Subgroups — C₃×#10610717 #14425201

Order 1920.

1448 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66283	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66156	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66082	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65811	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×C₅×#104	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65421	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#3937	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65116	C₂	1	2	yes	maximal, complemented
9	C₃×#65115	C₂	1	2	yes	maximal, complemented
10	C₃×#65114	C₂	1	2	yes	maximal, complemented
11	C₃×#65111	C₂	1	2	yes	maximal, complemented
12	#10610717	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₃×#4150	—	2	1	no	—
15	C₃×#4150	C₂²	1	2	yes	—
16	C₃×#4149	—	2	1	no	—
17	C₃×#4149	C₂²	1	2	yes	—
18	C₃×D₅×#41	—	2	2	no	—
19	C₃×D₅×#41	—	2	2	no	—
20	C₃×#4147	—	2	1	no	—
21	C₃×#4144	—	2	1	no	—
22	C₃×#4144	—	2	2	no	—
23	C₂×C₃×#709	—	2	2	no	—
24	C₂×C₃×#709	C₂²	1	1	yes	characteristic
25	C₂×C₃×#709	C₂²	1	1	yes	characteristic
26	C₂×C₃×#709	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
29	C₃×#4097	C₂²	1	2	yes	complemented
30	C₃×#4096	—	2	2	no	—
31	C₃×#4095	C₂²	1	2	yes	complemented
32	C₃×#4088	—	2	1	no	—
33	C₃×#4078	—	2	1	no	—
34	C₃×#4076	—	2	2	no	—
35	C₂×C₃×#681	C₂²	1	1	yes	characteristic, complemented
36	C₃×#4055	—	2	1	no	—
37	C₃×#4055	C₂²	1	2	yes	complemented
38	C₃×#4054	—	2	1	no	—
39	C₃×#4054	C₂²	1	2	yes	complemented
40	C₃×#4050	—	2	2	no	—
41	C₃×#4021	C₂²	1	1	yes	characteristic, complemented
42	C₃×#4021	C₂²	1	1	yes	characteristic, complemented
43	C₃×#4020	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₄×D₂₀	—	2	2	no	—
45	C₃×#4015	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₅×#104	C₂²	1	2	yes	complemented
47	C₃×C₅×#104	C₂²	1	2	yes	complemented
48	C₃×#3956	C₂²	1	2	yes	complemented
49	C₃×#3955	C₂²	1	2	yes	complemented
50	C₃×#3937	C₂²	1	2	yes	complemented
51	C₃×#3937	C₂²	1	2	yes	complemented
52	C₃×#3018	—	5	1	no	maximal, Hall
53	#66283	C₂×C₃	1	1	yes	characteristic, complemented
54	#66156	C₂×C₃	1	1	yes	characteristic, complemented
55	#66082	C₂×C₃	1	1	yes	characteristic, complemented
56	#65811	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂×C₅×#104	C₂×C₃	1	1	yes	characteristic, complemented
58	#65421	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×#3937	C₂×C₃	1	1	yes	characteristic, complemented
60	#65116	C₂×C₃	1	2	yes	complemented
61	#65115	C₂×C₃	1	2	yes	complemented
62	#65114	C₂×C₃	1	2	yes	complemented
63	#65111	C₂×C₃	1	2	yes	complemented
64	C₃×C₅×#41	—	2	1	no	—
65	C₃×C₅×#41	—	2	1	no	—
66	C₃×C₅×#41	D₄	1	2	yes	complemented
67	C₃×C₅×#41	C₂³	1	2	yes	—
68	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic, complemented
69	C₂×C₃×C₅×D₄	—	2	1	no	—
70	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic, complemented
71	C₂²×C₃×C₄×C₅	—	2	1	no	—
72	C₂²×C₃×C₄×C₅	—	2	1	no	—
73	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
75	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
76	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
77	C₂×C₃×C₂²⋊D₅	D₄	1	2	yes	—
78	C₃×#713	—	2	2	no	—
79	C₃×#713	—	2	2	no	—
80	C₃×Q₈×D₅	—	2	2	no	—
81	C₃×Q₈×D₅	—	2	2	no	—
82	C₃×#711	—	2	4	no	—
83	C₃×#711	—	2	2	no	—
84	C₃×#711	—	2	2	no	—
85	C₃×#711	—	2	4	no	—
86	C₃×D₄×D₅	—	2	4	no	—
87	C₃×D₄×D₅	—	2	2	no	—
88	C₃×D₄×D₅	—	2	4	no	—
89	C₃×D₄×D₅	—	2	2	no	—
90	C₃×#709	—	2	4	no	—
91	C₃×#709	—	2	4	no	—
92	C₃×#709	—	2	1	no	—
93	C₃×#709	—	2	1	no	—
94	C₃×#709	—	2	1	no	—
95	C₃×#709	—	2	1	no	—
96	C₃×#709	—	2	1	no	—
97	C₃×#709	—	2	1	no	—
98	C₃×#709	—	2	2	no	—
