Subgroups — #16776771

Order 3328.

10836 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×#585	C₂	1	2	yes	maximal, complemented
2	#13129621	C₂	1	8	yes	maximal, complemented
3	#13129618	C₂	1	8	yes	maximal, complemented
4	#13129614	C₂	1	8	yes	maximal, complemented
5	#13129611	C₂	1	8	yes	maximal, complemented
6	#13129610	C₂	1	1	yes	maximal, characteristic, complemented
7	#13129609	C₂	1	6	yes	maximal, complemented
8	#13129607	C₂	1	2	yes	maximal, complemented
9	#13129605	C₂	1	6	yes	maximal, complemented
10	C₂×#11719473	C₂	1	6	yes	maximal, complemented
11	D₁₃×#575	C₂	1	6	yes	maximal, complemented
12	C₂×#11719455	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#3584	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#585	C₂²	1	2	yes	complemented
15	#11719652	—	2	2	no	—
16	#11719652	C₂²	1	8	yes	complemented
17	D₁₃×2₋¹⁺⁴	—	2	2	no	—
18	D₁₃×2₋¹⁺⁴	C₂²	1	8	yes	complemented
19	#11719650	—	2	6	no	—
20	#11719650	C₂²	1	8	yes	complemented
21	D₁₃×H(5,𝔽₂)	—	2	6	no	—
22	D₁₃×H(5,𝔽₂)	C₂²	1	8	yes	complemented
23	#11719648	—	2	8	no	—
24	#11719648	C₂²	1	12	yes	complemented
25	#11719648	C₂²	1	2	yes	complemented
26	C₂×#41×D₁₃	—	2	8	no	—
27	C₂×#41×D₁₃	C₂²	1	1	yes	characteristic
28	C₂×#41×D₁₃	C₂²	1	12	yes	complemented
29	C₁₃×#578	C₂²	1	4	yes	complemented
30	C₁₃×#577	C₂²	1	8	yes	complemented
31	C₁₃×#576	C₂²	1	4	yes	complemented
32	C₁₃×#575	C₂²	1	6	yes	complemented
33	C₂×C₁₃×#135	C₂²	1	6	yes	complemented
34	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic, complemented
35	#11719543	C₂²	1	8	yes	complemented
36	#11719542	C₂²	1	8	yes	complemented
37	#11719541	C₂²	1	8	yes	complemented
38	#11719540	C₂²	1	8	yes	complemented
39	#11719527	C₂²	1	12	yes	complemented
40	C₂×#88204	C₂²	1	12	yes	complemented
41	C₂×#88202	C₂²	1	1	yes	characteristic, complemented
42	#11719484	C₂²	1	24	yes	complemented
43	#11719483	C₂²	1	24	yes	complemented
44	#11719482	C₂²	1	24	yes	complemented
45	D₁₃×#137	C₂²	1	24	yes	complemented
46	#11719480	C₂²	1	24	yes	complemented
47	#11719479	C₂²	1	24	yes	complemented
48	#11719478	C₂²	1	24	yes	complemented
49	D₁₃×AGL(1,ℤ/8)	C₂²	1	24	yes	complemented
50	#11719476	C₂²	1	12	yes	complemented
51	#11719475	C₂²	1	24	yes	complemented
52	#11719474	C₂²	1	12	yes	complemented
53	#11719473	C₂²	1	12	yes	complemented
54	#11719473	C₂²	1	4	yes	complemented
55	#11719473	C₂²	1	24	yes	complemented
56	#11719473	C₂²	1	24	yes	complemented
57	#11719473	C₂²	1	12	yes	complemented
58	#11719473	C₂²	1	12	yes	complemented
59	D₁₃×#135	C₂²	1	24	yes	complemented
60	#11719471	C₂²	1	12	yes	complemented
61	C₂×#88172	C₂²	1	12	yes	complemented
62	#11719467	C₂²	1	24	yes	complemented
63	C₂×#88169	C₂²	1	12	yes	complemented
64	C₂×#88168	C₂²	1	12	yes	complemented
65	#11719462	C₂²	1	12	yes	complemented
66	C₂×#88165	C₂²	1	12	yes	complemented
67	#11719458	C₂²	1	4	yes	complemented
68	#11719457	C₂²	1	4	yes	complemented
69	#11719456	C₂²	1	8	yes	complemented
70	#11719455	C₂²	1	8	yes	complemented
71	#11719455	C₂²	1	8	yes	complemented
72	#11719453	C₂²	1	6	yes	complemented
73	C₂×#88161	C₂²	1	3	yes	complemented
74	C₂×M₁₆×D₁₃	C₂²	1	3	yes	complemented
75	C₂×#88158	C₂²	1	6	yes	complemented
76	C₂×#88155	C₂²	1	3	yes	complemented
77	C₂²×#6094	C₂²	1	3	yes	complemented
78	C₁₃×2₋¹⁺⁴	—	2	2	no	—
79	C₁₃×2₋¹⁺⁴	C₂³	1	8	yes	complemented
80	C₁₃×H(5,𝔽₂)	—	2	6	no	—
81	C₁₃×H(5,𝔽₂)	C₂³	1	8	yes	complemented
82	C₂×C₁₃×#41	—	2	8	no	—
83	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×#41	C₂³	1	12	yes	complemented
85	#88257	—	2	8	no	—
86	#88257	—	2	24	no	—
87	#88257	—	2	12	no	—
88	#88257	C₂³	1	24	yes	complemented
89	#88257	C₂³	1	8	yes	complemented
90	#88256	—	2	8	no	—
91	#88256	—	2	24	no	—
92	#88256	—	2	12	no	—
93	#88256	C₂³	1	24	yes	complemented
94	#88256	C₂³	1	8	yes	complemented
95	#41×D₁₃	—	2	8	no	—
96	#41×D₁₃	—	2	8	no	—
97	#41×D₁₃	—	2	8	no	—
98	#41×D₁₃	—	2	24	no	—
99	#41×D₁₃	—	2	24	no	—
