Subgroups — C₅×#79700 #14472076

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5569	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5568	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5185	C₂	1	1	yes	maximal, characteristic
5	C₅×#5182	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5028	C₂	1	1	yes	maximal, characteristic
7	C₅×#5022	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4890	C₂	1	1	yes	maximal, characteristic
9	C₅×#4877	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4800	C₂	1	1	yes	maximal, characteristic
11	C₅×#4792	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#4790	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#4788	C₂	1	1	yes	maximal, characteristic
14	C₅×#4697	C₂	1	1	yes	maximal, characteristic
15	C₅×C₈×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3364	—	3	1	no	maximal, Hall
17	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
18	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₅×#947	C₂²	1	1	yes	characteristic
21	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
22	C₅×Q₈×Dic₃	C₂²	1	1	yes	characteristic
23	C₅×#944	C₂²	1	1	yes	characteristic
24	C₂×C₅×#216	C₂²	1	1	yes	characteristic
25	C₂×C₅×#215	C₂²	1	1	yes	characteristic
26	C₅×#898	—	2	1	no	—
27	C₅×#896	—	2	1	no	—
28	C₅×#893	C₂²	1	1	yes	characteristic
29	C₅×#890	—	2	1	no	—
30	C₅×#890	C₂²	1	1	yes	characteristic
31	C₅×#888	—	2	1	no	—
32	C₅×#888	C₂²	1	1	yes	characteristic
33	C₅×#887	C₂²	1	1	yes	characteristic
34	C₅×#876	—	2	1	no	—
35	C₅×#875	C₂²	1	1	yes	characteristic
36	C₅×#872	—	2	1	no	—
37	C₅×#870	—	2	1	no	—
38	C₅×#870	C₂²	1	1	yes	characteristic
39	C₄×C₅×Dic₆	—	2	1	no	—
40	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
41	C₃×C₅×#107	C₂²	1	1	yes	characteristic
42	C₃×C₅×#103	C₂²	1	1	yes	characteristic
43	C₃×C₅×#103	C₂²	1	1	yes	characteristic
44	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
45	C₅×#835	C₂²	1	1	yes	characteristic
46	C₅×#835	C₂²	1	1	yes	characteristic
47	C₅×#821	C₂²	1	1	yes	characteristic
48	C₅×#821	C₂²	1	1	yes	characteristic
49	C₅×#816	C₂²	1	1	yes	characteristic
50	C₅×#816	C₂²	1	1	yes	characteristic
51	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
52	C₅×Dic₃⋊C₈	C₂²	1	1	yes	characteristic
53	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
54	C₅×C₈×Dic₃	C₂²	1	1	yes	characteristic
55	C₅×#810	C₂²	1	1	yes	characteristic
56	C₅×#809	C₂²	1	1	yes	characteristic
57	C₅×#808	C₂²	1	1	yes	characteristic
58	C₅×#807	C₂²	1	1	yes	characteristic
59	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
60	#79700	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#557	—	3	1	no	—
62	C₅×#556	—	3	1	no	—
63	C₅×#488	—	3	1	no	—
64	C₅×#488	—	3	1	no	—
