Subgroups — C₅×#33756 #11956476

Order 1280.

594 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3050	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#467	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2237	C₂	1	2	yes	maximal, complemented
4	C₅×#2235	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2232	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2217	C₂	1	2	yes	maximal, complemented
7	C₅×#2216	C₂	1	2	yes	maximal, complemented
8	C₅×#2189	C₂	1	2	yes	maximal, complemented
9	C₅×#2188	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2185	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	C₂²	1	1	yes	characteristic
13	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₅×#525	—	2	1	no	—
16	C₂×C₅×C₂²⋊Q₈	—	2	1	no	—
17	C₂×C₅×Q₃₂	C₂²	1	2	yes	complemented
18	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
19	C₂²×C₅×C₁₆	C₂²	1	2	yes	—
20	C₅×#467	—	2	1	no	—
21	C₅×#467	—	2	1	no	—
22	C₅×#467	C₂²	1	2	yes	—
23	C₅×#467	C₂²	1	2	yes	—
24	C₅×#467	C₂²	1	1	yes	characteristic
25	C₅×#467	C₂²	1	1	yes	characteristic
26	C₅×#466	C₂²	1	1	yes	characteristic
27	C₅×#466	C₂²	1	1	yes	characteristic
28	C₅×#465	—	2	1	no	—
29	C₅×#465	—	2	1	no	—
30	C₅×#427	C₂²	1	1	yes	characteristic
31	C₂×C₅×#107	C₂²	1	1	yes	characteristic
32	C₅×#416	—	2	1	no	—
33	C₂×C₅×#103	—	2	1	no	—
34	C₅×#367	C₂²	1	2	yes	complemented
35	C₅×#366	C₂²	1	2	yes	complemented
36	C₅×#358	C₂²	1	2	yes	complemented
37	C₅×#358	C₂²	1	2	yes	complemented
38	C₅×#358	C₂²	1	2	yes	complemented
39	C₅×#357	C₂²	1	2	yes	complemented
40	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
41	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
42	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
43	#33756	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₅×#41	—	2	1	no	—
45	C₂²×C₅×Q₈	—	2	1	no	—
46	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
47	C₅×#135	—	4	2	no	—
48	C₂×C₅×Q₁₆	—	2	1	no	—
49	C₂×C₅×Q₁₆	—	4	2	no	—
50	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
51	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
52	C₂×C₅×SD₁₆	—	2	1	no	—
53	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
54	C₂²×C₅×C₈	—	4	2	no	—
55	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
56	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
57	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
58	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
61	C₅×#123	—	4	1	no	—
62	C₅×C₂²⋊Q₈	—	2	1	no	—
63	C₅×C₂²⋊Q₈	—	2	1	no	—
64	C₅×C₂²⋊Q₈	—	2	2	no	—
65	C₅×C₂²⋊Q₈	—	2	2	no	—
66	C₅×C₂²⋊Q₈	—	4	1	no	—
67	C₅×C₂²⋊Q₈	—	4	1	no	—
68	C₅×#121	—	2	1	no	—
69	C₅×#121	—	2	1	no	—
70	C₅×#120	—	4	1	no	—
71	C₄×C₅×D₄	—	4	1	no	—
72	C₄×C₅×D₄	—	4	1	no	—
73	C₅×#117	—	2	1	no	—