99	C₃×#709	—	2	1	no	—
100	C₃×#709	—	2	1	no	—
101	C₃×#709	—	2	1	no	—
102	C₃×#709	—	2	1	no	—
103	C₃×#709	—	2	2	no	—
104	C₃×#709	D₄	1	2	yes	complemented
105	C₃×#709	C₂³	1	2	yes	—
106	C₂×C₃×D₂₀	—	2	2	no	—
107	C₂×C₃×D₂₀	—	2	2	no	—
108	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic, complemented
109	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
110	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
111	C₂×C₃×C₄×D₅	—	2	4	no	—
112	C₂×C₃×C₄×D₅	—	2	1	no	—
113	C₂×C₃×C₄×D₅	—	2	1	no	—
114	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
115	C₂×C₃×Dic₁₀	—	2	2	no	—
116	C₂×C₃×Dic₁₀	D₄	1	1	yes	characteristic, complemented
117	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
118	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
119	C₃×C₅×M₁₆	—	2	1	no	—
120	C₃×C₅×M₁₆	C₂³	1	2	yes	—
121	C₂×C₃×C₅×C₈	—	2	1	no	—
122	C₃×C₄²×C₅	—	2	1	no	—
123	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
124	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
125	C₃×#689	—	2	2	no	—
126	C₃×#688	—	2	2	no	—
127	C₃×#687	—	2	2	no	—
128	C₃×#686	—	2	2	no	—
129	C₃×#685	—	2	2	no	—
130	C₃×#685	—	2	2	no	—
131	C₃×C₄⋊Dic₅	—	2	2	no	—
132	C₃×#681	—	2	1	no	—
133	C₃×#681	C₂³	1	2	yes	—
134	C₂×C₃×#168	—	2	1	no	—
135	C₃×Dic₂₀	—	2	2	no	—
136	C₃×D₄₀	—	2	2	no	—
137	C₃×#677	—	2	2	no	—
138	C₃×#677	—	2	2	no	—
139	C₃×#585	—	5	1	no	—
140	C₃×#575	—	5	1	no	—
141	C₃×#575	—	5	1	no	—
142	C₃×#532	—	5	1	no	—
143	C₃×#456	—	5	2	no	—
144	C₃×#455	—	5	2	no	—
145	C₃×#454	—	5	2	no	—
146	C₃×#453	—	5	2	no	—
147	C₂×C₃×#104	—	5	1	no	—
148	C₂×C₃×#104	D₅	1	1	yes	characteristic, complemented
149	C₃×#413	—	5	1	no	—
150	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
151	#4150	—	2	1	no	—
152	#4150	C₂²×C₃	1	2	yes	—
153	#4149	—	2	1	no	—
154	#4149	C₂²×C₃	1	2	yes	—
155	D₅×#41	—	2	2	no	—
156	D₅×#41	—	2	2	no	—
157	#4147	—	2	1	no	—
158	#4144	—	2	1	no	—
159	#4144	—	2	2	no	—
160	C₂×#709	—	2	2	no	—
161	C₂×#709	C₂²×C₃	1	1	yes	characteristic
162	C₂×#709	C₂²×C₃	1	1	yes	characteristic
163	C₂×#709	C₂²×C₃	1	1	yes	characteristic, complemented
164	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
165	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
166	#4097	C₂²×C₃	1	2	yes	complemented
167	#4096	—	2	2	no	—
168	#4095	C₂²×C₃	1	2	yes	complemented
169	#4088	—	2	1	no	—
170	#4078	—	2	1	no	—
171	#4076	—	2	2	no	—
172	C₂×#681	C₂²×C₃	1	1	yes	characteristic, complemented
173	#4055	—	2	1	no	—
174	#4055	C₂²×C₃	1	2	yes	complemented
175	#4054	—	2	1	no	—
176	#4054	C₂²×C₃	1	2	yes	complemented
177	#4050	—	2	2	no	—
178	#4021	C₂²×C₃	1	1	yes	characteristic, complemented
179	#4021	C₂²×C₃	1	1	yes	characteristic, complemented
180	#4020	C₂²×C₃	1	1	yes	characteristic, complemented
181	C₄×D₂₀	—	2	2	no	—
182	#4015	C₂²×C₃	1	1	yes	characteristic, complemented
183	C₅×#104	C₂²×C₃	1	2	yes	complemented
184	C₅×#104	C₂²×C₃	1	2	yes	complemented
185	#3956	C₂²×C₃	1	2	yes	complemented
186	#3955	C₂²×C₃	1	2	yes	complemented
187	#3937	C₂²×C₃	1	2	yes	complemented
188	#3937	C₂²×C₃	1	2	yes	complemented
189	#3018	—	5	1	no	Sylow
190	C₂³×C₃×C₅	—	2	1	no	—
191	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
192	C₂²×C₃×D₅	—	2	4	no	—
193	C₂²×C₃×D₅	—	2	1	no	—
194	C₂²×C₃×D₅	—	2	1	no	—
195	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
196	C₃×C₅×Q₈	—	2	1	no	—
197	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
198	C₃×C₅×D₄	—	2	2	no	—
199	C₃×C₅×D₄	—	2	2	no	—
200	C₃×C₅×D₄	—	2	1	no	—
201	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
202	C₂×C₃×C₄×C₅	—	2	1	no	—
203	C₂×C₃×C₄×C₅	—	2	1	no	—
204	C₂×C₃×C₄×C₅	—	2	2	no	—
205	C₂×C₃×C₄×C₅	—	2	2	no	—
206	C₂×C₃×C₄×C₅	—	2	1	no	—
207	C₂×C₃×C₄×C₅	—	4	2	no	—