65	C₅×#487	—	3	1	no	—
66	C₅×#479	—	3	1	no	—
67	C₅×#479	—	3	1	no	—
68	C₅×#474	—	3	1	no	—
69	C₅×#464	—	3	1	no	—
70	C₅×#464	—	3	1	no	—
71	C₅×#462	—	3	1	no	—
72	C₅×C₈×Q₈	—	3	1	no	—
73	C₄×C₅×Q₁₆	—	3	1	no	—
74	C₄×C₅×Q₁₆	D₃	1	1	yes	characteristic, complemented
75	C₄×C₅×SD₁₆	—	3	1	no	—
76	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
78	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
79	C₂×C₄×C₅×D₃	—	2	1	no	—
80	C₂×C₅×Dic₆	—	2	1	no	—
81	C₂×C₅×Dic₆	D₄	1	1	yes	characteristic
82	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
83	C₃×C₅×Q₁₆	—	2	2	no	—
84	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
86	C₃×C₅×C₄⋊C₄	—	2	1	no	—
87	C₃×C₅×C₄⋊C₄	—	2	1	no	—
88	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₃×C₄²×C₅	—	2	1	no	—
91	C₃×C₄²×C₅	—	2	1	no	—
92	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
93	C₅×#216	—	2	2	no	—
94	C₅×#215	—	2	2	no	—
95	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
96	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
97	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
98	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
99	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
100	C₅×C₄⋊Dic₃	—	2	1	no	—
101	C₅×C₄⋊Dic₃	—	2	1	no	—
102	C₅×C₄⋊Dic₃	—	2	1	no	—
103	C₅×C₄⋊Dic₃	D₄	1	1	yes	characteristic
104	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
105	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
106	C₅×Dic₃⋊C₄	—	2	1	no	—
107	C₅×Dic₃⋊C₄	—	2	1	no	—
108	C₅×Dic₃⋊C₄	—	2	1	no	—
109	C₅×Dic₃⋊C₄	—	2	1	no	—
110	C₅×Dic₃⋊C₄	—	2	1	no	—
111	C₅×Dic₃⋊C₄	—	2	1	no	—
112	C₅×Dic₃⋊C₄	—	2	1	no	—
113	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
114	C₅×Dic₃⋊C₄	D₄	1	1	yes	characteristic
115	C₄×C₅×Dic₃	—	2	1	no	—
116	C₄×C₅×Dic₃	—	2	1	no	—
117	C₄×C₅×Dic₃	—	2	1	no	—
118	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
119	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
120	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
121	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
122	#5569	C₂×C₅	1	1	yes	characteristic, complemented
123	#5568	C₂×C₅	1	1	yes	characteristic
124	C₃×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
125	#5185	C₂×C₅	1	1	yes	characteristic
126	#5182	C₂×C₅	1	1	yes	characteristic, complemented
127	#5028	C₂×C₅	1	1	yes	characteristic
128	#5022	C₂×C₅	1	1	yes	characteristic, complemented
129	#4890	C₂×C₅	1	1	yes	characteristic
130	#4877	C₂×C₅	1	1	yes	characteristic, complemented
131	#4800	C₂×C₅	1	1	yes	characteristic
132	#4792	C₂×C₅	1	1	yes	characteristic, complemented
133	#4790	C₂×C₅	1	1	yes	characteristic, complemented
134	#4788	C₂×C₅	1	1	yes	characteristic
135	#4697	C₂×C₅	1	1	yes	characteristic
