Subgroups — C₅×#78531 #14439288

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#909	C₂	1	2	yes	maximal, complemented
2	C₂×C₅×#908	C₂	1	2	yes	maximal, complemented
3	C₅×#5477	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#875	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4715	C₂	1	2	yes	maximal, complemented
7	C₅×#4712	C₂	1	2	yes	maximal, complemented
8	C₅×#4696	C₂	1	4	yes	maximal, complemented
9	C₅×#3153	—	3	1	no	maximal, Hall
10	C₂×C₅×#235	C₂²	1	2	yes	—
11	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
12	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₅×#930	—	2	2	no	—
16	C₂×C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
17	C₅×#909	—	2	8	no	—
18	C₅×#908	—	2	8	no	—
19	C₂×C₅×Dic₁₂	C₂²	1	4	yes	complemented
20	C₂×C₅×D₂₄	C₂²	1	4	yes	—
21	C₂×C₅×#204	C₂²	1	4	yes	—
22	C₂×C₅×#204	C₂²	1	4	yes	complemented
23	C₅×#875	—	2	2	no	—
24	C₅×#875	C₂²	1	2	yes	—
25	C₅×#875	C₂²	1	2	yes	—
26	C₅×#875	C₂²	1	2	yes	complemented
27	C₅×#874	C₂²	1	1	yes	characteristic, complemented
28	C₄×C₅×D₁₂	—	2	2	no	—
29	C₅×#869	C₂²	1	1	yes	characteristic, complemented
30	C₃×C₅×#97	C₂²	1	2	yes	complemented
31	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
32	#78531	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂×C₅×#137	—	3	2	no	—
34	C₂×C₅×AGL(1,ℤ/8)	—	3	2	no	—
35	C₅×#532	—	3	1	no	—
36	C₂×C₅×#124	—	3	1	no	—
37	C₅×#497	—	3	2	no	—
38	C₅×#496	—	3	2	no	—
39	C₅×#495	—	3	4	no	—
40	C₄×C₅×M₁₆	D₃	1	1	yes	characteristic, complemented
41	C₂³×C₅×D₃	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂×C₅×#67	—	2	2	no	—
45	C₂²×C₅×Dic₃	—	2	1	no	—
46	C₅×#235	—	2	4	no	—
47	C₅×#235	—	2	4	no	—
48	C₂×C₅×D₁₂	—	2	4	no	—
49	C₂×C₅×D₁₂	—	2	2	no	—
50	C₂×C₅×D₁₂	—	2	1	no	—
51	C₂×C₅×D₁₂	C₂³	1	2	yes	—
52	C₂×C₅×D₁₂	C₂³	1	2	yes	—
53	C₂×C₄×C₅×D₃	—	2	2	no	—
54	C₂×C₅×Dic₆	—	2	4	no	—
55	C₂×C₅×Dic₆	—	2	1	no	—
56	C₂×C₅×Dic₆	C₂³	1	2	yes	—
57	C₂×C₅×Dic₆	C₂³	1	2	yes	—
58	C₃×C₅×M₁₆	D₄	1	8	yes	complemented
59	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
60	C₃×C₄²×C₅	D₄	1	2	yes	—
61	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
63	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
64	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
65	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
66	C₅×C₄⋊Dic₃	—	2	2	no	—
67	C₅×Dic₁₂	—	2	8	no	—
68	C₅×D₂₄	—	2	8	no	—
69	C₅×#204	—	2	8	no	—
70	C₅×#204	—	2	8	no	—
71	C₂×#909	C₂×C₅	1	2	yes	complemented
