Subgroups — D₃₁×#577 #16860465

Order 3968.

1460 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	2₋¹⁺⁴×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	H(5,𝔽₂)×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#14521861	C₂	1	1	yes	maximal, characteristic, complemented
4	#14521860	C₂	1	1	yes	maximal, characteristic, complemented
5	#14521859	C₂	1	3	yes	maximal, complemented
6	#14521858	C₂	1	3	yes	maximal, complemented
7	#14521857	C₂	1	1	yes	maximal, characteristic, complemented
8	#14521856	C₂	1	3	yes	maximal, complemented
9	#14521855	C₂	1	3	yes	maximal, complemented
10	#137×D₃₁	C₂	1	3	yes	maximal, complemented
11	AGL(1,ℤ/8)×D₃₁	C₂	1	3	yes	maximal, complemented
12	#135×D₃₁	C₂	1	3	yes	maximal, complemented
13	C₂×SD₁₆×D₃₁	C₂	1	3	yes	maximal, complemented
14	#131×D₃₁	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃₁×#577	C₂	1	1	yes	maximal, characteristic, complemented
16	C₃₁×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
17	C₃₁×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
18	#11758567	—	2	3	no	—
19	#11758567	C₂²	1	3	yes	complemented
20	#11758567	C₂²	1	1	yes	characteristic, complemented
21	#11758566	—	2	1	no	—
22	#11758566	C₂²	1	3	yes	complemented
23	#11758566	C₂²	1	1	yes	characteristic, complemented
24	#41×D₃₁	—	2	1	no	—
25	#41×D₃₁	—	2	3	no	—
26	#41×D₃₁	C₂²	1	3	yes	—
27	#41×D₃₁	C₂²	1	1	yes	characteristic
28	#41×D₃₁	C₂²	1	3	yes	complemented
29	#11758564	—	2	1	no	—
30	#11758564	C₂²	1	3	yes	complemented
31	C₂×Q₈×D₃₁	—	2	1	no	—
32	C₂×Q₈×D₃₁	C₂²	1	3	yes	complemented
33	#11758561	—	2	3	no	—
34	#11758561	C₂²	1	3	yes	complemented
35	C₂×D₄×D₃₁	—	2	3	no	—
36	C₂×D₄×D₃₁	C₂²	1	3	yes	—
37	C₃₁×#137	C₂²	1	3	yes	complemented
38	C₃₁×AGL(1,ℤ/8)	C₂²	1	3	yes	complemented
39	C₃₁×#135	C₂²	1	3	yes	complemented
40	C₂×SD₁₆×C₃₁	C₂²	1	3	yes	complemented
41	C₃₁×#131	C₂²	1	1	yes	characteristic, complemented
42	#11758528	C₂²	1	3	yes	complemented
43	#11758527	C₂²	1	3	yes	complemented
44	#11758527	C₂²	1	3	yes	complemented
45	#11758526	C₂²	1	3	yes	complemented
46	#11758525	C₂²	1	1	yes	characteristic, complemented
47	#11758519	C₂²	1	3	yes	complemented
48	C₂×#92481	C₂²	1	3	yes	complemented
49	C₂×#92480	C₂²	1	3	yes	complemented
50	#11758509	C₂²	1	3	yes	complemented
51	#11758496	C₂²	1	3	yes	complemented
52	#11758495	C₂²	1	6	yes	complemented