100	#41×D₁₃	—	2	24	no	—
101	#41×D₁₃	—	2	12	no	—
102	#41×D₁₃	—	2	12	no	—
103	#41×D₁₃	—	2	12	no	—
104	#41×D₁₃	—	2	12	no	—
105	#41×D₁₃	D₄	1	8	yes	—
106	#41×D₁₃	C₂³	1	8	yes	—
107	#41×D₁₃	C₂³	1	24	yes	—
108	#41×D₁₃	C₂³	1	8	yes	—
109	#41×D₁₃	C₂³	1	24	yes	complemented
110	#41×D₁₃	C₂³	1	24	yes	complemented
111	#88254	—	2	2	no	—
112	#88254	—	2	8	no	—
113	#88254	—	2	8	no	—
114	#88254	C₂³	1	24	yes	complemented
115	C₂×#6131	—	2	8	no	—
116	C₂×#6131	D₄	1	1	yes	characteristic
117	C₂×#6131	C₂³	1	12	yes	—
118	C₂×Q₈×D₁₃	—	2	8	no	—
119	C₂×Q₈×D₁₃	D₄	1	1	yes	characteristic
120	C₂×Q₈×D₁₃	C₂³	1	12	yes	complemented
121	#88251	—	2	6	no	—
122	#88251	—	2	24	no	—
123	#88251	—	2	24	no	—
124	#88251	—	2	24	no	—
125	#88251	C₂³	1	24	yes	complemented
126	C₂×#6129	—	2	12	no	—
127	C₂×#6129	—	2	24	no	—
128	C₂×#6129	D₄	1	3	yes	—
129	C₂×#6129	C₂³	1	12	yes	—
130	C₂×D₄×D₁₃	—	2	12	no	—
131	C₂×D₄×D₁₃	—	2	24	no	—
132	C₂×D₄×D₁₃	D₄	1	3	yes	—
133	C₂×D₄×D₁₃	C₂³	1	12	yes	complemented
134	C₂×#6127	—	2	24	no	—
135	C₂×#6127	—	2	12	no	—
136	C₂×#6127	C₂³	1	3	yes	—
137	C₂×#6127	C₂³	1	12	yes	complemented
138	C₂²×C₄×D₁₃	—	2	12	no	—
139	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
140	C₁₃×#137	C₂³	1	24	yes	complemented
141	C₁₃×AGL(1,ℤ/8)	C₂³	1	24	yes	complemented
142	C₁₃×#135	C₂³	1	12	yes	complemented
143	C₁₃×#135	C₂³	1	4	yes	complemented
144	C₁₃×#135	C₂³	1	12	yes	complemented
145	C₁₃×#135	C₂³	1	12	yes	complemented
146	C₂×C₁₃×Q₁₆	C₂³	1	6	yes	complemented
147	C₂×C₁₃×SD₁₆	C₂³	1	12	yes	complemented
148	C₂×C₁₃×D₈	C₂³	1	6	yes	complemented
149	C₁₃×#131	C₂³	1	4	yes	complemented
150	C₁₃×#131	C₂³	1	4	yes	complemented
151	C₂×C₁₃×M₁₆	C₂³	1	3	yes	complemented
152	C₂²×C₈×C₁₃	C₂³	1	3	yes	complemented
153	#88205	C₂³	1	24	yes	complemented
154	#88204	C₂³	1	24	yes	complemented
155	#88204	C₂³	1	8	yes	complemented
156	#88204	C₂³	1	24	yes	complemented
157	#88204	C₂³	1	24	yes	complemented
158	#88203	C₂³	1	24	yes	complemented
159	#88202	C₂³	1	8	yes	complemented
160	C₂×#6107	C₂³	1	12	yes	complemented
161	#88196	C₂³	1	24	yes	complemented
162	C₂×#6106	C₂³	1	12	yes	complemented
163	C₂×#6105	C₂³	1	12	yes	complemented
164	#88186	C₂³	1	24	yes	complemented
165	C₂×#6104	C₂³	1	12	yes	complemented
166	C₂×#6099	C₂³	1	3	yes	complemented
167	C₂²×#1055	C₂³	1	3	yes	complemented
168	#88173	C₂³	1	24	yes	complemented
169	#88172	C₂³	1	8	yes	complemented
170	#88172	C₂³	1	24	yes	complemented
171	#88172	C₂³	1	24	yes	complemented
172	#88172	C₂³	1	24	yes	complemented
173	Q₁₆×D₁₃	C₂³	1	24	yes	complemented
174	#88170	C₂³	1	48	yes	complemented
175	#88169	C₂³	1	8	yes	complemented
176	#88169	C₂³	1	24	yes	complemented
177	#88169	C₂³	1	24	yes	complemented
178	#88169	C₂³	1	24	yes	complemented
179	#88168	C₂³	1	8	yes	complemented
180	#88168	C₂³	1	24	yes	complemented
181	#88168	C₂³	1	24	yes	complemented
182	#88168	C₂³	1	24	yes	complemented
183	SD₁₆×D₁₃	C₂³	1	48	yes	complemented
184	#88166	C₂³	1	24	yes	complemented
185	#88165	C₂³	1	8	yes	complemented
186	#88165	C₂³	1	24	yes	complemented
187	#88165	C₂³	1	24	yes	complemented
188	#88165	C₂³	1	24	yes	complemented
189	D₈×D₁₃	C₂³	1	24	yes	complemented
190	#88163	C₂³	1	24	yes	complemented
191	#88162	C₂³	1	24	yes	complemented
192	#88161	C₂³	1	24	yes	complemented
193	M₁₆×D₁₃	C₂³	1	24	yes	complemented
194	C₂×Dic₅₂	C₂³	1	6	yes	complemented
195	#88158	C₂³	1	4	yes	complemented
196	#88158	C₂³	1	12	yes	complemented
197	#88158	C₂³	1	12	yes	complemented
198	#88158	C₂³	1	12	yes	complemented
199	C₂×D₁₀₄	C₂³	1	6	yes	complemented
200	C₂×#6095	C₂³	1	12	yes	complemented
201	#88155	C₂³	1	12	yes	complemented
202	#88155	C₂³	1	12	yes	complemented
203	C₂×#6094	C₂³	1	1	yes	characteristic
204	C₂×#6094	C₂³	1	3	yes	—
205	C₂×#6094	C₂³	1	3	yes	complemented
206	C₂×#6094	C₂³	1	3	yes	complemented
207	C₂×#6094	C₂³	1	12	yes	complemented
208	C₂×#6094	C₂³	1	12	yes	complemented
