Subgroups — C₅×#78716 #14425206

Order 1920.

1448 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	C₅×#5964	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5832	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5748	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#413	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#825	C₂	1	2	yes	maximal, complemented
6	C₅×#4753	C₂	1	2	yes	maximal, complemented
7	C₅×#4752	C₂	1	2	yes	maximal, complemented
8	C₅×#4747	C₂	1	2	yes	maximal, complemented
9	C₅×#4746	C₂	1	2	yes	maximal, complemented
10	C₅×#3018	—	3	1	no	maximal, Hall
11	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
12	C₅×#1010	—	2	2	no	—
13	C₅×#1009	—	2	2	no	—
14	C₅×D₃×#41	—	2	4	no	—
15	C₅×#1007	C₂²	1	2	yes	—
16	C₅×#1004	—	2	2	no	—
17	C₅×#1004	C₂²	1	2	yes	—
18	C₂×C₅×#235	—	2	2	no	—
19	C₂×C₅×#235	C₂²	1	2	yes	—
20	C₂×C₅×#235	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	complemented
22	C₅×#947	C₂²	1	1	yes	characteristic, complemented
23	C₅×#944	C₂²	1	1	yes	characteristic, complemented
24	C₅×#940	C₂²	1	1	yes	characteristic, complemented
25	C₅×#939	—	2	2	no	—
26	C₅×#936	C₂²	1	1	yes	characteristic, complemented
27	C₄×C₅×#67	—	2	2	no	—
28	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
29	C₅×#909	—	2	2	no	—
30	C₅×#909	C₂²	1	4	yes	complemented
31	C₅×#908	—	2	2	no	—
32	C₅×#908	C₂²	1	4	yes	complemented
33	C₅×#904	—	2	4	no	—
34	C₃×C₅×#101	C₂²	1	2	yes	complemented
35	C₃×C₅×#100	C₂²	1	2	yes	complemented
36	C₅×#825	C₂²	1	4	yes	complemented
37	C₅×#825	C₂²	1	4	yes	complemented
38	#78716	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₅×#585	—	3	1	no	—
40	C₅×#575	—	3	2	no	—
41	C₅×#532	—	3	1	no	—
42	C₅×#456	—	3	2	no	—
43	C₅×#455	—	3	2	no	—
44	C₅×#454	—	3	2	no	—
45	C₅×#453	—	3	2	no	—
46	C₂×C₅×#104	—	3	2	no	—
47	C₅×#413	D₃	1	1	yes	characteristic, complemented
48	C₃×C₅×#41	—	2	2	no	—
49	C₃×C₅×#41	—	2	2	no	—
50	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
52	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂×C₅×#67	—	2	4	no	—
56	C₂×C₅×#67	—	2	2	no	—
57	C₂×C₅×#67	—	2	2	no	—
58	C₂×C₅×#67	—	2	1	no	—
59	C₂²×C₅×Dic₃	—	2	1	no	—
60	C₅×#239	—	2	4	no	—
61	C₅×D₃×Q₈	—	2	4	no	—
62	C₅×#237	—	2	8	no	—
63	C₅×#237	—	2	4	no	—
64	C₅×D₃×D₄	—	2	8	no	—
65	C₅×D₃×D₄	—	2	4	no	—
66	C₅×#235	—	2	4	no	—
67	C₅×#235	—	2	4	no	—
68	C₅×#235	—	2	2	no	—
69	C₅×#235	—	2	4	no	—
70	C₅×#235	—	2	2	no	—
71	C₅×#235	—	2	2	no	—
72	C₅×#235	—	2	2	no	—
73	C₅×#235	D₄	1	4	yes	complemented
74	C₅×#235	C₂³	1	4	yes	—
