Subgroups — #22603115

Order 9088.

1464 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17986834	C₂	1	1	yes	maximal, characteristic, complemented
2	H(5,𝔽₂)×D₇₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#17986811	C₂	1	1	yes	maximal, characteristic, complemented
4	#17986810	C₂	1	1	yes	maximal, characteristic, complemented
5	#17986809	C₂	1	3	yes	maximal, complemented
6	#17986806	C₂	1	3	yes	maximal, complemented
7	#17986803	C₂	1	3	yes	maximal, complemented
8	#17986802	C₂	1	1	yes	maximal, characteristic, complemented
9	#17986800	C₂	1	3	yes	maximal, complemented
10	#17986796	C₂	1	3	yes	maximal, complemented
11	#17986795	C₂	1	3	yes	maximal, complemented
12	C₂×#14556152	C₂	1	3	yes	maximal, complemented
13	AGL(1,ℤ/8)×D₇₁	C₂	1	3	yes	maximal, complemented
14	#17986764	C₂	1	1	yes	maximal, characteristic, complemented
15	#576×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
16	#14556175	—	2	1	no	—
17	#14556175	C₂²	1	1	yes	characteristic, complemented
18	#14556175	C₂²	1	3	yes	complemented
19	#14556174	—	2	1	no	—
20	#14556174	C₂²	1	1	yes	characteristic, complemented
21	#14556174	C₂²	1	3	yes	complemented
22	#14556173	—	2	3	no	—
23	#14556173	—	2	3	no	—
24	#14556173	C₂²	1	3	yes	complemented
25	#14556173	C₂²	1	3	yes	complemented
26	C₂×#11765864	—	2	3	no	—
27	C₂×#11765864	C₂²	1	3	yes	complemented
28	#41×D₇₁	—	2	1	no	—
29	#41×D₇₁	—	2	1	no	—
30	#41×D₇₁	C₂²	1	1	yes	characteristic
31	#41×D₇₁	C₂²	1	3	yes	complemented
32	#41×D₇₁	C₂²	1	3	yes	complemented
33	C₂×D₄×D₇₁	—	2	3	no	—
34	C₂×D₄×D₇₁	C₂²	1	3	yes	complemented
35	#14556161	C₂²	1	3	yes	complemented
36	#14556160	C₂²	1	1	yes	characteristic, complemented
37	#14556160	C₂²	1	3	yes	complemented
38	#14556158	C₂²	1	3	yes	complemented
39	#14556157	C₂²	1	3	yes	complemented
40	#14556157	C₂²	1	3	yes	complemented
41	#14556156	C₂²	1	3	yes	complemented
42	#14556155	C₂²	1	3	yes	complemented
43	#14556155	C₂²	1	3	yes	complemented
44	#14556154	C₂²	1	3	yes	complemented
45	#14556154	C₂²	1	3	yes	complemented
46	#14556153	C₂²	1	3	yes	complemented
47	#14556152	C₂²	1	6	yes	complemented
48	#14556152	C₂²	1	3	yes	complemented
49	#14556152	C₂²	1	6	yes	complemented
50	#14556152	C₂²	1	6	yes	complemented
51	#14556152	C₂²	1	3	yes	complemented
52	#14556150	C₂²	1	3	yes	complemented
53	#14556149	C₂²	1	6	yes	complemented