53	Q₁₆×D₃₁	C₂²	1	3	yes	complemented
54	#11758493	C₂²	1	3	yes	complemented
55	#11758493	C₂²	1	3	yes	complemented
56	#11758492	C₂²	1	6	yes	complemented
57	#11758491	C₂²	1	6	yes	complemented
58	SD₁₆×D₃₁	C₂²	1	3	yes	complemented
59	SD₁₆×D₃₁	C₂²	1	6	yes	complemented
60	SD₁₆×D₃₁	C₂²	1	1	yes	characteristic, complemented
61	SD₁₆×D₃₁	C₂²	1	6	yes	complemented
62	SD₁₆×D₃₁	C₂²	1	6	yes	complemented
63	#11758489	C₂²	1	3	yes	complemented
64	#11758488	C₂²	1	6	yes	complemented
65	D₈×D₃₁	C₂²	1	3	yes	complemented
66	#11758486	C₂²	1	3	yes	complemented
67	#11758485	C₂²	1	3	yes	complemented
68	#11758484	C₂²	1	3	yes	complemented
69	M₁₆×D₃₁	C₂²	1	3	yes	complemented
70	#11758481	C₂²	1	3	yes	complemented
71	C₂×#92470	C₂²	1	3	yes	complemented
72	#11758478	C₂²	1	3	yes	complemented
73	C₂×C₈×D₃₁	C₂²	1	3	yes	complemented
74	C₂³×D₃₁	—	2	3	no	—
75	#41×C₃₁	—	2	1	no	—
76	#41×C₃₁	—	2	3	no	—
77	#41×C₃₁	C₂³	1	3	yes	—
78	#41×C₃₁	C₂³	1	1	yes	characteristic
79	#41×C₃₁	C₂³	1	3	yes	complemented
80	C₂×Q₈×C₃₁	—	2	1	no	—
81	C₂×Q₈×C₃₁	C₂³	1	3	yes	complemented
82	C₂×D₄×C₃₁	—	2	3	no	—
83	C₂×D₄×C₃₁	C₂³	1	3	yes	—
84	C₂×C₂²⋊D₃₁	—	2	6	no	—
85	C₂×C₂²⋊D₃₁	—	2	3	no	—
86	#92499	—	2	1	no	—
87	#92499	—	2	3	no	—
88	#92499	D₄	1	1	yes	characteristic
89	#92499	C₂³	1	3	yes	—
90	#92499	C₂³	1	3	yes	complemented
91	Q₈×D₃₁	—	2	1	no	—
92	Q₈×D₃₁	—	2	3	no	—
93	Q₈×D₃₁	—	2	3	no	—
94	Q₈×D₃₁	—	2	3	no	—
95	Q₈×D₃₁	D₄	1	1	yes	characteristic
96	Q₈×D₃₁	C₂³	1	3	yes	—
97	Q₈×D₃₁	C₂³	1	1	yes	characteristic
98	Q₈×D₃₁	C₂³	1	6	yes	complemented
99	#92497	—	2	3	no	—
100	#92497	—	2	6	no	—
101	#92497	—	2	3	no	—
102	#92497	—	2	3	no	—
103	#92497	—	2	3	no	—
104	#92497	D₄	1	3	yes	—
105	#92497	C₂³	1	3	yes	—
106	#92497	C₂³	1	3	yes	complemented
107	D₄×D₃₁	—	2	3	no	—
108	D₄×D₃₁	—	2	3	no	—
109	D₄×D₃₁	—	2	3	no	—
110	D₄×D₃₁	—	2	6	no	—
111	D₄×D₃₁	—	2	3	no	—
112	D₄×D₃₁	—	2	3	no	—
113	D₄×D₃₁	—	2	3	no	—
114	D₄×D₃₁	D₄	1	3	yes	—
115	D₄×D₃₁	C₂³	1	1	yes	characteristic
116	D₄×D₃₁	C₂³	1	3	yes	—
117	D₄×D₃₁	C₂³	1	6	yes	—
118	#92495	—	2	6	no	—
119	#92495	—	2	3	no	—
120	#92495	—	2	3	no	—
121	#92495	—	2	3	no	—
122	#92495	—	2	3	no	—
123	#92495	C₂³	1	3	yes	—
124	#92495	C₂³	1	3	yes	—
125	#92495	C₂³	1	3	yes	complemented
126	C₂×D₁₂₄	—	2	3	no	—
127	C₂×D₁₂₄	C₂³	1	3	yes	—
128	C₂×C₄×D₃₁	—	2	3	no	—
129	C₂×C₄×D₃₁	—	2	3	no	—