75	C₂×C₅×D₁₂	—	2	2	no	—
76	C₂×C₅×D₁₂	D₄	1	2	yes	complemented
77	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
78	C₂×C₄×C₅×D₃	—	2	4	no	—
79	C₂×C₄×C₅×D₃	—	2	2	no	—
80	C₂×C₄×C₅×D₃	—	2	1	no	—
81	C₂×C₅×Dic₆	—	2	2	no	—
82	C₂×C₅×Dic₆	D₄	1	2	yes	complemented
83	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
84	C₃×C₅×M₁₆	—	2	2	no	—
85	C₃×C₅×M₁₆	C₂³	1	4	yes	—
86	C₂×C₃×C₅×C₈	—	2	2	no	—
87	C₅×#217	—	2	2	no	—
88	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
89	C₅×Dic₃⋊C₄	—	2	2	no	—
90	C₄×C₅×Dic₃	—	2	1	no	—
91	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
92	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
93	C₅×Dic₁₂	—	2	4	no	—
94	C₅×D₂₄	—	2	4	no	—
95	C₅×#204	—	2	4	no	—
96	C₅×#204	—	2	4	no	—
97	#5964	C₂×C₅	1	1	yes	characteristic, complemented
98	#5832	C₂×C₅	1	1	yes	characteristic, complemented
99	#5748	C₂×C₅	1	2	yes	complemented
100	C₃×#413	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂×#825	C₂×C₅	1	2	yes	complemented
102	#4753	C₂×C₅	1	2	yes	complemented
103	#4752	C₂×C₅	1	2	yes	complemented
104	#4747	C₂×C₅	1	2	yes	complemented
105	#4746	C₂×C₅	1	2	yes	complemented
106	C₅×2₋¹⁺⁴	—	3	2	no	—
107	C₅×2₋¹⁺⁴	—	6	2	no	—
108	C₅×H(5,𝔽₂)	—	3	2	no	—
109	C₅×H(5,𝔽₂)	—	6	2	no	—
110	C₅×H(5,𝔽₂)	—	6	2	no	—
111	C₂×C₅×#41	—	3	2	no	—
112	C₂×C₅×#41	—	3	1	no	—
113	C₂×C₅×#41	—	6	4	no	—
114	C₂×C₅×#41	—	6	2	no	—
115	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
116	C₅×#137	—	3	4	no	—
117	C₅×#137	—	6	2	no	—
118	C₅×AGL(1,ℤ/8)	—	3	4	no	—
119	C₅×AGL(1,ℤ/8)	—	6	2	no	—
120	C₅×#135	—	6	4	no	—
121	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	complemented
122	C₅×C₄⋊Q₈	—	3	1	no	—
123	C₅×#127	—	3	1	no	—
124	C₅×#124	—	3	1	no	—
125	C₅×#124	—	3	1	no	—
126	C₅×#121	—	6	2	no	—
127	C₄×C₅×D₄	—	6	2	no	—
128	C₂×C₄²×C₅	—	3	1	no	—
129	C₅×#104	—	3	4	no	—
130	C₅×#104	—	3	4	no	—
131	C₅×#101	C₂×D₃	1	2	yes	complemented
132	C₅×#100	C₂×D₃	1	2	yes	complemented
133	#3018	—	3	1	no	Sylow
134	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
135	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₅×D₃	—	2	4	no	—
137	C₂²×C₅×D₃	—	2	2	no	—
138	C₂²×C₅×D₃	—	2	1	no	—
139	C₃×C₅×Q₈	—	2	2	no	—
140	C₃×C₅×D₄	—	2	4	no	—
141	C₃×C₅×D₄	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
148	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
149	C₅×#67	—	2	8	no	—
150	C₅×#67	—	2	4	no	—
151	C₅×#67	—	2	4	no	—
152	C₅×#67	—	4	4	no	—
153	C₅×#67	—	4	2	no	—
154	C₂×C₅×Dic₃	—	2	4	no	—
155	C₂×C₅×Dic₃	—	2	2	no	—