209	C₂×C₈×D₁₃	C₂³	1	6	yes	complemented
210	#63090	—	13	1	no	maximal, Sylow
211	C₂³×D₁₃	—	2	12	no	—
212	C₂³×D₁₃	C₂×D₄	1	3	yes	—
213	C₁₃×#41	—	2	8	no	—
214	C₁₃×#41	—	2	24	no	—
215	C₁₃×#41	—	2	12	no	—
216	C₁₃×#41	—	2	12	no	—
217	C₁₃×#41	C₂×D₄	1	4	yes	—
218	C₁₃×#41	C₂⁴	1	24	yes	—
219	C₁₃×#41	C₂⁴	1	8	yes	—
220	C₁₃×#41	C₂⁴	1	4	yes	—
221	C₂×Q₈×C₁₃	—	2	8	no	—
222	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
223	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
224	C₂×D₄×C₁₃	—	2	12	no	—
225	C₂×D₄×C₁₃	—	2	24	no	—
226	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
227	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
228	C₂²×C₄×C₁₃	—	2	12	no	—
229	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
230	C₂×C₂²⋊D₁₃	—	2	12	no	—
231	C₂×C₂²⋊D₁₃	—	2	12	no	—
232	C₂×C₂²⋊D₁₃	—	2	48	no	—
233	C₂×C₂²⋊D₁₃	—	2	12	no	—
234	C₂×C₂²⋊D₁₃	C₂×D₄	1	6	yes	—
235	C₂²×Dic₁₃	—	2	12	no	—
236	C₂²×Dic₁₃	C₂×D₄	1	3	yes	—
237	#6131	—	2	8	no	—
238	#6131	—	2	24	no	—
239	#6131	—	2	12	no	—
240	#6131	—	2	12	no	—
241	#6131	C₂×D₄	1	8	yes	—
242	#6131	C₂⁴	1	8	yes	—
243	#6131	C₂⁴	1	24	yes	—
244	Q₈×D₁₃	—	2	8	no	—
245	Q₈×D₁₃	—	2	12	no	—
246	Q₈×D₁₃	—	2	12	no	—
247	Q₈×D₁₃	—	2	24	no	—
248	Q₈×D₁₃	C₂×D₄	1	8	yes	—
249	Q₈×D₁₃	C₂⁴	1	24	yes	—
250	Q₈×D₁₃	C₂⁴	1	8	yes	—
251	#6129	—	2	24	no	—
252	#6129	—	2	48	no	—
253	#6129	—	2	24	no	—
254	#6129	—	2	8	no	—
255	#6129	—	2	24	no	—
256	#6129	—	2	24	no	—
257	#6129	—	2	12	no	—
258	#6129	—	2	12	no	—
259	#6129	—	2	24	no	—
260	#6129	C₂×D₄	1	24	yes	—
261	#6129	C₂⁴	1	8	yes	—
262	#6129	C₂⁴	1	24	yes	—
263	D₄×D₁₃	—	2	8	no	—
264	D₄×D₁₃	—	2	24	no	—
265	D₄×D₁₃	—	2	24	no	—
266	D₄×D₁₃	—	2	24	no	—
267	D₄×D₁₃	—	2	24	no	—
268	D₄×D₁₃	—	2	48	no	—
269	D₄×D₁₃	—	2	24	no	—
270	D₄×D₁₃	—	2	12	no	—
271	D₄×D₁₃	—	2	12	no	—
272	D₄×D₁₃	C₂×D₄	1	24	yes	—
273	D₄×D₁₃	C₂⁴	1	24	yes	—
274	D₄×D₁₃	C₂⁴	1	8	yes	—
275	#6127	—	2	12	no	—
276	#6127	—	2	12	no	—
277	#6127	—	2	48	no	—
278	#6127	—	2	24	no	—
279	#6127	—	2	8	no	—
280	#6127	—	2	24	no	—
281	#6127	—	2	24	no	—
282	#6127	—	2	24	no	—
283	#6127	—	2	24	no	—
284	#6127	C₂×D₄	1	12	yes	—
285	#6127	C₂⁴	1	12	yes	—
286	#6127	C₂⁴	1	8	yes	—
287	#6127	C₂⁴	1	24	yes	—
288	C₂×D₅₂	—	2	12	no	—
289	C₂×D₅₂	—	2	24	no	—
290	C₂×D₅₂	C₂×D₄	1	3	yes	—
291	C₂×D₅₂	C₂⁴	1	12	yes	—
292	C₂×C₄×D₁₃	—	2	12	no	—
293	C₂×C₄×D₁₃	—	2	12	no	—
294	C₂×C₄×D₁₃	—	2	12	no	—
295	C₂×C₄×D₁₃	—	2	8	no	—
296	C₂×C₄×D₁₃	—	2	24	no	—
297	C₂×C₄×D₁₃	—	2	24	no	—
298	C₂×C₄×D₁₃	—	2	24	no	—
299	C₂×C₄×D₁₃	C₂×D₄	1	12	yes	—
300	C₂×C₄×D₁₃	C₂×D₄	1	3	yes	—
301	C₂×C₄×D₁₃	C₂×D₄	1	3	yes	—
302	C₂×C₄×D₁₃	C₂⁴	1	3	yes	—
303	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
304	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
305	C₂×Dic₂₆	—	2	12	no	—
306	C₂×Dic₂₆	—	2	24	no	—
307	C₂×Dic₂₆	C₂×D₄	1	3	yes	—
308	C₂×Dic₂₆	C₂⁴	1	12	yes	—
309	C₁₃×Q₁₆	C₂⁴	1	12	yes	—
310	C₁₃×Q₁₆	C₂⁴	1	4	yes	—
311	C₁₃×SD₁₆	C₂⁴	1	24	yes	—
312	C₁₃×SD₁₆	C₂⁴	1	8	yes	—
313	C₁₃×D₈	C₂⁴	1	12	yes	—
314	C₁₃×D₈	C₂⁴	1	4	yes	—
315	C₁₃×M₁₆	C₂⁴	1	12	yes	—
316	C₂×C₈×C₁₃	C₂⁴	1	3	yes	—
317	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
318	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
319	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
320	#6107	C₂⁴	1	8	yes	—
321	#6107	C₂⁴	1	24	yes	—
322	#6106	C₂⁴	1	24	yes	—
323	#6106	C₂⁴	1	8	yes	—
324	#6105	C₂⁴	1	8	yes	—
325	#6105	C₂⁴	1	24	yes	—
326	#6104	C₂⁴	1	24	yes	—
327	#6104	C₂⁴	1	8	yes	—
328	#6099	C₂⁴	1	12	yes	—
329	C₂×#1055	C₂⁴	1	3	yes	—
330	C₂×#1055	C₂⁴	1	1	yes	characteristic
331	C₂×#1055	C₂⁴	1	12	yes	—
332	Dic₅₂	C₂⁴	1	4	yes	—
333	Dic₅₂	C₂⁴	1	12	yes	—
334	D₁₀₄	C₂⁴	1	4	yes	—
335	D₁₀₄	C₂⁴	1	12	yes	—
336	#6095	C₂⁴	1	8	yes	—
337	#6095	C₂⁴	1	24	yes	—
338	#6094	C₂⁴	1	2	yes	—
339	#6094	C₂⁴	1	2	yes	—
340	#6094	C₂⁴	1	12	yes	—
341	#6094	C₂⁴	1	6	yes	—
342	#6094	C₂⁴	1	6	yes	—
343	#6094	C₂⁴	1	12	yes	—
344	C₈×D₁₃	C₂⁴	1	24	yes	—
345	C₂×#585	—	13	2	no	—
346	#3586	—	13	8	no	—