136	C₈×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
137	C₂×C₅×Q₁₆	—	3	1	no	—
138	C₂×C₅×Q₁₆	C₂×D₃	1	1	yes	characteristic
139	C₂×C₅×SD₁₆	—	3	1	no	—
140	C₅×C₄⋊Q₈	—	3	1	no	—
141	C₅×C₄⋊Q₈	—	3	1	no	—
142	C₅×C₄⋊Q₈	—	6	1	no	—
143	C₅×#126	—	6	1	no	—
144	C₅×#126	—	6	1	no	—
145	C₅×#125	—	3	1	no	—
146	C₅×#125	—	3	1	no	—
147	C₅×#125	—	6	1	no	—
148	C₅×#125	—	6	1	no	—
149	C₅×#124	—	3	1	no	—
150	C₅×#124	—	3	1	no	—
151	C₅×C₂²⋊Q₈	—	6	1	no	—
152	C₄×C₅×Q₈	—	3	1	no	—
153	C₄×C₅×Q₈	—	3	1	no	—
154	C₄×C₅×Q₈	—	3	1	no	—
155	C₄×C₅×Q₈	—	3	1	no	—
156	C₄×C₅×Q₈	—	6	1	no	—
157	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
158	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
159	C₄×C₅×D₄	—	3	1	no	—
160	C₅×#117	—	6	1	no	—
161	C₅×#107	—	3	1	no	—
162	C₅×#107	C₂×D₃	1	1	yes	characteristic
163	C₅×#106	—	3	1	no	—
164	C₅×C₄⋊C₈	—	3	1	no	—
165	C₅×C₄⋊C₈	—	3	1	no	—
166	C₅×C₄⋊C₈	—	3	1	no	—
167	C₅×#103	—	3	1	no	—
168	C₅×#103	—	3	1	no	—
169	C₅×#103	—	3	1	no	—
170	C₅×#103	—	3	1	no	—
171	C₅×#103	—	3	1	no	—
172	C₅×#103	C₂×D₃	1	1	yes	characteristic
173	C₅×#103	C₂×D₃	1	1	yes	characteristic
174	C₅×#102	—	3	1	no	—
175	C₅×#102	—	3	1	no	—
176	C₅×#102	—	3	1	no	—
177	C₄×C₅×C₈	—	3	1	no	—
178	C₄×C₅×C₈	—	3	1	no	—
179	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic
180	#3364	—	3	1	no	Sylow
181	C₂²×C₅×D₃	—	2	1	no	—
182	C₃×C₅×Q₈	—	2	1	no	—
183	C₃×C₅×Q₈	—	2	1	no	—
184	C₃×C₅×Q₈	—	2	1	no	—
185	C₃×C₅×Q₈	#41	1	2	yes	—
186	C₂×C₃×C₄×C₅	—	2	1	no	—
187	C₂×C₃×C₄×C₅	—	2	1	no	—
188	C₂×C₃×C₄×C₅	—	2	1	no	—
189	C₂×C₃×C₄×C₅	—	2	1	no	—
190	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
191	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
192	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
193	C₂×C₅×Dic₃	—	2	1	no	—
194	C₂×C₅×Dic₃	—	2	1	no	—
195	C₂×C₅×Dic₃	—	2	1	no	—
196	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
197	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
198	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
199	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
200	C₅×D₁₂	—	2	1	no	—
201	C₅×D₁₂	—	2	1	no	—
202	C₄×C₅×D₃	—	4	2	no	—
203	C₅×Dic₆	—	2	2	no	—
204	C₅×Dic₆	—	2	1	no	—
205	C₅×Dic₆	—	2	1	no	—
206	C₅×Dic₆	—	4	2	no	—
207	C₃×C₅×C₈	—	2	1	no	—
208	C₃×C₅×C₈	—	2	1	no	—
209	C₅×C₃⋊C₈	—	2	1	no	—
210	C₅×C₃⋊C₈	—	2	1	no	—
211	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
212	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
213	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
214	#947	C₂²×C₅	1	1	yes	characteristic
215	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
216	Q₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
217	#944	C₂²×C₅	1	1	yes	characteristic
218	C₂×#216	C₂²×C₅	1	1	yes	characteristic
