Subgroups — C₅×#78980 #14418107

Order 1920.

916 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5822	C₂	1	1	yes	maximal, characteristic
2	C₅×#5819	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5745	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₅×#104	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5124	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#805	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4824	C₂	1	4	yes	maximal, complemented
9	C₅×#4823	C₂	1	4	yes	maximal, complemented
10	C₅×#2956	—	3	1	no	maximal, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₂×C₅×#235	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₅×#951	C₄	1	2	yes	complemented
16	C₅×#950	C₂²	1	4	yes	—
17	C₅×#949	C₄	1	2	yes	complemented
18	C₅×#948	—	2	2	no	—
19	C₅×#948	C₂²	1	4	yes	complemented
20	C₅×#942	C₄	1	2	yes	complemented
21	C₅×#932	C₄	1	2	yes	complemented
22	C₂×C₅×#208	—	2	2	no	—
23	C₂×C₅×#208	C₂²	1	1	yes	characteristic
24	C₂×C₅×#208	C₂²	1	1	yes	characteristic
25	C₂×C₅×#208	C₂²	1	1	yes	characteristic
26	C₅×#907	C₂²	1	4	yes	complemented
27	C₅×D₃×M₁₆	—	2	2	no	—
28	C₅×#901	—	2	2	no	—
29	C₃×C₅×#104	C₂²	1	2	yes	complemented
30	C₃×C₅×#104	C₂²	1	2	yes	complemented
31	C₅×#822	C₂²	1	4	yes	complemented
32	C₅×#805	C₂²	1	2	yes	complemented
33	C₅×#805	C₂²	1	2	yes	complemented
34	C₅×#803	C₂²	1	2	yes	complemented
35	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	complemented
36	#78980	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
37	C₅×#575	—	3	1	no	—
38	C₅×#568	—	3	1	no	—
39	C₅×#568	—	3	1	no	—
40	C₅×#444	—	3	4	no	—
41	C₅×#443	—	3	4	no	—
42	C₅×#430	—	3	1	no	—
43	C₂×C₅×#104	—	3	1	no	—
44	C₂×C₅×#104	D₃	1	1	yes	characteristic, complemented
45	C₄×C₅×M₁₆	—	3	1	no	—
46	C₃×C₅×#41	—	2	1	no	—
47	C₃×C₅×#41	—	2	1	no	—
48	C₃×C₅×#41	C₂×C₄	1	2	yes	—
49	C₃×C₅×#41	C₂³	1	2	yes	—
50	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃×C₅×D₄	—	2	1	no	—
52	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	—	2	1	no	—
54	C₂²×C₃×C₄×C₅	—	2	1	no	—
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂×C₅×#67	—	2	1	no	—
57	C₅×#235	—	2	1	no	—
58	C₅×#235	—	2	1	no	—
59	C₅×#235	C₂×C₄	1	2	yes	—
60	C₅×#235	C₂³	1	2	yes	—
61	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×C₅×D₃	—	2	1	no	—
63	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
64	C₃×C₅×M₁₆	—	2	1	no	—
65	C₃×C₅×M₁₆	C₂³	1	2	yes	—
66	C₂×C₃×C₅×C₈	—	2	1	no	—
67	C₃×C₄²×C₅	—	2	1	no	—
68	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₅×#216	C₂×C₄	1	4	yes	complemented
71	C₅×#215	C₂×C₄	1	4	yes	complemented
72	C₅×#214	C₂×C₄	1	4	yes	complemented
73	C₅×#213	C₂×C₄	1	4	yes	complemented
74	C₅×#208	—	2	1	no	—
75	C₅×#208	—	2	4	no	—
76	C₅×#208	C₂×C₄	1	2	yes	—
