Subgroups — C₅×#33595 #11956315

Order 1280.

706 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	C₅×#3414	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#509	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3155	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2957	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2213	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×#361	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×AGL(1,ℤ/8)	—	2	1	no	—
11	C₂×C₅×#135	C₂²	1	1	yes	characteristic
12	C₂×C₅×#135	C₂²	1	1	yes	characteristic
13	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
14	C₅×#568	—	2	1	no	—
15	C₅×#535	—	2	1	no	—
16	C₅×#510	—	2	1	no	—
17	C₅×#510	C₂²	1	2	yes	complemented
18	C₅×#509	—	2	2	no	—
19	C₅×#509	—	2	1	no	—
20	C₅×#509	C₂²	1	4	yes	—
21	C₅×#509	C₂²	1	2	yes	complemented
22	C₅×#508	—	2	2	no	—
23	C₂×C₅×SD₃₂	—	2	1	no	—
24	C₂×C₅×D₁₆	—	2	1	no	—
25	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
26	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
27	C₅×#496	—	2	2	no	—
28	C₅×#495	C₂²	1	2	yes	complemented
29	C₅×#493	C₂²	1	2	yes	complemented
30	C₅×#444	—	2	2	no	—
31	C₅×#443	C₂²	1	4	yes	complemented
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	2	yes	complemented
37	C₅×#361	C₂²	1	4	yes	complemented
38	C₅×#361	C₂²	1	2	yes	complemented
39	#33595	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×D₄	—	2	1	no	—
43	C₅×AGL(1,ℤ/8)	—	4	2	no	—
44	C₅×AGL(1,ℤ/8)	—	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	complemented
52	C₅×#135	C₂³	1	2	yes	—
53	C₂×C₅×Q₁₆	D₄	1	1	yes	characteristic, complemented
54	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
55	C₂×C₅×SD₁₆	—	2	2	no	—
56	C₂×C₅×SD₁₆	—	2	1	no	—
57	C₂×C₅×SD₁₆	—	2	1	no	—
58	C₂×C₅×D₈	—	2	1	no	—
59	C₂×C₅×D₈	—	2	1	no	—
60	C₂×C₅×D₈	—	2	2	no	—
61	C₂×C₅×D₈	—	2	1	no	—
62	C₂×C₅×D₈	—	2	1	no	—
63	C₂×C₅×D₈	—	2	1	no	—
64	C₂×C₅×D₈	D₄	1	1	yes	characteristic, complemented
65	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
66	C₂×C₅×D₈	C₂³	1	2	yes	—
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×#127	—	2	2	no	—
74	C₅×#124	—	2	2	no	—
75	C₅×#121	—	4	2	no	—
76	C₅×#120	—	4	2	no	—
77	C₅×#117	D₄	1	1	yes	characteristic
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	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, complemented
96	C₂×#509	C₂×C₅	1	1	yes	characteristic, complemented
97	#3155	C₂×C₅	1	1	yes	characteristic, complemented
98	#2957	C₂×C₅	1	1	yes	characteristic, complemented
99	#2213	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×#361	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂⁴×C₅	—	4	1	no	—
105	C₅×#41	—	2	2	no	—