130	C₂×C₄×D₃₁	—	2	3	no	—
131	C₂×C₄×D₃₁	C₂³	1	3	yes	—
132	C₂×Dic₆₂	—	2	3	no	—
133	C₂×Dic₆₂	—	2	3	no	—
134	C₂×Dic₆₂	C₂³	1	3	yes	complemented
135	Q₁₆×C₃₁	C₂³	1	3	yes	complemented
136	SD₁₆×C₃₁	C₂³	1	3	yes	complemented
137	SD₁₆×C₃₁	C₂³	1	6	yes	complemented
138	SD₁₆×C₃₁	C₂³	1	1	yes	characteristic, complemented
139	D₈×C₃₁	C₂³	1	3	yes	complemented
140	M₁₆×C₃₁	C₂³	1	3	yes	complemented
141	C₂×C₈×C₃₁	C₂³	1	3	yes	complemented
142	#92482	C₂³	1	3	yes	complemented
143	#92482	C₂³	1	3	yes	complemented
144	#92481	C₂³	1	3	yes	complemented
145	#92481	C₂³	1	6	yes	complemented
146	#92481	C₂³	1	1	yes	characteristic, complemented
147	#92480	C₂³	1	6	yes	complemented
148	#92480	C₂³	1	1	yes	characteristic, complemented
149	#92480	C₂³	1	3	yes	complemented
150	#92479	C₂³	1	3	yes	complemented
151	#92479	C₂³	1	3	yes	complemented
152	#92474	C₂³	1	3	yes	complemented
153	C₂×C₃₁⋊C₈	C₂³	1	3	yes	complemented
154	Dic₁₂₄	C₂³	1	3	yes	complemented
155	D₂₄₈	C₂³	1	3	yes	complemented
156	#92470	C₂³	1	3	yes	complemented
157	#92470	C₂³	1	6	yes	complemented
158	#92470	C₂³	1	1	yes	characteristic, complemented
159	#92469	C₂³	1	6	yes	complemented
160	C₈×D₃₁	C₂³	1	1	yes	characteristic
161	C₈×D₃₁	C₂³	1	3	yes	—
162	C₈×D₃₁	C₂³	1	3	yes	complemented
163	C₈×D₃₁	C₂³	1	3	yes	complemented
164	C₂³×C₃₁	—	2	3	no	—
165	C₂²×D₃₁	—	2	3	no	—
166	C₂²×D₃₁	—	2	1	no	—
167	C₂²×D₃₁	—	2	3	no	—
168	C₂²×D₃₁	—	2	6	no	—
169	C₂²×D₃₁	—	8	6	no	—
170	C₂²×D₃₁	C₂×D₄	1	3	yes	—
171	Q₈×C₃₁	—	2	3	no	—
172	Q₈×C₃₁	C₂×D₄	1	1	yes	characteristic
173	Q₈×C₃₁	C₂⁴	1	3	yes	—
174	Q₈×C₃₁	C₂⁴	1	1	yes	characteristic
175	D₄×C₃₁	—	2	3	no	—
176	D₄×C₃₁	—	2	3	no	—
177	D₄×C₃₁	—	2	3	no	—
178	D₄×C₃₁	C₂×D₄	1	3	yes	—
179	D₄×C₃₁	C₂⁴	1	1	yes	characteristic
180	D₄×C₃₁	C₂⁴	1	3	yes	—
181	C₂×C₄×C₃₁	—	2	3	no	—
182	C₂×C₄×C₃₁	—	2	3	no	—
183	C₂×C₄×C₃₁	—	2	3	no	—
184	C₂×C₄×C₃₁	C₂⁴	1	3	yes	—
185	C₂²⋊D₃₁	—	2	3	no	—
186	C₂²⋊D₃₁	—	2	3	no	—
187	C₂²⋊D₃₁	—	2	3	no	—
188	C₂²⋊D₃₁	—	2	3	no	—
189	C₂²⋊D₃₁	—	2	1	no	—
190	C₂²⋊D₃₁	—	2	3	no	—
191	C₂²⋊D₃₁	—	2	6	no	—
192	C₂²⋊D₃₁	C₂×D₄	1	6	yes	—
193	C₂×Dic₃₁	—	2	3	no	—
194	C₂×Dic₃₁	—	2	3	no	—
195	C₂×Dic₃₁	—	2	3	no	—
196	C₂×Dic₃₁	C₂×D₄	1	3	yes	—
197	D₁₂₄	—	2	3	no	—
198	D₁₂₄	—	2	3	no	—
199	D₁₂₄	—	2	3	no	—
200	D₁₂₄	C₂×D₄	1	3	yes	—
201	D₁₂₄	C₂⁴	1	3	yes	—
202	D₁₂₄	C₂⁴	1	1	yes	characteristic
203	C₄×D₃₁	—	2	1	no	—
204	C₄×D₃₁	—	2	3	no	—
