Subgroups — C₅×#33589 #11956309

Order 1280.

726 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#508	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3155	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2951	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2211	C₂	1	2	yes	maximal, complemented
6	C₅×#2210	C₂	1	2	yes	maximal, complemented
7	C₅×#2207	C₂	1	2	yes	maximal, complemented
8	C₅×#2206	C₂	1	2	yes	maximal, complemented
9	C₅×#2151	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2139	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×#357	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×AGL(1,ℤ/8)	—	2	1	no	—
13	C₂×C₅×#135	C₂²	1	1	yes	characteristic
14	C₂×C₅×#135	C₂²	1	1	yes	characteristic
15	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
16	C₅×#535	—	2	1	no	—
17	C₅×#520	—	2	1	no	—
18	C₅×#509	—	2	4	no	—
19	C₅×#508	—	2	4	no	—
20	C₂×C₅×Q₃₂	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
22	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₅×D₁₆	C₂²	1	2	yes	—
25	C₂×C₅×D₁₆	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
27	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
28	C₅×#496	—	2	2	no	—
29	C₅×#495	C₂²	1	2	yes	—
30	C₅×#493	C₂²	1	2	yes	—
31	C₅×#440	—	2	2	no	—
32	C₄×C₅×Q₁₆	C₂²	1	2	yes	complemented
33	C₄×C₅×D₈	C₂²	1	2	yes	complemented
34	C₂×C₅×#107	C₂²	1	1	yes	characteristic
35	C₅×#417	—	2	1	no	—
36	C₅×#405	C₂²	1	1	yes	characteristic
37	C₅×C₄⋊C₁₆	C₂²	1	2	yes	complemented
38	C₅×C₄⋊C₁₆	C₂²	1	2	yes	complemented
39	C₅×#358	C₂²	1	2	yes	complemented
40	C₅×#357	C₂²	1	2	yes	—
41	C₅×#357	C₂²	1	2	yes	—
42	C₅×#357	C₂²	1	2	yes	complemented
43	#33589	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₅×#41	—	2	1	no	—
45	C₂×C₅×#41	—	2	1	no	—
46	C₂²×C₅×D₄	—	2	1	no	—
47	C₅×AGL(1,ℤ/8)	—	4	4	no	—
48	C₅×#135	—	2	2	no	—
49	C₅×#135	—	2	2	no	—
50	C₅×#135	—	2	2	no	—
51	C₅×#135	D₄	1	4	yes	complemented
52	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
54	C₂×C₅×SD₁₆	—	2	1	no	—
55	C₂×C₅×SD₁₆	—	2	2	no	—
56	C₂×C₅×SD₁₆	—	2	1	no	—
57	C₂×C₅×D₈	—	2	2	no	—
58	C₂×C₅×D₈	—	2	2	no	—
59	C₂×C₅×D₈	—	2	1	no	—
60	C₂×C₅×D₈	—	2	2	no	—
61	C₂×C₅×D₈	C₂³	1	2	yes	—
62	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
63	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
64	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₅×#127	—	2	2	no	—
67	C₅×#124	—	2	2	no	—
68	C₅×#121	—	4	1	no	—
69	C₅×#121	—	4	1	no	—
70	C₅×#120	—	4	2	no	—
71	C₄×C₅×Q₈	—	2	2	no	—
72	C₄×C₅×D₄	—	2	2	no	—
73	C₄×C₅×D₄	—	4	2	no	—
74	C₅×#117	—	4	1	no	—
75	C₅×#117	D₄	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	—	2	1	no	—
77	C₂×C₅×C₄⋊C₄	—	4	1	no	—
78	C₅×Q₃₂	—	2	2	no	—
79	C₅×SD₃₂	—	2	4	no	—
80	C₅×SD₃₂	—	2	2	no	—
81	C₅×SD₃₂	—	2	2	no	—
82	C₅×D₁₆	—	2	4	no	—
83	C₅×D₁₆	—	2	2	no	—
84	C₅×M₃₂	—	2	2	no	—
85	C₂×C₅×C₁₆	—	2	2	no	—
86	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
