Subgroups — C₅×#83394 #14425299

Order 1920.

1524 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#1004	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5822	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#833	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5077	C₂	1	4	yes	maximal, complemented
6	C₅×#5061	C₂	1	4	yes	maximal, complemented
7	C₅×#5005	C₂	1	2	yes	maximal, complemented
8	C₅×#3019	—	3	1	no	maximal, Hall
9	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
10	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂²×C₅×#67	—	2	2	no	—
12	C₅×#1004	—	2	2	no	—
13	C₅×#1004	—	2	4	no	—
14	C₅×#1004	C₂²	1	4	yes	—
15	C₂×C₅×#237	—	2	2	no	—
16	C₂×C₅×D₃×D₄	—	2	2	no	—
17	C₂×C₅×#235	C₂²	1	2	yes	—
18	C₃×C₅×#127	C₂²	1	2	yes	complemented
19	C₃×C₅×#124	C₂²	1	2	yes	complemented
20	C₃×C₅×#121	—	2	2	no	—
21	C₃×C₅×#120	—	2	2	no	—
22	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
23	C₅×#951	—	2	2	no	—
24	C₅×#950	—	2	4	no	—
25	C₅×#949	—	2	2	no	—
26	C₅×#942	C₂²	1	4	yes	complemented
27	C₅×#932	C₂²	1	4	yes	complemented
28	C₂×C₅×#208	C₂²	1	2	yes	complemented
29	C₅×#833	C₂²	1	4	yes	complemented
30	C₅×#805	C₂²	1	8	yes	complemented
31	#83394	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₅×H(5,𝔽₂)	—	3	1	no	—
33	C₅×#575	—	3	2	no	—
34	C₅×#535	D₃	1	1	yes	characteristic, complemented
35	C₅×#455	—	3	4	no	—
36	C₅×#453	—	3	4	no	—
37	C₅×#421	—	3	2	no	—
38	C₂×C₅×#100	—	3	1	no	—
39	C₂⁴×C₃×C₅	D₄	1	2	yes	—
40	C₂³×C₅×D₃	—	2	2	no	—
41	C₃×C₅×#41	—	2	2	no	—
42	C₃×C₅×#41	—	2	2	no	—
43	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic, complemented
44	C₂×C₃×C₅×D₄	—	2	1	no	—
45	C₂×C₃×C₅×D₄	—	2	4	no	—
46	C₂×C₃×C₅×D₄	—	2	2	no	—
47	C₂×C₃×C₅×D₄	—	2	2	no	—
48	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
49	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
50	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic, complemented
51	C₂²×C₃×C₄×C₅	—	2	1	no	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂×C₅×#67	—	2	4	no	—
54	C₂×C₅×#67	—	2	8	no	—
55	C₂×C₅×#67	—	2	2	no	—
56	C₂×C₅×#67	—	2	8	no	—
57	C₂²×C₅×Dic₃	—	2	2	no	—
58	C₅×#237	—	2	8	no	—
59	C₅×#237	—	2	8	no	—
60	C₅×D₃×D₄	—	2	8	no	—
61	C₅×D₃×D₄	—	2	8	no	—
62	C₅×#235	—	2	2	no	—
63	C₅×#235	—	2	2	no	—
64	C₅×#235	D₄	1	4	yes	complemented
65	C₅×#235	C₂³	1	4	yes	—
66	C₂×C₅×D₁₂	D₄	1	2	yes	complemented
67	C₂×C₄×C₅×D₃	—	2	2	no	—
68	C₂×C₅×Dic₆	D₄	1	2	yes	complemented
69	C₃×C₅×C₄⋊C₄	—	2	1	no	—
70	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
71	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
