Subgroups — C₅×#21551 #11944271

Order 1280.

938 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3054	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#444	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2930	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1974	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1945	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1938	C₂	1	2	yes	maximal, complemented
8	C₅×#1896	C₂	1	2	yes	maximal, complemented
9	C₅×#1811	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1773	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1764	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#135	C₂²	1	1	yes	characteristic
13	C₂×C₅×#131	C₂²	1	2	yes	—
14	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₅×#525	C₂²	1	2	yes	—
17	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₅×#470	C₄	1	2	yes	complemented
19	C₅×#469	C₄	1	2	yes	complemented
20	C₅×#468	C₄	1	4	yes	complemented
21	C₅×#444	—	2	4	no	—
22	C₅×#436	—	2	4	no	—
23	C₅×#435	—	2	4	no	—
24	C₂×C₅×#108	C₂²	1	1	yes	characteristic
25	C₂×C₅×#108	C₂²	1	1	yes	characteristic
26	C₅×#427	C₂²	1	1	yes	characteristic
27	C₅×#424	C₂²	1	2	yes	—
28	C₂×C₅×#104	C₂²	1	2	yes	—
29	C₂×C₅×#104	C₂²	1	2	yes	—
30	C₅×#416	C₂²	1	2	yes	—
31	C₅×#408	C₂²	1	2	yes	—
32	C₅×#407	C₂²	1	2	yes	—
33	C₅×#405	C₂²	1	2	yes	—
34	C₄×C₅×M₁₆	—	2	4	no	—
35	C₂×C₅×#97	C₂²	1	1	yes	characteristic
36	C₂×C₅×#97	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
39	C₅×#341	C₂²	1	2	yes	—
40	C₅×#339	C₂²	1	2	yes	—
41	C₅×#339	C₂²	1	2	yes	—
42	#21551	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂×C₅×#41	C₂³	1	2	yes	—
44	C₂³×C₄×C₅	—	2	1	no	—
45	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₅×#135	—	2	2	no	—
47	C₅×#135	—	2	2	no	—
48	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
49	C₂×C₅×SD₁₆	C₂×C₄	1	2	yes	complemented
50	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic, complemented
51	C₅×#131	—	2	4	no	—
52	C₅×#131	—	2	4	no	—
53	C₂×C₅×M₁₆	—	2	2	no	—
54	C₂×C₅×M₁₆	—	2	2	no	—
55	C₂×C₅×M₁₆	—	2	2	no	—
56	C₂×C₅×M₁₆	—	2	2	no	—
57	C₂×C₅×M₁₆	—	2	2	no	—
58	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
59	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
60	C₂×C₅×M₁₆	D₄	1	4	yes	—
61	C₂×C₅×M₁₆	C₂³	1	2	yes	—
62	C₂×C₅×M₁₆	C₂³	1	2	yes	—
63	C₂²×C₅×C₈	—	2	2	no	—
64	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
68	C₅×#123	—	2	2	no	—
69	C₅×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
70	C₅×#121	C₂×C₄	1	4	yes	—
71	C₅×#120	—	2	2	no	—
72	C₄×C₅×D₄	—	2	4	no	—
73	C₅×#117	C₂³	1	2	yes	—
74	C₂×C₄²×C₅	—	2	1	no	—
75	C₂×C₄²×C₅	—	2	2	no	—
76	C₂×C₄²×C₅	—	2	2	no	—
77	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₅×#108	—	2	2	no	—
80	C₅×#108	—	2	2	no	—
81	C₅×#107	C₂×C₄	1	2	yes	complemented
82	C₅×#106	C₂×C₄	1	2	yes	complemented
83	C₅×C₄⋊C₈	—	2	4	no	—
84	C₅×#104	—	2	4	no	—
85	C₅×#104	—	2	4	no	—
86	C₅×#103	C₂×C₄	1	4	yes	complemented
87	C₅×#102	C₂×C₄	1	4	yes	complemented
88	C₅×C₂²⋊C₈	—	2	4	no	—
89	C₅×C₂²⋊C₈	—	2	4	no	—
90	C₅×#97	—	2	2	no	—
91	C₅×#97	—	2	2	no	—
92	C₅×#97	D₄	1	4	yes	complemented
93	C₄×C₅×C₈	—	2	2	no	—
94	C₄×C₅×C₈	—	2	2	no	—
95	C₄×C₅×C₈	—	2	2	no	—
96	#3054	C₂×C₅	1	1	yes	characteristic
97	C₂×#444	C₂×C₅	1	1	yes	characteristic, complemented
98	#2930	C₂×C₅	1	2	yes	complemented
99	C₂×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
100	#1974	C₂×C₅	1	1	yes	characteristic, complemented
101	#1945	C₂×C₅	1	1	yes	characteristic, complemented
102	#1938	C₂×C₅	1	2	yes	complemented
103	#1896	C₂×C₅	1	2	yes	complemented
