Subgroups — #13128689

Order 1664.

1140 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719437	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719430	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719414	C₂	1	4	yes	maximal, complemented
5	#11719409	C₂	1	4	yes	maximal, complemented
6	#11719386	C₂	1	2	yes	maximal, complemented
7	#11719379	C₂	1	2	yes	maximal, complemented
8	#11719336	C₂	1	2	yes	maximal, complemented
9	#11719332	C₂	1	2	yes	maximal, complemented
10	#11719290	C₂	1	2	yes	maximal, complemented
11	#11719283	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719282	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719279	C₂	1	2	yes	maximal, complemented
14	#11719258	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719237	C₂	1	2	yes	maximal, complemented
17	#11719229	C₂	1	2	yes	maximal, complemented
18	C₂×#6131	C₂²	1	2	yes	—
19	C₂×#6131	C₂²	1	2	yes	complemented
20	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
21	C₂×#6127	C₂²	1	2	yes	complemented
22	C₂²×C₄×D₁₃	C₂²	1	2	yes	—
23	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#126	C₂²	1	4	yes	complemented
25	C₁₃×#124	C₂²	1	2	yes	—
26	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
28	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#117	C₂²	1	2	yes	complemented
31	#88201	C₂²	1	2	yes	—
32	#88201	C₂²	1	2	yes	complemented
33	#88200	C₂²	1	1	yes	characteristic
34	Q₈×Dic₁₃	C₂²	1	2	yes	complemented
35	#88198	C₂²	1	1	yes	characteristic, complemented
36	#88194	C₂²	1	2	yes	—
37	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
38	#88184	C₂²	1	2	yes	complemented
39	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
40	#88152	C₂²	1	4	yes	complemented
41	#88151	C₂²	1	1	yes	characteristic
42	#88151	C₂²	1	2	yes	complemented
43	#88150	C₂²	1	2	yes	—
44	#88149	C₂²	1	2	yes	—
45	#88149	C₂²	1	2	yes	—
46	#88149	C₂²	1	2	yes	complemented
47	#88149	C₂²	1	4	yes	complemented
48	#88148	C₂²	1	4	yes	complemented
49	#88148	C₂²	1	4	yes	complemented
50	#88147	C₂²	1	1	yes	characteristic
51	#88147	C₂²	1	4	yes	—
52	#88147	C₂²	1	2	yes	complemented
53	#88147	C₂²	1	2	yes	complemented
54	#88147	C₂²	1	2	yes	complemented
55	#88146	C₂²	1	2	yes	complemented
56	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
57	C₄⋊C₄×D₁₃	C₂²	1	4	yes	complemented
58	#88143	C₂²	1	2	yes	complemented
59	#88142	C₂²	1	1	yes	characteristic, complemented
60	#88140	C₂²	1	4	yes	complemented
61	#88139	C₂²	1	4	yes	complemented
62	#88138	C₂²	1	4	yes	—
63	#88138	C₂²	1	4	yes	—
64	#88138	C₂²	1	4	yes	complemented
65	#88137	C₂²	1	4	yes	complemented
66	#88136	C₂²	1	4	yes	—
67	#88136	C₂²	1	4	yes	—
68	#88135	C₂²	1	2	yes	—
