Subgroups — #13128538

Order 1664.

1124 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719533	C₂	1	2	yes	maximal, complemented
3	#11719529	C₂	1	2	yes	maximal, complemented
4	#11719435	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719434	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719366	C₂	1	2	yes	maximal, complemented
7	#11719365	C₂	1	2	yes	maximal, complemented
8	#11719361	C₂	1	2	yes	maximal, complemented
9	#11719355	C₂	1	2	yes	maximal, complemented
10	#11719343	C₂	1	2	yes	maximal, complemented
11	#11719341	C₂	1	2	yes	maximal, complemented
12	#11719319	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719316	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719313	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719311	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719263	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719252	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719251	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719246	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719218	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719216	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719209	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄⋊C₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#41	C₂²	1	2	yes	—
25	C₂×#6129	C₂²	1	1	yes	characteristic
26	C₂×#6129	C₂²	1	2	yes	—
27	C₂×#6127	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₃	C₂²	1	2	yes	—
30	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#123	C₂²	1	2	yes	—
32	C₁₃×#123	C₂²	1	2	yes	complemented
33	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₁₃×#121	C₂²	1	1	yes	characteristic
35	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	#88200	C₂²	1	2	yes	—
41	#88200	C₂²	1	2	yes	—
42	#88200	C₂²	1	2	yes	complemented
43	#88198	C₂²	1	2	yes	complemented
44	#88193	C₂²	1	1	yes	characteristic
45	#88193	C₂²	1	2	yes	complemented
46	#88192	C₂²	1	1	yes	characteristic
47	#88192	C₂²	1	2	yes	—
48	#88192	C₂²	1	2	yes	—
49	#88192	C₂²	1	1	yes	characteristic, complemented
50	#88191	C₂²	1	1	yes	characteristic
51	#88191	C₂²	1	2	yes	—
52	#88189	C₂²	1	2	yes	—
53	#88189	C₂²	1	2	yes	—
54	#88189	C₂²	1	2	yes	complemented
55	D₄×Dic₁₃	C₂²	1	2	yes	—
56	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
57	#88183	C₂²	1	2	yes	—
58	#88183	C₂²	1	2	yes	complemented
59	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
60	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
61	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
62	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
63	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
64	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
65	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
66	#88180	C₂²	1	2	yes	—
67	#88180	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
69	#88178	C₂²	1	1	yes	characteristic
70	#88178	C₂²	1	1	yes	characteristic, complemented
71	#88178	C₂²	1	2	yes	complemented
72	C₂×#6101	C₂²	1	2	yes	—
