Subgroups — #13128705

Order 1664.

1232 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719539	C₂	1	2	yes	maximal, complemented
3	#11719534	C₂	1	2	yes	maximal, complemented
4	#11719433	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719430	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719421	C₂	1	1	yes	maximal, characteristic, complemented
7	D₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719386	C₂	1	2	yes	maximal, complemented
9	#11719381	C₂	1	2	yes	maximal, complemented
10	#11719324	C₂	1	2	yes	maximal, complemented
11	#11719317	C₂	1	2	yes	maximal, complemented
12	#11719312	C₂	1	2	yes	maximal, complemented
13	#11719304	C₂	1	2	yes	maximal, complemented
14	#11719267	C₂	1	2	yes	maximal, complemented
15	#11719264	C₂	1	2	yes	maximal, complemented
16	#11719259	C₂	1	2	yes	maximal, complemented
17	#11719250	C₂	1	2	yes	maximal, complemented
18	#11719182	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#6127	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₁₃×#41	C₂²	1	2	yes	complemented
21	C₂×#6131	C₂²	1	2	yes	complemented
22	C₂×#6129	C₂²	1	2	yes	complemented
23	C₂×D₄×D₁₃	C₂²	1	2	yes	—
24	C₂×D₄×D₁₃	C₂²	1	2	yes	—
25	C₂×D₄×D₁₃	C₂²	1	2	yes	—
26	C₂×#6127	C₂²	1	1	yes	characteristic
27	C₂×#6127	C₂²	1	2	yes	complemented
28	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#127	C₂²	1	1	yes	characteristic
30	C₁₃×#124	C₂²	1	2	yes	complemented
31	C₁₃×#121	C₂²	1	2	yes	complemented
32	C₁₃×#121	C₂²	1	2	yes	complemented
33	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
34	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
35	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	#88201	C₂²	1	2	yes	complemented
37	#88200	C₂²	1	2	yes	—
38	Q₈×Dic₁₃	C₂²	1	2	yes	complemented
39	#88194	C₂²	1	2	yes	—
40	#88194	C₂²	1	2	yes	—
41	#88194	C₂²	1	2	yes	—
42	#88194	C₂²	1	4	yes	complemented
43	#88193	C₂²	1	4	yes	complemented
44	#88192	C₂²	1	2	yes	complemented
45	#88192	C₂²	1	4	yes	complemented
46	#88192	C₂²	1	2	yes	complemented
47	#88191	C₂²	1	4	yes	—
48	#88190	C₂²	1	2	yes	complemented
49	D₄×Dic₁₃	C₂²	1	2	yes	complemented
50	D₄×Dic₁₃	C₂²	1	2	yes	complemented
51	#88184	C₂²	1	2	yes	complemented
52	#88184	C₂²	1	2	yes	complemented
53	#88184	C₂²	1	4	yes	complemented
54	#88183	C₂²	1	4	yes	complemented
55	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
58	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
60	C₂×#6103	C₂²	1	4	yes	—
61	#88180	C₂²	1	1	yes	characteristic, complemented
62	#88151	C₂²	1	2	yes	—
63	#88149	C₂²	1	2	yes	complemented
64	#88149	C₂²	1	2	yes	complemented
65	#88147	C₂²	1	2	yes	complemented
66	#88147	C₂²	1	2	yes	complemented
67	#88146	C₂²	1	2	yes	—
