Subgroups — #12069348

Order 1280.

692 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#713	C₂	1	1	yes	maximal, characteristic, complemented
2	#10611426	C₂	1	1	yes	maximal, characteristic
3	#10611269	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1583	C₂	1	1	yes	maximal, characteristic, complemented
5	#10601726	C₂	1	1	yes	maximal, characteristic, complemented
6	SD₁₆⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
7	#10601655	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599328	C₂	1	1	yes	maximal, characteristic, complemented
9	#10599311	C₂	1	1	yes	maximal, characteristic, complemented
10	#10599031	C₂	1	1	yes	maximal, characteristic, complemented
11	#10599007	C₂	1	1	yes	maximal, characteristic, complemented
12	#10598964	C₂	1	1	yes	maximal, characteristic, complemented
13	#10598944	C₂	1	1	yes	maximal, characteristic, complemented
14	#10598871	C₂	1	1	yes	maximal, characteristic, complemented
15	#10598862	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#4053	—	2	1	no	—
17	C₄×#713	C₂²	1	1	yes	characteristic
18	#65882	C₂²	1	1	yes	characteristic
19	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
20	C₄×C₅×SD₁₆	C₂²	1	1	yes	characteristic
21	C₅×#436	C₂²	1	1	yes	characteristic
22	#65461	C₄	1	1	yes	characteristic
23	#65452	C₄	1	1	yes	characteristic
24	#65417	—	2	1	no	—
25	C₄×#688	C₂²	1	1	yes	characteristic
26	Q₈×#168	C₂²	1	1	yes	characteristic
27	C₄×#686	C₂²	1	1	yes	characteristic
28	D₄×#168	C₂²	1	1	yes	characteristic
29	#65159	C₄	1	1	yes	characteristic
30	#65155	C₄	1	1	yes	characteristic
31	#65126	C₂²	1	1	yes	characteristic
32	#65123	—	2	1	no	—
33	#65123	C₂²	1	1	yes	characteristic
34	#65123	C₂²	1	1	yes	characteristic
35	#65122	—	2	1	no	—
36	#65122	C₂²	1	1	yes	characteristic
37	#65100	C₄	1	1	yes	characteristic
38	#65083	C₄	1	1	yes	characteristic
39	#65075	C₄	1	1	yes	characteristic
40	#65073	C₄	1	1	yes	characteristic
41	#65016	—	2	1	no	—
42	#65014	—	2	1	no	—
43	C₄×D₄₀	C₂²	1	1	yes	characteristic
44	#64977	C₂²	1	1	yes	characteristic
45	C₄×#676	C₂²	1	1	yes	characteristic
46	C₈×D₂₀	—	2	1	no	—
47	C₈×D₂₀	C₂²	1	1	yes	characteristic
48	#64974	C₂²	1	1	yes	characteristic
49	C₄×C₈×D₅	—	2	1	no	—
50	C₄×C₈×D₅	C₂²	1	1	yes	characteristic
51	C₅×#334	C₂²	1	1	yes	characteristic
52	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
53	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
54	C₅×#322	C₂²	1	1	yes	characteristic
55	Q₈⋊#168	C₂²	1	1	yes	characteristic
56	D₄⋊#168	C₂²	1	1	yes	characteristic
57	#64703	C₂²	1	1	yes	characteristic
58	#64703	C₂²	1	1	yes	characteristic
59	#64700	C₂²	1	1	yes	characteristic
60	#64699	C₂²	1	1	yes	characteristic