73	C₂×#6101	C₂²	1	2	yes	complemented
74	#88152	C₂²	1	2	yes	complemented
75	#88151	C₂²	1	1	yes	characteristic
76	#88151	C₂²	1	1	yes	characteristic, complemented
77	#88150	C₂²	1	2	yes	—
78	#88150	C₂²	1	2	yes	—
79	#88150	C₂²	1	1	yes	characteristic
80	#88148	C₂²	1	1	yes	characteristic
81	#88147	C₂²	1	2	yes	—
82	#88147	C₂²	1	2	yes	—
83	#88146	C₂²	1	1	yes	characteristic
84	#88146	C₂²	1	1	yes	characteristic, complemented
85	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
86	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
87	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
88	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
89	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
90	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
91	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
92	#88144	C₂²	1	1	yes	characteristic, complemented
93	#88144	C₂²	1	2	yes	complemented
94	#88143	C₂²	1	2	yes	complemented
95	#88143	C₂²	1	2	yes	complemented
96	#88143	C₂²	1	2	yes	complemented
97	#88143	C₂²	1	2	yes	complemented
98	#88142	C₂²	1	1	yes	characteristic, complemented
99	#88141	C₂²	1	2	yes	complemented
100	#88141	C₂²	1	1	yes	characteristic, complemented
101	#88138	C₂²	1	1	yes	characteristic
102	#88138	C₂²	1	2	yes	—
103	#88138	C₂²	1	2	yes	—
104	#88137	C₂²	1	1	yes	characteristic
105	#88137	C₂²	1	2	yes	—
106	#88137	C₂²	1	2	yes	complemented
107	#88136	C₂²	1	1	yes	characteristic
108	#88135	C₂²	1	2	yes	—
109	#88135	C₂²	1	2	yes	—
110	#88135	C₂²	1	2	yes	—
111	#88133	C₂²	1	2	yes	complemented
112	#88133	C₂²	1	2	yes	complemented
113	#88133	C₂²	1	2	yes	complemented
114	#88132	C₂²	1	1	yes	characteristic
115	#88132	C₂²	1	2	yes	complemented
116	#88132	C₂²	1	2	yes	complemented
117	#88131	C₂²	1	2	yes	—
118	#88131	C₂²	1	2	yes	complemented
119	C₄×D₅₂	C₂²	1	1	yes	characteristic
120	#88126	C₂²	1	1	yes	characteristic
121	#88124	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃	C₂³	1	1	yes	characteristic
124	C₁₃×#41	—	4	4	no	—
125	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
126	C₂×D₄×C₁₃	C₂³	1	2	yes	—
127	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₃	C₂³	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
140	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
141	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
142	C₂²×Dic₁₃	C₂³	1	2	yes	—
143	C₂²×Dic₁₃	C₂³	1	2	yes	—
144	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
145	C₂²×Dic₁₃	C₂³	1	2	yes	—
146	#6129	—	2	4	no	—
147	#6129	—	4	4	no	—
148	#6127	—	2	4	no	—
149	C₂×D₅₂	C₂³	1	1	yes	characteristic
150	C₂×D₅₂	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₃	—	2	4	no	—
152	C₂×C₄×D₁₃	—	4	4	no	—
153	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₃	C₂³	1	2	yes	—
158	C₂×C₄×D₁₃	C₂³	1	2	yes	—
159	C₂×C₄×D₁₃	C₂³	1	2	yes	—
160	C₂×C₄×D₁₃	C₂³	1	2	yes	—
161	C₂×C₄×D₁₃	C₂³	1	2	yes	—
162	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
163	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
164	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
