Subgroups — #16776776

Order 3328.

10894 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129646	C₂	1	2	yes	maximal, complemented
2	#13129616	C₂	1	2	yes	maximal, complemented
3	#13129612	C₂	1	12	yes	maximal, complemented
4	#13129611	C₂	1	16	yes	maximal, complemented
5	#13129610	C₂	1	1	yes	maximal, characteristic, complemented
6	#13129605	C₂	1	6	yes	maximal, complemented
7	#13129604	C₂	1	8	yes	maximal, complemented
8	C₂×#11719462	C₂	1	6	yes	maximal, complemented
9	D₁₃×#576	C₂	1	8	yes	maximal, complemented
10	#13129547	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#576	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
13	#11719650	—	2	8	no	—
14	#11719650	C₂²	1	16	yes	complemented
15	D₁₃×H(5,𝔽₂)	—	2	8	no	—
16	D₁₃×H(5,𝔽₂)	C₂²	1	16	yes	complemented
17	#11719648	—	2	4	no	—
18	#11719648	C₂²	1	1	yes	characteristic
19	#11719648	C₂²	1	12	yes	complemented
20	#11719648	C₂²	1	2	yes	complemented
21	C₂×#88251	—	2	12	no	—
22	C₂×#88251	C₂²	1	12	yes	complemented
23	C₁₃×#576	C₂²	1	8	yes	complemented
24	C₁₃×#576	C₂²	1	8	yes	complemented
25	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	6	yes	complemented
26	C₂×C₁₃×#135	C₂²	1	3	yes	complemented
27	C₂²×C₁₃×D₈	C₂²	1	3	yes	complemented
28	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
29	#11719541	C₂²	1	16	yes	complemented
30	#11719540	C₂²	1	16	yes	complemented
31	#11719527	C₂²	1	12	yes	complemented
32	#11719524	C₂²	1	1	yes	characteristic, complemented
33	C₂×#88186	C₂²	1	12	yes	complemented
34	#11719480	C₂²	1	48	yes	complemented
35	#11719479	C₂²	1	48	yes	complemented
36	#11719478	C₂²	1	48	yes	complemented
37	D₁₃×AGL(1,ℤ/8)	C₂²	1	48	yes	complemented
38	#11719476	C₂²	1	12	yes	complemented
39	#11719475	C₂²	1	24	yes	complemented
40	#11719474	C₂²	1	12	yes	complemented
41	#11719473	C₂²	1	24	yes	complemented
42	D₁₃×#135	C₂²	1	24	yes	complemented
43	#11719471	C₂²	1	4	yes	complemented
44	#11719467	C₂²	1	24	yes	complemented
45	#11719462	C₂²	1	24	yes	complemented
46	#11719462	C₂²	1	12	yes	complemented
47	#11719462	C₂²	1	24	yes	complemented
48	#11719462	C₂²	1	24	yes	complemented
49	C₂×#88166	C₂²	1	12	yes	complemented
50	C₂×#88165	C₂²	1	24	yes	complemented
51	C₂×D₈×D₁₃	C₂²	1	12	yes	complemented
52	#11719458	C₂²	1	4	yes	complemented
53	#11719457	C₂²	1	4	yes	complemented
54	#11719456	C₂²	1	8	yes	complemented
55	#11719455	C₂²	1	8	yes	complemented
56	D₁₃×#131	C₂²	1	8	yes	complemented
57	#11719453	C₂²	1	6	yes	complemented
58	#11719450	C₂²	1	6	yes	complemented
59	C₂×#88158	C₂²	1	6	yes	complemented
60	C₂×#88155	C₂²	1	6	yes	complemented
61	C₁₃×H(5,𝔽₂)	—	2	8	no	—
62	C₁₃×H(5,𝔽₂)	C₂³	1	16	yes	complemented
63	C₂×C₁₃×#41	—	2	2	no	—
64	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×#41	C₂³	1	6	yes	complemented
66	C₂²×D₄×C₁₃	—	2	6	no	—
67	C₂²×D₄×C₁₃	C₂³	1	6	yes	complemented
68	C₂²×C₂²⋊D₁₃	—	2	24	no	—
69	#88257	—	2	16	no	—
70	#88257	—	2	12	no	—
71	#88257	D₄	1	4	yes	—
72	#88257	C₂³	1	24	yes	complemented
73	#88257	C₂³	1	8	yes	complemented
74	#88256	—	2	16	no	—
75	#88256	—	2	12	no	—
76	#88256	D₄	1	4	yes	—