68	#88144	C₂²	1	2	yes	complemented
69	#88141	C₂²	1	2	yes	complemented
70	#88140	C₂²	1	4	yes	complemented
71	#88139	C₂²	1	4	yes	complemented
72	#88138	C₂²	1	4	yes	complemented
73	#88137	C₂²	1	4	yes	complemented
74	#88137	C₂²	1	4	yes	complemented
75	#88136	C₂²	1	4	yes	—
76	#88135	C₂²	1	4	yes	complemented
77	C₂²⋊C₄×D₁₃	C₂²	1	4	yes	—
78	#88129	C₂²	1	2	yes	complemented
79	#88128	C₂²	1	1	yes	characteristic
80	C₄×D₅₂	C₂²	1	1	yes	characteristic
81	C₄×D₅₂	C₂²	1	1	yes	characteristic
82	C₄×D₅₂	C₂²	1	2	yes	complemented
83	C₄×D₅₂	C₂²	1	2	yes	complemented
84	#88126	C₂²	1	1	yes	characteristic
85	#88126	C₂²	1	1	yes	characteristic, complemented
86	C₄²×D₁₃	C₂²	1	1	yes	characteristic
87	C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
88	#88123	C₂²	1	1	yes	characteristic, complemented
89	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
90	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
91	C₂³×D₁₃	C₂³	1	4	yes	—
92	C₁₃×#41	—	4	4	no	—
93	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
94	C₂×D₄×C₁₃	C₂³	1	2	yes	—
95	C₂×D₄×C₁₃	C₂³	1	2	yes	—
96	C₂×D₄×C₁₃	C₂³	1	2	yes	—
97	C₂×D₄×C₁₃	C₂³	1	4	yes	—
98	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
102	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
103	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
104	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
105	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
106	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
107	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
108	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
109	C₂²×Dic₁₃	C₂³	1	4	yes	—
110	#6131	—	4	4	no	—
111	#6129	—	4	4	no	—
112	D₄×D₁₃	—	2	8	no	—
113	D₄×D₁₃	—	4	4	no	—
114	D₄×D₁₃	—	4	4	no	—
115	#6127	—	2	4	no	—
116	#6127	—	4	4	no	—
117	C₂×D₅₂	C₂³	1	1	yes	characteristic
118	C₂×D₅₂	C₂³	1	2	yes	—
119	C₂×D₅₂	C₂³	1	2	yes	—
120	C₂×D₅₂	C₂³	1	2	yes	—
121	C₂×D₅₂	C₂³	1	4	yes	—
122	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
123	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
124	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
125	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
126	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
127	C₂×C₄×D₁₃	C₂³	1	4	yes	—
128	C₂×C₄×D₁₃	C₂³	1	4	yes	—
129	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
130	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
131	C₂×Dic₂₆	C₂³	1	2	yes	—
132	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
133	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
134	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
135	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