208	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
209	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
210	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
211	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
212	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
213	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
214	C₃×C₂²⋊D₅	—	2	4	no	—
215	C₃×C₂²⋊D₅	—	2	4	no	—
216	C₃×C₂²⋊D₅	—	2	2	no	—
217	C₃×C₂²⋊D₅	—	2	2	no	—
218	C₃×C₂²⋊D₅	—	2	2	no	—
219	C₃×C₂²⋊D₅	—	2	2	no	—
220	C₃×C₂²⋊D₅	—	4	1	no	—
221	C₃×C₂²⋊D₅	—	4	1	no	—
222	C₂×C₃×Dic₅	—	2	4	no	—
223	C₂×C₃×Dic₅	—	2	1	no	—
224	C₂×C₃×Dic₅	—	2	1	no	—
225	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
226	C₃×D₂₀	—	2	4	no	—
227	C₃×D₂₀	—	2	1	no	—
228	C₃×D₂₀	—	2	1	no	—
229	C₃×D₂₀	—	2	1	no	—
230	C₃×D₂₀	—	2	1	no	—
231	C₃×D₂₀	—	2	1	no	—
232	C₃×D₂₀	—	4	4	no	—
233	C₃×D₂₀	C₂×D₄	1	2	yes	—
234	C₃×C₄×D₅	—	2	4	no	—
235	C₃×C₄×D₅	—	2	4	no	—
236	C₃×C₄×D₅	—	2	2	no	—
237	C₃×C₄×D₅	—	2	2	no	—
238	C₃×C₄×D₅	—	2	2	no	—
239	C₃×C₄×D₅	—	2	2	no	—
240	C₃×C₄×D₅	—	4	1	no	—
241	C₃×C₄×D₅	—	4	1	no	—
242	C₃×Dic₁₀	—	2	4	no	—
243	C₃×Dic₁₀	—	2	1	no	—
244	C₃×Dic₁₀	—	2	1	no	—
245	C₃×Dic₁₀	—	2	1	no	—
246	C₃×Dic₁₀	—	2	1	no	—
247	C₃×Dic₁₀	—	2	1	no	—
248	C₃×Dic₁₀	C₂×D₄	1	2	yes	—
249	C₃×C₅×C₈	—	2	2	no	—
250	C₃×#168	—	2	2	no	—
251	C₃×2₋¹⁺⁴	—	5	2	no	—
252	C₃×2₋¹⁺⁴	—	10	1	no	—
253	C₃×2₋¹⁺⁴	—	10	1	no	—
254	C₃×H(5,𝔽₂)	—	5	2	no	—
255	C₃×H(5,𝔽₂)	—	10	2	no	—
256	C₃×H(5,𝔽₂)	—	10	1	no	—
257	C₃×H(5,𝔽₂)	—	10	1	no	—
258	C₂×C₃×#41	—	5	1	no	—
259	C₂×C₃×#41	—	5	1	no	—
260	C₂×C₃×#41	—	5	1	no	—
261	C₂×C₃×#41	—	10	2	no	—
262	C₂×C₃×#41	—	10	2	no	—
263	C₂×C₃×#41	—	10	2	no	—
264	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
265	C₃×#137	—	5	2	no	—
266	C₃×#137	—	5	2	no	—
267	C₃×#137	—	10	1	no	—
268	C₃×#137	—	10	1	no	—
269	C₃×AGL(1,ℤ/8)	—	5	2	no	—
270	C₃×AGL(1,ℤ/8)	—	5	2	no	—
271	C₃×AGL(1,ℤ/8)	—	10	1	no	—
272	C₃×AGL(1,ℤ/8)	—	10	1	no	—
273	C₃×#135	—	10	2	no	—
274	C₃×#135	—	10	2	no	—
275	C₂×C₃×M₁₆	—	5	1	no	—
276	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic, complemented
277	C₃×C₄⋊Q₈	—	5	1	no	—
278	C₃×#127	—	5	1	no	—
279	C₃×#124	—	5	1	no	—
280	C₃×#124	—	5	1	no	—
281	C₃×#121	—	10	2	no	—
282	C₃×C₄×D₄	—	10	2	no	—
283	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic, complemented
284	C₃×#104	—	5	2	no	—
285	C₃×#104	—	5	2	no	—
286	C₃×#104	C₂×D₅	1	2	yes	complemented
287	C₃×#104	C₂×D₅	1	2	yes	complemented
288	C₃×#101	—	5	2	no	—
289	C₃×#100	—	5	2	no	—
290	C₅×#41	—	2	1	no	—
291	C₅×#41	—	2	1	no	—
292	C₅×#41	C₃×D₄	1	2	yes	complemented
293	C₅×#41	C₂³×C₃	1	2	yes	—
294	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic, complemented
295	C₂×C₅×D₄	—	2	1	no	—
296	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic, complemented
297	C₂²×C₄×C₅	—	2	1	no	—
298	C₂²×C₄×C₅	—	2	1	no	—
299	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
300	C₂×C₂²⋊D₅	—	2	4	no	—
301	C₂×C₂²⋊D₅	—	2	1	no	—
302	C₂×C₂²⋊D₅	—	2	1	no	—
303	C₂×C₂²⋊D₅	C₃×D₄	1	2	yes	—
304	#713	—	2	2	no	—
305	#713	—	2	2	no	—
306	Q₈×D₅	—	2	2	no	—
307	Q₈×D₅	—	2	2	no	—
308	#711	—	2	4	no	—
309	#711	—	2	2	no	—
310	#711	—	2	2	no	—
311	#711	—	2	4	no	—
312	D₄×D₅	—	2	4	no	—
313	D₄×D₅	—	2	2	no	—
314	D₄×D₅	—	2	4	no	—
315	D₄×D₅	—	2	2	no	—
316	#709	—	2	4	no	—
317	#709	—	2	4	no	—
318	#709	—	2	1	no	—
319	#709	—	2	1	no	—
320	#709	—	2	1	no	—
321	#709	—	2	1	no	—
322	#709	—	2	1	no	—
323	#709	—	2	1	no	—
324	#709	—	2	2	no	—
325	#709	—	2	1	no	—
326	#709	—	2	1	no	—
327	#709	—	2	1	no	—
328	#709	—	2	1	no	—
329	#709	—	2	2	no	—
330	#709	C₃×D₄	1	2	yes	complemented
331	#709	C₂³×C₃	1	2	yes	—
332	C₂×D₂₀	—	2	2	no	—
333	C₂×D₂₀	—	2	2	no	—