165	C₂×Dic₂₆	C₂³	1	2	yes	—
166	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
168	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
171	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
172	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
174	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₄²×C₁₃	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
186	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
187	#6103	C₂³	1	1	yes	characteristic
188	#6103	C₂³	1	1	yes	characteristic
189	#6103	C₂³	1	1	yes	characteristic
190	#6103	C₂³	1	1	yes	characteristic
191	#6103	C₂³	1	1	yes	characteristic
192	#6103	C₂³	1	2	yes	—
193	#6103	C₂³	1	2	yes	—
194	#6103	C₂³	1	1	yes	characteristic
195	#6103	C₂³	1	2	yes	—
196	#6103	C₂³	1	2	yes	—
197	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₃	C₂³	1	2	yes	—
202	C₄⋊Dic₁₃	C₂³	1	2	yes	—
203	C₄⋊Dic₁₃	C₂³	1	2	yes	—
204	C₄⋊Dic₁₃	C₂³	1	2	yes	—
205	#6101	C₂³	1	2	yes	—
206	#6101	C₂³	1	2	yes	—
207	#6101	C₂³	1	2	yes	—
208	#6101	C₂³	1	1	yes	characteristic
209	#6101	C₂³	1	1	yes	characteristic
210	#6101	C₂³	1	2	yes	—
211	#6101	C₂³	1	2	yes	—
212	#6101	C₂³	1	1	yes	characteristic
213	#6101	C₂³	1	1	yes	characteristic
214	#6101	C₂³	1	2	yes	—
215	#6101	C₂³	1	2	yes	—
216	#6101	C₂³	1	2	yes	—
217	#6101	C₂³	1	2	yes	—
218	#6101	C₂³	1	2	yes	—
219	#6101	C₂³	1	2	yes	—
220	#6101	C₂³	1	2	yes	—
221	#6101	C₂³	1	2	yes	—
222	C₄×Dic₁₃	C₂³	1	2	yes	—
223	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₃	C₂³	1	2	yes	—
225	C₄×Dic₁₃	C₂³	1	2	yes	—
226	C₄×Dic₁₃	C₂³	1	2	yes	—
227	C₄×Dic₁₃	C₂³	1	2	yes	—
228	#3492	—	13	1	no	maximal, Sylow
229	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂³×C₁₃	C₂⁴	1	2	yes	—
231	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₃	—	2	2	no	—
233	C₂²×D₁₃	—	2	2	no	—
234	C₂²×D₁₃	—	2	2	no	—
235	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
236	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
237	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
238	Q₈×C₁₃	—	4	2	no	—
239	D₄×C₁₃	—	2	4	no	—
240	D₄×C₁₃	—	2	2	no	—
241	D₄×C₁₃	—	2	2	no	—
242	D₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	—	2	4	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	—	4	2	no	—
248	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂²⋊D₁₃	—	2	2	no	—
257	C₂²⋊D₁₃	—	2	2	no	—
258	C₂²⋊D₁₃	—	2	4	no	—
259	C₂²⋊D₁₃	—	2	4	no	—
260	C₂²⋊D₁₃	—	2	2	no	—
261	C₂²⋊D₁₃	—	2	2	no	—
262	C₂²⋊D₁₃	—	4	2	no	—
263	C₂×Dic₁₃	—	2	4	no	—
264	C₂×Dic₁₃	—	2	2	no	—
265	C₂×Dic₁₃	—	2	4	no	—
266	C₂×Dic₁₃	—	4	2	no	—
267	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₃	C₂⁴	1	2	yes	—
269	C₂×Dic₁₃	C₂⁴	1	2	yes	—
270	C₂×Dic₁₃	C₂⁴	1	2	yes	—
271	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₁₃	C₂⁴	1	2	yes	—
274	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
276	D₅₂	—	2	2	no	—
277	D₅₂	—	2	2	no	—
278	C₄×D₁₃	—	2	2	no	—
279	C₄×D₁₃	—	2	2	no	—
280	C₄×D₁₃	—	2	2	no	—
281	C₄×D₁₃	—	2	2	no	—
282	C₄×D₁₃	—	4	2	no	—
283	C₄×D₁₃	—	4	2	no	—
284	C₄×D₁₃	—	4	2	no	—
285	C₄×D₁₃	—	4	2	no	—
286	C₄×D₁₃	—	4	2	no	—