61	#64679	C₂²	1	1	yes	characteristic
62	#64679	C₂²	1	1	yes	characteristic
63	#64678	C₂²	1	1	yes	characteristic
64	#64675	C₂²	1	1	yes	characteristic
65	#64675	C₂²	1	1	yes	characteristic
66	#64674	C₂²	1	1	yes	characteristic
67	#17917	—	5	1	no	maximal, Sylow
68	C₂×#713	C₂×C₄	1	1	yes	characteristic
69	C₂×#709	—	2	1	no	—
70	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
71	C₂×C₅×M₁₆	—	2	1	no	—
72	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
73	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
74	Q₈×Dic₅	C₂×C₄	1	1	yes	characteristic
75	C₂×#688	C₂×C₄	1	1	yes	characteristic
76	#4086	C₂×C₄	1	1	yes	characteristic
77	#4084	C₂×C₄	1	1	yes	characteristic
78	C₂×#686	C₂×C₄	1	1	yes	characteristic
79	C₄×C₂²⋊D₅	—	2	1	no	—
80	C₂²×#168	—	2	1	no	—
81	#4053	—	4	4	no	—
82	C₂×D₄₀	C₂×C₄	1	1	yes	characteristic
83	C₂×#676	—	2	1	no	—
84	C₂×#676	—	2	1	no	—
85	C₂×#676	—	2	1	no	—
86	C₂×C₈×D₅	—	2	1	no	—
87	C₂×C₈×D₅	—	2	1	no	—
88	C₂×C₈×D₅	—	2	1	no	—
89	C₂×C₈×D₅	D₄	1	1	yes	characteristic
90	C₂×C₈×D₅	D₄	1	1	yes	characteristic
91	#4041	C₂×C₄	1	1	yes	characteristic
92	#4039	—	2	1	no	—
93	#4039	C₂×C₄	1	1	yes	characteristic
94	#4038	—	2	1	no	—
95	#4038	C₂×C₄	1	1	yes	characteristic
96	#4034	C₂×C₄	1	1	yes	characteristic
97	#4031	—	2	1	no	—
98	#4030	—	2	1	no	—
99	C₄×D₂₀	—	2	1	no	—
100	C₄×D₂₀	C₂³	1	1	yes	characteristic
101	C₄×D₂₀	C₂³	1	1	yes	characteristic
102	C₄²×D₅	—	2	1	no	—
103	C₄²×D₅	C₂³	1	1	yes	characteristic
104	C₅×#106	C₂×C₄	1	1	yes	characteristic
105	C₅×C₄⋊C₈	—	2	1	no	—
106	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
107	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
108	C₅×#103	C₂×C₄	1	1	yes	characteristic
109	C₅×#102	C₂×C₄	1	1	yes	characteristic
110	C₅×C₂²⋊C₈	—	2	1	no	—
111	C₄×C₅×C₈	—	2	1	no	—
112	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
113	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
114	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
115	#3967	C₂×C₄	1	1	yes	characteristic
116	#3964	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊#168	—	2	1	no	—
118	#3953	C₂×C₄	1	1	yes	characteristic
119	#3953	C₂×C₄	1	1	yes	characteristic
120	#3952	—	2	1	no	—
121	#3952	—	2	1	no	—
122	#3952	—	2	1	no	—
123	#3952	—	2	1	no	—
124	#3952	—	2	1	no	—
125	#3952	C₂×C₄	1	1	yes	characteristic
126	#3952	C₂×C₄	1	1	yes	characteristic
127	#3950	C₂×C₄	1	1	yes	characteristic
128	#3947	—	2	1	no	—
129	#3946	—	2	1	no	—
130	#3946	C₂×C₄	1	1	yes	characteristic
131	#3946	C₂×C₄	1	1	yes	characteristic
132	C₈×Dic₅	—	2	1	no	—
133	C₈×Dic₅	D₄	1	1	yes	characteristic
134	C₈×Dic₅	D₄	1	1	yes	characteristic
135	#3941	C₂×C₄	1	1	yes	characteristic
136	#3941	C₂×C₄	1	1	yes	characteristic