106	C₅×#41	—	2	2	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	C₅×#41	—	4	1	no	—
113	C₂×C₅×Q₈	—	2	1	no	—
114	C₂×C₅×Q₈	—	2	1	no	—
115	C₂×C₅×D₄	—	2	1	no	—
116	C₂×C₅×D₄	—	2	2	no	—
117	C₂×C₅×D₄	—	2	1	no	—
118	C₂×C₅×D₄	—	4	4	no	—
119	C₂×C₅×D₄	—	4	1	no	—
120	C₂×C₅×D₄	—	4	1	no	—
121	C₂×C₅×D₄	—	4	1	no	—
122	C₂×C₅×D₄	—	4	1	no	—
123	C₂×C₅×D₄	—	4	1	no	—
124	C₂×C₅×D₄	—	4	1	no	—
125	C₂×C₅×D₄	—	4	1	no	—
126	C₂²×C₄×C₅	—	4	1	no	—
127	C₂²×C₄×C₅	—	4	1	no	—
128	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₅×Q₁₆	—	2	1	no	—
130	C₅×Q₁₆	—	2	1	no	—
131	C₅×Q₁₆	—	2	1	no	—
132	C₅×Q₁₆	C₂×D₄	1	2	yes	—
133	C₅×SD₁₆	—	2	2	no	—
134	C₅×SD₁₆	—	2	2	no	—
135	C₅×SD₁₆	—	4	1	no	—
136	C₅×SD₁₆	—	4	1	no	—
137	C₅×SD₁₆	—	4	4	no	—
138	C₅×D₈	—	2	1	no	—
139	C₅×D₈	—	2	2	no	—
140	C₅×D₈	—	2	1	no	—
141	C₅×D₈	—	2	2	no	—
142	C₅×D₈	—	2	1	no	—
143	C₅×D₈	—	4	1	no	—
144	C₅×D₈	—	4	1	no	—
145	C₅×D₈	—	4	4	no	—
146	C₅×D₈	C₂×D₄	1	2	yes	—
147	C₅×M₁₆	—	2	2	no	—
148	C₅×M₁₆	—	4	1	no	—
149	C₅×M₁₆	—	4	4	no	—
150	C₅×M₁₆	D₈	1	2	yes	—
151	C₅×M₁₆	D₈	1	2	yes	—
152	C₂×C₅×C₈	—	4	1	no	—
153	C₂×C₅×C₈	—	4	4	no	—
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	1	yes	characteristic
157	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
158	C₂×C₅×C₈	#41	1	1	yes	characteristic
159	C₂×C₅×C₈	#41	1	1	yes	characteristic
160	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
161	C₅×C₄⋊C₄	—	2	1	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×AGL(1,ℤ/8)	—	2	1	no	—
168	C₂×#135	C₂²×C₅	1	1	yes	characteristic
169	C₂×#135	C₂²×C₅	1	1	yes	characteristic
170	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
171	#568	—	2	1	no	—
172	#535	—	2	1	no	—
173	#510	—	2	1	no	—
174	#510	C₂²×C₅	1	2	yes	complemented
175	#509	—	2	2	no	—
176	#509	—	2	1	no	—
177	#509	C₂²×C₅	1	4	yes	—
178	#509	C₂²×C₅	1	2	yes	complemented
179	#508	—	2	2	no	—
180	C₂×SD₃₂	—	2	1	no	—
181	C₂×D₁₆	—	2	1	no	—
182	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
183	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
184	#496	—	2	2	no	—
185	#495	C₂²×C₅	1	2	yes	complemented
186	#493	C₂²×C₅	1	2	yes	complemented
187	#444	—	2	2	no	—
188	#443	C₂²×C₅	1	4	yes	complemented
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	2	yes	complemented
194	#361	C₂²×C₅	1	4	yes	complemented
195	#361	C₂²×C₅	1	2	yes	complemented
196	C₂³×C₅	—	4	1	no	—
197	C₂³×C₅	—	4	2	no	—
198	C₂³×C₅	—	4	1	no	—
199	C₂³×C₅	—	8	1	no	—
200	C₂³×C₅	—	8	1	no	—
201	C₂³×C₅	—	16	2	no	—
202	C₂³×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₅×Q₈	—	2	2	no	—
204	C₅×Q₈	—	4	1	no	—
205	C₅×Q₈	—	4	1	no	—
206	C₅×Q₈	—	4	1	no	—
207	C₅×D₄	—	2	2	no	—
208	C₅×D₄	—	4	2	no	—
209	C₅×D₄	—	4	2	no	—
210	C₅×D₄	—	4	2	no	—
211	C₅×D₄	—	4	1	no	—
