Subgroups — C₅×#83938 #14439276

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 604 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	C₅×#5832	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#951	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#936	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#932	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#909	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5168	C₂	1	2	yes	maximal, complemented
8	C₅×#5167	C₂	1	2	yes	maximal, complemented
9	C₅×#5155	C₂	1	2	yes	maximal, complemented
10	C₅×#5154	C₂	1	2	yes	maximal, complemented
11	C₅×Dic₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3153	—	3	1	no	maximal, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₅×#235	C₂²	1	1	yes	characteristic
16	C₂²×C₅×Dic₆	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	C₂×C₅×#217	—	2	2	no	—
22	C₅×#951	—	2	4	no	—
23	C₅×#947	C₂²	1	1	yes	characteristic, complemented
24	C₅×#944	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₅×#216	C₂²	1	2	yes	complemented
26	C₅×#940	C₂²	1	1	yes	characteristic, complemented
27	C₅×#939	—	2	2	no	—
28	C₅×#936	—	2	2	no	—
29	C₅×#936	C₂²	1	2	yes	—
30	C₅×#936	C₂²	1	2	yes	—
31	C₅×#936	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₅×#214	C₂²	1	2	yes	—
33	C₂×C₅×#214	C₂²	1	2	yes	complemented
34	C₅×#932	—	2	4	no	—
35	C₂×C₅×#213	C₂²	1	2	yes	—
36	C₄×C₅×#67	—	2	2	no	—
37	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
38	C₂×C₅×#208	C₂²	1	1	yes	characteristic
39	C₅×#909	—	2	4	no	—
40	C₂×C₅×Dic₁₂	C₂²	1	2	yes	complemented
41	C₂×C₅×#204	C₂²	1	2	yes	complemented
42	C₅×#815	C₂²	1	2	yes	complemented
43	C₅×C₈×Dic₃	C₂²	1	2	yes	complemented
44	#83938	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×#137	—	3	1	no	—
46	C₂×C₅×#137	—	3	1	no	—
47	C₂×C₅×AGL(1,ℤ/8)	—	3	1	no	—
48	C₂×C₅×AGL(1,ℤ/8)	D₃	1	1	yes	characteristic, complemented
49	C₅×#532	—	3	1	no	—
50	C₂×C₅×#124	—	3	1	no	—
51	C₅×#497	—	3	2	no	—
52	C₅×#496	—	3	2	no	—
53	C₅×#495	—	3	2	no	—
54	C₅×#495	—	3	2	no	—
55	C₄×C₅×M₁₆	—	3	1	no	—
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	2	yes	—
65	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	—	2	1	no	—
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₅×#67	—	2	1	no	—
69	C₂×C₅×#67	—	2	2	no	—
70	C₂²×C₅×Dic₃	—	2	1	no	—
71	C₂²×C₅×Dic₃	D₄	1	2	yes	—
72	C₅×#235	—	2	2	no	—
73	C₅×#235	—	2	2	no	—
74	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
75	C₂×C₄×C₅×D₃	—	2	1	no	—
76	C₂×C₅×Dic₆	—	2	2	no	—
77	C₂×C₅×Dic₆	—	2	2	no	—
78	C₂×C₅×Dic₆	—	2	1	no	—
79	C₂×C₅×Dic₆	C₂³	1	2	yes	—
80	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
81	C₃×C₅×SD₁₆	—	2	4	no	—
82	C₃×C₅×D₈	—	2	4	no	—
83	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
84	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
85	C₅×#217	—	2	2	no	—
86	C₅×#217	—	2	4	no	—
87	C₅×#217	—	2	4	no	—