77	C₅×#208	C₂×C₄	1	2	yes	—
78	C₅×#208	D₄	1	2	yes	—
79	C₅×#208	D₄	1	2	yes	—
80	C₅×#208	C₂³	1	2	yes	—
81	C₂×C₅×C₃⋊C₈	—	2	1	no	—
82	C₂×C₅×C₃⋊C₈	—	2	4	no	—
83	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
84	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
85	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
86	C₅×D₃×C₈	—	2	4	no	—
87	#5822	C₂×C₅	1	1	yes	characteristic
88	#5819	C₂×C₅	1	1	yes	characteristic, complemented
89	#5745	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂×C₃×#104	C₂×C₅	1	1	yes	characteristic, complemented
91	#5124	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂×#805	C₂×C₅	1	1	yes	characteristic, complemented
93	C₄×#208	C₂×C₅	1	1	yes	characteristic, complemented
94	#4824	C₂×C₅	1	4	yes	complemented
95	#4823	C₂×C₅	1	4	yes	complemented
96	C₂×C₅×#41	—	3	1	no	—
97	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
98	C₅×#137	—	3	2	no	—
99	C₅×#137	—	3	2	no	—
100	C₅×AGL(1,ℤ/8)	—	3	2	no	—
101	C₅×AGL(1,ℤ/8)	—	3	2	no	—
102	C₅×#135	—	3	4	no	—
103	C₅×#131	—	3	4	no	—
104	C₅×#131	—	3	4	no	—
105	C₅×#131	—	6	2	no	—
106	C₅×#131	—	6	2	no	—
107	C₂×C₅×M₁₆	—	3	1	no	—
108	C₂×C₅×M₁₆	—	3	1	no	—
109	C₂×C₅×M₁₆	—	3	1	no	—
110	C₂×C₅×M₁₆	—	6	2	no	—
111	C₂×C₅×M₁₆	—	6	2	no	—
112	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
113	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
114	C₅×#108	—	3	4	no	—
115	C₅×#104	—	3	2	no	—
116	C₅×#104	—	3	2	no	—
117	C₅×#104	C₂×D₃	1	2	yes	complemented
118	C₅×#104	C₂×D₃	1	2	yes	complemented
119	C₅×#97	—	3	2	no	—
120	C₄×C₅×C₈	—	3	2	no	—
121	#2956	—	3	1	no	Sylow
122	C₂³×C₃×C₅	—	2	1	no	—
123	C₂³×C₃×C₅	#41	1	1	yes	characteristic
124	C₂²×C₅×D₃	—	2	1	no	—
125	C₃×C₅×Q₈	—	2	1	no	—
126	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
127	C₃×C₅×D₄	—	2	2	no	—
128	C₃×C₅×D₄	—	2	2	no	—
129	C₃×C₅×D₄	—	2	1	no	—
130	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	—	2	1	no	—
132	C₂×C₃×C₄×C₅	—	2	1	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	2	1	no	—
136	C₂×C₃×C₄×C₅	—	4	2	no	—
137	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
142	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
143	C₅×#67	—	2	2	no	—
144	C₅×#67	—	2	2	no	—
145	C₂×C₅×Dic₃	—	2	1	no	—
146	C₅×D₁₂	—	2	1	no	—
147	C₅×D₁₂	C₂²×C₄	1	2	yes	—
148	C₄×C₅×D₃	—	2	2	no	—
149	C₄×C₅×D₃	—	2	2	no	—
150	C₅×Dic₆	—	2	1	no	—
151	C₅×Dic₆	C₂²×C₄	1	2	yes	—
152	C₃×C₅×C₈	—	2	2	no	—
153	C₅×C₃⋊C₈	—	2	2	no	—
154	C₅×C₃⋊C₈	C₂²×C₄	1	4	yes	—
155	C₅×C₃⋊C₈	C₂×D₄	1	4	yes	—
156	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
157	C₂×#235	C₂²×C₅	1	1	yes	characteristic
158	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
159	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