136	C₄²×C₁₃	C₂³	1	1	yes	characteristic
137	C₄²×C₁₃	C₂³	1	1	yes	characteristic
138	C₄²×C₁₃	C₂³	1	1	yes	characteristic
139	C₄²×C₁₃	C₂³	1	1	yes	characteristic
140	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
141	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
142	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
143	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
144	#6103	C₂³	1	1	yes	characteristic
145	#6103	C₂³	1	1	yes	characteristic
146	#6103	C₂³	1	1	yes	characteristic
147	#6103	C₂³	1	1	yes	characteristic
148	#6103	C₂³	1	4	yes	—
149	#6103	C₂³	1	4	yes	—
150	#6103	C₂³	1	4	yes	—
151	#6103	C₂³	1	4	yes	—
152	#6103	C₂³	1	4	yes	—
153	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
154	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
155	C₄⋊Dic₁₃	C₂³	1	2	yes	—
156	C₄⋊Dic₁₃	C₂³	1	2	yes	—
157	C₄⋊Dic₁₃	C₂³	1	4	yes	—
158	#6101	C₂³	1	1	yes	characteristic
159	#6101	C₂³	1	1	yes	characteristic
160	#6101	C₂³	1	1	yes	characteristic
161	#6101	C₂³	1	1	yes	characteristic
162	#6101	C₂³	1	4	yes	—
163	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
164	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
165	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
166	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
167	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
168	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
169	C₄×Dic₁₃	C₂³	1	4	yes	—
170	#3508	—	13	1	no	maximal, Sylow
171	C₂³×C₁₃	C₂⁴	1	4	yes	—
172	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₂²×D₁₃	—	2	8	no	—
174	C₂²×D₁₃	—	4	4	no	—
175	C₂²×D₁₃	—	4	4	no	—
176	C₂²×D₁₃	C₂⁴	1	4	yes	—
177	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
178	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
179	Q₈×C₁₃	—	2	4	no	—
180	D₄×C₁₃	—	2	4	no	—
181	D₄×C₁₃	—	2	4	no	—
182	D₄×C₁₃	—	2	4	no	—
183	D₄×C₁₃	—	4	4	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	4	4	no	—
188	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
189	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
195	C₂²⋊D₁₃	—	2	2	no	—
196	C₂²⋊D₁₃	—	2	2	no	—
197	C₂²⋊D₁₃	—	2	8	no	—
198	C₂²⋊D₁₃	—	4	4	no	—
199	C₂²⋊D₁₃	—	4	4	no	—
200	C₂²⋊D₁₃	—	4	4	no	—
201	C₂²⋊D₁₃	—	4	4	no	—
202	C₂×Dic₁₃	—	4	4	no	—
203	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
204	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
205	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
206	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
207	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
208	C₂×Dic₁₃	C₂⁴	1	4	yes	—
209	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
210	D₅₂	—	2	2	no	—
211	D₅₂	—	2	4	no	—