88	C₅×#216	—	2	4	no	—
89	C₅×#214	—	2	4	no	—
90	C₅×#214	—	2	4	no	—
91	C₅×#213	—	2	4	no	—
92	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
93	C₅×Dic₃⋊C₄	—	2	2	no	—
94	C₄×C₅×Dic₃	D₄	1	2	yes	—
95	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
96	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
97	C₅×#208	D₄	1	4	yes	complemented
98	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
99	C₅×Dic₁₂	—	2	4	no	—
100	C₅×#204	—	2	4	no	—
101	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic, complemented
102	#5832	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂×#951	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂×#936	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂×#932	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂×#909	C₂×C₅	1	1	yes	characteristic, complemented
107	#5168	C₂×C₅	1	2	yes	complemented
108	#5167	C₂×C₅	1	2	yes	complemented
109	#5155	C₂×C₅	1	2	yes	complemented
110	#5154	C₂×C₅	1	2	yes	complemented
111	Dic₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×C₅×#41	—	3	1	no	—
113	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
114	C₂²×C₅×Q₈	—	3	1	no	—
115	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
116	C₅×#137	—	6	4	no	—
117	C₅×#137	—	6	4	no	—
118	C₅×AGL(1,ℤ/8)	—	2	4	no	—
119	C₅×AGL(1,ℤ/8)	—	6	4	no	—
120	C₂×C₅×Q₁₆	—	3	2	no	—
121	C₂×C₅×Q₁₆	—	3	2	no	—
122	C₂×C₅×SD₁₆	—	3	2	no	—
123	C₂×C₅×SD₁₆	—	3	2	no	—
124	C₂×C₅×SD₁₆	—	3	2	no	—
125	C₂×C₅×SD₁₆	C₂×D₃	1	2	yes	—
126	C₂×C₅×D₈	—	3	2	no	—
127	C₂×C₅×D₈	C₂×D₃	1	2	yes	—
128	C₂×C₅×M₁₆	—	3	1	no	—
129	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
130	C₅×C₄⋊Q₈	—	3	1	no	—
131	C₅×#127	—	3	1	no	—
132	C₅×#124	—	3	1	no	—
133	C₅×#124	—	3	2	no	—
134	C₅×#124	—	3	2	no	—
135	C₅×#124	—	3	1	no	—
136	C₅×#124	—	6	2	no	—
137	C₅×#121	—	6	2	no	—
138	C₄×C₅×D₄	—	6	2	no	—
139	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
140	C₂×C₄²×C₅	—	3	1	no	—
141	C₅×#97	—	3	2	no	—
142	C₄×C₅×C₈	—	3	2	no	—
143	#3153	—	3	1	no	Sylow
144	C₂³×C₃×C₅	—	2	2	no	—
145	C₂³×C₃×C₅	—	2	1	no	—
146	C₂³×C₃×C₅	—	4	4	no	—
147	C₂³×C₃×C₅	—	4	2	no	—
148	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₅×D₃	—	2	1	no	—
150	C₃×C₅×Q₈	—	2	1	no	—
151	C₃×C₅×Q₈	—	2	1	no	—
152	C₃×C₅×D₄	—	2	2	no	—
153	C₃×C₅×D₄	—	2	1	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	C₅×#67	—	4	4	no	—
165	C₅×#67	—	4	2	no	—
166	C₂×C₅×Dic₃	—	2	1	no	—
167	C₂×C₅×Dic₃	—	2	2	no	—
168	C₂×C₅×Dic₃	—	4	2	no	—
169	C₂×C₅×Dic₃	—	4	2	no	—
170	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
171	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
172	C₅×D₁₂	—	2	1	no	—
173	C₅×D₁₂	—	2	1	no	—
174	C₄×C₅×D₃	—	4	2	no	—
175	C₅×Dic₆	—	2	2	no	—
176	C₅×Dic₆	—	2	1	no	—
177	C₅×Dic₆	—	2	1	no	—
178	C₅×Dic₆	—	2	2	no	—
179	C₅×Dic₆	—	4	2	no	—
180	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
181	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