212	C₅×D₄	—	4	1	no	—
213	C₅×D₄	—	4	2	no	—
214	C₅×D₄	—	4	1	no	—
215	C₅×D₄	—	8	1	no	—
216	C₅×D₄	—	8	1	no	—
217	C₅×D₄	—	8	1	no	—
218	C₅×D₄	—	8	1	no	—
219	C₅×D₄	—	16	4	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	4	1	no	—
222	C₂×C₄×C₅	—	4	2	no	—
223	C₂×C₄×C₅	—	4	2	no	—
224	C₂×C₄×C₅	—	4	1	no	—
225	C₂×C₄×C₅	—	8	1	no	—
226	C₂×C₄×C₅	—	8	1	no	—
227	C₂×C₄×C₅	#121	1	1	yes	characteristic
228	C₂×C₄×C₅	#121	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
231	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
233	C₅×C₈	—	4	2	no	—
234	C₅×C₈	#121	1	1	yes	characteristic
235	C₅×C₈	#121	1	1	yes	characteristic
236	C₅×C₈	C₂×D₈	1	4	yes	—
237	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
238	C₅×C₈	C₂×#41	1	1	yes	characteristic
239	C₂×#41	—	2	1	no	—
240	C₂×#41	—	2	1	no	—
241	C₂²×D₄	—	2	1	no	—
242	AGL(1,ℤ/8)	—	4	2	no	—
243	AGL(1,ℤ/8)	—	4	2	no	—
244	#135	—	2	1	no	—
245	#135	—	2	1	no	—
246	#135	—	2	1	no	—
247	#135	—	2	1	no	—
248	#135	—	2	1	no	—
249	#135	—	2	1	no	—
250	#135	C₅×D₄	1	2	yes	complemented
251	#135	C₂³×C₅	1	2	yes	—
252	C₂×Q₁₆	C₅×D₄	1	1	yes	characteristic, complemented
253	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
254	C₂×SD₁₆	—	2	1	no	—
255	C₂×SD₁₆	—	2	2	no	—
256	C₂×SD₁₆	—	2	1	no	—
257	C₂×D₈	—	2	1	no	—
258	C₂×D₈	—	2	1	no	—
259	C₂×D₈	—	2	1	no	—
260	C₂×D₈	—	2	2	no	—
261	C₂×D₈	—	2	1	no	—
262	C₂×D₈	—	2	1	no	—
263	C₂×D₈	C₅×D₄	1	1	yes	characteristic, complemented
264	C₂×D₈	C₂³×C₅	1	2	yes	—
265	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
266	#131	—	2	4	no	—
267	#131	—	4	2	no	—
268	C₂×M₁₆	—	2	1	no	—
269	C₂×M₁₆	—	4	2	no	—
270	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
272	#127	—	2	2	no	—
273	#124	—	2	2	no	—
274	#121	—	4	2	no	—
275	#120	—	4	2	no	—
276	#117	C₅×D₄	1	1	yes	characteristic
277	Q₃₂	—	2	2	no	—
278	SD₃₂	—	2	4	no	—
279	SD₃₂	—	2	2	no	—
280	SD₃₂	—	2	2	no	—
281	D₁₆	—	2	4	no	—
282	D₁₆	—	2	2	no	—
283	M₃₂	—	2	1	no	—
284	M₃₂	—	2	1	no	—
285	M₃₂	C₂³×C₅	1	2	yes	—
286	M₃₂	C₂³×C₅	1	2	yes	—
287	C₂×C₁₆	—	2	1	no	—
288	C₂×C₁₆	—	2	1	no	—
289	#108	—	2	1	no	—
290	#108	C₂³×C₅	1	2	yes	—
291	#104	—	2	4	no	—
292	#97	C₅×D₄	1	2	yes	—
293	C₄×C₈	C₂³×C₅	1	2	yes	—
294	C₂²×C₅	—	4	1	no	—
295	C₂²×C₅	—	4	2	no	—
296	C₂²×C₅	—	8	2	no	—
297	C₂²×C₅	—	8	4	no	—
298	C₂²×C₅	—	8	1	no	—
299	C₂²×C₅	—	8	2	no	—
300	C₂²×C₅	—	16	1	no	—
301	C₂²×C₅	—	16	2	no	—
302	C₂²×C₅	—	16	2	no	—
303	C₂²×C₅	#459	1	1	yes	characteristic
304	C₂²×C₅	#459	1	1	yes	characteristic
305	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
306	C₄×C₅	—	4	2	no	—
307	C₄×C₅	—	4	2	no	—
308	C₄×C₅	—	8	1	no	—
309	C₄×C₅	#459	1	1	yes	characteristic
310	C₄×C₅	#459	1	1	yes	characteristic
311	C₄×C₅	C₂×#121	1	1	yes	characteristic