219	C₂×#215	C₂²×C₅	1	1	yes	characteristic
220	#898	—	2	1	no	—
221	#896	—	2	1	no	—
222	#893	C₂²×C₅	1	1	yes	characteristic
223	#890	—	2	1	no	—
224	#890	C₂²×C₅	1	1	yes	characteristic
225	#888	—	2	1	no	—
226	#888	C₂²×C₅	1	1	yes	characteristic
227	#887	C₂²×C₅	1	1	yes	characteristic
228	#876	—	2	1	no	—
229	#875	C₂²×C₅	1	1	yes	characteristic
230	#872	—	2	1	no	—
231	#870	—	2	1	no	—
232	#870	C₂²×C₅	1	1	yes	characteristic
233	C₄×Dic₆	—	2	1	no	—
234	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
235	C₃×#107	C₂²×C₅	1	1	yes	characteristic
236	C₃×#103	C₂²×C₅	1	1	yes	characteristic
237	C₃×#103	C₂²×C₅	1	1	yes	characteristic
238	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
239	#835	C₂²×C₅	1	1	yes	characteristic
240	#835	C₂²×C₅	1	1	yes	characteristic
241	#821	C₂²×C₅	1	1	yes	characteristic
242	#821	C₂²×C₅	1	1	yes	characteristic
243	#816	C₂²×C₅	1	1	yes	characteristic
244	#816	C₂²×C₅	1	1	yes	characteristic
245	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
246	Dic₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
247	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
248	C₈×Dic₃	C₂²×C₅	1	1	yes	characteristic
249	#810	C₂²×C₅	1	1	yes	characteristic
250	#809	C₂²×C₅	1	1	yes	characteristic
251	#808	C₂²×C₅	1	1	yes	characteristic
252	#807	C₂²×C₅	1	1	yes	characteristic
253	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
254	C₂×C₅×Q₈	—	3	1	no	—
255	C₂×C₅×Q₈	—	3	1	no	—
256	C₂×C₅×Q₈	—	6	1	no	—
257	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
258	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
259	C₂×C₅×D₄	—	3	1	no	—
260	C₂²×C₄×C₅	—	6	1	no	—
261	C₅×Q₁₆	—	2	2	no	—
262	C₅×Q₁₆	—	6	2	no	—
263	C₅×SD₁₆	—	6	2	no	—
264	C₂×C₅×C₈	—	3	1	no	—
265	C₂×C₅×C₈	—	3	1	no	—
266	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
267	C₂×C₅×C₈	C₂²×D₃	1	1	yes	characteristic
268	C₅×C₄⋊C₄	—	2	1	no	—
269	C₅×C₄⋊C₄	—	2	1	no	—
270	C₅×C₄⋊C₄	—	3	1	no	—
271	C₅×C₄⋊C₄	—	3	1	no	—
272	C₅×C₄⋊C₄	—	3	1	no	—
273	C₅×C₄⋊C₄	—	3	1	no	—
274	C₅×C₄⋊C₄	—	3	1	no	—
275	C₅×C₄⋊C₄	—	6	1	no	—
276	C₅×C₄⋊C₄	—	6	1	no	—
277	C₅×C₄⋊C₄	—	6	1	no	—
278	C₅×C₄⋊C₄	—	6	1	no	—
279	C₅×C₄⋊C₄	—	6	1	no	—
280	C₅×C₄⋊C₄	—	6	1	no	—
281	C₅×C₄⋊C₄	—	6	1	no	—
282	C₅×C₄⋊C₄	—	6	1	no	—
283	C₅×C₄⋊C₄	—	6	1	no	—
284	C₅×C₄⋊C₄	—	6	1	no	—
285	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
286	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
287	C₅×C₂²⋊C₄	—	6	1	no	—
288	C₅×C₂²⋊C₄	—	6	1	no	—
289	C₅×C₂²⋊C₄	—	6	1	no	—
290	C₅×C₂²⋊C₄	—	6	1	no	—
291	C₅×C₂²⋊C₄	—	6	1	no	—
292	C₄²×C₅	—	2	1	no	—
293	C₄²×C₅	—	2	1	no	—
294	C₄²×C₅	—	3	1	no	—
295	C₄²×C₅	—	3	1	no	—
296	C₄²×C₅	—	6	1	no	—
297	C₄²×C₅	—	6	1	no	—
298	C₄²×C₅	—	6	1	no	—
