Subgroups — #13128992

Order 1664.

1336 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#551	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719416	C₂	1	2	yes	maximal, complemented
3	#11719409	C₂	1	2	yes	maximal, complemented
4	#11719388	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719379	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719371	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719359	C₂	1	2	yes	maximal, complemented
8	#11719358	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719358	C₂	1	2	yes	maximal, complemented
10	#11719349	C₂	1	2	yes	maximal, complemented
11	#11719335	C₂	1	2	yes	maximal, complemented
12	#11719295	C₂	1	1	yes	maximal, characteristic, complemented
13	D₁₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719265	C₂	1	2	yes	maximal, complemented
15	D₄×D₅₂	C₂	1	2	yes	maximal, complemented
16	#11719232	C₂	1	2	yes	maximal, complemented
17	#11719230	C₂	1	2	yes	maximal, complemented
18	#11719195	C₂	1	2	yes	maximal, complemented
19	C₂×#88136	C₂	1	2	yes	maximal, complemented
20	C₂⁴×D₁₃	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
22	C₂×#6131	C₂²	1	1	yes	characteristic, complemented
23	C₂×D₄×D₁₃	C₂²	1	2	yes	complemented
24	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×D₄×D₁₃	C₂²	1	2	yes	complemented
26	C₂×#6127	C₂²	1	2	yes	complemented
27	C₂²×D₅₂	C₂²	1	2	yes	complemented
28	C₂²×D₅₂	C₂²	1	2	yes	complemented
29	C₂²×D₅₂	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#126	C₂²	1	2	yes	complemented
31	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#123	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#123	C₂²	1	2	yes	complemented
34	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
35	C₁₃×#120	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
37	C₁₃×#117	C₂²	1	2	yes	complemented
38	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
39	#88207	C₂²	1	1	yes	characteristic, complemented
40	#88201	C₂²	1	2	yes	complemented
41	#88201	C₂²	1	1	yes	characteristic, complemented
42	#88194	C₂²	1	1	yes	characteristic, complemented
43	#88193	C₂²	1	2	yes	complemented
44	#88191	C₂²	1	2	yes	complemented
45	#88191	C₂²	1	1	yes	characteristic, complemented
46	#88191	C₂²	1	1	yes	characteristic, complemented
47	#88184	C₂²	1	2	yes	complemented
48	#88184	C₂²	1	2	yes	complemented
49	#88183	C₂²	1	1	yes	characteristic, complemented
50	#88183	C₂²	1	2	yes	complemented
51	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
52	C₂×#6103	C₂²	1	2	yes	complemented
53	C₂×#6103	C₂²	1	2	yes	complemented
54	#88152	C₂²	1	2	yes	complemented
55	#88152	C₂²	1	2	yes	complemented
56	#88150	C₂²	1	2	yes	complemented
57	#88149	C₂²	1	2	yes	complemented
58	#88149	C₂²	1	2	yes	complemented
59	#88149	C₂²	1	2	yes	complemented
60	#88149	C₂²	1	2	yes	complemented
61	#88149	C₂²	1	2	yes	complemented
62	#88149	C₂²	1	2	yes	complemented
63	#88149	C₂²	1	2	yes	complemented
64	#88148	C₂²	1	2	yes	complemented
65	#88148	C₂²	1	2	yes	complemented
66	#88148	C₂²	1	2	yes	complemented
67	#88148	C₂²	1	2	yes	complemented
68	#88148	C₂²	1	2	yes	complemented
69	#88147	C₂²	1	2	yes	complemented
70	#88139	C₂²	1	2	yes	complemented
71	#88139	C₂²	1	2	yes	complemented
72	#88138	C₂²	1	2	yes	complemented
73	#88138	C₂²	1	2	yes	complemented
74	#88138	C₂²	1	2	yes	complemented
75	#88138	C₂²	1	2	yes	complemented
76	#88138	C₂²	1	2	yes	complemented
77	#88137	C₂²	1	2	yes	complemented
78	#88136	C₂²	1	2	yes	—
79	#88136	C₂²	1	2	yes	complemented
80	#88136	C₂²	1	2	yes	complemented
81	#88136	C₂²	1	2	yes	complemented
82	#88136	C₂²	1	2	yes	complemented
83	#88136	C₂²	1	2	yes	complemented
84	#88136	C₂²	1	2	yes	complemented
85	#88136	C₂²	1	2	yes	complemented
86	#88136	C₂²	1	2	yes	complemented
87	#88136	C₂²	1	1	yes	characteristic, complemented
88	#88136	C₂²	1	2	yes	complemented
89	#88136	C₂²	1	2	yes	complemented
90	#88136	C₂²	1	2	yes	complemented
91	#88136	C₂²	1	2	yes	complemented
92	#88136	C₂²	1	1	yes	characteristic, complemented
93	#88135	C₂²	1	2	yes	complemented
94	#88135	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
97	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
98	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