69	#88135	C₂²	1	4	yes	complemented
70	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
71	#88129	C₂²	1	4	yes	complemented
72	#88128	C₂²	1	2	yes	—
73	#88128	C₂²	1	1	yes	characteristic, complemented
74	C₄×D₅₂	C₂²	1	1	yes	characteristic
75	C₄×D₅₂	C₂²	1	4	yes	—
76	C₄×D₅₂	C₂²	1	4	yes	complemented
77	C₄×D₅₂	C₂²	1	2	yes	complemented
78	#88126	C₂²	1	2	yes	—
79	#88126	C₂²	1	4	yes	complemented
80	C₄²×D₁₃	C₂²	1	1	yes	characteristic
81	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
82	C₄×Dic₂₆	C₂²	1	2	yes	complemented
83	C₂³×D₁₃	C₂³	1	2	yes	—
84	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
86	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
88	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
89	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
91	C₂²×Dic₁₃	C₂³	1	2	yes	—
92	#6131	—	2	8	no	—
93	#6131	—	4	4	no	—
94	D₄×D₁₃	—	2	4	no	—
95	#6127	—	4	4	no	—
96	C₂×D₅₂	C₂³	1	1	yes	characteristic
97	C₂×D₅₂	C₂³	1	4	yes	—
98	C₂×D₅₂	C₂³	1	2	yes	—
99	C₂×D₅₂	C₂³	1	2	yes	—
100	C₂×D₅₂	C₂³	1	4	yes	—
101	C₂×D₅₂	C₂³	1	4	yes	—
102	C₂×D₅₂	C₂³	1	2	yes	—
103	C₂×C₄×D₁₃	—	4	4	no	—
104	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₂³	1	4	yes	—
106	C₂×C₄×D₁₃	C₂³	1	2	yes	—
107	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂³	1	2	yes	—
109	C₂×C₄×D₁₃	C₂³	1	4	yes	—
110	C₂×C₄×D₁₃	C₂³	1	2	yes	—
111	C₂×C₄×D₁₃	C₂³	1	4	yes	—
112	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
113	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
114	C₂×Dic₂₆	C₂³	1	2	yes	—
115	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
117	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
118	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
119	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
120	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
122	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
124	C₄²×C₁₃	C₂³	1	1	yes	characteristic
125	C₄²×C₁₃	C₂³	1	2	yes	—
126	C₄²×C₁₃	C₂³	1	4	yes	—
127	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
128	#6103	C₂³	1	2	yes	—
129	#6103	C₂³	1	2	yes	—
130	#6103	C₂³	1	4	yes	—
131	#6103	C₂³	1	4	yes	—
132	#6103	C₂³	1	2	yes	—
133	#6103	C₂³	1	4	yes	—
134	#6103	C₂³	1	4	yes	—
135	#6103	C₂³	1	2	yes	—
136	#6103	C₂³	1	4	yes	—
137	#6103	C₂³	1	4	yes	—
138	C₄⋊Dic₁₃	C₂³	1	2	yes	—
139	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
140	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
141	C₄⋊Dic₁₃	C₂³	1	4	yes	—
142	#6101	C₂³	1	2	yes	—
143	#6101	C₂³	1	2	yes	—
144	#6101	C₂³	1	2	yes	—
145	#6101	C₂³	1	2	yes	—
146	#6101	C₂³	1	2	yes	—
147	#6101	C₂³	1	2	yes	—
148	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
149	C₄×Dic₁₃	C₂³	1	2	yes	—
