Subgroups — C₅×#33754 #11956474

Order 1280.

646 conjugacy classes of subgroups.

The subgroup lattice has 464 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, complemented
2	C₂×C₅×#466	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2236	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2234	C₂	1	2	yes	maximal, complemented
5	C₅×#2233	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2217	C₂	1	2	yes	maximal, complemented
7	C₅×#2215	C₂	1	2	yes	maximal, complemented
8	C₅×#2187	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2186	C₂	1	2	yes	maximal, complemented
10	C₅×#2184	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, complemented
13	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
14	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₅×#525	—	2	1	no	—
16	C₂×C₅×#121	—	2	1	no	—
17	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
18	C₂×C₅×D₁₆	C₂²	1	2	yes	complemented
19	C₂²×C₅×C₁₆	C₂²	1	2	yes	complemented
20	C₅×#467	C₂²	1	1	yes	characteristic
21	C₅×#467	C₂²	1	1	yes	characteristic, complemented
22	C₅×#466	—	2	1	no	—
23	C₅×#466	—	2	1	no	—
24	C₅×#466	C₂²	1	2	yes	—
25	C₅×#466	C₂²	1	2	yes	—
26	C₅×#466	C₂²	1	1	yes	characteristic
27	C₅×#466	C₂²	1	1	yes	characteristic, complemented
28	C₅×#465	—	2	1	no	—
29	C₅×#465	—	2	1	no	—
30	C₅×#427	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₅×#107	C₂²	1	1	yes	characteristic
32	C₅×#416	—	2	1	no	—
33	C₂×C₅×#102	—	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×#357	C₂²	1	2	yes	complemented
38	C₅×#357	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	complemented
43	#33754	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₅×#41	—	2	1	no	—
45	C₂²×C₅×D₄	—	2	1	no	—
46	C₂²×C₅×D₄	—	4	1	no	—
47	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
48	C₅×#135	—	4	2	no	—
49	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
50	C₂×C₅×SD₁₆	—	2	1	no	—
51	C₂×C₅×D₈	—	2	1	no	—
52	C₂×C₅×D₈	—	4	2	no	—
53	C₂×C₅×D₈	C₂³	1	2	yes	—
54	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
55	C₂²×C₅×C₈	—	4	2	no	—
56	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
57	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
58	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
59	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
62	C₅×#123	—	4	1	no	—
63	C₅×C₂²⋊Q₈	—	2	1	no	—
64	C₅×C₂²⋊Q₈	—	2	1	no	—
65	C₅×#121	—	2	1	no	—
66	C₅×#121	—	2	1	no	—
67	C₅×#121	—	2	2	no	—
68	C₅×#121	—	2	2	no	—
69	C₅×#121	—	4	1	no	—
70	C₅×#121	—	4	1	no	—
71	C₅×#120	—	4	1	no	—
72	C₄×C₅×D₄	—	4	1	no	—
73	C₄×C₅×D₄	—	4	1	no	—
74	C₅×#117	—	2	1	no	—
75	C₂×C₅×C₄⋊C₄	—	2	1	no	—
76	C₂×C₅×C₂²⋊C₄	—	4	1	no	—
77	C₅×SD₃₂	—	4	2	no	—
78	C₅×D₁₆	—	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	1	no	—
88	C₅×#103	—	2	1	no	—
89	C₅×#102	—	2	2	no	—
90	C₅×#102	—	2	2	no	—
91	C₅×#102	—	2	1	no	—
92	C₅×#102	—	2	1	no	—