156	C₂×C₅×Dic₃	—	2	1	no	—
157	C₂×C₅×Dic₃	—	2	1	no	—
158	C₂×C₅×Dic₃	—	2	1	no	—
159	C₂×C₅×Dic₃	—	4	2	no	—
160	C₅×D₁₂	—	2	4	no	—
161	C₅×D₁₂	—	2	2	no	—
162	C₅×D₁₂	—	2	2	no	—
163	C₅×D₁₂	C₂×D₄	1	4	yes	—
164	C₄×C₅×D₃	—	2	8	no	—
165	C₄×C₅×D₃	—	2	4	no	—
166	C₄×C₅×D₃	—	2	4	no	—
167	C₄×C₅×D₃	—	4	1	no	—
168	C₄×C₅×D₃	—	4	1	no	—
169	C₅×Dic₆	—	2	4	no	—
170	C₅×Dic₆	—	2	2	no	—
171	C₅×Dic₆	—	2	2	no	—
172	C₅×Dic₆	C₂×D₄	1	4	yes	—
173	C₃×C₅×C₈	—	2	4	no	—
174	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
175	#1010	—	2	2	no	—
176	#1009	—	2	2	no	—
177	D₃×#41	—	2	4	no	—
178	#1007	C₂²×C₅	1	2	yes	—
179	#1004	—	2	2	no	—
180	#1004	C₂²×C₅	1	2	yes	—
181	C₂×#235	—	2	2	no	—
182	C₂×#235	C₂²×C₅	1	2	yes	—
183	C₂×#235	C₂²×C₅	1	1	yes	characteristic, complemented
184	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	complemented
185	#947	C₂²×C₅	1	1	yes	characteristic, complemented
186	#944	C₂²×C₅	1	1	yes	characteristic, complemented
187	#940	C₂²×C₅	1	1	yes	characteristic, complemented
188	#939	—	2	2	no	—
189	#936	C₂²×C₅	1	1	yes	characteristic, complemented
190	C₄×#67	—	2	2	no	—
191	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic, complemented
192	#909	—	2	2	no	—
193	#909	C₂²×C₅	1	4	yes	complemented
194	#908	—	2	2	no	—
195	#908	C₂²×C₅	1	4	yes	complemented
196	#904	—	2	4	no	—
197	C₃×#101	C₂²×C₅	1	2	yes	complemented
198	C₃×#100	C₂²×C₅	1	2	yes	complemented
199	#825	C₂²×C₅	1	4	yes	complemented
200	#825	C₂²×C₅	1	4	yes	complemented
201	C₅×#41	—	2	2	no	—
202	C₅×#41	—	2	2	no	—
203	C₅×#41	—	3	4	no	—
204	C₅×#41	—	3	4	no	—
205	C₅×#41	—	6	4	no	—
206	C₅×#41	—	6	4	no	—
207	C₅×#41	—	6	4	no	—
208	C₅×#41	—	6	8	no	—
209	C₅×#41	—	6	4	no	—
210	C₅×#41	—	6	2	no	—
211	C₅×#41	—	6	4	no	—
212	C₅×#41	—	6	2	no	—
213	C₅×#41	—	6	2	no	—
214	C₅×#41	—	6	2	no	—
215	C₂×C₅×Q₈	—	3	2	no	—
216	C₂×C₅×Q₈	—	3	1	no	—
217	C₂×C₅×Q₈	—	6	2	no	—
218	C₂×C₅×Q₈	—	6	4	no	—
219	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
220	C₂×C₅×D₄	—	3	2	no	—
221	C₂×C₅×D₄	—	3	1	no	—
222	C₂×C₅×D₄	—	6	2	no	—
223	C₂×C₅×D₄	—	6	4	no	—
224	C₂×C₅×D₄	—	6	8	no	—
225	C₂×C₅×D₄	—	6	2	no	—
226	C₂×C₅×D₄	—	6	4	no	—
227	C₂×C₅×D₄	—	6	2	no	—
228	C₂×C₅×D₄	—	6	1	no	—
229	C₂×C₅×D₄	D₁₂	1	2	yes	—
230	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
231	C₂²×C₄×C₅	—	6	4	no	—
232	C₂²×C₄×C₅	—	6	2	no	—
233	C₂²×C₄×C₅	—	6	1	no	—
234	C₂²×C₄×C₅	—	6	1	no	—
235	C₂²×C₄×C₅	D₁₂	1	2	yes	—
236	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
237	C₅×Q₁₆	—	6	4	no	—
238	C₅×SD₁₆	—	6	4	no	—