104	#1811	C₂×C₅	1	1	yes	characteristic, complemented
105	#1773	C₂×C₅	1	1	yes	characteristic, complemented
106	#1764	C₂×C₅	1	2	yes	complemented
107	C₂⁴×C₅	#41	1	1	yes	characteristic
108	C₅×#41	—	2	2	no	—
109	C₅×#41	—	2	2	no	—
110	C₅×#41	—	2	2	no	—
111	C₅×#41	—	2	2	no	—
112	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
113	C₂×C₅×D₄	—	2	2	no	—
114	C₂×C₅×D₄	—	2	4	no	—
115	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	1	no	—
118	C₂²×C₄×C₅	—	2	1	no	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	4	no	—
122	C₂²×C₄×C₅	—	2	1	no	—
123	C₂²×C₄×C₅	—	2	2	no	—
124	C₂²×C₄×C₅	—	4	4	no	—
125	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₅	#41	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
129	C₅×Q₁₆	—	2	2	no	—
130	C₅×SD₁₆	—	2	4	no	—
131	C₅×D₈	—	2	2	no	—
132	C₅×M₁₆	—	2	4	no	—
133	C₅×M₁₆	—	2	4	no	—
134	C₅×M₁₆	—	2	8	no	—
135	C₅×M₁₆	—	2	2	no	—
136	C₅×M₁₆	—	2	2	no	—
137	C₅×M₁₆	—	2	2	no	—
138	C₅×M₁₆	—	2	2	no	—
139	C₅×M₁₆	—	4	4	no	—
140	C₂×C₅×C₈	—	2	1	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	2	1	no	—
143	C₂×C₅×C₈	—	2	1	no	—
144	C₂×C₅×C₈	—	2	2	no	—
145	C₂×C₅×C₈	—	2	2	no	—
146	C₂×C₅×C₈	—	4	4	no	—
147	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
148	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
151	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
152	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
153	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
154	C₂×C₅×C₈	#41	1	2	yes	—
155	C₂×C₅×C₈	#41	1	2	yes	—
156	C₅×C₄⋊C₄	—	2	4	no	—
157	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
158	C₅×C₂²⋊C₄	—	2	4	no	—
159	C₅×C₂²⋊C₄	—	2	2	no	—
160	C₅×C₂²⋊C₄	—	2	4	no	—
161	C₄²×C₅	—	2	4	no	—
162	C₄²×C₅	—	2	1	no	—
163	C₄²×C₅	—	2	2	no	—
164	C₄²×C₅	—	2	1	no	—
165	C₄²×C₅	C₂×D₄	1	2	yes	—
166	C₄²×C₅	#41	1	2	yes	—
167	C₂×#135	C₂²×C₅	1	1	yes	characteristic
168	C₂×#131	C₂²×C₅	1	2	yes	—
169	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
170	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
171	#525	C₂²×C₅	1	2	yes	—
172	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
173	#470	C₄×C₅	1	2	yes	complemented
174	#469	C₄×C₅	1	2	yes	complemented
175	#468	C₄×C₅	1	4	yes	complemented
176	#444	—	2	4	no	—
177	#436	—	2	4	no	—
178	#435	—	2	4	no	—
179	C₂×#108	C₂²×C₅	1	1	yes	characteristic
180	C₂×#108	C₂²×C₅	1	1	yes	characteristic
181	#427	C₂²×C₅	1	1	yes	characteristic
182	#424	C₂²×C₅	1	2	yes	—
183	C₂×#104	C₂²×C₅	1	2	yes	—
184	C₂×#104	C₂²×C₅	1	2	yes	—
185	#416	C₂²×C₅	1	2	yes	—
186	#408	C₂²×C₅	1	2	yes	—
187	#407	C₂²×C₅	1	2	yes	—
188	#405	C₂²×C₅	1	2	yes	—
189	C₄×M₁₆	—	2	4	no	—
190	C₂×#97	C₂²×C₅	1	1	yes	characteristic
191	C₂×#97	C₂²×C₅	1	1	yes	characteristic
192	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
193	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
194	#341	C₂²×C₅	1	2	yes	—
195	#339	C₂²×C₅	1	2	yes	—
196	#339	C₂²×C₅	1	2	yes	—
197	C₂³×C₅	—	2	1	no	—
198	C₂³×C₅	—	2	1	no	—
199	C₂³×C₅	—	2	2	no	—
200	C₂³×C₅	—	4	2	no	—
201	C₂³×C₅	C₄×D₄	1	2	yes	—
202	C₂³×C₅	C₂×#41	1	1	yes	characteristic
203	C₅×Q₈	—	2	2	no	—
204	C₅×Q₈	—	2	2	no	—
205	C₅×D₄	—	2	2	no	—
206	C₅×D₄	—	2	2	no	—
207	C₅×D₄	—	4	2	no	—
208	C₅×D₄	—	4	2	no	—
209	C₅×D₄	—	8	4	no	—
210	C₂×C₄×C₅	—	2	4	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	2	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	2	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	2	2	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	4	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	4	8	no	—
222	C₂×C₄×C₅	—	4	2	no	—
223	C₂×C₄×C₅	—	4	2	no	—
