Subgroups — #13128871

Order 1664.

1252 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719435	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719430	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719383	C₂	1	4	yes	maximal, complemented
5	#11719381	C₂	1	4	yes	maximal, complemented
6	#11719324	C₂	1	2	yes	maximal, complemented
7	#11719317	C₂	1	2	yes	maximal, complemented
8	#11719314	C₂	1	2	yes	maximal, complemented
9	D₁₃×#121	C₂	1	2	yes	maximal, complemented
10	#11719262	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719258	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719235	C₂	1	2	yes	maximal, complemented
15	#11719235	C₂	1	2	yes	maximal, complemented
16	#11719229	C₂	1	2	yes	maximal, complemented
17	#11719226	C₂	1	2	yes	maximal, complemented
18	C₂×#6131	C₂²	1	2	yes	complemented
19	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
20	C₂×D₄×D₁₃	C₂²	1	2	yes	complemented
21	C₂×D₄×D₁₃	C₂²	1	4	yes	complemented
22	C₂×#6127	C₂²	1	2	yes	complemented
23	C₂²×D₅₂	C₂²	1	2	yes	—
24	C₂²×C₄×D₁₃	C₂²	1	2	yes	complemented
25	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
26	C₁₃×#124	C₂²	1	4	yes	complemented
27	C₁₃×#121	C₂²	1	2	yes	complemented
28	C₁₃×#121	C₂²	1	2	yes	complemented
29	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
30	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#117	C₂²	1	2	yes	complemented
32	C₁₃×#117	C₂²	1	2	yes	complemented
33	#88201	C₂²	1	2	yes	complemented
34	#88200	C₂²	1	4	yes	complemented
35	#88194	C₂²	1	2	yes	complemented
36	#88193	C₂²	1	4	yes	complemented
37	#88192	C₂²	1	1	yes	characteristic
38	#88192	C₂²	1	4	yes	complemented
39	#88191	C₂²	1	4	yes	complemented
40	#88190	C₂²	1	1	yes	characteristic, complemented
41	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
42	#88184	C₂²	1	2	yes	complemented
43	#88184	C₂²	1	2	yes	complemented
44	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
45	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
46	#88180	C₂²	1	2	yes	complemented
47	#88151	C₂²	1	2	yes	complemented
48	#88151	C₂²	1	1	yes	characteristic, complemented
49	#88149	C₂²	1	2	yes	complemented
50	#88149	C₂²	1	2	yes	complemented
51	#88149	C₂²	1	2	yes	complemented
52	#88147	C₂²	1	2	yes	—
53	#88147	C₂²	1	1	yes	characteristic
54	#88147	C₂²	1	2	yes	complemented
55	#88147	C₂²	1	2	yes	complemented
56	#88147	C₂²	1	2	yes	complemented
57	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
58	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
59	#88144	C₂²	1	2	yes	complemented
60	#88144	C₂²	1	1	yes	characteristic, complemented
61	#88140	C₂²	1	4	yes	complemented
62	#88138	C₂²	1	4	yes	complemented
63	#88138	C₂²	1	4	yes	complemented
64	#88138	C₂²	1	4	yes	complemented
65	#88137	C₂²	1	4	yes	complemented
66	#88137	C₂²	1	4	yes	complemented
67	#88137	C₂²	1	2	yes	complemented
68	#88136	C₂²	1	4	yes	complemented