239	C₅×SD₁₆	—	6	4	no	—
240	C₅×D₈	—	6	4	no	—
241	C₅×M₁₆	—	2	2	no	—
242	C₅×M₁₆	C₂²×D₃	1	4	yes	—
243	C₂×C₅×C₈	—	2	2	no	—
244	C₅×C₄⋊C₄	—	6	2	no	—
245	C₅×C₂²⋊C₄	—	6	2	no	—
246	C₅×C₂²⋊C₄	—	6	2	no	—
247	C₄²×C₅	—	3	1	no	—
248	C₄²×C₅	—	3	1	no	—
249	C₄²×C₅	—	6	1	no	—
250	#585	—	3	1	no	—
251	#575	—	3	2	no	—
252	#532	—	3	1	no	—
253	#456	—	3	2	no	—
254	#455	—	3	2	no	—
255	#454	—	3	2	no	—
256	#453	—	3	2	no	—
257	C₂×#104	—	3	2	no	—
258	#413	C₅×D₃	1	1	yes	characteristic, complemented
259	C₂²×C₃×C₅	—	2	2	no	—
260	C₂²×C₃×C₅	—	4	1	no	—
261	C₂²×C₃×C₅	—	4	2	no	—
262	C₂²×C₃×C₅	#120	1	2	yes	—
263	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₅×D₃	—	2	4	no	—
265	C₂×C₅×D₃	—	4	2	no	—
266	C₂×C₅×D₃	—	4	1	no	—
267	C₂×C₅×D₃	—	8	2	no	—
268	C₂×C₅×D₃	—	8	4	no	—
269	C₃×C₄×C₅	—	2	2	no	—
270	C₃×C₄×C₅	#120	1	1	yes	characteristic
271	C₃×C₄×C₅	#120	1	1	yes	characteristic
272	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
273	C₅×Dic₃	—	2	2	no	—
274	C₅×Dic₃	—	2	4	no	—
275	C₅×Dic₃	—	4	1	no	—
276	C₅×Dic₃	—	4	1	no	—
277	C₃×#41	—	2	2	no	—
278	C₃×#41	—	2	2	no	—
279	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
280	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
281	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
282	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
283	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
284	C₂×#67	—	2	4	no	—
285	C₂×#67	—	2	2	no	—
286	C₂×#67	—	2	2	no	—
287	C₂×#67	—	2	1	no	—
288	C₂²×Dic₃	—	2	1	no	—
289	#239	—	2	4	no	—
290	D₃×Q₈	—	2	4	no	—
291	#237	—	2	8	no	—
292	#237	—	2	4	no	—
293	D₃×D₄	—	2	8	no	—
294	D₃×D₄	—	2	4	no	—
295	#235	—	2	4	no	—
296	#235	—	2	4	no	—
297	#235	—	2	2	no	—
298	#235	—	2	4	no	—
299	#235	—	2	2	no	—
300	#235	—	2	2	no	—
301	#235	—	2	2	no	—
302	#235	C₅×D₄	1	4	yes	complemented
303	#235	C₂³×C₅	1	4	yes	—
304	C₂×D₁₂	—	2	2	no	—
305	C₂×D₁₂	C₅×D₄	1	2	yes	complemented
306	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
307	C₂×C₄×D₃	—	2	4	no	—
308	C₂×C₄×D₃	—	2	2	no	—
309	C₂×C₄×D₃	—	2	1	no	—
310	C₂×Dic₆	—	2	2	no	—
311	C₂×Dic₆	C₅×D₄	1	2	yes	complemented
312	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
313	C₃×M₁₆	—	2	2	no	—
314	C₃×M₁₆	C₂³×C₅	1	4	yes	—
315	C₂×C₃×C₈	—	2	2	no	—
316	#217	—	2	2	no	—
317	(C₂×D₃)⋊C₄	—	2	2	no	—
318	Dic₃⋊C₄	—	2	2	no	—
319	C₄×Dic₃	—	2	1	no	—
320	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
321	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
322	Dic₁₂	—	2	4	no	—
323	D₂₄	—	2	4	no	—
324	#204	—	2	4	no	—
325	#204	—	2	4	no	—