77	#88256	C₂³	1	24	yes	complemented
78	#88256	C₂³	1	8	yes	complemented
79	#41×D₁₃	—	2	8	no	—
80	#41×D₁₃	—	2	16	no	—
81	#41×D₁₃	—	2	16	no	—
82	#41×D₁₃	—	2	24	no	—
83	#41×D₁₃	C₂³	1	8	yes	—
84	#41×D₁₃	C₂³	1	48	yes	complemented
85	#88254	—	2	2	no	—
86	#88254	D₄	1	2	yes	—
87	#88254	C₂³	1	8	yes	complemented
88	#88251	—	2	6	no	—
89	#88251	—	2	24	no	—
90	#88251	—	2	48	no	—
91	#88251	—	2	48	no	—
92	#88251	—	2	24	no	—
93	#88251	—	2	24	no	—
94	#88251	D₄	1	6	yes	—
95	#88251	C₂³	1	24	yes	complemented
96	#88251	C₂³	1	48	yes	complemented
97	C₂×#6129	—	2	48	no	—
98	C₂×#6129	—	2	12	no	—
99	C₂×#6129	C₂³	1	24	yes	complemented
100	C₂×D₄×D₁₃	—	2	48	no	—
101	C₂×D₄×D₁₃	—	2	12	no	—
102	C₂×D₄×D₁₃	C₂³	1	24	yes	complemented
103	C₂×#6127	—	2	24	no	—
104	C₂×#6127	C₂³	1	6	yes	—
105	C₂×#6127	C₂³	1	12	yes	complemented
106	C₁₃×AGL(1,ℤ/8)	C₂³	1	48	yes	complemented
107	C₁₃×#135	C₂³	1	12	yes	complemented
108	C₁₃×#135	C₂³	1	12	yes	complemented
109	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic, complemented
110	C₂×C₁₃×SD₁₆	C₂³	1	6	yes	complemented
111	C₂×C₁₃×D₈	C₂³	1	12	yes	complemented
112	C₂×C₁₃×D₈	C₂³	1	12	yes	complemented
113	C₂×C₁₃×D₈	C₂³	1	3	yes	complemented
114	C₂×C₁₃×D₈	C₂³	1	6	yes	complemented
115	C₁₃×#131	C₂³	1	4	yes	complemented
116	C₁₃×#131	C₂³	1	4	yes	complemented
117	C₂×C₁₃×M₁₆	C₂³	1	3	yes	complemented
118	C₂²×C₈×C₁₃	C₂³	1	3	yes	complemented
119	#88205	C₂³	1	24	yes	complemented
120	#88204	C₂³	1	48	yes	complemented
121	#88203	C₂³	1	24	yes	complemented
122	#88202	C₂³	1	8	yes	complemented
123	#88196	C₂³	1	8	yes	complemented
124	C₂×#6105	C₂³	1	24	yes	complemented
125	#88186	C₂³	1	24	yes	complemented
126	#88186	C₂³	1	48	yes	complemented
127	C₂×#6104	C₂³	1	24	yes	complemented
128	C₂×#6099	C₂³	1	6	yes	complemented
129	#88173	C₂³	1	8	yes	complemented
130	#88172	C₂³	1	16	yes	complemented
131	Q₁₆×D₁₃	C₂³	1	8	yes	complemented
132	#88170	C₂³	1	48	yes	complemented
133	#88169	C₂³	1	48	yes	complemented
134	#88168	C₂³	1	48	yes	complemented
135	SD₁₆×D₁₃	C₂³	1	48	yes	complemented
136	#88166	C₂³	1	24	yes	complemented
137	#88166	C₂³	1	48	yes	complemented
138	#88165	C₂³	1	48	yes	complemented
139	#88165	C₂³	1	96	yes	complemented
140	D₈×D₁₃	C₂³	1	24	yes	complemented
141	D₈×D₁₃	C₂³	1	48	yes	complemented
142	#88163	C₂³	1	24	yes	complemented
143	#88162	C₂³	1	24	yes	complemented
144	#88161	C₂³	1	24	yes	complemented
145	M₁₆×D₁₃	C₂³	1	24	yes	complemented
146	C₂×Dic₅₂	C₂³	1	6	yes	complemented
147	#88158	C₂³	1	4	yes	complemented
148	#88158	C₂³	1	12	yes	complemented
149	#88158	C₂³	1	12	yes	complemented
150	#88158	C₂³	1	12	yes	complemented
151	C₂×D₁₀₄	C₂³	1	6	yes	complemented
152	C₂×#6095	C₂³	1	12	yes	complemented
153	#88155	C₂³	1	4	yes	complemented
154	#88155	C₂³	1	12	yes	complemented
155	#88155	C₂³	1	12	yes	complemented
156	#88155	C₂³	1	12	yes	complemented
157	C₂×#6094	C₂³	1	12	yes	complemented
158	C₂×C₈×D₁₃	C₂³	1	12	yes	complemented
159	#63091	—	13	1	no	maximal, Sylow
160	C₂⁴×C₁₃	—	2	6	no	—
161	C₂³×D₁₃	—	2	24	no	—
162	C₁₃×#41	—	2	16	no	—
163	C₁₃×#41	—	2	12	no	—
