Subgroups — C₅×#33596 #11956316

Order 1280.

674 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3414	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3156	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2957	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2214	C₂	1	4	yes	maximal, complemented
6	C₅×#2212	C₂	1	4	yes	maximal, complemented
7	C₅×#2153	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2148	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#362	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#137	—	2	1	no	—
11	C₂×C₅×#135	C₂²	1	1	yes	characteristic
12	C₂×C₅×#135	C₂²	1	1	yes	characteristic
13	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
14	C₅×#568	—	2	1	no	—
15	C₅×#536	—	2	1	no	—
16	C₅×#510	—	2	2	no	—
17	C₅×#510	—	2	1	no	—
18	C₅×#510	C₂²	1	4	yes	—
19	C₅×#510	C₂²	1	2	yes	—
20	C₅×#509	—	2	1	no	—
21	C₅×#509	C₂²	1	2	yes	—
22	C₅×#508	—	2	2	no	—
23	C₂×C₅×Q₃₂	—	2	1	no	—
24	C₂×C₅×SD₃₂	—	2	1	no	—
25	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
26	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
27	C₅×#497	—	2	2	no	—
28	C₅×#495	C₂²	1	2	yes	complemented
29	C₅×#494	C₂²	1	2	yes	complemented
30	C₅×#444	—	2	2	no	—
31	C₅×#443	C₂²	1	4	yes	—
32	C₂×C₅×#108	C₂²	1	1	yes	characteristic
33	C₅×#421	—	2	1	no	—
34	C₅×#405	C₂²	1	1	yes	characteristic
35	C₅×#364	C₂²	1	4	yes	complemented
36	C₅×#362	C₂²	1	4	yes	complemented
37	C₅×#362	C₂²	1	2	yes	complemented
38	C₅×#361	C₂²	1	2	yes	complemented
39	#33596	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂×C₅×#41	—	2	1	no	—
41	C₂×C₅×#41	—	2	1	no	—
42	C₂²×C₅×Q₈	—	2	1	no	—
43	C₅×#137	—	4	2	no	—
44	C₅×#137	—	4	2	no	—
45	C₅×#135	—	2	1	no	—
46	C₅×#135	—	2	1	no	—
47	C₅×#135	—	2	1	no	—
48	C₅×#135	—	2	1	no	—
49	C₅×#135	—	2	1	no	—
50	C₅×#135	—	2	1	no	—
51	C₅×#135	D₄	1	2	yes	—
52	C₅×#135	C₂³	1	2	yes	—
53	C₂×C₅×Q₁₆	—	2	1	no	—
54	C₂×C₅×Q₁₆	—	2	1	no	—
55	C₂×C₅×Q₁₆	—	2	2	no	—
56	C₂×C₅×Q₁₆	—	2	1	no	—
57	C₂×C₅×Q₁₆	—	2	1	no	—
58	C₂×C₅×Q₁₆	—	2	1	no	—
59	C₂×C₅×Q₁₆	D₄	1	1	yes	characteristic
60	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
62	C₂×C₅×SD₁₆	—	2	2	no	—
63	C₂×C₅×SD₁₆	—	2	1	no	—
64	C₂×C₅×SD₁₆	—	2	1	no	—
65	C₂×C₅×D₈	D₄	1	1	yes	characteristic
66	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
67	C₅×#131	—	2	4	no	—
68	C₅×#131	—	4	2	no	—
69	C₂×C₅×M₁₆	—	2	1	no	—
70	C₂×C₅×M₁₆	—	4	2	no	—
71	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
72	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₅×C₄⋊Q₈	—	2	2	no	—
74	C₅×#124	—	2	2	no	—
75	C₅×#123	—	4	2	no	—
76	C₅×C₂²⋊Q₈	—	4	2	no	—
77	C₅×#117	D₄	1	1	yes	characteristic
78	C₅×Q₃₂	—	2	4	no	—
79	C₅×Q₃₂	—	2	2	no	—
80	C₅×SD₃₂	—	2	2	no	—
81	C₅×SD₃₂	—	2	4	no	—
82	C₅×SD₃₂	—	2	2	no	—
83	C₅×D₁₆	—	2	2	no	—