160	#951	C₄×C₅	1	2	yes	complemented
161	#950	C₂²×C₅	1	4	yes	—
162	#949	C₄×C₅	1	2	yes	complemented
163	#948	—	2	2	no	—
164	#948	C₂²×C₅	1	4	yes	complemented
165	#942	C₄×C₅	1	2	yes	complemented
166	#932	C₄×C₅	1	2	yes	complemented
167	C₂×#208	—	2	2	no	—
168	C₂×#208	C₂²×C₅	1	1	yes	characteristic
169	C₂×#208	C₂²×C₅	1	1	yes	characteristic
170	C₂×#208	C₂²×C₅	1	1	yes	characteristic
171	#907	C₂²×C₅	1	4	yes	complemented
172	D₃×M₁₆	—	2	2	no	—
173	#901	—	2	2	no	—
174	C₃×#104	C₂²×C₅	1	2	yes	complemented
175	C₃×#104	C₂²×C₅	1	2	yes	complemented
176	#822	C₂²×C₅	1	4	yes	complemented
177	#805	C₂²×C₅	1	2	yes	complemented
178	#805	C₂²×C₅	1	2	yes	complemented
179	#803	C₂²×C₅	1	2	yes	complemented
180	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	complemented
181	C₅×#41	—	2	1	no	—
182	C₅×#41	—	2	1	no	—
183	C₅×#41	—	3	2	no	—
184	C₅×#41	—	3	2	no	—
185	C₅×#41	—	6	1	no	—
186	C₅×#41	—	6	1	no	—
187	C₅×#41	C₄×D₃	1	2	yes	—
188	C₅×#41	C₂²×D₃	1	2	yes	—
189	C₂×C₅×Q₈	—	3	1	no	—
190	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
191	C₂×C₅×D₄	—	2	1	no	—
192	C₂×C₅×D₄	—	3	1	no	—
193	C₂×C₅×D₄	—	6	1	no	—
194	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
195	C₂²×C₄×C₅	—	2	1	no	—
196	C₂²×C₄×C₅	—	2	1	no	—
197	C₂²×C₄×C₅	—	6	1	no	—
198	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
199	C₅×Q₁₆	—	3	4	no	—
200	C₅×SD₁₆	—	3	4	no	—
201	C₅×SD₁₆	—	3	4	no	—
202	C₅×D₈	—	3	4	no	—
203	C₅×M₁₆	—	2	1	no	—
204	C₅×M₁₆	—	3	2	no	—
205	C₅×M₁₆	—	3	2	no	—
206	C₅×M₁₆	—	3	2	no	—
207	C₅×M₁₆	—	3	2	no	—
208	C₅×M₁₆	—	3	2	no	—
209	C₅×M₁₆	—	6	4	no	—
210	C₅×M₁₆	—	6	4	no	—
211	C₅×M₁₆	—	6	1	no	—
212	C₅×M₁₆	C₂²×D₃	1	2	yes	—
213	C₂×C₅×C₈	—	2	1	no	—
214	C₂×C₅×C₈	—	3	2	no	—
215	C₂×C₅×C₈	—	3	2	no	—
216	C₂×C₅×C₈	—	6	4	no	—
217	C₂×C₅×C₈	—	6	4	no	—
218	C₂×C₅×C₈	—	6	1	no	—
219	C₄²×C₅	—	2	1	no	—
220	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
221	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
222	#575	—	3	1	no	—
223	#568	—	3	1	no	—
224	#568	—	3	1	no	—
225	#444	—	3	4	no	—
226	#443	—	3	4	no	—
227	#430	—	3	1	no	—
228	C₂×#104	—	3	1	no	—
229	C₂×#104	C₅×D₃	1	1	yes	characteristic, complemented
230	C₄×M₁₆	—	3	1	no	—
231	C₂²×C₃×C₅	—	2	2	no	—
232	C₂²×C₃×C₅	—	4	1	no	—
233	C₂²×C₃×C₅	—	8	1	no	—
234	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
235	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
236	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
237	C₂×C₅×D₃	—	2	2	no	—
238	C₂×C₅×D₃	—	8	1	no	—
239	C₃×C₄×C₅	—	2	2	no	—
240	C₃×C₄×C₅	—	2	2	no	—
241	C₃×C₄×C₅	—	4	1	no	—
242	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
243	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
244	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