224	C₂×C₄×C₅	—	4	2	no	—
225	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
226	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
232	C₅×C₈	—	2	2	no	—
233	C₅×C₈	—	2	2	no	—
234	C₅×C₈	—	4	2	no	—
235	C₅×C₈	—	4	2	no	—
236	C₅×C₈	C₄×D₄	1	2	yes	—
237	C₅×C₈	C₄×D₄	1	2	yes	—
238	C₅×C₈	#121	1	4	yes	—
239	C₂×#41	C₂³×C₅	1	2	yes	—
240	C₂³×C₄	—	2	1	no	—
241	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
242	#135	—	2	2	no	—
243	#135	—	2	2	no	—
244	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic, complemented
245	C₂×SD₁₆	C₂×C₄×C₅	1	2	yes	complemented
246	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
247	#131	—	2	4	no	—
248	#131	—	2	4	no	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	2	2	no	—
253	C₂×M₁₆	—	2	2	no	—
254	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
255	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
256	C₂×M₁₆	C₅×D₄	1	4	yes	—
257	C₂×M₁₆	C₂³×C₅	1	2	yes	—
258	C₂×M₁₆	C₂³×C₅	1	2	yes	—
259	C₂²×C₈	—	2	2	no	—
260	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
261	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
264	#123	—	2	2	no	—
265	C₂²⋊Q₈	C₂×C₄×C₅	1	4	yes	—
266	#121	C₂×C₄×C₅	1	4	yes	—
267	#120	—	2	2	no	—
268	C₄×D₄	—	2	4	no	—
269	#117	C₂³×C₅	1	2	yes	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
275	#108	—	2	2	no	—
276	#108	—	2	2	no	—
277	#107	C₂×C₄×C₅	1	2	yes	complemented
278	#106	C₂×C₄×C₅	1	2	yes	complemented
279	C₄⋊C₈	—	2	4	no	—
280	#104	—	2	4	no	—
281	#104	—	2	4	no	—
282	#103	C₂×C₄×C₅	1	4	yes	complemented
283	#102	C₂×C₄×C₅	1	4	yes	complemented
284	C₂²⋊C₈	—	2	4	no	—
285	C₂²⋊C₈	—	2	4	no	—
286	#97	—	2	2	no	—
287	#97	—	2	2	no	—
288	#97	C₅×D₄	1	4	yes	complemented
289	C₄×C₈	—	2	2	no	—
290	C₄×C₈	—	2	2	no	—
291	C₄×C₈	—	2	2	no	—
292	C₂²×C₅	—	2	2	no	—
293	C₂²×C₅	—	2	4	no	—
294	C₂²×C₅	—	2	2	no	—
295	C₂²×C₅	—	4	2	no	—
296	C₂²×C₅	—	4	2	no	—
297	C₂²×C₅	—	4	4	no	—
298	C₂²×C₅	—	4	2	no	—
299	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
300	C₂²×C₅	#525	1	1	yes	characteristic
301	C₂²×C₅	#529	1	1	yes	characteristic
302	C₄×C₅	—	2	4	no	—
303	C₄×C₅	—	2	2	no	—
304	C₄×C₅	—	4	2	no	—
305	C₄×C₅	—	4	4	no	—
306	C₄×C₅	—	4	2	no	—
307	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
308	C₄×C₅	C₄×#41	1	1	yes	characteristic
309	C₄×C₅	C₂×#121	1	1	yes	characteristic
310	C₄×C₅	#532	1	1	yes	characteristic
311	C₂⁴	C₅×#41	1	1	yes	characteristic
312	#41	—	2	2	no	—
313	#41	—	2	2	no	—
314	#41	—	2	2	no	—
315	#41	—	2	2	no	—
316	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	4	4	no	—
329	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
330	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
331	C₂²×C₄	C₅×#41	1	1	yes	characteristic
332	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
333	Q₁₆	—	2	2	no	—
334	SD₁₆	—	2	4	no	—
335	D₈	—	2	2	no	—
336	M₁₆	—	2	4	no	—
337	M₁₆	—	2	4	no	—
338	M₁₆	—	2	8	no	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	2	2	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	4	4	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	4	4	no	—
351	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
352	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
353	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
354	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
355	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
356	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
357	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
358	C₂×C₈	C₅×#41	1	2	yes	—