150	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
151	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
152	C₄×Dic₁₃	C₂³	1	4	yes	—
153	#3506	—	13	1	no	maximal, Sylow
154	C₂³×C₁₃	C₂⁴	1	2	yes	—
155	C₂²×D₁₃	—	2	4	no	—
156	C₂²×D₁₃	—	4	2	no	—
157	C₂²×D₁₃	—	4	2	no	—
158	C₂²×D₁₃	C₂⁴	1	2	yes	—
159	C₂²×D₁₃	C₂⁴	1	4	yes	—
160	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
161	Q₈×C₁₃	—	2	4	no	—
162	Q₈×C₁₃	—	2	2	no	—
163	D₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	4	no	—
165	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
167	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
168	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
169	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
170	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₂²⋊D₁₃	—	2	4	no	—
173	C₂²⋊D₁₃	—	4	4	no	—
174	C₂²⋊D₁₃	—	4	4	no	—
175	C₂×Dic₁₃	—	4	2	no	—
176	C₂×Dic₁₃	C₂⁴	1	2	yes	—
177	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
178	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
179	C₂×Dic₁₃	C₂⁴	1	2	yes	—
180	C₂×Dic₁₃	C₂⁴	1	2	yes	—
181	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
182	D₅₂	—	2	8	no	—
183	D₅₂	—	2	2	no	—
184	D₅₂	—	2	4	no	—
185	D₅₂	—	2	4	no	—
186	D₅₂	—	4	4	no	—
187	D₅₂	—	4	2	no	—
188	D₅₂	—	4	4	no	—
189	C₄×D₁₃	—	2	2	no	—
190	C₄×D₁₃	—	2	4	no	—
191	C₄×D₁₃	—	2	8	no	—
192	C₄×D₁₃	—	4	2	no	—
193	C₄×D₁₃	—	4	2	no	—
194	C₄×D₁₃	—	4	1	no	—
195	C₄×D₁₃	—	4	4	no	—
196	C₄×D₁₃	—	4	4	no	—
197	C₄×D₁₃	#41	1	4	yes	complemented
198	Dic₂₆	—	2	2	no	—
199	Dic₂₆	—	4	2	no	—
200	#559	—	13	2	no	—
201	#559	—	13	2	no	—
202	#556	—	13	1	no	—
203	#556	D₁₃	1	1	yes	characteristic, complemented
204	#555	—	13	2	no	—
205	#553	—	13	4	no	—
206	#550	—	13	1	no	—
207	#550	—	13	1	no	—
208	#547	—	13	2	no	—
209	#538	—	13	4	no	—
210	#535	—	13	2	no	—
211	#533	—	13	1	no	—
212	#532	—	13	1	no	—
213	#525	—	13	2	no	—
214	#525	—	13	2	no	—
215	#520	—	13	2	no	—
216	C₂×C₄×D₄	—	13	1	no	—
217	C₂²×C₁₃	—	2	2	no	—
218	C₂²×C₁₃	—	2	2	no	—
219	C₂²×C₁₃	—	2	2	no	—
220	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
221	C₂×D₁₃	—	2	1	no	—
222	C₂×D₁₃	—	2	1	no	—
223	C₂×D₁₃	—	2	4	no	—
224	C₂×D₁₃	—	2	2	no	—
225	C₂×D₁₃	—	2	2	no	—
226	C₂×D₁₃	—	2	4	no	—
227	C₂×D₁₃	—	2	4	no	—
228	C₂×D₁₃	—	2	2	no	—
229	C₂×D₁₃	—	4	8	no	—
230	C₂×D₁₃	C₂×#41	1	2	yes	—
231	C₄×C₁₃	—	2	4	no	—
232	C₄×C₁₃	—	2	2	no	—
233	C₄×C₁₃	—	2	2	no	—
234	C₄×C₁₃	—	2	2	no	—
235	C₄×C₁₃	—	2	1	no	—
236	C₄×C₁₃	C₂×#41	1	2	yes	—
237	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
238	Dic₁₃	—	2	2	no	—
239	Dic₁₃	—	2	2	no	—
240	Dic₁₃	—	2	1	no	—
241	Dic₁₃	—	2	1	no	—
242	Dic₁₃	—	2	2	no	—
243	Dic₁₃	C₂×#41	1	2	yes	—
244	C₂×#41	—	13	2	no	—