245	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
246	C₅×Dic₃	—	2	2	no	—
247	C₃×#41	—	2	1	no	—
248	C₃×#41	—	2	1	no	—
249	C₃×#41	C₂×C₄×C₅	1	2	yes	—
250	C₃×#41	C₂³×C₅	1	2	yes	—
251	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
252	C₂×C₃×D₄	—	2	1	no	—
253	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
254	C₂²×C₃×C₄	—	2	1	no	—
255	C₂²×C₃×C₄	—	2	1	no	—
256	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
257	C₂×#67	—	2	1	no	—
258	#235	—	2	1	no	—
259	#235	—	2	1	no	—
260	#235	C₂×C₄×C₅	1	2	yes	—
261	#235	C₂³×C₅	1	2	yes	—
262	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
263	C₂×C₄×D₃	—	2	1	no	—
264	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
265	C₃×M₁₆	—	2	1	no	—
266	C₃×M₁₆	C₂³×C₅	1	2	yes	—
267	C₂×C₃×C₈	—	2	1	no	—
268	C₃×C₄²	—	2	1	no	—
269	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
270	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
271	#216	C₂×C₄×C₅	1	4	yes	complemented
272	#215	C₂×C₄×C₅	1	4	yes	complemented
273	#214	C₂×C₄×C₅	1	4	yes	complemented
274	#213	C₂×C₄×C₅	1	4	yes	complemented
275	#208	—	2	1	no	—
276	#208	—	2	4	no	—
277	#208	C₂×C₄×C₅	1	2	yes	—
278	#208	C₂×C₄×C₅	1	2	yes	—
279	#208	C₅×D₄	1	2	yes	—
280	#208	C₅×D₄	1	2	yes	—
281	#208	C₂³×C₅	1	2	yes	—
282	C₂×C₃⋊C₈	—	2	1	no	—
283	C₂×C₃⋊C₈	—	2	4	no	—
284	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
285	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
286	ΓL(1,𝔽₂₅)	—	2	4	no	—
287	D₃×C₈	—	2	4	no	—
288	C₂³×C₅	—	2	1	no	—
289	C₂³×C₅	—	6	1	no	—
290	C₂³×C₅	#237	1	1	yes	characteristic
291	C₅×Q₈	—	2	1	no	—
292	C₅×Q₈	—	3	2	no	—
293	C₅×Q₈	—	6	1	no	—
294	C₅×Q₈	C₂×C₄×D₃	1	2	yes	—
295	C₅×D₄	—	2	2	no	—
296	C₅×D₄	—	2	2	no	—
297	C₅×D₄	—	2	1	no	—
298	C₅×D₄	—	3	2	no	—
299	C₅×D₄	—	6	2	no	—
300	C₅×D₄	—	6	2	no	—
301	C₅×D₄	—	6	1	no	—
302	C₅×D₄	C₂×C₄×D₃	1	2	yes	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	2	2	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	4	2	no	—
309	C₂×C₄×C₅	—	6	1	no	—
310	C₂×C₄×C₅	—	6	2	no	—
311	C₂×C₄×C₅	—	6	2	no	—
312	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
313	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
314	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
315	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
316	C₂×C₄×C₅	#237	1	1	yes	characteristic
317	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
318	C₅×C₈	—	2	2	no	—
319	C₅×C₈	—	3	4	no	—
320	C₅×C₈	—	3	4	no	—
321	C₅×C₈	—	6	2	no	—
322	C₂×#41	—	3	1	no	—
323	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
324	#137	—	3	2	no	—
325	#137	—	3	2	no	—
326	AGL(1,ℤ/8)	—	3	2	no	—
327	AGL(1,ℤ/8)	—	3	2	no	—
328	#135	—	3	4	no	—
329	#131	—	3	4	no	—
330	#131	—	3	4	no	—
331	#131	—	6	2	no	—
332	#131	—	6	2	no	—
333	C₂×M₁₆	—	3	1	no	—
