Subgroups — C₅×#23679 #11946399

Order 1280.

848 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×Q₁₆	C₂	1	2	yes	maximal
2	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₅×#2295	C₂	1	1	yes	maximal, characteristic
4	C₅×#2083	C₂	1	1	yes	maximal, characteristic
5	C₅×#2072	C₂	1	1	yes	maximal, characteristic
6	C₅×#2068	C₂	1	2	yes	maximal
7	C₅×#2056	C₂	1	2	yes	maximal
8	C₅×#2043	C₂	1	1	yes	maximal, characteristic
9	C₅×#2016	C₂	1	1	yes	maximal, characteristic
10	C₄×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
11	C₄×C₅×#103	C₂	1	2	yes	maximal
12	C₂²×C₅×Q₁₆	C₂²	1	2	yes	—
13	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
15	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₄×C₅×Q₁₆	—	2	8	no	—
17	C₂×C₅×#107	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₅×#103	C₂²	1	2	yes	—
20	C₂×C₅×#103	C₂²	1	2	yes	—
21	C₂×C₅×#103	C₂²	1	2	yes	—
22	C₂×C₅×#103	C₂²	1	2	yes	—
23	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
24	C₅×#391	C₂²	1	1	yes	characteristic
25	C₅×#391	C₂²	1	1	yes	characteristic
26	C₅×#391	C₂²	1	2	yes	—
27	C₅×#389	—	2	1	no	—
28	C₅×#389	—	2	1	no	—
29	C₅×#389	C₂²	1	1	yes	characteristic
30	C₅×#389	C₂²	1	1	yes	characteristic
31	C₅×#387	—	2	1	no	—
32	C₅×#387	—	2	1	no	—
33	C₅×#384	C₂²	1	1	yes	characteristic
34	C₄×C₅×C₄⋊C₄	—	2	1	no	—
35	C₄×C₅×C₄⋊C₄	—	2	1	no	—
36	C₄×C₅×C₄⋊C₄	—	2	1	no	—
37	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₅×#376	—	2	1	no	—
39	C₄³×C₅	C₂²	1	1	yes	characteristic
40	C₅×#340	C₂²	1	2	yes	—
41	C₅×#340	C₂²	1	2	yes	—
42	C₅×#336	C₂²	1	1	yes	characteristic
43	C₅×#336	C₂²	1	1	yes	characteristic
44	#23679	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
46	C₂²×C₅×Q₈	C₂³	1	2	yes	—
47	C₂×C₅×Q₁₆	—	2	4	no	—
48	C₂×C₅×Q₁₆	—	2	4	no	—
49	C₂×C₅×Q₁₆	—	2	4	no	—
50	C₂²×C₅×C₈	C₂³	1	2	yes	—
51	C₂²×C₅×C₈	C₂³	1	2	yes	—
52	C₅×C₄⋊Q₈	—	2	4	no	—
53	C₄×C₅×Q₈	—	2	2	no	—
54	C₄×C₅×Q₈	—	2	4	no	—
55	C₄×C₅×Q₈	—	2	4	no	—
56	C₄×C₅×Q₈	D₄	1	4	yes	—
57	C₂×C₅×C₄⋊C₄	—	2	1	no	—
58	C₂×C₅×C₄⋊C₄	—	2	1	no	—
59	C₂×C₅×C₄⋊C₄	—	2	1	no	—
60	C₂×C₅×C₄⋊C₄	—	2	1	no	—
61	C₂×C₅×C₄⋊C₄	—	2	1	no	—
62	C₂×C₅×C₄⋊C₄	—	2	1	no	—
63	C₂×C₅×C₄⋊C₄	—	2	1	no	—
64	C₂×C₅×C₄⋊C₄	—	2	2	no	—
65	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
67	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₅	—	2	1	no	—
70	C₂×C₄²×C₅	—	2	1	no	—
71	C₂×C₄²×C₅	—	2	2	no	—
72	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₅×#107	—	2	4	no	—
80	C₅×C₄⋊C₈	—	2	4	no	—
81	C₅×#103	—	2	4	no	—
82	C₅×#103	—	2	4	no	—
83	C₅×#103	—	2	4	no	—
84	C₅×#103	—	2	4	no	—
85	C₄×C₅×C₈	—	2	4	no	—
86	C₅×#95	—	2	1	no	—
87	C₅×#95	—	2	1	no	—
88	C₅×#95	—	2	1	no	—
89	C₅×#95	—	2	1	no	—
90	C₅×#95	—	2	1	no	—
91	C₅×#95	—	2	1	no	—
92	C₅×#95	—	2	2	no	—
93	C₅×#95	—	2	2	no	—
94	C₅×#95	—	2	1	no	—
95	C₂×C₄×Q₁₆	C₂×C₅	1	2	yes	—
96	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
97	#2295	C₂×C₅	1	1	yes	characteristic
98	#2083	C₂×C₅	1	1	yes	characteristic
99	#2072	C₂×C₅	1	1	yes	characteristic