347	#3586	—	13	8	no	—
348	#3585	—	13	8	no	—
349	#3585	—	13	8	no	—
350	#3584	—	13	2	no	—
351	#3584	—	13	6	no	—
352	#3584	—	13	6	no	—
353	#3584	—	13	1	no	—
354	#3584	D₁₃	1	1	yes	characteristic, complemented
355	C₂×#575	—	13	6	no	—
356	C₂×#575	—	13	6	no	—
357	C₂×#568	—	13	1	no	—
358	C₂³×C₁₃	—	2	12	no	—
359	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
360	C₂²×D₁₃	—	2	12	no	—
361	C₂²×D₁₃	—	2	8	no	—
362	C₂²×D₁₃	—	2	24	no	—
363	C₂²×D₁₃	—	8	3	no	—
364	C₂²×D₁₃	—	8	24	no	—
365	C₂²×D₁₃	C₂²×D₄	1	12	yes	—
366	C₂²×D₁₃	C₂²×D₄	1	1	yes	characteristic
367	C₂²×D₁₃	C₂²×D₄	1	3	yes	—
368	Q₈×C₁₃	—	2	12	no	—
369	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
370	Q₈×C₁₃	C₂⁵	1	8	yes	—
371	D₄×C₁₃	—	2	24	no	—
372	D₄×C₁₃	—	2	8	no	—
373	D₄×C₁₃	—	2	12	no	—
374	D₄×C₁₃	C₂²×D₄	1	12	yes	—
375	D₄×C₁₃	C₂⁵	1	8	yes	—
376	C₂×C₄×C₁₃	—	2	12	no	—
377	C₂×C₄×C₁₃	—	2	24	no	—
378	C₂×C₄×C₁₃	—	2	8	no	—
379	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
380	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
381	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
382	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
383	C₂²⋊D₁₃	—	2	24	no	—
384	C₂²⋊D₁₃	—	2	8	no	—
385	C₂²⋊D₁₃	—	2	8	no	—
386	C₂²⋊D₁₃	—	2	24	no	—
387	C₂²⋊D₁₃	—	2	24	no	—
388	C₂²⋊D₁₃	—	2	8	no	—
389	C₂²⋊D₁₃	C₂²×D₄	1	24	yes	—
390	C₂×Dic₁₃	—	2	12	no	—
391	C₂×Dic₁₃	—	2	24	no	—
392	C₂×Dic₁₃	—	2	8	no	—
393	C₂×Dic₁₃	C₂²×D₄	1	12	yes	—
394	C₂×Dic₁₃	C₂²×D₄	1	3	yes	—
395	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
396	D₅₂	—	2	8	no	—
397	D₅₂	—	2	24	no	—
398	D₅₂	—	2	12	no	—
399	D₅₂	C₂²×D₄	1	12	yes	—
400	D₅₂	C₂⁵	1	8	yes	—
401	C₄×D₁₃	—	2	8	no	—
402	C₄×D₁₃	—	2	24	no	—
403	C₄×D₁₃	—	2	8	no	—
404	C₄×D₁₃	—	2	24	no	—
405	C₄×D₁₃	—	2	8	no	—
406	C₄×D₁₃	—	2	24	no	—
407	C₄×D₁₃	C₂²×D₄	1	2	yes	—
408	C₄×D₁₃	C₂²×D₄	1	6	yes	—
409	C₄×D₁₃	C₂²×D₄	1	12	yes	—
410	C₄×D₁₃	C₂²×D₄	1	12	yes	—
411	C₄×D₁₃	C₂⁵	1	6	yes	—
412	C₄×D₁₃	C₂⁵	1	2	yes	—
413	Dic₂₆	—	2	12	no	—
414	Dic₂₆	—	2	24	no	—
415	Dic₂₆	—	2	8	no	—
416	Dic₂₆	C₂²×D₄	1	12	yes	—
417	Dic₂₆	C₂⁵	1	8	yes	—
418	C₈×C₁₃	C₂⁵	1	6	yes	—
419	C₈×C₁₃	C₂⁵	1	1	yes	characteristic
420	C₈×C₁₃	C₂⁵	1	1	yes	characteristic
421	#1055	C₂⁵	1	6	yes	—
422	#1055	C₂⁵	1	2	yes	—
423	#585	—	13	8	no	—
424	#585	—	13	8	no	—
425	#585	—	13	2	no	—
426	#585	—	13	12	no	—
427	#585	—	26	8	no	—
428	#585	—	26	6	no	—
429	#585	—	26	2	no	—
430	#585	C₂×D₁₃	1	2	yes	complemented
431	C₂×2₋¹⁺⁴	—	13	8	no	—
432	C₂×2₋¹⁺⁴	—	26	2	no	—
433	C₂×H(5,𝔽₂)	—	13	8	no	—
434	C₂×H(5,𝔽₂)	—	26	6	no	—
435	C₂²×#41	—	13	1	no	—
436	C₂²×#41	—	13	12	no	—
437	C₂²×#41	—	26	8	no	—
438	#578	—	13	8	no	—
439	#578	—	13	24	no	—
440	#578	—	13	12	no	—
441	#578	—	13	12	no	—
442	#578	—	13	4	no	—
443	#578	C₂×D₁₃	1	4	yes	complemented
444	#577	—	13	8	no	—
445	#577	—	13	8	no	—
446	#577	—	13	24	no	—
447	#577	—	13	24	no	—
448	#577	—	13	24	no	—
449	#577	—	13	24	no	—
450	#577	—	13	8	no	—
451	#577	C₂×D₁₃	1	8	yes	complemented
452	#576	—	13	8	no	—
453	#576	—	13	24	no	—
454	#576	—	13	12	no	—
455	#576	—	13	12	no	—
456	#576	—	13	4	no	—
457	#576	C₂×D₁₃	1	4	yes	complemented
458	#575	—	13	12	no	—
459	#575	—	13	24	no	—
460	#575	—	13	24	no	—
461	#575	—	13	12	no	—
462	#575	—	13	12	no	—
463	#575	—	13	24	no	—
464	#575	—	13	24	no	—
465	#575	—	13	12	no	—
466	#575	—	13	4	no	—
467	#575	—	13	6	no	—
468	#575	C₂×D₁₃	1	6	yes	complemented
469	C₂×#137	—	13	24	no	—
470	C₂×#137	—	13	12	no	—
471	C₂×#137	—	13	12	no	—
472	C₂×AGL(1,ℤ/8)	—	13	24	no	—
473	C₂×AGL(1,ℤ/8)	—	13	12	no	—
474	C₂×AGL(1,ℤ/8)	—	13	12	no	—
475	C₂×#135	—	13	12	no	—
476	C₂×#135	—	13	24	no	—
477	C₂×#135	—	13	6	no	—
478	C₂×#135	C₂×D₁₃	1	6	yes	complemented
479	#568	—	13	8	no	—
480	#568	—	13	8	no	—
481	C₂×#131	—	13	1	no	—
482	C₂×#131	—	13	3	no	—
483	C₂×#131	—	13	3	no	—
484	C₂×#131	C₂×D₁₃	1	1	yes	characteristic, complemented
485	C₂²×M₁₆	—	13	3	no	—
486	C₂²×M₁₆	—	13	3	no	—
487	C₂²×C₁₃	—	2	8	no	—