326	C₂³×C₅	—	6	4	no	—
327	C₂³×C₅	—	6	2	no	—
328	C₂³×C₅	—	6	1	no	—
329	C₂³×C₅	C₂×D₁₂	1	2	yes	—
330	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
331	C₅×Q₈	—	2	2	no	—
332	C₅×Q₈	—	3	4	no	—
333	C₅×Q₈	—	6	4	no	—
334	C₅×Q₈	—	6	2	no	—
335	C₅×Q₈	—	6	2	no	—
336	C₅×D₄	—	2	4	no	—
337	C₅×D₄	—	2	2	no	—
338	C₅×D₄	—	3	4	no	—
339	C₅×D₄	—	6	4	no	—
340	C₅×D₄	—	6	8	no	—
341	C₅×D₄	—	6	4	no	—
342	C₅×D₄	—	6	4	no	—
343	C₅×D₄	—	6	2	no	—
344	C₅×D₄	—	6	2	no	—
345	C₅×D₄	—	12	4	no	—
346	C₅×D₄	—	12	2	no	—
347	C₂×C₄×C₅	—	2	2	no	—
348	C₂×C₄×C₅	—	2	2	no	—
349	C₂×C₄×C₅	—	6	8	no	—
350	C₂×C₄×C₅	—	6	4	no	—
351	C₂×C₄×C₅	—	6	2	no	—
352	C₂×C₄×C₅	—	6	1	no	—
353	C₂×C₄×C₅	—	6	4	no	—
354	C₂×C₄×C₅	—	6	4	no	—
355	C₂×C₄×C₅	—	6	1	no	—
356	C₂×C₄×C₅	—	6	1	no	—
357	C₂×C₄×C₅	—	12	2	no	—
358	C₂×C₄×C₅	—	12	1	no	—
359	C₂×C₄×C₅	—	12	1	no	—
360	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
361	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
362	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
363	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
364	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
365	C₅×C₈	—	2	4	no	—
366	2₋¹⁺⁴	—	3	2	no	—
367	2₋¹⁺⁴	—	6	2	no	—
368	H(5,𝔽₂)	—	3	2	no	—
369	H(5,𝔽₂)	—	6	2	no	—
370	H(5,𝔽₂)	—	6	2	no	—
371	C₂×#41	—	3	2	no	—
372	C₂×#41	—	3	1	no	—
373	C₂×#41	—	6	4	no	—
374	C₂×#41	—	6	2	no	—
375	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
376	#137	—	3	4	no	—
377	#137	—	6	2	no	—
378	AGL(1,ℤ/8)	—	3	4	no	—
379	AGL(1,ℤ/8)	—	6	2	no	—
380	#135	—	6	4	no	—
381	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	complemented
382	C₄⋊Q₈	—	3	1	no	—
383	#127	—	3	1	no	—
384	#124	—	3	1	no	—
385	#124	—	3	1	no	—
386	#121	—	6	2	no	—
387	C₄×D₄	—	6	2	no	—
388	C₂×C₄²	—	3	1	no	—
389	#104	—	3	4	no	—
390	#104	—	3	4	no	—
391	#101	C₂×C₅×D₃	1	2	yes	complemented
392	#100	C₂×C₅×D₃	1	2	yes	complemented
393	C₂×C₃×C₅	—	2	1	no	—
394	C₂×C₃×C₅	—	2	2	no	—
395	C₂×C₃×C₅	—	4	2	no	—
396	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
397	C₅×D₃	—	4	4	no	—
398	C₅×D₃	—	8	1	no	—
399	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
400	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
401	C₂²×D₃	—	2	4	no	—
402	C₂²×D₃	—	2	2	no	—
403	C₂²×D₃	—	2	1	no	—
404	C₃×Q₈	—	2	2	no	—
405	C₃×D₄	—	2	4	no	—
406	C₃×D₄	—	2	2	no	—
407	C₂×C₃×C₄	—	2	2	no	—
408	C₂×C₃×C₄	—	2	2	no	—
409	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
410	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