137	#3940	C₂×C₄	1	1	yes	characteristic
138	#3939	C₂×C₄	1	1	yes	characteristic
139	C₄⋊#168	—	2	1	no	—
140	C₄⋊#168	C₂³	1	1	yes	characteristic
141	C₄⋊#168	C₂³	1	1	yes	characteristic
142	C₄×#168	—	2	1	no	—
143	C₄×#168	C₂³	1	1	yes	characteristic
144	C₄×#168	C₂³	1	1	yes	characteristic
145	C₄×#168	C₂³	1	1	yes	characteristic
146	#3106	—	5	1	no	—
147	C₈×#41	—	5	1	no	—
148	#2931	—	5	1	no	—
149	#1583	—	5	1	no	—
150	#1583	D₅	1	1	yes	characteristic, complemented
151	#1581	—	5	1	no	—
152	#1581	—	5	1	no	—
153	#1580	—	5	1	no	—
154	#1580	—	5	1	no	—
155	SD₁₆⋊C₈	—	5	1	no	—
156	SD₁₆⋊C₈	—	5	1	no	—
157	#1574	—	5	1	no	—
158	#1489	—	5	1	no	—
159	#1484	—	5	1	no	—
160	#1451	—	5	1	no	—
161	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	—	2	1	no	—
164	C₂×C₂²⋊D₅	—	2	1	no	—
165	C₂×C₂²⋊D₅	—	2	1	no	—
166	C₂×C₂²⋊D₅	—	2	1	no	—
167	#713	—	2	2	no	—
168	#713	—	2	2	no	—
169	#709	—	4	2	no	—
170	#709	—	4	2	no	—
171	C₂×D₂₀	—	2	1	no	—
172	C₂×D₂₀	—	2	1	no	—
173	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
174	C₂×D₂₀	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₄×D₅	—	2	1	no	—
176	C₂×C₄×D₅	—	2	1	no	—
177	C₂×C₄×D₅	—	2	1	no	—
178	C₂×C₄×D₅	—	2	1	no	—
179	C₂×C₄×D₅	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₄×D₅	C₂×D₄	1	1	yes	characteristic
181	C₂×C₄×D₅	#41	1	1	yes	characteristic
182	C₂×Dic₁₀	—	2	1	no	—
183	C₅×SD₁₆	—	2	2	no	—
184	C₅×M₁₆	—	4	2	no	—
185	C₂×C₅×C₈	—	2	1	no	—
186	C₂×C₅×C₈	—	2	1	no	—
187	C₂×C₅×C₈	—	2	1	no	—
188	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
191	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
192	C₅×C₄⋊C₄	—	2	1	no	—
193	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
194	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
195	C₅×C₂²⋊C₄	—	2	1	no	—
196	C₄²×C₅	—	2	1	no	—
197	C₄²×C₅	C₂⁴	1	1	yes	characteristic
198	C₂²⋊Dic₅	—	2	1	no	—
199	#688	—	2	2	no	—
200	#686	—	2	2	no	—
201	#685	—	2	1	no	—
202	#685	—	2	1	no	—
203	#685	—	2	1	no	—
204	#685	—	2	1	no	—
205	#685	—	2	1	no	—
206	C₄⋊Dic₅	—	2	1	no	—
207	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
208	C₄⋊Dic₅	C₂²×C₄	1	1	yes	characteristic
209	#683	—	2	1	no	—
210	C₄×Dic₅	—	2	1	no	—
211	C₄×Dic₅	—	2	1	no	—
212	C₄×Dic₅	C₂²×C₄	1	1	yes	characteristic
213	C₄×Dic₅	C₂×D₄	1	1	yes	characteristic
214	C₄×Dic₅	#41	1	1	yes	characteristic
215	C₂×#168	—	2	1	no	—
216	C₂×#168	—	2	1	no	—
217	C₂×#168	—	2	1	no	—
218	C₂×#168	—	4	2	no	—
219	C₂×#168	C₂²×C₄	1	1	yes	characteristic
220	C₂×#168	C₂²×C₄	1	1	yes	characteristic
221	C₂×#168	C₂×D₄	1	1	yes	characteristic
222	C₂×#168	C₂×D₄	1	1	yes	characteristic
223	D₄₀	—	2	2	no	—
224	#676	—	4	2	no	—
225	#676	—	4	2	no	—
226	#676	—	4	2	no	—
227	C₈×D₅	—	2	2	no	—