87	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
88	C₂×C₅×C₁₆	C₂³	1	2	yes	—
89	C₅×#107	—	2	1	no	—
90	C₅×#107	C₂³	1	2	yes	—
91	C₅×#103	—	2	2	no	—
92	C₅×#102	—	2	2	no	—
93	C₅×#97	D₄	1	2	yes	—
94	C₄×C₅×C₈	C₂³	1	2	yes	—
95	C₂×#509	C₂×C₅	1	1	yes	characteristic, complemented
96	C₂×#508	C₂×C₅	1	1	yes	characteristic, complemented
97	#3155	C₂×C₅	1	1	yes	characteristic, complemented
98	#2951	C₂×C₅	1	1	yes	characteristic, complemented
99	#2211	C₂×C₅	1	2	yes	complemented
100	#2210	C₂×C₅	1	2	yes	complemented
101	#2207	C₂×C₅	1	2	yes	complemented
102	#2206	C₂×C₅	1	2	yes	complemented
103	#2151	C₂×C₅	1	1	yes	characteristic, complemented
104	#2139	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂×#357	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂⁴×C₅	—	4	1	no	—
107	C₅×#41	—	2	4	no	—
108	C₅×#41	—	4	2	no	—
109	C₅×#41	—	4	2	no	—
110	C₅×#41	—	4	2	no	—
111	C₂×C₅×Q₈	—	2	1	no	—
112	C₂×C₅×Q₈	—	2	1	no	—
113	C₂×C₅×D₄	—	2	1	no	—
114	C₂×C₅×D₄	—	2	2	no	—
115	C₂×C₅×D₄	—	2	1	no	—
116	C₂×C₅×D₄	—	4	1	no	—
117	C₂×C₅×D₄	—	4	1	no	—
118	C₂×C₅×D₄	—	4	2	no	—
119	C₂×C₅×D₄	—	4	1	no	—
120	C₂×C₅×D₄	—	4	2	no	—
121	C₂×C₅×D₄	—	4	2	no	—
122	C₂×C₅×D₄	—	4	2	no	—
123	C₂²×C₄×C₅	—	4	1	no	—
124	C₂²×C₄×C₅	—	4	1	no	—
125	C₂²×C₄×C₅	—	4	1	no	—
126	C₂²×C₄×C₅	—	4	2	no	—
127	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₅×Q₁₆	—	2	1	no	—
129	C₅×Q₁₆	—	2	1	no	—
130	C₅×Q₁₆	—	2	1	no	—
131	C₅×Q₁₆	C₂×D₄	1	2	yes	—
132	C₅×SD₁₆	—	2	4	no	—
133	C₅×SD₁₆	—	4	4	no	—
134	C₅×SD₁₆	—	4	2	no	—
135	C₅×D₈	—	2	2	no	—
136	C₅×D₈	—	2	1	no	—
137	C₅×D₈	—	2	1	no	—
138	C₅×D₈	—	2	2	no	—
139	C₅×D₈	—	2	1	no	—
140	C₅×D₈	—	4	4	no	—
141	C₅×D₈	—	4	2	no	—
142	C₅×D₈	C₂×D₄	1	2	yes	—
143	C₅×M₁₆	—	2	2	no	—
144	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
145	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
146	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
147	C₂×C₅×C₈	#41	1	2	yes	—
148	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
149	C₅×C₄⋊C₄	—	2	2	no	—
150	C₅×C₄⋊C₄	—	4	1	no	—
151	C₅×C₄⋊C₄	—	4	2	no	—
152	C₅×C₄⋊C₄	D₈	1	1	yes	characteristic
153	C₅×C₄⋊C₄	D₈	1	1	yes	characteristic
154	C₅×C₂²⋊C₄	—	4	2	no	—
155	C₅×C₂²⋊C₄	—	4	2	no	—
156	C₅×C₂²⋊C₄	—	4	2	no	—
157	C₅×C₂²⋊C₄	D₈	1	2	yes	—
158	C₄²×C₅	—	4	2	no	—
159	C₄²×C₅	C₂×D₄	1	2	yes	—
160	C₅×C₁₆	—	2	1	no	—
161	C₅×C₁₆	—	2	1	no	—
162	C₅×C₁₆	—	2	2	no	—
163	C₂×AGL(1,ℤ/8)	—	2	1	no	—
164	C₂×#135	C₂²×C₅	1	1	yes	characteristic
165	C₂×#135	C₂²×C₅	1	1	yes	characteristic
166	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
167	#535	—	2	1	no	—
168	#520	—	2	1	no	—
169	#509	—	2	4	no	—
170	#508	—	2	4	no	—
171	C₂×Q₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
172	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
173	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
174	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic, complemented
175	C₂×D₁₆	C₂²×C₅	1	2	yes	—
176	C₂×D₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