411	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
412	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
413	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
414	#67	—	2	8	no	—
415	#67	—	2	4	no	—
416	#67	—	2	4	no	—
417	#67	—	4	4	no	—
418	#67	—	4	2	no	—
419	C₂×Dic₃	—	2	4	no	—
420	C₂×Dic₃	—	2	2	no	—
421	C₂×Dic₃	—	2	1	no	—
422	C₂×Dic₃	—	2	1	no	—
423	C₂×Dic₃	—	2	1	no	—
424	C₂×Dic₃	—	4	2	no	—
425	D₁₂	—	2	4	no	—
426	D₁₂	—	2	2	no	—
427	D₁₂	—	2	2	no	—
428	D₁₂	C₂×C₅×D₄	1	4	yes	—
429	C₄×D₃	—	2	8	no	—
430	C₄×D₃	—	2	4	no	—
431	C₄×D₃	—	2	4	no	—
432	C₄×D₃	—	4	1	no	—
433	C₄×D₃	—	4	1	no	—
434	Dic₆	—	2	4	no	—
435	Dic₆	—	2	2	no	—
436	Dic₆	—	2	2	no	—
437	Dic₆	C₂×C₅×D₄	1	4	yes	—
438	C₃×C₈	—	2	4	no	—
439	C₂²×C₅	—	2	2	no	—
440	C₂²×C₅	—	4	1	no	—
441	C₂²×C₅	—	4	2	no	—
442	C₂²×C₅	—	6	4	no	—
443	C₂²×C₅	—	12	2	no	—
444	C₂²×C₅	—	12	1	no	—
445	C₂²×C₅	—	24	2	no	—
446	C₂²×C₅	—	24	4	no	—
447	C₂²×C₅	#882	1	2	yes	—
448	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
449	C₄×C₅	—	2	2	no	—
450	C₄×C₅	—	6	2	no	—
451	C₄×C₅	—	6	4	no	—
452	C₄×C₅	—	12	1	no	—
453	C₄×C₅	—	12	1	no	—
454	C₄×C₅	#882	1	1	yes	characteristic
455	C₄×C₅	#882	1	1	yes	characteristic
456	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
457	#41	—	2	2	no	—
458	#41	—	2	2	no	—
459	#41	—	3	4	no	—
460	#41	—	3	4	no	—
461	#41	—	6	4	no	—
462	#41	—	6	4	no	—
463	#41	—	6	4	no	—
464	#41	—	6	8	no	—
465	#41	—	6	4	no	—
466	#41	—	6	2	no	—
467	#41	—	6	4	no	—
468	#41	—	6	2	no	—
469	#41	—	6	2	no	—
470	#41	—	6	2	no	—
471	C₂×Q₈	—	3	2	no	—
472	C₂×Q₈	—	3	1	no	—
473	C₂×Q₈	—	6	2	no	—
474	C₂×Q₈	—	6	4	no	—
475	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
476	C₂×D₄	—	3	2	no	—
477	C₂×D₄	—	3	1	no	—
478	C₂×D₄	—	6	2	no	—
479	C₂×D₄	—	6	4	no	—
480	C₂×D₄	—	6	8	no	—
481	C₂×D₄	—	6	2	no	—
482	C₂×D₄	—	6	4	no	—
483	C₂×D₄	—	6	2	no	—
484	C₂×D₄	—	6	1	no	—
485	C₂×D₄	C₅×D₁₂	1	2	yes	—
486	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
487	C₂²×C₄	—	6	4	no	—
488	C₂²×C₄	—	6	2	no	—
489	C₂²×C₄	—	6	1	no	—
490	C₂²×C₄	—	6	1	no	—
491	C₂²×C₄	C₅×D₁₂	1	2	yes	—
492	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
493	Q₁₆	—	6	4	no	—
494	SD₁₆	—	6	4	no	—
495	SD₁₆	—	6	4	no	—
496	D₈	—	6	4	no	—
497	M₁₆	—	2	2	no	—
498	M₁₆	C₂²×C₅×D₃	1	4	yes	—
499	C₂×C₈	—	2	2	no	—
500	C₄⋊C₄	—	6	2	no	—
501	C₂²⋊C₄	—	6	2	no	—
502	C₂²⋊C₄	—	6	2	no	—
503	C₄²	—	3	1	no	—
504	C₄²	—	3	1	no	—
505	C₄²	—	6	1	no	—
506	C₃×C₅	#3018	1	1	yes	characteristic, complemented, Hall
507	C₂²×C₃	—	2	2	no	—
508	C₂²×C₃	—	4	1	no	—
509	C₂²×C₃	—	4	2	no	—