287	C₄×D₁₃	#41	1	4	yes	complemented
288	Dic₂₆	—	2	2	no	—
289	Dic₂₆	—	2	2	no	—
290	Dic₂₆	—	4	2	no	—
291	#554	—	13	1	no	—
292	#554	—	13	2	no	—
293	#554	—	13	1	no	—
294	#553	—	13	2	no	—
295	#553	—	13	1	no	—
296	#553	—	13	1	no	—
297	#552	—	13	2	no	—
298	#552	—	13	1	no	—
299	#552	—	13	1	no	—
300	#547	—	13	2	no	—
301	#547	—	13	1	no	—
302	#547	D₁₃	1	1	yes	characteristic, complemented
303	#544	—	13	1	no	—
304	#539	—	13	2	no	—
305	#539	—	13	2	no	—
306	#537	—	13	1	no	—
307	#525	—	13	2	no	—
308	#525	—	13	2	no	—
309	#525	—	13	1	no	—
310	#525	—	13	1	no	—
311	#520	—	13	1	no	—
312	#520	—	13	1	no	—
313	C₂²×C₄⋊C₄	—	13	1	no	—
314	C₂²×C₁₃	—	2	1	no	—
315	C₂²×C₁₃	—	2	1	no	—
316	C₂²×C₁₃	—	2	2	no	—
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	—	2	2	no	—
319	C₂²×C₁₃	—	2	1	no	—
320	C₂²×C₁₃	—	2	1	no	—
321	C₂²×C₁₃	—	2	2	no	—
322	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
323	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
324	C₂×D₁₃	—	2	8	no	—
325	C₂×D₁₃	—	2	1	no	—
326	C₂×D₁₃	—	2	1	no	—
327	C₂×D₁₃	—	2	1	no	—
328	C₂×D₁₃	—	2	1	no	—
329	C₂×D₁₃	—	2	1	no	—
330	C₂×D₁₃	—	2	1	no	—
331	C₂×D₁₃	—	2	1	no	—
332	C₂×D₁₃	C₂×#41	1	2	yes	—
333	C₂×D₁₃	2₋¹⁺⁴	1	2	yes	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	2	2	no	—
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	2	1	no	—
340	C₄×C₁₃	—	2	1	no	—
341	C₄×C₁₃	C₂×#41	1	2	yes	—
342	Dic₁₃	—	2	1	no	—
343	Dic₁₃	—	2	2	no	—
344	Dic₁₃	—	2	1	no	—
345	Dic₁₃	—	2	1	no	—
346	Dic₁₃	—	2	2	no	—
347	Dic₁₃	—	2	2	no	—
348	Dic₁₃	—	2	1	no	—
349	Dic₁₃	—	2	2	no	—
350	Dic₁₃	C₂×#41	1	2	yes	—
351	C₂×#41	—	13	1	no	—
352	C₂×#41	—	13	2	no	—
353	C₂×#41	—	13	1	no	—
354	C₂×#41	C₂×D₁₃	1	2	yes	—
355	C₂³×C₄	—	13	1	no	—
356	C₂³×C₄	—	13	2	no	—
357	C₄⋊Q₈	—	13	2	no	—
358	C₄⋊Q₈	—	13	1	no	—
359	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
360	#126	—	13	2	no	—
361	#126	—	13	2	no	—
362	#126	—	13	2	no	—
363	#126	—	13	2	no	—
364	#125	—	13	2	no	—
365	#125	—	13	2	no	—
366	#125	—	13	2	no	—
367	#125	—	13	2	no	—
368	#125	—	13	2	no	—
369	#125	—	13	1	no	—
370	#125	—	13	1	no	—
371	#123	—	13	2	no	—
372	#123	—	13	2	no	—
373	#123	—	13	2	no	—
374	#123	—	13	2	no	—
375	#123	—	13	2	no	—
376	#123	—	13	1	no	—
377	#123	—	13	1	no	—
378	#123	—	13	2	no	—
379	#123	—	13	2	no	—
380	#123	C₂×D₁₃	1	2	yes	—
381	#123	C₂×D₁₃	1	2	yes	complemented
382	C₂²⋊Q₈	—	13	2	no	—
383	C₂²⋊Q₈	—	13	2	no	—
384	C₂²⋊Q₈	—	13	2	no	—
385	C₂²⋊Q₈	—	13	1	no	—
386	C₂²⋊Q₈	—	13	1	no	—
387	C₂²⋊Q₈	—	13	2	no	—
388	C₂²⋊Q₈	—	13	2	no	—
389	C₂²⋊Q₈	—	13	1	no	—
390	C₂²⋊Q₈	—	13	2	no	—
391	C₂²⋊Q₈	—	13	1	no	—
392	C₂²⋊Q₈	—	13	1	no	—
393	C₂²⋊Q₈	—	13	1	no	—
394	C₂²⋊Q₈	—	13	2	no	—
395	C₂²⋊Q₈	—	13	2	no	—
396	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
397	#121	—	13	2	no	—
398	#121	—	13	1	no	—
399	#121	—	13	2	no	—
400	#121	—	13	1	no	—
401	#121	—	13	1	no	—
402	#121	—	13	2	no	—
403	#121	—	13	2	no	—
404	#121	—	13	2	no	—
405	#121	—	13	1	no	—
406	#121	C₂×D₁₃	1	1	yes	characteristic
407	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
408	#120	—	13	2	no	—
409	#120	—	13	1	no	—