245	C₂×#41	—	13	2	no	—
246	C₂×#41	—	13	2	no	—
247	C₂²×D₄	—	13	1	no	—
248	C₂³×C₄	—	13	2	no	—
249	C₄⋊Q₈	—	13	1	no	—
250	C₄⋊Q₈	—	13	1	no	—
251	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
252	#127	—	13	2	no	—
253	#127	—	13	1	no	—
254	#127	—	13	2	no	—
255	#126	—	13	4	no	—
256	#126	C₂×D₁₃	1	4	yes	complemented
257	#125	—	13	2	no	—
258	#124	—	13	2	no	—
259	#124	—	13	2	no	—
260	#124	—	13	4	no	—
261	#124	—	13	4	no	—
262	#124	C₂×D₁₃	1	2	yes	—
263	#123	—	13	4	no	—
264	#123	—	13	4	no	—
265	#123	—	13	4	no	—
266	#123	—	13	4	no	—
267	C₂²⋊Q₈	—	13	1	no	—
268	C₂²⋊Q₈	—	13	1	no	—
269	C₂²⋊Q₈	—	13	2	no	—
270	C₂²⋊Q₈	—	13	2	no	—
271	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
272	#121	—	13	2	no	—
273	#121	—	13	2	no	—
274	#121	—	13	2	no	—
275	#121	—	13	2	no	—
276	#121	—	13	4	no	—
277	#121	—	13	4	no	—
278	#121	—	13	4	no	—
279	#121	—	13	4	no	—
280	#120	—	13	4	no	—
281	#120	—	13	4	no	—
282	C₄×Q₈	—	13	2	no	—
283	C₄×Q₈	—	13	1	no	—
284	C₄×Q₈	—	13	2	no	—
285	C₄×Q₈	C₂×D₁₃	1	2	yes	complemented
286	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
287	C₄×D₄	—	13	1	no	—
288	C₄×D₄	—	13	2	no	—
289	C₄×D₄	—	13	1	no	—
290	C₄×D₄	—	13	4	no	—
291	C₄×D₄	—	13	2	no	—
292	C₄×D₄	—	13	2	no	—
293	C₄×D₄	—	13	2	no	—
294	C₄×D₄	—	13	2	no	—
295	C₄×D₄	—	13	4	no	—
296	C₄×D₄	—	13	1	no	—
297	C₄×D₄	—	13	4	no	—
298	C₄×D₄	—	13	2	no	—
299	C₄×D₄	—	13	4	no	—
300	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
301	#117	—	13	2	no	—
302	#117	—	13	2	no	—
303	#117	—	13	4	no	—
304	#117	C₂×D₁₃	1	2	yes	complemented
305	C₂×C₄⋊C₄	—	13	1	no	—
306	C₂×C₄⋊C₄	—	13	4	no	—
307	C₂×C₂²⋊C₄	—	13	2	no	—
308	C₂×C₄²	—	13	1	no	—
309	C₂×C₁₃	—	4	2	no	—
310	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
311	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
312	C₂×C₁₃	#585	1	1	yes	characteristic
313	D₁₃	—	2	2	no	—
314	D₁₃	—	4	4	no	—
315	D₁₃	—	4	2	no	—
316	C₂⁴	—	13	2	no	—
317	#41	—	26	8	no	—
318	#41	—	52	4	no	—
319	#41	—	52	4	no	—
320	C₂×Q₈	—	13	1	no	—
321	C₂×Q₈	—	13	2	no	—
322	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
323	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
324	C₂×D₄	—	13	2	no	—
325	C₂×D₄	—	13	4	no	—
326	C₂×D₄	—	13	4	no	—
327	C₂×D₄	—	13	4	no	—
328	C₂×D₄	—	13	1	no	—
329	C₂×D₄	—	13	2	no	—
330	C₂×D₄	—	13	2	no	—
331	C₂×D₄	—	13	4	no	—
332	C₂×D₄	—	13	2	no	—
333	C₂×D₄	—	13	4	no	—
334	C₂×D₄	—	26	4	no	—
335	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
336	C₂²×C₄	—	13	1	no	—
337	C₂²×C₄	—	13	2	no	—
338	C₂²×C₄	—	13	1	no	—
339	C₂²×C₄	—	13	4	no	—
340	C₂²×C₄	—	13	2	no	—
341	C₂²×C₄	—	13	1	no	—
342	C₂²×C₄	—	13	2	no	—
343	C₂²×C₄	—	13	4	no	—
344	C₂²×C₄	—	13	4	no	—
345	C₂²×C₄	—	13	2	no	—
