Subgroups — #13029153

Order 1280.

704 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10617196	C₂	1	1	yes	maximal, characteristic
2	#10617187	C₂	1	1	yes	maximal, characteristic
3	#10611669	C₂	1	1	yes	maximal, characteristic
4	#10604014	C₂	1	1	yes	maximal, characteristic, complemented
5	#10604014	C₂	1	1	yes	maximal, characteristic, complemented
6	#10604013	C₂	1	1	yes	maximal, characteristic, complemented
7	#10604013	C₂	1	1	yes	maximal, characteristic, complemented
8	#10604012	C₂	1	1	yes	maximal, characteristic, complemented
9	#10604011	C₂	1	1	yes	maximal, characteristic, complemented
10	#10603864	C₂	1	1	yes	maximal, characteristic, complemented
11	#10603863	C₂	1	1	yes	maximal, characteristic, complemented
12	#10603861	C₂	1	1	yes	maximal, characteristic, complemented
13	#10603861	C₂	1	1	yes	maximal, characteristic, complemented
14	#10603810	C₂	1	1	yes	maximal, characteristic, complemented
15	#10603809	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#713	C₂²	1	1	yes	characteristic
17	#65788	C₄	1	2	yes	—
18	#65787	C₄	1	2	yes	—
19	#65708	C₄	1	2	yes	—
20	#65706	C₄	1	2	yes	—
21	#65706	C₄	1	2	yes	—
22	#65705	C₄	1	2	yes	—
23	#65704	C₄	1	2	yes	—
24	#65704	C₄	1	2	yes	—
25	#65680	C₂²	1	1	yes	characteristic
26	#65680	C₂²	1	1	yes	characteristic
27	#65680	C₂²	1	1	yes	characteristic
28	#65678	C₂²	1	1	yes	characteristic
29	#65678	C₂²	1	1	yes	characteristic
30	#65678	C₂²	1	1	yes	characteristic
31	#65678	C₂²	1	1	yes	characteristic
32	C₄×#700	C₂²	1	1	yes	characteristic
33	C₄×#700	C₂²	1	1	yes	characteristic
34	C₄×#700	C₂²	1	1	yes	characteristic
35	C₄×D₅⋊C₈	C₂²	1	1	yes	characteristic
36	C₄×D₅⋊C₈	C₂²	1	1	yes	characteristic
37	C₅×#446	C₄	1	1	yes	characteristic
38	#65313	C₄	1	1	yes	characteristic
39	#65127	C₄	1	1	yes	characteristic
40	#65125	C₄	1	1	yes	characteristic
41	#65125	C₄	1	1	yes	characteristic
42	#65122	C₂²	1	1	yes	characteristic
43	#65122	C₂²	1	1	yes	characteristic
44	#65122	C₂²	1	1	yes	characteristic
45	#64996	C₂²	1	1	yes	characteristic
46	#64996	C₂²	1	1	yes	characteristic
47	#64995	C₄	1	1	yes	characteristic
48	#64995	C₄	1	1	yes	characteristic
49	#64977	C₄	1	1	yes	characteristic
50	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
51	#170⋊C₈	C₂²	1	1	yes	characteristic
52	#170⋊C₈	C₂²	1	1	yes	characteristic
53	#170⋊C₈	C₂²	1	1	yes	characteristic
54	#170⋊C₈	C₂²	1	1	yes	characteristic
55	#170⋊C₈	C₂²	1	1	yes	characteristic
56	#170⋊C₈	C₂²	1	1	yes	characteristic
57	#64879	C₂²	1	1	yes	characteristic