228	C₈×D₅	—	4	1	no	—
229	C₈×D₅	—	4	2	no	—
230	C₈×D₅	—	4	2	no	—
231	C₈×D₅	—	4	2	no	—
232	C₂×#131	—	10	1	no	—
233	#532	—	5	1	no	—
234	C₄×#41	—	5	1	no	—
235	#482	—	5	1	no	—
236	#482	—	5	1	no	—
237	#477	—	5	1	no	—
238	#476	—	5	1	no	—
239	#460	—	5	1	no	—
240	#459	—	5	1	no	—
241	#449	—	5	1	no	—
242	#449	—	5	1	no	—
243	C₈×Q₈	—	5	1	no	—
244	C₈×Q₈	C₂×D₅	1	1	yes	characteristic
245	C₄×SD₁₆	—	5	1	no	—
246	C₄×SD₁₆	C₂×D₅	1	1	yes	characteristic
247	C₄×D₈	—	5	1	no	—
248	C₄×D₈	—	5	1	no	—
249	#436	—	5	1	no	—
250	#436	—	10	1	no	—
251	#436	C₂×D₅	1	1	yes	characteristic
252	C₈×D₄	—	5	1	no	—
253	C₈×D₄	—	5	1	no	—
254	C₈×D₄	—	5	1	no	—
255	C₈×D₄	—	5	1	no	—
256	C₈×D₄	—	10	1	no	—
257	C₈×D₄	—	10	1	no	—
258	C₈×D₄	—	10	1	no	—
259	#431	—	5	1	no	—
260	#431	—	5	1	no	—
261	#431	—	10	1	no	—
262	#423	—	5	1	no	—
263	#408	—	10	1	no	—
264	C₄×M₁₆	—	5	1	no	—
265	C₂×C₄×C₈	—	5	1	no	—
266	C₂×C₄×C₈	—	10	1	no	—
267	#335	—	5	1	no	—
268	#335	—	5	1	no	—
269	#334	—	5	1	no	—
270	#334	C₂×D₅	1	1	yes	characteristic
271	Q₈⋊C₈	—	5	1	no	—
272	Q₈⋊C₈	C₂×D₅	1	1	yes	characteristic
273	D₄⋊C₈	—	5	1	no	—
274	D₄⋊C₈	—	5	1	no	—
275	D₄⋊C₈	—	5	1	no	—
276	D₄⋊C₈	—	5	1	no	—
277	D₄⋊C₈	—	5	1	no	—
278	D₄⋊C₈	C₂×D₅	1	1	yes	characteristic
279	#322	—	5	1	no	—
280	#322	—	5	1	no	—
281	#322	—	5	1	no	—
282	#322	C₂×D₅	1	1	yes	characteristic
283	C₂³×C₅	—	2	1	no	—
284	C₂²×D₅	—	2	1	no	—
285	C₂²×D₅	—	2	1	no	—
286	C₂²×D₅	C₄×D₄	1	1	yes	characteristic
287	C₅×Q₈	—	2	1	no	—
288	C₅×Q₈	#131	1	2	yes	complemented
289	C₅×D₄	—	2	1	no	—
290	C₅×D₄	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	4	1	no	—
295	C₂×C₄×C₅	—	4	1	no	—
296	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
297	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
298	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
299	C₂²⋊D₅	—	4	2	no	—
300	C₂²⋊D₅	—	4	2	no	—
301	C₂²⋊D₅	—	4	2	no	—
302	C₂×Dic₅	—	2	1	no	—
303	C₂×Dic₅	—	2	1	no	—
304	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
305	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
306	C₂×Dic₅	C₄×D₄	1	1	yes	characteristic
307	D₂₀	—	2	4	no	—
308	D₂₀	—	2	1	no	—
309	D₂₀	—	2	1	no	—
310	D₂₀	—	2	1	no	—
311	D₂₀	—	4	2	no	—
312	D₂₀	#131	1	2	yes	complemented
313	C₄×D₅	—	2	4	no	—
314	C₄×D₅	—	2	1	no	—
315	C₄×D₅	—	2	1	no	—
316	C₄×D₅	—	2	1	no	—
317	C₄×D₅	—	2	1	no	—
318	C₄×D₅	—	2	2	no	—
319	C₄×D₅	—	4	1	no	—
320	C₄×D₅	—	4	1	no	—
321	C₄×D₅	—	4	1	no	—
322	C₄×D₅	—	4	1	no	—
323	C₄×D₅	—	4	2	no	—
324	Dic₁₀	—	4	2	no	—
325	C₅×C₈	—	2	1	no	—
326	C₅×C₈	—	2	1	no	—
327	C₅×C₈	—	2	1	no	—
328	C₅×C₈	—	4	1	no	—
329	C₅×C₈	—	4	1	no	—
330	C₅×C₈	—	4	1	no	—
331	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
332	#168	—	2	1	no	—