72	C₃×C₄²×C₅	C₂³	1	2	yes	complemented
73	C₅×#216	—	2	4	no	—
74	C₅×#215	—	2	4	no	—
75	C₅×#214	—	2	4	no	—
76	C₅×#213	—	2	4	no	—
77	C₅×#208	—	2	2	no	—
78	C₅×#208	C₂³	1	4	yes	complemented
79	C₂×C₅×C₃⋊C₈	—	2	2	no	—
80	C₂×#1004	C₂×C₅	1	1	yes	characteristic, complemented
81	C₃×#535	C₂×C₅	1	1	yes	characteristic, complemented
82	#5822	C₂×C₅	1	2	yes	complemented
83	C₂×#833	C₂×C₅	1	1	yes	characteristic, complemented
84	#5077	C₂×C₅	1	4	yes	complemented
85	#5061	C₂×C₅	1	4	yes	complemented
86	#5005	C₂×C₅	1	2	yes	complemented
87	C₅×H(5,𝔽₂)	—	3	4	no	—
88	C₅×H(5,𝔽₂)	—	6	4	no	—
89	C₅×H(5,𝔽₂)	—	6	2	no	—
90	C₂×C₅×#41	—	3	2	no	—
91	C₂×C₅×#41	—	6	2	no	—
92	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic, complemented
93	C₂²×C₅×D₄	—	6	2	no	—
94	C₂²×C₅×D₄	—	6	2	no	—
95	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
96	C₅×#137	—	3	4	no	—
97	C₅×#137	—	6	2	no	—
98	C₅×AGL(1,ℤ/8)	—	3	4	no	—
99	C₅×AGL(1,ℤ/8)	—	6	2	no	—
100	C₅×#135	—	6	4	no	—
101	C₂×C₅×M₁₆	—	3	2	no	—
102	C₅×#127	C₂×D₃	1	2	yes	complemented
103	C₅×#124	C₂×D₃	1	2	yes	complemented
104	C₅×#121	—	2	2	no	—
105	C₅×#120	—	2	2	no	—
106	C₅×#117	C₂×D₃	1	1	yes	characteristic, complemented
107	C₅×#104	—	3	8	no	—
108	C₅×#100	—	3	4	no	—
109	#3019	—	3	1	no	Sylow
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	—	2	2	no	—
112	C₂³×C₃×C₅	—	2	1	no	—
113	C₂³×C₃×C₅	—	8	2	no	—
114	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
115	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₅×D₃	—	2	2	no	—
117	C₂²×C₅×D₃	—	2	8	no	—
118	C₂²×C₅×D₃	—	8	4	no	—
119	C₃×C₅×Q₈	—	2	2	no	—
120	C₃×C₅×D₄	—	2	4	no	—
121	C₃×C₅×D₄	—	2	4	no	—
122	C₃×C₅×D₄	—	2	2	no	—
123	C₃×C₅×D₄	—	4	1	no	—
124	C₃×C₅×D₄	—	4	1	no	—
125	C₃×C₅×D₄	—	8	4	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	1	no	—
128	C₂×C₃×C₄×C₅	—	4	2	no	—
129	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
133	C₅×#67	—	2	16	no	—
134	C₅×#67	—	2	4	no	—
135	C₅×#67	—	2	4	no	—
136	C₂×C₅×Dic₃	—	2	8	no	—
137	C₂×C₅×Dic₃	—	2	2	no	—
138	C₅×D₁₂	—	2	2	no	—
139	C₅×D₁₂	C₂×D₄	1	4	yes	—
140	C₄×C₅×D₃	—	2	4	no	—
141	C₄×C₅×D₃	—	2	4	no	—
142	C₅×Dic₆	—	2	2	no	—
143	C₅×Dic₆	C₂×D₄	1	4	yes	—
144	C₅×C₃⋊C₈	—	2	4	no	—
145	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
146	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
147	C₂²×#67	—	2	2	no	—
148	#1004	—	2	2	no	—
149	#1004	—	2	4	no	—
150	#1004	C₂²×C₅	1	4	yes	—
151	C₂×#237	—	2	2	no	—
152	C₂×D₃×D₄	—	2	2	no	—
153	C₂×#235	C₂²×C₅	1	2	yes	—
154	C₃×#127	C₂²×C₅	1	2	yes	complemented
155	C₃×#124	C₂²×C₅	1	2	yes	complemented
156	C₃×#121	—	2	2	no	—
157	C₃×#120	—	2	2	no	—