510	C₂²×C₃	C₅×#120	1	2	yes	—
511	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
512	C₂×D₃	—	2	4	no	—
513	C₂×D₃	—	4	2	no	—
514	C₂×D₃	—	4	1	no	—
515	C₂×D₃	—	8	2	no	—
516	C₂×D₃	—	8	4	no	—
517	C₃×C₄	—	2	2	no	—
518	C₃×C₄	C₅×#120	1	1	yes	characteristic
519	C₃×C₄	C₅×#120	1	1	yes	characteristic
520	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
521	Dic₃	—	2	2	no	—
522	Dic₃	—	2	4	no	—
523	Dic₃	—	4	1	no	—
524	Dic₃	—	4	1	no	—
525	C₂×C₅	—	2	1	no	—
526	C₂×C₅	—	2	2	no	—
527	C₂×C₅	—	4	2	no	—
528	C₂×C₅	—	12	4	no	—
529	C₂×C₅	—	24	1	no	—
530	C₂×C₅	C₂×#882	1	1	yes	characteristic
531	C₂³	—	6	4	no	—
532	C₂³	—	6	2	no	—
533	C₂³	—	6	1	no	—
534	C₂³	C₂×C₅×D₁₂	1	2	yes	—
535	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
536	Q₈	—	2	2	no	—
537	Q₈	—	3	4	no	—
538	Q₈	—	6	4	no	—
539	Q₈	—	6	2	no	—
540	Q₈	—	6	2	no	—
541	D₄	—	2	4	no	—
542	D₄	—	2	2	no	—
543	D₄	—	3	4	no	—
544	D₄	—	6	4	no	—
545	D₄	—	6	8	no	—
546	D₄	—	6	4	no	—
547	D₄	—	6	4	no	—
548	D₄	—	6	2	no	—
549	D₄	—	6	2	no	—
550	D₄	—	12	4	no	—
551	D₄	—	12	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	6	8	no	—
555	C₂×C₄	—	6	4	no	—
556	C₂×C₄	—	6	2	no	—
557	C₂×C₄	—	6	1	no	—
558	C₂×C₄	—	6	4	no	—
559	C₂×C₄	—	6	4	no	—
560	C₂×C₄	—	6	1	no	—
561	C₂×C₄	—	6	1	no	—
562	C₂×C₄	—	12	2	no	—
563	C₂×C₄	—	12	1	no	—
564	C₂×C₄	—	12	1	no	—
565	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
566	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
567	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
568	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
569	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
570	C₈	—	2	4	no	—
571	C₂×C₃	—	2	1	no	—
572	C₂×C₃	—	2	2	no	—
573	C₂×C₃	—	4	2	no	—
574	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
575	D₃	—	4	4	no	—
576	D₃	—	8	1	no	—
577	C₅	#78716	1	1	yes	characteristic, direct product factor, Sylow
578	C₂²	—	2	2	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	6	4	no	—
582	C₂²	—	12	2	no	—
583	C₂²	—	12	1	no	—
584	C₂²	—	24	2	no	—
585	C₂²	—	24	4	no	—
586	C₂²	C₅×#882	1	2	yes	—
587	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
588	C₄	—	2	2	no	—
589	C₄	—	6	2	no	—
590	C₄	—	6	4	no	—
591	C₄	—	12	1	no	—
592	C₄	—	12	1	no	—
593	C₄	C₅×#882	1	1	yes	characteristic
594	C₄	C₅×#882	1	1	yes	characteristic
595	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
596	C₃	C₅×#3018	1	1	yes	characteristic, complemented, Sylow
597	C₂	—	2	1	no	—
598	C₂	—	2	2	no	—
599	C₂	—	4	2	no	—
600	C₂	—	12	4	no	—
601	C₂	—	24	1	no	—
