Q₈	—	10	2	no	—
746	Q₈	—	20	4	no	—
747	D₄	—	2	4	no	—
748	D₄	—	2	2	no	—
749	D₄	—	10	4	no	—
750	D₄	—	10	2	no	—
751	D₄	—	20	4	no	—
752	D₄	—	20	4	no	—
753	D₄	—	20	4	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	4	no	—
757	C₂×C₄	—	5	2	no	—
758	C₂×C₄	—	5	2	no	—
759	C₂×C₄	—	5	4	no	—
760	C₂×C₄	—	5	2	no	—
761	C₂×C₄	—	5	2	no	—
762	C₂×C₄	—	10	2	no	—
763	C₂×C₄	—	10	4	no	—
764	C₂×C₄	—	10	4	no	—
765	C₂×C₄	—	10	4	no	—
766	C₂×C₄	—	20	4	no	—
767	C₂×C₄	—	20	2	no	—
768	C₂×C₄	C₃×#709	1	4	yes	—
769	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
770	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
771	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
772	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
773	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
774	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
775	C₂×C₃	—	2	2	no	—
776	C₂×C₃	—	4	2	no	—
777	C₂×C₃	—	20	2	no	—
778	C₂×C₃	—	20	2	no	—
779	C₂×C₃	C₂²×#709	1	1	yes	characteristic
780	C₂×C₃	#66283	1	2	yes	—
781	C₅	C₃×#3455	1	1	yes	characteristic, complemented, Sylow
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	4	no	—
785	C₂²	—	10	2	no	—
786	C₂²	—	10	2	no	—
787	C₂²	—	10	4	no	—
788	C₂²	—	10	2	no	—
789	C₂²	—	10	2	no	—
790	C₂²	—	20	4	no	—
791	C₂²	C₂×C₃×#709	1	2	yes	—
792	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
793	C₄	—	2	2	no	—
794	C₄	—	2	2	no	—
795	C₄	—	2	2	no	—
796	C₄	—	2	4	no	—
797	C₄	—	10	2	no	—
798	C₄	—	10	2	no	—
799	C₄	—	10	2	no	—
800	C₄	—	10	4	no	—
801	C₄	—	10	2	no	—
802	C₄	C₂×C₃×#709	1	2	yes	—
803	C₄	C₂×C₃×#709	1	2	yes	—
804	C₃	#10617738	1	1	yes	characteristic, direct product factor, Sylow
805	C₂	—	2	2	no	—
806	C₂	—	4	2	no	—
807	C₂	—	20	2	no	—
808	C₂	—	20	2	no	—
809	C₂	C₂²×C₃×#709	1	1	yes	characteristic
810	C₂	C₃×#66283	1	2	yes	—