212	D₅₂	—	2	4	no	—
213	D₅₂	—	2	4	no	—
214	D₅₂	—	4	4	no	—
215	C₄×D₁₃	—	2	2	no	—
216	C₄×D₁₃	—	2	2	no	—
217	C₄×D₁₃	—	2	2	no	—
218	C₄×D₁₃	—	2	2	no	—
219	C₄×D₁₃	—	2	2	no	—
220	C₄×D₁₃	—	4	4	no	—
221	C₄×D₁₃	—	4	4	no	—
222	C₄×D₁₃	#41	1	4	yes	complemented
223	Dic₂₆	—	2	4	no	—
224	Dic₂₆	—	2	2	no	—
225	#559	—	13	2	no	—
226	#559	—	13	2	no	—
227	#550	—	13	2	no	—
228	#550	—	13	2	no	—
229	#546	—	13	2	no	—
230	#546	—	13	2	no	—
231	#546	—	13	2	no	—
232	#546	—	13	2	no	—
233	#540	—	13	2	no	—
234	#540	—	13	2	no	—
235	#535	—	13	2	no	—
236	#533	—	13	1	no	—
237	#532	—	13	1	no	—
238	#532	—	13	1	no	—
239	#532	—	13	1	no	—
240	#532	D₁₃	1	1	yes	characteristic, complemented
241	C₂×#127	—	13	1	no	—
242	#518	—	13	2	no	—
243	C₄×#41	—	13	1	no	—
244	C₂²×C₁₃	—	2	1	no	—
245	C₂²×C₁₃	—	2	4	no	—
246	C₂²×C₁₃	—	2	4	no	—
247	C₂²×C₁₃	—	2	1	no	—
248	C₂²×C₁₃	—	2	4	no	—
249	C₂²×C₁₃	—	2	1	no	—
250	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
251	C₂×D₁₃	—	2	1	no	—
252	C₂×D₁₃	—	2	1	no	—
253	C₂×D₁₃	—	2	1	no	—
254	C₂×D₁₃	—	2	4	no	—
255	C₂×D₁₃	—	2	1	no	—
256	C₂×D₁₃	—	2	1	no	—
257	C₂×D₁₃	—	2	4	no	—
258	C₂×D₁₃	—	2	4	no	—
259	C₂×D₁₃	—	8	8	no	—
260	C₂×D₁₃	C₂×#41	1	2	yes	—
261	C₄×C₁₃	—	2	1	no	—
262	C₄×C₁₃	—	2	1	no	—
263	C₄×C₁₃	—	2	4	no	—
264	C₄×C₁₃	—	2	1	no	—
265	C₄×C₁₃	C₂×#41	1	2	yes	—
266	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
267	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
268	Dic₁₃	—	2	1	no	—
269	Dic₁₃	—	2	4	no	—
270	Dic₁₃	—	2	1	no	—
271	Dic₁₃	—	2	1	no	—
272	Dic₁₃	—	2	1	no	—
273	Dic₁₃	—	2	1	no	—
274	Dic₁₃	C₂×#41	1	2	yes	—
275	C₂×#41	—	13	2	no	—
276	C₂×#41	—	13	2	no	—
277	C₂×#41	—	13	1	no	—
278	C₂×#41	—	13	2	no	—
279	C₂×#41	C₂×D₁₃	1	2	yes	complemented
280	C₂²×D₄	—	13	2	no	—
281	C₂²×D₄	—	13	2	no	—
282	C₂²×D₄	—	13	2	no	—
283	C₄⋊Q₈	—	13	1	no	—
284	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
285	#127	—	13	2	no	—
286	#127	—	13	2	no	—
287	#127	—	13	2	no	—
288	#127	—	13	4	no	—
289	#127	—	13	1	no	—
290	#127	C₂×D₁₃	1	1	yes	characteristic
291	#125	—	13	2	no	—
292	#124	—	13	2	no	—
293	#124	—	13	2	no	—
294	#124	—	13	4	no	—
295	#124	—	13	2	no	—
296	#124	C₂×D₁₃	1	2	yes	complemented
297	#123	—	13	4	no	—
298	#123	—	13	4	no	—
299	#123	—	13	4	no	—
300	#123	—	13	4	no	—
301	C₂²⋊Q₈	—	13	2	no	—
302	C₂²⋊Q₈	—	13	2	no	—
303	#121	—	13	2	no	—
304	#121	—	13	2	no	—
305	#121	—	13	4	no	—
306	#121	—	13	4	no	—
307	#121	—	13	2	no	—
308	#121	—	13	2	no	—
309	#121	—	13	4	no	—
310	#121	—	13	2	no	—
311	#121	—	13	2	no	—
312	#121	—	13	4	no	—
313	#121	C₂×D₁₃	1	2	yes	complemented
314	#121	C₂×D₁₃	1	2	yes	complemented
315	#120	—	13	4	no	—
316	#120	—	13	4	no	—
317	C₄×Q₈	—	13	2	no	—
318	C₄×Q₈	—	13	2	no	—
319	C₄×Q₈	—	13	1	no	—