72	C₂×#908	C₂×C₅	1	2	yes	complemented
73	#5477	C₂×C₅	1	1	yes	characteristic, complemented
74	C₂×#875	C₂×C₅	1	1	yes	characteristic, complemented
75	C₃×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
76	#4715	C₂×C₅	1	2	yes	complemented
77	#4712	C₂×C₅	1	2	yes	complemented
78	#4696	C₂×C₅	1	4	yes	complemented
79	C₂×C₅×#41	—	3	2	no	—
80	C₂²×C₅×Q₈	—	3	1	no	—
81	C₂²×C₅×D₄	—	3	1	no	—
82	C₅×#137	—	6	8	no	—
83	C₅×AGL(1,ℤ/8)	—	6	8	no	—
84	C₂×C₅×Q₁₆	—	3	4	no	—
85	C₂×C₅×SD₁₆	—	3	4	no	—
86	C₂×C₅×SD₁₆	—	3	4	no	—
87	C₂×C₅×D₈	—	3	4	no	—
88	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	—
89	C₅×C₄⋊Q₈	—	3	1	no	—
90	C₅×#127	—	3	1	no	—
91	C₅×#124	—	3	2	no	—
92	C₅×#124	—	3	2	no	—
93	C₅×#124	—	3	2	no	—
94	C₅×#124	—	6	2	no	—
95	C₅×#121	—	6	2	no	—
96	C₄×C₅×D₄	—	6	2	no	—
97	C₂×C₅×C₂²⋊C₄	—	6	2	no	—
98	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
99	C₅×#97	C₂×D₃	1	2	yes	complemented
100	C₄×C₅×C₈	C₂×D₃	1	2	yes	complemented
101	#3153	—	3	1	no	Sylow
102	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₅×D₃	—	2	2	no	—
104	C₂²×C₅×D₃	—	2	2	no	—
105	C₂²×C₅×D₃	—	4	4	no	—
106	C₂²×C₅×D₃	—	4	2	no	—
107	C₂×C₃×C₄×C₅	—	4	2	no	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
109	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
112	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
113	C₅×#67	—	4	4	no	—
114	C₂×C₅×Dic₃	—	2	2	no	—
115	C₂×C₅×Dic₃	—	2	2	no	—
116	C₂×C₅×Dic₃	—	4	2	no	—
117	C₅×D₁₂	—	2	2	no	—
118	C₅×D₁₂	—	2	4	no	—
119	C₅×D₁₂	—	2	2	no	—
120	C₅×D₁₂	—	4	4	no	—
121	C₅×D₁₂	—	4	2	no	—
122	C₄×C₅×D₃	—	4	4	no	—
123	C₅×Dic₆	—	2	2	no	—
124	C₅×Dic₆	—	2	4	no	—
125	C₅×Dic₆	—	2	2	no	—
126	C₅×Dic₆	—	4	2	no	—
127	C₃×C₅×C₈	C₂×D₄	1	8	yes	—
128	C₂×#235	C₂²×C₅	1	2	yes	—
129	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
130	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
131	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
132	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
133	#930	—	2	2	no	—
134	C₂×(C₂×D₃)⋊C₄	—	2	2	no	—
135	#909	—	2	8	no	—
136	#908	—	2	8	no	—
137	C₂×Dic₁₂	C₂²×C₅	1	4	yes	complemented
138	C₂×D₂₄	C₂²×C₅	1	4	yes	—
139	C₂×#204	C₂²×C₅	1	4	yes	—
140	C₂×#204	C₂²×C₅	1	4	yes	complemented
141	#875	—	2	2	no	—
142	#875	C₂²×C₅	1	2	yes	—
143	#875	C₂²×C₅	1	2	yes	—
144	#875	C₂²×C₅	1	2	yes	complemented
145	#874	C₂²×C₅	1	1	yes	characteristic, complemented
146	C₄×D₁₂	—	2	2	no	—
147	#869	C₂²×C₅	1	1	yes	characteristic, complemented