312	C₄×C₅	C₂²×D₈	1	1	yes	characteristic
313	C₂⁴	—	4	1	no	—
314	#41	—	2	2	no	—
315	#41	—	2	2	no	—
316	#41	—	4	1	no	—
317	#41	—	4	1	no	—
318	#41	—	4	1	no	—
319	#41	—	4	1	no	—
320	#41	—	4	1	no	—
321	#41	—	4	1	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	4	4	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	—	4	1	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	1	no	—
334	C₂×D₄	—	4	1	no	—
335	C₂²×C₄	—	4	1	no	—
336	C₂²×C₄	—	4	1	no	—
337	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
338	Q₁₆	—	2	1	no	—
339	Q₁₆	—	2	1	no	—
340	Q₁₆	—	2	1	no	—
341	Q₁₆	C₂×C₅×D₄	1	2	yes	—
342	SD₁₆	—	2	2	no	—
343	SD₁₆	—	2	2	no	—
344	SD₁₆	—	4	1	no	—
345	SD₁₆	—	4	1	no	—
346	SD₁₆	—	4	4	no	—
347	D₈	—	2	1	no	—
348	D₈	—	2	2	no	—
349	D₈	—	2	1	no	—
350	D₈	—	2	2	no	—
351	D₈	—	2	1	no	—
352	D₈	—	4	1	no	—
353	D₈	—	4	1	no	—
354	D₈	—	4	4	no	—
355	D₈	C₂×C₅×D₄	1	2	yes	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	4	1	no	—
358	M₁₆	—	4	4	no	—
359	M₁₆	C₅×D₈	1	2	yes	—
360	M₁₆	C₅×D₈	1	2	yes	—
361	C₂×C₈	—	4	1	no	—
362	C₂×C₈	—	4	4	no	—
363	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
364	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
365	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
366	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
367	C₂×C₈	C₅×#41	1	1	yes	characteristic
368	C₂×C₈	C₅×#41	1	1	yes	characteristic
369	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
370	C₄⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	2	1	no	—
372	C₂²⋊C₄	—	4	4	no	—
373	C₄²	C₂×C₅×D₄	1	2	yes	—
374	C₁₆	—	2	2	no	—
375	C₁₆	—	2	2	no	—
376	C₂×C₅	—	2	1	no	—
377	C₂×C₅	—	2	1	no	—
378	C₂×C₅	—	2	1	no	—
379	C₂×C₅	—	8	2	no	—
380	C₂×C₅	—	16	1	no	—
381	C₂×C₅	—	16	2	no	—
382	C₂×C₅	C₂×#459	1	1	yes	characteristic
383	C₂³	—	4	1	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	1	no	—
386	C₂³	—	8	1	no	—
387	C₂³	—	8	1	no	—
388	C₂³	—	16	2	no	—
389	C₂³	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
390	Q₈	—	2	2	no	—
391	Q₈	—	4	1	no	—
392	Q₈	—	4	1	no	—
393	Q₈	—	4	1	no	—
394	D₄	—	2	2	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	1	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	1	no	—
400	D₄	—	4	1	no	—
401	D₄	—	4	2	no	—
402	D₄	—	8	1	no	—
403	D₄	—	8	1	no	—
404	D₄	—	8	1	no	—
405	D₄	—	8	1	no	—
406	D₄	—	16	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	8	1	no	—
413	C₂×C₄	—	8	1	no	—
414	C₂×C₄	C₅×#121	1	1	yes	characteristic
415	C₂×C₄	C₅×#121	1	1	yes	characteristic
416	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
417	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
418	C₂×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