359	C₂×C₈	C₅×#41	1	2	yes	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₄²	—	2	4	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	1	no	—
369	C₄²	C₂×C₅×D₄	1	2	yes	—
370	C₄²	C₅×#41	1	2	yes	—
371	C₂×C₅	—	2	1	no	—
372	C₂×C₅	—	2	1	no	—
373	C₂×C₅	—	4	2	no	—
374	C₂×C₅	—	8	2	no	—
375	C₂×C₅	C₄×#121	1	1	yes	characteristic
376	C₂×C₅	#2956	1	2	yes	—
377	C₂³	—	2	1	no	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	C₄×C₅×D₄	1	2	yes	—
382	C₂³	C₂×C₅×#41	1	1	yes	characteristic
383	Q₈	—	2	2	no	—
384	Q₈	—	2	2	no	—
385	D₄	—	2	2	no	—
386	D₄	—	2	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	8	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	4	8	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
406	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
407	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
408	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
409	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
410	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
411	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
412	C₈	—	2	2	no	—
413	C₈	—	2	2	no	—
414	C₈	—	4	2	no	—
415	C₈	—	4	2	no	—
416	C₈	C₄×C₅×D₄	1	2	yes	—
417	C₈	C₄×C₅×D₄	1	2	yes	—
418	C₈	C₅×#121	1	4	yes	—
419	C₅	#21551	1	1	yes	characteristic, direct product factor, Sylow
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	4	2	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
428	C₂²	C₅×#525	1	1	yes	characteristic
429	C₂²	C₅×#529	1	1	yes	characteristic
430	C₄	—	2	4	no	—
431	C₄	—	2	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	4	no	—
435	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
436	C₄	C₄×C₅×#41	1	1	yes	characteristic
437	C₄	C₂×C₅×#121	1	1	yes	characteristic
438	C₄	C₅×#532	1	1	yes	characteristic
439	C₂	—	2	1	no	—
440	C₂	—	2	1	no	—
441	C₂	—	4	2	no	—
442	C₂	—	8	2	no	—
443	C₂	C₄×C₅×#121	1	1	yes	characteristic
444	C₂	C₅×#2956	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₅×#3054	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₅×M₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#444	C₂	semidirect
3. C₅×#2930	C₂	semidirect
4. C₂×C₄×C₅×M₁₆	C₂	semidirect
5. C₅×#1974	C₂	semidirect
6. C₅×#1945	C₂	semidirect
7. C₅×#1938	C₂	semidirect
8. C₅×#1896	C₂	semidirect
9. C₅×#1811	C₂	semidirect
10. C₅×#1773	C₂	semidirect
11. C₅×#1764	C₂	semidirect
18. C₅×#470	C₄	semidirect
19. C₅×#469	C₄	semidirect
20. C₅×#468	C₄	semidirect
42. #21551	C₅	direct (N × H)
48. C₂×C₅×Q₁₆	C₂×C₄	semidirect
49. C₂×C₅×SD₁₆	C₂×C₄	semidirect
50. C₂×C₅×D₈	C₂×C₄	semidirect
81. C₅×#107	C₂×C₄	semidirect
82. C₅×#106	C₂×C₄	semidirect
86. C₅×#103	C₂×C₄	semidirect
87. C₅×#102	C₂×C₄	semidirect
92. C₅×#97	D₄	semidirect
97. C₂×#444	C₂×C₅	semidirect
98. #2930	C₂×C₅	semidirect
99. C₂×C₄×M₁₆	C₂×C₅	semidirect
100. #1974	C₂×C₅	semidirect
101. #1945	C₂×C₅	semidirect
102. #1938	C₂×C₅	semidirect
103. #1896	C₂×C₅	semidirect
104. #1811	C₂×C₅	semidirect
105. #1773	C₂×C₅	semidirect
106. #1764	C₂×C₅	semidirect
173. #470	C₄×C₅	semidirect
174. #469	C₄×C₅	semidirect
175. #468	C₄×C₅	semidirect
244. C₂×Q₁₆	C₂×C₄×C₅	semidirect
245. C₂×SD₁₆	C₂×C₄×C₅	semidirect
246. C₂×D₈	C₂×C₄×C₅	semidirect
277. #107	C₂×C₄×C₅	semidirect
278. #106	C₂×C₄×C₅	semidirect
282. #103	C₂×C₄×C₅	semidirect
283. #102	C₂×C₄×C₅	semidirect
288. #97	C₅×D₄	semidirect
419. C₅	#21551	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3054	2
C₂×C₅×#444	2
C₅×#2930	2
C₂×C₄×C₅×M₁₆	2
C₅×#1974	2
C₅×#1945	2
C₅×#1938	2
C₅×#1896	2
C₅×#1811	2
C₅×#1773	2
C₅×#1764	2
#21551	5

Subgroups — C5×#21551 #11944271

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21551 #11944271