205	C₄×D₃₁	—	2	6	no	—
206	C₄×D₃₁	—	2	3	no	—
207	C₄×D₃₁	—	2	3	no	—
208	C₄×D₃₁	—	2	3	no	—
209	C₄×D₃₁	—	2	3	no	—
210	C₄×D₃₁	C₂×D₄	1	3	yes	—
211	C₄×D₃₁	C₂×D₄	1	3	yes	—
212	C₄×D₃₁	C₂⁴	1	1	yes	characteristic
213	C₄×D₃₁	C₂⁴	1	3	yes	—
214	Dic₆₂	—	2	3	no	—
215	Dic₆₂	—	2	3	no	—
216	Dic₆₂	—	2	6	no	—
217	Dic₆₂	—	2	1	no	—
218	Dic₆₂	C₂×D₄	1	3	yes	—
219	Dic₆₂	C₂⁴	1	3	yes	—
220	Dic₆₂	C₂⁴	1	1	yes	characteristic
221	C₈×C₃₁	C₂⁴	1	1	yes	characteristic
222	C₈×C₃₁	C₂⁴	1	3	yes	—
223	C₃₁⋊C₈	C₂⁴	1	1	yes	characteristic
224	C₃₁⋊C₈	C₂⁴	1	3	yes	—
225	C₂×#577	—	31	1	no	maximal, Sylow
226	C₂²×C₃₁	—	2	1	no	—
227	C₂²×C₃₁	—	2	3	no	—
228	C₂²×C₃₁	—	8	3	no	—
229	C₂²×C₃₁	C₂²×D₄	1	3	yes	—
230	C₂×D₃₁	—	2	6	no	—
231	C₂×D₃₁	—	2	1	no	—
232	C₂×D₃₁	—	2	3	no	—
233	C₂×D₃₁	—	4	2	no	—
234	C₂×D₃₁	—	4	6	no	—
235	C₂×D₃₁	—	8	6	no	—
236	C₂×D₃₁	—	8	3	no	—
237	C₂×D₃₁	C₂²×D₄	1	3	yes	—
238	C₂×D₃₁	C₂²×D₄	1	1	yes	characteristic
239	C₄×C₃₁	—	2	3	no	—
240	C₄×C₃₁	—	2	1	no	—
241	C₄×C₃₁	C₂²×D₄	1	3	yes	—
242	C₄×C₃₁	C₂⁵	1	1	yes	characteristic
243	Dic₃₁	—	2	3	no	—
244	Dic₃₁	—	2	1	no	—
245	Dic₃₁	C₂²×D₄	1	1	yes	characteristic
246	Dic₃₁	C₂²×D₄	1	3	yes	—
247	C₂×2₋¹⁺⁴	—	31	1	no	—
248	C₂×H(5,𝔽₂)	—	31	1	no	—
249	#577	—	31	1	no	—
250	#577	—	31	1	no	—
251	#577	—	31	3	no	—
252	#577	—	31	3	no	—
253	#577	—	31	3	no	—
254	#577	—	31	3	no	—
255	#577	—	31	1	no	—
256	#577	D₃₁	1	1	yes	characteristic, direct product factor
257	C₂×#137	—	31	3	no	—
258	C₂×AGL(1,ℤ/8)	—	31	3	no	—
259	C₂×#135	—	31	3	no	—
260	C₂²×SD₁₆	—	31	3	no	—
261	C₂×#131	—	31	1	no	—
262	C₂×C₃₁	—	2	3	no	—
263	C₂×C₃₁	—	4	3	no	—
264	C₂×C₃₁	—	4	1	no	—
265	C₂×C₃₁	C₂³×D₄	1	1	yes	characteristic
266	D₃₁	—	2	3	no	—
267	D₃₁	—	4	1	no	—
268	D₃₁	—	4	3	no	—
269	D₃₁	#577	1	2	yes	direct product factor
270	2₋¹⁺⁴	—	31	1	no	—
271	2₋¹⁺⁴	—	31	3	no	—
272	2₋¹⁺⁴	—	31	3	no	—
273	2₋¹⁺⁴	—	62	1	no	—
274	2₋¹⁺⁴	—	62	3	no	—
275	2₋¹⁺⁴	C₂×D₃₁	1	1	yes	characteristic, complemented
276	H(5,𝔽₂)	—	31	3	no	—
277	H(5,𝔽₂)	—	31	1	no	—
278	H(5,𝔽₂)	—	31	3	no	—
279	H(5,𝔽₂)	—	62	3	no	—
280	H(5,𝔽₂)	—	62	1	no	—
281	H(5,𝔽₂)	C₂×D₃₁	1	1	yes	characteristic, complemented
282	C₂×#41	—	31	1	no	—
283	C₂×#41	—	31	3	no	—
284	C₂×#41	—	31	3	no	—
285	C₂×#41	—	62	3	no	—
286	C₂×#41	—	62	1	no	—
287	C₂²×Q₈	—	31	3	no	—
288	C₂²×Q₈	—	62	1	no	—
289	C₂²×D₄	—	31	3	no	—
290	C₂²×D₄	—	62	3	no	—
291	#137	—	31	3	no	—