320	C₄×Q₈	—	13	1	no	—
321	C₄×D₄	—	13	2	no	—
322	C₄×D₄	—	13	2	no	—
323	C₄×D₄	—	13	1	no	—
324	C₄×D₄	—	13	1	no	—
325	C₄×D₄	—	13	1	no	—
326	C₄×D₄	—	13	1	no	—
327	C₄×D₄	—	13	4	no	—
328	C₄×D₄	—	13	2	no	—
329	C₄×D₄	—	13	2	no	—
330	C₄×D₄	—	13	4	no	—
331	C₄×D₄	—	13	1	no	—
332	C₄×D₄	—	13	1	no	—
333	C₄×D₄	—	13	2	no	—
334	C₄×D₄	—	13	2	no	—
335	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
336	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
337	#117	—	13	1	no	—
338	#117	—	13	2	no	—
339	#117	—	13	1	no	—
340	#117	—	13	1	no	—
341	C₂×C₂²⋊C₄	—	13	4	no	—
342	C₂×C₂²⋊C₄	—	13	4	no	—
343	C₂×C₄²	—	13	1	no	—
344	C₂×C₄²	—	13	1	no	—
345	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
346	C₂×C₁₃	—	4	4	no	—
347	C₂×C₁₃	—	4	1	no	—
348	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
349	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
350	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
351	D₁₃	—	2	2	no	—
352	D₁₃	—	4	1	no	—
353	D₁₃	—	4	4	no	—
354	C₂⁴	—	13	4	no	—
355	#41	—	4	4	no	—
356	#41	—	26	4	no	—
357	#41	—	52	4	no	—
358	#41	—	52	4	no	—
359	#41	—	52	4	no	—
360	C₂×Q₈	—	13	1	no	—
361	C₂×Q₈	—	13	2	no	—
362	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
363	C₂×D₄	—	13	1	no	—
364	C₂×D₄	—	13	4	no	—
365	C₂×D₄	—	13	1	no	—
366	C₂×D₄	—	13	4	no	—
367	C₂×D₄	—	13	4	no	—
368	C₂×D₄	—	13	4	no	—
369	C₂×D₄	—	13	4	no	—
370	C₂×D₄	—	13	1	no	—
371	C₂×D₄	—	13	2	no	—
372	C₂×D₄	—	13	2	no	—
373	C₂×D₄	—	13	2	no	—
374	C₂×D₄	—	13	4	no	—
375	C₂×D₄	—	26	8	no	—
376	C₂×D₄	—	52	4	no	—
377	C₂×D₄	—	52	4	no	—
378	C₂×D₄	C₂²×D₁₃	1	2	yes	—
379	C₂×D₄	C₂²×D₁₃	1	2	yes	—
380	C₂×D₄	C₂²×D₁₃	1	2	yes	—
381	C₂×D₄	C₂²×D₁₃	1	4	yes	—
382	C₂²×C₄	—	13	1	no	—
383	C₂²×C₄	—	13	4	no	—
384	C₂²×C₄	—	13	1	no	—
385	C₂²×C₄	—	13	1	no	—
386	C₂²×C₄	—	13	1	no	—
387	C₂²×C₄	—	13	1	no	—
388	C₂²×C₄	—	13	1	no	—
389	C₂²×C₄	—	13	4	no	—
390	C₂²×C₄	—	13	4	no	—
391	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
392	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
395	C₄⋊C₄	—	13	1	no	—
396	C₄⋊C₄	—	13	1	no	—
397	C₄⋊C₄	—	13	2	no	—
398	C₄⋊C₄	—	13	1	no	—
399	C₄⋊C₄	—	13	1	no	—
400	C₄⋊C₄	—	13	1	no	—
401	C₄⋊C₄	—	13	1	no	—
402	C₄⋊C₄	—	13	2	no	—
403	C₄⋊C₄	—	13	4	no	—
404	C₄⋊C₄	—	13	4	no	—
405	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
406	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
407	C₂²⋊C₄	—	13	4	no	—
408	C₂²⋊C₄	—	13	1	no	—
409	C₂²⋊C₄	—	13	1	no	—
410	C₂²⋊C₄	—	13	4	no	—
411	C₂²⋊C₄	—	13	1	no	—
412	C₂²⋊C₄	—	13	1	no	—
413	C₂²⋊C₄	—	13	4	no	—
414	C₂²⋊C₄	—	13	4	no	—
415	C₂²⋊C₄	—	13	4	no	—
416	C₂²⋊C₄	—	13	1	no	—
417	C₂²⋊C₄	—	13	1	no	—
418	C₂²⋊C₄	—	13	4	no	—
419	C₂²⋊C₄	—	13	4	no	—