158	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
159	#951	—	2	2	no	—
160	#950	—	2	4	no	—
161	#949	—	2	2	no	—
162	#942	C₂²×C₅	1	4	yes	complemented
163	#932	C₂²×C₅	1	4	yes	complemented
164	C₂×#208	C₂²×C₅	1	2	yes	complemented
165	#833	C₂²×C₅	1	4	yes	complemented
166	#805	C₂²×C₅	1	8	yes	complemented
167	C₂⁴×C₅	—	6	2	no	—
168	C₂⁴×C₅	#67	1	2	yes	—
169	C₅×#41	—	2	2	no	—
170	C₅×#41	—	2	2	no	—
171	C₅×#41	—	3	4	no	—
172	C₅×#41	—	3	4	no	—
173	C₅×#41	—	6	8	no	—
174	C₅×#41	—	6	8	no	—
175	C₅×#41	—	6	2	no	—
176	C₅×#41	—	6	2	no	—
177	C₂×C₅×Q₈	—	3	2	no	—
178	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic, complemented
179	C₂×C₅×D₄	—	2	1	no	—
180	C₂×C₅×D₄	—	2	4	no	—
181	C₂×C₅×D₄	—	2	2	no	—
182	C₂×C₅×D₄	—	2	2	no	—
183	C₂×C₅×D₄	—	3	2	no	—
184	C₂×C₅×D₄	—	6	8	no	—
185	C₂×C₅×D₄	—	6	8	no	—
186	C₂×C₅×D₄	—	6	4	no	—
187	C₂×C₅×D₄	—	6	8	no	—
188	C₂×C₅×D₄	—	6	2	no	—
189	C₂×C₅×D₄	—	6	8	no	—
190	C₂×C₅×D₄	#67	1	2	yes	—
191	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
192	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic, complemented
193	C₂²×C₄×C₅	—	2	1	no	—
194	C₂²×C₄×C₅	—	6	2	no	—
195	C₂²×C₄×C₅	—	6	2	no	—
196	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
197	C₅×Q₁₆	—	6	4	no	—
198	C₅×SD₁₆	—	6	4	no	—
199	C₅×SD₁₆	—	6	4	no	—
200	C₅×D₈	—	6	4	no	—
201	C₅×M₁₆	—	3	4	no	—
202	C₅×M₁₆	—	6	2	no	—
203	C₂×C₅×C₈	—	6	2	no	—
204	C₅×C₄⋊C₄	—	2	1	no	—
205	C₅×C₂²⋊C₄	—	2	1	no	—
206	C₅×C₂²⋊C₄	—	2	4	no	—
207	C₄²×C₅	C₂²×D₃	1	2	yes	complemented
208	C₂×H(5,𝔽₂)	—	3	1	no	—
209	#575	—	3	2	no	—
210	#535	C₅×D₃	1	1	yes	characteristic, complemented
211	#455	—	3	4	no	—
212	#453	—	3	4	no	—
213	#421	—	3	2	no	—
214	C₂×#100	—	3	1	no	—
215	C₂²×C₃×C₅	—	2	4	no	—
216	C₂²×C₃×C₅	—	4	1	no	—
217	C₂²×C₃×C₅	—	4	4	no	—
218	C₂²×C₃×C₅	—	4	4	no	—
219	C₂²×C₃×C₅	—	4	2	no	—
220	C₂²×C₃×C₅	—	4	1	no	—
221	C₂²×C₃×C₅	—	8	2	no	—
222	C₂²×C₃×C₅	#120	1	1	yes	characteristic
223	C₂²×C₃×C₅	#120	1	1	yes	characteristic
224	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₅×D₃	—	2	4	no	—
226	C₂×C₅×D₃	—	4	4	no	—
227	C₂×C₅×D₃	—	8	8	no	—
228	C₃×C₄×C₅	—	4	2	no	—
229	C₃×C₄×C₅	—	4	1	no	—
230	C₃×C₄×C₅	#120	1	2	yes	—
231	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
232	C₅×Dic₃	—	2	4	no	—
233	C₂⁴×C₃	C₅×D₄	1	2	yes	—
234	C₂³×D₃	—	2	2	no	—
235	C₃×#41	—	2	2	no	—
236	C₃×#41	—	2	2	no	—
237	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic, complemented
238	C₂×C₃×D₄	—	2	1	no	—
239	C₂×C₃×D₄	—	2	4	no	—
240	C₂×C₃×D₄	—	2	2	no	—
241	C₂×C₃×D₄	—	2	2	no	—
242	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
