Subgroups — C₃×#10615670 #14439388

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66159	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4096	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#66139	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₃×#687	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×#4055	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65464	C₂	1	2	yes	maximal, complemented
8	C₃×#65456	C₂	1	2	yes	maximal, complemented
9	C₃×#65444	C₂	1	2	yes	maximal, complemented
10	C₃×#65443	C₂	1	2	yes	maximal, complemented
11	C₃×#65411	C₂	1	1	yes	maximal, characteristic, complemented
12	#10615670	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×#709	C₂²	1	1	yes	characteristic
16	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
17	C₃×C₅×AGL(1,ℤ/8)	—	2	4	no	—
18	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
19	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
20	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
21	C₃×#4099	—	2	2	no	—
22	C₃×#4096	—	2	4	no	—
23	C₃×#4090	C₂²	1	2	yes	complemented
24	C₂×C₃×#689	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×#688	C₂²	1	1	yes	characteristic, complemented
26	C₃×#4086	C₂²	1	2	yes	—
27	C₃×#4084	—	2	2	no	—
28	C₃×#4082	C₂²	1	2	yes	—
29	C₃×#4082	C₂²	1	2	yes	complemented
30	C₃×#4081	—	2	2	no	—
31	C₂×C₃×#687	—	2	4	no	—
32	C₂×C₃×#687	C₂²	1	2	yes	—
33	C₂×C₃×#687	C₂²	1	2	yes	—
34	C₂×C₃×#687	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₃×#686	C₂²	1	1	yes	characteristic, complemented
36	C₃×#4072	C₂²	1	1	yes	characteristic
37	C₃×#4070	—	2	2	no	—
38	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
39	C₃×#4055	—	2	4	no	—
40	C₂×C₃×Dic₂₀	C₂²	1	2	yes	complemented
41	C₂×C₃×#677	C₂²	1	2	yes	complemented
42	C₃×#3947	C₂²	1	2	yes	complemented
43	C₃×C₈×Dic₅	C₂²	1	2	yes	complemented
44	C₃×#3154	—	5	1	no	maximal, Hall
45	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic, complemented
46	#66159	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×#4096	C₂×C₃	1	1	yes	characteristic, complemented
48	#66139	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂²×#687	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×#4055	C₂×C₃	1	1	yes	characteristic, complemented
51	#65464	C₂×C₃	1	2	yes	complemented
52	#65456	C₂×C₃	1	2	yes	complemented
53	#65444	C₂×C₃	1	2	yes	complemented
54	#65443	C₂×C₃	1	2	yes	complemented
55	#65411	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂⁴×C₃×C₅	—	2	1	no	—
57	C₃×C₅×#41	—	2	2	no	—
58	C₃×C₅×#41	—	2	2	no	—