148	C₃×#97	C₂²×C₅	1	2	yes	complemented
149	C₃×C₄×C₈	C₂²×C₅	1	2	yes	complemented
150	C₂⁴×C₅	—	6	1	no	—
151	C₅×#41	—	6	4	no	—
152	C₅×#41	—	6	4	no	—
153	C₂×C₅×Q₈	—	3	2	no	—
154	C₂×C₅×Q₈	—	3	2	no	—
155	C₂×C₅×Q₈	—	6	1	no	—
156	C₂×C₅×Q₈	—	6	4	no	—
157	C₂×C₅×D₄	—	3	2	no	—
158	C₂×C₅×D₄	—	3	2	no	—
159	C₂×C₅×D₄	—	6	2	no	—
160	C₂×C₅×D₄	—	6	4	no	—
161	C₂×C₅×D₄	—	6	2	no	—
162	C₂×C₅×D₄	—	6	1	no	—
163	C₂²×C₄×C₅	—	6	1	no	—
164	C₂²×C₄×C₅	—	6	2	no	—
165	C₂²×C₄×C₅	D₁₂	1	2	yes	—
166	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
167	C₅×Q₁₆	—	6	8	no	—
168	C₅×SD₁₆	—	6	8	no	—
169	C₅×SD₁₆	—	6	8	no	—
170	C₅×D₈	—	6	8	no	—
171	C₅×M₁₆	D₁₂	1	8	yes	complemented
172	C₂×C₅×C₈	C₂²×D₃	1	4	yes	—
173	C₅×C₄⋊C₄	—	6	2	no	—
174	C₅×C₂²⋊C₄	—	6	4	no	—
175	C₅×C₂²⋊C₄	—	6	4	no	—
176	C₅×C₂²⋊C₄	—	6	4	no	—
177	C₄²×C₅	D₁₂	1	2	yes	—
178	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
179	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
180	C₂×#137	—	3	2	no	—
181	C₂×AGL(1,ℤ/8)	—	3	2	no	—
182	#532	—	3	1	no	—
183	C₂×#124	—	3	1	no	—
184	#497	—	3	2	no	—
185	#496	—	3	2	no	—
186	#495	—	3	4	no	—
187	C₄×M₁₆	C₅×D₃	1	1	yes	characteristic, complemented
188	C₂²×C₃×C₅	—	2	2	no	—
189	C₂²×C₃×C₅	#127	1	2	yes	—
190	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₅×D₃	—	4	2	no	—
192	C₂×C₅×D₃	—	4	2	no	—
193	C₂×C₅×D₃	—	4	4	no	—
194	C₂×C₅×D₃	—	4	4	no	—
195	C₂×C₅×D₃	—	8	4	no	—
196	C₃×C₄×C₅	—	2	2	no	—
197	C₃×C₄×C₅	—	2	2	no	—
198	C₃×C₄×C₅	#127	1	2	yes	—
199	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
200	C₅×Dic₃	—	4	2	no	—
201	C₅×Dic₃	—	4	2	no	—
202	C₂³×D₃	—	2	1	no	—
203	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
204	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
205	C₂×#67	—	2	2	no	—
206	C₂²×Dic₃	—	2	1	no	—
207	#235	—	2	4	no	—
208	#235	—	2	4	no	—
209	C₂×D₁₂	—	2	4	no	—
210	C₂×D₁₂	—	2	2	no	—
211	C₂×D₁₂	—	2	1	no	—
212	C₂×D₁₂	C₂³×C₅	1	2	yes	—
213	C₂×D₁₂	C₂³×C₅	1	2	yes	—
214	C₂×C₄×D₃	—	2	2	no	—
215	C₂×Dic₆	—	2	4	no	—
216	C₂×Dic₆	—	2	1	no	—
217	C₂×Dic₆	C₂³×C₅	1	2	yes	—
218	C₂×Dic₆	C₂³×C₅	1	2	yes	—
219	C₃×M₁₆	C₅×D₄	1	8	yes	complemented
220	C₂×C₃×C₈	C₂³×C₅	1	4	yes	—
221	C₃×C₄²	C₅×D₄	1	2	yes	—
222	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
223	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
224	(C₂×D₃)⋊C₄	—	2	4	no	—
225	(C₂×D₃)⋊C₄	—	2	4	no	—
226	(C₂×D₃)⋊C₄	—	2	4	no	—
227	C₄⋊Dic₃	—	2	2	no	—
228	Dic₁₂	—	2	8	no	—
229	D₂₄	—	2	8	no	—
230	#204	—	2	8	no	—