164	C₁₃×#41	C₂×D₄	1	4	yes	—
165	C₁₃×#41	C₂⁴	1	24	yes	—
166	C₁₃×#41	C₂⁴	1	4	yes	—
167	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
169	C₂×D₄×C₁₃	—	2	6	no	—
170	C₂×D₄×C₁₃	—	2	48	no	—
171	C₂×D₄×C₁₃	—	2	12	no	—
172	C₂×D₄×C₁₃	—	2	6	no	—
173	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
174	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
175	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
176	C₂²×C₄×C₁₃	—	2	6	no	—
177	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
178	C₂×C₂²⋊D₁₃	—	2	12	no	—
179	C₂×C₂²⋊D₁₃	—	2	24	no	—
180	C₂×C₂²⋊D₁₃	—	2	48	no	—
181	C₂×C₂²⋊D₁₃	—	2	96	no	—
182	C₂×C₂²⋊D₁₃	—	2	24	no	—
183	C₂×C₂²⋊D₁₃	C₂×D₄	1	12	yes	—
184	C₂²×Dic₁₃	—	2	24	no	—
185	#6131	—	2	8	no	—
186	#6131	—	2	8	no	—
187	#6131	C₂×D₄	1	8	yes	—
188	#6131	C₂⁴	1	16	yes	—
189	Q₈×D₁₃	—	2	8	no	—
190	Q₈×D₁₃	—	2	8	no	—
191	Q₈×D₁₃	C₂×D₄	1	8	yes	—
192	Q₈×D₁₃	C₂⁴	1	16	yes	—
193	#6129	—	2	24	no	—
194	#6129	—	2	48	no	—
195	#6129	—	2	48	no	—
196	#6129	—	2	48	no	—
197	#6129	—	2	48	no	—
198	#6129	—	2	24	no	—
199	#6129	C₂×D₄	1	24	yes	—
200	#6129	C₂⁴	1	48	yes	—
201	D₄×D₁₃	—	2	48	no	—
202	D₄×D₁₃	—	2	24	no	—
203	D₄×D₁₃	—	2	48	no	—
204	D₄×D₁₃	—	2	48	no	—
205	D₄×D₁₃	—	2	24	no	—
206	D₄×D₁₃	—	2	48	no	—
207	D₄×D₁₃	C₂×D₄	1	24	yes	—
208	D₄×D₁₃	C₂⁴	1	48	yes	—
209	#6127	—	2	12	no	—
210	#6127	—	2	12	no	—
211	#6127	—	2	16	no	—
212	#6127	—	2	24	no	—
213	#6127	—	2	48	no	—
214	#6127	—	2	24	no	—
215	#6127	C₂×D₄	1	12	yes	—
216	#6127	C₂×D₄	1	12	yes	—
217	#6127	C₂⁴	1	4	yes	—
218	#6127	C₂⁴	1	12	yes	—
219	#6127	C₂⁴	1	8	yes	—
220	#6127	C₂⁴	1	24	yes	—
221	C₂×D₅₂	—	2	24	no	—
222	C₂×D₅₂	C₂×D₄	1	6	yes	—
223	C₂×D₅₂	C₂⁴	1	12	yes	—
224	C₂×C₄×D₁₃	—	2	12	no	—
225	C₂×C₄×D₁₃	—	2	48	no	—
226	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
227	C₂×Dic₂₆	—	2	24	no	—
228	C₂×Dic₂₆	C₂×D₄	1	6	yes	—
229	C₂×Dic₂₆	C₂⁴	1	12	yes	—
230	C₁₃×Q₁₆	C₂⁴	1	2	yes	—
231	C₁₃×Q₁₆	C₂⁴	1	2	yes	—
232	C₁₃×SD₁₆	C₂⁴	1	24	yes	—
233	C₁₃×D₈	C₂⁴	1	6	yes	—
234	C₁₃×D₈	C₂⁴	1	24	yes	—
235	C₁₃×D₈	C₂⁴	1	6	yes	—
236	C₁₃×M₁₆	C₂⁴	1	12	yes	—
237	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
238	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
239	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
241	#6107	C₂⁴	1	16	yes	—
242	#6106	C₂⁴	1	16	yes	—
243	#6105	C₂⁴	1	48	yes	—
244	#6104	C₂⁴	1	48	yes	—
245	#6099	C₂⁴	1	4	yes	—
246	#6099	C₂⁴	1	12	yes	—
247	C₂×#1055	C₂⁴	1	12	yes	—
248	Dic₅₂	C₂⁴	1	4	yes	—
249	Dic₅₂	C₂⁴	1	12	yes	—
250	D₁₀₄	C₂⁴	1	4	yes	—
251	D₁₀₄	C₂⁴	1	12	yes	—
252	#6095	C₂⁴	1	8	yes	—
253	#6095	C₂⁴	1	24	yes	—
254	#6094	C₂⁴	1	8	yes	—
255	#6094	C₂⁴	1	24	yes	—
256	C₈×D₁₃	C₂⁴	1	8	yes	—
257	C₈×D₁₃	C₂⁴	1	24	yes	—
258	H(7,𝔽₂)	—	13	2	no	—
259	#3585	—	13	2	no	—
260	#3585	—	13	16	no	—
261	#3585	—	13	12	no	—
262	#3584	—	13	8	no	—
263	#3584	—	13	6	no	—
264	#3584	—	13	1	no	—
265	C₂×#576	—	13	8	no	—
266	C₂×#576	—	13	6	no	—
267	C₂×#576	D₁₃	1	1	yes	characteristic, complemented
268	#3573	—	13	1	no	—
269	C₂³×C₁₃	—	2	24	no	—
270	C₂³×C₁₃	—	2	6	no	—
271	C₂³×C₁₃	—	16	6	no	—
272	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