69	#88136	C₂²	1	4	yes	complemented
70	#88135	C₂²	1	2	yes	complemented
71	C₂²⋊C₄×D₁₃	C₂²	1	4	yes	complemented
72	C₂²⋊C₄×D₁₃	C₂²	1	4	yes	complemented
73	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
74	#88133	C₂²	1	2	yes	complemented
75	#88130	C₂²	1	4	yes	complemented
76	#88128	C₂²	1	1	yes	characteristic, complemented
77	C₄×D₅₂	C₂²	1	1	yes	characteristic
78	C₄×D₅₂	C₂²	1	4	yes	complemented
79	C₄×D₅₂	C₂²	1	4	yes	complemented
80	C₄×D₅₂	C₂²	1	4	yes	complemented
81	C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
82	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
83	C₂³×D₁₃	C₂³	1	2	yes	—
84	C₂³×D₁₃	C₂³	1	4	yes	—
85	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
86	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×D₄×C₁₃	C₂³	1	4	yes	—
89	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
90	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
96	C₂²×Dic₁₃	C₂³	1	2	yes	—
97	#6131	—	4	4	no	—
98	D₄×D₁₃	—	2	4	no	—
99	D₄×D₁₃	—	4	4	no	—
100	D₄×D₁₃	—	4	8	no	—
101	#6127	—	4	4	no	—
102	C₂×D₅₂	—	2	8	no	—
103	C₂×D₅₂	C₂³	1	4	yes	—
104	C₂×D₅₂	C₂³	1	4	yes	—
105	C₂×D₅₂	C₂³	1	2	yes	—
106	C₂×D₅₂	C₂³	1	2	yes	—
107	C₂×D₅₂	C₂³	1	2	yes	—
108	C₂×D₅₂	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₁₃	—	4	4	no	—
110	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₂³	1	2	yes	—
114	C₂×C₄×D₁₃	C₂³	1	2	yes	—
115	C₂×C₄×D₁₃	C₂³	1	4	yes	—
116	C₂×C₄×D₁₃	C₂³	1	2	yes	—
117	C₂×C₄×D₁₃	C₂³	1	4	yes	—
118	C₂×C₄×D₁₃	C₂³	1	4	yes	—
119	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
120	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
121	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
123	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
125	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
126	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
127	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
128	C₄²×C₁₃	C₂³	1	1	yes	characteristic
129	C₄²×C₁₃	C₂³	1	4	yes	—
130	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
131	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
132	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
133	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
134	#6103	C₂³	1	2	yes	—
135	#6103	C₂³	1	2	yes	—
136	#6103	C₂³	1	2	yes	—
137	#6103	C₂³	1	4	yes	—
138	#6103	C₂³	1	4	yes	—
139	#6103	C₂³	1	4	yes	—
140	#6103	C₂³	1	4	yes	—
141	#6103	C₂³	1	4	yes	—
142	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
143	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
144	C₄⋊Dic₁₃	C₂³	1	2	yes	—
145	C₄⋊Dic₁₃	C₂³	1	2	yes	—
146	C₄⋊Dic₁₃	C₂³	1	4	yes	—
147	#6101	C₂³	1	2	yes	—
148	#6101	C₂³	1	2	yes	—
149	#6101	C₂³	1	2	yes	—
150	#6101	C₂³	1	4	yes	—
151	C₄×Dic₁₃	C₂³	1	2	yes	—
152	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
153	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
154	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