84	C₅×M₃₂	—	2	1	no	—
85	C₅×M₃₂	—	2	1	no	—
86	C₅×M₃₂	C₂³	1	2	yes	—
87	C₅×M₃₂	C₂³	1	2	yes	—
88	C₂×C₅×C₁₆	—	2	1	no	—
89	C₂×C₅×C₁₆	—	2	1	no	—
90	C₅×#108	—	2	1	no	—
91	C₅×#108	C₂³	1	2	yes	—
92	C₅×#104	—	2	4	no	—
93	C₅×#97	D₄	1	2	yes	—
94	C₄×C₅×C₈	C₂³	1	2	yes	—
95	#3414	C₂×C₅	1	1	yes	characteristic
96	C₂×#510	C₂×C₅	1	1	yes	characteristic, complemented
97	#3156	C₂×C₅	1	1	yes	characteristic, complemented
98	#2957	C₂×C₅	1	1	yes	characteristic, complemented
99	#2214	C₂×C₅	1	4	yes	complemented
100	#2212	C₂×C₅	1	4	yes	complemented
101	#2153	C₂×C₅	1	1	yes	characteristic, complemented
102	#2148	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂×#362	C₂×C₅	1	1	yes	characteristic, complemented
104	C₅×#41	—	2	2	no	—
105	C₅×#41	—	2	2	no	—
106	C₅×#41	—	4	1	no	—
107	C₅×#41	—	4	1	no	—
108	C₅×#41	—	4	1	no	—
109	C₅×#41	—	4	1	no	—
110	C₅×#41	—	4	1	no	—
111	C₅×#41	—	4	1	no	—
112	C₂×C₅×Q₈	—	2	1	no	—
113	C₂×C₅×Q₈	—	2	2	no	—
114	C₂×C₅×Q₈	—	2	1	no	—
115	C₂×C₅×Q₈	—	4	1	no	—
116	C₂×C₅×Q₈	—	4	1	no	—
117	C₂×C₅×Q₈	—	4	1	no	—
118	C₂×C₅×Q₈	—	4	1	no	—
119	C₂×C₅×Q₈	—	4	1	no	—
120	C₂×C₅×D₄	—	2	1	no	—
121	C₂×C₅×D₄	—	2	1	no	—
122	C₂×C₅×D₄	—	4	1	no	—
123	C₂×C₅×D₄	—	4	1	no	—
124	C₂²×C₄×C₅	—	4	1	no	—
125	C₂²×C₄×C₅	—	4	1	no	—
126	C₂²×C₄×C₅	—	4	1	no	—
127	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₅×Q₁₆	—	2	1	no	—
129	C₅×Q₁₆	—	2	2	no	—
130	C₅×Q₁₆	—	2	1	no	—
131	C₅×Q₁₆	—	2	2	no	—
132	C₅×Q₁₆	—	2	1	no	—
133	C₅×Q₁₆	—	4	1	no	—
134	C₅×Q₁₆	—	4	1	no	—
135	C₅×Q₁₆	—	4	4	no	—
136	C₅×Q₁₆	C₂×D₄	1	2	yes	—
137	C₅×SD₁₆	—	2	2	no	—
138	C₅×SD₁₆	—	2	2	no	—
139	C₅×SD₁₆	—	4	1	no	—
140	C₅×SD₁₆	—	4	1	no	—
141	C₅×SD₁₆	—	4	4	no	—
142	C₅×D₈	—	2	1	no	—
143	C₅×D₈	—	2	1	no	—
144	C₅×D₈	—	2	1	no	—
145	C₅×D₈	C₂×D₄	1	2	yes	—
146	C₅×M₁₆	—	2	2	no	—
147	C₅×M₁₆	—	4	1	no	—
148	C₅×M₁₆	—	4	4	no	—
149	C₅×M₁₆	D₈	1	2	yes	—
150	C₅×M₁₆	D₈	1	2	yes	—
151	C₂×C₅×C₈	—	4	1	no	—
152	C₂×C₅×C₈	—	4	4	no	—
153	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
154	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
156	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
157	C₂×C₅×C₈	#41	1	1	yes	characteristic
158	C₂×C₅×C₈	#41	1	1	yes	characteristic
159	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
160	C₅×C₄⋊C₄	—	2	1	no	—
161	C₅×C₄⋊C₄	—	4	4	no	—
162	C₅×C₂²⋊C₄	—	2	1	no	—
163	C₅×C₂²⋊C₄	—	4	4	no	—
164	C₄²×C₅	C₂×D₄	1	2	yes	—
165	C₅×C₁₆	—	2	2	no	—
166	C₅×C₁₆	—	2	2	no	—
167	C₂×#137	—	2	1	no	—
168	C₂×#135	C₂²×C₅	1	1	yes	characteristic
169	C₂×#135	C₂²×C₅	1	1	yes	characteristic
170	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
171	#568	—	2	1	no	—
172	#536	—	2	1	no	—
173	#510	—	2	2	no	—
174	#510	—	2	1	no	—
175	#510	C₂²×C₅	1	4	yes	—
176	#510	C₂²×C₅	1	2	yes	—
177	#509	—	2	1	no	—
