Subgroups — C₃×#10617448 #14418026

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅⋊#131	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4131	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66107	C₂	1	1	yes	maximal, characteristic
4	C₃×#65795	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65769	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65737	C₂	1	2	yes	maximal, complemented
7	C₃×#65736	C₂	1	2	yes	maximal, complemented
8	C₃×#65733	C₂	1	2	yes	maximal, complemented
9	C₃×#65732	C₂	1	2	yes	maximal, complemented
10	C₃×#65729	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#65728	C₂	1	1	yes	maximal, characteristic, complemented
12	#10617448	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×D₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×#711	C₂²	1	1	yes	characteristic
15	C₂×C₃×#704	—	2	1	no	—
16	C₂²×C₃×#170	—	2	1	no	—
17	C₃×#4133	C₂²	1	1	yes	characteristic, complemented
18	C₃×#4133	C₂²	1	1	yes	characteristic, complemented
19	C₃×#4131	—	2	1	no	—
20	C₃×#4131	—	2	1	no	—
21	C₃×#4131	—	2	1	no	—
22	C₃×#4131	—	2	1	no	—
23	C₃×#4131	C₂²	1	1	yes	characteristic, complemented
24	C₃×#4131	C₂²	1	2	yes	complemented
25	C₃×#4131	C₂²	1	1	yes	characteristic, complemented
26	C₃×#4131	C₂²	1	2	yes	complemented
27	C₃×#4130	C₂²	1	1	yes	characteristic
28	C₃×D₅⋊M₁₆	—	2	1	no	—
29	C₃×D₅⋊M₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₃×#700	C₂²	1	1	yes	characteristic
31	C₂×C₃×D₅⋊C₈	—	2	1	no	—
32	C₂×C₃×D₅⋊C₈	C₂²	1	1	yes	characteristic
33	C₃×C₅×AGL(1,ℤ/8)	C₄	1	1	yes	characteristic, complemented
34	C₃×#4097	C₄	1	1	yes	characteristic, complemented
35	C₃×#4078	C₄	1	1	yes	characteristic, complemented
36	C₃×#4062	C₂²	1	2	yes	—
37	C₃×#4061	C₄	1	2	yes	complemented
38	C₃×#4058	C₂²	1	2	yes	—
39	C₃×#4057	C₄	1	2	yes	complemented
40	C₃×#4055	C₄	1	1	yes	characteristic, complemented
41	C₃×D₅×M₁₆	C₂²	1	1	yes	characteristic
42	C₃×#4010	C₂²	1	2	yes	complemented
43	C₃×#4008	C₂²	1	2	yes	complemented
44	C₃×#4008	C₂²	1	2	yes	complemented
45	C₃×#4008	C₂²	1	2	yes	complemented
46	C₃×#3996	C₂²	1	2	yes	complemented
47	C₃×#3995	C₂²	1	2	yes	complemented
48	C₃×#3992	C₂²	1	2	yes	complemented
49	C₃×C₈×AGL(1,𝔽₅)	C₂²	1	2	yes	complemented
50	C₃×#2955	—	5	1	no	maximal, Hall
51	D₅⋊#131	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×#4131	C₂×C₃	1	1	yes	characteristic, complemented
53	#66107	C₂×C₃	1	1	yes	characteristic
54	#65795	C₂×C₃	1	1	yes	characteristic, complemented
55	#65769	C₂×C₃	1	1	yes	characteristic, complemented
56	#65737	C₂×C₃	1	2	yes	complemented
57	#65736	C₂×C₃	1	2	yes	complemented
58	#65733	C₂×C₃	1	2	yes	complemented
59	#65732	C₂×C₃	1	2	yes	complemented
60	#65729	C₂×C₃	1	1	yes	characteristic, complemented
61	#65728	C₂×C₃	1	1	yes	characteristic, complemented
62	C₃×C₅×#41	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
65	C₂²×C₃×Dic₅	—	2	1	no	—
66	C₃×#713	C₂³	1	1	yes	characteristic
67	C₃×Q₈×D₅	C₂×C₄	1	1	yes	characteristic
68	C₃×#711	—	2	1	no	—
69	C₃×#711	—	2	1	no	—
70	C₃×#711	—	2	1	no	—