100	#2068	C₂×C₅	1	2	yes	—
101	#2056	C₂×C₅	1	2	yes	—
102	#2043	C₂×C₅	1	1	yes	characteristic
103	#2016	C₂×C₅	1	1	yes	characteristic
104	C₄×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
105	C₄×#103	C₂×C₅	1	2	yes	—
106	C₂×C₅×Q₈	—	2	1	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	—	2	2	no	—
110	C₂×C₅×Q₈	—	2	2	no	—
111	C₂×C₅×Q₈	—	2	2	no	—
112	C₂×C₅×Q₈	—	2	2	no	—
113	C₂×C₅×Q₈	—	2	2	no	—
114	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
115	C₂×C₅×Q₈	#41	1	4	yes	—
116	C₂²×C₄×C₅	—	2	1	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	2	1	no	—
119	C₂²×C₄×C₅	—	2	2	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
129	C₅×Q₁₆	—	2	16	no	—
130	C₂×C₅×C₈	—	2	2	no	—
131	C₂×C₅×C₈	—	2	2	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	#41	1	4	yes	—
136	C₅×C₄⋊C₄	—	2	4	no	—
137	C₅×C₄⋊C₄	—	2	4	no	—
138	C₅×C₄⋊C₄	—	2	4	no	—
139	C₅×C₄⋊C₄	—	2	1	no	—
140	C₅×C₄⋊C₄	—	2	2	no	—
141	C₅×C₄⋊C₄	—	2	2	no	—
142	C₅×C₄⋊C₄	—	2	2	no	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	—	4	2	no	—
145	C₅×C₄⋊C₄	—	4	2	no	—
146	C₅×C₄⋊C₄	—	4	4	no	—
147	C₅×C₄⋊C₄	—	4	2	no	—
148	C₅×C₄⋊C₄	—	4	2	no	—
149	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
150	C₄²×C₅	—	2	4	no	—
151	C₄²×C₅	—	2	2	no	—
152	C₄²×C₅	—	2	2	no	—
153	C₄²×C₅	—	2	2	no	—
154	C₄²×C₅	—	2	2	no	—
155	C₄²×C₅	—	4	1	no	—
156	C₄²×C₅	—	4	4	no	—
157	C₄²×C₅	—	4	2	no	—
158	C₄²×C₅	Q₁₆	1	4	yes	complemented
159	C₄²×C₅	C₂×D₄	1	2	yes	—
160	C₄²×C₅	#41	1	2	yes	—
161	C₂²×Q₁₆	C₂²×C₅	1	2	yes	—
162	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
163	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
164	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
165	C₄×Q₁₆	—	2	8	no	—
166	C₂×#107	C₂²×C₅	1	2	yes	—
167	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
168	C₂×#103	C₂²×C₅	1	2	yes	—
169	C₂×#103	C₂²×C₅	1	2	yes	—
170	C₂×#103	C₂²×C₅	1	2	yes	—
171	C₂×#103	C₂²×C₅	1	2	yes	—
172	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
173	#391	C₂²×C₅	1	2	yes	—
174	#391	C₂²×C₅	1	1	yes	characteristic
175	#391	C₂²×C₅	1	1	yes	characteristic
176	#389	—	2	1	no	—
177	#389	—	2	1	no	—
178	#389	C₂²×C₅	1	1	yes	characteristic
179	#389	C₂²×C₅	1	1	yes	characteristic
180	#387	—	2	1	no	—
181	#387	—	2	1	no	—
182	#384	C₂²×C₅	1	1	yes	characteristic
183	C₄×C₄⋊C₄	—	2	1	no	—
184	C₄×C₄⋊C₄	—	2	1	no	—
185	C₄×C₄⋊C₄	—	2	1	no	—
186	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
187	#376	—	2	1	no	—
188	C₄³	C₂²×C₅	1	1	yes	characteristic
189	#340	C₂²×C₅	1	2	yes	—
190	#340	C₂²×C₅	1	2	yes	—
191	#336	C₂²×C₅	1	1	yes	characteristic
192	#336	C₂²×C₅	1	1	yes	characteristic
193	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
194	C₅×Q₈	—	2	4	no	—
195	C₅×Q₈	—	2	4	no	—
196	C₅×Q₈	—	2	4	no	—
197	C₅×Q₈	—	4	2	no	—
198	C₅×Q₈	—	4	2	no	—
199	C₅×Q₈	—	4	2	no	—
200	C₂×C₄×C₅	—	2	1	no	—
201	C₂×C₄×C₅	—	2	1	no	—
202	C₂×C₄×C₅	—	2	1	no	—
203	C₂×C₄×C₅	—	2	1	no	—
204	C₂×C₄×C₅	—	2	1	no	—
205	C₂×C₄×C₅	—	2	1	no	—