59	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
60	C₂×C₃×C₅×D₄	—	2	1	no	—
61	C₂×C₃×C₅×D₄	—	2	2	no	—
62	C₂×C₃×C₅×D₄	—	2	2	no	—
63	C₂×C₃×C₅×D₄	—	2	1	no	—
64	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
66	C₂²×C₃×C₄×C₅	—	2	1	no	—
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
69	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
70	C₂²×C₃×Dic₅	—	2	1	no	—
71	C₃×#709	—	2	2	no	—
72	C₃×#709	—	2	2	no	—
73	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
74	C₂×C₃×C₄×D₅	—	2	1	no	—
75	C₂×C₃×Dic₁₀	—	2	2	no	—
76	C₂×C₃×Dic₁₀	—	2	2	no	—
77	C₂×C₃×Dic₁₀	—	2	1	no	—
78	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
79	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
80	C₃×C₅×SD₁₆	—	2	4	no	—
81	C₃×C₅×D₈	—	2	4	no	—
82	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
83	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
84	C₃×C₂²⋊Dic₅	—	2	4	no	—
85	C₃×C₂²⋊Dic₅	—	2	4	no	—
86	C₃×C₂²⋊Dic₅	D₄	1	2	yes	—
87	C₃×#689	—	2	2	no	—
88	C₃×#688	—	2	2	no	—
89	C₃×#687	—	2	4	no	—
90	C₃×#687	—	2	4	no	—
91	C₃×#687	—	2	2	no	—
92	C₃×#686	—	2	2	no	—
93	C₃×C₄⋊Dic₅	D₄	1	2	yes	—
94	C₃×#683	—	2	4	no	—
95	C₃×C₄×Dic₅	C₂³	1	2	yes	—
96	C₂×C₃×#168	D₄	1	4	yes	complemented
97	C₂×C₃×#168	C₂³	1	1	yes	characteristic
98	C₂×C₃×#168	C₂³	1	1	yes	characteristic
99	C₃×Dic₂₀	—	2	4	no	—
100	C₃×#677	—	2	4	no	—
101	C₂×C₃×#137	—	5	1	no	—
102	C₂×C₃×AGL(1,ℤ/8)	D₅	1	1	yes	characteristic, complemented
103	C₂×C₃×#135	—	5	1	no	—
104	C₂²×C₃×SD₁₆	—	5	1	no	—
105	C₃×#536	—	5	1	no	—
106	C₃×#535	—	5	1	no	—
107	C₃×#497	—	5	2	no	—
108	C₃×#496	—	5	2	no	—
109	C₃×#495	—	5	2	no	—
110	C₃×#492	—	5	2	no	—
111	C₃×#405	—	5	1	no	—
112	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
113	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
114	C₂×#709	C₂²×C₃	1	1	yes	characteristic
115	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
116	C₅×AGL(1,ℤ/8)	—	2	4	no	—
117	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
118	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
119	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
120	#4099	—	2	2	no	—
121	#4096	—	2	4	no	—
122	#4090	C₂²×C₃	1	2	yes	complemented
123	C₂×#689	C₂²×C₃	1	1	yes	characteristic, complemented
124	C₂×#688	C₂²×C₃	1	1	yes	characteristic, complemented
125	#4086	C₂²×C₃	1	2	yes	—
126	#4084	—	2	2	no	—
127	#4082	C₂²×C₃	1	2	yes	—
128	#4082	C₂²×C₃	1	2	yes	complemented
129	#4081	—	2	2	no	—
130	C₂×#687	—	2	4	no	—
131	C₂×#687	C₂²×C₃	1	2	yes	—
132	C₂×#687	C₂²×C₃	1	2	yes	—
133	C₂×#687	C₂²×C₃	1	1	yes	characteristic, complemented