58	#64879	C₂²	1	1	yes	characteristic
59	#64879	C₂²	1	1	yes	characteristic
60	#64879	C₂²	1	1	yes	characteristic
61	#64879	C₂²	1	1	yes	characteristic
62	#64879	C₂²	1	1	yes	characteristic
63	C₈×#170	C₂²	1	1	yes	characteristic
64	C₈×#170	C₂²	1	1	yes	characteristic
65	C₈×#170	C₂²	1	1	yes	characteristic
66	C₈×#170	C₂²	1	1	yes	characteristic
67	#17340	—	5	1	no	maximal, Sylow
68	C₂×#713	C₂×C₄	1	1	yes	characteristic
69	C₂×#700	C₂×C₄	1	2	yes	—
70	C₂×#700	C₂×C₄	1	2	yes	—
71	C₂×#700	C₂×C₄	1	2	yes	—
72	C₂×D₅⋊C₈	C₂×C₄	1	2	yes	—
73	C₂×D₅⋊C₈	C₂×C₄	1	2	yes	—
74	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
75	Q₈×Dic₅	C₂×C₄	1	1	yes	characteristic
76	C₂×#676	C₂×C₄	1	1	yes	characteristic
77	C₂×#676	C₂×C₄	1	1	yes	characteristic
78	C₂×#676	C₂×C₄	1	1	yes	characteristic
79	C₂×#676	C₂×C₄	1	1	yes	characteristic
80	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
81	C₂×C₈×D₅	C₂×C₄	1	1	yes	characteristic
82	#4039	C₂×C₄	1	1	yes	characteristic
83	#4039	C₂×C₄	1	1	yes	characteristic
84	#4039	C₂×C₄	1	1	yes	characteristic
85	#4038	C₂×C₄	1	1	yes	characteristic
86	#4038	C₂×C₄	1	1	yes	characteristic
87	#4038	C₂×C₄	1	1	yes	characteristic
88	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
89	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
90	C₄×D₂₀	C₂×C₄	1	1	yes	characteristic
91	C₄²×D₅	C₂³	1	1	yes	characteristic
92	C₄²×D₅	C₂³	1	1	yes	characteristic
93	C₄²×D₅	C₂³	1	1	yes	characteristic
94	#4004	C₂×C₄	1	2	yes	—
95	#4004	C₂×C₄	1	2	yes	—
96	#4004	C₂×C₄	1	2	yes	—
97	#4004	C₂×C₄	1	2	yes	—
98	#4003	C₂×C₄	1	2	yes	—
99	#4003	C₂×C₄	1	2	yes	—
100	#4003	C₂×C₄	1	2	yes	—
101	#4003	C₂×C₄	1	2	yes	—
102	#4003	C₂×C₄	1	2	yes	—
103	#4003	C₂×C₄	1	2	yes	—
104	#4003	C₂×C₄	1	2	yes	—
105	#4002	C₂×C₄	1	2	yes	—
106	#4002	C₂×C₄	1	2	yes	—
107	#4002	C₂×C₄	1	2	yes	—
108	C₄⋊#170	C₂×C₄	1	2	yes	—
109	C₄⋊#170	C₂×C₄	1	2	yes	—
110	C₄⋊#170	C₂×C₄	1	2	yes	—
111	C₄×#170	C₂×C₄	1	2	yes	—
112	C₄×#170	C₂×C₄	1	2	yes	—
113	C₄×#170	C₂³	1	1	yes	characteristic
114	C₄×#170	C₂³	1	1	yes	characteristic
115	C₄×#170	C₂³	1	1	yes	characteristic
116	C₄×#170	C₂³	1	1	yes	characteristic
117	C₄×#170	C₂³	1	1	yes	characteristic
118	C₄×#170	C₂³	1	1	yes	characteristic
119	C₄×#170	C₂³	1	1	yes	characteristic
120	C₄×#170	C₂³	1	1	yes	characteristic
121	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
122	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
123	C₅×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
124	C₅×#97	C₂×C₄	1	1	yes	characteristic
125	C₅×#97	C₂×C₄	1	1	yes	characteristic