206	C₂×C₄×C₅	—	2	1	no	—
207	C₂×C₄×C₅	—	2	1	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	4	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	4	2	no	—
215	C₂×C₄×C₅	—	4	1	no	—
216	C₂×C₄×C₅	—	4	2	no	—
217	C₂×C₄×C₅	—	4	1	no	—
218	C₂×C₄×C₅	—	4	1	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	—	4	2	no	—
221	C₂×C₄×C₅	—	4	1	no	—
222	C₂×C₄×C₅	—	4	1	no	—
223	C₂×C₄×C₅	—	4	1	no	—
224	C₂×C₄×C₅	—	4	2	no	—
225	C₂×C₄×C₅	—	4	1	no	—
226	C₂×C₄×C₅	—	4	1	no	—
227	C₂×C₄×C₅	—	4	1	no	—
228	C₂×C₄×C₅	—	4	2	no	—
229	C₂×C₄×C₅	#121	1	2	yes	—
230	C₂×C₄×C₅	#121	1	2	yes	—
231	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
232	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
233	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
234	C₂×C₄×C₅	#135	1	2	yes	—
235	C₂×C₄×C₅	#137	1	2	yes	—
236	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂×#41	1	2	yes	—
238	C₂×C₄×C₅	C₂×#41	1	2	yes	—
239	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
240	C₅×C₈	—	2	4	no	—
241	C₅×C₈	—	4	2	no	—
242	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
243	C₂²×Q₈	C₂³×C₅	1	2	yes	—
244	C₂×Q₁₆	—	2	4	no	—
245	C₂×Q₁₆	—	2	4	no	—
246	C₂×Q₁₆	—	2	4	no	—
247	C₂²×C₈	C₂³×C₅	1	2	yes	—
248	C₂²×C₈	C₂³×C₅	1	2	yes	—
249	C₄⋊Q₈	—	2	4	no	—
250	C₄×Q₈	—	2	2	no	—
251	C₄×Q₈	—	2	4	no	—
252	C₄×Q₈	—	2	4	no	—
253	C₄×Q₈	C₅×D₄	1	4	yes	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
264	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
265	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	—	2	1	no	—
269	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
270	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
271	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
272	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
276	#107	—	2	4	no	—
277	C₄⋊C₈	—	2	4	no	—
278	#103	—	2	4	no	—
279	#103	—	2	4	no	—
280	#103	—	2	4	no	—
281	#103	—	2	4	no	—
282	C₄×C₈	—	2	4	no	—
283	#95	—	2	1	no	—
284	#95	—	2	1	no	—
285	#95	—	2	1	no	—
286	#95	—	2	1	no	—
287	#95	—	2	1	no	—
288	#95	—	2	1	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	1	no	—
292	C₂²×C₅	C₂×#121	1	1	yes	characteristic
293	C₂²×C₅	#525	1	1	yes	characteristic
294	C₂²×C₅	#532	1	1	yes	characteristic
295	C₂²×C₅	C₂²×Q₁₆	1	1	yes	characteristic
296	C₂²×C₅	C₂×#135	1	1	yes	characteristic
297	C₂²×C₅	C₂×#137	1	1	yes	characteristic
298	C₂²×C₅	#575	1	1	yes	characteristic
299	C₄×C₅	—	2	2	no	—
300	C₄×C₅	—	2	2	no	—
301	C₄×C₅	—	2	2	no	—
302	C₄×C₅	—	2	2	no	—
303	C₄×C₅	—	4	2	no	—
304	C₄×C₅	—	4	4	no	—
305	C₄×C₅	—	4	1	no	—
306	C₄×C₅	—	4	2	no	—
307	C₄×C₅	—	8	1	no	—
308	C₄×C₅	—	8	1	no	—
309	C₄×C₅	—	8	2	no	—
310	C₄×C₅	#462	1	4	yes	—
311	C₄×C₅	#525	1	2	yes	—
312	C₄×C₅	#529	1	2	yes	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
322	C₂×Q₈	C₅×#41	1	4	yes	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
330	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
332	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