488	C₂²×C₁₃	—	4	3	no	—
489	C₂²×C₁₃	—	8	12	no	—
490	C₂²×C₁₃	C₂³×D₄	1	6	yes	—
491	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
492	C₂×D₁₃	—	2	8	no	—
493	C₂×D₁₃	—	4	1	no	—
494	C₂×D₁₃	—	4	12	no	—
495	C₂×D₁₃	—	4	3	no	—
496	C₂×D₁₃	—	4	16	no	—
497	C₂×D₁₃	—	8	24	no	—
498	C₂×D₁₃	—	8	12	no	—
499	C₂×D₁₃	C₂³×D₄	1	2	yes	—
500	C₂×D₁₃	C₂³×D₄	1	6	yes	—
501	C₄×C₁₃	—	2	8	no	—
502	C₄×C₁₃	C₂³×D₄	1	6	yes	—
503	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
504	C₄×C₁₃	C₂⁶	1	1	yes	characteristic
505	Dic₁₃	—	2	8	no	—
506	Dic₁₃	C₂³×D₄	1	6	yes	—
507	Dic₁₃	C₂³×D₄	1	2	yes	—
508	2₋¹⁺⁴	—	2	2	no	—
509	2₋¹⁺⁴	—	13	24	no	—
510	2₋¹⁺⁴	—	13	8	no	—
511	2₋¹⁺⁴	—	13	24	no	—
512	2₋¹⁺⁴	—	26	8	no	—
513	2₋¹⁺⁴	—	26	8	no	—
514	2₋¹⁺⁴	—	26	8	no	—
515	2₋¹⁺⁴	—	26	12	no	—
516	2₋¹⁺⁴	—	26	24	no	—
517	2₋¹⁺⁴	—	26	2	no	—
518	2₋¹⁺⁴	C₂²×D₁₃	1	8	yes	complemented
519	H(5,𝔽₂)	—	2	6	no	—
520	H(5,𝔽₂)	—	13	24	no	—
521	H(5,𝔽₂)	—	13	8	no	—
522	H(5,𝔽₂)	—	13	24	no	—
523	H(5,𝔽₂)	—	26	24	no	—
524	H(5,𝔽₂)	—	26	24	no	—
525	H(5,𝔽₂)	—	26	24	no	—
526	H(5,𝔽₂)	—	26	24	no	—
527	H(5,𝔽₂)	—	26	12	no	—
528	H(5,𝔽₂)	—	26	8	no	—
529	H(5,𝔽₂)	—	26	6	no	—
530	H(5,𝔽₂)	C₂²×D₁₃	1	8	yes	complemented
531	C₂×#41	—	2	8	no	—
532	C₂×#41	—	13	8	no	—
533	C₂×#41	—	13	8	no	—
534	C₂×#41	—	13	1	no	—
535	C₂×#41	—	13	3	no	—
536	C₂×#41	—	13	3	no	—
537	C₂×#41	—	13	24	no	—
538	C₂×#41	—	13	24	no	—
539	C₂×#41	—	13	8	no	—
540	C₂×#41	—	13	24	no	—
541	C₂×#41	—	13	12	no	—
542	C₂×#41	—	13	12	no	—
543	C₂×#41	—	13	12	no	—
544	C₂×#41	—	26	12	no	—
545	C₂×#41	—	26	24	no	—
546	C₂×#41	—	26	12	no	—
547	C₂×#41	—	26	12	no	—
548	C₂×#41	—	26	12	no	—
549	C₂×#41	—	26	12	no	—
550	C₂×#41	—	26	12	no	—
551	C₂×#41	—	26	24	no	—
552	C₂×#41	—	26	24	no	—
553	C₂×#41	—	26	8	no	—
554	C₂×#41	—	26	8	no	—
555	C₂×#41	—	26	8	no	—
556	C₂×#41	—	26	24	no	—
557	C₂×#41	—	26	24	no	—
558	C₂×#41	—	26	8	no	—
559	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
560	C₂×#41	C₂²×D₁₃	1	12	yes	complemented
561	C₂²×Q₈	—	13	1	no	—
562	C₂²×Q₈	—	13	12	no	—
563	C₂²×Q₈	—	26	8	no	—
564	C₂²×D₄	—	13	3	no	—
565	C₂²×D₄	—	13	12	no	—
566	C₂²×D₄	—	26	24	no	—
567	C₂²×D₄	—	26	12	no	—
568	C₂³×C₄	—	13	3	no	—
569	C₂³×C₄	—	26	12	no	—
570	#137	—	13	24	no	—
571	#137	—	13	24	no	—
572	#137	—	13	24	no	—
573	#137	—	13	8	no	—
574	#137	—	13	24	no	—
575	#137	—	13	24	no	—
576	#137	—	13	24	no	—
577	#137	—	13	8	no	—
578	#137	—	13	24	no	—
579	#137	—	13	24	no	—
580	#137	—	13	24	no	—
581	#137	C₂²×D₁₃	1	24	yes	complemented
582	AGL(1,ℤ/8)	—	13	24	no	—
583	AGL(1,ℤ/8)	—	13	24	no	—
584	AGL(1,ℤ/8)	—	13	24	no	—
585	AGL(1,ℤ/8)	—	13	8	no	—
586	AGL(1,ℤ/8)	—	13	24	no	—
587	AGL(1,ℤ/8)	—	13	24	no	—
588	AGL(1,ℤ/8)	—	13	24	no	—
589	AGL(1,ℤ/8)	—	13	8	no	—
590	AGL(1,ℤ/8)	—	13	24	no	—
591	AGL(1,ℤ/8)	—	13	24	no	—
592	AGL(1,ℤ/8)	—	13	24	no	—
593	AGL(1,ℤ/8)	C₂²×D₁₃	1	24	yes	complemented
594	#135	—	13	8	no	—
595	#135	—	13	24	no	—
596	#135	—	13	24	no	—
597	#135	—	13	24	no	—
598	#135	—	13	24	no	—
599	#135	—	13	48	no	—
600	#135	—	13	24	no	—
601	#135	—	13	12	no	—
602	#135	—	13	4	no	—
603	#135	—	13	12	no	—
604	#135	—	13	12	no	—
605	#135	C₂²×D₁₃	1	12	yes	complemented
606	#135	C₂²×D₁₃	1	4	yes	complemented
607	#135	C₂²×D₁₃	1	12	yes	complemented
608	#135	C₂²×D₁₃	1	12	yes	complemented
609	C₂×Q₁₆	—	13	12	no	—
610	C₂×Q₁₆	—	13	24	no	—
611	C₂×Q₁₆	—	13	6	no	—
612	C₂×Q₁₆	C₂²×D₁₃	1	6	yes	complemented
613	C₂×SD₁₆	—	13	12	no	—
614	C₂×SD₁₆	—	13	12	no	—
615	C₂×SD₁₆	—	13	48	no	—
616	C₂×SD₁₆	—	13	12	no	—
617	C₂×SD₁₆	C₂²×D₁₃	1	12	yes	complemented
618	C₂×D₈	—	13	12	no	—
619	C₂×D₈	—	13	24	no	—
620	C₂×D₈	—	13	6	no	—
621	C₂×D₈	C₂²×D₁₃	1	6	yes	complemented
622	#131	—	13	8	no	—
623	#131	—	13	24	no	—
624	#131	—	13	12	no	—
625	#131	—	13	12	no	—
626	#131	C₂²×D₁₃	1	4	yes	complemented
627	#131	C₂²×D₁₃	1	4	yes	complemented
628	C₂×M₁₆	—	13	3	no	—
629	C₂×M₁₆	—	13	24	no	—
630	C₂×M₁₆	—	13	3	no	—
631	C₂×M₁₆	—	13	1	no	—
632	C₂×M₁₆	—	13	3	no	—