	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×#3455
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×#66166	C₂	semidirect
3. C₃×#66162	C₂	semidirect
4. C₃×#65917	C₂	semidirect
5. C₃×#65916	C₂	semidirect
6. C₃×#65898	C₂	semidirect
7. C₃×#65896	C₂	semidirect
8. C₃×#65895	C₂	semidirect
9. C₃×#65894	C₂	semidirect
10. C₃×#65862	C₂	semidirect
11. C₃×#65858	C₂	semidirect
12. C₃×#65851	C₂	semidirect
13. C₃×#65813	C₂	semidirect
14. C₃×C₄×#709	C₂	semidirect
15. C₂×C₃×#4018	C₂	semidirect
16. #10617738	C₃	direct (N × H)
20. C₃×C₄×C₅×Q₈	C₂²	semidirect
22. C₃×C₄×C₅×D₄	C₂²	semidirect
24. C₃×C₅×#117	C₂²	semidirect
26. C₂×C₃×C₄²×C₅	C₂²	semidirect
27. C₃×#4093	C₂²	semidirect
29. C₃×#4090	C₂²	semidirect
30. C₃×#4086	C₂²	semidirect
34. C₃×#4082	C₂²	semidirect
38. C₃×#4075	C₂²	semidirect
41. C₃×C₄×C₂²⋊D₅	C₂²	semidirect
44. C₃×#4070	C₂²	semidirect
49. C₃×#4042	C₂²	semidirect
52. C₃×#4036	C₂²	semidirect
53. C₃×#4035	C₂²	semidirect
54. C₃×#4034	C₂²	semidirect
58. C₃×#4029	C₂²	semidirect
60. C₃×#4025	C₂²	semidirect
63. C₃×#4022	C₂²	semidirect
66. C₃×C₄×D₂₀	C₂²	semidirect
71. C₃×#4018	C₂²	semidirect
72. C₃×C₄²×D₅	C₂²	semidirect
73. C₃×#4016	C₂²	semidirect
74. C₃×C₄×Dic₁₀	C₂²	semidirect
75. C₃×C₄×Dic₁₀	C₂²	semidirect
77. C₄×C₅×#41	C₂×C₃	semidirect
78. #66166	C₂×C₃	semidirect
79. #66162	C₂×C₃	semidirect
80. #65917	C₂×C₃	semidirect
81. #65916	C₂×C₃	semidirect
82. #65898	C₂×C₃	semidirect
83. #65896	C₂×C₃	semidirect
84. #65895	C₂×C₃	semidirect
85. #65894	C₂×C₃	semidirect
86. #65862	C₂×C₃	semidirect
87. #65858	C₂×C₃	semidirect
88. #65851	C₂×C₃	semidirect
89. #65813	C₂×C₃	semidirect
90. C₄×#709	C₂×C₃	semidirect
91. C₂×#4018	C₂×C₃	semidirect
167. C₃×C₄×#41	D₅	semidirect
172. C₄×C₅×Q₈	C₂²×C₃	semidirect
174. C₄×C₅×D₄	C₂²×C₃	semidirect
176. C₅×#117	C₂²×C₃	semidirect
178. C₂×C₄²×C₅	C₂²×C₃	semidirect
179. #4093	C₂²×C₃	semidirect
181. #4090	C₂²×C₃	semidirect
182. #4086	C₂²×C₃	semidirect
186. #4082	C₂²×C₃	semidirect
190. #4075	C₂²×C₃	semidirect
193. C₄×C₂²⋊D₅	C₂²×C₃	semidirect
196. #4070	C₂²×C₃	semidirect
201. #4042	C₂²×C₃	semidirect
204. #4036	C₂²×C₃	semidirect
205. #4035	C₂²×C₃	semidirect
206. #4034	C₂²×C₃	semidirect
210. #4029	C₂²×C₃	semidirect
212. #4025	C₂²×C₃	semidirect
215. #4022	C₂²×C₃	semidirect
218. C₄×D₂₀	C₂²×C₃	semidirect
223. #4018	C₂²×C₃	semidirect
224. C₄²×D₅	C₂²×C₃	semidirect
225. #4016	C₂²×C₃	semidirect
226. C₄×Dic₁₀	C₂²×C₃	semidirect
227. C₄×Dic₁₀	C₂²×C₃	semidirect
303. C₃×C₄×Q₈	C₂×D₅	semidirect
310. C₃×C₄×D₄	C₂×D₅	semidirect
318. C₃×#117	C₂×D₅	semidirect
324. C₂×C₃×C₄²	C₂×D₅	semidirect
400. C₄×#41	C₃×D₅	semidirect
560. C₄×Q₈	C₂×C₃×D₅	semidirect
567. C₄×D₄	C₂×C₃×D₅	semidirect
575. #117	C₂×C₃×D₅	semidirect
581. C₂×C₄²	C₂×C₃×D₅	semidirect
709. C₃×C₅	#3455	semidirect
781. C₅	C₃×#3455	semidirect
804. C₃	#10617738	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×#66166	2
C₃×#66162	2
C₃×#65917	2
C₃×#65916	2
C₃×#65898	2
C₃×#65896	2
C₃×#65895	2
C₃×#65894	2
C₃×#65862	2
C₃×#65858	2
C₃×#65851	2
C₃×#65813	2
C₃×C₄×#709	2
C₂×C₃×#4018	2
#10617738	3
C₃×#3455	5

Subgroups — C3×#10617738 #14481503

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617738 #14481503