126	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
127	#3952	C₂×C₄	1	1	yes	characteristic
128	#3952	C₂×C₄	1	1	yes	characteristic
129	#3952	C₂×C₄	1	1	yes	characteristic
130	#3952	C₂×C₄	1	1	yes	characteristic
131	#3952	C₂×C₄	1	1	yes	characteristic
132	#3952	C₂×C₄	1	1	yes	characteristic
133	C₈×Dic₅	C₂³	1	1	yes	characteristic
134	C₈×Dic₅	C₂³	1	1	yes	characteristic
135	C₈×Dic₅	C₂³	1	1	yes	characteristic
136	C₈×Dic₅	C₂³	1	1	yes	characteristic
137	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
138	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
139	C₄⋊#168	C₂×C₄	1	1	yes	characteristic
140	#3935	C₂×C₄	1	1	yes	characteristic
141	#3935	C₂×C₄	1	1	yes	characteristic
142	C₄×#168	C₂×C₄	1	1	yes	characteristic
143	#2965	—	5	1	no	—
144	#2965	—	5	1	no	—
145	#2922	—	5	1	no	—
146	#1455	—	5	1	no	—
147	#1454	—	5	1	no	—
148	#1454	—	5	1	no	—
149	#1453	—	5	1	no	—
150	#1453	—	5	1	no	—
151	#1453	—	5	1	no	—
152	#1452	—	5	1	no	—
153	#1451	—	5	1	no	—
154	#1451	—	5	1	no	—
155	#1450	—	5	1	no	—
156	C₈×M₁₆	—	5	1	no	—
157	C₈×M₁₆	—	5	1	no	—
158	C₂×C₅×Q₈	C₄²	1	1	yes	characteristic
159	#713	—	4	2	no	—
160	C₂×D₂₀	C₄²	1	1	yes	characteristic
161	C₂×D₂₀	C₄²	1	1	yes	characteristic
162	C₂×D₂₀	C₄²	1	1	yes	characteristic
163	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
172	C₂×#170	C₂²×C₄	1	2	yes	—
173	C₂×#170	C₂²×C₄	1	2	yes	—
174	C₂×#170	C₂²×C₄	1	2	yes	—
175	C₂×#170	C₂²×C₄	1	2	yes	—
176	C₂×#170	C₂²×C₄	1	2	yes	—
177	C₂×#170	C₂²×C₄	1	2	yes	—
178	C₂×#170	C₂²×C₄	1	2	yes	—
179	C₂×#170	C₂²×C₄	1	2	yes	—
180	#700	—	4	2	no	—
181	#700	—	4	2	no	—
182	#700	—	4	2	no	—
183	D₅⋊C₈	—	4	2	no	—
184	D₅⋊C₈	—	4	2	no	—
185	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
189	C₅×C₄⋊C₄	C₄²	1	1	yes	characteristic
190	C₅×C₄⋊C₄	C₄²	1	1	yes	characteristic
191	C₅×C₄⋊C₄	C₄²	1	1	yes	characteristic
192	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
193	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
194	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
195	#685	C₄²	1	1	yes	characteristic
196	#685	C₄²	1	1	yes	characteristic
197	#685	C₄²	1	1	yes	characteristic
198	#685	C₄²	1	1	yes	characteristic
199	#685	C₄²	1	1	yes	characteristic
200	#685	C₄²	1	1	yes	characteristic
201	C₄⋊Dic₅	C₄²	1	1	yes	characteristic
202	C₄⋊Dic₅	C₄²	1	1	yes	characteristic
203	C₄⋊Dic₅	C₄²	1	1	yes	characteristic
204	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
205	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
206	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