155	#3519	—	13	1	no	maximal, Sylow
156	C₂³×C₁₃	C₂⁴	1	2	yes	—
157	C₂³×C₁₃	C₂⁴	1	2	yes	—
158	C₂²×D₁₃	—	2	4	no	—
159	C₂²×D₁₃	—	2	4	no	—
160	C₂²×D₁₃	—	2	8	no	—
161	C₂²×D₁₃	—	4	2	no	—
162	C₂²×D₁₃	—	4	4	no	—
163	C₂²×D₁₃	—	4	4	no	—
164	C₂²×D₁₃	C₂⁴	1	4	yes	—
165	C₂²×D₁₃	C₂⁴	1	2	yes	—
166	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
167	Q₈×C₁₃	—	4	2	no	—
168	D₄×C₁₃	—	2	2	no	—
169	D₄×C₁₃	—	2	2	no	—
170	D₄×C₁₃	—	4	4	no	—
171	C₂×C₄×C₁₃	—	2	4	no	—
172	C₂×C₄×C₁₃	—	2	4	no	—
173	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
175	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
176	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
177	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂²⋊D₁₃	—	2	4	no	—
180	C₂²⋊D₁₃	—	2	4	no	—
181	C₂²⋊D₁₃	—	4	4	no	—
182	C₂²⋊D₁₃	—	4	4	no	—
183	C₂²⋊D₁₃	—	4	4	no	—
184	C₂×Dic₁₃	—	4	2	no	—
185	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
186	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
187	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
188	C₂×Dic₁₃	C₂⁴	1	2	yes	—
189	C₂×Dic₁₃	C₂⁴	1	2	yes	—
190	C₂×Dic₁₃	C₂⁴	1	2	yes	—
191	D₅₂	—	2	8	no	—
192	D₅₂	—	2	8	no	—
193	D₅₂	—	2	4	no	—
194	D₅₂	—	2	4	no	—
195	D₅₂	—	4	2	no	—
196	D₅₂	#41	1	4	yes	complemented
197	C₄×D₁₃	—	2	2	no	—
198	C₄×D₁₃	—	2	2	no	—
199	C₄×D₁₃	—	2	2	no	—
200	C₄×D₁₃	—	2	4	no	—
201	C₄×D₁₃	—	4	2	no	—
202	C₄×D₁₃	—	4	2	no	—
203	C₄×D₁₃	—	4	4	no	—
204	C₄×D₁₃	—	4	4	no	—
205	C₄×D₁₃	—	4	4	no	—
206	Dic₂₆	—	2	2	no	—
207	#555	D₁₃	1	1	yes	characteristic, complemented
208	#554	—	13	1	no	—
209	#553	—	13	2	no	—
210	#553	—	13	2	no	—
211	#550	—	13	1	no	—
212	#546	—	13	4	no	—
213	#546	—	13	2	no	—
214	D₄²	—	13	2	no	—
215	D₄²	—	13	1	no	—
216	#540	—	13	2	no	—
217	#538	—	13	4	no	—
218	#532	—	13	1	no	—
219	#529	—	13	1	no	—
220	#525	—	13	2	no	—
221	C₂×#121	—	13	2	no	—
222	#518	—	13	2	no	—
223	C₂×C₄×D₄	—	13	1	no	—
224	C₂²×C₁₃	—	2	2	no	—
225	C₂²×C₁₃	—	2	2	no	—
226	C₂²×C₁₃	—	2	2	no	—
227	C₂²×C₁₃	—	2	2	no	—
228	C₂²×C₁₃	—	2	2	no	—
229	C₂²×C₁₃	—	2	2	no	—
230	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
231	C₂×D₁₃	—	2	1	no	—
232	C₂×D₁₃	—	2	1	no	—
233	C₂×D₁₃	—	2	2	no	—
234	C₂×D₁₃	—	2	2	no	—
235	C₂×D₁₃	—	2	4	no	—
236	C₂×D₁₃	—	2	4	no	—
237	C₂×D₁₃	—	2	4	no	—
238	C₂×D₁₃	—	4	8	no	—
239	C₂×D₁₃	—	8	8	no	—
240	C₂×D₁₃	C₂×#41	1	4	yes	—
241	C₂×D₁₃	H(5,𝔽₂)	1	2	yes	—
242	C₄×C₁₃	—	2	2	no	—
243	C₄×C₁₃	—	2	1	no	—
244	C₄×C₁₃	—	2	2	no	—
245	C₄×C₁₃	—	2	4	no	—
246	C₄×C₁₃	C₂×#41	1	2	yes	—
247	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
248	Dic₁₃	—	2	1	no	—
249	Dic₁₃	—	2	2	no	—
250	Dic₁₃	—	2	1	no	—
251	Dic₁₃	—	2	1	no	—
252	Dic₁₃	—	2	2	no	—
253	Dic₁₃	—	2	2	no	—
254	C₂×#41	—	13	2	no	—
255	C₂×#41	—	13	2	no	—
256	C₂²×D₄	—	13	1	no	—
257	C₂²×D₄	—	13	2	no	—
258	C₂²×D₄	—	13	4	no	—
259	C₂²×D₄	—	13	2	no	—
260	C₂³×C₄	—	13	2	no	—
261	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
262	#127	—	13	2	no	—