273	C₂²×D₁₃	—	2	12	no	—
274	C₂²×D₁₃	—	2	48	no	—
275	C₂²×D₁₃	—	16	24	no	—
276	C₂²×D₁₃	C₂²×D₄	1	12	yes	—
277	Q₈×C₁₃	—	2	2	no	—
278	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
279	Q₈×C₁₃	C₂⁵	1	4	yes	—
280	D₄×C₁₃	—	2	24	no	—
281	D₄×C₁₃	—	2	24	no	—
282	D₄×C₁₃	—	2	6	no	—
283	D₄×C₁₃	C₂²×D₄	1	12	yes	—
284	D₄×C₁₃	C₂⁵	1	12	yes	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	24	no	—
287	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
288	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
289	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
290	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
291	C₂²⋊D₁₃	—	2	8	no	—
292	C₂²⋊D₁₃	—	2	24	no	—
293	C₂²⋊D₁₃	—	2	48	no	—
294	C₂²⋊D₁₃	—	2	48	no	—
295	C₂²⋊D₁₃	C₂²×D₄	1	8	yes	—
296	C₂²⋊D₁₃	C₂²×D₄	1	24	yes	—
297	C₂×Dic₁₃	—	2	12	no	—
298	C₂×Dic₁₃	—	2	48	no	—
299	C₂×Dic₁₃	C₂²×D₄	1	12	yes	—
300	D₅₂	—	2	16	no	—
301	D₅₂	—	2	12	no	—
302	D₅₂	C₂²×D₄	1	12	yes	—
303	D₅₂	C₂²×D₄	1	4	yes	—
304	D₅₂	C₂⁵	1	8	yes	—
305	C₄×D₁₃	—	2	16	no	—
306	C₄×D₁₃	—	2	24	no	—
307	C₄×D₁₃	—	2	8	no	—
308	C₄×D₁₃	—	2	16	no	—
309	C₄×D₁₃	C₂²×D₄	1	24	yes	—
310	C₄×D₁₃	C₂⁵	1	8	yes	—
311	Dic₂₆	—	2	12	no	—
312	Dic₂₆	—	2	16	no	—
313	Dic₂₆	C₂²×D₄	1	12	yes	—
314	Dic₂₆	C₂²×D₄	1	4	yes	—
315	Dic₂₆	C₂⁵	1	8	yes	—
316	C₈×C₁₃	C₂⁵	1	1	yes	characteristic
317	C₈×C₁₃	C₂⁵	1	6	yes	—
318	C₈×C₁₃	C₂⁵	1	1	yes	characteristic
319	#1055	C₂⁵	1	8	yes	—
320	#585	—	13	1	no	—
321	#585	—	13	16	no	—
322	#585	—	13	2	no	—
323	#585	—	13	12	no	—
324	#585	—	26	4	no	—
325	#585	—	26	8	no	—
326	C₂×H(5,𝔽₂)	—	13	16	no	—
327	C₂×H(5,𝔽₂)	—	13	12	no	—
328	C₂×H(5,𝔽₂)	—	26	12	no	—
329	C₂×H(5,𝔽₂)	—	26	8	no	—
330	C₂×H(5,𝔽₂)	C₂×D₁₃	1	2	yes	complemented
331	#578	—	13	12	no	—
332	#578	—	13	4	no	—
333	#578	—	13	4	no	—
334	#577	—	13	16	no	—
335	#577	—	13	48	no	—
336	#577	—	13	24	no	—
337	#577	—	13	24	no	—
338	#577	—	13	8	no	—
339	#576	—	13	16	no	—
340	#576	—	13	48	no	—
341	#576	—	13	12	no	—
342	#576	—	13	24	no	—
343	#576	—	13	12	no	—
344	#576	—	13	24	no	—
345	#576	—	13	24	no	—
346	#576	—	13	4	no	—
347	#576	C₂×D₁₃	1	8	yes	complemented
348	#576	C₂×D₁₃	1	8	yes	complemented
349	#575	—	13	12	no	—
350	#575	—	13	48	no	—
351	#575	—	13	24	no	—
352	#575	—	13	6	no	—
353	C₂×AGL(1,ℤ/8)	—	13	12	no	—
354	C₂×AGL(1,ℤ/8)	—	13	48	no	—
355	C₂×AGL(1,ℤ/8)	—	13	24	no	—
356	C₂×AGL(1,ℤ/8)	C₂×D₁₃	1	6	yes	complemented
357	C₂×#135	—	13	24	no	—
358	C₂×#135	—	13	12	no	—
359	C₂×#135	—	13	6	no	—
360	C₂×#135	C₂×D₁₃	1	3	yes	complemented
361	C₂²×D₈	—	13	12	no	—
362	C₂²×D₈	C₂×D₁₃	1	3	yes	complemented
363	#568	—	13	1	no	—
364	#568	—	13	8	no	—
365	#568	—	13	6	no	—
366	C₂×#131	—	13	8	no	—
367	C₂×#131	—	13	6	no	—
368	C₂×#131	C₂×D₁₃	1	1	yes	characteristic, complemented
369	C₂²×C₁₃	—	2	12	no	—
370	C₂²×C₁₃	—	4	3	no	—
371	C₂²×C₁₃	—	8	24	no	—
372	C₂²×C₁₃	—	8	6	no	—
373	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
374	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
375	C₂×D₁₃	—	2	8	no	—
376	C₂×D₁₃	—	4	12	no	—
377	C₂×D₁₃	—	8	48	no	—
378	C₂×D₁₃	—	8	12	no	—
379	C₂×D₁₃	C₂³×D₄	1	8	yes	—
380	C₄×C₁₃	—	2	4	no	—