633	C₂×M₁₆	—	13	3	no	—
634	C₂×M₁₆	—	13	12	no	—
635	C₂×M₁₆	—	13	12	no	—
636	C₂×M₁₆	C₂²×D₁₃	1	3	yes	complemented
637	C₂²×C₈	—	13	3	no	—
638	C₂²×C₈	—	13	6	no	—
639	C₂²×C₈	C₂²×D₁₃	1	3	yes	complemented
640	C₂×C₁₃	—	2	1	no	—
641	C₂×C₁₃	—	2	6	no	—
642	C₂×C₁₃	—	4	8	no	—
643	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
644	D₁₃	—	2	2	no	—
645	D₁₃	—	2	6	no	—
646	D₁₃	—	4	8	no	—
647	C₂⁴	—	13	3	no	—
648	C₂⁴	—	26	12	no	—
649	#41	—	2	8	no	—
650	#41	—	2	24	no	—
651	#41	—	2	12	no	—
652	#41	—	2	12	no	—
653	#41	—	13	8	no	—
654	#41	—	13	24	no	—
655	#41	—	13	12	no	—
656	#41	—	13	12	no	—
657	#41	—	13	24	no	—
658	#41	—	13	8	no	—
659	#41	—	13	24	no	—
660	#41	—	13	8	no	—
661	#41	—	13	8	no	—
662	#41	—	13	24	no	—
663	#41	—	26	8	no	—
664	#41	—	26	24	no	—
665	#41	—	26	24	no	—
666	#41	—	26	24	no	—
667	#41	—	26	48	no	—
668	#41	—	26	24	no	—
669	#41	—	26	24	no	—
670	#41	—	26	8	no	—
671	#41	—	26	24	no	—
672	#41	—	26	12	no	—
673	#41	—	26	24	no	—
674	#41	—	26	24	no	—
675	#41	—	26	12	no	—
676	#41	—	26	12	no	—
677	#41	—	26	12	no	—
678	#41	—	26	48	no	—
679	#41	—	26	24	no	—
680	#41	—	26	24	no	—
681	#41	—	26	8	no	—
682	#41	—	26	24	no	—
683	#41	—	26	12	no	—
684	#41	—	26	12	no	—
685	#41	D₄×D₁₃	1	4	yes	—
686	#41	C₂³×D₁₃	1	8	yes	—
687	#41	C₂³×D₁₃	1	24	yes	—
688	#41	C₂³×D₁₃	1	4	yes	—
689	C₂×Q₈	—	2	8	no	—
690	C₂×Q₈	—	13	8	no	—
691	C₂×Q₈	—	13	3	no	—
692	C₂×Q₈	—	13	24	no	—
693	C₂×Q₈	—	13	8	no	—
694	C₂×Q₈	—	13	12	no	—
695	C₂×Q₈	—	26	12	no	—
696	C₂×Q₈	—	26	24	no	—
697	C₂×Q₈	—	26	12	no	—
698	C₂×Q₈	—	26	12	no	—
699	C₂×Q₈	—	26	24	no	—
700	C₂×Q₈	—	26	8	no	—
701	C₂×Q₈	D₄×D₁₃	1	1	yes	characteristic
702	C₂×Q₈	C₂³×D₁₃	1	12	yes	—
703	C₂×D₄	—	2	12	no	—
704	C₂×D₄	—	2	24	no	—
705	C₂×D₄	—	13	6	no	—
706	C₂×D₄	—	13	24	no	—
707	C₂×D₄	—	13	24	no	—
708	C₂×D₄	—	13	8	no	—
709	C₂×D₄	—	13	3	no	—
710	C₂×D₄	—	13	12	no	—
711	C₂×D₄	—	26	24	no	—
712	C₂×D₄	—	26	12	no	—
713	C₂×D₄	—	26	12	no	—
714	C₂×D₄	—	26	12	no	—
715	C₂×D₄	—	26	12	no	—
716	C₂×D₄	—	26	48	no	—
717	C₂×D₄	—	26	24	no	—
718	C₂×D₄	—	26	8	no	—
719	C₂×D₄	—	26	24	no	—
720	C₂×D₄	—	26	24	no	—
721	C₂×D₄	—	26	24	no	—
722	C₂×D₄	—	26	48	no	—
723	C₂×D₄	—	26	12	no	—
724	C₂×D₄	—	26	12	no	—
725	C₂×D₄	—	26	24	no	—
726	C₂×D₄	D₄×D₁₃	1	3	yes	—
727	C₂×D₄	C₂³×D₁₃	1	12	yes	—
728	C₂²×C₄	—	2	12	no	—
729	C₂²×C₄	—	13	3	no	—
730	C₂²×C₄	—	13	12	no	—
731	C₂²×C₄	—	13	3	no	—
732	C₂²×C₄	—	13	3	no	—
733	C₂²×C₄	—	13	3	no	—
734	C₂²×C₄	—	13	1	no	—
735	C₂²×C₄	—	13	12	no	—
736	C₂²×C₄	—	26	8	no	—
737	C₂²×C₄	—	26	24	no	—
738	C₂²×C₄	—	26	12	no	—
739	C₂²×C₄	—	26	24	no	—
740	C₂²×C₄	—	26	24	no	—
741	C₂²×C₄	—	26	12	no	—
742	C₂²×C₄	—	26	12	no	—
743	C₂²×C₄	—	26	12	no	—
744	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
745	Q₁₆	—	13	8	no	—
746	Q₁₆	—	13	24	no	—
747	Q₁₆	—	13	12	no	—
748	Q₁₆	—	13	4	no	—
749	Q₁₆	C₂³×D₁₃	1	12	yes	—
750	Q₁₆	C₂³×D₁₃	1	4	yes	—
751	SD₁₆	—	13	8	no	—
752	SD₁₆	—	13	24	no	—
753	SD₁₆	—	13	8	no	—
754	SD₁₆	—	13	24	no	—
755	SD₁₆	—	13	24	no	—
756	SD₁₆	—	13	8	no	—
757	SD₁₆	C₂³×D₁₃	1	24	yes	—
758	SD₁₆	C₂³×D₁₃	1	8	yes	—
759	D₈	—	13	8	no	—
760	D₈	—	13	24	no	—
761	D₈	—	13	12	no	—
762	D₈	—	13	4	no	—
763	D₈	C₂³×D₁₃	1	12	yes	—
764	D₈	C₂³×D₁₃	1	4	yes	—
765	M₁₆	—	13	12	no	—
766	M₁₆	—	13	12	no	—
767	M₁₆	—	13	2	no	—
768	M₁₆	—	13	2	no	—
769	M₁₆	—	13	12	no	—
770	M₁₆	—	13	6	no	—
771	M₁₆	—	13	6	no	—
772	M₁₆	C₂³×D₁₃	1	12	yes	—
773	C₂×C₈	—	13	1	no	—
774	C₂×C₈	—	13	3	no	—
775	C₂×C₈	—	13	12	no	—
776	C₂×C₈	—	13	24	no	—
777	C₂×C₈	C₂³×D₁₃	1	3	yes	—
778	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
779	C₂×C₈	C₂³×D₁₃	1	6	yes	—
780	C₂×C₈	C₂³×D₁₃	1	6	yes	—
781	C₁₃	#63090	1	1	yes	characteristic, complemented, Sylow
782	C₂³	—	2	12	no	—
783	C₂³	—	13	1	no	—
784	C₂³	—	13	12	no	—
785	C₂³	—	13	3	no	—
786	C₂³	—	26	8	no	—
787	C₂³	—	26	24	no	—
788	C₂³	—	26	12	no	—
789	C₂³	—	104	3	no	—
790	C₂³	—	104	24	no	—
791	C₂³	C₂×D₄×D₁₃	1	3	yes	—
792	Q₈	—	2	12	no	—
793	Q₈	—	13	12	no	—