333	#168	—	2	1	no	—
334	#168	—	2	1	no	—
335	#168	—	2	1	no	—
336	#168	—	4	1	no	—
337	#168	—	4	1	no	—
338	#168	—	4	1	no	—
339	C₂×#41	—	5	1	no	—
340	C₂×#41	—	10	1	no	—
341	C₂×SD₁₆	—	5	1	no	—
342	C₂×SD₁₆	C₄×D₅	1	1	yes	characteristic
343	C₂×D₈	—	5	1	no	—
344	C₂×D₈	—	5	1	no	—
345	#131	—	20	4	no	—
346	C₂×M₁₆	—	2	1	no	—
347	C₂×M₁₆	—	10	1	no	—
348	C₂×M₁₆	—	10	1	no	—
349	C₂×M₁₆	—	10	1	no	—
350	C₂²×C₈	—	5	1	no	—
351	C₂²×C₈	—	5	1	no	—
352	C₂²×C₈	—	10	1	no	—
353	C₂²×C₈	—	10	1	no	—
354	C₂²×C₈	—	10	1	no	—
355	C₂²×C₈	—	10	1	no	—
356	C₄⋊Q₈	—	5	1	no	—
357	#127	—	5	1	no	—
358	#124	—	10	1	no	—
359	#121	—	5	1	no	—
360	#121	—	5	1	no	—
361	#121	—	10	1	no	—
362	C₄×Q₈	—	5	1	no	—
363	C₄×Q₈	C₂²×D₅	1	1	yes	characteristic
364	C₄×D₄	—	5	1	no	—
365	C₄×D₄	—	5	1	no	—
366	C₄×D₄	—	5	1	no	—
367	C₄×D₄	—	10	1	no	—
368	C₄×D₄	—	10	1	no	—
369	C₄×D₄	—	10	1	no	—
370	C₄×D₄	C₂²×D₅	1	1	yes	characteristic
371	#117	—	5	1	no	—
372	#117	—	10	1	no	—
373	C₂×C₄²	—	5	1	no	—
374	C₂×C₄²	—	10	1	no	—
375	#107	—	5	1	no	—
376	#107	—	5	1	no	—
377	#106	—	5	1	no	—
378	#106	C₄×D₅	1	1	yes	characteristic
379	C₄⋊C₈	—	2	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	—	10	1	no	—
385	C₄⋊C₈	—	10	1	no	—
386	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
387	C₄⋊C₈	C₂²×D₅	1	1	yes	characteristic
388	#103	—	5	1	no	—
389	#103	C₄×D₅	1	1	yes	characteristic
390	#102	—	5	1	no	—
391	#102	—	5	1	no	—
392	#102	—	5	1	no	—
393	#102	—	5	1	no	—
394	#102	—	5	1	no	—
395	#102	C₄×D₅	1	1	yes	characteristic
396	C₂²⋊C₈	—	2	1	no	—
397	C₂²⋊C₈	—	5	1	no	—
398	C₂²⋊C₈	—	5	1	no	—
399	C₂²⋊C₈	—	10	1	no	—
400	C₂²⋊C₈	—	10	1	no	—
401	C₂²⋊C₈	—	10	1	no	—
402	C₂²⋊C₈	—	10	1	no	—
403	C₂²⋊C₈	—	10	1	no	—
404	C₂²⋊C₈	—	10	1	no	—
405	#97	—	10	1	no	—
406	C₄×C₈	—	2	1	no	—
407	C₄×C₈	—	5	1	no	—
408	C₄×C₈	—	5	1	no	—
409	C₄×C₈	—	5	1	no	—
410	C₄×C₈	—	5	1	no	—
411	C₄×C₈	—	5	1	no	—
412	C₄×C₈	—	10	1	no	—
413	C₄×C₈	—	10	1	no	—
414	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
415	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
416	C₄×C₈	C₂²×D₅	1	1	yes	characteristic
417	C₂²×C₅	—	4	1	no	—
418	C₂²×C₅	—	4	1	no	—
419	C₂²×C₅	—	4	1	no	—
420	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
421	C₂×D₅	—	2	1	no	—
422	C₂×D₅	—	2	2	no	—
423	C₂×D₅	—	2	1	no	—
424	C₂×D₅	—	2	1	no	—
425	C₂×D₅	—	4	1	no	—
426	C₂×D₅	—	4	1	no	—
427	C₂×D₅	—	4	1	no	—
428	C₂×D₅	—	4	1	no	—
429	C₂×D₅	—	4	1	no	—
430	C₄×C₅	—	2	2	no	—
431	C₄×C₅	—	2	1	no	—
432	C₄×C₅	—	4	1	no	—
433	C₄×C₅	—	4	1	no	—
434	C₄×C₅	C₂×#131	1	1	yes	characteristic
435	C₄×C₅	C₂×#131	1	1	yes	characteristic
436	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
437	C₄×C₅	#575	1	1	yes	characteristic
438	Dic₅	—	2	1	no	—