93	#3050	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂×#466	C₂×C₅	1	1	yes	characteristic, complemented
95	#2236	C₂×C₅	1	1	yes	characteristic, complemented
96	#2234	C₂×C₅	1	2	yes	complemented
97	#2233	C₂×C₅	1	1	yes	characteristic, complemented
98	#2217	C₂×C₅	1	2	yes	complemented
99	#2215	C₂×C₅	1	2	yes	complemented
100	#2187	C₂×C₅	1	1	yes	characteristic, complemented
101	#2186	C₂×C₅	1	2	yes	complemented
102	#2184	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂×C₂²⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂⁴×C₅	—	4	1	no	—
105	C₂⁴×C₅	D₈	1	1	yes	characteristic
106	C₅×#41	—	4	2	no	—
107	C₅×#41	—	4	2	no	—
108	C₂×C₅×Q₈	—	2	1	no	—
109	C₂×C₅×D₄	—	2	2	no	—
110	C₂×C₅×D₄	—	2	1	no	—
111	C₂×C₅×D₄	—	4	2	no	—
112	C₂×C₅×D₄	—	4	2	no	—
113	C₂×C₅×D₄	—	4	1	no	—
114	C₂×C₅×D₄	—	4	1	no	—
115	C₂×C₅×D₄	—	4	1	no	—
116	C₂×C₅×D₄	—	4	2	no	—
117	C₂×C₅×D₄	—	4	2	no	—
118	C₂×C₅×D₄	—	4	1	no	—
119	C₂×C₅×D₄	—	8	4	no	—
120	C₂²×C₄×C₅	—	4	1	no	—
121	C₂²×C₄×C₅	—	4	1	no	—
122	C₂²×C₄×C₅	—	4	1	no	—
123	C₂²×C₄×C₅	—	4	1	no	—
124	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
125	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
126	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₅×Q₁₆	—	2	2	no	—
131	C₅×SD₁₆	—	4	2	no	—
132	C₅×D₈	—	2	2	no	—
133	C₅×D₈	—	2	2	no	—
134	C₅×D₈	—	2	2	no	—
135	C₅×D₈	—	4	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	2	2	no	—
139	C₂×C₅×C₈	—	4	1	no	—
140	C₂×C₅×C₈	—	4	1	no	—
141	C₂×C₅×C₈	—	4	1	no	—
142	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
143	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
144	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
145	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	4	1	no	—
150	C₅×C₄⋊C₄	—	4	1	no	—
151	C₅×C₄⋊C₄	—	4	1	no	—
152	C₅×C₂²⋊C₄	—	4	1	no	—
153	C₅×C₂²⋊C₄	—	4	1	no	—
154	C₅×C₂²⋊C₄	—	4	1	no	—
155	C₅×C₂²⋊C₄	—	4	2	no	—
156	C₅×C₂²⋊C₄	—	4	2	no	—
157	C₅×C₂²⋊C₄	—	4	1	no	—
158	C₅×C₂²⋊C₄	—	4	1	no	—
159	C₄²×C₅	—	4	1	no	—
160	C₅×C₁₆	—	2	2	no	—
161	C₅×C₁₆	—	2	2	no	—
162	C₂×#135	C₂²×C₅	1	1	yes	characteristic, complemented
163	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
164	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
165	#525	—	2	1	no	—
166	C₂×#121	—	2	1	no	—
167	C₂×SD₃₂	C₂²×C₅	1	2	yes	complemented
168	C₂×D₁₆	C₂²×C₅	1	2	yes	complemented
169	C₂²×C₁₆	C₂²×C₅	1	2	yes	complemented
170	#467	C₂²×C₅	1	1	yes	characteristic
171	#467	C₂²×C₅	1	1	yes	characteristic, complemented
172	#466	—	2	1	no	—
173	#466	—	2	1	no	—
174	#466	C₂²×C₅	1	1	yes	characteristic
175	#466	C₂²×C₅	1	2	yes	—
176	#466	C₂²×C₅	1	2	yes	—
177	#466	C₂²×C₅	1	1	yes	characteristic, complemented
178	#465	—	2	1	no	—
179	#465	—	2	1	no	—
180	#427	C₂²×C₅	1	1	yes	characteristic, complemented
181	C₂×#107	C₂²×C₅	1	1	yes	characteristic
182	#416	—	2	1	no	—
183	C₂×#102	—	2	1	no	—
184	#367	C₂²×C₅	1	2	yes	complemented