182	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
183	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
184	C₂×#235	C₂²×C₅	1	1	yes	characteristic
185	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
186	C₃×AGL(1,ℤ/8)	—	2	4	no	—
187	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
188	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
189	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
190	C₂×#217	—	2	2	no	—
191	#951	—	2	4	no	—
192	#947	C₂²×C₅	1	1	yes	characteristic, complemented
193	#944	C₂²×C₅	1	1	yes	characteristic, complemented
194	C₂×#216	C₂²×C₅	1	2	yes	complemented
195	#940	C₂²×C₅	1	1	yes	characteristic, complemented
196	#939	—	2	2	no	—
197	#936	—	2	2	no	—
198	#936	C₂²×C₅	1	2	yes	—
199	#936	C₂²×C₅	1	2	yes	—
200	#936	C₂²×C₅	1	1	yes	characteristic, complemented
201	C₂×#214	C₂²×C₅	1	2	yes	—
202	C₂×#214	C₂²×C₅	1	2	yes	complemented
203	#932	—	2	4	no	—
204	C₂×#213	C₂²×C₅	1	2	yes	—
205	C₄×#67	—	2	2	no	—
206	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
207	C₂×#208	C₂²×C₅	1	1	yes	characteristic
208	#909	—	2	4	no	—
209	C₂×Dic₁₂	C₂²×C₅	1	2	yes	complemented
210	C₂×#204	C₂²×C₅	1	2	yes	complemented
211	#815	C₂²×C₅	1	2	yes	complemented
212	C₈×Dic₃	C₂²×C₅	1	2	yes	complemented
213	C₂⁴×C₅	—	2	1	no	—
214	C₅×#41	—	2	2	no	—
215	C₅×#41	—	2	2	no	—
216	C₅×#41	—	6	2	no	—
217	C₅×#41	—	6	2	no	—
218	C₂×C₅×Q₈	—	3	2	no	—
219	C₂×C₅×Q₈	—	3	1	no	—
220	C₂×C₅×Q₈	—	6	1	no	—
221	C₂×C₅×Q₈	—	6	2	no	—
222	C₂×C₅×Q₈	—	6	2	no	—
223	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
224	C₂×C₅×D₄	—	2	1	no	—
225	C₂×C₅×D₄	—	2	2	no	—
226	C₂×C₅×D₄	—	2	1	no	—
227	C₂×C₅×D₄	—	2	2	no	—
228	C₂×C₅×D₄	—	3	1	no	—
229	C₂×C₅×D₄	—	6	2	no	—
230	C₂×C₅×D₄	—	6	1	no	—
231	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
232	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
233	C₂²×C₄×C₅	—	2	1	no	—
234	C₂²×C₄×C₅	—	3	2	no	—
235	C₂²×C₄×C₅	—	6	1	no	—
236	C₂²×C₄×C₅	—	6	1	no	—
237	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
238	C₅×Q₁₆	—	6	4	no	—
239	C₅×Q₁₆	—	6	4	no	—
240	C₅×SD₁₆	—	2	4	no	—
241	C₅×SD₁₆	—	6	4	no	—
242	C₅×SD₁₆	—	6	4	no	—
243	C₅×SD₁₆	—	6	4	no	—
244	C₅×D₈	—	2	4	no	—
245	C₅×D₈	—	6	4	no	—
246	C₅×M₁₆	—	3	4	no	—
247	C₅×M₁₆	#67	1	4	yes	complemented
248	C₂×C₅×C₈	—	3	2	no	—
249	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
250	C₅×C₄⋊C₄	—	6	2	no	—
251	C₅×C₂²⋊C₄	—	6	2	no	—
252	C₅×C₂²⋊C₄	—	6	4	no	—
253	C₅×C₂²⋊C₄	—	6	4	no	—
254	C₅×C₂²⋊C₄	—	6	2	no	—
255	C₄²×C₅	—	3	2	no	—
256	C₄²×C₅	—	3	1	no	—
257	C₄²×C₅	—	3	1	no	—
258	C₂×#137	—	3	1	no	—
259	C₂×#137	—	3	1	no	—
260	C₂×AGL(1,ℤ/8)	—	3	1	no	—
261	C₂×AGL(1,ℤ/8)	C₅×D₃	1	1	yes	characteristic, complemented
262	#532	—	3	1	no	—
263	C₂×#124	—	3	1	no	—
264	#497	—	3	2	no	—
265	#496	—	3	2	no	—
266	#495	—	3	2	no	—
267	#495	—	3	2	no	—
268	C₄×M₁₆	—	3	1	no	—
269	C₂²×C₃×C₅	—	2	2	no	—
270	C₂²×C₃×C₅	—	4	1	no	—