263	#127	—	13	1	no	—
264	#126	—	13	2	no	—
265	#126	—	13	4	no	—
266	#125	—	13	1	no	—
267	#125	—	13	2	no	—
268	#124	—	13	2	no	—
269	#124	—	13	1	no	—
270	#124	C₂×D₁₃	1	4	yes	complemented
271	#123	—	13	4	no	—
272	#123	—	13	2	no	—
273	#123	—	13	4	no	—
274	#123	—	13	4	no	—
275	C₂²⋊Q₈	—	13	4	no	—
276	C₂²⋊Q₈	—	13	1	no	—
277	C₂²⋊Q₈	—	13	2	no	—
278	#121	—	13	1	no	—
279	#121	—	13	4	no	—
280	#121	—	13	4	no	—
281	#121	—	13	2	no	—
282	#121	—	13	2	no	—
283	#121	—	13	2	no	—
284	#121	—	13	2	no	—
285	#121	—	13	2	no	—
286	#121	—	13	4	no	—
287	#121	—	13	4	no	—
288	#121	—	13	4	no	—
289	#121	C₂×D₁₃	1	2	yes	complemented
290	#121	C₂×D₁₃	1	2	yes	complemented
291	#120	—	13	4	no	—
292	#120	—	13	4	no	—
293	#120	—	13	4	no	—
294	C₄×Q₈	—	13	1	no	—
295	C₄×D₄	—	13	1	no	—
296	C₄×D₄	—	13	2	no	—
297	C₄×D₄	—	13	2	no	—
298	C₄×D₄	—	13	1	no	—
299	C₄×D₄	—	13	2	no	—
300	C₄×D₄	—	13	2	no	—
301	C₄×D₄	—	13	2	no	—
302	C₄×D₄	—	13	2	no	—
303	C₄×D₄	—	13	2	no	—
304	C₄×D₄	—	13	1	no	—
305	C₄×D₄	—	13	4	no	—
306	C₄×D₄	—	13	4	no	—
307	C₄×D₄	—	13	4	no	—
308	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
309	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
310	#117	—	13	2	no	—
311	#117	C₂×D₁₃	1	2	yes	complemented
312	#117	C₂×D₁₃	1	2	yes	complemented
313	C₂×C₄⋊C₄	—	13	1	no	—
314	C₂×C₄⋊C₄	—	13	2	no	—
315	C₂×C₂²⋊C₄	—	13	2	no	—
316	C₂×C₂²⋊C₄	—	13	4	no	—
317	C₂×C₂²⋊C₄	—	13	4	no	—
318	C₂×C₄²	—	13	1	no	—
319	C₂×C₁₃	—	4	2	no	—
320	C₂×C₁₃	—	4	2	no	—
321	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
322	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
323	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
324	D₁₃	—	2	2	no	—
325	D₁₃	—	2	4	no	—
326	D₁₃	—	4	4	no	—
327	C₂⁴	—	13	2	no	—
328	C₂⁴	—	13	4	no	—
329	#41	—	52	4	no	—
330	#41	—	52	4	no	—
331	C₂×Q₈	—	13	1	no	—
332	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
333	C₂×D₄	—	13	2	no	—
334	C₂×D₄	—	13	2	no	—
335	C₂×D₄	—	13	4	no	—
336	C₂×D₄	—	13	4	no	—
337	C₂×D₄	—	13	4	no	—
338	C₂×D₄	—	13	1	no	—
339	C₂×D₄	—	13	4	no	—
340	C₂×D₄	—	13	2	no	—
341	C₂×D₄	—	13	4	no	—
342	C₂×D₄	—	13	2	no	—
343	C₂×D₄	—	13	2	no	—
344	C₂×D₄	—	26	8	no	—
345	C₂×D₄	—	26	4	no	—
346	C₂×D₄	—	52	4	no	—
347	C₂×D₄	—	52	8	no	—
348	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
349	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
350	C₂×D₄	C₂²×D₁₃	1	4	yes	—
351	C₂²×C₄	—	13	2	no	—
352	C₂²×C₄	—	13	1	no	—
353	C₂²×C₄	—	13	1	no	—
354	C₂²×C₄	—	13	1	no	—
355	C₂²×C₄	—	13	2	no	—
356	C₂²×C₄	—	13	2	no	—
357	C₂²×C₄	—	13	2	no	—
358	C₂²×C₄	—	13	4	no	—
359	C₂²×C₄	—	13	4	no	—
360	C₂²×C₄	—	13	4	no	—
361	C₂²×C₄	—	52	4	no	—
362	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
363	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
364	C₄⋊C₄	—	13	1	no	—
365	C₄⋊C₄	—	13	1	no	—
366	C₄⋊C₄	—	13	2	no	—
367	C₄⋊C₄	—	13	4	no	—
368	C₄⋊C₄	—	13	2	no	—
369	C₄⋊C₄	—	13	2	no	—
370	C₄⋊C₄	—	13	2	no	—
371	C₄⋊C₄	—	13	4	no	—