381	C₄×C₁₃	C₂³×D₄	1	6	yes	—
382	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
383	C₄×C₁₃	C₂⁶	1	1	yes	characteristic
384	Dic₁₃	—	2	8	no	—
385	Dic₁₃	C₂³×D₄	1	8	yes	—
386	2₋¹⁺⁴	—	13	4	no	—
387	2₋¹⁺⁴	—	13	2	no	—
388	2₋¹⁺⁴	—	13	24	no	—
389	2₋¹⁺⁴	—	13	8	no	—
390	2₋¹⁺⁴	—	13	8	no	—
391	2₋¹⁺⁴	—	26	16	no	—
392	2₋¹⁺⁴	—	26	12	no	—
393	2₋¹⁺⁴	—	26	2	no	—
394	H(5,𝔽₂)	—	2	8	no	—
395	H(5,𝔽₂)	—	13	4	no	—
396	H(5,𝔽₂)	—	13	6	no	—
397	H(5,𝔽₂)	—	13	24	no	—
398	H(5,𝔽₂)	—	13	8	no	—
399	H(5,𝔽₂)	—	13	48	no	—
400	H(5,𝔽₂)	—	13	24	no	—
401	H(5,𝔽₂)	—	26	24	no	—
402	H(5,𝔽₂)	—	26	48	no	—
403	H(5,𝔽₂)	—	26	48	no	—
404	H(5,𝔽₂)	—	26	24	no	—
405	H(5,𝔽₂)	—	26	24	no	—
406	H(5,𝔽₂)	—	26	12	no	—
407	H(5,𝔽₂)	—	26	16	no	—
408	H(5,𝔽₂)	—	26	6	no	—
409	H(5,𝔽₂)	C₂²×D₁₃	1	16	yes	complemented
410	C₂×#41	—	2	2	no	—
411	C₂×#41	—	13	8	no	—
412	C₂×#41	—	13	6	no	—
413	C₂×#41	—	13	48	no	—
414	C₂×#41	—	13	24	no	—
415	C₂×#41	—	13	12	no	—
416	C₂×#41	—	26	24	no	—
417	C₂×#41	—	26	12	no	—
418	C₂×#41	—	26	48	no	—
419	C₂×#41	—	26	16	no	—
420	C₂×#41	—	26	16	no	—
421	C₂×#41	—	26	24	no	—
422	C₂×#41	—	26	8	no	—
423	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
424	C₂×#41	C₂²×D₁₃	1	6	yes	complemented
425	C₂²×D₄	—	2	6	no	—
426	C₂²×D₄	—	13	24	no	—
427	C₂²×D₄	—	26	48	no	—
428	C₂²×D₄	—	26	12	no	—
429	C₂²×D₄	—	26	24	no	—
430	C₂²×D₄	C₂²×D₁₃	1	6	yes	complemented
431	#137	—	13	24	no	—
432	#137	—	13	8	no	—
433	#137	—	13	16	no	—
434	#137	—	13	48	no	—
435	#137	—	13	24	no	—
436	AGL(1,ℤ/8)	—	13	24	no	—
437	AGL(1,ℤ/8)	—	13	48	no	—
438	AGL(1,ℤ/8)	—	13	24	no	—
439	AGL(1,ℤ/8)	—	13	48	no	—
440	AGL(1,ℤ/8)	—	13	96	no	—
441	AGL(1,ℤ/8)	—	13	48	no	—
442	AGL(1,ℤ/8)	—	13	24	no	—
443	AGL(1,ℤ/8)	C₂²×D₁₃	1	48	yes	complemented
444	#135	—	13	48	no	—
445	#135	—	13	8	no	—
446	#135	—	13	48	no	—
447	#135	—	13	24	no	—
448	#135	—	13	48	no	—
449	#135	—	13	12	no	—
450	#135	—	13	4	no	—
451	#135	—	13	12	no	—
452	#135	—	13	12	no	—
453	#135	C₂²×D₁₃	1	12	yes	complemented
454	#135	C₂²×D₁₃	1	12	yes	complemented
455	C₂×Q₁₆	—	13	8	no	—
456	C₂×Q₁₆	—	13	6	no	—
457	C₂×Q₁₆	C₂²×D₁₃	1	1	yes	characteristic, complemented
458	C₂×SD₁₆	—	13	24	no	—
459	C₂×SD₁₆	—	13	48	no	—
460	C₂×SD₁₆	—	13	12	no	—
461	C₂×SD₁₆	C₂²×D₁₃	1	6	yes	complemented
462	C₂×D₈	—	13	24	no	—
463	C₂×D₈	—	13	24	no	—
464	C₂×D₈	—	13	48	no	—
465	C₂×D₈	—	13	6	no	—
466	C₂×D₈	C₂²×D₁₃	1	12	yes	complemented
467	C₂×D₈	C₂²×D₁₃	1	3	yes	complemented
468	C₂×D₈	C₂²×D₁₃	1	12	yes	complemented
469	C₂×D₈	C₂²×D₁₃	1	6	yes	complemented
470	#131	—	13	8	no	—
471	#131	—	13	24	no	—
472	#131	—	13	12	no	—
473	#131	—	13	4	no	—
474	#131	—	13	12	no	—
475	#131	—	13	12	no	—
476	#131	C₂²×D₁₃	1	4	yes	complemented
477	#131	C₂²×D₁₃	1	4	yes	complemented
478	C₂×M₁₆	—	13	6	no	—
479	C₂×M₁₆	—	13	24	no	—
480	C₂×M₁₆	—	13	12	no	—
481	C₂×M₁₆	C₂²×D₁₃	1	3	yes	complemented
482	C₂²×C₈	—	13	12	no	—
483	C₂²×C₈	C₂²×D₁₃	1	3	yes	complemented
484	C₂×C₁₃	—	2	6	no	—
485	C₂×C₁₃	—	2	1	no	—
486	C₂×C₁₃	—	4	12	no	—
487	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
488	D₁₃	—	2	8	no	—
489	D₁₃	—	4	8	no	—
490	C₂⁴	—	2	6	no	—