334	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic, complemented
335	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
336	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
337	C₂×C₄×D₅	—	2	4	no	—
338	C₂×C₄×D₅	—	2	1	no	—
339	C₂×C₄×D₅	—	2	1	no	—
340	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
341	C₂×Dic₁₀	—	2	2	no	—
342	C₂×Dic₁₀	C₃×D₄	1	1	yes	characteristic, complemented
343	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
344	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
345	C₅×M₁₆	—	2	1	no	—
346	C₅×M₁₆	C₂³×C₃	1	2	yes	—
347	C₂×C₅×C₈	—	2	1	no	—
348	C₄²×C₅	—	2	1	no	—
349	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
350	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
351	#689	—	2	2	no	—
352	#688	—	2	2	no	—
353	#687	—	2	2	no	—
354	#686	—	2	2	no	—
355	#685	—	2	2	no	—
356	#685	—	2	2	no	—
357	C₄⋊Dic₅	—	2	2	no	—
358	#681	—	2	1	no	—
359	#681	C₂³×C₃	1	2	yes	—
360	C₂×#168	—	2	1	no	—
361	Dic₂₀	—	2	2	no	—
362	D₄₀	—	2	2	no	—
363	#677	—	2	2	no	—
364	#677	—	2	2	no	—
365	#585	—	5	1	no	—
366	#575	—	5	1	no	—
367	#575	—	5	1	no	—
368	#532	—	5	1	no	—
369	#456	—	5	2	no	—
370	#455	—	5	2	no	—
371	#454	—	5	2	no	—
372	#453	—	5	2	no	—
373	C₂×#104	—	5	1	no	—
374	C₂×#104	C₃×D₅	1	1	yes	characteristic, complemented
375	#413	—	5	1	no	—
376	C₂²×C₃×C₅	—	2	2	no	—
377	C₂²×C₃×C₅	—	4	1	no	—
378	C₂²×C₃×C₅	—	8	1	no	—
379	C₂²×C₃×C₅	#120	1	1	yes	characteristic
380	C₂²×C₃×C₅	#120	1	1	yes	characteristic
381	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
382	C₂×C₃×D₅	—	2	2	no	—
383	C₂×C₃×D₅	—	2	2	no	—
384	C₂×C₃×D₅	—	4	2	no	—
385	C₂×C₃×D₅	—	4	2	no	—
386	C₂×C₃×D₅	—	4	1	no	—
387	C₂×C₃×D₅	—	8	1	no	—
388	C₂×C₃×D₅	—	8	4	no	—
389	C₃×C₄×C₅	—	2	2	no	—
390	C₃×C₄×C₅	—	2	2	no	—
391	C₃×C₄×C₅	—	4	1	no	—
392	C₃×C₄×C₅	#120	1	1	yes	characteristic
393	C₃×C₄×C₅	#120	1	1	yes	characteristic
394	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
395	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
396	C₃×Dic₅	—	2	2	no	—
397	C₃×Dic₅	—	2	2	no	—
398	C₃×Dic₅	—	4	1	no	—
399	C₃×#41	—	2	1	no	—
400	C₃×#41	—	2	1	no	—
401	C₃×#41	—	5	2	no	—
402	C₃×#41	—	5	2	no	—
403	C₃×#41	—	10	2	no	—
404	C₃×#41	—	10	2	no	—
405	C₃×#41	—	10	4	no	—
406	C₃×#41	—	10	4	no	—
407	C₃×#41	—	10	4	no	—
408	C₃×#41	—	10	4	no	—
409	C₃×#41	—	10	2	no	—
410	C₃×#41	—	10	2	no	—
411	C₃×#41	—	10	2	no	—
412	C₃×#41	—	10	2	no	—
413	C₃×#41	—	10	1	no	—
414	C₃×#41	—	10	1	no	—
415	C₃×#41	—	10	1	no	—
416	C₃×#41	—	10	1	no	—
417	C₃×#41	—	10	1	no	—
418	C₃×#41	—	10	1	no	—
419	C₃×#41	—	10	1	no	—
420	C₃×#41	—	10	1	no	—
421	C₃×#41	—	10	1	no	—
422	C₃×#41	—	10	1	no	—
423	C₃×#41	D₂₀	1	2	yes	complemented
424	C₃×#41	C₂²×D₅	1	2	yes	—
425	C₂×C₃×Q₈	—	5	1	no	—
426	C₂×C₃×Q₈	—	5	1	no	—
427	C₂×C₃×Q₈	—	5	1	no	—
428	C₂×C₃×Q₈	—	10	2	no	—
429	C₂×C₃×Q₈	—	10	2	no	—
430	C₂×C₃×Q₈	—	10	2	no	—
431	C₂×C₃×Q₈	D₂₀	1	1	yes	characteristic, complemented
432	C₂×C₃×D₄	—	2	1	no	—
433	C₂×C₃×D₄	—	5	2	no	—
434	C₂×C₃×D₄	—	5	1	no	—
435	C₂×C₃×D₄	—	5	1	no	—
436	C₂×C₃×D₄	—	5	1	no	—
437	C₂×C₃×D₄	—	10	2	no	—
438	C₂×C₃×D₄	—	10	2	no	—
439	C₂×C₃×D₄	—	10	4	no	—
440	C₂×C₃×D₄	—	10	4	no	—
441	C₂×C₃×D₄	—	10	2	no	—
442	C₂×C₃×D₄	—	10	4	no	—
443	C₂×C₃×D₄	—	10	1	no	—
444	C₂×C₃×D₄	—	10	2	no	—
445	C₂×C₃×D₄	—	10	1	no	—
446	C₂×C₃×D₄	D₂₀	1	1	yes	characteristic, complemented
447	C₂²×C₃×C₄	—	2	1	no	—
448	C₂²×C₃×C₄	—	2	1	no	—
449	C₂²×C₃×C₄	—	5	2	no	—
450	C₂²×C₃×C₄	—	10	4	no	—
451	C₂²×C₃×C₄	—	10	1	no	—
452	C₂²×C₃×C₄	—	10	1	no	—
453	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
454	C₃×Q₁₆	—	10	2	no	—
455	C₃×Q₁₆	—	10	2	no	—
456	C₃×SD₁₆	—	10	2	no	—
457	C₃×SD₁₆	—	10	2	no	—
458	C₃×SD₁₆	—	10	2	no	—
459	C₃×SD₁₆	—	10	2	no	—
460	C₃×D₈	—	10	2	no	—