54	#14556148	C₂²	1	3	yes	complemented
55	#14556148	C₂²	1	3	yes	complemented
56	#14556147	C₂²	1	6	yes	complemented
57	C₂×#11765854	C₂²	1	3	yes	complemented
58	C₂×#11765853	C₂²	1	3	yes	complemented
59	SD₁₆×D₇₁	C₂²	1	6	yes	complemented
60	C₂×#11765850	C₂²	1	3	yes	complemented
61	D₈×D₇₁	C₂²	1	6	yes	complemented
62	#14556136	C₂²	1	3	yes	complemented
63	#14556135	C₂²	1	1	yes	characteristic, complemented
64	#14556134	C₂²	1	3	yes	complemented
65	C₂×#11765848	C₂²	1	3	yes	complemented
66	M₁₆×D₇₁	C₂²	1	3	yes	complemented
67	H(5,𝔽₂)×C₇₁	C₂²	1	1	yes	characteristic, complemented
68	H(5,𝔽₂)×C₇₁	C₂²	1	1	yes	characteristic, complemented
69	AGL(1,ℤ/8)×C₇₁	C₂²	1	3	yes	complemented
70	AGL(1,ℤ/8)×C₇₁	C₂²	1	3	yes	complemented
71	#135×C₇₁	C₂²	1	3	yes	complemented
72	C₂×D₈×C₇₁	C₂²	1	3	yes	complemented
73	#131×C₇₁	C₂²	1	1	yes	characteristic, complemented
74	C₂³×D₇₁	—	2	3	no	—
75	#11765866	—	2	1	no	—
76	#11765866	D₄	1	1	yes	characteristic
77	#11765866	C₂³	1	1	yes	characteristic
78	#11765866	C₂³	1	3	yes	—
79	#11765865	—	2	3	no	—
80	#11765865	—	2	3	no	—
81	#11765865	—	2	3	no	—
82	#11765865	—	2	3	no	—
83	#11765865	C₂³	1	3	yes	—
84	#11765865	C₂³	1	3	yes	—
85	#11765865	C₂³	1	3	yes	complemented
86	#11765864	—	2	3	no	—
87	#11765864	—	2	6	no	—
88	#11765864	—	2	3	no	—
89	#11765864	—	2	3	no	—
90	#11765864	—	2	3	no	—
91	#11765864	—	2	3	no	—
92	#11765864	—	2	3	no	—
93	#11765864	—	2	3	no	—
94	#11765864	D₄	1	3	yes	—
95	#11765864	C₂³	1	3	yes	—
96	#11765864	C₂³	1	3	yes	—
97	#11765864	C₂³	1	6	yes	complemented
98	C₂×Dic₁₄₂	—	2	3	no	—
99	C₂×Dic₁₄₂	C₂³	1	3	yes	complemented
100	Q₈×D₇₁	—	2	1	no	—
101	Q₈×D₇₁	D₄	1	1	yes	characteristic
102	Q₈×D₇₁	C₂³	1	1	yes	characteristic
103	Q₈×D₇₁	C₂³	1	3	yes	complemented
104	C₂×D₂₈₄	—	2	3	no	—
105	C₂×D₂₈₄	C₂³	1	3	yes	—
106	C₂×C₂²⋊D₇₁	—	2	3	no	—
107	C₂×C₂²⋊D₇₁	—	2	6	no	—
108	C₂×C₂²⋊D₇₁	—	2	6	no	—
109	C₂×C₂²⋊D₇₁	—	2	3	no	—
110	D₄×D₇₁	—	2	3	no	—
111	D₄×D₇₁	—	2	3	no	—
112	D₄×D₇₁	—	2	3	no	—
113	D₄×D₇₁	—	2	6	no	—
114	D₄×D₇₁	—	2	3	no	—
115	D₄×D₇₁	—	2	3	no	—
116	D₄×D₇₁	—	2	3	no	—
117	D₄×D₇₁	—	2	3	no	—
118	D₄×D₇₁	D₄	1	3	yes	—
119	D₄×D₇₁	C₂³	1	3	yes	—
120	D₄×D₇₁	C₂³	1	6	yes	—
121	D₄×D₇₁	C₂³	1	3	yes	complemented
122	C₂²×Dic₇₁	—	2	3	no	—
123	C₂×C₄×D₇₁	—	2	3	no	—
124	C₂×C₄×D₇₁	—	2	3	no	—
125	C₂×C₄×D₇₁	C₂³	1	3	yes	—