71	C₃×#711	C₂×C₄	1	2	yes	—
72	C₃×#711	C₂³	1	2	yes	—
73	C₃×#711	C₂³	1	1	yes	characteristic
74	C₃×D₄×D₅	—	2	1	no	—
75	C₃×D₄×D₅	C₂×C₄	1	1	yes	characteristic
76	C₃×#709	—	2	1	no	—
77	C₃×#709	C₂×C₄	1	1	yes	characteristic
78	C₂×C₃×C₄×D₅	—	2	1	no	—
79	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
80	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
81	C₃×C₂²⋊AGL(1,𝔽₅)	—	2	1	no	—
82	C₃×#704	—	2	1	no	—
83	C₃×#704	—	2	1	no	—
84	C₃×#704	—	2	1	no	—
85	C₃×#704	—	2	2	no	—
86	C₃×#704	—	2	2	no	—
87	C₂×C₃×#170	—	2	1	no	—
88	C₂×C₃×#170	—	2	1	no	—
89	C₂×C₃×#170	—	2	1	no	—
90	C₂×C₃×#170	—	2	2	no	—
91	C₂×C₃×#170	—	2	2	no	—
92	C₂×C₃×#170	D₄	1	1	yes	characteristic
93	C₂×C₃×#170	D₄	1	1	yes	characteristic
94	C₃×C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
95	C₃×C₄×AGL(1,𝔽₅)	C₂³	1	2	yes	—
96	C₃×#700	—	2	1	no	—
97	C₃×#700	—	2	1	no	—
98	C₃×#700	—	2	1	no	—
99	C₃×#700	C₂³	1	1	yes	characteristic
100	C₃×#700	C₂³	1	2	yes	—
101	C₃×#700	C₂³	1	1	yes	characteristic
102	C₃×D₅⋊C₈	—	2	1	no	—
103	C₃×D₅⋊C₈	—	2	1	no	—
104	C₃×D₅⋊C₈	—	2	1	no	—
105	C₃×D₅⋊C₈	D₄	1	1	yes	characteristic
106	C₃×D₅⋊C₈	D₄	1	1	yes	characteristic
107	C₃×D₅⋊C₈	C₂³	1	1	yes	characteristic
108	C₃×D₅⋊C₈	C₂³	1	1	yes	characteristic
109	C₃×C₅×SD₁₆	C₂×C₄	1	2	yes	—
110	C₃×C₅×D₈	C₂×C₄	1	2	yes	—
111	C₃×C₅×M₁₆	C₂×C₄	1	1	yes	characteristic
112	C₃×#689	C₂×C₄	1	2	yes	—
113	C₃×#687	C₂×C₄	1	2	yes	—
114	C₃×#687	C₂×C₄	1	2	yes	—
115	C₃×#686	C₂×C₄	1	2	yes	—
116	C₃×#681	C₂×C₄	1	1	yes	characteristic
117	C₃×Dic₂₀	C₂×C₄	1	2	yes	—
118	C₃×#677	C₂×C₄	1	2	yes	—
119	C₃×#676	C₂×C₄	1	2	yes	—
120	C₃×C₈×D₅	C₂³	1	2	yes	—
121	C₃×#575	—	5	1	no	—
122	C₂×C₃×#131	—	5	1	no	—
123	C₂×C₃×#131	—	5	1	no	—
124	C₃×#444	—	5	2	no	—
125	C₃×#444	—	5	2	no	—
126	C₃×#443	—	5	2	no	—
127	C₃×#443	—	5	2	no	—
128	C₃×#430	—	5	1	no	—
129	C₃×#421	—	5	1	no	—
130	C₃×#421	—	5	1	no	—
131	C₃×#405	—	5	1	no	—
132	D₅×#41	C₂²×C₃	1	1	yes	characteristic
133	C₂×#711	C₂²×C₃	1	1	yes	characteristic
134	C₂×#704	—	2	1	no	—
135	C₂²×#170	—	2	1	no	—
136	#4133	C₂²×C₃	1	1	yes	characteristic, complemented
137	#4133	C₂²×C₃	1	1	yes	characteristic, complemented
138	#4131	—	2	1	no	—
139	#4131	—	2	1	no	—
140	#4131	—	2	1	no	—
141	#4131	—	2	1	no	—
142	#4131	C₂²×C₃	1	1	yes	characteristic, complemented
143	#4131	C₂²×C₃	1	2	yes	complemented
144	#4131	C₂²×C₃	1	1	yes	characteristic, complemented
145	#4131	C₂²×C₃	1	2	yes	complemented
146	#4130	C₂²×C₃	1	1	yes	characteristic
147	D₅⋊M₁₆	—	2	1	no	—
148	D₅⋊M₁₆	C₂²×C₃	1	1	yes	characteristic
149	C₂×#700	C₂²×C₃	1	1	yes	characteristic
150	C₂×D₅⋊C₈	—	2	1	no	—
151	C₂×D₅⋊C₈	C₂²×C₃	1	1	yes	characteristic
152	C₅×AGL(1,ℤ/8)	C₃×C₄	1	1	yes	characteristic, complemented
153	#4097	C₃×C₄	1	1	yes	characteristic, complemented
154	#4078	C₃×C₄	1	1	yes	characteristic, complemented
155	#4062	C₂²×C₃	1	2	yes	—
156	#4061	C₃×C₄	1	2	yes	complemented
157	#4058	C₂²×C₃	1	2	yes	—
158	#4057	C₃×C₄	1	2	yes	complemented
159	#4055	C₃×C₄	1	1	yes	characteristic, complemented
160	D₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