439	Dic₅	—	2	1	no	—
440	Dic₅	—	4	1	no	—
441	Dic₅	—	4	1	no	—
442	Dic₅	#444	1	2	yes	—
443	#41	—	10	2	no	—
444	#41	—	10	2	no	—
445	#41	—	20	2	no	—
446	#41	—	20	2	no	—
447	C₂×Q₈	—	10	1	no	—
448	C₂×Q₈	C₂×C₄×D₅	1	1	yes	characteristic
449	C₂×D₄	—	5	1	no	—
450	C₂×D₄	—	5	1	no	—
451	C₂×D₄	—	10	1	no	—
452	C₂×D₄	—	10	1	no	—
453	C₂×D₄	—	10	1	no	—
454	C₂×D₄	—	10	1	no	—
455	C₂×D₄	—	10	1	no	—
456	C₂×D₄	C₂×C₄×D₅	1	1	yes	characteristic
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	5	1	no	—
459	C₂²×C₄	—	5	1	no	—
460	C₂²×C₄	—	5	1	no	—
461	C₂²×C₄	—	10	1	no	—
462	C₂²×C₄	—	10	1	no	—
463	C₂²×C₄	—	10	1	no	—
464	C₂²×C₄	—	10	1	no	—
465	SD₁₆	—	2	2	no	—
466	SD₁₆	—	10	2	no	—
467	D₈	—	10	2	no	—
468	D₈	—	10	2	no	—
469	M₁₆	—	4	2	no	—
470	M₁₆	—	20	2	no	—
471	M₁₆	—	20	2	no	—
472	M₁₆	—	20	2	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	5	1	no	—
477	C₂×C₈	—	5	1	no	—
478	C₂×C₈	—	5	1	no	—
479	C₂×C₈	—	5	1	no	—
480	C₂×C₈	—	10	2	no	—
481	C₂×C₈	—	10	1	no	—
482	C₂×C₈	—	10	1	no	—
483	C₂×C₈	—	10	1	no	—
484	C₂×C₈	—	20	1	no	—
485	C₂×C₈	—	20	2	no	—
486	C₂×C₈	—	20	2	no	—
487	C₂×C₈	—	20	2	no	—
488	C₂×C₈	—	20	2	no	—
489	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
490	C₂×C₈	C₂×C₄×D₅	1	1	yes	characteristic
491	C₂×C₈	D₄×D₅	1	1	yes	characteristic
492	C₂×C₈	D₄×D₅	1	1	yes	characteristic
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	5	1	no	—
495	C₄⋊C₄	—	5	1	no	—
496	C₄⋊C₄	—	10	1	no	—
497	C₄⋊C₄	—	10	1	no	—
498	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
499	C₄⋊C₄	C₂×C₄×D₅	1	1	yes	characteristic
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	10	1	no	—
502	C₂²⋊C₄	—	10	1	no	—
503	C₂²⋊C₄	—	10	1	no	—
504	C₂²⋊C₄	—	10	1	no	—
505	C₂²⋊C₄	—	10	1	no	—
506	C₂²⋊C₄	—	10	1	no	—
507	C₄²	—	2	1	no	—
508	C₄²	—	5	1	no	—
509	C₄²	—	5	1	no	—
510	C₄²	—	5	1	no	—
511	C₄²	—	10	1	no	—
512	C₄²	—	10	1	no	—
513	C₄²	C₂³×D₅	1	1	yes	characteristic
514	C₂×C₅	—	8	1	no	—
515	C₂×C₅	#2929	1	1	yes	characteristic
516	C₂×C₅	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
517	C₂×C₅	C₂×#444	1	1	yes	characteristic
518	D₅	—	4	1	no	—
519	D₅	—	4	2	no	—
520	D₅	—	8	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	5	1	no	—
523	C₂³	—	10	1	no	—
524	C₂³	—	10	1	no	—
525	Q₈	—	2	1	no	—
526	Q₈	—	20	2	no	—
527	Q₈	#4053	1	2	yes	complemented
528	D₄	—	2	1	no	—
529	D₄	—	2	1	no	—
530	D₄	—	5	2	no	—
531	D₄	—	10	4	no	—
532	D₄	—	10	1	no	—
533	D₄	—	10	1	no	—
534	D₄	—	10	1	no	—
535	D₄	—	20	2	no	—
536	D₄	—	20	2	no	—
537	D₄	—	20	2	no	—
538	D₄	—	20	2	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	5	1	no	—
545	C₂×C₄	—	5	1	no	—
546	C₂×C₄	—	5	1	no	—
547	C₂×C₄	—	10	2	no	—
548	C₂×C₄	—	10	4	no	—
549	C₂×C₄	—	10	1	no	—
550	C₂×C₄	—	10	1	no	—