271	C₂²×C₃×C₅	—	4	2	no	—
272	C₂²×C₃×C₅	—	4	2	no	—
273	C₂²×C₃×C₅	—	4	4	no	—
274	C₂²×C₃×C₅	—	8	4	no	—
275	C₂²×C₃×C₅	#127	1	2	yes	—
276	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₅×D₃	—	4	1	no	—
278	C₂×C₅×D₃	—	4	2	no	—
279	C₃×C₄×C₅	—	4	1	no	—
280	C₃×C₄×C₅	#127	1	2	yes	—
281	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
282	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
283	C₅×Dic₃	—	2	2	no	—
284	C₅×Dic₃	—	2	2	no	—
285	C₅×Dic₃	—	4	2	no	—
286	C₅×Dic₃	—	4	1	no	—
287	C₂⁴×C₃	—	2	1	no	—
288	C₃×#41	—	2	2	no	—
289	C₃×#41	—	2	2	no	—
290	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
291	C₂×C₃×D₄	—	2	1	no	—
292	C₂×C₃×D₄	—	2	2	no	—
293	C₂×C₃×D₄	—	2	2	no	—
294	C₂×C₃×D₄	—	2	1	no	—
295	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
296	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
297	C₂²×C₃×C₄	—	2	1	no	—
298	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
299	C₂×#67	—	2	1	no	—
300	C₂×#67	—	2	2	no	—
301	C₂²×Dic₃	—	2	1	no	—
302	C₂²×Dic₃	C₅×D₄	1	2	yes	—
303	#235	—	2	2	no	—
304	#235	—	2	2	no	—
305	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
306	C₂×C₄×D₃	—	2	1	no	—
307	C₂×Dic₆	—	2	2	no	—
308	C₂×Dic₆	—	2	2	no	—
309	C₂×Dic₆	—	2	1	no	—
310	C₂×Dic₆	C₂³×C₅	1	2	yes	—
311	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
312	C₃×SD₁₆	—	2	4	no	—
313	C₃×D₈	—	2	4	no	—
314	C₃×M₁₆	C₅×D₄	1	4	yes	complemented
315	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
316	#217	—	2	2	no	—
317	#217	—	2	4	no	—
318	#217	—	2	4	no	—
319	#216	—	2	4	no	—
320	#214	—	2	4	no	—
321	#214	—	2	4	no	—
322	#213	—	2	4	no	—
323	(C₂×D₃)⋊C₄	—	2	2	no	—
324	Dic₃⋊C₄	—	2	2	no	—
325	C₄×Dic₃	C₅×D₄	1	2	yes	—
326	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
327	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
328	#208	C₅×D₄	1	4	yes	complemented
329	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
330	Dic₁₂	—	2	4	no	—
331	#204	—	2	4	no	—
332	C₂³×C₅	—	2	2	no	—
333	C₂³×C₅	—	2	1	no	—
334	C₂³×C₅	—	4	4	no	—
335	C₂³×C₅	—	4	2	no	—
336	C₂³×C₅	—	6	1	no	—
337	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
338	C₅×Q₈	—	2	1	no	—
339	C₅×Q₈	—	2	1	no	—
340	C₅×Q₈	—	6	1	no	—
341	C₅×Q₈	—	6	2	no	—
342	C₅×Q₈	—	6	2	no	—
343	C₅×Q₈	—	6	1	no	—
344	C₅×Q₈	—	12	2	no	—
345	C₅×D₄	—	2	2	no	—
346	C₅×D₄	—	2	1	no	—
347	C₅×D₄	—	2	1	no	—
348	C₅×D₄	—	2	2	no	—
349	C₅×D₄	—	4	2	no	—
350	C₅×D₄	—	4	2	no	—
351	C₅×D₄	—	6	1	no	—
352	C₅×D₄	—	6	1	no	—
353	C₅×D₄	—	12	4	no	—
354	C₅×D₄	—	12	2	no	—
355	C₂×C₄×C₅	—	2	1	no	—
356	C₂×C₄×C₅	—	3	2	no	—
357	C₂×C₄×C₅	—	3	2	no	—
358	C₂×C₄×C₅	—	4	2	no	—
359	C₂×C₄×C₅	—	6	2	no	—
360	C₂×C₄×C₅	—	6	1	no	—
361	C₂×C₄×C₅	—	12	2	no	—
362	C₂×C₄×C₅	—	12	2	no	—
363	C₂×C₄×C₅	—	12	2	no	—
364	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
365	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
366	C₂×C₄×C₅	C₂×#67	1	2	yes	—