161	#4010	C₂²×C₃	1	2	yes	complemented
162	#4008	C₂²×C₃	1	2	yes	complemented
163	#4008	C₂²×C₃	1	2	yes	complemented
164	#4008	C₂²×C₃	1	2	yes	complemented
165	#3996	C₂²×C₃	1	2	yes	complemented
166	#3995	C₂²×C₃	1	2	yes	complemented
167	#3992	C₂²×C₃	1	2	yes	complemented
168	C₈×AGL(1,𝔽₅)	C₂²×C₃	1	2	yes	complemented
169	#2955	—	5	1	no	Sylow
170	C₂³×C₃×C₅	—	2	1	no	—
171	C₂²×C₃×D₅	—	2	1	no	—
172	C₂²×C₃×D₅	#41	1	1	yes	characteristic
173	C₂×C₃×AGL(1,𝔽₅)	—	2	2	no	—
174	C₃×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
175	C₃×C₅×D₄	—	2	1	no	—
176	C₃×C₅×D₄	—	2	1	no	—
177	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
178	C₃×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₃×C₄×C₅	—	2	1	no	—
180	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
181	C₃×C₂²⋊D₅	—	2	1	no	—
182	C₃×C₂²⋊D₅	—	2	2	no	—
183	C₃×C₂²⋊D₅	—	2	1	no	—
184	C₃×C₂²⋊D₅	—	2	2	no	—
185	C₃×C₂²⋊D₅	—	2	1	no	—
186	C₂×C₃×Dic₅	—	2	1	no	—
187	C₂×C₃×Dic₅	—	2	2	no	—
188	C₂×C₃×Dic₅	—	2	1	no	—
189	C₂×C₃×Dic₅	—	2	2	no	—
190	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
191	C₃×D₂₀	—	2	1	no	—
192	C₃×D₂₀	C₂²×C₄	1	1	yes	characteristic
193	C₃×C₄×D₅	—	2	1	no	—
194	C₃×C₄×D₅	—	2	1	no	—
195	C₃×C₄×D₅	—	2	1	no	—
196	C₃×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
197	C₃×C₄×D₅	C₂×D₄	1	1	yes	characteristic
198	C₃×C₄×D₅	#41	1	1	yes	characteristic
199	C₃×C₄×D₅	C₂⁴	1	1	yes	characteristic
200	C₃×Dic₁₀	—	2	1	no	—
201	C₃×Dic₁₀	—	2	1	no	—
202	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
203	C₃×Dic₁₀	C₂²×C₄	1	1	yes	characteristic
204	C₃×#170	—	2	1	no	—
205	C₃×#170	—	2	1	no	—
206	C₃×#170	—	2	2	no	—
207	C₃×#170	C₂×D₄	1	1	yes	characteristic
208	C₃×#170	C₂×D₄	1	1	yes	characteristic
209	C₃×#170	C₂×D₄	1	1	yes	characteristic
210	C₃×#170	C₂×D₄	1	1	yes	characteristic
211	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
212	C₃×#168	C₂²×C₄	1	2	yes	—
213	C₂×C₃×#41	—	5	1	no	—
214	C₂×C₃×#41	—	5	1	no	—
215	C₃×#137	—	5	1	no	—
216	C₃×#137	—	5	2	no	—
217	C₃×#137	—	5	1	no	—
218	C₃×AGL(1,ℤ/8)	—	5	1	no	—
219	C₃×AGL(1,ℤ/8)	—	5	2	no	—
220	C₃×AGL(1,ℤ/8)	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
221	C₃×#135	—	5	2	no	—
222	C₃×#135	—	5	2	no	—
223	C₃×#131	—	5	2	no	—
224	C₃×#131	—	5	1	no	—
225	C₃×#131	—	5	2	no	—
226	C₃×#131	—	5	1	no	—
227	C₃×#131	—	5	1	no	—
228	C₃×#131	—	5	1	no	—
229	C₃×#131	—	10	1	no	—
230	C₃×#131	—	10	1	no	—
231	C₃×#131	—	10	1	no	—
232	C₃×#131	—	10	1	no	—
233	C₂×C₃×M₁₆	—	5	1	no	—
234	C₂×C₃×M₁₆	—	5	1	no	—
235	C₂×C₃×M₁₆	—	5	1	no	—
236	C₂×C₃×M₁₆	—	10	1	no	—
237	C₂×C₃×M₁₆	—	10	1	no	—
238	C₂²×C₃×C₈	—	5	1	no	—
239	C₂²×C₃×C₈	—	10	1	no	—
240	C₂²×C₃×C₈	—	10	1	no	—
241	C₃×#117	—	5	1	no	—
242	C₃×#108	—	5	2	no	—
243	C₃×#108	—	5	2	no	—
244	C₃×#104	—	5	2	no	—
245	C₃×#104	—	5	2	no	—
246	C₃×#104	—	5	2	no	—
247	C₃×#104	—	5	2	no	—
248	C₃×#97	—	5	2	no	—
249	C₃×C₄×C₈	—	5	2	no	—
250	C₅×#41	C₂×C₃×C₄	1	1	yes	characteristic
251	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
252	C₂×C₂²⋊D₅	—	2	1	no	—
253	C₂²×Dic₅	—	2	1	no	—