243	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
244	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic, complemented
245	C₂²×C₃×C₄	—	2	1	no	—
246	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
247	C₂×#67	—	2	4	no	—
248	C₂×#67	—	2	8	no	—
249	C₂×#67	—	2	2	no	—
250	C₂×#67	—	2	8	no	—
251	C₂²×Dic₃	—	2	2	no	—
252	#237	—	2	8	no	—
253	#237	—	2	8	no	—
254	D₃×D₄	—	2	8	no	—
255	D₃×D₄	—	2	8	no	—
256	#235	—	2	2	no	—
257	#235	—	2	2	no	—
258	#235	C₅×D₄	1	4	yes	complemented
259	#235	C₂³×C₅	1	4	yes	—
260	C₂×D₁₂	C₅×D₄	1	2	yes	complemented
261	C₂×C₄×D₃	—	2	2	no	—
262	C₂×Dic₆	C₅×D₄	1	2	yes	complemented
263	C₃×C₄⋊C₄	—	2	1	no	—
264	C₃×C₂²⋊C₄	—	2	1	no	—
265	C₃×C₂²⋊C₄	—	2	4	no	—
266	C₃×C₄²	C₂³×C₅	1	2	yes	complemented
267	#216	—	2	4	no	—
268	#215	—	2	4	no	—
269	#214	—	2	4	no	—
270	#213	—	2	4	no	—
271	#208	—	2	2	no	—
272	#208	C₂³×C₅	1	4	yes	complemented
273	C₂×C₃⋊C₈	—	2	2	no	—
274	C₂³×C₅	—	2	2	no	—
275	C₂³×C₅	—	2	2	no	—
276	C₂³×C₅	—	2	1	no	—
277	C₂³×C₅	—	6	8	no	—
278	C₂³×C₅	—	6	2	no	—
279	C₂³×C₅	—	8	2	no	—
280	C₂³×C₅	—	24	4	no	—
281	C₂³×C₅	C₂×#67	1	4	yes	—
282	C₂³×C₅	C₂×#67	1	1	yes	characteristic
283	C₅×Q₈	—	2	2	no	—
284	C₅×Q₈	—	3	4	no	—
285	C₅×Q₈	—	6	2	no	—
286	C₅×D₄	—	2	4	no	—
287	C₅×D₄	—	2	4	no	—
288	C₅×D₄	—	2	2	no	—
289	C₅×D₄	—	3	4	no	—
290	C₅×D₄	—	4	1	no	—
291	C₅×D₄	—	4	1	no	—
292	C₅×D₄	—	6	16	no	—
293	C₅×D₄	—	6	4	no	—
294	C₅×D₄	—	6	4	no	—
295	C₅×D₄	—	6	2	no	—
296	C₅×D₄	—	8	4	no	—
297	C₂×C₄×C₅	—	2	2	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	4	2	no	—
300	C₂×C₄×C₅	—	6	8	no	—
301	C₂×C₄×C₅	—	6	2	no	—
302	C₂×C₄×C₅	—	6	4	no	—
303	C₂×C₄×C₅	—	6	4	no	—
304	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
305	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
306	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
307	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
308	C₅×C₈	—	6	4	no	—
309	H(5,𝔽₂)	—	3	4	no	—
310	H(5,𝔽₂)	—	6	4	no	—
311	H(5,𝔽₂)	—	6	2	no	—
312	C₂×#41	—	3	2	no	—
313	C₂×#41	—	6	2	no	—
314	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic, complemented
315	C₂²×D₄	—	6	2	no	—
316	C₂²×D₄	—	6	2	no	—
317	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
318	#137	—	3	4	no	—
319	#137	—	6	2	no	—
320	AGL(1,ℤ/8)	—	3	4	no	—
321	AGL(1,ℤ/8)	—	6	2	no	—
322	#135	—	6	4	no	—
323	C₂×M₁₆	—	3	2	no	—
324	#127	C₂×C₅×D₃	1	2	yes	complemented
325	#124	C₂×C₅×D₃	1	2	yes	complemented
326	#121	—	2	2	no	—
327	#120	—	2	2	no	—
328	#117	C₂×C₅×D₃	1	1	yes	characteristic, complemented
329	#104	—	3	8	no	—
330	#100	—	3	4	no	—
331	C₂×C₃×C₅	—	2	1	no	—
332	C₂×C₃×C₅	—	2	1	no	—