410	#120	—	13	1	no	—
411	C₄×Q₈	—	13	2	no	—
412	C₄×Q₈	—	13	1	no	—
413	C₄×Q₈	—	13	1	no	—
414	C₄×D₄	—	13	1	no	—
415	C₄×D₄	—	13	2	no	—
416	C₄×D₄	—	13	2	no	—
417	C₄×D₄	—	13	2	no	—
418	C₄×D₄	—	13	2	no	—
419	C₄×D₄	—	13	1	no	—
420	C₄×D₄	—	13	2	no	—
421	C₄×D₄	—	13	2	no	—
422	C₄×D₄	—	13	1	no	—
423	C₄×D₄	—	13	2	no	—
424	C₄×D₄	—	13	2	no	—
425	C₄×D₄	—	13	2	no	—
426	C₄×D₄	—	13	2	no	—
427	C₄×D₄	—	13	2	no	—
428	C₄×D₄	—	13	1	no	—
429	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
430	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
431	#117	—	13	1	no	—
432	#117	—	13	2	no	—
433	#117	—	13	1	no	—
434	#117	—	13	1	no	—
435	#117	—	13	2	no	—
436	#117	—	13	2	no	—
437	#117	—	13	1	no	—
438	C₂×C₄⋊C₄	—	13	2	no	—
439	C₂×C₄⋊C₄	—	13	1	no	—
440	C₂×C₄⋊C₄	—	13	2	no	—
441	C₂×C₄⋊C₄	—	13	1	no	—
442	C₂×C₄⋊C₄	—	13	1	no	—
443	C₂×C₄⋊C₄	—	13	2	no	—
444	C₂×C₄⋊C₄	—	13	2	no	—
445	C₂×C₄⋊C₄	—	13	1	no	—
446	C₂×C₄⋊C₄	—	13	1	no	—
447	C₂×C₄⋊C₄	—	13	1	no	—
448	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
450	C₂×C₁₃	—	2	2	no	—
451	C₂×C₁₃	—	4	2	no	—
452	C₂×C₁₃	—	4	1	no	—
453	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
454	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
455	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
456	D₁₃	—	2	2	no	—
457	D₁₃	—	2	2	no	—
458	D₁₃	—	4	1	no	—
459	C₂⁴	—	13	1	no	—
460	#41	—	4	4	no	—
461	#41	—	26	4	no	—
462	#41	—	26	4	no	—
463	#41	—	52	4	no	—
464	C₂×Q₈	—	13	1	no	—
465	C₂×Q₈	—	13	1	no	—
466	C₂×Q₈	—	13	2	no	—
467	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
468	C₂×D₄	—	13	1	no	—
469	C₂×D₄	—	13	2	no	—
470	C₂×D₄	—	13	1	no	—
471	C₂×D₄	—	13	2	no	—
472	C₂×D₄	—	13	1	no	—
473	C₂×D₄	—	13	1	no	—
474	C₂×D₄	—	13	2	no	—
475	C₂×D₄	—	13	1	no	—
476	C₂×D₄	—	13	1	no	—
477	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
478	C₂×D₄	C₂²×D₁₃	1	2	yes	—
479	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
480	C₂×D₄	C₂²×D₁₃	1	2	yes	—
481	C₂²×C₄	—	13	1	no	—
482	C₂²×C₄	—	13	2	no	—
483	C₂²×C₄	—	13	1	no	—
484	C₂²×C₄	—	13	2	no	—
485	C₂²×C₄	—	13	2	no	—
486	C₂²×C₄	—	13	1	no	—
487	C₂²×C₄	—	13	1	no	—
488	C₂²×C₄	—	13	1	no	—
489	C₂²×C₄	—	13	1	no	—
490	C₂²×C₄	—	13	2	no	—
491	C₂²×C₄	—	13	2	no	—
492	C₂²×C₄	—	13	2	no	—
493	C₂²×C₄	—	13	2	no	—
494	C₂²×C₄	—	13	2	no	—
495	C₂²×C₄	—	26	4	no	—
496	C₂²×C₄	—	52	4	no	—
497	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
498	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
499	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
500	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
501	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
502	C₄⋊C₄	—	13	2	no	—
503	C₄⋊C₄	—	13	1	no	—
504	C₄⋊C₄	—	13	2	no	—
505	C₄⋊C₄	—	13	1	no	—
506	C₄⋊C₄	—	13	2	no	—
507	C₄⋊C₄	—	13	2	no	—
508	C₄⋊C₄	—	13	2	no	—
509	C₄⋊C₄	—	13	1	no	—
510	C₄⋊C₄	—	13	2	no	—
511	C₄⋊C₄	—	13	2	no	—
512	C₄⋊C₄	—	13	2	no	—
513	C₄⋊C₄	—	13	1	no	—
514	C₄⋊C₄	—	13	1	no	—
515	C₄⋊C₄	—	13	2	no	—
516	C₄⋊C₄	—	13	2	no	—
517	C₄⋊C₄	—	13	2	no	—
518	C₄⋊C₄	—	13	2	no	—
519	C₄⋊C₄	—	13	1	no	—
520	C₄⋊C₄	—	13	2	no	—