177	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
178	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
179	#496	—	2	2	no	—
180	#495	C₂²×C₅	1	2	yes	—
181	#493	C₂²×C₅	1	2	yes	—
182	#440	—	2	2	no	—
183	C₄×Q₁₆	C₂²×C₅	1	2	yes	complemented
184	C₄×D₈	C₂²×C₅	1	2	yes	complemented
185	C₂×#107	C₂²×C₅	1	1	yes	characteristic
186	#417	—	2	1	no	—
187	#405	C₂²×C₅	1	1	yes	characteristic
188	C₄⋊C₁₆	C₂²×C₅	1	2	yes	complemented
189	C₄⋊C₁₆	C₂²×C₅	1	2	yes	complemented
190	#358	C₂²×C₅	1	2	yes	complemented
191	#357	C₂²×C₅	1	2	yes	—
192	#357	C₂²×C₅	1	2	yes	—
193	#357	C₂²×C₅	1	2	yes	complemented
194	C₂³×C₅	—	4	1	no	—
195	C₂³×C₅	—	4	2	no	—
196	C₂³×C₅	—	4	1	no	—
197	C₂³×C₅	—	8	2	no	—
198	C₂³×C₅	—	16	1	no	—
199	C₂³×C₅	—	16	1	no	—
200	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
201	C₅×Q₈	—	2	2	no	—
202	C₅×Q₈	—	4	1	no	—
203	C₅×Q₈	—	4	1	no	—
204	C₅×Q₈	—	4	1	no	—
205	C₅×D₄	—	2	2	no	—
206	C₅×D₄	—	4	4	no	—
207	C₅×D₄	—	4	2	no	—
208	C₅×D₄	—	4	1	no	—
209	C₅×D₄	—	4	1	no	—
210	C₅×D₄	—	4	1	no	—
211	C₅×D₄	—	4	2	no	—
212	C₅×D₄	—	8	2	no	—
213	C₅×D₄	—	8	2	no	—
214	C₅×D₄	—	16	2	no	—
215	C₅×D₄	—	16	2	no	—
216	C₂×C₄×C₅	—	4	1	no	—
217	C₂×C₄×C₅	—	4	4	no	—
218	C₂×C₄×C₅	—	4	2	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	—	8	2	no	—
221	C₂×C₄×C₅	—	16	2	no	—
222	C₂×C₄×C₅	—	16	1	no	—
223	C₂×C₄×C₅	#121	1	2	yes	—
224	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
225	C₂×C₄×C₅	C₂×D₈	1	2	yes	—
226	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
227	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
228	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
229	C₅×C₈	—	2	2	no	—
230	C₅×C₈	#121	1	2	yes	—
231	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
232	C₅×C₈	C₂×#41	1	1	yes	characteristic
233	C₂×#41	—	2	1	no	—
234	C₂×#41	—	2	1	no	—
235	C₂²×D₄	—	2	1	no	—
236	AGL(1,ℤ/8)	—	4	4	no	—
237	#135	—	2	2	no	—
238	#135	—	2	2	no	—
239	#135	—	2	2	no	—
240	#135	C₅×D₄	1	4	yes	complemented
241	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
242	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
243	C₂×SD₁₆	—	2	1	no	—
244	C₂×SD₁₆	—	2	1	no	—
245	C₂×SD₁₆	—	2	2	no	—
246	C₂×D₈	—	2	2	no	—
247	C₂×D₈	—	2	1	no	—
248	C₂×D₈	—	2	2	no	—
249	C₂×D₈	—	2	2	no	—
250	C₂×D₈	C₂³×C₅	1	2	yes	—
251	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
252	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
253	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
254	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
255	#127	—	2	2	no	—
256	#124	—	2	2	no	—
257	#121	—	4	1	no	—
258	#121	—	4	1	no	—
259	#120	—	4	2	no	—
260	C₄×Q₈	—	2	2	no	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	—	4	2	no	—
263	#117	—	4	1	no	—
264	#117	C₅×D₄	1	1	yes	characteristic
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	4	1	no	—
267	Q₃₂	—	2	2	no	—
268	SD₃₂	—	2	4	no	—
269	SD₃₂	—	2	2	no	—
270	SD₃₂	—	2	2	no	—
271	D₁₆	—	2	4	no	—