134	C₂×#686	C₂²×C₃	1	1	yes	characteristic, complemented
135	#4072	C₂²×C₃	1	1	yes	characteristic
136	#4070	—	2	2	no	—
137	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
138	#4055	—	2	4	no	—
139	C₂×Dic₂₀	C₂²×C₃	1	2	yes	complemented
140	C₂×#677	C₂²×C₃	1	2	yes	complemented
141	#3947	C₂²×C₃	1	2	yes	complemented
142	C₈×Dic₅	C₂²×C₃	1	2	yes	complemented
143	#3154	—	5	1	no	Sylow
144	C₂³×C₃×C₅	—	2	1	no	—
145	C₂³×C₃×C₅	—	2	2	no	—
146	C₂³×C₃×C₅	—	4	2	no	—
147	C₂³×C₃×C₅	—	8	2	no	—
148	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₃×D₅	—	2	1	no	—
150	C₃×C₅×Q₈	—	2	1	no	—
151	C₃×C₅×Q₈	—	2	1	no	—
152	C₃×C₅×D₄	—	2	1	no	—
153	C₃×C₅×D₄	—	2	2	no	—
154	C₃×C₅×D₄	—	2	1	no	—
155	C₃×C₅×D₄	—	2	2	no	—
156	C₃×C₅×D₄	—	4	2	no	—
157	C₃×C₅×D₄	—	4	2	no	—
158	C₂×C₃×C₄×C₅	—	2	1	no	—
159	C₂×C₃×C₄×C₅	—	4	2	no	—
160	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
161	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
162	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
163	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
164	C₃×C₂²⋊D₅	—	4	2	no	—
165	C₃×C₂²⋊D₅	—	8	4	no	—
166	C₂×C₃×Dic₅	—	2	2	no	—
167	C₂×C₃×Dic₅	—	2	1	no	—
168	C₂×C₃×Dic₅	—	4	2	no	—
169	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
170	C₃×D₂₀	—	2	1	no	—
171	C₃×D₂₀	—	2	1	no	—
172	C₃×C₄×D₅	—	4	2	no	—
173	C₃×Dic₁₀	—	2	2	no	—
174	C₃×Dic₁₀	—	2	1	no	—
175	C₃×Dic₁₀	—	2	2	no	—
176	C₃×Dic₁₀	—	2	1	no	—
177	C₃×Dic₁₀	—	4	2	no	—
178	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
179	C₃×#168	C₂×D₄	1	2	yes	—
180	C₃×#168	C₂×D₄	1	2	yes	—
181	C₂×C₃×#41	—	5	1	no	—
182	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
183	C₂²×C₃×Q₈	—	5	1	no	—
184	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
185	C₃×#137	—	10	4	no	—
186	C₃×AGL(1,ℤ/8)	—	2	4	no	—
187	C₃×#135	—	10	4	no	—
188	C₂×C₃×Q₁₆	—	5	1	no	—
189	C₂×C₃×Q₁₆	—	5	2	no	—
190	C₂×C₃×SD₁₆	—	5	1	no	—
191	C₂×C₃×SD₁₆	—	5	2	no	—
192	C₂×C₃×SD₁₆	—	5	2	no	—
193	C₂×C₃×SD₁₆	—	5	1	no	—
194	C₂×C₃×SD₁₆	—	5	2	no	—
195	C₂×C₃×SD₁₆	—	10	4	no	—
196	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	—
197	C₂×C₃×D₈	—	5	1	no	—
198	C₂×C₃×D₈	C₂×D₅	1	2	yes	—
199	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
200	C₂²×C₃×C₈	—	5	1	no	—
201	C₃×C₄⋊Q₈	—	5	2	no	—
202	C₃×#127	—	5	2	no	—
203	C₃×#124	—	5	2	no	—
204	C₃×#124	—	5	2	no	—
205	C₃×#123	—	10	2	no	—
206	C₃×C₂²⋊Q₈	—	10	2	no	—
207	C₃×#121	—	10	2	no	—
208	C₃×#120	—	10	2	no	—
209	C₃×#117	—	5	1	no	—
210	C₃×#97	—	5	2	no	—
211	C₃×C₄×C₈	—	5	2	no	—
212	C₂⁴×C₅	—	2	1	no	—
213	C₅×#41	—	2	2	no	—
214	C₅×#41	—	2	2	no	—