521	C₄⋊C₄	—	13	2	no	—
522	C₄⋊C₄	—	13	2	no	—
523	C₄⋊C₄	—	13	2	no	—
524	C₄⋊C₄	—	13	2	no	—
525	C₄⋊C₄	—	13	1	no	—
526	C₄⋊C₄	—	13	1	no	—
527	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
528	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
529	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
530	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
532	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
533	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
534	C₂²⋊C₄	—	13	1	no	—
535	C₂²⋊C₄	—	13	2	no	—
536	C₂²⋊C₄	—	13	2	no	—
537	C₂²⋊C₄	—	13	2	no	—
538	C₂²⋊C₄	—	13	2	no	—
539	C₂²⋊C₄	—	13	2	no	—
540	C₂²⋊C₄	—	13	1	no	—
541	C₂²⋊C₄	—	13	2	no	—
542	C₂²⋊C₄	—	13	2	no	—
543	C₂²⋊C₄	—	13	1	no	—
544	C₂²⋊C₄	—	13	1	no	—
545	C₂²⋊C₄	—	13	2	no	—
546	C₂²⋊C₄	—	13	2	no	—
547	C₂²⋊C₄	—	13	1	no	—
548	C₂²⋊C₄	—	13	1	no	—
549	C₂²⋊C₄	—	13	2	no	—
550	C₂²⋊C₄	—	13	1	no	—
551	C₂²⋊C₄	—	13	1	no	—
552	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
553	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
556	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
557	C₄²	—	13	2	no	—
558	C₄²	—	13	2	no	—
559	C₄²	—	13	2	no	—
560	C₄²	—	13	2	no	—
561	C₄²	—	13	2	no	—
562	C₄²	—	13	1	no	—
563	C₄²	C₂²×D₁₃	1	1	yes	characteristic
564	C₁₃	#3492	1	1	yes	characteristic, complemented, Sylow
565	C₂³	—	13	1	no	—
566	C₂³	—	13	1	no	—
567	C₂³	—	13	1	no	—
568	C₂³	—	26	2	no	—
569	C₂³	—	26	2	no	—
570	C₂³	—	26	2	no	—
571	C₂³	C₂³×D₁₃	1	1	yes	characteristic
572	C₂³	C₂³×D₁₃	1	2	yes	—
573	C₂³	C₂³×D₁₃	1	1	yes	characteristic
574	Q₈	—	4	2	no	—
575	Q₈	—	26	2	no	—
576	Q₈	—	26	2	no	—
577	Q₈	—	52	2	no	—
578	D₄	—	2	2	no	—
579	D₄	—	2	4	no	—
580	D₄	—	2	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	26	2	no	—
583	D₄	—	26	2	no	—
584	D₄	—	26	2	no	—
585	D₄	—	26	2	no	—
586	D₄	—	26	4	no	—
587	D₄	—	26	2	no	—
588	D₄	—	26	4	no	—
589	D₄	—	26	2	no	—
590	D₄	—	52	2	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	13	1	no	—
597	C₂×C₄	—	13	4	no	—
598	C₂×C₄	—	13	1	no	—
599	C₂×C₄	—	13	2	no	—
600	C₂×C₄	—	13	1	no	—
601	C₂×C₄	—	13	2	no	—
602	C₂×C₄	—	13	2	no	—
603	C₂×C₄	—	13	1	no	—
604	C₂×C₄	—	13	1	no	—
605	C₂×C₄	—	13	2	no	—
606	C₂×C₄	—	26	2	no	—
607	C₂×C₄	—	26	2	no	—
608	C₂×C₄	—	26	2	no	—
609	C₂×C₄	—	26	4	no	—
610	C₂×C₄	—	26	4	no	—
611	C₂×C₄	—	26	2	no	—
612	C₂×C₄	—	26	2	no	—
613	C₂×C₄	—	52	2	no	—
614	C₂×C₄	—	52	2	no	—
615	C₂×C₄	—	52	2	no	—
616	C₂×C₄	—	52	2	no	—
617	C₂×C₄	—	52	2	no	—
618	C₂×C₄	—	52	2	no	—
619	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₁₃	1	2	yes	—
622	C₂×C₄	C₂³×D₁₃	1	2	yes	—
623	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₃	1	2	yes	—
626	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	13	2	no	—
636	C₂²	—	13	2	no	—
637	C₂²	—	26	8	no	—
638	C₂²	—	26	1	no	—
639	C₂²	—	26	1	no	—
640	C₂²	—	26	1	no	—
641	C₂²	—	26	1	no	—
642	C₂²	—	26	1	no	—
643	C₂²	—	26	1	no	—
644	C₂²	—	26	1	no	—
645	C₂²	#88251	1	2	yes	—
646	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	1	no	—
652	C₄	—	2	1	no	—
653	C₄	—	2	1	no	—
654	C₄	—	13	2	no	—
655	C₄	—	26	2	no	—
656	C₄	—	26	2	no	—