333	C₂×C₃×C₅	—	2	1	no	—
334	C₂×C₃×C₅	—	4	4	no	—
335	C₂×C₃×C₅	—	8	1	no	—
336	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
337	C₅×D₃	—	4	4	no	—
338	C₂³×C₃	—	2	2	no	—
339	C₂³×C₃	—	2	2	no	—
340	C₂³×C₃	—	2	1	no	—
341	C₂³×C₃	—	8	2	no	—
342	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
343	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
344	C₂²×D₃	—	2	2	no	—
345	C₂²×D₃	—	2	8	no	—
346	C₂²×D₃	—	8	4	no	—
347	C₃×Q₈	—	2	2	no	—
348	C₃×D₄	—	2	4	no	—
349	C₃×D₄	—	2	4	no	—
350	C₃×D₄	—	2	2	no	—
351	C₃×D₄	—	4	1	no	—
352	C₃×D₄	—	4	1	no	—
353	C₃×D₄	—	8	4	no	—
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	—	2	1	no	—
356	C₂×C₃×C₄	—	4	2	no	—
357	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
358	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
359	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
360	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
361	#67	—	2	16	no	—
362	#67	—	2	4	no	—
363	#67	—	2	4	no	—
364	C₂×Dic₃	—	2	8	no	—
365	C₂×Dic₃	—	2	2	no	—
366	D₁₂	—	2	2	no	—
367	D₁₂	C₂×C₅×D₄	1	4	yes	—
368	C₄×D₃	—	2	4	no	—
369	C₄×D₃	—	2	4	no	—
370	Dic₆	—	2	2	no	—
371	Dic₆	C₂×C₅×D₄	1	4	yes	—
372	C₃⋊C₈	—	2	4	no	—
373	C₂²×C₅	—	2	4	no	—
374	C₂²×C₅	—	4	1	no	—
375	C₂²×C₅	—	4	4	no	—
376	C₂²×C₅	—	4	4	no	—
377	C₂²×C₅	—	4	2	no	—
378	C₂²×C₅	—	4	1	no	—
379	C₂²×C₅	—	6	4	no	—
380	C₂²×C₅	—	8	2	no	—
381	C₂²×C₅	—	12	4	no	—
382	C₂²×C₅	—	24	8	no	—
383	C₂²×C₅	#937	1	1	yes	characteristic
384	C₂²×C₅	#937	1	1	yes	characteristic
385	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
386	C₄×C₅	—	4	2	no	—
387	C₄×C₅	—	4	1	no	—
388	C₄×C₅	—	6	4	no	—
389	C₄×C₅	#937	1	2	yes	—
390	C₄×C₅	C₂×D₃×D₄	1	2	yes	—
391	C₂⁴	—	6	2	no	—
392	C₂⁴	C₅×#67	1	2	yes	—
393	#41	—	2	2	no	—
394	#41	—	2	2	no	—
395	#41	—	3	4	no	—
396	#41	—	3	4	no	—
397	#41	—	6	8	no	—
398	#41	—	6	8	no	—
399	#41	—	6	2	no	—
400	#41	—	6	2	no	—
401	C₂×Q₈	—	3	2	no	—
402	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic, complemented
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	3	2	no	—
408	C₂×D₄	—	6	8	no	—
409	C₂×D₄	—	6	8	no	—
410	C₂×D₄	—	6	4	no	—
411	C₂×D₄	—	6	8	no	—
412	C₂×D₄	—	6	2	no	—
413	C₂×D₄	—	6	8	no	—
414	C₂×D₄	C₅×#67	1	2	yes	—
415	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
416	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic, complemented
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	6	2	no	—
419	C₂²×C₄	—	6	2	no	—
420	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
421	Q₁₆	—	6	4	no	—
422	SD₁₆	—	6	4	no	—
423	SD₁₆	—	6	4	no	—
424	D₈	—	6	4	no	—
425	M₁₆	—	3	4	no	—