178	#509	C₂²×C₅	1	2	yes	—
179	#508	—	2	2	no	—
180	C₂×Q₃₂	—	2	1	no	—
181	C₂×SD₃₂	—	2	1	no	—
182	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
183	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
184	#497	—	2	2	no	—
185	#495	C₂²×C₅	1	2	yes	complemented
186	#494	C₂²×C₅	1	2	yes	complemented
187	#444	—	2	2	no	—
188	#443	C₂²×C₅	1	4	yes	—
189	C₂×#108	C₂²×C₅	1	1	yes	characteristic
190	#421	—	2	1	no	—
191	#405	C₂²×C₅	1	1	yes	characteristic
192	#364	C₂²×C₅	1	4	yes	complemented
193	#362	C₂²×C₅	1	4	yes	complemented
194	#362	C₂²×C₅	1	2	yes	complemented
195	#361	C₂²×C₅	1	2	yes	complemented
196	C₂³×C₅	—	4	1	no	—
197	C₂³×C₅	—	4	1	no	—
198	C₂³×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₅×Q₈	—	2	2	no	—
200	C₅×Q₈	—	4	1	no	—
201	C₅×Q₈	—	4	1	no	—
202	C₅×Q₈	—	4	2	no	—
203	C₅×Q₈	—	4	2	no	—
204	C₅×Q₈	—	4	1	no	—
205	C₅×Q₈	—	8	1	no	—
206	C₅×Q₈	—	8	1	no	—
207	C₅×D₄	—	2	2	no	—
208	C₅×D₄	—	4	2	no	—
209	C₅×D₄	—	4	2	no	—
210	C₅×D₄	—	4	1	no	—
211	C₅×D₄	—	4	1	no	—
212	C₅×D₄	—	4	1	no	—
213	C₅×D₄	—	8	1	no	—
214	C₅×D₄	—	8	1	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	4	1	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	—	4	2	no	—
219	C₂×C₄×C₅	—	4	2	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	8	1	no	—
222	C₂×C₄×C₅	—	8	1	no	—
223	C₂×C₄×C₅	—	8	1	no	—
224	C₂×C₄×C₅	—	8	1	no	—
225	C₂×C₄×C₅	#121	1	1	yes	characteristic
226	C₂×C₄×C₅	#121	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
229	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
231	C₅×C₈	—	4	2	no	—
232	C₅×C₈	#121	1	1	yes	characteristic
233	C₅×C₈	#121	1	1	yes	characteristic
234	C₅×C₈	C₂×D₈	1	4	yes	—
235	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
236	C₅×C₈	C₂×#41	1	1	yes	characteristic
237	C₂×#41	—	2	1	no	—
238	C₂×#41	—	2	1	no	—
239	C₂²×Q₈	—	2	1	no	—
240	#137	—	4	2	no	—
241	#137	—	4	2	no	—
242	#135	—	2	1	no	—
243	#135	—	2	1	no	—
244	#135	—	2	1	no	—
245	#135	—	2	1	no	—
246	#135	—	2	1	no	—
247	#135	—	2	1	no	—
248	#135	C₅×D₄	1	2	yes	—
249	#135	C₂³×C₅	1	2	yes	—
250	C₂×Q₁₆	—	2	1	no	—
251	C₂×Q₁₆	—	2	1	no	—
252	C₂×Q₁₆	—	2	1	no	—
253	C₂×Q₁₆	—	2	2	no	—
254	C₂×Q₁₆	—	2	1	no	—
255	C₂×Q₁₆	—	2	1	no	—
256	C₂×Q₁₆	C₅×D₄	1	1	yes	characteristic
257	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
258	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
259	C₂×SD₁₆	—	2	1	no	—
260	C₂×SD₁₆	—	2	2	no	—
261	C₂×SD₁₆	—	2	1	no	—
262	C₂×D₈	C₅×D₄	1	1	yes	characteristic
263	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
264	#131	—	2	4	no	—
265	#131	—	4	2	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	4	2	no	—
268	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
270	C₄⋊Q₈	—	2	2	no	—
271	#124	—	2	2	no	—
272	#123	—	4	2	no	—
273	C₂²⋊Q₈	—	4	2	no	—