74	C₂×C₅×C₄⋊C₄	—	2	1	no	—
75	C₂×C₅×C₄⋊C₄	—	4	1	no	—
76	C₂×C₅×C₂²⋊C₄	—	4	1	no	—
77	C₅×Q₃₂	—	4	2	no	—
78	C₅×SD₃₂	—	4	2	no	—
79	C₂×C₅×C₁₆	—	4	2	no	—
80	C₂×C₅×C₁₆	C₂³	1	2	yes	—
81	C₂×C₅×C₁₆	C₂³	1	2	yes	—
82	C₅×#107	—	2	1	no	—
83	C₅×#107	C₂³	1	2	yes	—
84	C₅×#107	C₂³	1	1	yes	characteristic
85	C₅×#107	C₂³	1	1	yes	characteristic
86	C₅×#106	—	2	1	no	—
87	C₅×#103	—	2	2	no	—
88	C₅×#103	—	2	2	no	—
89	C₅×#103	—	2	1	no	—
90	C₅×#103	—	2	1	no	—
91	C₅×#102	—	2	1	no	—
92	C₅×#102	—	2	1	no	—
93	#3050	C₂×C₅	1	1	yes	characteristic
94	C₂×#467	C₂×C₅	1	1	yes	characteristic, complemented
95	#2237	C₂×C₅	1	2	yes	complemented
96	#2235	C₂×C₅	1	1	yes	characteristic, complemented
97	#2232	C₂×C₅	1	1	yes	characteristic, complemented
98	#2217	C₂×C₅	1	2	yes	complemented
99	#2216	C₂×C₅	1	2	yes	complemented
100	#2189	C₂×C₅	1	2	yes	complemented
101	#2188	C₂×C₅	1	1	yes	characteristic, complemented
102	#2185	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂×C₂²⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂⁴×C₅	D₈	1	1	yes	characteristic
105	C₅×#41	—	4	2	no	—
106	C₅×#41	—	4	2	no	—
107	C₂×C₅×Q₈	—	2	1	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	—	4	2	no	—
110	C₂×C₅×Q₈	—	4	2	no	—
111	C₂×C₅×Q₈	—	4	1	no	—
112	C₂×C₅×D₄	—	2	1	no	—
113	C₂×C₅×D₄	—	4	1	no	—
114	C₂×C₅×D₄	—	4	1	no	—
115	C₂×C₅×D₄	—	4	1	no	—
116	C₂²×C₄×C₅	—	4	1	no	—
117	C₂²×C₄×C₅	—	4	1	no	—
118	C₂²×C₄×C₅	—	4	1	no	—
119	C₂²×C₄×C₅	—	4	1	no	—
120	C₂²×C₄×C₅	—	4	1	no	—
121	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
122	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
123	C₂²×C₄×C₅	D₈	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	C₅×Q₁₆	—	2	2	no	—
128	C₅×Q₁₆	—	2	2	no	—
129	C₅×Q₁₆	—	2	2	no	—
130	C₅×Q₁₆	—	4	2	no	—
131	C₅×SD₁₆	—	4	2	no	—
132	C₅×D₈	—	2	2	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	4	1	no	—
137	C₂×C₅×C₈	—	4	1	no	—
138	C₂×C₅×C₈	—	4	1	no	—
139	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
140	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
141	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
142	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	—	2	1	no	—
145	C₅×C₄⋊C₄	—	2	1	no	—
146	C₅×C₄⋊C₄	—	4	1	no	—
147	C₅×C₄⋊C₄	—	4	2	no	—
148	C₅×C₄⋊C₄	—	4	2	no	—
149	C₅×C₄⋊C₄	—	4	1	no	—
150	C₅×C₄⋊C₄	—	4	1	no	—
151	C₅×C₂²⋊C₄	—	4	2	no	—
152	C₅×C₂²⋊C₄	—	4	2	no	—
153	C₅×C₂²⋊C₄	—	4	1	no	—
154	C₅×C₂²⋊C₄	—	4	1	no	—
155	C₅×C₂²⋊C₄	—	4	1	no	—
156	C₅×C₂²⋊C₄	—	4	1	no	—
157	C₅×C₂²⋊C₄	—	4	1	no	—
158	C₄²×C₅	—	4	1	no	—
159	C₅×C₁₆	—	2	2	no	—
160	C₅×C₁₆	—	2	2	no	—
161	C₂×#135	C₂²×C₅	1	1	yes	characteristic
162	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
163	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
164	#525	—	2	1	no	—
165	C₂×C₂²⋊Q₈	—	2	1	no	—