420	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
421	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
422	C₄²	—	13	1	no	—
423	C₄²	—	13	1	no	—
424	C₄²	—	13	1	no	—
425	C₄²	—	13	1	no	—
426	C₄²	—	13	1	no	—
427	C₄²	—	13	1	no	—
428	C₄²	—	13	4	no	—
429	C₄²	C₂²×D₁₃	1	1	yes	characteristic
430	C₄²	C₂²×D₁₃	1	1	yes	characteristic
431	C₄²	C₂²×D₁₃	1	1	yes	characteristic
432	C₄²	C₂²×D₁₃	1	1	yes	characteristic
433	C₁₃	#3508	1	1	yes	characteristic, complemented, Sylow
434	C₂³	—	13	1	no	—
435	C₂³	—	13	4	no	—
436	C₂³	—	13	1	no	—
437	C₂³	—	26	8	no	—
438	C₂³	—	52	4	no	—
439	C₂³	—	52	4	no	—
440	C₂³	C₂³×D₁₃	1	4	yes	—
441	C₂³	C₂³×D₁₃	1	1	yes	characteristic
442	Q₈	—	2	4	no	—
443	Q₈	—	26	2	no	—
444	Q₈	—	26	4	no	—
445	D₄	—	2	4	no	—
446	D₄	—	2	4	no	—
447	D₄	—	2	4	no	—
448	D₄	—	4	4	no	—
449	D₄	—	26	2	no	—
450	D₄	—	26	8	no	—
451	D₄	—	26	2	no	—
452	D₄	—	26	2	no	—
453	D₄	—	26	4	no	—
454	D₄	—	26	4	no	—
455	D₄	—	26	4	no	—
456	D₄	—	52	4	no	—
457	D₄	—	52	4	no	—
458	D₄	—	52	4	no	—
459	D₄	—	52	4	no	—
460	D₄	—	52	4	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	13	1	no	—
466	C₂×C₄	—	13	4	no	—
467	C₂×C₄	—	13	1	no	—
468	C₂×C₄	—	13	1	no	—
469	C₂×C₄	—	13	1	no	—
470	C₂×C₄	—	13	1	no	—
471	C₂×C₄	—	13	1	no	—
472	C₂×C₄	—	13	4	no	—
473	C₂×C₄	—	26	2	no	—
474	C₂×C₄	—	26	2	no	—
475	C₂×C₄	—	26	2	no	—
476	C₂×C₄	—	26	2	no	—
477	C₂×C₄	—	26	2	no	—
478	C₂×C₄	—	52	4	no	—
479	C₂×C₄	—	52	4	no	—
480	C₂×C₄	—	52	4	no	—
481	C₂×C₄	C₂³×D₁₃	1	4	yes	—
482	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
483	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
484	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
485	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
486	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
487	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
488	C₂²	—	2	1	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	13	2	no	—
495	C₂²	—	26	1	no	—
496	C₂²	—	26	1	no	—
497	C₂²	—	26	1	no	—
498	C₂²	—	26	4	no	—
499	C₂²	—	26	1	no	—
500	C₂²	—	26	4	no	—
501	C₂²	—	26	1	no	—
502	C₂²	—	26	4	no	—
503	C₂²	—	104	8	no	—
504	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
505	C₄	—	2	1	no	—
506	C₄	—	2	4	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	13	2	no	—
510	C₄	—	26	1	no	—
511	C₄	—	26	1	no	—
512	C₄	—	26	1	no	—
513	C₄	—	26	1	no	—
514	C₄	—	26	1	no	—
515	C₄	—	26	4	no	—
516	C₄	#88251	1	2	yes	—
517	C₄	#41×D₁₃	1	2	yes	—
518	C₄	#88256	1	2	yes	—
519	C₂	—	4	4	no	—
520	C₂	—	4	1	no	—
521	C₂	—	26	2	no	—
522	C₂	—	52	4	no	—
523	C₂	—	52	1	no	—
524	C₂	C₂×#88251	1	1	yes	characteristic
525	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
526	C₂	C₂×#88256	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#532	C₂