231	#204	—	2	8	no	—
232	C₂³×C₅	—	6	2	no	—
233	C₂³×C₅	—	6	2	no	—
234	C₂³×C₅	—	12	4	no	—
235	C₂³×C₅	—	12	2	no	—
236	C₂³×C₅	C₂×D₁₂	1	1	yes	characteristic
237	C₅×Q₈	—	6	2	no	—
238	C₅×Q₈	—	6	4	no	—
239	C₅×Q₈	—	6	2	no	—
240	C₅×Q₈	—	12	2	no	—
241	C₅×D₄	—	6	2	no	—
242	C₅×D₄	—	6	4	no	—
243	C₅×D₄	—	6	2	no	—
244	C₅×D₄	—	12	4	no	—
245	C₅×D₄	—	12	4	no	—
246	C₅×D₄	—	12	2	no	—
247	C₂×C₄×C₅	—	4	2	no	—
248	C₂×C₄×C₅	—	6	2	no	—
249	C₂×C₄×C₅	—	6	2	no	—
250	C₂×C₄×C₅	—	12	2	no	—
251	C₂×C₄×C₅	—	12	4	no	—
252	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
253	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
254	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
255	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
256	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
257	C₅×C₈	C₂×D₁₂	1	8	yes	—
258	C₂×#41	—	3	2	no	—
259	C₂²×Q₈	—	3	1	no	—
260	C₂²×D₄	—	3	1	no	—
261	#137	—	6	8	no	—
262	AGL(1,ℤ/8)	—	6	8	no	—
263	C₂×Q₁₆	—	3	4	no	—
264	C₂×SD₁₆	—	3	4	no	—
265	C₂×SD₁₆	—	3	4	no	—
266	C₂×D₈	—	3	4	no	—
267	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	—
268	C₄⋊Q₈	—	3	1	no	—
269	#127	—	3	1	no	—
270	#124	—	3	2	no	—
271	#124	—	3	2	no	—
272	#124	—	3	2	no	—
273	#124	—	6	2	no	—
274	#121	—	6	2	no	—
275	C₄×D₄	—	6	2	no	—
276	C₂×C₂²⋊C₄	—	6	2	no	—
277	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
278	#97	C₂×C₅×D₃	1	2	yes	complemented
279	C₄×C₈	C₂×C₅×D₃	1	2	yes	complemented
280	C₂×C₃×C₅	—	2	2	no	—
281	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
282	C₂×C₃×C₅	#575	1	2	yes	—
283	C₅×D₃	—	8	2	no	—
284	C₅×D₃	—	8	2	no	—
285	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
286	C₂²×D₃	—	2	2	no	—
287	C₂²×D₃	—	2	2	no	—
288	C₂²×D₃	—	4	4	no	—
289	C₂²×D₃	—	4	2	no	—
290	C₂×C₃×C₄	—	4	2	no	—
291	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
292	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
293	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
295	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
296	#67	—	4	4	no	—
297	C₂×Dic₃	—	2	2	no	—
298	C₂×Dic₃	—	2	2	no	—
299	C₂×Dic₃	—	4	2	no	—
300	D₁₂	—	2	2	no	—
301	D₁₂	—	2	4	no	—
302	D₁₂	—	2	2	no	—
303	D₁₂	—	4	4	no	—
304	D₁₂	—	4	2	no	—
305	C₄×D₃	—	4	4	no	—
306	Dic₆	—	2	2	no	—
307	Dic₆	—	2	4	no	—
308	Dic₆	—	2	2	no	—
309	Dic₆	—	4	2	no	—
310	C₃×C₈	C₂×C₅×D₄	1	8	yes	—
311	C₂²×C₅	—	2	2	no	—
312	C₂²×C₅	—	12	2	no	—
313	C₂²×C₅	—	12	2	no	—
314	C₂²×C₅	—	12	4	no	—
315	C₂²×C₅	—	12	4	no	—