292	#137	—	31	3	no	—
293	#137	—	31	6	no	—
294	#137	—	31	6	no	—
295	#137	—	31	3	no	—
296	#137	C₂×D₃₁	1	3	yes	complemented
297	AGL(1,ℤ/8)	—	31	3	no	—
298	AGL(1,ℤ/8)	—	31	3	no	—
299	AGL(1,ℤ/8)	—	31	6	no	—
300	AGL(1,ℤ/8)	—	31	6	no	—
301	AGL(1,ℤ/8)	—	31	3	no	—
302	AGL(1,ℤ/8)	C₂×D₃₁	1	3	yes	complemented
303	#135	—	31	3	no	—
304	#135	—	31	3	no	—
305	#135	—	31	3	no	—
306	#135	—	31	3	no	—
307	#135	—	31	3	no	—
308	#135	—	31	3	no	—
309	#135	—	31	3	no	—
310	#135	C₂×D₃₁	1	3	yes	complemented
311	C₂×Q₁₆	—	31	3	no	—
312	C₂×SD₁₆	—	31	3	no	—
313	C₂×SD₁₆	—	31	3	no	—
314	C₂×SD₁₆	—	31	3	no	—
315	C₂×SD₁₆	—	31	6	no	—
316	C₂×SD₁₆	—	31	6	no	—
317	C₂×SD₁₆	—	31	6	no	—
318	C₂×SD₁₆	—	31	1	no	—
319	C₂×SD₁₆	—	31	3	no	—
320	C₂×SD₁₆	C₂×D₃₁	1	3	yes	complemented
321	C₂×D₈	—	31	3	no	—
322	#131	—	31	1	no	—
323	#131	—	31	3	no	—
324	#131	—	31	3	no	—
325	#131	C₂×D₃₁	1	1	yes	characteristic, complemented
326	C₂×M₁₆	—	31	3	no	—
327	C₂²×C₈	—	31	3	no	—
328	C₃₁	C₂×#577	1	1	yes	characteristic, complemented, Sylow
329	C₂⁴	—	62	3	no	—
330	#41	—	2	1	no	—
331	#41	—	2	3	no	—
332	#41	—	31	1	no	—
333	#41	—	31	3	no	—
334	#41	—	31	3	no	—
335	#41	—	31	3	no	—
336	#41	—	31	3	no	—
337	#41	—	31	3	no	—
338	#41	—	31	3	no	—
339	#41	—	31	3	no	—
340	#41	—	31	3	no	—
341	#41	—	62	3	no	—
342	#41	—	62	3	no	—
343	#41	—	62	6	no	—
344	#41	—	62	3	no	—
345	#41	—	62	3	no	—
346	#41	—	62	3	no	—
347	#41	—	62	3	no	—
348	#41	—	62	6	no	—
349	#41	—	62	3	no	—
350	#41	—	62	3	no	—
351	#41	—	62	1	no	—
352	#41	—	62	3	no	—
353	#41	C₂²×D₃₁	1	3	yes	—
354	#41	C₂²×D₃₁	1	1	yes	characteristic
355	#41	C₂²×D₃₁	1	3	yes	complemented
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	31	1	no	—
358	C₂×Q₈	—	31	3	no	—
359	C₂×Q₈	—	31	1	no	—
360	C₂×Q₈	—	31	6	no	—
361	C₂×Q₈	—	31	3	no	—
362	C₂×Q₈	—	62	3	no	—
363	C₂×Q₈	—	62	3	no	—
364	C₂×Q₈	—	62	3	no	—
365	C₂×Q₈	—	62	3	no	—
366	C₂×Q₈	—	62	3	no	—
367	C₂×Q₈	—	62	1	no	—
368	C₂×Q₈	C₂²×D₃₁	1	3	yes	complemented
369	C₂×D₄	—	2	3	no	—
370	C₂×D₄	—	31	3	no	—
371	C₂×D₄	—	31	1	no	—
372	C₂×D₄	—	31	3	no	—
373	C₂×D₄	—	31	6	no	—
374	C₂×D₄	—	31	3	no	—
375	C₂×D₄	—	62	3	no	—
376	C₂×D₄	—	62	3	no	—
377	C₂×D₄	—	62	3	no	—
378	C₂×D₄	—	62	3	no	—
379	C₂×D₄	—	62	6	no	—
380	C₂×D₄	—	62	3	no	—
381	C₂×D₄	—	62	3	no	—
382	C₂×D₄	—	62	3	no	—
383	C₂×D₄	—	62	6	no	—
384	C₂×D₄	—	62	3	no	—
385	C₂×D₄	C₂²×D₃₁	1	3	yes	—