426	M₁₆	—	6	2	no	—
427	C₂×C₈	—	6	2	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	2	4	no	—
431	C₄²	C₂²×C₅×D₃	1	2	yes	complemented
432	C₃×C₅	#3019	1	1	yes	characteristic, complemented, Hall
433	C₂²×C₃	—	2	4	no	—
434	C₂²×C₃	—	4	1	no	—
435	C₂²×C₃	—	4	4	no	—
436	C₂²×C₃	—	4	4	no	—
437	C₂²×C₃	—	4	2	no	—
438	C₂²×C₃	—	4	1	no	—
439	C₂²×C₃	—	8	2	no	—
440	C₂²×C₃	C₅×#120	1	1	yes	characteristic
441	C₂²×C₃	C₅×#120	1	1	yes	characteristic
442	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
443	C₂×D₃	—	2	4	no	—
444	C₂×D₃	—	4	4	no	—
445	C₂×D₃	—	8	8	no	—
446	C₃×C₄	—	4	2	no	—
447	C₃×C₄	—	4	1	no	—
448	C₃×C₄	C₅×#120	1	2	yes	—
449	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
450	Dic₃	—	2	4	no	—
451	C₂×C₅	—	2	1	no	—
452	C₂×C₅	—	2	1	no	—
453	C₂×C₅	—	2	1	no	—
454	C₂×C₅	—	4	4	no	—
455	C₂×C₅	—	8	1	no	—
456	C₂×C₅	—	12	4	no	—
457	C₂×C₅	C₂×#937	1	1	yes	characteristic
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	6	8	no	—
462	C₂³	—	6	2	no	—
463	C₂³	—	8	2	no	—
464	C₂³	—	24	4	no	—
465	C₂³	C₂×C₅×#67	1	4	yes	—
466	C₂³	C₂×C₅×#67	1	1	yes	characteristic
467	Q₈	—	2	2	no	—
468	Q₈	—	3	4	no	—
469	Q₈	—	6	2	no	—
470	D₄	—	2	4	no	—
471	D₄	—	2	4	no	—
472	D₄	—	2	2	no	—
473	D₄	—	3	4	no	—
474	D₄	—	4	1	no	—
475	D₄	—	4	1	no	—
476	D₄	—	6	16	no	—
477	D₄	—	6	4	no	—
478	D₄	—	6	4	no	—
479	D₄	—	6	2	no	—
480	D₄	—	8	4	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	6	8	no	—
485	C₂×C₄	—	6	2	no	—
486	C₂×C₄	—	6	4	no	—
487	C₂×C₄	—	6	4	no	—
488	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
489	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
490	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
491	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
492	C₈	—	6	4	no	—
493	C₂×C₃	—	2	1	no	—
494	C₂×C₃	—	2	1	no	—
495	C₂×C₃	—	2	1	no	—
496	C₂×C₃	—	4	4	no	—
497	C₂×C₃	—	8	1	no	—
498	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
499	D₃	—	4	4	no	—
500	C₅	#83394	1	1	yes	characteristic, direct product factor, Sylow
501	C₂²	—	2	4	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	4	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	6	4	no	—
508	C₂²	—	8	2	no	—
509	C₂²	—	12	4	no	—
510	C₂²	—	24	8	no	—
511	C₂²	C₅×#937	1	1	yes	characteristic
512	C₂²	C₅×#937	1	1	yes	characteristic
513	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
514	C₄	—	4	2	no	—
515	C₄	—	4	1	no	—
516	C₄	—	6	4	no	—
517	C₄	C₅×#937	1	2	yes	—
518	C₄	C₂×C₅×D₃×D₄	1	2	yes	—
519	C₃	C₅×#3019	1	1	yes	characteristic, complemented, Sylow
520	C₂	—	2	1	no	—
521	C₂	—	2	1	no	—
522	C₂	—	2	1	no	—
523	C₂	—	4	4	no	—