346	C₂²×C₄	—	52	4	no	—
347	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
348	C₄⋊C₄	—	13	2	no	—
349	C₄⋊C₄	—	13	2	no	—
350	C₄⋊C₄	—	13	1	no	—
351	C₄⋊C₄	—	13	4	no	—
352	C₄⋊C₄	—	13	2	no	—
353	C₄⋊C₄	—	13	1	no	—
354	C₄⋊C₄	—	13	2	no	—
355	C₄⋊C₄	—	13	2	no	—
356	C₄⋊C₄	—	13	2	no	—
357	C₄⋊C₄	—	13	2	no	—
358	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
359	C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
360	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
361	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
362	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
363	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
364	C₂²⋊C₄	—	13	2	no	—
365	C₂²⋊C₄	—	13	2	no	—
366	C₂²⋊C₄	—	13	2	no	—
367	C₂²⋊C₄	—	13	2	no	—
368	C₂²⋊C₄	—	13	2	no	—
369	C₂²⋊C₄	—	13	4	no	—
370	C₂²⋊C₄	—	13	4	no	—
371	C₂²⋊C₄	—	13	4	no	—
372	C₂²⋊C₄	—	13	4	no	—
373	C₂²⋊C₄	—	13	4	no	—
374	C₂²⋊C₄	—	13	4	no	—
375	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
376	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
377	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
378	C₄²	—	13	1	no	—
379	C₄²	—	13	1	no	—
380	C₄²	—	13	1	no	—
381	C₄²	—	13	4	no	—
382	C₄²	—	13	2	no	—
383	C₄²	C₂²×D₁₃	1	1	yes	characteristic
384	C₄²	C₂²×D₁₃	1	4	yes	—
385	C₄²	C₂²×D₁₃	1	2	yes	—
386	C₁₃	#3506	1	1	yes	characteristic, complemented, Sylow
387	C₂³	—	13	1	no	—
388	C₂³	—	13	2	no	—
389	C₂³	—	13	4	no	—
390	C₂³	—	26	4	no	—
391	C₂³	—	52	2	no	—
392	C₂³	—	52	2	no	—
393	C₂³	C₂³×D₁₃	1	2	yes	—
394	Q₈	—	2	4	no	—
395	Q₈	—	2	2	no	—
396	Q₈	—	26	2	no	—
397	Q₈	—	52	2	no	—
398	D₄	—	2	2	no	—
399	D₄	—	26	8	no	—
400	D₄	—	26	4	no	—
401	D₄	—	26	2	no	—
402	D₄	—	26	4	no	—
403	D₄	—	26	4	no	—
404	D₄	—	52	2	no	—
405	D₄	—	52	4	no	—
406	D₄	—	52	4	no	—
407	D₄	—	52	4	no	—
408	D₄	—	52	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	13	1	no	—
411	C₂×C₄	—	13	4	no	—
412	C₂×C₄	—	13	2	no	—
413	C₂×C₄	—	13	1	no	—
414	C₂×C₄	—	13	1	no	—
415	C₂×C₄	—	13	2	no	—
416	C₂×C₄	—	13	2	no	—
417	C₂×C₄	—	26	8	no	—
418	C₂×C₄	—	26	2	no	—
419	C₂×C₄	—	26	4	no	—
420	C₂×C₄	—	52	1	no	—
421	C₂×C₄	—	52	2	no	—
422	C₂×C₄	—	52	2	no	—
423	C₂×C₄	—	52	4	no	—
424	C₂×C₄	—	52	4	no	—
425	C₂×C₄	—	52	2	no	—
426	C₂×C₄	C₂³×D₁₃	1	4	yes	—
427	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
428	C₂×C₄	C₂³×D₁₃	1	2	yes	—
429	C₂×C₄	C₂³×D₁₃	1	2	yes	—
430	C₂×C₄	C₂³×D₁₃	1	2	yes	—
431	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
433	C₂²	—	2	2	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	13	2	no	—
437	C₂²	—	26	1	no	—
438	C₂²	—	26	1	no	—
439	C₂²	—	26	4	no	—
440	C₂²	—	26	2	no	—
441	C₂²	—	26	2	no	—
442	C₂²	—	26	4	no	—
443	C₂²	—	26	4	no	—
444	C₂²	—	26	2	no	—