367	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
368	C₅×C₈	—	3	4	no	—
369	C₅×C₈	C₂×#67	1	4	yes	—
370	C₂×#41	—	3	1	no	—
371	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
372	C₂²×Q₈	—	3	1	no	—
373	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
374	#137	—	6	4	no	—
375	#137	—	6	4	no	—
376	AGL(1,ℤ/8)	—	2	4	no	—
377	AGL(1,ℤ/8)	—	6	4	no	—
378	C₂×Q₁₆	—	3	2	no	—
379	C₂×Q₁₆	—	3	2	no	—
380	C₂×SD₁₆	—	3	2	no	—
381	C₂×SD₁₆	—	3	2	no	—
382	C₂×SD₁₆	—	3	2	no	—
383	C₂×SD₁₆	C₂×C₅×D₃	1	2	yes	—
384	C₂×D₈	—	3	2	no	—
385	C₂×D₈	C₂×C₅×D₃	1	2	yes	—
386	C₂×M₁₆	—	3	1	no	—
387	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
388	C₄⋊Q₈	—	3	1	no	—
389	#127	—	3	1	no	—
390	#124	—	3	1	no	—
391	#124	—	3	2	no	—
392	#124	—	3	2	no	—
393	#124	—	3	1	no	—
394	#124	—	6	2	no	—
395	#121	—	6	2	no	—
396	C₄×D₄	—	6	2	no	—
397	C₂×C₂²⋊C₄	—	6	2	no	—
398	C₂×C₄²	—	3	1	no	—
399	#97	—	3	2	no	—
400	C₄×C₈	—	3	2	no	—
401	C₂×C₃×C₅	—	2	2	no	—
402	C₂×C₃×C₅	—	8	1	no	—
403	C₂×C₃×C₅	—	8	2	no	—
404	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
405	C₂×C₃×C₅	#575	1	2	yes	—
406	C₅×D₃	—	8	1	no	—
407	C₂³×C₃	—	2	2	no	—
408	C₂³×C₃	—	2	1	no	—
409	C₂³×C₃	—	4	4	no	—
410	C₂³×C₃	—	4	2	no	—
411	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
412	C₂²×D₃	—	2	1	no	—
413	C₃×Q₈	—	2	1	no	—
414	C₃×Q₈	—	2	1	no	—
415	C₃×D₄	—	2	2	no	—
416	C₃×D₄	—	2	1	no	—
417	C₃×D₄	—	2	1	no	—
418	C₃×D₄	—	2	2	no	—
419	C₃×D₄	—	4	2	no	—
420	C₃×D₄	—	4	2	no	—
421	C₂×C₃×C₄	—	2	1	no	—
422	C₂×C₃×C₄	—	4	2	no	—
423	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
424	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
425	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
426	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
427	#67	—	4	4	no	—
428	#67	—	4	2	no	—
429	C₂×Dic₃	—	2	1	no	—
430	C₂×Dic₃	—	2	2	no	—
431	C₂×Dic₃	—	4	2	no	—
432	C₂×Dic₃	—	4	2	no	—
433	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
434	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
435	D₁₂	—	2	1	no	—
436	D₁₂	—	2	1	no	—
437	C₄×D₃	—	4	2	no	—
438	Dic₆	—	2	2	no	—
439	Dic₆	—	2	1	no	—
440	Dic₆	—	2	1	no	—
441	Dic₆	—	2	2	no	—
442	Dic₆	—	4	2	no	—
443	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
444	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	—
445	C₂²×C₅	—	2	2	no	—
446	C₂²×C₅	—	4	2	no	—
447	C₂²×C₅	—	4	4	no	—
448	C₂²×C₅	—	4	1	no	—
449	C₂²×C₅	—	4	2	no	—
450	C₂²×C₅	—	8	4	no	—
451	C₂²×C₅	—	12	2	no	—
452	C₂²×C₅	—	12	1	no	—
453	C₂²×C₅	#940	1	2	yes	—
454	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
455	C₄×C₅	—	4	1	no	—
456	C₄×C₅	—	6	2	no	—
457	C₄×C₅	—	6	2	no	—
458	C₄×C₅	—	12	1	no	—
459	C₄×C₅	—	12	2	no	—
460	C₄×C₅	#940	1	2	yes	—
461	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
462	C₄×C₅	C₂²×#67	1	1	yes	characteristic
463	C₂⁴	—	2	1	no	—
464	#41	—	2	2	no	—
465	#41	—	2	2	no	—
466	#41	—	6	2	no	—
467	#41	—	6	2	no	—
468	C₂×Q₈	—	3	2	no	—