126	Dic₂₈₄	C₂³	1	3	yes	complemented
127	#11765855	C₂³	1	1	yes	characteristic, complemented
128	#11765855	C₂³	1	3	yes	complemented
129	#11765854	C₂³	1	3	yes	complemented
130	#11765854	C₂³	1	1	yes	characteristic, complemented
131	#11765854	C₂³	1	6	yes	complemented
132	#11765853	C₂³	1	6	yes	complemented
133	#11765853	C₂³	1	3	yes	complemented
134	#11765853	C₂³	1	3	yes	complemented
135	#11765852	C₂³	1	3	yes	complemented
136	#11765852	C₂³	1	1	yes	characteristic, complemented
137	D₅₆₈	C₂³	1	3	yes	complemented
138	#11765850	C₂³	1	3	yes	complemented
139	#11765850	C₂³	1	6	yes	complemented
140	#11765850	C₂³	1	3	yes	complemented
141	#11765849	C₂³	1	3	yes	complemented
142	#11765848	C₂³	1	1	yes	characteristic
143	#11765848	C₂³	1	3	yes	—
144	#11765848	C₂³	1	3	yes	complemented
145	#11765848	C₂³	1	3	yes	complemented
146	C₂×C₇₁⋊C₈	C₂³	1	3	yes	complemented
147	C₈×D₇₁	C₂³	1	6	yes	complemented
148	#41×C₇₁	—	2	1	no	—
149	#41×C₇₁	—	2	1	no	—
150	#41×C₇₁	C₂³	1	3	yes	—
151	#41×C₇₁	C₂³	1	1	yes	characteristic
152	#41×C₇₁	C₂³	1	3	yes	complemented
153	C₂×D₄×C₇₁	—	2	3	no	—
154	C₂×D₄×C₇₁	—	2	3	no	—
155	C₂×D₄×C₇₁	C₂³	1	3	yes	—
156	C₂×D₄×C₇₁	C₂³	1	3	yes	complemented
157	Q₁₆×C₇₁	C₂³	1	1	yes	characteristic, complemented
158	SD₁₆×C₇₁	C₂³	1	3	yes	complemented
159	SD₁₆×C₇₁	C₂³	1	3	yes	complemented
160	D₈×C₇₁	C₂³	1	3	yes	complemented
161	D₈×C₇₁	C₂³	1	6	yes	complemented
162	M₁₆×C₇₁	C₂³	1	3	yes	complemented
163	C₂×C₈×C₇₁	C₂³	1	3	yes	complemented
164	C₂³×C₇₁	—	2	3	no	—
165	C₂³×C₇₁	—	2	3	no	—
166	C₂²×D₇₁	—	2	3	no	—
167	C₂²×D₇₁	—	2	3	no	—
168	C₂²×D₇₁	—	2	3	no	—
169	C₂²×D₇₁	—	2	6	no	—
170	C₂²×D₇₁	—	8	6	no	—
171	C₂²×D₇₁	C₂×D₄	1	3	yes	—
172	Q₈×C₇₁	C₂×D₄	1	1	yes	characteristic
173	Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
174	Q₈×C₇₁	C₂⁴	1	1	yes	characteristic
175	D₄×C₇₁	—	2	3	no	—
176	D₄×C₇₁	—	2	3	no	—
177	D₄×C₇₁	—	2	3	no	—
178	D₄×C₇₁	—	2	3	no	—
179	D₄×C₇₁	C₂×D₄	1	3	yes	—
180	D₄×C₇₁	C₂⁴	1	3	yes	—
181	D₄×C₇₁	C₂⁴	1	3	yes	—
182	C₂×C₄×C₇₁	—	2	3	no	—
183	C₂×C₄×C₇₁	—	2	3	no	—
184	C₂×C₄×C₇₁	C₂⁴	1	3	yes	—
185	C₂²⋊D₇₁	—	2	3	no	—
186	C₂²⋊D₇₁	—	2	3	no	—
187	C₂²⋊D₇₁	—	2	3	no	—
188	C₂²⋊D₇₁	—	2	3	no	—
189	C₂²⋊D₇₁	—	2	6	no	—
190	C₂²⋊D₇₁	—	2	6	no	—
191	C₂²⋊D₇₁	—	2	3	no	—
192	C₂²⋊D₇₁	—	2	3	no	—
193	C₂²⋊D₇₁	C₂×D₄	1	6	yes	—
194	C₂×Dic₇₁	—	2	3	no	—
195	C₂×Dic₇₁	—	2	3	no	—