185	#366	C₂²×C₅	1	2	yes	complemented
186	#358	C₂²×C₅	1	2	yes	complemented
187	#357	C₂²×C₅	1	2	yes	complemented
188	#357	C₂²×C₅	1	2	yes	complemented
189	#357	C₂²×C₅	1	2	yes	complemented
190	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
191	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
192	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	complemented
193	C₂³×C₅	—	2	2	no	—
194	C₂³×C₅	—	2	2	no	—
195	C₂³×C₅	—	4	1	no	—
196	C₂³×C₅	—	4	1	no	—
197	C₂³×C₅	—	4	2	no	—
198	C₂³×C₅	—	8	2	no	—
199	C₂³×C₅	—	8	2	no	—
200	C₂³×C₅	—	8	2	no	—
201	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
202	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
203	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
204	C₅×Q₈	—	4	1	no	—
205	C₅×Q₈	—	4	1	no	—
206	C₅×D₄	—	4	2	no	—
207	C₅×D₄	—	4	1	no	—
208	C₅×D₄	—	4	2	no	—
209	C₅×D₄	—	4	1	no	—
210	C₅×D₄	—	8	2	no	—
211	C₅×D₄	—	8	4	no	—
212	C₅×D₄	—	8	2	no	—
213	C₅×D₄	—	8	2	no	—
214	C₅×D₄	—	8	2	no	—
215	C₅×D₄	—	8	4	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	1	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	4	1	no	—
223	C₂×C₄×C₅	—	4	1	no	—
224	C₂×C₄×C₅	—	4	1	no	—
225	C₂×C₄×C₅	—	4	1	no	—
226	C₂×C₄×C₅	—	4	1	no	—
227	C₂×C₄×C₅	—	4	2	no	—
228	C₂×C₄×C₅	—	4	1	no	—
229	C₂×C₄×C₅	—	8	2	no	—
230	C₂×C₄×C₅	—	8	2	no	—
231	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
235	C₅×C₈	—	2	1	no	—
236	C₅×C₈	—	2	1	no	—
237	C₅×C₈	—	2	1	no	—
238	C₅×C₈	H(5,𝔽₂)	1	2	yes	—
239	C₂×#41	—	2	1	no	—
240	C₂²×D₄	—	2	1	no	—
241	C₂²×D₄	—	4	1	no	—
242	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
243	#135	—	4	2	no	—
244	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
245	C₂×SD₁₆	—	2	1	no	—
246	C₂×D₈	—	2	1	no	—
247	C₂×D₈	—	4	2	no	—
248	C₂×D₈	C₂³×C₅	1	2	yes	—
249	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
250	C₂²×C₈	—	4	2	no	—
251	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
252	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
253	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
254	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
256	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
257	#123	—	4	1	no	—
258	C₂²⋊Q₈	—	2	1	no	—
259	C₂²⋊Q₈	—	2	1	no	—
260	#121	—	2	2	no	—
261	#121	—	2	2	no	—
262	#121	—	2	1	no	—
263	#121	—	2	1	no	—
264	#121	—	4	1	no	—
265	#121	—	4	1	no	—
266	#120	—	4	1	no	—
267	C₄×D₄	—	4	1	no	—
268	C₄×D₄	—	4	1	no	—
269	#117	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₂²⋊C₄	—	4	1	no	—
272	SD₃₂	—	4	2	no	—
273	D₁₆	—	4	2	no	—
274	C₂×C₁₆	—	4	2	no	—
275	C₂×C₁₆	C₂³×C₅	1	2	yes	—
276	C₂×C₁₆	C₂³×C₅	1	2	yes	—
277	#107	—	2	1	no	—
278	#107	C₂³×C₅	1	1	yes	characteristic
279	#107	C₂³×C₅	1	1	yes	characteristic
280	#107	C₂³×C₅	1	2	yes	—
281	#106	—	2	1	no	—
282	#103	—	2	1	no	—
283	#103	—	2	1	no	—
284	#102	—	2	2	no	—
285	#102	—	2	2	no	—
286	#102	—	2	1	no	—
287	#102	—	2	1	no	—