491	C₂⁴	—	26	24	no	—
492	#41	—	2	16	no	—
493	#41	—	2	12	no	—
494	#41	—	13	8	no	—
495	#41	—	13	24	no	—
496	#41	—	13	12	no	—
497	#41	—	13	12	no	—
498	#41	—	13	12	no	—
499	#41	—	13	4	no	—
500	#41	—	13	16	no	—
501	#41	—	13	48	no	—
502	#41	—	13	24	no	—
503	#41	—	13	8	no	—
504	#41	—	26	48	no	—
505	#41	—	26	16	no	—
506	#41	—	26	24	no	—
507	#41	—	26	24	no	—
508	#41	—	26	48	no	—
509	#41	—	26	48	no	—
510	#41	—	26	48	no	—
511	#41	—	26	24	no	—
512	#41	—	26	48	no	—
513	#41	—	26	8	no	—
514	#41	—	26	8	no	—
515	#41	—	26	24	no	—
516	#41	—	26	12	no	—
517	#41	—	26	12	no	—
518	#41	D₄×D₁₃	1	4	yes	—
519	#41	C₂³×D₁₃	1	24	yes	—
520	#41	C₂³×D₁₃	1	4	yes	—
521	C₂×Q₈	—	13	8	no	—
522	C₂×Q₈	—	13	6	no	—
523	C₂×Q₈	—	13	16	no	—
524	C₂×Q₈	—	13	12	no	—
525	C₂×Q₈	—	26	24	no	—
526	C₂×Q₈	—	26	8	no	—
527	C₂×Q₈	—	26	8	no	—
528	C₂×Q₈	D₄×D₁₃	1	1	yes	characteristic
529	C₂×Q₈	C₂³×D₁₃	1	2	yes	—
530	C₂×D₄	—	2	6	no	—
531	C₂×D₄	—	2	48	no	—
532	C₂×D₄	—	2	6	no	—
533	C₂×D₄	—	2	12	no	—
534	C₂×D₄	—	13	12	no	—
535	C₂×D₄	—	13	24	no	—
536	C₂×D₄	—	13	48	no	—
537	C₂×D₄	—	13	6	no	—
538	C₂×D₄	—	13	12	no	—
539	C₂×D₄	—	26	24	no	—
540	C₂×D₄	—	26	48	no	—
541	C₂×D₄	—	26	24	no	—
542	C₂×D₄	—	26	48	no	—
543	C₂×D₄	—	26	48	no	—
544	C₂×D₄	—	26	24	no	—
545	C₂×D₄	—	26	48	no	—
546	C₂×D₄	—	26	48	no	—
547	C₂×D₄	—	26	96	no	—
548	C₂×D₄	—	26	24	no	—
549	C₂×D₄	—	26	12	no	—
550	C₂×D₄	—	26	24	no	—
551	C₂×D₄	D₄×D₁₃	1	3	yes	—
552	C₂×D₄	C₂³×D₁₃	1	24	yes	—
553	C₂×D₄	C₂³×D₁₃	1	6	yes	—
554	C₂²×C₄	—	2	6	no	—
555	C₂²×C₄	—	13	12	no	—
556	C₂²×C₄	—	26	48	no	—
557	C₂²×C₄	—	26	24	no	—
558	C₂²×C₄	—	26	12	no	—
559	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
560	Q₁₆	—	13	16	no	—
561	Q₁₆	—	13	4	no	—
562	Q₁₆	—	13	12	no	—
563	Q₁₆	C₂³×D₁₃	1	2	yes	—
564	Q₁₆	C₂³×D₁₃	1	2	yes	—
565	SD₁₆	—	13	16	no	—
566	SD₁₆	—	13	48	no	—
567	SD₁₆	—	13	24	no	—
568	SD₁₆	—	13	8	no	—
569	SD₁₆	C₂³×D₁₃	1	24	yes	—
570	D₈	—	13	48	no	—
571	D₈	—	13	4	no	—
572	D₈	—	13	12	no	—
573	D₈	C₂³×D₁₃	1	6	yes	—
574	D₈	C₂³×D₁₃	1	24	yes	—
575	D₈	C₂³×D₁₃	1	6	yes	—
576	M₁₆	—	13	12	no	—
577	M₁₆	—	13	4	no	—
578	M₁₆	—	13	24	no	—
579	M₁₆	—	13	8	no	—
580	M₁₆	C₂³×D₁₃	1	12	yes	—
581	C₂×C₈	—	13	12	no	—
582	C₂×C₈	—	13	8	no	—
583	C₂×C₈	—	13	24	no	—
584	C₂×C₈	C₂³×D₁₃	1	6	yes	—
585	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
586	C₂×C₈	C₂³×D₁₃	1	6	yes	—
587	C₂×C₈	C₂³×D₁₃	1	3	yes	—
588	C₁₃	#63091	1	1	yes	characteristic, complemented, Sylow
589	C₂³	—	2	6	no	—
590	C₂³	—	2	24	no	—
591	C₂³	—	13	12	no	—
592	C₂³	—	16	6	no	—
593	C₂³	—	26	48	no	—
594	C₂³	—	26	12	no	—
595	C₂³	—	208	24	no	—
596	C₂³	C₂×D₄×D₁₃	1	3	yes	—
597	Q₈	—	2	2	no	—
598	Q₈	—	13	12	no	—
599	Q₈	—	13	4	no	—
600	Q₈	—	13	8	no	—
601	Q₈	—	26	16	no	—
602	Q₈	—	26	12	no	—
603	Q₈	C₂×D₄×D₁₃	1	4	yes	—
604	Q₈	C₂⁴×D₁₃	1	4	yes	—
605	D₄	—	2	24	no	—
606	D₄	—	2	24	no	—
607	D₄	—	2	6	no	—
608	D₄	—	13	8	no	—
609	D₄	—	13	24	no	—
610	D₄	—	13	12	no	—
611	D₄	—	13	4	no	—
612	D₄	—	13	8	no	—
613	D₄	—	26	16	no	—
614	D₄	—	26	48	no	—
615	D₄	—	26	48	no	—
616	D₄	—	26	8	no	—
617	D₄	—	26	24	no	—
618	D₄	—	26	12	no	—
619	D₄	C₂×D₄×D₁₃	1	12	yes	—