386	C₂²×C₄	—	31	3	no	—
387	C₂²×C₄	—	62	3	no	—
388	C₂²×C₄	—	62	3	no	—
389	C₂²×C₄	—	62	3	no	—
390	Q₁₆	—	31	3	no	—
391	Q₁₆	—	31	3	no	—
392	Q₁₆	—	31	3	no	—
393	Q₁₆	C₂²×D₃₁	1	3	yes	complemented
394	SD₁₆	—	31	3	no	—
395	SD₁₆	—	31	6	no	—
396	SD₁₆	—	31	1	no	—
397	SD₁₆	—	31	3	no	—
398	SD₁₆	—	31	6	no	—
399	SD₁₆	—	31	1	no	—
400	SD₁₆	—	31	3	no	—
401	SD₁₆	—	31	6	no	—
402	SD₁₆	—	31	1	no	—
403	SD₁₆	C₂²×D₃₁	1	3	yes	complemented
404	SD₁₆	C₂²×D₃₁	1	6	yes	complemented
405	SD₁₆	C₂²×D₃₁	1	1	yes	characteristic, complemented
406	D₈	—	31	3	no	—
407	D₈	—	31	3	no	—
408	D₈	—	31	3	no	—
409	D₈	C₂²×D₃₁	1	3	yes	complemented
410	M₁₆	—	31	3	no	—
411	M₁₆	—	31	6	no	—
412	M₁₆	C₂²×D₃₁	1	3	yes	complemented
413	C₂×C₈	—	31	3	no	—
414	C₂×C₈	—	31	1	no	—
415	C₂×C₈	—	31	3	no	—
416	C₂×C₈	—	31	3	no	—
417	C₂×C₈	—	31	3	no	—
418	C₂×C₈	C₂²×D₃₁	1	3	yes	complemented
419	C₂³	—	2	3	no	—
420	C₂³	—	31	3	no	—
421	C₂³	—	62	1	no	—
422	C₂³	—	62	3	no	—
423	C₂³	—	62	6	no	—
424	C₂³	—	62	3	no	—
425	C₂³	—	248	6	no	—
426	Q₈	—	2	3	no	—
427	Q₈	—	31	3	no	—
428	Q₈	—	31	3	no	—
429	Q₈	—	31	1	no	—
430	Q₈	—	62	3	no	—
431	Q₈	—	62	6	no	—
432	Q₈	—	62	1	no	—
433	Q₈	—	62	3	no	—
434	Q₈	D₄×D₃₁	1	1	yes	characteristic
435	Q₈	C₂³×D₃₁	1	3	yes	—
436	Q₈	C₂³×D₃₁	1	1	yes	characteristic
437	D₄	—	2	3	no	—
438	D₄	—	2	3	no	—
439	D₄	—	2	3	no	—
440	D₄	—	31	6	no	—
441	D₄	—	31	3	no	—
442	D₄	—	31	1	no	—
443	D₄	—	31	3	no	—
444	D₄	—	62	3	no	—
445	D₄	—	62	3	no	—
446	D₄	—	62	3	no	—
447	D₄	—	62	6	no	—
448	D₄	—	62	1	no	—
449	D₄	—	62	3	no	—
450	D₄	—	62	3	no	—
451	D₄	—	62	3	no	—
452	D₄	—	62	3	no	—
453	D₄	—	62	3	no	—
454	D₄	D₄×D₃₁	1	3	yes	—
455	D₄	C₂³×D₃₁	1	1	yes	characteristic
456	D₄	C₂³×D₃₁	1	3	yes	—
457	C₂×C₄	—	2	3	no	—
458	C₂×C₄	—	2	3	no	—
459	C₂×C₄	—	2	3	no	—
460	C₂×C₄	—	31	3	no	—
461	C₂×C₄	—	31	3	no	—
462	C₂×C₄	—	31	3	no	—
463	C₂×C₄	—	31	1	no	—
464	C₂×C₄	—	31	3	no	—
465	C₂×C₄	—	62	3	no	—
466	C₂×C₄	—	62	3	no	—
467	C₂×C₄	—	62	1	no	—
468	C₂×C₄	—	62	3	no	—
469	C₂×C₄	—	62	6	no	—
470	C₂×C₄	—	62	3	no	—
471	C₂×C₄	—	62	3	no	—
472	C₂×C₄	—	62	3	no	—
473	C₂×C₄	—	62	3	no	—
474	C₂×C₄	—	62	3	no	—
475	C₂×C₄	C₂³×D₃₁	1	3	yes	—
476	C₈	—	31	1	no	—
477	C₈	—	31	3	no	—
478	C₈	C₂³×D₃₁	1	1	yes	characteristic
479	C₈	C₂³×D₃₁	1	3	yes	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	3	no	—
482	C₂²	—	8	3	no	—
483	C₂²	—	31	1	no	—