419	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
420	C₈	—	4	2	no	—
421	C₈	C₅×#121	1	1	yes	characteristic
422	C₈	C₅×#121	1	1	yes	characteristic
423	C₈	C₂×C₅×D₈	1	4	yes	—
424	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
425	C₈	C₂×C₅×#41	1	1	yes	characteristic
426	C₅	#33595	1	1	yes	characteristic, direct product factor, Sylow
427	C₂²	—	4	1	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	4	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	16	1	no	—
434	C₂²	—	16	2	no	—
435	C₂²	—	16	2	no	—
436	C₂²	C₅×#459	1	1	yes	characteristic
437	C₂²	C₅×#459	1	1	yes	characteristic
438	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
439	C₄	—	4	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	8	1	no	—
442	C₄	C₅×#459	1	1	yes	characteristic
443	C₄	C₅×#459	1	1	yes	characteristic
444	C₄	C₂×C₅×#121	1	1	yes	characteristic
445	C₄	C₂²×C₅×D₈	1	1	yes	characteristic
446	C₂	—	2	1	no	—
447	C₂	—	2	1	no	—
448	C₂	—	2	1	no	—
449	C₂	—	8	2	no	—
450	C₂	—	16	2	no	—
451	C₂	—	16	1	no	—
452	C₂	C₂×C₅×#459	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₅	C₂×#459
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
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
1. C₅×#3414	C₂	semidirect
2. C₂×C₅×#509	C₂	semidirect
3. C₅×#3155	C₂	semidirect
4. C₅×#2957	C₂	semidirect
5. C₅×#2213	C₂	semidirect
6. C₅×#2212	C₂	semidirect
7. C₅×#2153	C₂	semidirect
8. C₅×#2148	C₂	semidirect
9. C₂×C₅×#361	C₂	semidirect
17. C₅×#510	C₂²	semidirect
21. C₅×#509	C₂²	semidirect
28. C₅×#495	C₂²	semidirect
29. C₅×#493	C₂²	semidirect
31. C₅×#443	C₂²	semidirect
35. C₅×#364	C₂²	semidirect
36. C₅×#362	C₂²	semidirect
37. C₅×#361	C₂²	semidirect
38. C₅×#361	C₂²	semidirect
39. #33595	C₅	direct (N × H)
51. C₅×#135	D₄	semidirect
53. C₂×C₅×Q₁₆	D₄	semidirect
64. C₂×C₅×D₈	D₄	semidirect
95. #3414	C₂×C₅	semidirect
96. C₂×#509	C₂×C₅	semidirect
97. #3155	C₂×C₅	semidirect
98. #2957	C₂×C₅	semidirect
99. #2213	C₂×C₅	semidirect
100. #2212	C₂×C₅	semidirect
101. #2153	C₂×C₅	semidirect
102. #2148	C₂×C₅	semidirect
103. C₂×#361	C₂×C₅	semidirect
174. #510	C₂²×C₅	semidirect
178. #509	C₂²×C₅	semidirect
185. #495	C₂²×C₅	semidirect
186. #493	C₂²×C₅	semidirect
188. #443	C₂²×C₅	semidirect
192. #364	C₂²×C₅	semidirect
193. #362	C₂²×C₅	semidirect
194. #361	C₂²×C₅	semidirect
195. #361	C₂²×C₅	semidirect
250. #135	C₅×D₄	semidirect
252. C₂×Q₁₆	C₅×D₄	semidirect
263. C₂×D₈	C₅×D₄	semidirect
426. C₅	#33595	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×#509	2
C₅×#3155	2
C₅×#2957	2
C₅×#2213	2
C₅×#2212	2
C₅×#2153	2
C₅×#2148	2
C₂×C₅×#361	2
#33595	5

Subgroups — C5×#33595 #11956315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33595 #11956315