215	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
216	C₂×C₅×D₄	—	2	1	no	—
217	C₂×C₅×D₄	—	2	2	no	—
218	C₂×C₅×D₄	—	2	2	no	—
219	C₂×C₅×D₄	—	2	1	no	—
220	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
221	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
222	C₂²×C₄×C₅	—	2	1	no	—
223	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
224	C₂×C₂²⋊D₅	—	2	1	no	—
225	C₂×C₂²⋊D₅	—	2	4	no	—
226	C₂²×Dic₅	—	2	1	no	—
227	#709	—	2	2	no	—
228	#709	—	2	2	no	—
229	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
230	C₂×C₄×D₅	—	2	1	no	—
231	C₂×Dic₁₀	—	2	2	no	—
232	C₂×Dic₁₀	—	2	2	no	—
233	C₂×Dic₁₀	—	2	1	no	—
234	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
235	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
236	C₅×SD₁₆	—	2	4	no	—
237	C₅×D₈	—	2	4	no	—
238	C₅×M₁₆	C₃×D₄	1	4	yes	complemented
239	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
240	C₂²⋊Dic₅	—	2	4	no	—
241	C₂²⋊Dic₅	—	2	4	no	—
242	C₂²⋊Dic₅	C₃×D₄	1	2	yes	—
243	#689	—	2	2	no	—
244	#688	—	2	2	no	—
245	#687	—	2	2	no	—
246	#687	—	2	4	no	—
247	#687	—	2	4	no	—
248	#686	—	2	2	no	—
249	C₄⋊Dic₅	C₃×D₄	1	2	yes	—
250	#683	—	2	4	no	—
251	C₄×Dic₅	C₂³×C₃	1	2	yes	—
252	C₂×#168	C₃×D₄	1	4	yes	complemented
253	C₂×#168	C₂³×C₃	1	1	yes	characteristic
254	C₂×#168	C₂³×C₃	1	1	yes	characteristic
255	Dic₂₀	—	2	4	no	—
256	#677	—	2	4	no	—
257	C₂×#137	—	5	1	no	—
258	C₂×AGL(1,ℤ/8)	C₃×D₅	1	1	yes	characteristic, complemented
259	C₂×#135	—	5	1	no	—
260	C₂²×SD₁₆	—	5	1	no	—
261	#536	—	5	1	no	—
262	#535	—	5	1	no	—
263	#497	—	5	2	no	—
264	#496	—	5	2	no	—
265	#495	—	5	2	no	—
266	#492	—	5	2	no	—
267	#405	—	5	1	no	—
268	C₂²×C₃×C₅	—	2	2	no	—
269	C₂²×C₃×C₅	—	4	1	no	—
270	C₂²×C₃×C₅	—	4	2	no	—
271	C₂²×C₃×C₅	—	4	4	no	—
272	C₂²×C₃×C₅	—	4	2	no	—
273	C₂²×C₃×C₅	—	8	4	no	—
274	C₂²×C₃×C₅	#127	1	2	yes	—
275	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₃×D₅	—	4	1	no	—
277	C₂×C₃×D₅	—	4	2	no	—
278	C₃×C₄×C₅	—	4	1	no	—
279	C₃×C₄×C₅	#127	1	2	yes	—
280	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
281	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
282	C₃×Dic₅	—	2	4	no	—
283	C₃×Dic₅	—	4	2	no	—
284	C₃×Dic₅	—	4	1	no	—
285	C₂⁴×C₃	—	2	1	no	—
286	C₃×#41	—	2	2	no	—
287	C₃×#41	—	2	2	no	—
288	C₃×#41	—	10	2	no	—
289	C₃×#41	—	10	2	no	—
290	C₂×C₃×Q₈	—	5	1	no	—
291	C₂×C₃×Q₈	—	5	2	no	—
292	C₂×C₃×Q₈	—	10	1	no	—
293	C₂×C₃×Q₈	—	10	2	no	—
294	C₂×C₃×Q₈	—	10	2	no	—
295	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
296	C₂×C₃×D₄	—	2	1	no	—
297	C₂×C₃×D₄	—	2	2	no	—
298	C₂×C₃×D₄	—	2	1	no	—
299	C₂×C₃×D₄	—	2	2	no	—
300	C₂×C₃×D₄	—	5	1	no	—