461	C₃×D₈	—	10	2	no	—
462	C₃×M₁₆	—	2	1	no	—
463	C₃×M₁₆	—	5	2	no	—
464	C₃×M₁₆	—	10	1	no	—
465	C₃×M₁₆	C₂²×D₅	1	2	yes	—
466	C₂×C₃×C₈	—	2	1	no	—
467	C₂×C₃×C₈	—	10	1	no	—
468	C₃×C₄⋊C₄	—	10	2	no	—
469	C₃×C₂²⋊C₄	—	10	2	no	—
470	C₃×C₂²⋊C₄	—	10	2	no	—
471	C₃×C₄²	—	2	1	no	—
472	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
473	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
474	C₂³×C₅	—	2	1	no	—
475	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
476	C₂²×D₅	—	2	4	no	—
477	C₂²×D₅	—	2	1	no	—
478	C₂²×D₅	—	2	1	no	—
479	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
480	C₅×Q₈	—	2	1	no	—
481	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
482	C₅×D₄	—	2	2	no	—
483	C₅×D₄	—	2	2	no	—
484	C₅×D₄	—	2	1	no	—
485	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
486	C₂×C₄×C₅	—	2	1	no	—
487	C₂×C₄×C₅	—	2	1	no	—
488	C₂×C₄×C₅	—	2	2	no	—
489	C₂×C₄×C₅	—	2	2	no	—
490	C₂×C₄×C₅	—	2	1	no	—
491	C₂×C₄×C₅	—	4	2	no	—
492	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
493	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
494	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
495	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
496	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
497	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
498	C₂²⋊D₅	—	2	4	no	—
499	C₂²⋊D₅	—	2	4	no	—
500	C₂²⋊D₅	—	2	2	no	—
501	C₂²⋊D₅	—	2	2	no	—
502	C₂²⋊D₅	—	2	2	no	—
503	C₂²⋊D₅	—	2	2	no	—
504	C₂²⋊D₅	—	4	1	no	—
505	C₂²⋊D₅	—	4	1	no	—
506	C₂×Dic₅	—	2	4	no	—
507	C₂×Dic₅	—	2	1	no	—
508	C₂×Dic₅	—	2	1	no	—
509	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
510	D₂₀	—	2	4	no	—
511	D₂₀	—	2	1	no	—
512	D₂₀	—	2	1	no	—
513	D₂₀	—	2	1	no	—
514	D₂₀	—	2	1	no	—
515	D₂₀	—	2	1	no	—
516	D₂₀	—	4	4	no	—
517	D₂₀	C₂×C₃×D₄	1	2	yes	—
518	C₄×D₅	—	2	4	no	—
519	C₄×D₅	—	2	4	no	—
520	C₄×D₅	—	2	2	no	—
521	C₄×D₅	—	2	2	no	—
522	C₄×D₅	—	2	2	no	—
523	C₄×D₅	—	2	2	no	—
524	C₄×D₅	—	4	1	no	—
525	C₄×D₅	—	4	1	no	—
526	Dic₁₀	—	2	4	no	—
527	Dic₁₀	—	2	1	no	—
528	Dic₁₀	—	2	1	no	—
529	Dic₁₀	—	2	1	no	—
530	Dic₁₀	—	2	1	no	—
531	Dic₁₀	—	2	1	no	—
532	Dic₁₀	C₂×C₃×D₄	1	2	yes	—
533	C₅×C₈	—	2	2	no	—
534	#168	—	2	2	no	—
535	2₋¹⁺⁴	—	5	2	no	—
536	2₋¹⁺⁴	—	10	1	no	—
537	2₋¹⁺⁴	—	10	1	no	—
538	H(5,𝔽₂)	—	5	2	no	—
539	H(5,𝔽₂)	—	10	2	no	—
540	H(5,𝔽₂)	—	10	1	no	—
541	H(5,𝔽₂)	—	10	1	no	—
542	C₂×#41	—	5	1	no	—
543	C₂×#41	—	5	1	no	—
544	C₂×#41	—	5	1	no	—
545	C₂×#41	—	10	2	no	—
546	C₂×#41	—	10	2	no	—
547	C₂×#41	—	10	2	no	—
548	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
549	#137	—	5	2	no	—
550	#137	—	5	2	no	—
551	#137	—	10	1	no	—
552	#137	—	10	1	no	—
553	AGL(1,ℤ/8)	—	5	2	no	—
554	AGL(1,ℤ/8)	—	5	2	no	—
555	AGL(1,ℤ/8)	—	10	1	no	—
556	AGL(1,ℤ/8)	—	10	1	no	—
557	#135	—	10	2	no	—
558	#135	—	10	2	no	—
559	C₂×M₁₆	—	5	1	no	—
560	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic, complemented
561	C₄⋊Q₈	—	5	1	no	—
562	#127	—	5	1	no	—
563	#124	—	5	1	no	—
564	#124	—	5	1	no	—
565	#121	—	10	2	no	—
566	C₄×D₄	—	10	2	no	—
567	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic, complemented
568	#104	—	5	2	no	—
569	#104	—	5	2	no	—
570	#104	C₂×C₃×D₅	1	2	yes	complemented
571	#104	C₂×C₃×D₅	1	2	yes	complemented
572	#101	—	5	2	no	—
573	#100	—	5	2	no	—
574	C₂×C₃×C₅	—	2	1	no	—
575	C₂×C₃×C₅	—	2	1	no	—
576	C₂×C₃×C₅	—	2	1	no	—
577	C₂×C₃×C₅	—	4	2	no	—
578	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
579	C₃×D₅	—	4	2	no	—
580	C₃×D₅	—	4	2	no	—
581	C₃×D₅	—	8	1	no	—
582	C₂³×C₃	—	2	1	no	—
583	C₂³×C₃	—	5	2	no	—
584	C₂³×C₃	—	10	4	no	—
585	C₂³×C₃	—	10	1	no	—
586	C₂³×C₃	—	10	1	no	—
587	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
588	C₃×Q₈	—	2	1	no	—