469	C₂×Q₈	—	3	1	no	—
470	C₂×Q₈	—	6	1	no	—
471	C₂×Q₈	—	6	2	no	—
472	C₂×Q₈	—	6	2	no	—
473	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	—	2	2	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	3	1	no	—
479	C₂×D₄	—	6	2	no	—
480	C₂×D₄	—	6	1	no	—
481	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
482	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	3	2	no	—
485	C₂²×C₄	—	6	1	no	—
486	C₂²×C₄	—	6	1	no	—
487	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
488	Q₁₆	—	6	4	no	—
489	Q₁₆	—	6	4	no	—
490	SD₁₆	—	2	4	no	—
491	SD₁₆	—	6	4	no	—
492	SD₁₆	—	6	4	no	—
493	SD₁₆	—	6	4	no	—
494	D₈	—	2	4	no	—
495	D₈	—	6	4	no	—
496	M₁₆	—	3	4	no	—
497	M₁₆	C₅×#67	1	4	yes	complemented
498	C₂×C₈	—	3	2	no	—
499	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
500	C₄⋊C₄	—	6	2	no	—
501	C₂²⋊C₄	—	6	2	no	—
502	C₂²⋊C₄	—	6	4	no	—
503	C₂²⋊C₄	—	6	4	no	—
504	C₂²⋊C₄	—	6	2	no	—
505	C₄²	—	3	2	no	—
506	C₄²	—	3	1	no	—
507	C₄²	—	3	1	no	—
508	C₃×C₅	#3153	1	1	yes	characteristic, complemented, Hall
509	C₂²×C₃	—	2	2	no	—
510	C₂²×C₃	—	4	1	no	—
511	C₂²×C₃	—	4	2	no	—
512	C₂²×C₃	—	4	2	no	—
513	C₂²×C₃	—	4	4	no	—
514	C₂²×C₃	—	8	4	no	—
515	C₂²×C₃	C₅×#127	1	2	yes	—
516	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
517	C₂×D₃	—	4	1	no	—
518	C₂×D₃	—	4	2	no	—
519	C₃×C₄	—	4	1	no	—
520	C₃×C₄	C₅×#127	1	2	yes	—
521	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
522	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
523	Dic₃	—	2	2	no	—
524	Dic₃	—	2	2	no	—
525	Dic₃	—	4	2	no	—
526	Dic₃	—	4	1	no	—
527	C₂×C₅	—	2	2	no	—
528	C₂×C₅	—	8	2	no	—
529	C₂×C₅	—	8	1	no	—
530	C₂×C₅	—	24	1	no	—
531	C₂×C₅	#5773	1	2	yes	—
532	C₂×C₅	C₂×#940	1	1	yes	characteristic
533	C₂³	—	2	2	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	4	4	no	—
536	C₂³	—	4	2	no	—
537	C₂³	—	6	1	no	—
538	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
539	Q₈	—	2	1	no	—
540	Q₈	—	2	1	no	—
541	Q₈	—	6	1	no	—
542	Q₈	—	6	2	no	—
543	Q₈	—	6	2	no	—
544	Q₈	—	6	1	no	—
545	Q₈	—	12	2	no	—
546	D₄	—	2	2	no	—
547	D₄	—	2	1	no	—
548	D₄	—	2	1	no	—
549	D₄	—	2	2	no	—
550	D₄	—	4	2	no	—
551	D₄	—	4	2	no	—
552	D₄	—	6	1	no	—
553	D₄	—	6	1	no	—
554	D₄	—	12	4	no	—
555	D₄	—	12	2	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	3	2	no	—
558	C₂×C₄	—	3	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	6	2	no	—
561	C₂×C₄	—	6	1	no	—
562	C₂×C₄	—	12	2	no	—
563	C₂×C₄	—	12	2	no	—
564	C₂×C₄	—	12	2	no	—
565	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
566	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
567	C₂×C₄	C₂×C₅×#67	1	2	yes	—
568	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
569	C₈	—	3	4	no	—
570	C₈	C₂×C₅×#67	1	4	yes	—
571	C₂×C₃	—	2	2	no	—
572	C₂×C₃	—	8	2	no	—
573	C₂×C₃	—	8	1	no	—
574	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
575	C₂×C₃	C₅×#575	1	2	yes	—
576	D₃	—	8	1	no	—