620	D₄	C₂⁴×D₁₃	1	12	yes	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	24	no	—
623	C₂×C₄	—	13	12	no	—
624	C₂×C₄	—	13	24	no	—
625	C₂×C₄	—	13	8	no	—
626	C₂×C₄	—	26	16	no	—
627	C₂×C₄	—	26	16	no	—
628	C₂×C₄	—	26	48	no	—
629	C₂×C₄	—	26	12	no	—
630	C₂×C₄	—	26	24	no	—
631	C₂×C₄	—	26	8	no	—
632	C₂×C₄	C₂×D₄×D₁₃	1	3	yes	—
633	C₂×C₄	C₂×D₄×D₁₃	1	6	yes	—
634	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
635	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
636	C₈	—	13	8	no	—
637	C₈	C₂⁴×D₁₃	1	1	yes	characteristic
638	C₈	C₂⁴×D₁₃	1	6	yes	—
639	C₈	C₂⁴×D₁₃	1	1	yes	characteristic
640	C₂²	—	2	12	no	—
641	C₂²	—	4	3	no	—
642	C₂²	—	8	6	no	—
643	C₂²	—	8	24	no	—
644	C₂²	—	13	8	no	—
645	C₂²	—	26	8	no	—
646	C₂²	—	52	12	no	—
647	C₂²	—	104	12	no	—
648	C₂²	—	104	48	no	—
649	C₂²	C₂²×D₄×D₁₃	1	1	yes	characteristic
650	C₂²	C₂²×D₄×D₁₃	1	6	yes	—
651	C₄	—	2	4	no	—
652	C₄	—	13	8	no	—
653	C₄	—	26	8	no	—
654	C₄	C₂²×D₄×D₁₃	1	6	yes	—
655	C₄	C₂²×D₄×D₁₃	1	1	yes	characteristic
656	C₄	C₂⁵×D₁₃	1	1	yes	characteristic
657	C₂	—	2	1	no	—
658	C₂	—	2	6	no	—
659	C₂	—	4	12	no	—
660	C₂	—	26	8	no	—
661	C₂	—	52	8	no	—
662	C₂	C₂³×D₄×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂³×D₄×D₁₃
commutator, cosocle	C₄×C₁₃	C₂⁶
Frattini	C₄	C₂⁵×D₁₃
Fitting	C₂×C₁₃×#576	C₂
socle	C₂×C₁₃	C₂⁴×D₄
hypercenter	C₂×#576	D₁₃
hypocenter	C₁₃	#63091
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×#41 ◁ C₂×#576

Complements

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

N	H ≅ G/N	type
1. #13129646	C₂	semidirect
2. #13129616	C₂	semidirect
3. #13129612	C₂	semidirect
4. #13129611	C₂	semidirect
5. #13129610	C₂	semidirect
6. #13129605	C₂	semidirect
7. #13129604	C₂	semidirect
8. C₂×#11719462	C₂	semidirect
9. D₁₃×#576	C₂	semidirect
10. #13129547	C₂	semidirect
11. C₂×C₁₃×#576	C₂	semidirect
12. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
14. #11719650	C₂²	semidirect
16. D₁₃×H(5,𝔽₂)	C₂²	semidirect
19. #11719648	C₂²	semidirect
20. #11719648	C₂²	semidirect
22. C₂×#88251	C₂²	semidirect
23. C₁₃×#576	C₂²	semidirect
24. C₁₃×#576	C₂²	semidirect
25. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
26. C₂×C₁₃×#135	C₂²	semidirect
27. C₂²×C₁₃×D₈	C₂²	semidirect
28. C₂×C₁₃×#131	C₂²	semidirect
29. #11719541	C₂²	semidirect
30. #11719540	C₂²	semidirect
31. #11719527	C₂²	semidirect
32. #11719524	C₂²	semidirect
33. C₂×#88186	C₂²	semidirect
34. #11719480	C₂²	semidirect
35. #11719479	C₂²	semidirect
36. #11719478	C₂²	semidirect
37. D₁₃×AGL(1,ℤ/8)	C₂²	semidirect
38. #11719476	C₂²	semidirect
39. #11719475	C₂²	semidirect
40. #11719474	C₂²	semidirect
41. #11719473	C₂²	semidirect
42. D₁₃×#135	C₂²	semidirect
43. #11719471	C₂²	semidirect
44. #11719467	C₂²	semidirect
45. #11719462	C₂²	semidirect
46. #11719462	C₂²	semidirect
47. #11719462	C₂²	semidirect
48. #11719462	C₂²	semidirect
49. C₂×#88166	C₂²	semidirect
50. C₂×#88165	C₂²	semidirect
51. C₂×D₈×D₁₃	C₂²	semidirect
52. #11719458	C₂²	semidirect
53. #11719457	C₂²	semidirect
54. #11719456	C₂²	semidirect
55. #11719455	C₂²	semidirect
56. D₁₃×#131	C₂²	semidirect