299	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
300	#557	—	3	1	no	—
301	#556	—	3	1	no	—
302	#488	—	3	1	no	—
303	#488	—	3	1	no	—
304	#487	—	3	1	no	—
305	#479	—	3	1	no	—
306	#479	—	3	1	no	—
307	#474	—	3	1	no	—
308	#464	—	3	1	no	—
309	#464	—	3	1	no	—
310	#462	—	3	1	no	—
311	C₈×Q₈	—	3	1	no	—
312	C₄×Q₁₆	—	3	1	no	—
313	C₄×Q₁₆	C₅×D₃	1	1	yes	characteristic, complemented
314	C₄×SD₁₆	—	3	1	no	—
315	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₅×D₃	—	4	1	no	—
317	C₂×C₅×D₃	—	4	1	no	—
318	C₂×C₅×D₃	—	4	1	no	—
319	C₃×C₄×C₅	—	2	2	no	—
320	C₃×C₄×C₅	—	2	1	no	—
321	C₃×C₄×C₅	—	2	1	no	—
322	C₃×C₄×C₅	—	4	1	no	—
323	C₃×C₄×C₅	—	4	1	no	—
324	C₃×C₄×C₅	—	4	1	no	—
325	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
326	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
327	C₅×Dic₃	—	2	1	no	—
328	C₅×Dic₃	—	2	1	no	—
329	C₅×Dic₃	—	2	1	no	—
330	C₅×Dic₃	—	4	1	no	—
331	C₅×Dic₃	—	4	1	no	—
332	C₅×Dic₃	—	4	1	no	—
333	C₅×Dic₃	#135	1	2	yes	—
334	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
335	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
336	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
337	C₂×C₄×D₃	—	2	1	no	—
338	C₂×Dic₆	—	2	1	no	—
339	C₂×Dic₆	C₅×D₄	1	1	yes	characteristic
340	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
341	C₃×Q₁₆	—	2	2	no	—
342	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
343	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
344	C₃×C₄⋊C₄	—	2	1	no	—
345	C₃×C₄⋊C₄	—	2	1	no	—
346	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
347	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
348	C₃×C₄²	—	2	1	no	—
349	C₃×C₄²	—	2	1	no	—
350	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
351	#216	—	2	2	no	—
352	#215	—	2	2	no	—
353	(C₂×D₃)⋊C₄	—	2	1	no	—
354	(C₂×D₃)⋊C₄	—	2	1	no	—
355	(C₂×D₃)⋊C₄	—	2	1	no	—
356	(C₂×D₃)⋊C₄	—	2	1	no	—
357	(C₂×D₃)⋊C₄	—	2	1	no	—
358	C₄⋊Dic₃	—	2	1	no	—
359	C₄⋊Dic₃	—	2	1	no	—
360	C₄⋊Dic₃	—	2	1	no	—
361	C₄⋊Dic₃	C₅×D₄	1	1	yes	characteristic
362	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
363	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
364	Dic₃⋊C₄	—	2	1	no	—
365	Dic₃⋊C₄	—	2	1	no	—
366	Dic₃⋊C₄	—	2	1	no	—
367	Dic₃⋊C₄	—	2	1	no	—
368	Dic₃⋊C₄	—	2	1	no	—
369	Dic₃⋊C₄	—	2	1	no	—
370	Dic₃⋊C₄	—	2	1	no	—
371	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
372	Dic₃⋊C₄	C₅×D₄	1	1	yes	characteristic
373	C₄×Dic₃	—	2	1	no	—
374	C₄×Dic₃	—	2	1	no	—
375	C₄×Dic₃	—	2	1	no	—
376	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
377	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
378	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
379	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
380	C₂³×C₅	—	6	1	no	—
381	C₅×Q₈	—	2	1	no	—