254	#713	C₂³×C₃	1	1	yes	characteristic
255	Q₈×D₅	C₂×C₃×C₄	1	1	yes	characteristic
256	#711	—	2	1	no	—
257	#711	—	2	1	no	—
258	#711	—	2	1	no	—
259	#711	C₂×C₃×C₄	1	2	yes	—
260	#711	C₂³×C₃	1	2	yes	—
261	#711	C₂³×C₃	1	1	yes	characteristic
262	D₄×D₅	—	2	1	no	—
263	D₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
264	#709	—	2	1	no	—
265	#709	C₂×C₃×C₄	1	1	yes	characteristic
266	C₂×C₄×D₅	—	2	1	no	—
267	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
268	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
269	C₂²⋊AGL(1,𝔽₅)	—	2	1	no	—
270	#704	—	2	1	no	—
271	#704	—	2	1	no	—
272	#704	—	2	1	no	—
273	#704	—	2	2	no	—
274	#704	—	2	2	no	—
275	C₂×#170	—	2	1	no	—
276	C₂×#170	—	2	1	no	—
277	C₂×#170	—	2	1	no	—
278	C₂×#170	—	2	2	no	—
279	C₂×#170	—	2	2	no	—
280	C₂×#170	C₃×D₄	1	1	yes	characteristic
281	C₂×#170	C₃×D₄	1	1	yes	characteristic
282	C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
283	C₄×AGL(1,𝔽₅)	C₂³×C₃	1	2	yes	—
284	#700	—	2	1	no	—
285	#700	—	2	1	no	—
286	#700	—	2	1	no	—
287	#700	C₂³×C₃	1	2	yes	—
288	#700	C₂³×C₃	1	1	yes	characteristic
289	#700	C₂³×C₃	1	1	yes	characteristic
290	D₅⋊C₈	—	2	1	no	—
291	D₅⋊C₈	—	2	1	no	—
292	D₅⋊C₈	—	2	1	no	—
293	D₅⋊C₈	C₃×D₄	1	1	yes	characteristic
294	D₅⋊C₈	C₃×D₄	1	1	yes	characteristic
295	D₅⋊C₈	C₂³×C₃	1	1	yes	characteristic
296	D₅⋊C₈	C₂³×C₃	1	1	yes	characteristic
297	C₅×SD₁₆	C₂×C₃×C₄	1	2	yes	—
298	C₅×D₈	C₂×C₃×C₄	1	2	yes	—
299	C₅×M₁₆	C₂×C₃×C₄	1	1	yes	characteristic
300	#689	C₂×C₃×C₄	1	2	yes	—
301	#687	C₂×C₃×C₄	1	2	yes	—
302	#687	C₂×C₃×C₄	1	2	yes	—
303	#686	C₂×C₃×C₄	1	2	yes	—
304	#681	C₂×C₃×C₄	1	1	yes	characteristic
305	Dic₂₀	C₂×C₃×C₄	1	2	yes	—
306	#677	C₂×C₃×C₄	1	2	yes	—
307	#676	C₂×C₃×C₄	1	2	yes	—
308	C₈×D₅	C₂³×C₃	1	2	yes	—
309	#575	—	5	1	no	—
310	C₂×#131	—	5	1	no	—
311	C₂×#131	—	5	1	no	—
312	#444	—	5	2	no	—
313	#444	—	5	2	no	—
314	#443	—	5	2	no	—
315	#443	—	5	2	no	—
316	#430	—	5	1	no	—
317	#421	—	5	1	no	—
318	#421	—	5	1	no	—
319	#405	—	5	1	no	—
320	C₂²×C₃×C₅	—	2	2	no	—
321	C₂²×C₃×C₅	—	2	1	no	—
322	C₂²×C₃×C₅	—	4	2	no	—
323	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
324	C₂×C₃×D₅	—	2	1	no	—
325	C₂×C₃×D₅	—	4	1	no	—
326	C₂×C₃×D₅	—	4	2	no	—
327	C₂×C₃×D₅	C₄×D₄	1	1	yes	characteristic
328	C₂×C₃×D₅	C₂×#41	1	1	yes	characteristic
329	C₃×AGL(1,𝔽₅)	—	4	2	no	—
330	C₃×C₄×C₅	—	2	1	no	—
331	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
332	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
333	C₃×Dic₅	—	2	1	no	—
334	C₃×Dic₅	—	2	2	no	—
335	C₃×Dic₅	C₄×D₄	1	1	yes	characteristic
336	C₃×Dic₅	C₂²×D₄	1	1	yes	characteristic
337	C₃×#41	—	5	1	no	—
338	C₃×#41	—	5	2	no	—
339	C₃×#41	—	5	1	no	—
340	C₃×#41	—	5	2	no	—
341	C₃×#41	—	5	1	no	—
342	C₃×#41	—	10	1	no	—
343	C₃×#41	—	10	1	no	—
344	C₃×#41	—	10	1	no	—
345	C₃×#41	—	10	1	no	—
346	C₃×#41	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
347	C₂×C₃×Q₈	—	5	1	no	—
348	C₂×C₃×Q₈	—	5	1	no	—
349	C₂×C₃×D₄	—	5	1	no	—
350	C₂×C₃×D₄	—	10	1	no	—
351	C₂×C₃×D₄	—	10	1	no	—
352	C₂×C₃×D₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