274	#117	C₅×D₄	1	1	yes	characteristic
275	Q₃₂	—	2	4	no	—
276	Q₃₂	—	2	2	no	—
277	SD₃₂	—	2	2	no	—
278	SD₃₂	—	2	4	no	—
279	SD₃₂	—	2	2	no	—
280	D₁₆	—	2	2	no	—
281	M₃₂	—	2	1	no	—
282	M₃₂	—	2	1	no	—
283	M₃₂	C₂³×C₅	1	2	yes	—
284	M₃₂	C₂³×C₅	1	2	yes	—
285	C₂×C₁₆	—	2	1	no	—
286	C₂×C₁₆	—	2	1	no	—
287	#108	—	2	1	no	—
288	#108	C₂³×C₅	1	2	yes	—
289	#104	—	2	4	no	—
290	#97	C₅×D₄	1	2	yes	—
291	C₄×C₈	C₂³×C₅	1	2	yes	—
292	C₂²×C₅	—	4	1	no	—
293	C₂²×C₅	—	4	2	no	—
294	C₂²×C₅	—	8	2	no	—
295	C₂²×C₅	—	8	1	no	—
296	C₂²×C₅	—	16	1	no	—
297	C₂²×C₅	#459	1	1	yes	characteristic
298	C₂²×C₅	#459	1	1	yes	characteristic
299	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
300	C₄×C₅	—	4	2	no	—
301	C₄×C₅	—	4	2	no	—
302	C₄×C₅	—	8	1	no	—
303	C₄×C₅	—	8	2	no	—
304	C₄×C₅	#459	1	1	yes	characteristic
305	C₄×C₅	#459	1	1	yes	characteristic
306	C₄×C₅	C₂×#121	1	1	yes	characteristic
307	C₄×C₅	C₂²×D₈	1	1	yes	characteristic
308	#41	—	2	2	no	—
309	#41	—	2	2	no	—
310	#41	—	4	1	no	—
311	#41	—	4	1	no	—
312	#41	—	4	1	no	—
313	#41	—	4	1	no	—
314	#41	—	4	1	no	—
315	#41	—	4	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	4	1	no	—
320	C₂×Q₈	—	4	1	no	—
321	C₂×Q₈	—	4	1	no	—
322	C₂×Q₈	—	4	1	no	—
323	C₂×Q₈	—	4	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
332	Q₁₆	—	2	1	no	—
333	Q₁₆	—	2	2	no	—
334	Q₁₆	—	2	1	no	—
335	Q₁₆	—	2	2	no	—
336	Q₁₆	—	2	1	no	—
337	Q₁₆	—	4	1	no	—
338	Q₁₆	—	4	1	no	—
339	Q₁₆	—	4	4	no	—
340	Q₁₆	C₂×C₅×D₄	1	2	yes	—
341	SD₁₆	—	2	2	no	—
342	SD₁₆	—	2	2	no	—
343	SD₁₆	—	4	1	no	—
344	SD₁₆	—	4	1	no	—
345	SD₁₆	—	4	4	no	—
346	D₈	—	2	1	no	—
347	D₈	—	2	1	no	—
348	D₈	—	2	1	no	—
349	D₈	C₂×C₅×D₄	1	2	yes	—
350	M₁₆	—	2	2	no	—
351	M₁₆	—	4	1	no	—
352	M₁₆	—	4	4	no	—
353	M₁₆	C₅×D₈	1	2	yes	—
354	M₁₆	C₅×D₈	1	2	yes	—
355	C₂×C₈	—	4	1	no	—
356	C₂×C₈	—	4	4	no	—
357	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
358	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
359	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
360	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
361	C₂×C₈	C₅×#41	1	1	yes	characteristic
362	C₂×C₈	C₅×#41	1	1	yes	characteristic
363	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	4	4	no	—
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	4	4	no	—
368	C₄²	C₂×C₅×D₄	1	2	yes	—
369	C₁₆	—	2	2	no	—
370	C₁₆	—	2	2	no	—
371	C₂×C₅	—	2	1	no	—
372	C₂×C₅	—	2	1	no	—
373	C₂×C₅	—	2	1	no	—
374	C₂×C₅	—	8	2	no	—
375	C₂×C₅	—	16	1	no	—
376	C₂×C₅	C₂×#459	1	1	yes	characteristic
377	C₂³	—	4	1	no	—
378	C₂³	—	4	1	no	—
379	C₂³	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	4	1	no	—
382	Q₈	—	4	1	no	—
383	Q₈	—	4	2	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	4	1	no	—
386	Q₈	—	8	1	no	—
387	Q₈	—	8	1	no	—
388	D₄	—	2	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	1	no	—