196	C₂×Dic₇₁	—	2	3	no	—
197	C₂×Dic₇₁	—	2	6	no	—
198	C₂×Dic₇₁	C₂×D₄	1	3	yes	—
199	D₂₈₄	—	2	3	no	—
200	D₂₈₄	—	2	1	no	—
201	D₂₈₄	—	2	3	no	—
202	D₂₈₄	C₂×D₄	1	3	yes	—
203	D₂₈₄	C₂⁴	1	1	yes	characteristic
204	D₂₈₄	C₂⁴	1	3	yes	—
205	C₄×D₇₁	—	2	1	no	—
206	C₄×D₇₁	—	2	3	no	—
207	C₄×D₇₁	—	2	3	no	—
208	C₄×D₇₁	—	2	3	no	—
209	C₄×D₇₁	—	2	1	no	—
210	C₄×D₇₁	—	2	3	no	—
211	C₄×D₇₁	C₂×D₄	1	3	yes	—
212	C₄×D₇₁	C₂×D₄	1	3	yes	—
213	C₄×D₇₁	C₂⁴	1	3	yes	—
214	C₄×D₇₁	C₂⁴	1	1	yes	characteristic
215	Dic₁₄₂	—	2	3	no	—
216	Dic₁₄₂	—	2	1	no	—
217	Dic₁₄₂	—	2	3	no	—
218	Dic₁₄₂	C₂×D₄	1	3	yes	—
219	Dic₁₄₂	C₂⁴	1	3	yes	—
220	Dic₁₄₂	C₂⁴	1	1	yes	characteristic
221	C₈×C₇₁	C₂⁴	1	1	yes	characteristic
222	C₈×C₇₁	C₂⁴	1	3	yes	—
223	C₇₁⋊C₈	C₂⁴	1	3	yes	—
224	C₇₁⋊C₈	C₂⁴	1	1	yes	characteristic
225	C₂²×C₇₁	—	2	3	no	—
226	C₂²×C₇₁	—	2	3	no	—
227	C₂²×C₇₁	—	8	3	no	—
228	C₂²×C₇₁	—	8	3	no	—
229	C₂²×C₇₁	C₂²×D₄	1	3	yes	—
230	C₂×D₇₁	—	2	1	no	—
231	C₂×D₇₁	—	2	3	no	—
232	C₂×D₇₁	—	4	3	no	—
233	C₂×D₇₁	—	4	6	no	—
234	C₂×D₇₁	—	8	3	no	—
235	C₂×D₇₁	—	8	6	no	—
236	C₂×D₇₁	—	8	3	no	—
237	C₂×D₇₁	C₂²×D₄	1	1	yes	characteristic
238	C₂×D₇₁	C₂²×D₄	1	3	yes	—
239	C₄×C₇₁	—	2	1	no	—
240	C₄×C₇₁	—	2	1	no	—
241	C₄×C₇₁	C₂²×D₄	1	3	yes	—
242	C₄×C₇₁	C₂⁵	1	1	yes	characteristic
243	Dic₇₁	—	2	3	no	—
244	Dic₇₁	—	2	1	no	—
245	Dic₇₁	C₂²×D₄	1	3	yes	—
246	Dic₇₁	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₇₁	—	2	3	no	—
248	C₂×C₇₁	—	4	3	no	—
249	C₂×C₇₁	—	4	3	no	—
250	C₂×C₇₁	C₂³×D₄	1	1	yes	characteristic
251	D₇₁	—	2	1	no	—
252	D₇₁	—	2	3	no	—
253	D₇₁	—	4	3	no	—
254	D₇₁	—	4	1	no	—
255	#3585	—	71	1	no	maximal, Sylow
256	C₇₁	#3585	1	1	yes	characteristic, complemented, Sylow
257	#585	—	71	1	no	—
258	C₂×H(5,𝔽₂)	—	71	1	no	—
259	#577	—	71	1	no	—
260	#577	—	71	3	no	—
261	#577	—	71	3	no	—
262	#577	—	71	1	no	—
263	#576	—	71	1	no	—
264	#576	—	71	3	no	—
265	#576	—	71	3	no	—
266	#576	D₇₁	1	1	yes	characteristic, complemented
267	#575	—	71	3	no	—
268	#575	—	71	3	no	—
269	C₂×AGL(1,ℤ/8)	—	71	3	no	—
270	C₂×AGL(1,ℤ/8)	—	71	3	no	—
271	#568	—	71	1	no	—
272	2₋¹⁺⁴	—	71	1	no	—
273	2₋¹⁺⁴	—	71	3	no	—
274	2₋¹⁺⁴	—	142	1	no	—
275	H(5,𝔽₂)	—	71	3	no	—
276	H(5,𝔽₂)	—	71	1	no	—
277	H(5,𝔽₂)	—	71	3	no	—
278	H(5,𝔽₂)	—	71	3	no	—
279	H(5,𝔽₂)	—	142	3	no	—
280	H(5,𝔽₂)	—	142	3	no	—
281	H(5,𝔽₂)	—	142	1	no	—
282	H(5,𝔽₂)	C₂×D₇₁	1	1	yes	characteristic, complemented