794	Q₈	—	13	8	no	—
795	Q₈	—	26	8	no	—
796	Q₈	—	26	24	no	—
797	Q₈	—	26	12	no	—
798	Q₈	C₂×D₄×D₁₃	1	4	yes	—
799	Q₈	C₂⁴×D₁₃	1	8	yes	—
800	D₄	—	2	24	no	—
801	D₄	—	2	8	no	—
802	D₄	—	2	12	no	—
803	D₄	—	13	24	no	—
804	D₄	—	13	12	no	—
805	D₄	—	13	8	no	—
806	D₄	—	26	8	no	—
807	D₄	—	26	24	no	—
808	D₄	—	26	8	no	—
809	D₄	—	26	24	no	—
810	D₄	—	26	8	no	—
811	D₄	—	26	24	no	—
812	D₄	—	26	24	no	—
813	D₄	—	26	8	no	—
814	D₄	—	26	12	no	—
815	D₄	C₂×D₄×D₁₃	1	12	yes	—
816	D₄	C₂⁴×D₁₃	1	8	yes	—
817	C₂×C₄	—	2	12	no	—
818	C₂×C₄	—	2	24	no	—
819	C₂×C₄	—	2	8	no	—
820	C₂×C₄	—	13	1	no	—
821	C₂×C₄	—	13	12	no	—
822	C₂×C₄	—	13	3	no	—
823	C₂×C₄	—	13	12	no	—
824	C₂×C₄	—	13	12	no	—
825	C₂×C₄	—	13	2	no	—
826	C₂×C₄	—	13	6	no	—
827	C₂×C₄	—	13	6	no	—
828	C₂×C₄	—	13	2	no	—
829	C₂×C₄	—	26	8	no	—
830	C₂×C₄	—	26	24	no	—
831	C₂×C₄	—	26	8	no	—
832	C₂×C₄	—	26	24	no	—
833	C₂×C₄	—	26	8	no	—
834	C₂×C₄	—	26	24	no	—
835	C₂×C₄	—	26	12	no	—
836	C₂×C₄	—	26	24	no	—
837	C₂×C₄	—	26	8	no	—
838	C₂×C₄	C₂×D₄×D₁₃	1	3	yes	—
839	C₂×C₄	C₂×D₄×D₁₃	1	6	yes	—
840	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
841	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
842	C₈	—	13	6	no	—
843	C₈	—	13	2	no	—
844	C₈	C₂⁴×D₁₃	1	6	yes	—
845	C₈	C₂⁴×D₁₃	1	1	yes	characteristic
846	C₈	C₂⁴×D₁₃	1	1	yes	characteristic
847	C₂²	—	2	8	no	—
848	C₂²	—	4	3	no	—
849	C₂²	—	8	12	no	—
850	C₂²	—	13	2	no	—
851	C₂²	—	13	6	no	—
852	C₂²	—	26	8	no	—
853	C₂²	—	52	3	no	—
854	C₂²	—	52	1	no	—
855	C₂²	—	52	12	no	—
856	C₂²	—	52	16	no	—
857	C₂²	—	104	12	no	—
858	C₂²	—	104	24	no	—
859	C₂²	C₂²×D₄×D₁₃	1	6	yes	—
860	C₂²	C₂²×D₄×D₁₃	1	1	yes	characteristic
861	C₄	—	2	8	no	—
862	C₄	—	13	2	no	—
863	C₄	—	13	6	no	—
864	C₄	—	26	8	no	—
865	C₄	C₂²×D₄×D₁₃	1	6	yes	—
866	C₄	C₂²×D₄×D₁₃	1	1	yes	characteristic
867	C₄	C₂⁵×D₁₃	1	1	yes	characteristic
868	C₂	—	2	1	no	—
869	C₂	—	2	6	no	—
870	C₂	—	4	8	no	—
871	C₂	—	26	2	no	—
872	C₂	—	26	6	no	—
873	C₂	—	52	8	no	—
874	C₂	C₂³×D₄×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₄×D₁₃
commutator, cosocle	C₄×C₁₃	C₂⁶
Frattini	C₄	C₂⁵×D₁₃
Fitting	C₁₃×#3584	C₂
socle	C₂×C₁₃	C₂⁴×D₄
hypercenter	#3584	D₁₃
hypocenter	C₁₃	#63090
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×#41 ◁ #3584

Complements

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

N	H ≅ G/N	type
1. D₁₃×#585	C₂	semidirect
2. #13129621	C₂	semidirect
3. #13129618	C₂	semidirect
4. #13129614	C₂	semidirect
5. #13129611	C₂	semidirect
6. #13129610	C₂	semidirect
7. #13129609	C₂	semidirect
8. #13129607	C₂	semidirect
9. #13129605	C₂	semidirect
10. C₂×#11719473	C₂	semidirect
11. D₁₃×#575	C₂	semidirect
12. C₂×#11719455	C₂	semidirect
13. C₁₃×#3584	C₂	semidirect
14. C₁₃×#585	C₂²	semidirect
16. #11719652	C₂²	semidirect
18. D₁₃×2₋¹⁺⁴	C₂²	semidirect
20. #11719650	C₂²	semidirect
22. D₁₃×H(5,𝔽₂)	C₂²	semidirect
24. #11719648	C₂²	semidirect
25. #11719648	C₂²	semidirect
28. C₂×#41×D₁₃	C₂²	semidirect
29. C₁₃×#578	C₂²	semidirect
30. C₁₃×#577	C₂²	semidirect
31. C₁₃×#576	C₂²	semidirect
32. C₁₃×#575	C₂²	semidirect
33. C₂×C₁₃×#135	C₂²	semidirect
34. C₂×C₁₃×#131	C₂²	semidirect
35. #11719543	C₂²	semidirect
36. #11719542	C₂²	semidirect
37. #11719541	C₂²	semidirect
38. #11719540	C₂²	semidirect
39. #11719527	C₂²	semidirect
40. C₂×#88204	C₂²	semidirect
41. C₂×#88202	C₂²	semidirect
42. #11719484	C₂²	semidirect
43. #11719483	C₂²	semidirect
44. #11719482	C₂²	semidirect
45. D₁₃×#137	C₂²	semidirect
46. #11719480	C₂²	semidirect
47. #11719479	C₂²	semidirect
48. #11719478	C₂²	semidirect
49. D₁₃×AGL(1,ℤ/8)	C₂²	semidirect
50. #11719476	C₂²	semidirect
51. #11719475	C₂²	semidirect
52. #11719474	C₂²	semidirect
53. #11719473	C₂²	semidirect
54. #11719473	C₂²	semidirect
55. #11719473	C₂²	semidirect
56. #11719473	C₂²	semidirect
57. #11719473	C₂²	semidirect
58. #11719473	C₂²	semidirect
59. D₁₃×#135	C₂²	semidirect
60. #11719471	C₂²	semidirect
61. C₂×#88172	C₂²	semidirect