207	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
208	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
209	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
210	C₄×Dic₅	C₂⁴	1	1	yes	characteristic
211	C₂×#168	C₂²×C₄	1	1	yes	characteristic
212	C₂×#168	C₂²×C₄	1	1	yes	characteristic
213	C₂×#168	C₂²×C₄	1	1	yes	characteristic
214	C₂×#168	C₂²×C₄	1	1	yes	characteristic
215	#676	—	2	2	no	—
216	#676	—	2	2	no	—
217	#676	—	2	2	no	—
218	#676	—	2	2	no	—
219	C₈×D₅	—	2	2	no	—
220	C₈×D₅	—	2	2	no	—
221	C₄×#41	—	5	1	no	—
222	#446	—	5	2	no	—
223	#446	—	5	1	no	—
224	#446	AGL(1,𝔽₅)	1	1	yes	characteristic
225	#436	—	5	2	no	—
226	#436	—	5	1	no	—
227	#436	—	5	1	no	—
228	#435	—	5	2	no	—
229	#435	—	5	2	no	—
230	#435	—	5	1	no	—
231	#435	—	5	1	no	—
232	#435	—	5	1	no	—
233	#435	—	5	1	no	—
234	#433	—	5	2	no	—
235	#433	—	5	2	no	—
236	#431	—	5	1	no	—
237	#431	—	5	1	no	—
238	#431	—	5	1	no	—
239	#431	—	5	1	no	—
240	#431	—	5	1	no	—
241	#431	—	5	1	no	—
242	#431	—	5	1	no	—
243	#431	—	5	1	no	—
244	#431	—	5	1	no	—
245	#431	—	5	1	no	—
246	#424	—	5	2	no	—
247	#408	—	5	2	no	—
248	C₄×M₁₆	—	5	1	no	—
249	C₄×M₁₆	—	5	1	no	—
250	C₄×M₁₆	—	5	1	no	—
251	C₄×M₁₆	—	5	1	no	—
252	C₄×M₁₆	—	5	1	no	—
253	C₂×C₄×C₈	—	5	1	no	—
254	C₂×C₄×C₈	—	5	1	no	—
255	C₂×C₄×C₈	—	5	1	no	—
256	#322	—	5	1	no	—
257	#322	—	5	1	no	—
258	#322	—	5	1	no	—
259	#322	—	5	1	no	—
260	#322	—	5	1	no	—
261	#322	—	5	1	no	—
262	#322	—	5	1	no	—
263	#322	—	5	1	no	—
264	#322	—	5	1	no	—
265	#322	—	5	1	no	—
266	#322	—	5	1	no	—
267	#322	—	5	1	no	—
268	C₈²	—	5	1	no	—
269	C₈²	—	5	1	no	—
270	C₈²	—	5	1	no	—
271	C₈²	—	5	1	no	—
272	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
273	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
274	C₂²×D₅	C₂×C₄²	1	1	yes	characteristic
275	C₅×Q₈	—	4	1	no	—
276	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
283	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
284	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
285	C₂×Dic₅	C₂×C₄²	1	1	yes	characteristic
286	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
287	C₂×Dic₅	C₂³×C₄	1	1	yes	characteristic
288	D₂₀	—	4	1	no	—
289	D₂₀	—	4	1	no	—
290	D₂₀	—	4	1	no	—
291	C₄×D₅	—	2	1	no	—
292	C₄×D₅	—	2	1	no	—
293	C₄×D₅	—	2	1	no	—
294	C₄×D₅	—	2	1	no	—
295	C₄×D₅	—	2	1	no	—
296	C₄×D₅	—	2	1	no	—
297	C₄×D₅	—	2	2	no	—
298	C₄×D₅	—	2	2	no	—
299	C₄×D₅	—	2	2	no	—
300	C₄×D₅	—	2	2	no	—
301	C₄×D₅	—	2	2	no	—
302	C₄×D₅	—	2	2	no	—
303	#170	—	2	2	no	—
304	#170	—	2	2	no	—
305	#170	—	2	2	no	—
306	#170	—	2	2	no	—