445	C₂²	—	52	8	no	—
446	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
447	C₄	—	2	4	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	2	no	—
452	C₄	—	13	2	no	—
453	C₄	—	26	2	no	—
454	C₄	—	26	1	no	—
455	C₄	—	26	2	no	—
456	C₄	—	26	1	no	—
457	C₄	—	26	2	no	—
458	C₄	#41×D₁₃	1	2	yes	—
459	C₄	#88256	1	2	yes	—
460	C₂	—	4	2	no	—
461	C₂	—	26	2	no	—
462	C₂	—	52	2	no	—
463	C₂	—	52	4	no	—
464	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
465	C₂	C₂×#88256	1	1	yes	characteristic
466	C₂	#11719652	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#556	C₂
hypercenter	#556	D₁₃
hypocenter	C₁₃	#3506
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. C₁₃×#556	C₂	semidirect
2. #11719437	C₂	semidirect
3. #11719430	C₂	semidirect
4. #11719414	C₂	semidirect
5. #11719409	C₂	semidirect
6. #11719386	C₂	semidirect
7. #11719379	C₂	semidirect
8. #11719336	C₂	semidirect
9. #11719332	C₂	semidirect
10. #11719290	C₂	semidirect
11. #11719283	C₂	semidirect
12. #11719282	C₂	semidirect
13. #11719279	C₂	semidirect
14. #11719258	C₂	semidirect
15. C₄×D₄×D₁₃	C₂	semidirect
16. #11719237	C₂	semidirect
17. #11719229	C₂	semidirect
19. C₂×#6131	C₂²	semidirect
21. C₂×#6127	C₂²	semidirect
23. C₁₃×C₄⋊Q₈	C₂²	semidirect
24. C₁₃×#126	C₂²	semidirect
26. C₁₃×C₂²⋊Q₈	C₂²	semidirect
27. C₄×Q₈×C₁₃	C₂²	semidirect
28. C₄×Q₈×C₁₃	C₂²	semidirect
30. C₁₃×#117	C₂²	semidirect
32. #88201	C₂²	semidirect
34. Q₈×Dic₁₃	C₂²	semidirect
35. #88198	C₂²	semidirect
38. #88184	C₂²	semidirect
40. #88152	C₂²	semidirect
42. #88151	C₂²	semidirect
46. #88149	C₂²	semidirect
47. #88149	C₂²	semidirect
48. #88148	C₂²	semidirect
49. #88148	C₂²	semidirect
52. #88147	C₂²	semidirect
53. #88147	C₂²	semidirect
54. #88147	C₂²	semidirect
55. #88146	C₂²	semidirect
57. C₄⋊C₄×D₁₃	C₂²	semidirect
58. #88143	C₂²	semidirect
59. #88142	C₂²	semidirect
60. #88140	C₂²	semidirect
61. #88139	C₂²	semidirect
64. #88138	C₂²	semidirect
65. #88137	C₂²	semidirect
69. #88135	C₂²	semidirect
71. #88129	C₂²	semidirect
73. #88128	C₂²	semidirect
76. C₄×D₅₂	C₂²	semidirect
77. C₄×D₅₂	C₂²	semidirect
79. #88126	C₂²	semidirect
81. C₄×Dic₂₆	C₂²	semidirect
82. C₄×Dic₂₆	C₂²	semidirect
197. C₄×D₁₃	#41	semidirect
203. #556	D₁₃	semidirect
251. C₄⋊Q₈	C₂×D₁₃	semidirect
256. #126	C₂×D₁₃	semidirect
271. C₂²⋊Q₈	C₂×D₁₃	semidirect
285. C₄×Q₈	C₂×D₁₃	semidirect
286. C₄×Q₈	C₂×D₁₃	semidirect
304. #117	C₂×D₁₃	semidirect
386. C₁₃	#3506	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#556	2
#11719437	2
#11719430	2
#11719414	2
#11719409	2
#11719386	2
#11719379	2
#11719336	2
#11719332	2
#11719290	2
#11719283	2
#11719282	2
#11719279	2
#11719258	2
C₄×D₄×D₁₃	2
#11719237	2
#11719229	2
#3506	13