301	C₂×C₃×D₄	—	10	4	no	—
302	C₂×C₃×D₄	—	10	1	no	—
303	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
304	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
305	C₂²×C₃×C₄	—	2	1	no	—
306	C₂²×C₃×C₄	—	10	1	no	—
307	C₂²×C₃×C₄	—	10	1	no	—
308	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
309	C₃×Q₁₆	—	10	2	no	—
310	C₃×Q₁₆	—	10	4	no	—
311	C₃×SD₁₆	—	2	4	no	—
312	C₃×SD₁₆	—	10	4	no	—
313	C₃×SD₁₆	—	10	4	no	—
314	C₃×SD₁₆	—	10	2	no	—
315	C₃×SD₁₆	—	10	2	no	—
316	C₃×SD₁₆	—	10	4	no	—
317	C₃×D₈	—	2	4	no	—
318	C₃×D₈	—	10	2	no	—
319	C₃×M₁₆	C₂²⋊D₅	1	4	yes	complemented
320	C₂×C₃×C₈	—	5	4	no	—
321	C₂×C₃×C₈	—	5	1	no	—
322	C₂×C₃×C₈	—	5	1	no	—
323	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
324	C₃×C₄⋊C₄	—	5	2	no	—
325	C₃×C₄⋊C₄	—	10	4	no	—
326	C₃×C₂²⋊C₄	—	5	2	no	—
327	C₃×C₂²⋊C₄	—	10	4	no	—
328	C₃×C₂²⋊C₄	—	10	4	no	—
329	C₃×C₄²	—	5	2	no	—
330	C₂³×C₅	—	2	1	no	—
331	C₂³×C₅	—	2	2	no	—
332	C₂³×C₅	—	4	2	no	—
333	C₂³×C₅	—	8	2	no	—
334	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
335	C₂²×D₅	—	2	1	no	—
336	C₅×Q₈	—	2	1	no	—
337	C₅×Q₈	—	2	1	no	—
338	C₅×D₄	—	2	1	no	—
339	C₅×D₄	—	2	2	no	—
340	C₅×D₄	—	2	1	no	—
341	C₅×D₄	—	2	2	no	—
342	C₅×D₄	—	4	2	no	—
343	C₅×D₄	—	4	2	no	—
344	C₂×C₄×C₅	—	2	1	no	—
345	C₂×C₄×C₅	—	4	2	no	—
346	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
347	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
348	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
349	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
350	C₂²⋊D₅	—	4	2	no	—
351	C₂²⋊D₅	—	8	4	no	—
352	C₂×Dic₅	—	2	2	no	—
353	C₂×Dic₅	—	2	1	no	—
354	C₂×Dic₅	—	4	2	no	—
355	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
356	D₂₀	—	2	1	no	—
357	D₂₀	—	2	1	no	—
358	C₄×D₅	—	4	2	no	—
359	Dic₁₀	—	2	2	no	—
360	Dic₁₀	—	2	1	no	—
361	Dic₁₀	—	2	2	no	—
362	Dic₁₀	—	2	1	no	—
363	Dic₁₀	—	4	2	no	—
364	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
365	#168	C₂×C₃×D₄	1	2	yes	—
366	#168	C₂×C₃×D₄	1	2	yes	—
367	C₂×#41	—	5	1	no	—
368	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
369	C₂²×Q₈	—	5	1	no	—
370	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
371	#137	—	10	4	no	—
372	AGL(1,ℤ/8)	—	2	4	no	—
373	#135	—	10	4	no	—
374	C₂×Q₁₆	—	5	1	no	—
375	C₂×Q₁₆	—	5	2	no	—
376	C₂×SD₁₆	—	5	1	no	—
377	C₂×SD₁₆	—	5	2	no	—
378	C₂×SD₁₆	—	5	2	no	—
379	C₂×SD₁₆	—	5	1	no	—
380	C₂×SD₁₆	—	5	2	no	—
381	C₂×SD₁₆	—	10	4	no	—
382	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	—
383	C₂×D₈	—	5	1	no	—
384	C₂×D₈	C₂×C₃×D₅	1	2	yes	—
385	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
386	C₂²×C₈	—	5	1	no	—