316	C₂²×C₅	—	24	4	no	—
317	C₂²×C₅	#874	1	2	yes	—
318	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
319	C₄×C₅	—	2	2	no	—
320	C₄×C₅	—	2	2	no	—
321	C₄×C₅	—	12	2	no	—
322	C₄×C₅	—	12	2	no	—
323	C₄×C₅	#874	1	2	yes	—
324	C₄×C₅	C₂²×D₁₂	1	2	yes	—
325	C₂⁴	—	6	1	no	—
326	#41	—	6	4	no	—
327	#41	—	6	4	no	—
328	C₂×Q₈	—	3	2	no	—
329	C₂×Q₈	—	3	2	no	—
330	C₂×Q₈	—	6	1	no	—
331	C₂×Q₈	—	6	4	no	—
332	C₂×D₄	—	3	2	no	—
333	C₂×D₄	—	3	2	no	—
334	C₂×D₄	—	6	2	no	—
335	C₂×D₄	—	6	4	no	—
336	C₂×D₄	—	6	2	no	—
337	C₂×D₄	—	6	1	no	—
338	C₂²×C₄	—	6	1	no	—
339	C₂²×C₄	—	6	2	no	—
340	C₂²×C₄	C₅×D₁₂	1	2	yes	—
341	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
342	Q₁₆	—	6	8	no	—
343	SD₁₆	—	6	8	no	—
344	SD₁₆	—	6	8	no	—
345	D₈	—	6	8	no	—
346	M₁₆	C₅×D₁₂	1	8	yes	complemented
347	C₂×C₈	C₂²×C₅×D₃	1	4	yes	—
348	C₄⋊C₄	—	6	2	no	—
349	C₂²⋊C₄	—	6	4	no	—
350	C₂²⋊C₄	—	6	4	no	—
351	C₂²⋊C₄	—	6	4	no	—
352	C₄²	C₅×D₁₂	1	2	yes	—
353	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
354	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
355	C₃×C₅	#3153	1	1	yes	characteristic, complemented, Hall
356	C₂²×C₃	—	2	2	no	—
357	C₂²×C₃	C₅×#127	1	2	yes	—
358	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
359	C₂×D₃	—	4	2	no	—
360	C₂×D₃	—	4	2	no	—
361	C₂×D₃	—	4	4	no	—
362	C₂×D₃	—	4	4	no	—
363	C₂×D₃	—	8	4	no	—
364	C₃×C₄	—	2	2	no	—
365	C₃×C₄	—	2	2	no	—
366	C₃×C₄	C₅×#127	1	2	yes	—
367	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
368	Dic₃	—	4	2	no	—
369	Dic₃	—	4	2	no	—
370	C₂×C₅	—	2	2	no	—
371	C₂×C₅	—	24	2	no	—
372	C₂×C₅	—	24	2	no	—
373	C₂×C₅	C₂×#874	1	1	yes	characteristic
374	C₂×C₅	#5748	1	2	yes	—
375	C₂³	—	6	2	no	—
376	C₂³	—	6	2	no	—
377	C₂³	—	12	4	no	—
378	C₂³	—	12	2	no	—
379	C₂³	C₂×C₅×D₁₂	1	1	yes	characteristic
380	Q₈	—	6	2	no	—
381	Q₈	—	6	4	no	—
382	Q₈	—	6	2	no	—
383	Q₈	—	12	2	no	—
384	D₄	—	6	2	no	—
385	D₄	—	6	4	no	—
386	D₄	—	6	2	no	—
387	D₄	—	12	4	no	—
388	D₄	—	12	4	no	—
389	D₄	—	12	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	6	2	no	—
392	C₂×C₄	—	6	2	no	—
393	C₂×C₄	—	12	2	no	—
394	C₂×C₄	—	12	4	no	—
395	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
396	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
397	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
398	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
399	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
400	C₈	C₂×C₅×D₁₂	1	8	yes	—
401	C₂×C₃	—	2	2	no	—