353	C₂²×C₃×C₄	—	5	1	no	—
354	C₂²×C₃×C₄	—	10	1	no	—
355	C₂²×C₃×C₄	—	10	1	no	—
356	C₃×Q₁₆	—	5	2	no	—
357	C₃×Q₁₆	—	5	2	no	—
358	C₃×SD₁₆	—	5	2	no	—
359	C₃×SD₁₆	—	5	2	no	—
360	C₃×SD₁₆	—	5	2	no	—
361	C₃×SD₁₆	C₂×AGL(1,𝔽₅)	1	2	yes	—
362	C₃×D₈	—	5	2	no	—
363	C₃×D₈	C₂×AGL(1,𝔽₅)	1	2	yes	—
364	C₃×M₁₆	—	5	1	no	—
365	C₃×M₁₆	—	5	2	no	—
366	C₃×M₁₆	—	5	1	no	—
367	C₃×M₁₆	—	5	1	no	—
368	C₃×M₁₆	—	5	2	no	—
369	C₃×M₁₆	—	10	1	no	—
370	C₃×M₁₆	—	10	1	no	—
371	C₃×M₁₆	—	10	1	no	—
372	C₃×M₁₆	—	10	2	no	—
373	C₃×M₁₆	—	10	1	no	—
374	C₃×M₁₆	—	10	2	no	—
375	C₃×M₁₆	—	10	1	no	—
376	C₃×M₁₆	—	10	1	no	—
377	C₃×M₁₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
378	C₂×C₃×C₈	—	5	1	no	—
379	C₂×C₃×C₈	—	5	1	no	—
380	C₂×C₃×C₈	—	5	1	no	—
381	C₂×C₃×C₈	—	5	1	no	—
382	C₂×C₃×C₈	—	5	1	no	—
383	C₂×C₃×C₈	—	5	1	no	—
384	C₂×C₃×C₈	—	5	2	no	—
385	C₂×C₃×C₈	—	10	1	no	—
386	C₂×C₃×C₈	—	10	1	no	—
387	C₂×C₃×C₈	—	10	1	no	—
388	C₂×C₃×C₈	—	10	2	no	—
389	C₂×C₃×C₈	—	10	1	no	—
390	C₂×C₃×C₈	—	10	2	no	—
391	C₂×C₃×C₈	—	10	1	no	—
392	C₂×C₃×C₈	—	10	1	no	—
393	C₃×C₄⋊C₄	—	10	1	no	—
394	C₃×C₂²⋊C₄	—	10	1	no	—
395	C₃×C₄²	—	5	2	no	—
396	C₂³×C₅	—	2	1	no	—
397	C₂²×D₅	—	2	1	no	—
398	C₂²×D₅	C₃×#41	1	1	yes	characteristic
399	C₂×AGL(1,𝔽₅)	—	2	2	no	—
400	C₅×Q₈	C₂²×C₃×C₄	1	1	yes	characteristic
401	C₅×D₄	—	2	1	no	—
402	C₅×D₄	—	2	1	no	—
403	C₅×D₄	C₂²×C₃×C₄	1	2	yes	—
404	C₅×D₄	C₂²×C₃×C₄	1	1	yes	characteristic
405	C₂×C₄×C₅	—	2	1	no	—
406	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
407	C₂²⋊D₅	—	2	1	no	—
408	C₂²⋊D₅	—	2	2	no	—
409	C₂²⋊D₅	—	2	1	no	—
410	C₂²⋊D₅	—	2	2	no	—
411	C₂²⋊D₅	—	2	1	no	—
412	C₂×Dic₅	—	2	1	no	—
413	C₂×Dic₅	—	2	2	no	—
414	C₂×Dic₅	—	2	1	no	—
415	C₂×Dic₅	—	2	2	no	—
416	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
417	D₂₀	—	2	1	no	—
418	D₂₀	C₂²×C₃×C₄	1	1	yes	characteristic
419	C₄×D₅	—	2	1	no	—
420	C₄×D₅	—	2	1	no	—
421	C₄×D₅	—	2	1	no	—
422	C₄×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
423	C₄×D₅	C₂×C₃×D₄	1	1	yes	characteristic
424	C₄×D₅	C₃×#41	1	1	yes	characteristic
425	C₄×D₅	C₂⁴×C₃	1	1	yes	characteristic
426	Dic₁₀	—	2	1	no	—
427	Dic₁₀	—	2	1	no	—
428	Dic₁₀	C₂²×C₃×C₄	1	2	yes	—
429	Dic₁₀	C₂²×C₃×C₄	1	1	yes	characteristic
430	#170	—	2	1	no	—
431	#170	—	2	1	no	—
432	#170	—	2	2	no	—
433	#170	C₂×C₃×D₄	1	1	yes	characteristic
434	#170	C₂×C₃×D₄	1	1	yes	characteristic
435	#170	C₂×C₃×D₄	1	1	yes	characteristic
436	#170	C₂×C₃×D₄	1	1	yes	characteristic
437	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
438	#168	C₂²×C₃×C₄	1	2	yes	—
439	C₂×#41	—	5	1	no	—
440	C₂×#41	—	5	1	no	—
441	#137	—	5	1	no	—
442	#137	—	5	2	no	—
443	#137	—	5	1	no	—
444	AGL(1,ℤ/8)	—	5	1	no	—
445	AGL(1,ℤ/8)	—	5	2	no	—
446	AGL(1,ℤ/8)	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
447	#135	—	5	2	no	—
448	#135	—	5	2	no	—
449	#131	—	5	1	no	—
450	#131	—	5	2	no	—
451	#131	—	5	1	no	—
452	#131	—	5	2	no	—
453	#131	—	5	1	no	—
454	#131	—	5	1	no	—
455	#131	—	10	1	no	—
456	#131	—	10	1	no	—
457	#131	—	10	1	no	—
458	#131	—	10	1	no	—
459	C₂×M₁₆	—	5	1	no	—
460	C₂×M₁₆	—	5	1	no	—