484	C₂²	—	31	3	no	—
485	C₂²	—	62	6	no	—
486	C₂²	—	62	1	no	—
487	C₂²	—	62	3	no	—
488	C₂²	—	124	6	no	—
489	C₂²	—	124	2	no	—
490	C₂²	—	248	3	no	—
491	C₂²	—	248	6	no	—
492	C₂²	C₂×D₄×D₃₁	1	3	yes	—
493	C₄	—	2	1	no	—
494	C₄	—	2	3	no	—
495	C₄	—	31	1	no	—
496	C₄	—	31	3	no	—
497	C₄	—	62	1	no	—
498	C₄	—	62	3	no	—
499	C₄	C₂×D₄×D₃₁	1	3	yes	—
500	C₄	C₂⁴×D₃₁	1	1	yes	characteristic
501	C₂	—	2	3	no	—
502	C₂	—	4	3	no	—
503	C₂	—	4	1	no	—
504	C₂	—	31	2	no	—
505	C₂	—	62	3	no	—
506	C₂	—	124	3	no	—
507	C₂	—	124	1	no	—
508	C₂	C₂²×D₄×D₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²×D₄×D₃₁
commutator, cosocle	C₄×C₃₁	C₂⁵
Frattini	C₄	C₂⁴×D₃₁
Fitting	C₃₁×#577	C₂
socle	C₂×C₃₁	C₂³×D₄
hypercenter	#577	D₃₁
hypocenter	C₃₁	C₂×#577
LCS	G ▷ C₄×C₃₁ ▷ C₂×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂ ◁ #41 ◁ #577

Complements

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

N	H ≅ G/N	type
1. 2₋¹⁺⁴×D₃₁	C₂	semidirect
2. H(5,𝔽₂)×D₃₁	C₂	semidirect
3. #14521861	C₂	semidirect
4. #14521860	C₂	semidirect
5. #14521859	C₂	semidirect
6. #14521858	C₂	semidirect
7. #14521857	C₂	semidirect
8. #14521856	C₂	semidirect
9. #14521855	C₂	semidirect
10. #137×D₃₁	C₂	semidirect
11. AGL(1,ℤ/8)×D₃₁	C₂	semidirect
12. #135×D₃₁	C₂	semidirect
13. C₂×SD₁₆×D₃₁	C₂	semidirect
14. #131×D₃₁	C₂	semidirect
15. C₃₁×#577	C₂	semidirect
16. C₃₁×2₋¹⁺⁴	C₂²	semidirect
17. C₃₁×H(5,𝔽₂)	C₂²	semidirect
19. #11758567	C₂²	semidirect
20. #11758567	C₂²	semidirect
22. #11758566	C₂²	semidirect
23. #11758566	C₂²	semidirect
28. #41×D₃₁	C₂²	semidirect
30. #11758564	C₂²	semidirect
32. C₂×Q₈×D₃₁	C₂²	semidirect
34. #11758561	C₂²	semidirect
37. C₃₁×#137	C₂²	semidirect
38. C₃₁×AGL(1,ℤ/8)	C₂²	semidirect
39. C₃₁×#135	C₂²	semidirect
40. C₂×SD₁₆×C₃₁	C₂²	semidirect
41. C₃₁×#131	C₂²	semidirect
42. #11758528	C₂²	semidirect
43. #11758527	C₂²	semidirect
44. #11758527	C₂²	semidirect
45. #11758526	C₂²	semidirect
46. #11758525	C₂²	semidirect
47. #11758519	C₂²	semidirect
48. C₂×#92481	C₂²	semidirect
49. C₂×#92480	C₂²	semidirect
50. #11758509	C₂²	semidirect
51. #11758496	C₂²	semidirect
52. #11758495	C₂²	semidirect
53. Q₁₆×D₃₁	C₂²	semidirect
54. #11758493	C₂²	semidirect
55. #11758493	C₂²	semidirect
56. #11758492	C₂²	semidirect
57. #11758491	C₂²	semidirect
58. SD₁₆×D₃₁	C₂²	semidirect
59. SD₁₆×D₃₁	C₂²	semidirect