382	C₅×Q₈	—	2	1	no	—
383	C₅×Q₈	—	2	1	no	—
384	C₅×Q₈	—	6	2	no	—
385	C₅×Q₈	—	6	1	no	—
386	C₅×Q₈	—	6	1	no	—
387	C₅×Q₈	—	12	2	no	—
388	C₅×Q₈	#235	1	2	yes	—
389	C₅×D₄	—	6	1	no	—
390	C₅×D₄	—	6	1	no	—
391	C₂×C₄×C₅	—	2	1	no	—
392	C₂×C₄×C₅	—	2	1	no	—
393	C₂×C₄×C₅	—	2	1	no	—
394	C₂×C₄×C₅	—	2	1	no	—
395	C₂×C₄×C₅	—	3	1	no	—
396	C₂×C₄×C₅	—	3	1	no	—
397	C₂×C₄×C₅	—	3	1	no	—
398	C₂×C₄×C₅	—	3	1	no	—
399	C₂×C₄×C₅	—	6	1	no	—
400	C₂×C₄×C₅	—	6	1	no	—
401	C₂×C₄×C₅	—	6	1	no	—
402	C₂×C₄×C₅	—	12	2	no	—
403	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
404	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
405	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
406	C₅×C₈	—	2	1	no	—
407	C₅×C₈	—	2	1	no	—
408	C₅×C₈	—	6	1	no	—
409	C₅×C₈	—	6	1	no	—
410	C₂×Q₁₆	—	3	1	no	—
411	C₂×Q₁₆	C₂×C₅×D₃	1	1	yes	characteristic
412	C₂×SD₁₆	—	3	1	no	—
413	C₄⋊Q₈	—	3	1	no	—
414	C₄⋊Q₈	—	3	1	no	—
415	C₄⋊Q₈	—	6	1	no	—
416	#126	—	6	1	no	—
417	#126	—	6	1	no	—
418	#125	—	3	1	no	—
419	#125	—	3	1	no	—
420	#125	—	6	1	no	—
421	#125	—	6	1	no	—
422	#124	—	3	1	no	—
423	#124	—	3	1	no	—
424	C₂²⋊Q₈	—	6	1	no	—
425	C₄×Q₈	—	3	1	no	—
426	C₄×Q₈	—	3	1	no	—
427	C₄×Q₈	—	3	1	no	—
428	C₄×Q₈	—	3	1	no	—
429	C₄×Q₈	—	6	1	no	—
430	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
431	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
432	C₄×D₄	—	3	1	no	—
433	#117	—	6	1	no	—
434	#107	—	3	1	no	—
435	#107	C₂×C₅×D₃	1	1	yes	characteristic
436	#106	—	3	1	no	—
437	C₄⋊C₈	—	3	1	no	—
438	C₄⋊C₈	—	3	1	no	—
439	C₄⋊C₈	—	3	1	no	—
440	#103	—	3	1	no	—
441	#103	—	3	1	no	—
442	#103	—	3	1	no	—
443	#103	—	3	1	no	—
444	#103	—	3	1	no	—
445	#103	C₂×C₅×D₃	1	1	yes	characteristic
446	#103	C₂×C₅×D₃	1	1	yes	characteristic
447	#102	—	3	1	no	—
448	#102	—	3	1	no	—
449	#102	—	3	1	no	—
450	C₄×C₈	—	3	1	no	—
451	C₄×C₈	—	3	1	no	—
452	C₄×C₈	C₂×C₅×D₃	1	1	yes	characteristic
453	C₂×C₃×C₅	#548	1	1	yes	characteristic
454	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
455	C₂×C₃×C₅	#578	1	1	yes	characteristic
456	C₅×D₃	—	8	1	no	—
457	C₂²×D₃	—	2	1	no	—
458	C₃×Q₈	—	2	1	no	—
459	C₃×Q₈	—	2	1	no	—
460	C₃×Q₈	—	2	1	no	—
461	C₃×Q₈	C₅×#41	1	2	yes	—
462	C₂×C₃×C₄	—	2	1	no	—
463	C₂×C₃×C₄	—	2	1	no	—
464	C₂×C₃×C₄	—	2	1	no	—
465	C₂×C₃×C₄	—	2	1	no	—
466	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
467	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
468	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
469	C₂×Dic₃	—	2	1	no	—
470	C₂×Dic₃	—	2	1	no	—
471	C₂×Dic₃	—	2	1	no	—
472	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
473	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
474	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
475	C₂×Dic₃	C₂×C₅×D₄	1	1	yes	characteristic