166	C₂×Q₃₂	C₂²×C₅	1	2	yes	complemented
167	C₂×SD₃₂	C₂²×C₅	1	2	yes	complemented
168	C₂²×C₁₆	C₂²×C₅	1	2	yes	—
169	#467	—	2	1	no	—
170	#467	—	2	1	no	—
171	#467	C₂²×C₅	1	1	yes	characteristic
172	#467	C₂²×C₅	1	2	yes	—
173	#467	C₂²×C₅	1	1	yes	characteristic
174	#467	C₂²×C₅	1	2	yes	—
175	#466	C₂²×C₅	1	1	yes	characteristic
176	#466	C₂²×C₅	1	1	yes	characteristic
177	#465	—	2	1	no	—
178	#465	—	2	1	no	—
179	#427	C₂²×C₅	1	1	yes	characteristic
180	C₂×#107	C₂²×C₅	1	1	yes	characteristic
181	#416	—	2	1	no	—
182	C₂×#103	—	2	1	no	—
183	#367	C₂²×C₅	1	2	yes	complemented
184	#366	C₂²×C₅	1	2	yes	complemented
185	#358	C₂²×C₅	1	2	yes	complemented
186	#358	C₂²×C₅	1	2	yes	complemented
187	#358	C₂²×C₅	1	2	yes	complemented
188	#357	C₂²×C₅	1	2	yes	complemented
189	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
190	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
191	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
192	C₂³×C₅	—	2	2	no	—
193	C₂³×C₅	—	2	2	no	—
194	C₂³×C₅	—	4	1	no	—
195	C₂³×C₅	—	4	1	no	—
196	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
197	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
198	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
199	C₅×Q₈	—	4	1	no	—
200	C₅×Q₈	—	4	2	no	—
201	C₅×Q₈	—	4	2	no	—
202	C₅×Q₈	—	4	1	no	—
203	C₅×Q₈	—	8	2	no	—
204	C₅×D₄	—	4	1	no	—
205	C₅×D₄	—	4	1	no	—
206	C₅×D₄	—	8	2	no	—
207	C₅×D₄	—	8	2	no	—
208	C₅×D₄	—	8	2	no	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	2	1	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	—	2	1	no	—
215	C₂×C₄×C₅	—	4	1	no	—
216	C₂×C₄×C₅	—	4	1	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	2	no	—
223	C₂×C₄×C₅	—	8	2	no	—
224	C₂×C₄×C₅	—	8	2	no	—
225	C₂×C₄×C₅	—	8	2	no	—
226	C₂×C₄×C₅	C₂×D₈	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	C₂²×D₄	1	1	yes	characteristic
230	C₅×C₈	—	2	1	no	—
231	C₅×C₈	—	2	1	no	—
232	C₅×C₈	—	2	1	no	—
233	C₅×C₈	H(5,𝔽₂)	1	2	yes	—
234	C₂×#41	—	2	1	no	—
235	C₂²×Q₈	—	2	1	no	—
236	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
237	#135	—	4	2	no	—
238	C₂×Q₁₆	—	2	1	no	—
239	C₂×Q₁₆	—	4	2	no	—
240	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
241	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
242	C₂×SD₁₆	—	2	1	no	—
243	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
244	C₂²×C₈	—	4	2	no	—
245	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
246	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
247	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
251	#123	—	4	1	no	—
252	C₂²⋊Q₈	—	2	2	no	—
253	C₂²⋊Q₈	—	2	2	no	—
254	C₂²⋊Q₈	—	2	1	no	—
255	C₂²⋊Q₈	—	2	1	no	—
256	C₂²⋊Q₈	—	4	1	no	—
257	C₂²⋊Q₈	—	4	1	no	—
258	#121	—	2	1	no	—
259	#121	—	2	1	no	—
260	#120	—	4	1	no	—
261	C₄×D₄	—	4	1	no	—