334	C₂×M₁₆	—	3	1	no	—
335	C₂×M₁₆	—	3	1	no	—
336	C₂×M₁₆	—	6	2	no	—
337	C₂×M₁₆	—	6	2	no	—
338	C₂×M₁₆	C₂×C₅×D₃	1	1	yes	characteristic
339	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
340	#108	—	3	4	no	—
341	#104	—	3	2	no	—
342	#104	—	3	2	no	—
343	#104	C₂×C₅×D₃	1	2	yes	complemented
344	#104	C₂×C₅×D₃	1	2	yes	complemented
345	#97	—	3	2	no	—
346	C₄×C₈	—	3	2	no	—
347	C₂×C₃×C₅	—	2	1	no	—
348	C₂×C₃×C₅	—	2	1	no	—
349	C₂×C₃×C₅	—	2	1	no	—
350	C₂×C₃×C₅	—	4	2	no	—
351	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
352	C₅×D₃	—	4	2	no	—
353	C₂³×C₃	—	2	1	no	—
354	C₂³×C₃	C₅×#41	1	1	yes	characteristic
355	C₂²×D₃	—	2	1	no	—
356	C₃×Q₈	—	2	1	no	—
357	C₃×Q₈	C₂²×C₄×C₅	1	2	yes	—
358	C₃×D₄	—	2	2	no	—
359	C₃×D₄	—	2	2	no	—
360	C₃×D₄	—	2	1	no	—
361	C₃×D₄	C₂²×C₄×C₅	1	2	yes	—
362	C₂×C₃×C₄	—	2	1	no	—
363	C₂×C₃×C₄	—	2	1	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	2	1	no	—
367	C₂×C₃×C₄	—	4	2	no	—
368	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
369	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
370	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
371	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
372	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
373	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
374	#67	—	2	2	no	—
375	#67	—	2	2	no	—
376	C₂×Dic₃	—	2	1	no	—
377	D₁₂	—	2	1	no	—
378	D₁₂	C₂²×C₄×C₅	1	2	yes	—
379	C₄×D₃	—	2	2	no	—
380	C₄×D₃	—	2	2	no	—
381	Dic₆	—	2	1	no	—
382	Dic₆	C₂²×C₄×C₅	1	2	yes	—
383	C₃×C₈	—	2	2	no	—
384	C₃⋊C₈	—	2	2	no	—
385	C₃⋊C₈	C₂²×C₄×C₅	1	4	yes	—
386	C₃⋊C₈	C₂×C₅×D₄	1	4	yes	—
387	C₂²×C₅	—	2	2	no	—
388	C₂²×C₅	—	4	1	no	—
389	C₂²×C₅	—	6	2	no	—
390	C₂²×C₅	—	8	1	no	—
391	C₂²×C₅	—	24	1	no	—
392	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
393	C₂²×C₅	#67⋊C₄	1	1	yes	characteristic
394	C₂²×C₅	C₂×#237	1	1	yes	characteristic
395	C₄×C₅	—	2	2	no	—
396	C₄×C₅	—	2	2	no	—
397	C₄×C₅	—	4	1	no	—
398	C₄×C₅	—	6	2	no	—
399	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
400	C₄×C₅	#67⋊C₄	1	1	yes	characteristic
401	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
402	C₄×C₅	C₂×D₃×D₄	1	1	yes	characteristic
403	#41	—	2	1	no	—
404	#41	—	2	1	no	—
405	#41	—	3	2	no	—
406	#41	—	3	2	no	—
407	#41	—	6	1	no	—
408	#41	—	6	1	no	—
409	#41	C₄×C₅×D₃	1	2	yes	—
410	#41	C₂²×C₅×D₃	1	2	yes	—
411	C₂×Q₈	—	3	1	no	—
412	C₂×Q₈	C₄×C₅×D₃	1	1	yes	characteristic
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	3	1	no	—
415	C₂×D₄	—	6	1	no	—
416	C₂×D₄	C₄×C₅×D₃	1	1	yes	characteristic
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	6	1	no	—
420	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
421	Q₁₆	—	3	4	no	—
422	SD₁₆	—	3	4	no	—
423	SD₁₆	—	3	4	no	—
424	D₈	—	3	4	no	—