372	C₄⋊C₄	—	13	2	no	—
373	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
374	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
375	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
376	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
377	C₂²⋊C₄	—	13	2	no	—
378	C₂²⋊C₄	—	13	2	no	—
379	C₂²⋊C₄	—	13	2	no	—
380	C₂²⋊C₄	—	13	2	no	—
381	C₂²⋊C₄	—	13	2	no	—
382	C₂²⋊C₄	—	13	4	no	—
383	C₂²⋊C₄	—	13	2	no	—
384	C₂²⋊C₄	—	13	4	no	—
385	C₂²⋊C₄	—	13	4	no	—
386	C₂²⋊C₄	—	13	2	no	—
387	C₂²⋊C₄	—	13	4	no	—
388	C₂²⋊C₄	—	13	4	no	—
389	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
390	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
391	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
392	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
393	C₄²	—	13	1	no	—
394	C₄²	—	13	1	no	—
395	C₄²	—	13	1	no	—
396	C₄²	—	13	2	no	—
397	C₄²	C₂²×D₁₃	1	1	yes	characteristic
398	C₄²	C₂²×D₁₃	1	4	yes	—
399	C₁₃	#3519	1	1	yes	characteristic, complemented, Sylow
400	C₂³	—	13	2	no	—
401	C₂³	—	13	1	no	—
402	C₂³	—	13	4	no	—
403	C₂³	—	26	4	no	—
404	C₂³	—	26	4	no	—
405	C₂³	—	26	8	no	—
406	C₂³	—	52	2	no	—
407	C₂³	—	52	4	no	—
408	C₂³	—	52	4	no	—
409	C₂³	C₂³×D₁₃	1	2	yes	—
410	C₂³	C₂³×D₁₃	1	2	yes	—
411	Q₈	—	4	2	no	—
412	Q₈	—	26	2	no	—
413	D₄	—	2	2	no	—
414	D₄	—	2	2	no	—
415	D₄	—	4	4	no	—
416	D₄	—	13	4	no	—
417	D₄	—	26	8	no	—
418	D₄	—	26	8	no	—
419	D₄	—	26	4	no	—
420	D₄	—	26	4	no	—
421	D₄	—	26	4	no	—
422	D₄	—	26	4	no	—
423	D₄	—	52	2	no	—
424	D₄	—	52	4	no	—
425	D₄	—	52	4	no	—
426	D₄	—	52	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	13	1	no	—
430	C₂×C₄	—	13	1	no	—
431	C₂×C₄	—	13	1	no	—
432	C₂×C₄	—	13	2	no	—
433	C₂×C₄	—	13	2	no	—
434	C₂×C₄	—	13	2	no	—
435	C₂×C₄	—	26	2	no	—
436	C₂×C₄	—	26	2	no	—
437	C₂×C₄	—	26	2	no	—
438	C₂×C₄	—	26	4	no	—
439	C₂×C₄	—	52	2	no	—
440	C₂×C₄	—	52	2	no	—
441	C₂×C₄	—	52	4	no	—
442	C₂×C₄	—	52	4	no	—
443	C₂×C₄	—	52	4	no	—
444	C₂×C₄	—	52	2	no	—
445	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
446	C₂×C₄	C₂³×D₁₃	1	2	yes	—
447	C₂×C₄	C₂³×D₁₃	1	2	yes	—
448	C₂×C₄	C₂³×D₁₃	1	4	yes	—
449	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
450	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	2	no	—
457	C₂²	—	13	4	no	—
458	C₂²	—	13	2	no	—
459	C₂²	—	26	1	no	—
460	C₂²	—	26	1	no	—
461	C₂²	—	26	2	no	—
462	C₂²	—	26	2	no	—
463	C₂²	—	26	4	no	—
464	C₂²	—	26	4	no	—
465	C₂²	—	26	4	no	—
466	C₂²	—	52	8	no	—
467	C₂²	—	104	8	no	—
468	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	1	no	—
472	C₄	—	2	4	no	—
473	C₄	—	26	1	no	—
474	C₄	—	26	1	no	—
475	C₄	—	26	2	no	—
476	C₄	—	26	2	no	—
477	C₄	—	26	1	no	—
478	C₄	—	26	2	no	—
479	C₄	#41×D₁₃	1	2	yes	—
480	C₄	#88256	1	2	yes	—
481	C₂	—	4	2	no	—
482	C₂	—	4	2	no	—
483	C₂	—	26	2	no	—
484	C₂	—	26	4	no	—
485	C₂	—	52	4	no	—
486	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
487	C₂	C₂×#88256	1	1	yes	characteristic