262	C₄×D₄	—	4	1	no	—
263	#117	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	1	no	—
265	C₂×C₄⋊C₄	—	4	1	no	—
266	C₂×C₂²⋊C₄	—	4	1	no	—
267	Q₃₂	—	4	2	no	—
268	SD₃₂	—	4	2	no	—
269	C₂×C₁₆	—	4	2	no	—
270	C₂×C₁₆	C₂³×C₅	1	2	yes	—
271	C₂×C₁₆	C₂³×C₅	1	2	yes	—
272	#107	—	2	1	no	—
273	#107	C₂³×C₅	1	2	yes	—
274	#107	C₂³×C₅	1	1	yes	characteristic
275	#107	C₂³×C₅	1	1	yes	characteristic
276	#106	—	2	1	no	—
277	#103	—	2	2	no	—
278	#103	—	2	2	no	—
279	#103	—	2	1	no	—
280	#103	—	2	1	no	—
281	#102	—	2	1	no	—
282	#102	—	2	1	no	—
283	C₂²×C₅	—	2	1	no	—
284	C₂²×C₅	—	2	1	no	—
285	C₂²×C₅	—	2	1	no	—
286	C₂²×C₅	—	2	1	no	—
287	C₂²×C₅	—	2	1	no	—
288	C₂²×C₅	—	2	1	no	—
289	C₂²×C₅	—	2	1	no	—
290	C₂²×C₅	—	4	4	no	—
291	C₂²×C₅	—	8	1	no	—
292	C₂²×C₅	—	8	1	no	—
293	C₂²×C₅	—	8	1	no	—
294	C₂²×C₅	#508	1	2	yes	—
295	C₂²×C₅	#510	1	2	yes	—
296	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
297	C₄×C₅	—	2	1	no	—
298	C₄×C₅	—	2	1	no	—
299	C₄×C₅	—	2	1	no	—
300	C₄×C₅	—	8	2	no	—
301	C₄×C₅	—	8	1	no	—
302	C₄×C₅	—	8	1	no	—
303	C₄×C₅	—	8	1	no	—
304	C₄×C₅	—	8	2	no	—
305	C₄×C₅	#534	1	1	yes	characteristic
306	C₄×C₅	#575	1	1	yes	characteristic
307	C₂⁴	C₅×D₈	1	1	yes	characteristic
308	#41	—	4	2	no	—
309	#41	—	4	2	no	—
310	C₂×Q₈	—	2	1	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	4	2	no	—
313	C₂×Q₈	—	4	2	no	—
314	C₂×Q₈	—	4	1	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
325	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
326	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
328	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
329	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
330	Q₁₆	—	2	2	no	—
331	Q₁₆	—	2	2	no	—
332	Q₁₆	—	2	2	no	—
333	Q₁₆	—	4	2	no	—
334	SD₁₆	—	4	2	no	—
335	D₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
343	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
344	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
345	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₂²⋊C₄	—	4	2	no	—
355	C₂²⋊C₄	—	4	2	no	—
356	C₂²⋊C₄	—	4	1	no	—
357	C₂²⋊C₄	—	4	1	no	—
358	C₂²⋊C₄	—	4	1	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	4	1	no	—
361	C₄²	—	4	1	no	—
362	C₁₆	—	2	2	no	—
363	C₁₆	—	2	2	no	—
364	C₂×C₅	—	2	2	no	—
365	C₂×C₅	—	2	2	no	—
366	C₂×C₅	—	4	1	no	—
367	C₂×C₅	—	16	1	no	—
368	C₂×C₅	#3186	1	1	yes	characteristic
369	C₂×C₅	C₂×#508	1	1	yes	characteristic
370	C₂×C₅	C₂×#510	1	1	yes	characteristic
371	C₂³	—	2	2	no	—
372	C₂³	—	2	2	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	1	no	—
375	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
376	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
377	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
378	Q₈	—	4	1	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	4	2	no	—