461	C₂×M₁₆	—	5	1	no	—
462	C₂×M₁₆	—	10	1	no	—
463	C₂×M₁₆	—	10	1	no	—
464	C₂²×C₈	—	5	1	no	—
465	C₂²×C₈	—	10	1	no	—
466	C₂²×C₈	—	10	1	no	—
467	#117	—	5	1	no	—
468	#108	—	5	2	no	—
469	#108	—	5	2	no	—
470	#104	—	5	2	no	—
471	#104	—	5	2	no	—
472	#104	—	5	2	no	—
473	#104	—	5	2	no	—
474	#97	—	5	2	no	—
475	C₄×C₈	—	5	2	no	—
476	C₂×C₃×C₅	—	2	1	no	—
477	C₂×C₃×C₅	—	4	1	no	—
478	C₂×C₃×C₅	—	4	2	no	—
479	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
480	C₃×D₅	—	2	1	no	—
481	C₃×D₅	—	2	1	no	—
482	C₃×D₅	—	4	1	no	—
483	C₂³×C₃	—	2	1	no	—
484	C₂³×C₃	—	5	1	no	—
485	C₂³×C₃	—	10	1	no	—
486	C₃×Q₈	—	5	2	no	—
487	C₃×Q₈	—	5	1	no	—
488	C₃×Q₈	—	10	1	no	—
489	C₃×Q₈	—	10	1	no	—
490	C₃×Q₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
491	C₃×D₄	—	2	1	no	—
492	C₃×D₄	—	2	1	no	—
493	C₃×D₄	—	5	1	no	—
494	C₃×D₄	—	10	1	no	—
495	C₃×D₄	—	10	1	no	—
496	C₃×D₄	—	10	1	no	—
497	C₃×D₄	—	10	2	no	—
498	C₃×D₄	—	10	2	no	—
499	C₃×D₄	—	10	1	no	—
500	C₃×D₄	C₂²×AGL(1,𝔽₅)	1	2	yes	—
501	C₃×D₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
502	C₂×C₃×C₄	—	2	1	no	—
503	C₂×C₃×C₄	—	5	1	no	—
504	C₂×C₃×C₄	—	5	1	no	—
505	C₂×C₃×C₄	—	5	1	no	—
506	C₂×C₃×C₄	—	5	1	no	—
507	C₂×C₃×C₄	—	5	1	no	—
508	C₂×C₃×C₄	—	10	1	no	—
509	C₂×C₃×C₄	—	10	1	no	—
510	C₂×C₃×C₄	—	10	1	no	—
511	C₂×C₃×C₄	—	10	2	no	—
512	C₂×C₃×C₄	—	10	2	no	—
513	C₂×C₃×C₄	—	10	1	no	—
514	C₂×C₃×C₄	—	10	1	no	—
515	C₂×C₃×C₄	—	10	2	no	—
516	C₂×C₃×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
517	C₃×C₈	—	5	1	no	—
518	C₃×C₈	—	5	1	no	—
519	C₃×C₈	—	5	1	no	—
520	C₃×C₈	—	5	1	no	—
521	C₃×C₈	—	5	2	no	—
522	C₃×C₈	—	10	1	no	—
523	C₃×C₈	—	10	1	no	—
524	C₃×C₈	—	10	2	no	—
525	C₃×C₈	C₂²×AGL(1,𝔽₅)	1	2	yes	—
526	C₂²×C₅	—	2	2	no	—
527	C₂²×C₅	—	2	1	no	—
528	C₂²×C₅	—	4	2	no	—
529	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
530	C₂×D₅	—	2	1	no	—
531	C₂×D₅	—	4	1	no	—
532	C₂×D₅	—	4	2	no	—
533	C₂×D₅	C₃×C₄×D₄	1	1	yes	characteristic
534	C₂×D₅	C₂×C₃×#41	1	1	yes	characteristic
535	AGL(1,𝔽₅)	—	4	2	no	—
536	C₄×C₅	—	2	1	no	—
537	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
538	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
539	Dic₅	—	2	1	no	—
540	Dic₅	—	2	2	no	—
541	Dic₅	C₃×C₄×D₄	1	1	yes	characteristic
542	Dic₅	C₂²×C₃×D₄	1	1	yes	characteristic
543	#41	—	5	1	no	—
544	#41	—	5	2	no	—
545	#41	—	5	1	no	—
546	#41	—	5	2	no	—
547	#41	—	5	1	no	—
548	#41	—	10	1	no	—
549	#41	—	10	1	no	—
550	#41	—	10	1	no	—
551	#41	—	10	1	no	—
552	#41	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
553	C₂×Q₈	—	5	1	no	—
554	C₂×Q₈	—	5	1	no	—
555	C₂×D₄	—	5	1	no	—
556	C₂×D₄	—	10	1	no	—
557	C₂×D₄	—	10	1	no	—
558	C₂×D₄	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
559	C₂²×C₄	—	5	1	no	—
560	C₂²×C₄	—	10	1	no	—
561	C₂²×C₄	—	10	1	no	—
562	Q₁₆	—	5	2	no	—
563	Q₁₆	—	5	2	no	—
564	SD₁₆	—	5	2	no	—
565	SD₁₆	—	5	2	no	—
566	SD₁₆	—	5	2	no	—
567	SD₁₆	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
568	D₈	—	5	2	no	—
569	D₈	C₂×C₃×AGL(1,𝔽₅)	1	2	yes	—
570	M₁₆	—	5	1	no	—
571	M₁₆	—	5	2	no	—
572	M₁₆	—	5	1	no	—