476	D₁₂	—	2	1	no	—
477	D₁₂	—	2	1	no	—
478	C₄×D₃	—	4	2	no	—
479	Dic₆	—	2	2	no	—
480	Dic₆	—	2	1	no	—
481	Dic₆	—	2	1	no	—
482	Dic₆	—	4	2	no	—
483	C₃×C₈	—	2	1	no	—
484	C₃×C₈	—	2	1	no	—
485	C₃⋊C₈	—	2	1	no	—
486	C₃⋊C₈	—	2	1	no	—
487	C₂²×C₅	—	12	1	no	—
488	C₂²×C₅	—	12	1	no	—
489	C₂²×C₅	—	12	1	no	—
490	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
491	C₄×C₅	—	2	1	no	—
492	C₄×C₅	—	2	1	no	—
493	C₄×C₅	—	2	2	no	—
494	C₄×C₅	—	3	2	no	—
495	C₄×C₅	—	4	1	no	—
496	C₄×C₅	—	4	1	no	—
497	C₄×C₅	—	4	1	no	—
498	C₄×C₅	—	6	1	no	—
499	C₄×C₅	—	6	1	no	—
500	C₄×C₅	—	6	1	no	—
501	C₄×C₅	—	12	1	no	—
502	C₄×C₅	—	12	1	no	—
503	C₄×C₅	—	12	1	no	—
504	C₄×C₅	C₂×#235	1	1	yes	characteristic
505	C₄×C₅	#1010	1	1	yes	characteristic
506	C₂×Q₈	—	3	1	no	—
507	C₂×Q₈	—	3	1	no	—
508	C₂×Q₈	—	6	1	no	—
509	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
510	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
511	C₂×D₄	—	3	1	no	—
512	C₂²×C₄	—	6	1	no	—
513	Q₁₆	—	2	2	no	—
514	Q₁₆	—	6	2	no	—
515	SD₁₆	—	6	2	no	—
516	C₂×C₈	—	3	1	no	—
517	C₂×C₈	—	3	1	no	—
518	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
519	C₂×C₈	C₂²×C₅×D₃	1	1	yes	characteristic
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	3	1	no	—
523	C₄⋊C₄	—	3	1	no	—
524	C₄⋊C₄	—	3	1	no	—
525	C₄⋊C₄	—	3	1	no	—
526	C₄⋊C₄	—	3	1	no	—
527	C₄⋊C₄	—	6	1	no	—
528	C₄⋊C₄	—	6	1	no	—
529	C₄⋊C₄	—	6	1	no	—
530	C₄⋊C₄	—	6	1	no	—
531	C₄⋊C₄	—	6	1	no	—
532	C₄⋊C₄	—	6	1	no	—
533	C₄⋊C₄	—	6	1	no	—
534	C₄⋊C₄	—	6	1	no	—
535	C₄⋊C₄	—	6	1	no	—
536	C₄⋊C₄	—	6	1	no	—
537	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
538	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
539	C₂²⋊C₄	—	6	1	no	—
540	C₂²⋊C₄	—	6	1	no	—
541	C₂²⋊C₄	—	6	1	no	—
542	C₂²⋊C₄	—	6	1	no	—
543	C₂²⋊C₄	—	6	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	3	1	no	—
547	C₄²	—	3	1	no	—
548	C₄²	—	6	1	no	—
549	C₄²	—	6	1	no	—
550	C₄²	—	6	1	no	—
551	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
552	C₃×C₅	#3364	1	1	yes	characteristic, complemented, Hall
553	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
554	C₂×D₃	—	4	1	no	—
555	C₂×D₃	—	4	1	no	—
556	C₂×D₃	—	4	1	no	—
557	C₃×C₄	—	2	2	no	—
558	C₃×C₄	—	2	1	no	—
559	C₃×C₄	—	2	1	no	—
560	C₃×C₄	—	4	1	no	—
561	C₃×C₄	—	4	1	no	—
562	C₃×C₄	—	4	1	no	—
563	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
564	C₃×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
565	Dic₃	—	2	1	no	—
566	Dic₃	—	2	1	no	—
567	Dic₃	—	2	1	no	—
568	Dic₃	—	4	1	no	—
569	Dic₃	—	4	1	no	—
570	Dic₃	—	4	1	no	—
571	Dic₃	C₅×#135	1	2	yes	—
572	C₂×C₅	—	24	1	no	—
573	C₂×C₅	#5552	1	1	yes	characteristic
574	C₂×C₅	#5766	1	1	yes	characteristic
575	C₂×C₅	D₃×#135	1	1	yes	characteristic
576	C₂³	—	6	1	no	—