392	D₄	—	4	1	no	—
393	D₄	—	4	1	no	—
394	D₄	—	8	1	no	—
395	D₄	—	8	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	8	1	no	—
403	C₂×C₄	—	8	1	no	—
404	C₂×C₄	—	8	1	no	—
405	C₂×C₄	—	8	1	no	—
406	C₂×C₄	C₅×#121	1	1	yes	characteristic
407	C₂×C₄	C₅×#121	1	1	yes	characteristic
408	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
409	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
410	C₂×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
411	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
412	C₈	—	4	2	no	—
413	C₈	C₅×#121	1	1	yes	characteristic
414	C₈	C₅×#121	1	1	yes	characteristic
415	C₈	C₂×C₅×D₈	1	4	yes	—
416	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
417	C₈	C₂×C₅×#41	1	1	yes	characteristic
418	C₅	#33596	1	1	yes	characteristic, direct product factor, Sylow
419	C₂²	—	4	1	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	16	1	no	—
424	C₂²	C₅×#459	1	1	yes	characteristic
425	C₂²	C₅×#459	1	1	yes	characteristic
426	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	8	1	no	—
430	C₄	—	8	2	no	—
431	C₄	C₅×#459	1	1	yes	characteristic
432	C₄	C₅×#459	1	1	yes	characteristic
433	C₄	C₂×C₅×#121	1	1	yes	characteristic
434	C₄	C₂²×C₅×D₈	1	1	yes	characteristic
435	C₂	—	2	1	no	—
436	C₂	—	2	1	no	—
437	C₂	—	2	1	no	—
438	C₂	—	8	2	no	—
439	C₂	—	16	1	no	—
440	C₂	C₂×C₅×#459	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	C₂×#459
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
prime radical	C₅×#3414	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₅ ◁ C₂²×C₄×C₅ ◁ C₅×#405 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#510	C₂	semidirect
3. C₅×#3156	C₂	semidirect
4. C₅×#2957	C₂	semidirect
5. C₅×#2214	C₂	semidirect
6. C₅×#2212	C₂	semidirect
7. C₅×#2153	C₂	semidirect
8. C₅×#2148	C₂	semidirect
9. C₂×C₅×#362	C₂	semidirect
28. C₅×#495	C₂²	semidirect
29. C₅×#494	C₂²	semidirect
35. C₅×#364	C₂²	semidirect
36. C₅×#362	C₂²	semidirect
37. C₅×#362	C₂²	semidirect
38. C₅×#361	C₂²	semidirect
39. #33596	C₅	direct (N × H)
96. C₂×#510	C₂×C₅	semidirect
97. #3156	C₂×C₅	semidirect
98. #2957	C₂×C₅	semidirect
99. #2214	C₂×C₅	semidirect
100. #2212	C₂×C₅	semidirect
101. #2153	C₂×C₅	semidirect
102. #2148	C₂×C₅	semidirect
103. C₂×#362	C₂×C₅	semidirect
185. #495	C₂²×C₅	semidirect
186. #494	C₂²×C₅	semidirect
192. #364	C₂²×C₅	semidirect
193. #362	C₂²×C₅	semidirect
194. #362	C₂²×C₅	semidirect
195. #361	C₂²×C₅	semidirect
418. C₅	#33596	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×#3414	2
C₂×C₅×#510	2
C₅×#3156	2
C₅×#2957	2
C₅×#2214	2
C₅×#2212	2
C₅×#2153	2
C₅×#2148	2
C₂×C₅×#362	2
#33596	5

Subgroups — C5×#33596 #11956316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33596 #11956316