283	H(5,𝔽₂)	C₂×D₇₁	1	1	yes	characteristic, complemented
284	C₂×#41	—	71	1	no	—
285	C₂×#41	—	71	3	no	—
286	C₂×#41	—	71	3	no	—
287	C₂×#41	—	71	3	no	—
288	C₂×#41	—	142	3	no	—
289	C₂×#41	—	142	1	no	—
290	C₂×#41	—	142	1	no	—
291	C₂²×D₄	—	71	3	no	—
292	C₂²×D₄	—	142	3	no	—
293	#137	—	71	3	no	—
294	#137	—	71	1	no	—
295	#137	—	71	3	no	—
296	#137	—	71	3	no	—
297	#137	—	71	3	no	—
298	#137	—	71	3	no	—
299	AGL(1,ℤ/8)	—	71	3	no	—
300	AGL(1,ℤ/8)	—	71	3	no	—
301	AGL(1,ℤ/8)	—	71	3	no	—
302	AGL(1,ℤ/8)	—	71	3	no	—
303	AGL(1,ℤ/8)	—	71	3	no	—
304	AGL(1,ℤ/8)	—	71	6	no	—
305	AGL(1,ℤ/8)	—	71	3	no	—
306	AGL(1,ℤ/8)	—	71	6	no	—
307	AGL(1,ℤ/8)	—	71	6	no	—
308	AGL(1,ℤ/8)	—	71	3	no	—
309	AGL(1,ℤ/8)	—	71	3	no	—
310	AGL(1,ℤ/8)	C₂×D₇₁	1	3	yes	complemented
311	AGL(1,ℤ/8)	C₂×D₇₁	1	3	yes	complemented
312	#135	—	71	3	no	—
313	#135	—	71	3	no	—
314	#135	—	71	6	no	—
315	#135	—	71	6	no	—
316	#135	—	71	3	no	—
317	#135	C₂×D₇₁	1	3	yes	complemented
318	C₂×SD₁₆	—	71	3	no	—
319	C₂×SD₁₆	—	71	6	no	—
320	C₂×SD₁₆	—	71	3	no	—
321	C₂×D₈	—	71	3	no	—
322	C₂×D₈	—	71	6	no	—
323	C₂×D₈	C₂×D₇₁	1	3	yes	complemented
324	#131	—	71	1	no	—
325	#131	—	71	3	no	—
326	#131	—	71	3	no	—
327	#131	C₂×D₇₁	1	1	yes	characteristic, complemented
328	C₂×M₁₆	—	71	3	no	—
329	C₂×M₁₆	—	71	3	no	—
330	C₂⁴	—	142	3	no	—
331	#41	—	2	1	no	—
332	#41	—	2	1	no	—
333	#41	—	71	1	no	—
334	#41	—	71	3	no	—
335	#41	—	71	3	no	—
336	#41	—	71	3	no	—
337	#41	—	71	1	no	—
338	#41	—	71	3	no	—
339	#41	—	71	3	no	—
340	#41	—	71	6	no	—
341	#41	—	71	3	no	—
342	#41	—	71	3	no	—
343	#41	—	142	3	no	—
344	#41	—	142	3	no	—
345	#41	—	142	3	no	—
346	#41	—	142	3	no	—
347	#41	—	142	3	no	—
348	#41	—	142	3	no	—
349	#41	—	142	3	no	—
350	#41	—	142	3	no	—
351	#41	—	142	6	no	—
352	#41	—	142	3	no	—
353	#41	—	142	3	no	—
354	#41	—	142	1	no	—
355	#41	—	142	3	no	—
356	#41	C₂²×D₇₁	1	3	yes	—
357	#41	C₂²×D₇₁	1	1	yes	characteristic
358	#41	C₂²×D₇₁	1	3	yes	complemented
359	C₂×Q₈	—	71	1	no	—
360	C₂×Q₈	—	71	1	no	—
361	C₂×Q₈	—	71	3	no	—
362	C₂×Q₈	—	71	3	no	—
363	C₂×Q₈	—	142	3	no	—
364	C₂×Q₈	—	142	1	no	—
365	C₂×D₄	—	2	3	no	—
366	C₂×D₄	—	2	3	no	—
367	C₂×D₄	—	71	3	no	—
368	C₂×D₄	—	71	6	no	—
369	C₂×D₄	—	71	3	no	—
370	C₂×D₄	—	71	3	no	—
371	C₂×D₄	—	71	3	no	—
372	C₂×D₄	—	142	3	no	—
373	C₂×D₄	—	142	3	no	—
374	C₂×D₄	—	142	3	no	—
375	C₂×D₄	—	142	3	no	—