589	C₃×Q₈	—	5	2	no	—
590	C₃×Q₈	—	10	4	no	—
591	C₃×Q₈	—	10	1	no	—
592	C₃×Q₈	—	10	1	no	—
593	C₃×Q₈	—	10	1	no	—
594	C₃×Q₈	—	10	1	no	—
595	C₃×Q₈	—	10	1	no	—
596	C₃×Q₈	C₂×D₂₀	1	2	yes	—
597	C₃×D₄	—	2	2	no	—
598	C₃×D₄	—	2	2	no	—
599	C₃×D₄	—	2	1	no	—
600	C₃×D₄	—	5	2	no	—
601	C₃×D₄	—	10	4	no	—
602	C₃×D₄	—	10	4	no	—
603	C₃×D₄	—	10	4	no	—
604	C₃×D₄	—	10	2	no	—
605	C₃×D₄	—	10	2	no	—
606	C₃×D₄	—	10	2	no	—
607	C₃×D₄	—	10	2	no	—
608	C₃×D₄	—	10	1	no	—
609	C₃×D₄	—	10	1	no	—
610	C₃×D₄	—	10	1	no	—
611	C₃×D₄	—	10	1	no	—
612	C₃×D₄	—	10	1	no	—
613	C₃×D₄	—	20	4	no	—
614	C₃×D₄	—	20	1	no	—
615	C₃×D₄	—	20	1	no	—
616	C₃×D₄	C₂×D₂₀	1	2	yes	—
617	C₂×C₃×C₄	—	2	1	no	—
618	C₂×C₃×C₄	—	2	1	no	—
619	C₂×C₃×C₄	—	2	2	no	—
620	C₂×C₃×C₄	—	2	2	no	—
621	C₂×C₃×C₄	—	2	1	no	—
622	C₂×C₃×C₄	—	4	2	no	—
623	C₂×C₃×C₄	—	5	2	no	—
624	C₂×C₃×C₄	—	10	4	no	—
625	C₂×C₃×C₄	—	10	4	no	—
626	C₂×C₃×C₄	—	10	4	no	—
627	C₂×C₃×C₄	—	10	1	no	—
628	C₂×C₃×C₄	—	10	2	no	—
629	C₂×C₃×C₄	—	10	2	no	—
630	C₂×C₃×C₄	—	10	2	no	—
631	C₂×C₃×C₄	—	10	2	no	—
632	C₂×C₃×C₄	—	10	1	no	—
633	C₂×C₃×C₄	—	20	1	no	—
634	C₂×C₃×C₄	—	20	1	no	—
635	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
636	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
637	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
638	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
639	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
640	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
641	C₃×C₈	—	2	2	no	—
642	C₃×C₈	—	10	2	no	—
643	C₂²×C₅	—	2	2	no	—
644	C₂²×C₅	—	4	1	no	—
645	C₂²×C₅	—	8	1	no	—
646	C₂²×C₅	C₃×#120	1	1	yes	characteristic
647	C₂²×C₅	C₃×#120	1	1	yes	characteristic
648	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
649	C₂×D₅	—	2	2	no	—
650	C₂×D₅	—	2	2	no	—
651	C₂×D₅	—	4	2	no	—
652	C₂×D₅	—	4	2	no	—
653	C₂×D₅	—	4	1	no	—
654	C₂×D₅	—	8	1	no	—
655	C₂×D₅	—	8	4	no	—
656	C₄×C₅	—	2	2	no	—
657	C₄×C₅	—	2	2	no	—
658	C₄×C₅	—	4	1	no	—
659	C₄×C₅	C₃×#120	1	1	yes	characteristic
660	C₄×C₅	C₃×#120	1	1	yes	characteristic
661	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
662	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
663	Dic₅	—	2	2	no	—
664	Dic₅	—	2	2	no	—
665	Dic₅	—	4	1	no	—
666	#41	—	2	1	no	—
667	#41	—	2	1	no	—
668	#41	—	5	2	no	—
669	#41	—	5	2	no	—
670	#41	—	10	2	no	—
671	#41	—	10	2	no	—
672	#41	—	10	4	no	—
673	#41	—	10	4	no	—
674	#41	—	10	4	no	—
675	#41	—	10	4	no	—
676	#41	—	10	2	no	—
677	#41	—	10	2	no	—
678	#41	—	10	2	no	—
679	#41	—	10	2	no	—
680	#41	—	10	1	no	—
681	#41	—	10	1	no	—
682	#41	—	10	1	no	—
683	#41	—	10	1	no	—
684	#41	—	10	1	no	—
685	#41	—	10	1	no	—
686	#41	—	10	1	no	—
687	#41	—	10	1	no	—
688	#41	—	10	1	no	—
689	#41	—	10	1	no	—
690	#41	C₃×D₂₀	1	2	yes	complemented
691	#41	C₂²×C₃×D₅	1	2	yes	—
692	C₂×Q₈	—	5	1	no	—
693	C₂×Q₈	—	5	1	no	—
694	C₂×Q₈	—	5	1	no	—
695	C₂×Q₈	—	10	2	no	—
696	C₂×Q₈	—	10	2	no	—
697	C₂×Q₈	—	10	2	no	—
698	C₂×Q₈	C₃×D₂₀	1	1	yes	characteristic, complemented
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	5	2	no	—
701	C₂×D₄	—	5	1	no	—
702	C₂×D₄	—	5	1	no	—
703	C₂×D₄	—	5	1	no	—
704	C₂×D₄	—	10	2	no	—
705	C₂×D₄	—	10	2	no	—
706	C₂×D₄	—	10	4	no	—
707	C₂×D₄	—	10	4	no	—
708	C₂×D₄	—	10	2	no	—
709	C₂×D₄	—	10	4	no	—
710	C₂×D₄	—	10	1	no	—
711	C₂×D₄	—	10	2	no	—
712	C₂×D₄	—	10	1	no	—
713	C₂×D₄	C₃×D₂₀	1	1	yes	characteristic, complemented
714	C₂²×C₄	—	2	1	no	—
715	C₂²×C₄	—	2	1	no	—
716	C₂²×C₄	—	5	2	no	—
717	C₂²×C₄	—	10	4	no	—
718	C₂²×C₄	—	10	1	no	—
719	C₂²×C₄	—	10	1	no	—
720	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
721	Q₁₆	—	10	2	no	—
722	Q₁₆	—	10	2	no	—
723	SD₁₆	—	10	2	no	—
724	SD₁₆	—	10	2	no	—
725	SD₁₆	—	10	2	no	—
726	SD₁₆	—	10	2	no	—
727	D₈	—	10	2	no	—