402	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
403	C₂×C₃	C₅×#575	1	2	yes	—
404	D₃	—	8	2	no	—
405	D₃	—	8	2	no	—
406	C₅	#78531	1	1	yes	characteristic, direct product factor, Sylow
407	C₂²	—	2	2	no	—
408	C₂²	—	12	2	no	—
409	C₂²	—	12	2	no	—
410	C₂²	—	12	4	no	—
411	C₂²	—	12	4	no	—
412	C₂²	—	24	4	no	—
413	C₂²	C₅×#874	1	2	yes	—
414	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	12	2	no	—
418	C₄	—	12	2	no	—
419	C₄	C₅×#874	1	2	yes	—
420	C₄	C₂²×C₅×D₁₂	1	2	yes	—
421	C₃	C₅×#3153	1	1	yes	characteristic, complemented, Sylow
422	C₂	—	2	2	no	—
423	C₂	—	24	2	no	—
424	C₂	—	24	2	no	—
425	C₂	C₂×C₅×#874	1	1	yes	characteristic
426	C₂	C₅×#5748	1	2	yes	—

	subgroup	G/H
center	C₂²×C₅	C₂²×D₁₂
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₄×C₅×M₁₆	D₃
hypocenter	C₃	C₅×#3153
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ C₄×C₅×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#909	C₂	semidirect
2. C₂×C₅×#908	C₂	semidirect
3. C₅×#5477	C₂	semidirect
4. C₂×C₅×#875	C₂	semidirect
5. C₃×C₄×C₅×M₁₆	C₂	semidirect
6. C₅×#4715	C₂	semidirect
7. C₅×#4712	C₂	semidirect
8. C₅×#4696	C₂	semidirect
19. C₂×C₅×Dic₁₂	C₂²	semidirect
22. C₂×C₅×#204	C₂²	semidirect
26. C₅×#875	C₂²	semidirect
27. C₅×#874	C₂²	semidirect
29. C₅×#869	C₂²	semidirect
30. C₃×C₅×#97	C₂²	semidirect
31. C₃×C₄×C₅×C₈	C₂²	semidirect
32. #78531	C₅	direct (N × H)
40. C₄×C₅×M₁₆	D₃	semidirect
58. C₃×C₅×M₁₆	D₄	semidirect
71. C₂×#909	C₂×C₅	semidirect
72. C₂×#908	C₂×C₅	semidirect
73. #5477	C₂×C₅	semidirect
74. C₂×#875	C₂×C₅	semidirect
75. C₃×C₄×M₁₆	C₂×C₅	semidirect
76. #4715	C₂×C₅	semidirect
77. #4712	C₂×C₅	semidirect
78. #4696	C₂×C₅	semidirect
99. C₅×#97	C₂×D₃	semidirect
100. C₄×C₅×C₈	C₂×D₃	semidirect
137. C₂×Dic₁₂	C₂²×C₅	semidirect
140. C₂×#204	C₂²×C₅	semidirect
144. #875	C₂²×C₅	semidirect
145. #874	C₂²×C₅	semidirect
147. #869	C₂²×C₅	semidirect
148. C₃×#97	C₂²×C₅	semidirect
149. C₃×C₄×C₈	C₂²×C₅	semidirect
171. C₅×M₁₆	D₁₂	semidirect
187. C₄×M₁₆	C₅×D₃	semidirect
219. C₃×M₁₆	C₅×D₄	semidirect
278. #97	C₂×C₅×D₃	semidirect
279. C₄×C₈	C₂×C₅×D₃	semidirect
346. M₁₆	C₅×D₁₂	semidirect
355. C₃×C₅	#3153	semidirect
406. C₅	#78531	direct (N × H)
421. C₃	C₅×#3153	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#909	2
C₂×C₅×#908	2
C₅×#5477	2
C₂×C₅×#875	2
C₃×C₄×C₅×M₁₆	2
C₅×#4715	2
C₅×#4712	2
C₅×#4696	2
C₅×#3153	3
#78531	5

Subgroups — C5×#78531 #14439288

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#78531 #14439288