551	C₂×C₄	—	10	1	no	—
552	C₂×C₄	—	10	1	no	—
553	C₂×C₄	—	10	1	no	—
554	C₂×C₄	—	10	1	no	—
555	C₂×C₄	—	20	2	no	—
556	C₂×C₄	—	20	1	no	—
557	C₂×C₄	—	20	1	no	—
558	C₂×C₄	—	20	1	no	—
559	C₂×C₄	—	20	1	no	—
560	C₂×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
561	C₂×C₄	C₂×D₄×D₅	1	1	yes	characteristic
562	C₂×C₄	D₅×#41	1	1	yes	characteristic
563	C₈	—	2	1	no	—
564	C₈	—	2	1	no	—
565	C₈	—	2	1	no	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₈	—	4	1	no	—
569	C₈	—	10	1	no	—
570	C₈	—	10	1	no	—
571	C₈	—	10	1	no	—
572	C₈	—	10	1	no	—
573	C₈	—	20	1	no	—
574	C₈	—	20	1	no	—
575	C₈	—	20	1	no	—
576	C₈	#4060	1	2	yes	—
577	C₅	#17917	1	1	yes	characteristic, complemented, Sylow
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	10	2	no	—
582	C₂²	—	10	1	no	—
583	C₂²	—	10	1	no	—
584	C₂²	—	10	1	no	—
585	C₂²	—	20	1	no	—
586	C₂²	—	20	1	no	—
587	C₂²	—	20	1	no	—
588	C₂²	—	20	1	no	—
589	C₂²	—	20	1	no	—
590	C₂²	C₄×D₄×D₅	1	1	yes	characteristic
591	C₄	—	2	2	no	—
592	C₄	—	2	1	no	—
593	C₄	—	4	1	no	—
594	C₄	—	4	1	no	—
595	C₄	—	5	2	no	—
596	C₄	—	10	1	no	—
597	C₄	—	10	1	no	—
598	C₄	—	20	1	no	—
599	C₄	—	20	1	no	—
600	C₄	C₂×#4053	1	1	yes	characteristic
601	C₄	D₅×#131	1	1	yes	characteristic
602	C₄	C₂×#4060	1	1	yes	characteristic
603	C₄	#66102	1	1	yes	characteristic
604	C₂	—	8	1	no	—
605	C₂	—	20	1	no	—
606	C₂	—	20	2	no	—
607	C₂	—	40	1	no	—
608	C₂	#10611209	1	1	yes	characteristic
609	C₂	C₄×#4060	1	1	yes	characteristic
610	C₂	D₅×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅
commutator	C₂×C₄×C₅	C₂³×C₄
Frattini	C₄²	C₂³×D₅
Fitting	C₅×#1583	C₂
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	#10611426	C₂
cosocle	C₄²×C₅	C₂⁴
hypercenter	#1583	D₅
hypocenter	C₅	#17917
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1583

Complements

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

N	H ≅ G/N	type
1. C₈×#713	C₂	semidirect
3. #10611269	C₂	semidirect
4. C₅×#1583	C₂	semidirect
5. #10601726	C₂	semidirect
6. SD₁₆⋊#168	C₂	semidirect
7. #10601655	C₂	semidirect
8. #10599328	C₂	semidirect
9. #10599311	C₂	semidirect
10. #10599031	C₂	semidirect
11. #10599007	C₂	semidirect
12. #10598964	C₂	semidirect
13. #10598944	C₂	semidirect
14. #10598871	C₂	semidirect
15. #10598862	C₂	semidirect
150. #1583	D₅	semidirect
288. C₅×Q₈	#131	semidirect
312. D₂₀	#131	semidirect
527. Q₈	#4053	semidirect
577. C₅	#17917	semidirect

Maximal subgroups

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

subgroup	index
C₈×#713	2
#10611426	2
#10611269	2
C₅×#1583	2
#10601726	2
SD₁₆⋊#168	2
#10601655	2
#10599328	2
#10599311	2
#10599031	2
#10599007	2
#10598964	2
#10598944	2
#10598871	2
#10598862	2
#17917	5