272	D₁₆	—	2	2	no	—
273	M₃₂	—	2	2	no	—
274	C₂×C₁₆	—	2	2	no	—
275	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
276	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
277	C₂×C₁₆	C₂³×C₅	1	2	yes	—
278	#107	—	2	1	no	—
279	#107	C₂³×C₅	1	2	yes	—
280	#103	—	2	2	no	—
281	#102	—	2	2	no	—
282	#97	C₅×D₄	1	2	yes	—
283	C₄×C₈	C₂³×C₅	1	2	yes	—
284	C₂²×C₅	—	2	1	no	—
285	C₂²×C₅	—	2	1	no	—
286	C₂²×C₅	—	4	2	no	—
287	C₂²×C₅	—	8	1	no	—
288	C₂²×C₅	—	8	1	no	—
289	C₂²×C₅	—	8	1	no	—
290	C₂²×C₅	—	8	2	no	—
291	C₂²×C₅	—	8	1	no	—
292	C₂²×C₅	—	8	2	no	—
293	C₂²×C₅	—	8	1	no	—
294	C₂²×C₅	—	8	2	no	—
295	C₂²×C₅	—	16	4	no	—
296	C₂²×C₅	#459	1	2	yes	—
297	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
298	C₄×C₅	—	2	2	no	—
299	C₄×C₅	—	2	2	no	—
300	C₄×C₅	—	4	2	no	—
301	C₄×C₅	—	8	2	no	—
302	C₄×C₅	—	8	1	no	—
303	C₄×C₅	#459	1	2	yes	—
304	C₄×C₅	C₂×#121	1	1	yes	characteristic
305	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
306	C₂⁴	—	4	1	no	—
307	#41	—	2	4	no	—
308	#41	—	4	2	no	—
309	#41	—	4	2	no	—
310	#41	—	4	2	no	—
311	C₂×Q₈	—	2	1	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	—	4	2	no	—
322	C₂×D₄	—	4	2	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	4	2	no	—
327	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
328	Q₁₆	—	2	1	no	—
329	Q₁₆	—	2	1	no	—
330	Q₁₆	—	2	1	no	—
331	Q₁₆	C₂×C₅×D₄	1	2	yes	—
332	SD₁₆	—	2	4	no	—
333	SD₁₆	—	4	4	no	—
334	SD₁₆	—	4	2	no	—
335	D₈	—	2	2	no	—
336	D₈	—	2	1	no	—
337	D₈	—	2	1	no	—
338	D₈	—	2	2	no	—
339	D₈	—	2	1	no	—
340	D₈	—	4	4	no	—
341	D₈	—	4	2	no	—
342	D₈	C₂×C₅×D₄	1	2	yes	—
343	M₁₆	—	2	2	no	—
344	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
345	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
346	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
347	C₂×C₈	C₅×#41	1	2	yes	—
348	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	C₅×D₈	1	1	yes	characteristic
353	C₄⋊C₄	C₅×D₈	1	1	yes	characteristic
354	C₂²⋊C₄	—	4	2	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₂²⋊C₄	C₅×D₈	1	2	yes	—
358	C₄²	—	4	2	no	—
359	C₄²	C₂×C₅×D₄	1	2	yes	—
360	C₁₆	—	2	1	no	—
361	C₁₆	—	2	1	no	—
362	C₁₆	—	2	2	no	—
363	C₂×C₅	—	2	2	no	—
364	C₂×C₅	—	8	2	no	—
365	C₂×C₅	—	16	1	no	—
366	C₂×C₅	—	16	2	no	—
367	C₂×C₅	C₂×#459	1	1	yes	characteristic
368	C₂×C₅	#3415	1	1	yes	characteristic
369	C₂×C₅	#3416	1	1	yes	characteristic
370	C₂³	—	4	1	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	1	no	—
373	C₂³	—	8	2	no	—
374	C₂³	—	16	1	no	—
375	C₂³	—	16	1	no	—
376	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
377	Q₈	—	2	2	no	—
378	Q₈	—	4	1	no	—
379	Q₈	—	4	1	no	—
380	Q₈	—	4	1	no	—
381	D₄	—	2	2	no	—
382	D₄	—	4	4	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	1	no	—
385	D₄	—	4	1	no	—
386	D₄	—	4	1	no	—
387	D₄	—	4	2	no	—
388	D₄	—	8	2	no	—
389	D₄	—	8	2	no	—
390	D₄	—	16	2	no	—
391	D₄	—	16	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	4	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	8	2	no	—