573	M₁₆	—	5	1	no	—
574	M₁₆	—	5	2	no	—
575	M₁₆	—	10	1	no	—
576	M₁₆	—	10	1	no	—
577	M₁₆	—	10	1	no	—
578	M₁₆	—	10	2	no	—
579	M₁₆	—	10	1	no	—
580	M₁₆	—	10	2	no	—
581	M₁₆	—	10	1	no	—
582	M₁₆	—	10	1	no	—
583	M₁₆	C₂×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
584	C₂×C₈	—	5	1	no	—
585	C₂×C₈	—	5	1	no	—
586	C₂×C₈	—	5	1	no	—
587	C₂×C₈	—	5	1	no	—
588	C₂×C₈	—	5	1	no	—
589	C₂×C₈	—	5	1	no	—
590	C₂×C₈	—	5	2	no	—
591	C₂×C₈	—	10	1	no	—
592	C₂×C₈	—	10	1	no	—
593	C₂×C₈	—	10	1	no	—
594	C₂×C₈	—	10	2	no	—
595	C₂×C₈	—	10	1	no	—
596	C₂×C₈	—	10	2	no	—
597	C₂×C₈	—	10	1	no	—
598	C₂×C₈	—	10	1	no	—
599	C₄⋊C₄	—	10	1	no	—
600	C₂²⋊C₄	—	10	1	no	—
601	C₄²	—	5	2	no	—
602	C₃×C₅	#2955	1	1	yes	characteristic, complemented, Hall
603	C₂²×C₃	—	2	1	no	—
604	C₂²×C₃	—	2	2	no	—
605	C₂²×C₃	—	4	2	no	—
606	C₂²×C₃	—	5	1	no	—
607	C₂²×C₃	—	5	1	no	—
608	C₂²×C₃	—	10	1	no	—
609	C₂²×C₃	—	20	1	no	—
610	C₂²×C₃	—	20	2	no	—
611	C₂²×C₃	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
612	C₃×C₄	—	2	1	no	—
613	C₃×C₄	—	5	1	no	—
614	C₃×C₄	—	5	1	no	—
615	C₃×C₄	—	10	1	no	—
616	C₃×C₄	—	10	2	no	—
617	C₃×C₄	—	20	2	no	—
618	C₃×C₄	D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
619	C₃×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
620	C₂×C₅	—	2	1	no	—
621	C₂×C₅	—	4	1	no	—
622	C₂×C₅	—	4	2	no	—
623	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
624	D₅	—	2	1	no	—
625	D₅	—	2	1	no	—
626	D₅	—	4	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	5	1	no	—
629	C₂³	—	10	1	no	—
630	Q₈	—	5	1	no	—
631	Q₈	—	5	2	no	—
632	Q₈	—	10	1	no	—
633	Q₈	—	10	1	no	—
634	Q₈	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
635	D₄	—	2	1	no	—
636	D₄	—	2	1	no	—
637	D₄	—	5	1	no	—
638	D₄	—	10	1	no	—
639	D₄	—	10	1	no	—
640	D₄	—	10	1	no	—
641	D₄	—	10	2	no	—
642	D₄	—	10	2	no	—
643	D₄	—	10	1	no	—
644	D₄	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
645	D₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	5	1	no	—
648	C₂×C₄	—	5	1	no	—
649	C₂×C₄	—	5	1	no	—
650	C₂×C₄	—	5	1	no	—
651	C₂×C₄	—	5	1	no	—
652	C₂×C₄	—	10	1	no	—
653	C₂×C₄	—	10	1	no	—
654	C₂×C₄	—	10	1	no	—
655	C₂×C₄	—	10	2	no	—
656	C₂×C₄	—	10	2	no	—
657	C₂×C₄	—	10	1	no	—
658	C₂×C₄	—	10	1	no	—
659	C₂×C₄	—	10	2	no	—
660	C₂×C₄	C₂²×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
661	C₈	—	5	1	no	—
662	C₈	—	5	1	no	—
663	C₈	—	5	1	no	—
664	C₈	—	5	1	no	—
665	C₈	—	5	2	no	—
666	C₈	—	10	1	no	—
667	C₈	—	10	1	no	—
668	C₈	—	10	2	no	—
669	C₈	C₂²×C₃×AGL(1,𝔽₅)	1	2	yes	—
670	C₂×C₃	—	2	1	no	—
671	C₂×C₃	—	4	2	no	—
672	C₂×C₃	—	4	1	no	—
673	C₂×C₃	—	10	1	no	—
674	C₂×C₃	—	10	1	no	—
675	C₂×C₃	—	20	1	no	—
676	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
677	C₅	C₃×#2955	1	1	yes	characteristic, complemented, Sylow
678	C₂²	—	2	1	no	—
679	C₂²	—	2	2	no	—
680	C₂²	—	4	2	no	—
681	C₂²	—	5	1	no	—
682	C₂²	—	5	1	no	—
683	C₂²	—	10	1	no	—
684	C₂²	—	20	1	no	—
685	C₂²	—	20	2	no	—
686	C₂²	C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
687	C₄	—	2	1	no	—
688	C₄	—	5	1	no	—
689	C₄	—	5	1	no	—
690	C₄	—	10	1	no	—