387	C₄⋊Q₈	—	5	2	no	—
388	#127	—	5	2	no	—
389	#124	—	5	2	no	—
390	#124	—	5	2	no	—
391	#123	—	10	2	no	—
392	C₂²⋊Q₈	—	10	2	no	—
393	#121	—	10	2	no	—
394	#120	—	10	2	no	—
395	#117	—	5	1	no	—
396	#97	—	5	2	no	—
397	C₄×C₈	—	5	2	no	—
398	C₂×C₃×C₅	—	2	2	no	—
399	C₂×C₃×C₅	—	8	1	no	—
400	C₂×C₃×C₅	—	8	2	no	—
401	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
402	C₂×C₃×C₅	#577	1	2	yes	—
403	C₃×D₅	—	8	1	no	—
404	C₂³×C₃	—	2	1	no	—
405	C₂³×C₃	—	2	2	no	—
406	C₂³×C₃	—	4	2	no	—
407	C₂³×C₃	—	8	2	no	—
408	C₂³×C₃	—	10	1	no	—
409	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
410	C₃×Q₈	—	2	1	no	—
411	C₃×Q₈	—	2	1	no	—
412	C₃×Q₈	—	10	2	no	—
413	C₃×Q₈	—	10	1	no	—
414	C₃×Q₈	—	10	2	no	—
415	C₃×Q₈	—	10	1	no	—
416	C₃×Q₈	—	20	2	no	—
417	C₃×D₄	—	2	1	no	—
418	C₃×D₄	—	2	2	no	—
419	C₃×D₄	—	2	1	no	—
420	C₃×D₄	—	2	2	no	—
421	C₃×D₄	—	4	2	no	—
422	C₃×D₄	—	4	2	no	—
423	C₃×D₄	—	10	1	no	—
424	C₃×D₄	—	10	1	no	—
425	C₃×D₄	—	20	2	no	—
426	C₃×D₄	—	40	4	no	—
427	C₂×C₃×C₄	—	2	1	no	—
428	C₂×C₃×C₄	—	4	2	no	—
429	C₂×C₃×C₄	—	5	4	no	—
430	C₂×C₃×C₄	—	10	1	no	—
431	C₂×C₃×C₄	—	10	2	no	—
432	C₂×C₃×C₄	—	20	2	no	—
433	C₂×C₃×C₄	—	20	2	no	—
434	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
435	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
436	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
437	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
438	C₃×C₈	—	5	2	no	—
439	C₃×C₈	—	5	2	no	—
440	C₃×C₈	C₂×C₂²⋊D₅	1	4	yes	—
441	C₂²×C₅	—	2	2	no	—
442	C₂²×C₅	—	4	4	no	—
443	C₂²×C₅	—	4	2	no	—
444	C₂²×C₅	—	4	1	no	—
445	C₂²×C₅	—	4	2	no	—
446	C₂²×C₅	—	8	4	no	—
447	C₂²×C₅	C₃×#127	1	2	yes	—
448	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
449	C₂×D₅	—	4	2	no	—
450	C₂×D₅	—	4	1	no	—
451	C₄×C₅	—	4	1	no	—
452	C₄×C₅	C₃×#127	1	2	yes	—
453	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
454	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
455	Dic₅	—	2	4	no	—
456	Dic₅	—	4	2	no	—
457	Dic₅	—	4	1	no	—
458	C₂⁴	—	2	1	no	—
459	#41	—	2	2	no	—
460	#41	—	2	2	no	—
461	#41	—	10	2	no	—
462	#41	—	10	2	no	—
463	C₂×Q₈	—	5	1	no	—
464	C₂×Q₈	—	5	2	no	—
465	C₂×Q₈	—	10	1	no	—
466	C₂×Q₈	—	10	2	no	—
467	C₂×Q₈	—	10	2	no	—
468	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	2	no	—
473	C₂×D₄	—	5	1	no	—
474	C₂×D₄	—	10	4	no	—
475	C₂×D₄	—	10	1	no	—
476	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
477	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	10	1	no	—
480	C₂²×C₄	—	10	1	no	—
481	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
482	Q₁₆	—	10	2	no	—
483	Q₁₆	—	10	4	no	—