524	C₂	—	8	1	no	—
525	C₂	—	12	4	no	—
526	C₂	C₂×C₅×#937	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	C₂×#937
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#535	C₂
socle	C₂×C₃×C₅	C₂×#120
hypercenter	C₅×#535	D₃
hypocenter	C₃	C₅×#3019
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#535

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#1004	C₂	semidirect
2. C₃×C₅×#535	C₂	semidirect
3. C₅×#5822	C₂	semidirect
4. C₂×C₅×#833	C₂	semidirect
5. C₅×#5077	C₂	semidirect
6. C₅×#5061	C₂	semidirect
7. C₅×#5005	C₂	semidirect
9. C₂×C₃×C₅×#41	C₂²	semidirect
18. C₃×C₅×#127	C₂²	semidirect
19. C₃×C₅×#124	C₂²	semidirect
22. C₃×C₅×#117	C₂²	semidirect
26. C₅×#942	C₂²	semidirect
27. C₅×#932	C₂²	semidirect
28. C₂×C₅×#208	C₂²	semidirect
29. C₅×#833	C₂²	semidirect
30. C₅×#805	C₂²	semidirect
31. #83394	C₅	direct (N × H)
34. C₅×#535	D₃	semidirect
43. C₂×C₃×C₅×Q₈	C₂³	semidirect
50. C₂×C₃×C₅×D₄	C₂³	semidirect
64. C₅×#235	D₄	semidirect
66. C₂×C₅×D₁₂	D₄	semidirect
68. C₂×C₅×Dic₆	D₄	semidirect
72. C₃×C₄²×C₅	C₂³	semidirect
78. C₅×#208	C₂³	semidirect
80. C₂×#1004	C₂×C₅	semidirect
81. C₃×#535	C₂×C₅	semidirect
82. #5822	C₂×C₅	semidirect
83. C₂×#833	C₂×C₅	semidirect
84. #5077	C₂×C₅	semidirect
85. #5061	C₂×C₅	semidirect
86. #5005	C₂×C₅	semidirect
92. C₂×C₅×#41	C₂×D₃	semidirect
102. C₅×#127	C₂×D₃	semidirect
103. C₅×#124	C₂×D₃	semidirect
106. C₅×#117	C₂×D₃	semidirect
145. C₂×C₃×#41	C₂²×C₅	semidirect
154. C₃×#127	C₂²×C₅	semidirect
155. C₃×#124	C₂²×C₅	semidirect
158. C₃×#117	C₂²×C₅	semidirect
162. #942	C₂²×C₅	semidirect
163. #932	C₂²×C₅	semidirect
164. C₂×#208	C₂²×C₅	semidirect
165. #833	C₂²×C₅	semidirect
166. #805	C₂²×C₅	semidirect
178. C₂×C₅×Q₈	C₂²×D₃	semidirect
192. C₂×C₅×D₄	C₂²×D₃	semidirect
207. C₄²×C₅	C₂²×D₃	semidirect
210. #535	C₅×D₃	semidirect
237. C₂×C₃×Q₈	C₂³×C₅	semidirect
244. C₂×C₃×D₄	C₂³×C₅	semidirect
258. #235	C₅×D₄	semidirect
260. C₂×D₁₂	C₅×D₄	semidirect
262. C₂×Dic₆	C₅×D₄	semidirect
266. C₃×C₄²	C₂³×C₅	semidirect
272. #208	C₂³×C₅	semidirect
314. C₂×#41	C₂×C₅×D₃	semidirect
324. #127	C₂×C₅×D₃	semidirect
325. #124	C₂×C₅×D₃	semidirect
328. #117	C₂×C₅×D₃	semidirect
402. C₂×Q₈	C₂²×C₅×D₃	semidirect
416. C₂×D₄	C₂²×C₅×D₃	semidirect
431. C₄²	C₂²×C₅×D₃	semidirect
432. C₃×C₅	#3019	semidirect
500. C₅	#83394	direct (N × H)
519. C₃	C₅×#3019	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#1004	2
C₃×C₅×#535	2
C₅×#5822	2
C₂×C₅×#833	2
C₅×#5077	2
C₅×#5061	2
C₅×#5005	2
C₅×#3019	3
#83394	5

Subgroups — C5×#83394 #14425299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83394 #14425299