691	C₄	—	10	2	no	—
692	C₄	—	20	2	no	—
693	C₄	C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic
694	C₄	C₂³×C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
695	C₃	#10617448	1	1	yes	characteristic, direct product factor, Sylow
696	C₂	—	2	1	no	—
697	C₂	—	4	2	no	—
698	C₂	—	4	1	no	—
699	C₂	—	10	1	no	—
700	C₂	—	10	1	no	—
701	C₂	—	20	1	no	—
702	C₂	C₂×C₃×D₄×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₄×AGL(1,𝔽₅)
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₄	C₂³×C₃×AGL(1,𝔽₅)
Fitting	C₃×C₅×AGL(1,ℤ/8)	C₄
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	C₃×#66107	C₂
cosocle	C₄×D₅	C₂⁴×C₃
hypercenter	C₃×AGL(1,ℤ/8)	AGL(1,𝔽₅)
hypocenter	C₅	C₃×#2955
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₃×D₅⋊#131	C₂	semidirect
2. C₂×C₃×#4131	C₂	semidirect
4. C₃×#65795	C₂	semidirect
5. C₃×#65769	C₂	semidirect
6. C₃×#65737	C₂	semidirect
7. C₃×#65736	C₂	semidirect
8. C₃×#65733	C₂	semidirect
9. C₃×#65732	C₂	semidirect
10. C₃×#65729	C₂	semidirect
11. C₃×#65728	C₂	semidirect
12. #10617448	C₃	direct (N × H)
17. C₃×#4133	C₂²	semidirect
18. C₃×#4133	C₂²	semidirect
23. C₃×#4131	C₂²	semidirect
24. C₃×#4131	C₂²	semidirect
25. C₃×#4131	C₂²	semidirect
26. C₃×#4131	C₂²	semidirect
33. C₃×C₅×AGL(1,ℤ/8)	C₄	semidirect
34. C₃×#4097	C₄	semidirect
35. C₃×#4078	C₄	semidirect
37. C₃×#4061	C₄	semidirect
39. C₃×#4057	C₄	semidirect
40. C₃×#4055	C₄	semidirect
42. C₃×#4010	C₂²	semidirect
43. C₃×#4008	C₂²	semidirect
44. C₃×#4008	C₂²	semidirect
45. C₃×#4008	C₂²	semidirect
46. C₃×#3996	C₂²	semidirect
47. C₃×#3995	C₂²	semidirect
48. C₃×#3992	C₂²	semidirect
49. C₃×C₈×AGL(1,𝔽₅)	C₂²	semidirect
51. D₅⋊#131	C₂×C₃	semidirect
52. C₂×#4131	C₂×C₃	semidirect
54. #65795	C₂×C₃	semidirect
55. #65769	C₂×C₃	semidirect
56. #65737	C₂×C₃	semidirect
57. #65736	C₂×C₃	semidirect
58. #65733	C₂×C₃	semidirect
59. #65732	C₂×C₃	semidirect
60. #65729	C₂×C₃	semidirect
61. #65728	C₂×C₃	semidirect
136. #4133	C₂²×C₃	semidirect
137. #4133	C₂²×C₃	semidirect
142. #4131	C₂²×C₃	semidirect
143. #4131	C₂²×C₃	semidirect
144. #4131	C₂²×C₃	semidirect
145. #4131	C₂²×C₃	semidirect
152. C₅×AGL(1,ℤ/8)	C₃×C₄	semidirect
153. #4097	C₃×C₄	semidirect
154. #4078	C₃×C₄	semidirect
156. #4061	C₃×C₄	semidirect
158. #4057	C₃×C₄	semidirect
159. #4055	C₃×C₄	semidirect
161. #4010	C₂²×C₃	semidirect
162. #4008	C₂²×C₃	semidirect
163. #4008	C₂²×C₃	semidirect
164. #4008	C₂²×C₃	semidirect
165. #3996	C₂²×C₃	semidirect
166. #3995	C₂²×C₃	semidirect
167. #3992	C₂²×C₃	semidirect
168. C₈×AGL(1,𝔽₅)	C₂²×C₃	semidirect
220. C₃×AGL(1,ℤ/8)	AGL(1,𝔽₅)	semidirect
446. AGL(1,ℤ/8)	C₃×AGL(1,𝔽₅)	semidirect
602. C₃×C₅	#2955	semidirect
677. C₅	C₃×#2955	semidirect
695. C₃	#10617448	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×D₅⋊#131	2
C₂×C₃×#4131	2
C₃×#66107	2
C₃×#65795	2
C₃×#65769	2
C₃×#65737	2
C₃×#65736	2
C₃×#65733	2
C₃×#65732	2
C₃×#65729	2
C₃×#65728	2
#10617448	3
C₃×#2955	5

Subgroups — C3×#10617448 #14418026

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10617448 #14418026