hypercenter	#532	D₁₃
hypocenter	C₁₃	#3508
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #532

Complements

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

N	H ≅ G/N	type
1. C₁₃×#532	C₂	semidirect
2. #11719539	C₂	semidirect
3. #11719534	C₂	semidirect
4. #11719433	C₂	semidirect
5. #11719430	C₂	semidirect
6. #11719421	C₂	semidirect
7. D₁₃×#127	C₂	semidirect
8. #11719386	C₂	semidirect
9. #11719381	C₂	semidirect
10. #11719324	C₂	semidirect
11. #11719317	C₂	semidirect
12. #11719312	C₂	semidirect
13. #11719304	C₂	semidirect
14. #11719267	C₂	semidirect
15. #11719264	C₂	semidirect
16. #11719259	C₂	semidirect
17. #11719250	C₂	semidirect
18. #11719182	C₂	semidirect
19. C₄×#6127	C₂	semidirect
20. C₂×C₁₃×#41	C₂²	semidirect
21. C₂×#6131	C₂²	semidirect
22. C₂×#6129	C₂²	semidirect
27. C₂×#6127	C₂²	semidirect
28. C₁₃×C₄⋊Q₈	C₂²	semidirect
30. C₁₃×#124	C₂²	semidirect
31. C₁₃×#121	C₂²	semidirect
32. C₁₃×#121	C₂²	semidirect
33. C₄×D₄×C₁₃	C₂²	semidirect
34. C₄×D₄×C₁₃	C₂²	semidirect
35. C₂×C₄²×C₁₃	C₂²	semidirect
36. #88201	C₂²	semidirect
38. Q₈×Dic₁₃	C₂²	semidirect
42. #88194	C₂²	semidirect
43. #88193	C₂²	semidirect
44. #88192	C₂²	semidirect
45. #88192	C₂²	semidirect
46. #88192	C₂²	semidirect
48. #88190	C₂²	semidirect
49. D₄×Dic₁₃	C₂²	semidirect
50. D₄×Dic₁₃	C₂²	semidirect
51. #88184	C₂²	semidirect
52. #88184	C₂²	semidirect
53. #88184	C₂²	semidirect
54. #88183	C₂²	semidirect
57. C₄×C₂²⋊D₁₃	C₂²	semidirect
58. C₄×C₂²⋊D₁₃	C₂²	semidirect
59. C₄×C₂²⋊D₁₃	C₂²	semidirect
61. #88180	C₂²	semidirect
63. #88149	C₂²	semidirect
64. #88149	C₂²	semidirect
65. #88147	C₂²	semidirect
66. #88147	C₂²	semidirect
68. #88144	C₂²	semidirect
69. #88141	C₂²	semidirect
70. #88140	C₂²	semidirect
71. #88139	C₂²	semidirect
72. #88138	C₂²	semidirect
73. #88137	C₂²	semidirect
74. #88137	C₂²	semidirect
76. #88135	C₂²	semidirect
78. #88129	C₂²	semidirect
82. C₄×D₅₂	C₂²	semidirect
83. C₄×D₅₂	C₂²	semidirect
85. #88126	C₂²	semidirect
87. C₄²×D₁₃	C₂²	semidirect
88. #88123	C₂²	semidirect
89. C₄×Dic₂₆	C₂²	semidirect
90. C₄×Dic₂₆	C₂²	semidirect
222. C₄×D₁₃	#41	semidirect
240. #532	D₁₃	semidirect
279. C₂×#41	C₂×D₁₃	semidirect
284. C₄⋊Q₈	C₂×D₁₃	semidirect
296. #124	C₂×D₁₃	semidirect
313. #121	C₂×D₁₃	semidirect
314. #121	C₂×D₁₃	semidirect
335. C₄×D₄	C₂×D₁₃	semidirect
336. C₄×D₄	C₂×D₁₃	semidirect
345. C₂×C₄²	C₂×D₁₃	semidirect
433. C₁₃	#3508	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#532	2
#11719539	2
#11719534	2
#11719433	2
#11719430	2
#11719421	2
D₁₃×#127	2
#11719386	2
#11719381	2
#11719324	2
#11719317	2
#11719312	2
#11719304	2
#11719267	2
#11719264	2
#11719259	2
#11719250	2
#11719182	2
C₄×#6127	2
#3508	13