728	D₈	—	10	2	no	—
729	M₁₆	—	2	1	no	—
730	M₁₆	—	5	2	no	—
731	M₁₆	—	10	1	no	—
732	M₁₆	C₂²×C₃×D₅	1	2	yes	—
733	C₂×C₈	—	2	1	no	—
734	C₂×C₈	—	10	1	no	—
735	C₄⋊C₄	—	10	2	no	—
736	C₂²⋊C₄	—	10	2	no	—
737	C₂²⋊C₄	—	10	2	no	—
738	C₄²	—	2	1	no	—
739	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
740	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
741	C₃×C₅	#3018	1	1	yes	characteristic, complemented, Hall
742	C₂²×C₃	—	2	2	no	—
743	C₂²×C₃	—	4	1	no	—
744	C₂²×C₃	—	8	1	no	—
745	C₂²×C₃	—	10	2	no	—
746	C₂²×C₃	—	10	2	no	—
747	C₂²×C₃	—	20	2	no	—
748	C₂²×C₃	—	20	2	no	—
749	C₂²×C₃	—	20	1	no	—
750	C₂²×C₃	—	40	1	no	—
751	C₂²×C₃	—	40	4	no	—
752	C₂²×C₃	#4028	1	1	yes	characteristic
753	C₂²×C₃	#4028	1	1	yes	characteristic
754	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
755	C₃×C₄	—	2	2	no	—
756	C₃×C₄	—	2	2	no	—
757	C₃×C₄	—	4	1	no	—
758	C₃×C₄	—	10	2	no	—
759	C₃×C₄	—	10	2	no	—
760	C₃×C₄	—	20	1	no	—
761	C₃×C₄	#4028	1	1	yes	characteristic
762	C₃×C₄	#4028	1	1	yes	characteristic
763	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
764	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
765	C₂×C₅	—	2	1	no	—
766	C₂×C₅	—	2	1	no	—
767	C₂×C₅	—	2	1	no	—
768	C₂×C₅	—	4	2	no	—
769	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
770	D₅	—	4	2	no	—
771	D₅	—	4	2	no	—
772	D₅	—	8	1	no	—
773	C₂³	—	2	1	no	—
774	C₂³	—	5	2	no	—
775	C₂³	—	10	4	no	—
776	C₂³	—	10	1	no	—
777	C₂³	—	10	1	no	—
778	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
779	Q₈	—	2	1	no	—
780	Q₈	—	5	2	no	—
781	Q₈	—	10	4	no	—
782	Q₈	—	10	1	no	—
783	Q₈	—	10	1	no	—
784	Q₈	—	10	1	no	—
785	Q₈	—	10	1	no	—
786	Q₈	—	10	1	no	—
787	Q₈	C₂×C₃×D₂₀	1	2	yes	—
788	D₄	—	2	2	no	—
789	D₄	—	2	2	no	—
790	D₄	—	2	1	no	—
791	D₄	—	5	2	no	—
792	D₄	—	10	4	no	—
793	D₄	—	10	4	no	—
794	D₄	—	10	4	no	—
795	D₄	—	10	2	no	—
796	D₄	—	10	2	no	—
797	D₄	—	10	2	no	—
798	D₄	—	10	2	no	—
799	D₄	—	10	1	no	—
800	D₄	—	10	1	no	—
801	D₄	—	10	1	no	—
802	D₄	—	10	1	no	—
803	D₄	—	10	1	no	—
804	D₄	—	20	4	no	—
805	D₄	—	20	1	no	—
806	D₄	—	20	1	no	—
807	D₄	C₂×C₃×D₂₀	1	2	yes	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	1	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	5	2	no	—
815	C₂×C₄	—	10	4	no	—
816	C₂×C₄	—	10	4	no	—
817	C₂×C₄	—	10	4	no	—
818	C₂×C₄	—	10	1	no	—
819	C₂×C₄	—	10	2	no	—
820	C₂×C₄	—	10	2	no	—
821	C₂×C₄	—	10	2	no	—
822	C₂×C₄	—	10	2	no	—
823	C₂×C₄	—	10	1	no	—
824	C₂×C₄	—	20	1	no	—
825	C₂×C₄	—	20	1	no	—
826	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
827	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
828	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
829	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
830	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
831	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
832	C₈	—	2	2	no	—
833	C₈	—	10	2	no	—
834	C₂×C₃	—	2	1	no	—
835	C₂×C₃	—	2	1	no	—
836	C₂×C₃	—	2	1	no	—
837	C₂×C₃	—	4	2	no	—
838	C₂×C₃	—	20	2	no	—
839	C₂×C₃	—	20	2	no	—
840	C₂×C₃	—	40	1	no	—
841	C₂×C₃	C₂×#4028	1	1	yes	characteristic
842	C₅	C₃×#3018	1	1	yes	characteristic, complemented, Sylow
843	C₂²	—	2	2	no	—
844	C₂²	—	4	1	no	—
845	C₂²	—	8	1	no	—
846	C₂²	—	10	2	no	—
847	C₂²	—	10	2	no	—
848	C₂²	—	20	2	no	—
849	C₂²	—	20	2	no	—
850	C₂²	—	20	1	no	—
851	C₂²	—	40	1	no	—
852	C₂²	—	40	4	no	—
853	C₂²	C₃×#4028	1	1	yes	characteristic
854	C₂²	C₃×#4028	1	1	yes	characteristic
855	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
856	C₄	—	2	2	no	—
857	C₄	—	2	2	no	—
858	C₄	—	4	1	no	—
859	C₄	—	10	2	no	—
860	C₄	—	10	2	no	—
861	C₄	—	20	1	no	—
862	C₄	C₃×#4028	1	1	yes	characteristic
863	C₄	C₃×#4028	1	1	yes	characteristic
864	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