425	M₁₆	—	2	1	no	—
426	M₁₆	—	3	2	no	—
427	M₁₆	—	3	2	no	—
428	M₁₆	—	3	2	no	—
429	M₁₆	—	3	2	no	—
430	M₁₆	—	3	2	no	—
431	M₁₆	—	6	4	no	—
432	M₁₆	—	6	4	no	—
433	M₁₆	—	6	1	no	—
434	M₁₆	C₂²×C₅×D₃	1	2	yes	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	3	2	no	—
437	C₂×C₈	—	3	2	no	—
438	C₂×C₈	—	6	4	no	—
439	C₂×C₈	—	6	4	no	—
440	C₂×C₈	—	6	1	no	—
441	C₄²	—	2	1	no	—
442	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
443	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
444	C₃×C₅	#2956	1	1	yes	characteristic, complemented, Hall
445	C₂²×C₃	—	2	2	no	—
446	C₂²×C₃	—	4	1	no	—
447	C₂²×C₃	—	8	1	no	—
448	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
449	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
450	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
451	C₂×D₃	—	2	2	no	—
452	C₂×D₃	—	8	1	no	—
453	C₃×C₄	—	2	2	no	—
454	C₃×C₄	—	2	2	no	—
455	C₃×C₄	—	4	1	no	—
456	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
457	C₃×C₄	C₄×C₅×D₄	1	1	yes	characteristic
458	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
459	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
460	Dic₃	—	2	2	no	—
461	C₂×C₅	—	2	1	no	—
462	C₂×C₅	—	2	1	no	—
463	C₂×C₅	—	2	1	no	—
464	C₂×C₅	—	4	2	no	—
465	C₂×C₅	—	12	2	no	—
466	C₂×C₅	C₂×#67⋊C₄	1	1	yes	characteristic
467	C₂³	—	2	1	no	—
468	C₂³	—	6	1	no	—
469	C₂³	C₅×#237	1	1	yes	characteristic
470	Q₈	—	2	1	no	—
471	Q₈	—	3	2	no	—
472	Q₈	—	6	1	no	—
473	Q₈	C₂×C₄×C₅×D₃	1	2	yes	—
474	D₄	—	2	2	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	1	no	—
477	D₄	—	3	2	no	—
478	D₄	—	6	2	no	—
479	D₄	—	6	2	no	—
480	D₄	—	6	1	no	—
481	D₄	C₂×C₄×C₅×D₃	1	2	yes	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	6	1	no	—
489	C₂×C₄	—	6	2	no	—
490	C₂×C₄	—	6	2	no	—
491	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
492	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
493	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
494	C₂×C₄	C₅×D₃×D₄	1	1	yes	characteristic
495	C₂×C₄	C₅×#237	1	1	yes	characteristic
496	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	3	4	no	—
499	C₈	—	3	4	no	—
500	C₈	—	6	2	no	—
501	C₂×C₃	—	2	1	no	—
502	C₂×C₃	—	2	1	no	—
503	C₂×C₃	—	2	1	no	—
504	C₂×C₃	—	4	2	no	—
505	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
506	D₃	—	4	2	no	—
507	C₅	#78980	1	1	yes	characteristic, direct product factor, Sylow
508	C₂²	—	2	2	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	6	2	no	—
511	C₂²	—	8	1	no	—
512	C₂²	—	24	1	no	—
513	C₂²	C₅×#67⋊C₄	1	1	yes	characteristic
514	C₂²	C₅×#67⋊C₄	1	1	yes	characteristic
515	C₂²	C₂×C₅×#237	1	1	yes	characteristic
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	6	2	no	—
520	C₄	C₅×#67⋊C₄	1	1	yes	characteristic
521	C₄	C₅×#67⋊C₄	1	1	yes	characteristic