602	C₂	C₂×C₅×#882	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	#882
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#413	C₂
socle	C₂×C₃×C₅	C₂×#120
hypercenter	C₅×#413	D₃
hypocenter	C₃	C₅×#3018
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₄×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#413

Complements

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

N	H ≅ G/N	type
1. C₅×#5964	C₂	semidirect
2. C₅×#5832	C₂	semidirect
3. C₅×#5748	C₂	semidirect
4. C₃×C₅×#413	C₂	semidirect
5. C₂×C₅×#825	C₂	semidirect
6. C₅×#4753	C₂	semidirect
7. C₅×#4752	C₂	semidirect
8. C₅×#4747	C₂	semidirect
9. C₅×#4746	C₂	semidirect
20. C₂×C₅×#235	C₂²	semidirect
21. C₂×C₃×C₅×M₁₆	C₂²	semidirect
22. C₅×#947	C₂²	semidirect
23. C₅×#944	C₂²	semidirect
24. C₅×#940	C₂²	semidirect
26. C₅×#936	C₂²	semidirect
28. C₂×C₄×C₅×Dic₃	C₂²	semidirect
30. C₅×#909	C₂²	semidirect
32. C₅×#908	C₂²	semidirect
34. C₃×C₅×#101	C₂²	semidirect
35. C₃×C₅×#100	C₂²	semidirect
36. C₅×#825	C₂²	semidirect
37. C₅×#825	C₂²	semidirect
38. #78716	C₅	direct (N × H)
47. C₅×#413	D₃	semidirect
73. C₅×#235	D₄	semidirect
76. C₂×C₅×D₁₂	D₄	semidirect
82. C₂×C₅×Dic₆	D₄	semidirect
97. #5964	C₂×C₅	semidirect
98. #5832	C₂×C₅	semidirect
99. #5748	C₂×C₅	semidirect
100. C₃×#413	C₂×C₅	semidirect
101. C₂×#825	C₂×C₅	semidirect
102. #4753	C₂×C₅	semidirect
103. #4752	C₂×C₅	semidirect
104. #4747	C₂×C₅	semidirect
105. #4746	C₂×C₅	semidirect
121. C₂×C₅×M₁₆	C₂×D₃	semidirect
131. C₅×#101	C₂×D₃	semidirect
132. C₅×#100	C₂×D₃	semidirect
183. C₂×#235	C₂²×C₅	semidirect
184. C₂×C₃×M₁₆	C₂²×C₅	semidirect
185. #947	C₂²×C₅	semidirect
186. #944	C₂²×C₅	semidirect
187. #940	C₂²×C₅	semidirect
189. #936	C₂²×C₅	semidirect
191. C₂×C₄×Dic₃	C₂²×C₅	semidirect
193. #909	C₂²×C₅	semidirect
195. #908	C₂²×C₅	semidirect
197. C₃×#101	C₂²×C₅	semidirect
198. C₃×#100	C₂²×C₅	semidirect
199. #825	C₂²×C₅	semidirect
200. #825	C₂²×C₅	semidirect
258. #413	C₅×D₃	semidirect
302. #235	C₅×D₄	semidirect
305. C₂×D₁₂	C₅×D₄	semidirect
311. C₂×Dic₆	C₅×D₄	semidirect
381. C₂×M₁₆	C₂×C₅×D₃	semidirect
391. #101	C₂×C₅×D₃	semidirect
392. #100	C₂×C₅×D₃	semidirect
506. C₃×C₅	#3018	semidirect
577. C₅	#78716	direct (N × H)
596. C₃	C₅×#3018	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5964	2
C₅×#5832	2
C₅×#5748	2
C₃×C₅×#413	2
C₂×C₅×#825	2
C₅×#4753	2
C₅×#4752	2
C₅×#4747	2
C₅×#4746	2
C₅×#3018	3
#78716	5

Subgroups — C5×#78716 #14425206

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78716 #14425206