62. #11719467	C₂²	semidirect
63. C₂×#88169	C₂²	semidirect
64. C₂×#88168	C₂²	semidirect
65. #11719462	C₂²	semidirect
66. C₂×#88165	C₂²	semidirect
67. #11719458	C₂²	semidirect
68. #11719457	C₂²	semidirect
69. #11719456	C₂²	semidirect
70. #11719455	C₂²	semidirect
71. #11719455	C₂²	semidirect
72. #11719453	C₂²	semidirect
73. C₂×#88161	C₂²	semidirect
74. C₂×M₁₆×D₁₃	C₂²	semidirect
75. C₂×#88158	C₂²	semidirect
76. C₂×#88155	C₂²	semidirect
77. C₂²×#6094	C₂²	semidirect
79. C₁₃×2₋¹⁺⁴	C₂³	semidirect
81. C₁₃×H(5,𝔽₂)	C₂³	semidirect
84. C₂×C₁₃×#41	C₂³	semidirect
88. #88257	C₂³	semidirect
89. #88257	C₂³	semidirect
93. #88256	C₂³	semidirect
94. #88256	C₂³	semidirect
109. #41×D₁₃	C₂³	semidirect
110. #41×D₁₃	C₂³	semidirect
114. #88254	C₂³	semidirect
120. C₂×Q₈×D₁₃	C₂³	semidirect
125. #88251	C₂³	semidirect
133. C₂×D₄×D₁₃	C₂³	semidirect
137. C₂×#6127	C₂³	semidirect
140. C₁₃×#137	C₂³	semidirect
141. C₁₃×AGL(1,ℤ/8)	C₂³	semidirect
142. C₁₃×#135	C₂³	semidirect
143. C₁₃×#135	C₂³	semidirect
144. C₁₃×#135	C₂³	semidirect
145. C₁₃×#135	C₂³	semidirect
146. C₂×C₁₃×Q₁₆	C₂³	semidirect
147. C₂×C₁₃×SD₁₆	C₂³	semidirect
148. C₂×C₁₃×D₈	C₂³	semidirect
149. C₁₃×#131	C₂³	semidirect
150. C₁₃×#131	C₂³	semidirect
151. C₂×C₁₃×M₁₆	C₂³	semidirect
152. C₂²×C₈×C₁₃	C₂³	semidirect
153. #88205	C₂³	semidirect
154. #88204	C₂³	semidirect
155. #88204	C₂³	semidirect
156. #88204	C₂³	semidirect
157. #88204	C₂³	semidirect
158. #88203	C₂³	semidirect
159. #88202	C₂³	semidirect
160. C₂×#6107	C₂³	semidirect
161. #88196	C₂³	semidirect
162. C₂×#6106	C₂³	semidirect
163. C₂×#6105	C₂³	semidirect
164. #88186	C₂³	semidirect
165. C₂×#6104	C₂³	semidirect
166. C₂×#6099	C₂³	semidirect
167. C₂²×#1055	C₂³	semidirect
168. #88173	C₂³	semidirect
169. #88172	C₂³	semidirect
170. #88172	C₂³	semidirect
171. #88172	C₂³	semidirect
172. #88172	C₂³	semidirect
173. Q₁₆×D₁₃	C₂³	semidirect
174. #88170	C₂³	semidirect
175. #88169	C₂³	semidirect
176. #88169	C₂³	semidirect
177. #88169	C₂³	semidirect
178. #88169	C₂³	semidirect
179. #88168	C₂³	semidirect
180. #88168	C₂³	semidirect
181. #88168	C₂³	semidirect
182. #88168	C₂³	semidirect
183. SD₁₆×D₁₃	C₂³	semidirect
184. #88166	C₂³	semidirect
185. #88165	C₂³	semidirect
186. #88165	C₂³	semidirect
187. #88165	C₂³	semidirect
188. #88165	C₂³	semidirect
189. D₈×D₁₃	C₂³	semidirect
190. #88163	C₂³	semidirect
191. #88162	C₂³	semidirect
192. #88161	C₂³	semidirect
193. M₁₆×D₁₃	C₂³	semidirect
194. C₂×Dic₅₂	C₂³	semidirect
195. #88158	C₂³	semidirect
196. #88158	C₂³	semidirect
197. #88158	C₂³	semidirect
198. #88158	C₂³	semidirect
199. C₂×D₁₀₄	C₂³	semidirect
200. C₂×#6095	C₂³	semidirect
201. #88155	C₂³	semidirect
202. #88155	C₂³	semidirect
205. C₂×#6094	C₂³	semidirect
206. C₂×#6094	C₂³	semidirect
207. C₂×#6094	C₂³	semidirect
208. C₂×#6094	C₂³	semidirect
209. C₂×C₈×D₁₃	C₂³	semidirect
354. #3584	D₁₃	semidirect
430. #585	C₂×D₁₃	semidirect
443. #578	C₂×D₁₃	semidirect
451. #577	C₂×D₁₃	semidirect
457. #576	C₂×D₁₃	semidirect
468. #575	C₂×D₁₃	semidirect
478. C₂×#135	C₂×D₁₃	semidirect
484. C₂×#131	C₂×D₁₃	semidirect
518. 2₋¹⁺⁴	C₂²×D₁₃	semidirect
530. H(5,𝔽₂)	C₂²×D₁₃	semidirect
560. C₂×#41	C₂²×D₁₃	semidirect
581. #137	C₂²×D₁₃	semidirect
593. AGL(1,ℤ/8)	C₂²×D₁₃	semidirect
605. #135	C₂²×D₁₃	semidirect
606. #135	C₂²×D₁₃	semidirect
607. #135	C₂²×D₁₃	semidirect
608. #135	C₂²×D₁₃	semidirect
612. C₂×Q₁₆	C₂²×D₁₃	semidirect
617. C₂×SD₁₆	C₂²×D₁₃	semidirect
621. C₂×D₈	C₂²×D₁₃	semidirect
626. #131	C₂²×D₁₃	semidirect
627. #131	C₂²×D₁₃	semidirect
636. C₂×M₁₆	C₂²×D₁₃	semidirect
639. C₂²×C₈	C₂²×D₁₃	semidirect
781. C₁₃	#63090	semidirect

Maximal subgroups

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

subgroup	index
D₁₃×#585	2
#13129621	2
#13129618	2
#13129614	2
#13129611	2
#13129610	2
#13129609	2
#13129607	2
#13129605	2
C₂×#11719473	2
D₁₃×#575	2
C₂×#11719455	2
C₁₃×#3584	2
#63090	13