381	Q₈	—	4	1	no	—
382	Q₈	—	8	2	no	—
383	D₄	—	4	1	no	—
384	D₄	—	4	1	no	—
385	D₄	—	8	2	no	—
386	D₄	—	8	2	no	—
387	D₄	—	8	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	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	2	no	—
402	C₂×C₄	—	8	2	no	—
403	C₂×C₄	—	8	2	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
406	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
407	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
408	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
409	C₈	—	2	1	no	—
410	C₈	—	2	1	no	—
411	C₈	—	2	1	no	—
412	C₈	C₅×H(5,𝔽₂)	1	2	yes	—
413	C₅	#33756	1	1	yes	characteristic, direct product factor, Sylow
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	4	4	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	C₅×#508	1	2	yes	—
426	C₂²	C₅×#510	1	2	yes	—
427	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	8	2	no	—
432	C₄	—	8	1	no	—
433	C₄	—	8	1	no	—
434	C₄	—	8	1	no	—
435	C₄	—	8	2	no	—
436	C₄	C₅×#534	1	1	yes	characteristic
437	C₄	C₅×#575	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	2	2	no	—
440	C₂	—	4	1	no	—
441	C₂	—	16	1	no	—
442	C₂	C₅×#3186	1	1	yes	characteristic
443	C₂	C₂×C₅×#508	1	1	yes	characteristic
444	C₂	C₂×C₅×#510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
prime radical	C₅×#3050	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#467	C₂	semidirect
3. C₅×#2237	C₂	semidirect
4. C₅×#2235	C₂	semidirect
5. C₅×#2232	C₂	semidirect
6. C₅×#2217	C₂	semidirect
7. C₅×#2216	C₂	semidirect
8. C₅×#2189	C₂	semidirect
9. C₅×#2188	C₂	semidirect
10. C₅×#2185	C₂	semidirect
11. C₂×C₅×C₂²⋊C₁₆	C₂	semidirect
17. C₂×C₅×Q₃₂	C₂²	semidirect
18. C₂×C₅×SD₃₂	C₂²	semidirect
34. C₅×#367	C₂²	semidirect
35. C₅×#366	C₂²	semidirect
36. C₅×#358	C₂²	semidirect
37. C₅×#358	C₂²	semidirect
38. C₅×#358	C₂²	semidirect
39. C₅×#357	C₂²	semidirect
43. #33756	C₅	direct (N × H)
94. C₂×#467	C₂×C₅	semidirect
95. #2237	C₂×C₅	semidirect
96. #2235	C₂×C₅	semidirect
97. #2232	C₂×C₅	semidirect
98. #2217	C₂×C₅	semidirect
99. #2216	C₂×C₅	semidirect
100. #2189	C₂×C₅	semidirect
101. #2188	C₂×C₅	semidirect
102. #2185	C₂×C₅	semidirect
103. C₂×C₂²⋊C₁₆	C₂×C₅	semidirect
166. C₂×Q₃₂	C₂²×C₅	semidirect
167. C₂×SD₃₂	C₂²×C₅	semidirect
183. #367	C₂²×C₅	semidirect
184. #366	C₂²×C₅	semidirect
185. #358	C₂²×C₅	semidirect
186. #358	C₂²×C₅	semidirect
187. #358	C₂²×C₅	semidirect
188. #357	C₂²×C₅	semidirect
413. C₅	#33756	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×#3050	2
C₂×C₅×#467	2
C₅×#2237	2
C₅×#2235	2
C₅×#2232	2
C₅×#2217	2
C₅×#2216	2
C₅×#2189	2
C₅×#2188	2
C₅×#2185	2
C₂×C₅×C₂²⋊C₁₆	2
#33756	5

Subgroups — C5×#33756 #11956476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33756 #11956476