865	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
866	C₃	#10610717	1	1	yes	characteristic, direct product factor, Sylow
867	C₂	—	2	1	no	—
868	C₂	—	2	1	no	—
869	C₂	—	2	1	no	—
870	C₂	—	4	2	no	—
871	C₂	—	20	2	no	—
872	C₂	—	20	2	no	—
873	C₂	—	40	1	no	—
874	C₂	C₂×C₃×#4028	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄	#4028
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#104	C₂
socle	C₂×C₃×C₅	C₂×#120
hypercenter	C₂×C₃×#104	D₅
hypocenter	C₅	C₃×#3018
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#104

Complements

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

N	H ≅ G/N	type
1. C₃×#66283	C₂	semidirect
2. C₃×#66156	C₂	semidirect
3. C₃×#66082	C₂	semidirect
4. C₃×#65811	C₂	semidirect
5. C₂×C₃×C₅×#104	C₂	semidirect
6. C₃×#65421	C₂	semidirect
7. C₂×C₃×#3937	C₂	semidirect
8. C₃×#65116	C₂	semidirect
9. C₃×#65115	C₂	semidirect
10. C₃×#65114	C₂	semidirect
11. C₃×#65111	C₂	semidirect
12. #10610717	C₃	direct (N × H)
26. C₂×C₃×#709	C₂²	semidirect
27. C₂×C₃×C₅×M₁₆	C₂²	semidirect
28. C₂×C₃×C₄²×C₅	C₂²	semidirect
29. C₃×#4097	C₂²	semidirect
31. C₃×#4095	C₂²	semidirect
35. C₂×C₃×#681	C₂²	semidirect
37. C₃×#4055	C₂²	semidirect
39. C₃×#4054	C₂²	semidirect
41. C₃×#4021	C₂²	semidirect
42. C₃×#4021	C₂²	semidirect
43. C₃×#4020	C₂²	semidirect
45. C₃×#4015	C₂²	semidirect
46. C₃×C₅×#104	C₂²	semidirect
47. C₃×C₅×#104	C₂²	semidirect
48. C₃×#3956	C₂²	semidirect
49. C₃×#3955	C₂²	semidirect
50. C₃×#3937	C₂²	semidirect
51. C₃×#3937	C₂²	semidirect
53. #66283	C₂×C₃	semidirect
54. #66156	C₂×C₃	semidirect
55. #66082	C₂×C₃	semidirect
56. #65811	C₂×C₃	semidirect
57. C₂×C₅×#104	C₂×C₃	semidirect
58. #65421	C₂×C₃	semidirect
59. C₂×#3937	C₂×C₃	semidirect
60. #65116	C₂×C₃	semidirect
61. #65115	C₂×C₃	semidirect
62. #65114	C₂×C₃	semidirect
63. #65111	C₂×C₃	semidirect
66. C₃×C₅×#41	D₄	semidirect
68. C₂×C₃×C₅×Q₈	D₄	semidirect
70. C₂×C₃×C₅×D₄	D₄	semidirect
104. C₃×#709	D₄	semidirect
108. C₂×C₃×D₂₀	D₄	semidirect
116. C₂×C₃×Dic₁₀	D₄	semidirect
148. C₂×C₃×#104	D₅	semidirect
163. C₂×#709	C₂²×C₃	semidirect
164. C₂×C₅×M₁₆	C₂²×C₃	semidirect
165. C₂×C₄²×C₅	C₂²×C₃	semidirect
166. #4097	C₂²×C₃	semidirect
168. #4095	C₂²×C₃	semidirect
172. C₂×#681	C₂²×C₃	semidirect
174. #4055	C₂²×C₃	semidirect
176. #4054	C₂²×C₃	semidirect
178. #4021	C₂²×C₃	semidirect
179. #4021	C₂²×C₃	semidirect
180. #4020	C₂²×C₃	semidirect
182. #4015	C₂²×C₃	semidirect
183. C₅×#104	C₂²×C₃	semidirect
184. C₅×#104	C₂²×C₃	semidirect
185. #3956	C₂²×C₃	semidirect
186. #3955	C₂²×C₃	semidirect
187. #3937	C₂²×C₃	semidirect
188. #3937	C₂²×C₃	semidirect
276. C₂×C₃×M₁₆	C₂×D₅	semidirect
283. C₂×C₃×C₄²	C₂×D₅	semidirect
286. C₃×#104	C₂×D₅	semidirect
287. C₃×#104	C₂×D₅	semidirect
292. C₅×#41	C₃×D₄	semidirect
294. C₂×C₅×Q₈	C₃×D₄	semidirect
296. C₂×C₅×D₄	C₃×D₄	semidirect
330. #709	C₃×D₄	semidirect
334. C₂×D₂₀	C₃×D₄	semidirect
342. C₂×Dic₁₀	C₃×D₄	semidirect
374. C₂×#104	C₃×D₅	semidirect
423. C₃×#41	D₂₀	semidirect
431. C₂×C₃×Q₈	D₂₀	semidirect
446. C₂×C₃×D₄	D₂₀	semidirect
560. C₂×M₁₆	C₂×C₃×D₅	semidirect
567. C₂×C₄²	C₂×C₃×D₅	semidirect
570. #104	C₂×C₃×D₅	semidirect
571. #104	C₂×C₃×D₅	semidirect
690. #41	C₃×D₂₀	semidirect
698. C₂×Q₈	C₃×D₂₀	semidirect
713. C₂×D₄	C₃×D₂₀	semidirect
741. C₃×C₅	#3018	semidirect
842. C₅	C₃×#3018	semidirect
866. C₃	#10610717	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×#66283	2
C₃×#66156	2
C₃×#66082	2
C₃×#65811	2
C₂×C₃×C₅×#104	2
C₃×#65421	2
C₂×C₃×#3937	2
C₃×#65116	2
C₃×#65115	2
C₃×#65114	2
C₃×#65111	2
#10610717	3
C₃×#3018	5

Subgroups — C3×#10610717 #14425201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610717 #14425201