484	SD₁₆	—	2	4	no	—
485	SD₁₆	—	10	4	no	—
486	SD₁₆	—	10	4	no	—
487	SD₁₆	—	10	2	no	—
488	SD₁₆	—	10	2	no	—
489	SD₁₆	—	10	4	no	—
490	D₈	—	2	4	no	—
491	D₈	—	10	2	no	—
492	M₁₆	C₃×C₂²⋊D₅	1	4	yes	complemented
493	C₂×C₈	—	5	4	no	—
494	C₂×C₈	—	5	1	no	—
495	C₂×C₈	—	5	1	no	—
496	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
497	C₄⋊C₄	—	5	2	no	—
498	C₄⋊C₄	—	10	4	no	—
499	C₂²⋊C₄	—	5	2	no	—
500	C₂²⋊C₄	—	10	4	no	—
501	C₂²⋊C₄	—	10	4	no	—
502	C₄²	—	5	2	no	—
503	C₃×C₅	#3154	1	1	yes	characteristic, complemented, Hall
504	C₂²×C₃	—	2	2	no	—
505	C₂²×C₃	—	4	4	no	—
506	C₂²×C₃	—	4	2	no	—
507	C₂²×C₃	—	4	1	no	—
508	C₂²×C₃	—	4	2	no	—
509	C₂²×C₃	—	8	4	no	—
510	C₂²×C₃	—	20	2	no	—
511	C₂²×C₃	—	20	1	no	—
512	C₂²×C₃	#4086	1	2	yes	—
513	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
514	C₃×C₄	—	4	1	no	—
515	C₃×C₄	—	10	4	no	—
516	C₃×C₄	—	20	1	no	—
517	C₃×C₄	—	20	2	no	—
518	C₃×C₄	#4086	1	2	yes	—
519	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
520	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
521	C₂×C₅	—	2	2	no	—
522	C₂×C₅	—	8	2	no	—
523	C₂×C₅	—	8	1	no	—
524	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
525	C₂×C₅	C₃×#577	1	2	yes	—
526	D₅	—	8	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	4	2	no	—
530	C₂³	—	8	2	no	—
531	C₂³	—	10	1	no	—
532	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
533	Q₈	—	2	1	no	—
534	Q₈	—	2	1	no	—
535	Q₈	—	10	2	no	—
536	Q₈	—	10	1	no	—
537	Q₈	—	10	2	no	—
538	Q₈	—	10	1	no	—
539	Q₈	—	20	2	no	—
540	D₄	—	2	1	no	—
541	D₄	—	2	2	no	—
542	D₄	—	2	1	no	—
543	D₄	—	2	2	no	—
544	D₄	—	4	2	no	—
545	D₄	—	4	2	no	—
546	D₄	—	10	1	no	—
547	D₄	—	10	1	no	—
548	D₄	—	20	2	no	—
549	D₄	—	40	4	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	5	4	no	—
553	C₂×C₄	—	10	1	no	—
554	C₂×C₄	—	10	2	no	—
555	C₂×C₄	—	20	2	no	—
556	C₂×C₄	—	20	2	no	—
557	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
558	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
559	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
560	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
561	C₈	—	5	2	no	—
562	C₈	—	5	2	no	—
563	C₈	C₂×C₃×C₂²⋊D₅	1	4	yes	—
564	C₂×C₃	—	2	2	no	—
565	C₂×C₃	—	8	2	no	—
566	C₂×C₃	—	8	1	no	—
567	C₂×C₃	—	40	1	no	—
568	C₂×C₃	#66109	1	2	yes	—
569	C₂×C₃	C₂×#4086	1	1	yes	characteristic
570	C₅	C₃×#3154	1	1	yes	characteristic, complemented, Sylow
571	C₂²	—	2	2	no	—
572	C₂²	—	4	4	no	—
573	C₂²	—	4	2	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	2	no	—
576	C₂²	—	8	4	no	—
577	C₂²	—	20	2	no	—
578	C₂²	—	20	1	no	—
579	C₂²	C₃×#4086	1	2	yes	—