577	Q₈	—	2	1	no	—
578	Q₈	—	2	1	no	—
579	Q₈	—	2	1	no	—
580	Q₈	—	6	2	no	—
581	Q₈	—	6	1	no	—
582	Q₈	—	6	1	no	—
583	Q₈	—	12	2	no	—
584	Q₈	C₅×#235	1	2	yes	—
585	D₄	—	6	1	no	—
586	D₄	—	6	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	3	1	no	—
592	C₂×C₄	—	3	1	no	—
593	C₂×C₄	—	3	1	no	—
594	C₂×C₄	—	3	1	no	—
595	C₂×C₄	—	6	1	no	—
596	C₂×C₄	—	6	1	no	—
597	C₂×C₄	—	6	1	no	—
598	C₂×C₄	—	12	2	no	—
599	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
600	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
601	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
602	C₈	—	2	1	no	—
603	C₈	—	2	1	no	—
604	C₈	—	6	1	no	—
605	C₈	—	6	1	no	—
606	C₂×C₃	C₅×#548	1	1	yes	characteristic
607	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
608	C₂×C₃	C₅×#578	1	1	yes	characteristic
609	D₃	—	8	1	no	—
610	C₅	#79700	1	1	yes	characteristic, direct product factor, Sylow
611	C₂²	—	12	1	no	—
612	C₂²	—	12	1	no	—
613	C₂²	—	12	1	no	—
614	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	2	no	—
618	C₄	—	3	2	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	6	1	no	—
623	C₄	—	6	1	no	—
624	C₄	—	6	1	no	—
625	C₄	—	12	1	no	—
626	C₄	—	12	1	no	—
627	C₄	—	12	1	no	—
628	C₄	C₂×C₅×#235	1	1	yes	characteristic
629	C₄	C₅×#1010	1	1	yes	characteristic
630	C₃	C₅×#3364	1	1	yes	characteristic, complemented, Sylow
631	C₂	—	24	1	no	—
632	C₂	C₅×#5552	1	1	yes	characteristic
633	C₂	C₅×#5766	1	1	yes	characteristic
634	C₂	C₅×D₃×#135	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	C₃×C₄×C₅×Q₁₆	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×D₁₂	C₂³
hypercenter	C₄×C₅×Q₁₆	D₃
hypocenter	C₃	C₅×#3364
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ C₄×C₅×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₅×#5569	C₂	semidirect
3. C₃×C₄×C₅×Q₁₆	C₂	semidirect
5. C₅×#5182	C₂	semidirect
7. C₅×#5022	C₂	semidirect
9. C₅×#4877	C₂	semidirect
11. C₅×#4792	C₂	semidirect
12. C₅×#4790	C₂	semidirect
15. C₅×C₈×Dic₆	C₂	semidirect
60. #79700	C₅	direct (N × H)
74. C₄×C₅×Q₁₆	D₃	semidirect
122. #5569	C₂×C₅	semidirect
124. C₃×C₄×Q₁₆	C₂×C₅	semidirect
126. #5182	C₂×C₅	semidirect
128. #5022	C₂×C₅	semidirect
130. #4877	C₂×C₅	semidirect
132. #4792	C₂×C₅	semidirect
133. #4790	C₂×C₅	semidirect
136. C₈×Dic₆	C₂×C₅	semidirect
313. C₄×Q₁₆	C₅×D₃	semidirect
552. C₃×C₅	#3364	semidirect
610. C₅	#79700	direct (N × H)
630. C₃	C₅×#3364	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5569	2
C₅×#5568	2
C₃×C₄×C₅×Q₁₆	2
C₅×#5185	2
C₅×#5182	2
C₅×#5028	2
C₅×#5022	2
C₅×#4890	2
C₅×#4877	2
C₅×#4800	2
C₅×#4792	2
C₅×#4790	2
C₅×#4788	2
C₅×#4697	2
C₅×C₈×Dic₆	2
C₅×#3364	3
#79700	5

Subgroups — C5×#79700 #14472076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79700 #14472076