335	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
336	Q₁₆	—	2	16	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	C₅×#41	1	4	yes	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	4	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
357	C₄²	—	2	4	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	4	1	no	—
363	C₄²	—	4	4	no	—
364	C₄²	—	4	2	no	—
365	C₄²	C₅×Q₁₆	1	4	yes	complemented
366	C₄²	C₂×C₅×D₄	1	2	yes	—
367	C₄²	C₅×#41	1	2	yes	—
368	C₂×C₅	#2392	1	1	yes	characteristic
369	C₂×C₅	C₂×#462	1	1	yes	characteristic
370	C₂×C₅	#3035	1	1	yes	characteristic
371	C₂×C₅	#3104	1	1	yes	characteristic
372	C₂×C₅	#3108	1	1	yes	characteristic
373	C₂×C₅	#3170	1	1	yes	characteristic
374	C₂×C₅	#3172	1	1	yes	characteristic
375	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
376	Q₈	—	2	4	no	—
377	Q₈	—	2	4	no	—
378	Q₈	—	2	4	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	4	2	no	—
381	Q₈	—	4	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	C₅×#121	1	2	yes	—
412	C₂×C₄	C₅×#121	1	2	yes	—
413	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
414	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
415	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
416	C₂×C₄	C₅×#135	1	2	yes	—
417	C₂×C₄	C₅×#137	1	2	yes	—
418	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
419	C₂×C₄	C₂×C₅×#41	1	2	yes	—
420	C₂×C₄	C₂×C₅×#41	1	2	yes	—
421	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
422	C₈	—	2	4	no	—
423	C₈	—	4	2	no	—
424	C₅	#23679	1	1	yes	characteristic, direct product factor, Sylow
425	C₂²	C₂×C₅×#121	1	1	yes	characteristic
426	C₂²	C₅×#525	1	1	yes	characteristic
427	C₂²	C₅×#532	1	1	yes	characteristic
428	C₂²	C₂²×C₅×Q₁₆	1	1	yes	characteristic
429	C₂²	C₂×C₅×#135	1	1	yes	characteristic
430	C₂²	C₂×C₅×#137	1	1	yes	characteristic
431	C₂²	C₅×#575	1	1	yes	characteristic
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	1	no	—
440	C₄	—	8	2	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	1	no	—
443	C₄	C₅×#462	1	4	yes	—
444	C₄	C₅×#525	1	2	yes	—
445	C₄	C₅×#529	1	2	yes	—
446	C₂	C₅×#2392	1	1	yes	characteristic
447	C₂	C₂×C₅×#462	1	1	yes	characteristic
448	C₂	C₅×#3035	1	1	yes	characteristic
449	C₂	C₅×#3104	1	1	yes	characteristic
450	C₂	C₅×#3108	1	1	yes	characteristic
451	C₂	C₅×#3170	1	1	yes	characteristic
452	C₂	C₅×#3172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle, prime radical	C₂³×C₅	C₂²×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₄³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
44. #23679	C₅	direct (N × H)
158. C₄²×C₅	Q₁₆	semidirect
365. C₄²	C₅×Q₁₆	semidirect
424. C₅	#23679	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×Q₁₆	2
C₄×C₅×C₄⋊Q₈	2
C₅×#2295	2
C₅×#2083	2
C₅×#2072	2
C₅×#2068	2
C₅×#2056	2
C₅×#2043	2
C₅×#2016	2
C₄×C₅×C₄⋊C₈	2
C₄×C₅×#103	2
#23679	5

Subgroups — C5×#23679 #11946399

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23679 #11946399