376	C₂×D₄	—	142	6	no	—
377	C₂×D₄	—	142	3	no	—
378	C₂×D₄	—	142	3	no	—
379	C₂×D₄	—	142	3	no	—
380	C₂×D₄	—	142	3	no	—
381	C₂×D₄	—	142	6	no	—
382	C₂×D₄	—	142	6	no	—
383	C₂×D₄	—	142	3	no	—
384	C₂×D₄	—	142	3	no	—
385	C₂×D₄	C₂²×D₇₁	1	3	yes	—
386	C₂×D₄	C₂²×D₇₁	1	3	yes	complemented
387	C₂²×C₄	—	71	3	no	—
388	C₂²×C₄	—	142	3	no	—
389	C₂²×C₄	—	142	3	no	—
390	C₂²×C₄	—	142	3	no	—
391	Q₁₆	—	71	3	no	—
392	Q₁₆	—	71	1	no	—
393	Q₁₆	—	71	3	no	—
394	Q₁₆	C₂²×D₇₁	1	1	yes	characteristic, complemented
395	SD₁₆	—	71	3	no	—
396	SD₁₆	—	71	1	no	—
397	SD₁₆	—	71	6	no	—
398	SD₁₆	—	71	3	no	—
399	SD₁₆	—	71	3	no	—
400	SD₁₆	—	71	6	no	—
401	SD₁₆	—	71	3	no	—
402	SD₁₆	—	71	1	no	—
403	SD₁₆	C₂²×D₇₁	1	3	yes	complemented
404	SD₁₆	C₂²×D₇₁	1	3	yes	complemented
405	D₈	—	71	3	no	—
406	D₈	—	71	6	no	—
407	D₈	—	71	3	no	—
408	D₈	—	71	3	no	—
409	D₈	C₂²×D₇₁	1	6	yes	complemented
410	D₈	C₂²×D₇₁	1	3	yes	complemented
411	M₁₆	—	71	3	no	—
412	M₁₆	—	71	3	no	—
413	M₁₆	—	71	1	no	—
414	M₁₆	—	71	3	no	—
415	M₁₆	—	71	3	no	—
416	M₁₆	C₂²×D₇₁	1	3	yes	complemented
417	C₂×C₈	—	71	3	no	—
418	C₂×C₈	—	71	6	no	—
419	C₂×C₈	C₂²×D₇₁	1	3	yes	complemented
420	C₂³	—	2	3	no	—
421	C₂³	—	2	3	no	—
422	C₂³	—	568	6	no	—
423	C₂³	—	71	3	no	—
424	C₂³	—	142	3	no	—
425	C₂³	—	142	3	no	—
426	C₂³	—	142	6	no	—
427	C₂³	—	142	3	no	—
428	Q₈	—	71	3	no	—
429	Q₈	—	71	3	no	—
430	Q₈	—	71	1	no	—
431	Q₈	—	142	3	no	—
432	Q₈	—	142	1	no	—
433	Q₈	—	142	3	no	—
434	Q₈	D₄×D₇₁	1	1	yes	characteristic
435	Q₈	C₂³×D₇₁	1	1	yes	characteristic
436	Q₈	C₂³×D₇₁	1	1	yes	characteristic
437	D₄	—	2	3	no	—
438	D₄	—	2	3	no	—
439	D₄	—	2	3	no	—
440	D₄	—	2	3	no	—
441	D₄	—	71	6	no	—
442	D₄	—	71	3	no	—
443	D₄	—	71	1	no	—
444	D₄	—	71	3	no	—
445	D₄	—	142	3	no	—
446	D₄	—	142	1	no	—
447	D₄	—	142	3	no	—
448	D₄	—	142	6	no	—
449	D₄	—	142	3	no	—
450	D₄	—	142	3	no	—
451	D₄	—	142	3	no	—
452	D₄	—	142	6	no	—
453	D₄	—	142	3	no	—
454	D₄	—	142	3	no	—
455	D₄	—	142	3	no	—
456	D₄	D₄×D₇₁	1	3	yes	—
457	D₄	C₂³×D₇₁	1	3	yes	—
458	D₄	C₂³×D₇₁	1	3	yes	—
459	C₂×C₄	—	2	3	no	—
460	C₂×C₄	—	2	3	no	—
461	C₂×C₄	—	71	3	no	—
462	C₂×C₄	—	71	3	no	—
463	C₂×C₄	—	71	3	no	—
464	C₂×C₄	—	71	3	no	—
465	C₂×C₄	—	71	1	no	—
466	C₂×C₄	—	142	1	no	—
467	C₂×C₄	—	142	3	no	—
468	C₂×C₄	—	142	1	no	—
469	C₂×C₄	—	142	3	no	—
470	C₂×C₄	—	142	3	no	—
471	C₂×C₄	—	142	3	no	—
472	C₂×C₄	—	142	6	no	—
473	C₂×C₄	—	142	3	no	—