288	C₂²×C₅	—	2	1	no	—
289	C₂²×C₅	—	2	1	no	—
290	C₂²×C₅	—	2	1	no	—
291	C₂²×C₅	—	2	1	no	—
292	C₂²×C₅	—	2	1	no	—
293	C₂²×C₅	—	2	1	no	—
294	C₂²×C₅	—	2	1	no	—
295	C₂²×C₅	—	4	4	no	—
296	C₂²×C₅	—	8	1	no	—
297	C₂²×C₅	—	8	2	no	—
298	C₂²×C₅	—	8	2	no	—
299	C₂²×C₅	—	8	1	no	—
300	C₂²×C₅	—	8	1	no	—
301	C₂²×C₅	—	8	2	no	—
302	C₂²×C₅	—	16	4	no	—
303	C₂²×C₅	#508	1	2	yes	—
304	C₂²×C₅	#509	1	2	yes	—
305	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
306	C₄×C₅	—	2	1	no	—
307	C₄×C₅	—	2	1	no	—
308	C₄×C₅	—	2	1	no	—
309	C₄×C₅	—	8	1	no	—
310	C₄×C₅	—	8	2	no	—
311	C₄×C₅	—	8	1	no	—
312	C₄×C₅	—	8	1	no	—
313	C₄×C₅	#534	1	1	yes	characteristic
314	C₄×C₅	#575	1	1	yes	characteristic
315	C₂⁴	—	4	1	no	—
316	C₂⁴	C₅×D₈	1	1	yes	characteristic
317	#41	—	4	2	no	—
318	#41	—	4	2	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	4	2	no	—
323	C₂×D₄	—	4	2	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	4	1	no	—
326	C₂×D₄	—	4	1	no	—
327	C₂×D₄	—	4	2	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	—	8	4	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	4	1	no	—
334	C₂²×C₄	—	4	1	no	—
335	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
336	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
337	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
338	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
340	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
341	Q₁₆	—	2	2	no	—
342	SD₁₆	—	4	2	no	—
343	D₈	—	2	2	no	—
344	D₈	—	2	2	no	—
345	D₈	—	2	2	no	—
346	D₈	—	4	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	—	4	1	no	—
353	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
354	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
355	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
356	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₂²⋊C₄	—	4	1	no	—
364	C₂²⋊C₄	—	4	1	no	—
365	C₂²⋊C₄	—	4	1	no	—
366	C₂²⋊C₄	—	4	2	no	—
367	C₂²⋊C₄	—	4	2	no	—
368	C₂²⋊C₄	—	4	1	no	—
369	C₂²⋊C₄	—	4	1	no	—
370	C₄²	—	4	1	no	—
371	C₁₆	—	2	2	no	—
372	C₁₆	—	2	2	no	—
373	C₂×C₅	—	2	2	no	—
374	C₂×C₅	—	2	2	no	—
375	C₂×C₅	—	4	1	no	—
376	C₂×C₅	—	16	1	no	—
377	C₂×C₅	—	16	2	no	—
378	C₂×C₅	#3186	1	1	yes	characteristic
379	C₂×C₅	C₂×#508	1	1	yes	characteristic
380	C₂×C₅	C₂×#509	1	1	yes	characteristic
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	4	1	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	8	2	no	—
387	C₂³	—	8	2	no	—
388	C₂³	—	8	2	no	—
389	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
390	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
391	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
392	Q₈	—	4	1	no	—
393	Q₈	—	4	1	no	—
394	D₄	—	4	2	no	—
395	D₄	—	4	1	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	1	no	—
398	D₄	—	8	2	no	—
399	D₄	—	8	4	no	—
400	D₄	—	8	2	no	—
401	D₄	—	8	2	no	—
402	D₄	—	8	4	no	—
403	D₄	—	8	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	8	2	no	—