397	C₂×C₄	—	16	2	no	—
398	C₂×C₄	—	16	1	no	—
399	C₂×C₄	C₅×#121	1	2	yes	—
400	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
401	C₂×C₄	C₂×C₅×D₈	1	2	yes	—
402	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
403	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
404	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
405	C₈	—	2	2	no	—
406	C₈	C₅×#121	1	2	yes	—
407	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
408	C₈	C₂×C₅×#41	1	1	yes	characteristic
409	C₅	#33589	1	1	yes	characteristic, direct product factor, Sylow
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	1	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	1	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	16	4	no	—
422	C₂²	C₅×#459	1	2	yes	—
423	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	8	1	no	—
428	C₄	—	8	2	no	—
429	C₄	C₅×#459	1	2	yes	—
430	C₄	C₂×C₅×#121	1	1	yes	characteristic
431	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
432	C₂	—	2	2	no	—
433	C₂	—	8	2	no	—
434	C₂	—	16	2	no	—
435	C₂	—	16	1	no	—
436	C₂	C₂×C₅×#459	1	1	yes	characteristic
437	C₂	C₅×#3415	1	1	yes	characteristic
438	C₂	C₅×#3416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₅×#117 ◁ C₅×#405 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#509	C₂	semidirect
2. C₂×C₅×#508	C₂	semidirect
3. C₅×#3155	C₂	semidirect
4. C₅×#2951	C₂	semidirect
5. C₅×#2211	C₂	semidirect
6. C₅×#2210	C₂	semidirect
7. C₅×#2207	C₂	semidirect
8. C₅×#2206	C₂	semidirect
9. C₅×#2151	C₂	semidirect
10. C₅×#2139	C₂	semidirect
11. C₂×C₅×#357	C₂	semidirect
20. C₂×C₅×Q₃₂	C₂²	semidirect
22. C₂×C₅×SD₃₂	C₂²	semidirect
23. C₂×C₅×SD₃₂	C₂²	semidirect
25. C₂×C₅×D₁₆	C₂²	semidirect
32. C₄×C₅×Q₁₆	C₂²	semidirect
33. C₄×C₅×D₈	C₂²	semidirect
37. C₅×C₄⋊C₁₆	C₂²	semidirect
38. C₅×C₄⋊C₁₆	C₂²	semidirect
39. C₅×#358	C₂²	semidirect
42. C₅×#357	C₂²	semidirect
43. #33589	C₅	direct (N × H)
51. C₅×#135	D₄	semidirect
95. C₂×#509	C₂×C₅	semidirect
96. C₂×#508	C₂×C₅	semidirect
97. #3155	C₂×C₅	semidirect
98. #2951	C₂×C₅	semidirect
99. #2211	C₂×C₅	semidirect
100. #2210	C₂×C₅	semidirect
101. #2207	C₂×C₅	semidirect
102. #2206	C₂×C₅	semidirect
103. #2151	C₂×C₅	semidirect
104. #2139	C₂×C₅	semidirect
105. C₂×#357	C₂×C₅	semidirect
171. C₂×Q₃₂	C₂²×C₅	semidirect
173. C₂×SD₃₂	C₂²×C₅	semidirect
174. C₂×SD₃₂	C₂²×C₅	semidirect
176. C₂×D₁₆	C₂²×C₅	semidirect
183. C₄×Q₁₆	C₂²×C₅	semidirect
184. C₄×D₈	C₂²×C₅	semidirect
188. C₄⋊C₁₆	C₂²×C₅	semidirect
189. C₄⋊C₁₆	C₂²×C₅	semidirect
190. #358	C₂²×C₅	semidirect
193. #357	C₂²×C₅	semidirect
240. #135	C₅×D₄	semidirect
409. C₅	#33589	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×C₅×#509	2
C₂×C₅×#508	2
C₅×#3155	2
C₅×#2951	2
C₅×#2211	2
C₅×#2210	2
C₅×#2207	2
C₅×#2206	2
C₅×#2151	2
C₅×#2139	2
C₂×C₅×#357	2
#33589	5

Subgroups — C5×#33589 #11956309

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33589 #11956309