60. SD₁₆×D₃₁	C₂²	semidirect
61. SD₁₆×D₃₁	C₂²	semidirect
62. SD₁₆×D₃₁	C₂²	semidirect
63. #11758489	C₂²	semidirect
64. #11758488	C₂²	semidirect
65. D₈×D₃₁	C₂²	semidirect
66. #11758486	C₂²	semidirect
67. #11758485	C₂²	semidirect
68. #11758484	C₂²	semidirect
69. M₁₆×D₃₁	C₂²	semidirect
70. #11758481	C₂²	semidirect
71. C₂×#92470	C₂²	semidirect
72. #11758478	C₂²	semidirect
73. C₂×C₈×D₃₁	C₂²	semidirect
79. #41×C₃₁	C₂³	semidirect
81. C₂×Q₈×C₃₁	C₂³	semidirect
90. #92499	C₂³	semidirect
98. Q₈×D₃₁	C₂³	semidirect
106. #92497	C₂³	semidirect
125. #92495	C₂³	semidirect
134. C₂×Dic₆₂	C₂³	semidirect
135. Q₁₆×C₃₁	C₂³	semidirect
136. SD₁₆×C₃₁	C₂³	semidirect
137. SD₁₆×C₃₁	C₂³	semidirect
138. SD₁₆×C₃₁	C₂³	semidirect
139. D₈×C₃₁	C₂³	semidirect
140. M₁₆×C₃₁	C₂³	semidirect
141. C₂×C₈×C₃₁	C₂³	semidirect
142. #92482	C₂³	semidirect
143. #92482	C₂³	semidirect
144. #92481	C₂³	semidirect
145. #92481	C₂³	semidirect
146. #92481	C₂³	semidirect
147. #92480	C₂³	semidirect
148. #92480	C₂³	semidirect
149. #92480	C₂³	semidirect
150. #92479	C₂³	semidirect
151. #92479	C₂³	semidirect
152. #92474	C₂³	semidirect
153. C₂×C₃₁⋊C₈	C₂³	semidirect
154. Dic₁₂₄	C₂³	semidirect
155. D₂₄₈	C₂³	semidirect
156. #92470	C₂³	semidirect
157. #92470	C₂³	semidirect
158. #92470	C₂³	semidirect
159. #92469	C₂³	semidirect
162. C₈×D₃₁	C₂³	semidirect
163. C₈×D₃₁	C₂³	semidirect
256. #577	D₃₁	direct (N × H)
269. D₃₁	#577	direct (N × H)
275. 2₋¹⁺⁴	C₂×D₃₁	semidirect
281. H(5,𝔽₂)	C₂×D₃₁	semidirect
296. #137	C₂×D₃₁	semidirect
302. AGL(1,ℤ/8)	C₂×D₃₁	semidirect
310. #135	C₂×D₃₁	semidirect
320. C₂×SD₁₆	C₂×D₃₁	semidirect
325. #131	C₂×D₃₁	semidirect
328. C₃₁	C₂×#577	semidirect
355. #41	C₂²×D₃₁	semidirect
368. C₂×Q₈	C₂²×D₃₁	semidirect
393. Q₁₆	C₂²×D₃₁	semidirect
403. SD₁₆	C₂²×D₃₁	semidirect
404. SD₁₆	C₂²×D₃₁	semidirect
405. SD₁₆	C₂²×D₃₁	semidirect
409. D₈	C₂²×D₃₁	semidirect
412. M₁₆	C₂²×D₃₁	semidirect
418. C₂×C₈	C₂²×D₃₁	semidirect

Maximal subgroups

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

subgroup	index
2₋¹⁺⁴×D₃₁	2
H(5,𝔽₂)×D₃₁	2
#14521861	2
#14521860	2
#14521859	2
#14521858	2
#14521857	2
#14521856	2
#14521855	2
#137×D₃₁	2
AGL(1,ℤ/8)×D₃₁	2
#135×D₃₁	2
C₂×SD₁₆×D₃₁	2
#131×D₃₁	2
C₃₁×#577	2
C₂×#577	31

Subgroups — D31×#577 #16860465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃₁×#577 #16860465