418	C₂×C₄	—	8	2	no	—
419	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
420	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
421	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
423	C₈	—	2	1	no	—
424	C₈	—	2	1	no	—
425	C₈	—	2	1	no	—
426	C₈	C₅×H(5,𝔽₂)	1	2	yes	—
427	C₅	#33754	1	1	yes	characteristic, direct product factor, Sylow
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	2	no	—
438	C₂²	—	8	2	no	—
439	C₂²	—	8	1	no	—
440	C₂²	—	8	1	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	16	4	no	—
443	C₂²	C₅×#508	1	2	yes	—
444	C₂²	C₅×#509	1	2	yes	—
445	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	8	1	no	—
450	C₄	—	8	2	no	—
451	C₄	—	8	1	no	—
452	C₄	—	8	1	no	—
453	C₄	C₅×#534	1	1	yes	characteristic
454	C₄	C₅×#575	1	1	yes	characteristic
455	C₂	—	2	2	no	—
456	C₂	—	2	2	no	—
457	C₂	—	4	1	no	—
458	C₂	—	16	2	no	—
459	C₂	—	16	1	no	—
460	C₂	C₅×#3186	1	1	yes	characteristic
461	C₂	C₂×C₅×#508	1	1	yes	characteristic
462	C₂	C₂×C₅×#509	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 ◁ C₂³×C₄×C₅ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3050	C₂	semidirect
2. C₂×C₅×#466	C₂	semidirect
3. C₅×#2236	C₂	semidirect
4. C₅×#2234	C₂	semidirect
5. C₅×#2233	C₂	semidirect
6. C₅×#2217	C₂	semidirect
7. C₅×#2215	C₂	semidirect
8. C₅×#2187	C₂	semidirect
9. C₅×#2186	C₂	semidirect
10. C₅×#2184	C₂	semidirect
11. C₂×C₅×C₂²⋊C₁₆	C₂	semidirect
12. C₂×C₅×#135	C₂²	semidirect
17. C₂×C₅×SD₃₂	C₂²	semidirect
18. C₂×C₅×D₁₆	C₂²	semidirect
19. C₂²×C₅×C₁₆	C₂²	semidirect
21. C₅×#467	C₂²	semidirect
27. C₅×#466	C₂²	semidirect
30. C₅×#427	C₂²	semidirect
34. C₅×#367	C₂²	semidirect
35. C₅×#366	C₂²	semidirect
36. C₅×#358	C₂²	semidirect
37. C₅×#357	C₂²	semidirect
38. C₅×#357	C₂²	semidirect
39. C₅×#357	C₂²	semidirect
42. C₅×C₂²⋊C₁₆	C₂²	semidirect
43. #33754	C₅	direct (N × H)
93. #3050	C₂×C₅	semidirect
94. C₂×#466	C₂×C₅	semidirect
95. #2236	C₂×C₅	semidirect
96. #2234	C₂×C₅	semidirect
97. #2233	C₂×C₅	semidirect
98. #2217	C₂×C₅	semidirect
99. #2215	C₂×C₅	semidirect
100. #2187	C₂×C₅	semidirect
101. #2186	C₂×C₅	semidirect
102. #2184	C₂×C₅	semidirect
103. C₂×C₂²⋊C₁₆	C₂×C₅	semidirect
162. C₂×#135	C₂²×C₅	semidirect
167. C₂×SD₃₂	C₂²×C₅	semidirect
168. C₂×D₁₆	C₂²×C₅	semidirect
169. C₂²×C₁₆	C₂²×C₅	semidirect
171. #467	C₂²×C₅	semidirect
177. #466	C₂²×C₅	semidirect
180. #427	C₂²×C₅	semidirect
184. #367	C₂²×C₅	semidirect
185. #366	C₂²×C₅	semidirect
186. #358	C₂²×C₅	semidirect
187. #357	C₂²×C₅	semidirect
188. #357	C₂²×C₅	semidirect
189. #357	C₂²×C₅	semidirect
192. C₂²⋊C₁₆	C₂²×C₅	semidirect
427. C₅	#33754	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×#466	2
C₅×#2236	2
C₅×#2234	2
C₅×#2233	2
C₅×#2217	2
C₅×#2215	2
C₅×#2187	2
C₅×#2186	2
C₅×#2184	2
C₂×C₅×C₂²⋊C₁₆	2
#33754	5

Subgroups — C5×#33754 #11956474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33754 #11956474