57. #11719453	C₂²	semidirect
58. #11719450	C₂²	semidirect
59. C₂×#88158	C₂²	semidirect
60. C₂×#88155	C₂²	semidirect
62. C₁₃×H(5,𝔽₂)	C₂³	semidirect
65. C₂×C₁₃×#41	C₂³	semidirect
67. C₂²×D₄×C₁₃	C₂³	semidirect
72. #88257	C₂³	semidirect
73. #88257	C₂³	semidirect
77. #88256	C₂³	semidirect
78. #88256	C₂³	semidirect
84. #41×D₁₃	C₂³	semidirect
87. #88254	C₂³	semidirect
95. #88251	C₂³	semidirect
96. #88251	C₂³	semidirect
99. C₂×#6129	C₂³	semidirect
102. C₂×D₄×D₁₃	C₂³	semidirect
105. C₂×#6127	C₂³	semidirect
106. C₁₃×AGL(1,ℤ/8)	C₂³	semidirect
107. C₁₃×#135	C₂³	semidirect
108. C₁₃×#135	C₂³	semidirect
109. C₂×C₁₃×Q₁₆	C₂³	semidirect
110. C₂×C₁₃×SD₁₆	C₂³	semidirect
111. C₂×C₁₃×D₈	C₂³	semidirect
112. C₂×C₁₃×D₈	C₂³	semidirect
113. C₂×C₁₃×D₈	C₂³	semidirect
114. C₂×C₁₃×D₈	C₂³	semidirect
115. C₁₃×#131	C₂³	semidirect
116. C₁₃×#131	C₂³	semidirect
117. C₂×C₁₃×M₁₆	C₂³	semidirect
118. C₂²×C₈×C₁₃	C₂³	semidirect
119. #88205	C₂³	semidirect
120. #88204	C₂³	semidirect
121. #88203	C₂³	semidirect
122. #88202	C₂³	semidirect
123. #88196	C₂³	semidirect
124. C₂×#6105	C₂³	semidirect
125. #88186	C₂³	semidirect
126. #88186	C₂³	semidirect
127. C₂×#6104	C₂³	semidirect
128. C₂×#6099	C₂³	semidirect
129. #88173	C₂³	semidirect
130. #88172	C₂³	semidirect
131. Q₁₆×D₁₃	C₂³	semidirect
132. #88170	C₂³	semidirect
133. #88169	C₂³	semidirect
134. #88168	C₂³	semidirect
135. SD₁₆×D₁₃	C₂³	semidirect
136. #88166	C₂³	semidirect
137. #88166	C₂³	semidirect
138. #88165	C₂³	semidirect
139. #88165	C₂³	semidirect
140. D₈×D₁₃	C₂³	semidirect
141. D₈×D₁₃	C₂³	semidirect
142. #88163	C₂³	semidirect
143. #88162	C₂³	semidirect
144. #88161	C₂³	semidirect
145. M₁₆×D₁₃	C₂³	semidirect
146. C₂×Dic₅₂	C₂³	semidirect
147. #88158	C₂³	semidirect
148. #88158	C₂³	semidirect
149. #88158	C₂³	semidirect
150. #88158	C₂³	semidirect
151. C₂×D₁₀₄	C₂³	semidirect
152. C₂×#6095	C₂³	semidirect
153. #88155	C₂³	semidirect
154. #88155	C₂³	semidirect
155. #88155	C₂³	semidirect
156. #88155	C₂³	semidirect
157. C₂×#6094	C₂³	semidirect
158. C₂×C₈×D₁₃	C₂³	semidirect
267. C₂×#576	D₁₃	semidirect
330. C₂×H(5,𝔽₂)	C₂×D₁₃	semidirect
347. #576	C₂×D₁₃	semidirect
348. #576	C₂×D₁₃	semidirect
356. C₂×AGL(1,ℤ/8)	C₂×D₁₃	semidirect
360. C₂×#135	C₂×D₁₃	semidirect
362. C₂²×D₈	C₂×D₁₃	semidirect
368. C₂×#131	C₂×D₁₃	semidirect
409. H(5,𝔽₂)	C₂²×D₁₃	semidirect
424. C₂×#41	C₂²×D₁₃	semidirect
430. C₂²×D₄	C₂²×D₁₃	semidirect
443. AGL(1,ℤ/8)	C₂²×D₁₃	semidirect
453. #135	C₂²×D₁₃	semidirect
454. #135	C₂²×D₁₃	semidirect
457. C₂×Q₁₆	C₂²×D₁₃	semidirect
461. C₂×SD₁₆	C₂²×D₁₃	semidirect
466. C₂×D₈	C₂²×D₁₃	semidirect
467. C₂×D₈	C₂²×D₁₃	semidirect
468. C₂×D₈	C₂²×D₁₃	semidirect
469. C₂×D₈	C₂²×D₁₃	semidirect
476. #131	C₂²×D₁₃	semidirect
477. #131	C₂²×D₁₃	semidirect
481. C₂×M₁₆	C₂²×D₁₃	semidirect
483. C₂²×C₈	C₂²×D₁₃	semidirect
588. C₁₃	#63091	semidirect

Maximal subgroups

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

subgroup	index
#13129646	2
#13129616	2
#13129612	2
#13129611	2
#13129610	2
#13129605	2
#13129604	2
C₂×#11719462	2
D₁₃×#576	2
#13129547	2
C₂×C₁₃×#576	2
#63091	13