474	C₂×C₄	—	142	3	no	—
475	C₂×C₄	—	142	3	no	—
476	C₂×C₄	C₂³×D₇₁	1	3	yes	—
477	C₈	—	71	1	no	—
478	C₈	—	71	3	no	—
479	C₈	C₂³×D₇₁	1	3	yes	—
480	C₈	C₂³×D₇₁	1	1	yes	characteristic
481	C₂²	—	2	3	no	—
482	C₂²	—	2	3	no	—
483	C₂²	—	8	3	no	—
484	C₂²	—	8	3	no	—
485	C₂²	—	284	3	no	—
486	C₂²	—	284	6	no	—
487	C₂²	—	568	3	no	—
488	C₂²	—	568	6	no	—
489	C₂²	—	568	3	no	—
490	C₂²	—	71	1	no	—
491	C₂²	—	71	3	no	—
492	C₂²	—	142	1	no	—
493	C₂²	—	142	3	no	—
494	C₂²	C₂×D₄×D₇₁	1	3	yes	—
495	C₄	—	2	1	no	—
496	C₄	—	2	1	no	—
497	C₄	—	71	1	no	—
498	C₄	—	71	3	no	—
499	C₄	—	142	1	no	—
500	C₄	—	142	3	no	—
501	C₄	C₂×D₄×D₇₁	1	3	yes	—
502	C₄	C₂⁴×D₇₁	1	1	yes	characteristic
503	C₂	—	2	3	no	—
504	C₂	—	4	3	no	—
505	C₂	—	4	3	no	—
506	C₂	—	284	3	no	—
507	C₂	—	284	1	no	—
508	C₂	—	142	1	no	—
509	C₂	—	142	3	no	—
510	C₂	C₂²×D₄×D₇₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₇₁
commutator	C₄×C₇₁	C₂⁵
Frattini	C₄	C₂⁴×D₇₁
Fitting	#576×C₇₁	C₂
socle	C₂×C₇₁	C₂³×D₄
hypercenter	#576	D₇₁
hypocenter	C₇₁	#3585
LCS	G ▷ C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₂ ◁ #41 ◁ #576

Complements

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

N	H ≅ G/N	type
1. #17986834	C₂	semidirect
2. H(5,𝔽₂)×D₇₁	C₂	semidirect
3. #17986811	C₂	semidirect
4. #17986810	C₂	semidirect
5. #17986809	C₂	semidirect
6. #17986806	C₂	semidirect
7. #17986803	C₂	semidirect
8. #17986802	C₂	semidirect
9. #17986800	C₂	semidirect
10. #17986796	C₂	semidirect
11. #17986795	C₂	semidirect
12. C₂×#14556152	C₂	semidirect
13. AGL(1,ℤ/8)×D₇₁	C₂	semidirect
14. #17986764	C₂	semidirect
15. #576×C₇₁	C₂	semidirect
17. #14556175	C₂²	semidirect
18. #14556175	C₂²	semidirect
20. #14556174	C₂²	semidirect
21. #14556174	C₂²	semidirect
24. #14556173	C₂²	semidirect
25. #14556173	C₂²	semidirect
27. C₂×#11765864	C₂²	semidirect
31. #41×D₇₁	C₂²	semidirect
32. #41×D₇₁	C₂²	semidirect
34. C₂×D₄×D₇₁	C₂²	semidirect
35. #14556161	C₂²	semidirect
36. #14556160	C₂²	semidirect
37. #14556160	C₂²	semidirect
38. #14556158	C₂²	semidirect
39. #14556157	C₂²	semidirect
40. #14556157	C₂²	semidirect
41. #14556156	C₂²	semidirect
42. #14556155	C₂²	semidirect
43. #14556155	C₂²	semidirect
44. #14556154	C₂²	semidirect
45. #14556154	C₂²	semidirect
46. #14556153	C₂²	semidirect
47. #14556152	C₂²	semidirect
48. #14556152	C₂²	semidirect