657	C₄	—	26	1	no	—
658	C₄	—	26	1	no	—
659	C₄	—	26	1	no	—
660	C₄	—	26	2	no	—
661	C₄	—	26	1	no	—
662	C₄	—	26	2	no	—
663	C₄	#41×D₁₃	1	2	yes	—
664	C₂	—	2	2	no	—
665	C₂	—	4	1	no	—
666	C₂	—	4	2	no	—
667	C₂	—	26	2	no	—
668	C₂	—	26	2	no	—
669	C₂	—	52	1	no	—
670	C₂	C₂×#88251	1	1	yes	characteristic
671	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
672	C₂	D₁₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#547	C₂
hypercenter	#547	D₁₃
hypocenter	C₁₃	#3492
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #547

Complements

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

N	H ≅ G/N	type
1. C₁₃×#547	C₂	semidirect
2. #11719533	C₂	semidirect
3. #11719529	C₂	semidirect
4. #11719435	C₂	semidirect
5. #11719434	C₂	semidirect
6. #11719366	C₂	semidirect
7. #11719365	C₂	semidirect
8. #11719361	C₂	semidirect
9. #11719355	C₂	semidirect
10. #11719343	C₂	semidirect
11. #11719341	C₂	semidirect
12. #11719319	C₂	semidirect
13. #11719316	C₂	semidirect
14. #11719313	C₂	semidirect
15. #11719311	C₂	semidirect
16. #11719263	C₂	semidirect
17. #11719252	C₂	semidirect
18. #11719251	C₂	semidirect
19. #11719246	C₂	semidirect
20. #11719218	C₂	semidirect
21. #11719216	C₂	semidirect
22. #11719209	C₂	semidirect
23. C₂×C₄⋊C₄×D₁₃	C₂	semidirect
30. C₁₃×C₄⋊Q₈	C₂²	semidirect
32. C₁₃×#123	C₂²	semidirect
33. C₁₃×C₂²⋊Q₈	C₂²	semidirect
35. C₁₃×#121	C₂²	semidirect
37. C₄×D₄×C₁₃	C₂²	semidirect
39. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
42. #88200	C₂²	semidirect
43. #88198	C₂²	semidirect
45. #88193	C₂²	semidirect
49. #88192	C₂²	semidirect
54. #88189	C₂²	semidirect
56. D₄×Dic₁₃	C₂²	semidirect
58. #88183	C₂²	semidirect
65. C₄×C₂²⋊D₁₃	C₂²	semidirect
67. #88180	C₂²	semidirect
70. #88178	C₂²	semidirect
71. #88178	C₂²	semidirect
73. C₂×#6101	C₂²	semidirect
74. #88152	C₂²	semidirect
76. #88151	C₂²	semidirect
84. #88146	C₂²	semidirect
91. C₄⋊C₄×D₁₃	C₂²	semidirect
92. #88144	C₂²	semidirect
93. #88144	C₂²	semidirect
94. #88143	C₂²	semidirect
95. #88143	C₂²	semidirect
96. #88143	C₂²	semidirect
97. #88143	C₂²	semidirect
98. #88142	C₂²	semidirect
99. #88141	C₂²	semidirect
100. #88141	C₂²	semidirect
106. #88137	C₂²	semidirect
111. #88133	C₂²	semidirect
112. #88133	C₂²	semidirect
113. #88133	C₂²	semidirect
115. #88132	C₂²	semidirect
116. #88132	C₂²	semidirect
118. #88131	C₂²	semidirect
121. #88124	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
287. C₄×D₁₃	#41	semidirect
302. #547	D₁₃	semidirect
359. C₄⋊Q₈	C₂×D₁₃	semidirect
381. #123	C₂×D₁₃	semidirect
396. C₂²⋊Q₈	C₂×D₁₃	semidirect
407. #121	C₂×D₁₃	semidirect
430. C₄×D₄	C₂×D₁₃	semidirect
449. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
564. C₁₃	#3492	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#547	2
#11719533	2
#11719529	2
#11719435	2
#11719434	2
#11719366	2
#11719365	2
#11719361	2
#11719355	2
#11719343	2
#11719341	2
#11719319	2
#11719316	2
#11719313	2
#11719311	2
#11719263	2
#11719252	2
#11719251	2
#11719246	2
#11719218	2
#11719216	2
#11719209	2
C₂×C₄⋊C₄×D₁₃	2
#3492	13