307	#170	—	2	2	no	—
308	#170	—	2	2	no	—
309	#170	—	2	2	no	—
310	#170	—	2	2	no	—
311	C₅×C₈	—	2	1	no	—
312	C₅×C₈	—	2	1	no	—
313	C₅×C₈	—	2	1	no	—
314	C₅×C₈	#131	1	2	yes	—
315	#168	—	2	1	no	—
316	#168	—	2	1	no	—
317	#168	—	2	1	no	—
318	#168	#131	1	2	yes	—
319	C₂×#41	—	5	1	no	—
320	C₂×M₁₆	—	5	2	no	—
321	C₂×M₁₆	—	5	2	no	—
322	C₂×M₁₆	—	5	2	no	—
323	C₂×M₁₆	—	5	1	no	—
324	C₂×M₁₆	—	5	1	no	—
325	C₂×M₁₆	—	5	1	no	—
326	C₂×M₁₆	—	5	1	no	—
327	C₂²×C₈	—	5	2	no	—
328	C₂²×C₈	—	5	2	no	—
329	C₂²×C₈	—	5	1	no	—
330	C₂²×C₈	—	5	1	no	—
331	C₄×Q₈	—	5	1	no	—
332	C₄×Q₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
333	C₄×D₄	—	5	1	no	—
334	C₄×D₄	—	5	1	no	—
335	C₄×D₄	—	5	1	no	—
336	C₄×D₄	—	5	1	no	—
337	C₄×D₄	—	5	1	no	—
338	C₄×D₄	—	5	1	no	—
339	#117	—	5	1	no	—
340	#117	—	5	1	no	—
341	#117	—	5	1	no	—
342	C₂×C₄²	—	5	1	no	—
343	C₂×C₄²	—	5	1	no	—
344	C₂×C₄²	—	5	1	no	—
345	C₄⋊C₈	—	5	2	no	—
346	C₄⋊C₈	—	5	2	no	—
347	C₄⋊C₈	—	5	2	no	—
348	C₄⋊C₈	—	5	2	no	—
349	C₄⋊C₈	—	5	2	no	—
350	C₄⋊C₈	—	5	2	no	—
351	C₄⋊C₈	—	5	2	no	—
352	C₄⋊C₈	—	5	1	no	—
353	C₄⋊C₈	—	5	1	no	—
354	C₄⋊C₈	—	5	1	no	—
355	C₄⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
356	C₄⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
357	C₄⋊C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
358	C₂²⋊C₈	—	5	2	no	—
359	C₂²⋊C₈	—	5	2	no	—
360	C₂²⋊C₈	—	5	2	no	—
361	C₂²⋊C₈	—	5	2	no	—
362	C₂²⋊C₈	—	5	2	no	—
363	C₂²⋊C₈	—	5	2	no	—
364	C₂²⋊C₈	—	5	2	no	—
365	C₂²⋊C₈	—	5	1	no	—
366	C₂²⋊C₈	—	5	1	no	—
367	C₂²⋊C₈	—	5	1	no	—
368	C₂²⋊C₈	—	5	1	no	—
369	C₂²⋊C₈	—	5	1	no	—
370	C₂²⋊C₈	—	5	1	no	—
371	#97	—	5	2	no	—
372	#97	—	5	2	no	—
373	#97	—	5	2	no	—
374	#97	—	5	1	no	—
375	#97	—	5	1	no	—
376	#97	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
377	#97	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
378	C₄×C₈	—	5	1	no	—
379	C₄×C₈	—	5	1	no	—
380	C₄×C₈	—	5	1	no	—
381	C₄×C₈	—	5	1	no	—
382	C₄×C₈	—	5	1	no	—
383	C₄×C₈	—	5	1	no	—
384	C₄×C₈	—	5	1	no	—
385	C₄×C₈	—	5	1	no	—
386	C₄×C₈	—	5	2	no	—
387	C₄×C₈	—	5	2	no	—
388	C₄×C₈	—	5	1	no	—
389	C₄×C₈	—	5	1	no	—
390	C₄×C₈	—	5	1	no	—
391	C₄×C₈	—	5	1	no	—
392	C₄×C₈	—	5	1	no	—
393	C₄×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
394	C₂²×C₅	C₂²×C₄²	1	1	yes	characteristic
395	C₂×D₅	—	2	1	no	—
396	C₂×D₅	—	2	1	no	—
397	C₂×D₅	—	2	1	no	—
398	C₂×D₅	—	2	1	no	—
399	C₂×D₅	—	2	1	no	—
400	C₂×D₅	—	2	1	no	—
401	C₂×D₅	—	2	1	no	—
402	C₂×D₅	—	2	1	no	—
403	C₂×D₅	—	2	1	no	—
404	C₄×C₅	—	2	1	no	—
405	C₄×C₅	—	2	1	no	—
406	C₄×C₅	—	2	1	no	—
407	C₄×C₅	—	2	1	no	—