522	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
523	C₄	C₂×C₅×D₃×D₄	1	1	yes	characteristic
524	C₃	C₅×#2956	1	1	yes	characteristic, complemented, Sylow
525	C₂	—	2	1	no	—
526	C₂	—	2	1	no	—
527	C₂	—	2	1	no	—
528	C₂	—	4	2	no	—
529	C₂	—	12	2	no	—
530	C₂	C₂×C₅×#67⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	C₂×D₃×D₄
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#104	C₂
socle	C₂×C₃×C₅	C₂×C₄×D₄
prime radical	C₅×#5822	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂×C₅×#104	D₃
hypocenter	C₃	C₅×#2956
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#104

Complements

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

N	H ≅ G/N	type
2. C₅×#5819	C₂	semidirect
3. C₅×#5745	C₂	semidirect
4. C₂×C₃×C₅×#104	C₂	semidirect
5. C₅×#5124	C₂	semidirect
6. C₂×C₅×#805	C₂	semidirect
7. C₄×C₅×#208	C₂	semidirect
8. C₅×#4824	C₂	semidirect
9. C₅×#4823	C₂	semidirect
15. C₅×#951	C₄	semidirect
17. C₅×#949	C₄	semidirect
19. C₅×#948	C₂²	semidirect
20. C₅×#942	C₄	semidirect
21. C₅×#932	C₄	semidirect
26. C₅×#907	C₂²	semidirect
29. C₃×C₅×#104	C₂²	semidirect
30. C₃×C₅×#104	C₂²	semidirect
31. C₅×#822	C₂²	semidirect
32. C₅×#805	C₂²	semidirect
33. C₅×#805	C₂²	semidirect
34. C₅×#803	C₂²	semidirect
35. C₄×C₅×C₃⋊C₈	C₂²	semidirect
36. #78980	C₅	direct (N × H)
44. C₂×C₅×#104	D₃	semidirect
70. C₅×#216	C₂×C₄	semidirect
71. C₅×#215	C₂×C₄	semidirect
72. C₅×#214	C₂×C₄	semidirect
73. C₅×#213	C₂×C₄	semidirect
88. #5819	C₂×C₅	semidirect
89. #5745	C₂×C₅	semidirect
90. C₂×C₃×#104	C₂×C₅	semidirect
91. #5124	C₂×C₅	semidirect
92. C₂×#805	C₂×C₅	semidirect
93. C₄×#208	C₂×C₅	semidirect
94. #4824	C₂×C₅	semidirect
95. #4823	C₂×C₅	semidirect
117. C₅×#104	C₂×D₃	semidirect
118. C₅×#104	C₂×D₃	semidirect
160. #951	C₄×C₅	semidirect
162. #949	C₄×C₅	semidirect
164. #948	C₂²×C₅	semidirect
165. #942	C₄×C₅	semidirect
166. #932	C₄×C₅	semidirect
171. #907	C₂²×C₅	semidirect
174. C₃×#104	C₂²×C₅	semidirect
175. C₃×#104	C₂²×C₅	semidirect
176. #822	C₂²×C₅	semidirect
177. #805	C₂²×C₅	semidirect
178. #805	C₂²×C₅	semidirect
179. #803	C₂²×C₅	semidirect
180. C₄×C₃⋊C₈	C₂²×C₅	semidirect
229. C₂×#104	C₅×D₃	semidirect
271. #216	C₂×C₄×C₅	semidirect
272. #215	C₂×C₄×C₅	semidirect
273. #214	C₂×C₄×C₅	semidirect
274. #213	C₂×C₄×C₅	semidirect
343. #104	C₂×C₅×D₃	semidirect
344. #104	C₂×C₅×D₃	semidirect
444. C₃×C₅	#2956	semidirect
507. C₅	#78980	direct (N × H)
524. C₃	C₅×#2956	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5822	2
C₅×#5819	2
C₅×#5745	2
C₂×C₃×C₅×#104	2
C₅×#5124	2
C₂×C₅×#805	2
C₄×C₅×#208	2
C₅×#4824	2
C₅×#4823	2
C₅×#2956	3
#78980	5

Subgroups — C5×#78980 #14418107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78980 #14418107