577	C₅	#83938	1	1	yes	characteristic, direct product factor, Sylow
578	C₂²	—	2	2	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	4	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	8	4	no	—
584	C₂²	—	12	2	no	—
585	C₂²	—	12	1	no	—
586	C₂²	C₅×#940	1	2	yes	—
587	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
588	C₄	—	4	1	no	—
589	C₄	—	6	2	no	—
590	C₄	—	6	2	no	—
591	C₄	—	12	1	no	—
592	C₄	—	12	2	no	—
593	C₄	C₅×#940	1	2	yes	—
594	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
595	C₄	C₂²×C₅×#67	1	1	yes	characteristic
596	C₃	C₅×#3153	1	1	yes	characteristic, complemented, Sylow
597	C₂	—	2	2	no	—
598	C₂	—	8	2	no	—
599	C₂	—	8	1	no	—
600	C₂	—	24	1	no	—
601	C₂	C₅×#5773	1	2	yes	—
602	C₂	C₂×C₅×#940	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×D₃×D₄
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₅×AGL(1,ℤ/8)	D₃
hypocenter	C₃	C₅×#3153
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×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. C₅×#5832	C₂	semidirect
3. C₂×C₅×#951	C₂	semidirect
4. C₂×C₅×#936	C₂	semidirect
5. C₂×C₅×#932	C₂	semidirect
6. C₂×C₅×#909	C₂	semidirect
7. C₅×#5168	C₂	semidirect
8. C₅×#5167	C₂	semidirect
9. C₅×#5155	C₂	semidirect
10. C₅×#5154	C₂	semidirect
11. C₅×Dic₃×M₁₆	C₂	semidirect
23. C₅×#947	C₂²	semidirect
24. C₅×#944	C₂²	semidirect
25. C₂×C₅×#216	C₂²	semidirect
26. C₅×#940	C₂²	semidirect
31. C₅×#936	C₂²	semidirect
33. C₂×C₅×#214	C₂²	semidirect
40. C₂×C₅×Dic₁₂	C₂²	semidirect
41. C₂×C₅×#204	C₂²	semidirect
42. C₅×#815	C₂²	semidirect
43. C₅×C₈×Dic₃	C₂²	semidirect
44. #83938	C₅	direct (N × H)
48. C₂×C₅×AGL(1,ℤ/8)	D₃	semidirect
83. C₃×C₅×M₁₆	D₄	semidirect
97. C₅×#208	D₄	semidirect
101. C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
102. #5832	C₂×C₅	semidirect
103. C₂×#951	C₂×C₅	semidirect
104. C₂×#936	C₂×C₅	semidirect
105. C₂×#932	C₂×C₅	semidirect
106. C₂×#909	C₂×C₅	semidirect
107. #5168	C₂×C₅	semidirect
108. #5167	C₂×C₅	semidirect
109. #5155	C₂×C₅	semidirect
110. #5154	C₂×C₅	semidirect
111. Dic₃×M₁₆	C₂×C₅	semidirect
192. #947	C₂²×C₅	semidirect
193. #944	C₂²×C₅	semidirect
194. C₂×#216	C₂²×C₅	semidirect
195. #940	C₂²×C₅	semidirect
200. #936	C₂²×C₅	semidirect
202. C₂×#214	C₂²×C₅	semidirect
209. C₂×Dic₁₂	C₂²×C₅	semidirect
210. C₂×#204	C₂²×C₅	semidirect
211. #815	C₂²×C₅	semidirect
212. C₈×Dic₃	C₂²×C₅	semidirect
247. C₅×M₁₆	#67	semidirect
261. C₂×AGL(1,ℤ/8)	C₅×D₃	semidirect
314. C₃×M₁₆	C₅×D₄	semidirect
328. #208	C₅×D₄	semidirect
497. M₁₆	C₅×#67	semidirect
508. C₃×C₅	#3153	semidirect
577. C₅	#83938	direct (N × H)
596. C₃	C₅×#3153	semidirect

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
C₅×#5832	2
C₂×C₅×#951	2
C₂×C₅×#936	2
C₂×C₅×#932	2
C₂×C₅×#909	2
C₅×#5168	2
C₅×#5167	2
C₅×#5155	2
C₅×#5154	2
C₅×Dic₃×M₁₆	2
C₅×#3153	3
#83938	5

Subgroups — C5×#83938 #14439276

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83938 #14439276