408	C₄×C₅	—	2	1	no	—
409	C₄×C₅	—	2	1	no	—
410	C₄×C₅	C₂×#131	1	1	yes	characteristic
411	C₄×C₅	C₂×#131	1	1	yes	characteristic
412	Dic₅	—	2	1	no	—
413	Dic₅	—	2	1	no	—
414	Dic₅	—	2	1	no	—
415	Dic₅	#568	1	2	yes	—
416	Dic₅	#568	1	2	yes	—
417	#41	—	20	2	no	—
418	C₂×Q₈	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
419	C₂×D₄	—	5	1	no	—
420	C₂×D₄	—	5	1	no	—
421	C₂×D₄	—	5	1	no	—
422	C₂²×C₄	—	5	1	no	—
423	C₂²×C₄	—	5	1	no	—
424	C₂²×C₄	—	5	1	no	—
425	C₂²×C₄	—	5	1	no	—
426	C₂²×C₄	—	5	1	no	—
427	C₂²×C₄	—	5	1	no	—
428	C₂²×C₄	—	5	1	no	—
429	C₂²×C₄	—	5	1	no	—
430	C₂²×C₄	—	5	1	no	—
431	M₁₆	—	10	2	no	—
432	M₁₆	—	10	2	no	—
433	M₁₆	—	10	2	no	—
434	M₁₆	—	10	2	no	—
435	M₁₆	—	20	2	no	—
436	M₁₆	—	20	2	no	—
437	M₁₆	—	20	2	no	—
438	C₂×C₈	—	5	1	no	—
439	C₂×C₈	—	5	2	no	—
440	C₂×C₈	—	5	2	no	—
441	C₂×C₈	—	5	2	no	—
442	C₂×C₈	—	5	2	no	—
443	C₂×C₈	—	5	2	no	—
444	C₂×C₈	—	5	2	no	—
445	C₂×C₈	—	5	2	no	—
446	C₂×C₈	—	5	2	no	—
447	C₂×C₈	—	5	1	no	—
448	C₂×C₈	—	5	1	no	—
449	C₂×C₈	—	5	1	no	—
450	C₂×C₈	—	10	2	no	—
451	C₂×C₈	—	10	2	no	—
452	C₂×C₈	—	20	2	no	—
453	C₂×C₈	—	20	2	no	—
454	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
455	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
456	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
457	C₂×C₈	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
458	C₄⋊C₄	—	5	1	no	—
459	C₄⋊C₄	—	5	1	no	—
460	C₄⋊C₄	—	5	1	no	—
461	C₄⋊C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
462	C₄⋊C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
463	C₄⋊C₄	C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
464	C₂²⋊C₄	—	5	1	no	—
465	C₂²⋊C₄	—	5	1	no	—
466	C₂²⋊C₄	—	5	1	no	—
467	C₂²⋊C₄	—	5	1	no	—
468	C₂²⋊C₄	—	5	1	no	—
469	C₂²⋊C₄	—	5	1	no	—
470	C₄²	—	5	1	no	—
471	C₄²	—	5	1	no	—
472	C₄²	—	5	1	no	—
473	C₄²	—	5	1	no	—
474	C₄²	—	5	1	no	—
475	C₄²	—	5	1	no	—
476	C₄²	—	5	1	no	—
477	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
478	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
479	C₄²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
480	C₂×C₅	#2873	1	1	yes	characteristic
481	C₂×C₅	C₄×#131	1	1	yes	characteristic
482	C₂×C₅	#2875	1	1	yes	characteristic
483	D₅	—	4	1	no	—
484	D₅	—	4	1	no	—
485	D₅	—	4	1	no	—
486	C₂³	—	5	1	no	—
487	C₂³	—	5	1	no	—
488	C₂³	—	5	1	no	—
489	Q₈	—	4	1	no	—
490	D₄	—	20	1	no	—
491	D₄	—	20	1	no	—
492	D₄	—	20	1	no	—
493	C₂×C₄	—	5	1	no	—
494	C₂×C₄	—	5	1	no	—
495	C₂×C₄	—	5	1	no	—
496	C₂×C₄	—	5	1	no	—
497	C₂×C₄	—	5	1	no	—
498	C₂×C₄	—	10	2	no	—
499	C₂×C₄	—	10	2	no	—
500	C₂×C₄	—	10	2	no	—