49. #14556152	C₂²	semidirect
50. #14556152	C₂²	semidirect
51. #14556152	C₂²	semidirect
52. #14556150	C₂²	semidirect
53. #14556149	C₂²	semidirect
54. #14556148	C₂²	semidirect
55. #14556148	C₂²	semidirect
56. #14556147	C₂²	semidirect
57. C₂×#11765854	C₂²	semidirect
58. C₂×#11765853	C₂²	semidirect
59. SD₁₆×D₇₁	C₂²	semidirect
60. C₂×#11765850	C₂²	semidirect
61. D₈×D₇₁	C₂²	semidirect
62. #14556136	C₂²	semidirect
63. #14556135	C₂²	semidirect
64. #14556134	C₂²	semidirect
65. C₂×#11765848	C₂²	semidirect
66. M₁₆×D₇₁	C₂²	semidirect
67. H(5,𝔽₂)×C₇₁	C₂²	semidirect
68. H(5,𝔽₂)×C₇₁	C₂²	semidirect
69. AGL(1,ℤ/8)×C₇₁	C₂²	semidirect
70. AGL(1,ℤ/8)×C₇₁	C₂²	semidirect
71. #135×C₇₁	C₂²	semidirect
72. C₂×D₈×C₇₁	C₂²	semidirect
73. #131×C₇₁	C₂²	semidirect
85. #11765865	C₂³	semidirect
97. #11765864	C₂³	semidirect
99. C₂×Dic₁₄₂	C₂³	semidirect
103. Q₈×D₇₁	C₂³	semidirect
121. D₄×D₇₁	C₂³	semidirect
126. Dic₂₈₄	C₂³	semidirect
127. #11765855	C₂³	semidirect
128. #11765855	C₂³	semidirect
129. #11765854	C₂³	semidirect
130. #11765854	C₂³	semidirect
131. #11765854	C₂³	semidirect
132. #11765853	C₂³	semidirect
133. #11765853	C₂³	semidirect
134. #11765853	C₂³	semidirect
135. #11765852	C₂³	semidirect
136. #11765852	C₂³	semidirect
137. D₅₆₈	C₂³	semidirect
138. #11765850	C₂³	semidirect
139. #11765850	C₂³	semidirect
140. #11765850	C₂³	semidirect
141. #11765849	C₂³	semidirect
144. #11765848	C₂³	semidirect
145. #11765848	C₂³	semidirect
146. C₂×C₇₁⋊C₈	C₂³	semidirect
147. C₈×D₇₁	C₂³	semidirect
152. #41×C₇₁	C₂³	semidirect
156. C₂×D₄×C₇₁	C₂³	semidirect
157. Q₁₆×C₇₁	C₂³	semidirect
158. SD₁₆×C₇₁	C₂³	semidirect
159. SD₁₆×C₇₁	C₂³	semidirect
160. D₈×C₇₁	C₂³	semidirect
161. D₈×C₇₁	C₂³	semidirect
162. M₁₆×C₇₁	C₂³	semidirect
163. C₂×C₈×C₇₁	C₂³	semidirect
256. C₇₁	#3585	semidirect
266. #576	D₇₁	semidirect
282. H(5,𝔽₂)	C₂×D₇₁	semidirect
283. H(5,𝔽₂)	C₂×D₇₁	semidirect
310. AGL(1,ℤ/8)	C₂×D₇₁	semidirect
311. AGL(1,ℤ/8)	C₂×D₇₁	semidirect
317. #135	C₂×D₇₁	semidirect
323. C₂×D₈	C₂×D₇₁	semidirect
327. #131	C₂×D₇₁	semidirect
358. #41	C₂²×D₇₁	semidirect
386. C₂×D₄	C₂²×D₇₁	semidirect
394. Q₁₆	C₂²×D₇₁	semidirect
403. SD₁₆	C₂²×D₇₁	semidirect
404. SD₁₆	C₂²×D₇₁	semidirect
409. D₈	C₂²×D₇₁	semidirect
410. D₈	C₂²×D₇₁	semidirect
416. M₁₆	C₂²×D₇₁	semidirect
419. C₂×C₈	C₂²×D₇₁	semidirect