580	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
581	C₄	—	4	1	no	—
582	C₄	—	10	4	no	—
583	C₄	—	20	1	no	—
584	C₄	—	20	2	no	—
585	C₄	C₃×#4086	1	2	yes	—
586	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
587	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
588	C₃	#10615670	1	1	yes	characteristic, direct product factor, Sylow
589	C₂	—	2	2	no	—
590	C₂	—	8	2	no	—
591	C₂	—	8	1	no	—
592	C₂	—	40	1	no	—
593	C₂	C₃×#66109	1	2	yes	—
594	C₂	C₂×C₃×#4086	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₃×AGL(1,ℤ/8)	D₅
hypocenter	C₅	C₃×#3154
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
2. C₃×#66159	C₂	semidirect
3. C₂×C₃×#4096	C₂	semidirect
4. C₃×#66139	C₂	semidirect
5. C₂²×C₃×#687	C₂	semidirect
6. C₂×C₃×#4055	C₂	semidirect
7. C₃×#65464	C₂	semidirect
8. C₃×#65456	C₂	semidirect
9. C₃×#65444	C₂	semidirect
10. C₃×#65443	C₂	semidirect
11. C₃×#65411	C₂	semidirect
12. #10615670	C₃	direct (N × H)
23. C₃×#4090	C₂²	semidirect
24. C₂×C₃×#689	C₂²	semidirect
25. C₂×C₃×#688	C₂²	semidirect
29. C₃×#4082	C₂²	semidirect
34. C₂×C₃×#687	C₂²	semidirect
35. C₂×C₃×#686	C₂²	semidirect
40. C₂×C₃×Dic₂₀	C₂²	semidirect
41. C₂×C₃×#677	C₂²	semidirect
42. C₃×#3947	C₂²	semidirect
43. C₃×C₈×Dic₅	C₂²	semidirect
45. C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
46. #66159	C₂×C₃	semidirect
47. C₂×#4096	C₂×C₃	semidirect
48. #66139	C₂×C₃	semidirect
49. C₂²×#687	C₂×C₃	semidirect
50. C₂×#4055	C₂×C₃	semidirect
51. #65464	C₂×C₃	semidirect
52. #65456	C₂×C₃	semidirect
53. #65444	C₂×C₃	semidirect
54. #65443	C₂×C₃	semidirect
55. #65411	C₂×C₃	semidirect
82. C₃×C₅×M₁₆	D₄	semidirect
96. C₂×C₃×#168	D₄	semidirect
102. C₂×C₃×AGL(1,ℤ/8)	D₅	semidirect
122. #4090	C₂²×C₃	semidirect
123. C₂×#689	C₂²×C₃	semidirect
124. C₂×#688	C₂²×C₃	semidirect
128. #4082	C₂²×C₃	semidirect
133. C₂×#687	C₂²×C₃	semidirect
134. C₂×#686	C₂²×C₃	semidirect
139. C₂×Dic₂₀	C₂²×C₃	semidirect
140. C₂×#677	C₂²×C₃	semidirect
141. #3947	C₂²×C₃	semidirect
142. C₈×Dic₅	C₂²×C₃	semidirect
238. C₅×M₁₆	C₃×D₄	semidirect
252. C₂×#168	C₃×D₄	semidirect
258. C₂×AGL(1,ℤ/8)	C₃×D₅	semidirect
319. C₃×M₁₆	C₂²⋊D₅	semidirect
492. M₁₆	C₃×C₂²⋊D₅	semidirect
503. C₃×C₅	#3154	semidirect
570. C₅	C₃×#3154	semidirect
588. C₃	#10615670	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×AGL(1,ℤ/8)	2
C₃×#66159	2
C₂×C₃×#4096	2
C₃×#66139	2
C₂²×C₃×#687	2
C₂×C₃×#4055	2
C₃×#65464	2
C₃×#65456	2
C₃×#65444	2
C₃×#65443	2
C₃×#65411	2
#10615670	3
C₃×#3154	5

Subgroups — C3×#10615670 #14439388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615670 #14439388