501	C₂×C₄	—	10	2	no	—
502	C₂×C₄	—	10	2	no	—
503	C₂×C₄	—	10	2	no	—
504	C₂×C₄	—	10	1	no	—
505	C₂×C₄	—	10	1	no	—
506	C₂×C₄	—	10	1	no	—
507	C₂×C₄	—	10	1	no	—
508	C₂×C₄	—	10	1	no	—
509	C₂×C₄	—	10	1	no	—
510	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
511	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
512	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
513	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
514	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
515	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
516	C₂×C₄	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
517	C₈	—	2	1	no	—
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	—	5	2	no	—
521	C₈	—	10	2	no	—
522	C₈	—	10	2	no	—
523	C₈	—	10	2	no	—
524	C₈	—	10	2	no	—
525	C₈	—	10	2	no	—
526	C₈	—	10	2	no	—
527	C₈	—	10	2	no	—
528	C₈	—	10	2	no	—
529	C₈	—	10	1	no	—
530	C₈	—	10	1	no	—
531	C₈	—	10	1	no	—
532	C₈	#4133	1	2	yes	—
533	C₅	#17340	1	1	yes	characteristic, complemented, Sylow
534	C₂²	—	10	1	no	—
535	C₂²	—	10	1	no	—
536	C₂²	—	10	1	no	—
537	C₂²	—	10	1	no	—
538	C₂²	—	10	1	no	—
539	C₂²	—	10	1	no	—
540	C₂²	—	10	1	no	—
541	C₂²	—	10	1	no	—
542	C₂²	—	10	1	no	—
543	C₂²	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	5	2	no	—
551	C₄	—	5	2	no	—
552	C₄	—	10	1	no	—
553	C₄	—	10	1	no	—
554	C₄	—	10	1	no	—
555	C₄	C₂×#4133	1	1	yes	characteristic
556	C₄	D₅⋊#131	1	1	yes	characteristic
557	C₂	—	20	1	no	—
558	C₂	—	20	1	no	—
559	C₂	—	20	1	no	—
560	C₂	C₄×#4133	1	1	yes	characteristic
561	C₂	#10617407	1	1	yes	characteristic
562	C₂	#10617415	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×AGL(1,𝔽₅)
commutator, socle	C₂²×C₅	C₂²×C₄²
Fitting	C₅×#446	C₄
prime radical	C₂×#713	C₂×C₄
cosocle	C₄×Dic₅	C₂⁴
hypercenter	#446	AGL(1,𝔽₅)
hypocenter	C₅	#17340
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ #446

Complements

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

N	H ≅ G/N	type
4. #10604014	C₂	semidirect
5. #10604014	C₂	semidirect
6. #10604013	C₂	semidirect
7. #10604013	C₂	semidirect
8. #10604012	C₂	semidirect
9. #10604011	C₂	semidirect
10. #10603864	C₂	semidirect
11. #10603863	C₂	semidirect
12. #10603861	C₂	semidirect
13. #10603861	C₂	semidirect
14. #10603810	C₂	semidirect
15. #10603809	C₂	semidirect
533. C₅	#17340	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#10617196	2
#10617187	2
#10611669	2
#10604014	2
#10604013	2
#10604012	2
#10604011	2
#10603864	2
#10603863	2
#10603861	2
#10603810	2
#10603809	2
#17340	5