488	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#555	C₂
hypercenter	#555	D₁₃
hypocenter	C₁₃	#3519
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #555

Complements

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

N	H ≅ G/N	type
1. C₁₃×#555	C₂	semidirect
2. #11719435	C₂	semidirect
3. #11719430	C₂	semidirect
4. #11719383	C₂	semidirect
5. #11719381	C₂	semidirect
6. #11719324	C₂	semidirect
7. #11719317	C₂	semidirect
8. #11719314	C₂	semidirect
9. D₁₃×#121	C₂	semidirect
10. #11719262	C₂	semidirect
11. #11719258	C₂	semidirect
12. D₄×D₅₂	C₂	semidirect
13. C₄×D₄×D₁₃	C₂	semidirect
14. #11719235	C₂	semidirect
15. #11719235	C₂	semidirect
16. #11719229	C₂	semidirect
17. #11719226	C₂	semidirect
18. C₂×#6131	C₂²	semidirect
20. C₂×D₄×D₁₃	C₂²	semidirect
21. C₂×D₄×D₁₃	C₂²	semidirect
22. C₂×#6127	C₂²	semidirect
24. C₂²×C₄×D₁₃	C₂²	semidirect
25. C₁₃×C₄⋊Q₈	C₂²	semidirect
26. C₁₃×#124	C₂²	semidirect
27. C₁₃×#121	C₂²	semidirect
28. C₁₃×#121	C₂²	semidirect
29. C₄×D₄×C₁₃	C₂²	semidirect
30. C₄×D₄×C₁₃	C₂²	semidirect
31. C₁₃×#117	C₂²	semidirect
32. C₁₃×#117	C₂²	semidirect
33. #88201	C₂²	semidirect
34. #88200	C₂²	semidirect
35. #88194	C₂²	semidirect
36. #88193	C₂²	semidirect
38. #88192	C₂²	semidirect
39. #88191	C₂²	semidirect
40. #88190	C₂²	semidirect
41. D₄×Dic₁₃	C₂²	semidirect
42. #88184	C₂²	semidirect
43. #88184	C₂²	semidirect
44. C₄×C₂²⋊D₁₃	C₂²	semidirect
45. C₄×C₂²⋊D₁₃	C₂²	semidirect
46. #88180	C₂²	semidirect
47. #88151	C₂²	semidirect
48. #88151	C₂²	semidirect
49. #88149	C₂²	semidirect
50. #88149	C₂²	semidirect
51. #88149	C₂²	semidirect
54. #88147	C₂²	semidirect
55. #88147	C₂²	semidirect
56. #88147	C₂²	semidirect
57. C₄⋊C₄×D₁₃	C₂²	semidirect
58. C₄⋊C₄×D₁₃	C₂²	semidirect
59. #88144	C₂²	semidirect
60. #88144	C₂²	semidirect
61. #88140	C₂²	semidirect
62. #88138	C₂²	semidirect
63. #88138	C₂²	semidirect
64. #88138	C₂²	semidirect
65. #88137	C₂²	semidirect
66. #88137	C₂²	semidirect
67. #88137	C₂²	semidirect
68. #88136	C₂²	semidirect
69. #88136	C₂²	semidirect
70. #88135	C₂²	semidirect
71. C₂²⋊C₄×D₁₃	C₂²	semidirect
72. C₂²⋊C₄×D₁₃	C₂²	semidirect
73. C₂²⋊C₄×D₁₃	C₂²	semidirect
74. #88133	C₂²	semidirect
75. #88130	C₂²	semidirect
76. #88128	C₂²	semidirect
78. C₄×D₅₂	C₂²	semidirect
79. C₄×D₅₂	C₂²	semidirect
80. C₄×D₅₂	C₂²	semidirect
81. C₄²×D₁₃	C₂²	semidirect
82. C₄×Dic₂₆	C₂²	semidirect
196. D₅₂	#41	semidirect
207. #555	D₁₃	semidirect
261. C₄⋊Q₈	C₂×D₁₃	semidirect
270. #124	C₂×D₁₃	semidirect
289. #121	C₂×D₁₃	semidirect
290. #121	C₂×D₁₃	semidirect
308. C₄×D₄	C₂×D₁₃	semidirect
309. C₄×D₄	C₂×D₁₃	semidirect
311. #117	C₂×D₁₃	semidirect
312. #117	C₂×D₁₃	semidirect
399. C₁₃	#3519	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#555	2
#11719435	2
#11719430	2
#11719383	2
#11719381	2
#11719324	2
#11719317	2
#11719314	2
D₁₃×#121	2
#11719262	2
#11719258	2
D₄×D₅₂	2
C₄×D₄×D₁₃	2
#11719235	2
#11719229	2
#11719226	2
#3519	13