99	#88132	C₂²	1	2	yes	complemented
100	#88130	C₂²	1	2	yes	complemented
101	#88129	C₂²	1	2	yes	complemented
102	#88129	C₂²	1	2	yes	complemented
103	#88128	C₂²	1	1	yes	characteristic, complemented
104	#88128	C₂²	1	2	yes	complemented
105	C₄×D₅₂	C₂²	1	2	yes	complemented
106	#88126	C₂²	1	1	yes	characteristic, complemented
107	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
108	C₂³×D₁₃	—	4	2	no	—
109	C₂³×D₁₃	—	4	4	no	—
110	C₂³×D₁₃	C₂³	1	2	yes	—
111	C₂³×D₁₃	C₂³	1	1	yes	characteristic
112	C₂³×D₁₃	C₂³	1	2	yes	—
113	C₂³×D₁₃	C₂³	1	1	yes	characteristic
114	C₂³×D₁₃	C₂³	1	2	yes	—
115	C₂³×D₁₃	C₂³	1	1	yes	characteristic
116	C₂³×D₁₃	C₂³	1	1	yes	characteristic, complemented
117	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic, complemented
118	C₂×D₄×C₁₃	C₂³	1	2	yes	—
119	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
122	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic, complemented
123	C₂×C₂²⋊D₁₃	—	4	4	no	—
124	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	complemented
133	C₂²×Dic₁₃	C₂³	1	2	yes	—
134	#6131	—	4	2	no	—
135	D₄×D₁₃	—	4	2	no	—
136	D₄×D₁₃	—	4	4	no	—
137	D₄×D₁₃	—	4	4	no	—
138	#6127	—	4	4	no	—
139	C₂×D₅₂	—	4	2	no	—
140	C₂×D₅₂	—	4	4	no	—
141	C₂×D₅₂	—	4	4	no	—
142	C₂×D₅₂	C₂³	1	2	yes	—
143	C₂×D₅₂	C₂³	1	2	yes	—
144	C₂×D₅₂	C₂³	1	2	yes	—
145	C₂×D₅₂	C₂³	1	2	yes	—
146	C₂×D₅₂	C₂³	1	2	yes	—
147	C₂×D₅₂	C₂³	1	2	yes	—
148	C₂×D₅₂	C₂³	1	1	yes	characteristic
149	C₂×D₅₂	C₂³	1	2	yes	—
150	C₂×D₅₂	C₂³	1	2	yes	—
151	C₂×D₅₂	C₂³	1	2	yes	—
152	C₂×D₅₂	C₂³	1	2	yes	complemented
153	C₂×D₅₂	C₂³	1	1	yes	characteristic, complemented
154	C₂×D₅₂	C₂³	1	2	yes	complemented
155	C₂×D₅₂	C₂³	1	2	yes	complemented
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	complemented
159	C₂×C₄×D₁₃	C₂³	1	2	yes	complemented
160	C₂×C₄×D₁₃	C₂³	1	2	yes	complemented
161	C₂×C₄×D₁₃	C₂³	1	2	yes	complemented
162	C₂×Dic₂₆	C₂³	1	2	yes	complemented
163	C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
164	C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
165	C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
166	C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
167	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic, complemented
174	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	complemented
175	C₄²×C₁₃	C₂³	1	1	yes	characteristic, complemented
176	C₄²×C₁₃	C₂³	1	2	yes	complemented
177	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic, complemented
180	#6103	C₂³	1	2	yes	—
181	#6103	C₂³	1	2	yes	—
182	#6103	C₂³	1	2	yes	—
183	#6103	C₂³	1	2	yes	—
184	#6103	C₂³	1	2	yes	—
185	#6103	C₂³	1	2	yes	—
186	#6103	C₂³	1	2	yes	—
187	#6103	C₂³	1	2	yes	—
188	#6103	C₂³	1	2	yes	—
189	#6103	C₂³	1	2	yes	—
190	#6103	C₂³	1	2	yes	—
191	#6103	C₂³	1	2	yes	complemented
192	#6103	C₂³	1	2	yes	complemented
193	#6103	C₂³	1	2	yes	complemented
194	#6103	C₂³	1	2	yes	complemented
195	#6103	C₂³	1	2	yes	complemented
196	#6103	C₂³	1	2	yes	complemented
197	#6103	C₂³	1	2	yes	complemented
198	C₄⋊Dic₁₃	C₂³	1	2	yes	complemented
199	#6101	C₂³	1	2	yes	complemented
200	#6101	C₂³	1	2	yes	complemented
201	#6101	C₂³	1	2	yes	complemented
202	#6101	C₂³	1	2	yes	complemented
203	C₄×Dic₁₃	C₂³	1	1	yes	characteristic, complemented
204	C₄×Dic₁₃	C₂³	1	2	yes	complemented
205	#3532	—	13	1	no	maximal, Sylow
206	C₂³×C₁₃	—	2	4	no	—
207	C₂³×C₁₃	—	4	1	no	—
208	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
209	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
210	C₂³×C₁₃	C₂⁴	1	2	yes	—
211	C₂²×D₁₃	—	2	4	no	—
212	C₂²×D₁₃	—	2	4	no	—
213	C₂²×D₁₃	—	2	4	no	—
214	C₂²×D₁₃	—	2	4	no	—
215	C₂²×D₁₃	—	2	2	no	—
216	C₂²×D₁₃	—	2	2	no	—
217	C₂²×D₁₃	—	4	2	no	—
218	C₂²×D₁₃	—	4	2	no	—
219	C₂²×D₁₃	—	4	1	no	—
220	C₂²×D₁₃	—	4	2	no	—
221	C₂²×D₁₃	—	4	2	no	—
222	C₂²×D₁₃	—	4	2	no	—
223	C₂²×D₁₃	—	4	2	no	—
224	C₂²×D₁₃	—	4	1	no	—
225	C₂²×D₁₃	—	4	2	no	—
226	C₂²×D₁₃	—	4	2	no	—
227	C₂²×D₁₃	—	4	2	no	—
228	C₂²×D₁₃	—	4	16	no	—
229	C₂²×D₁₃	C₂⁴	1	2	yes	—
230	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₃	C₂⁴	1	2	yes	—
232	C₂²×D₁₃	C₂⁴	1	2	yes	—
233	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
234	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
235	Q₈×C₁₃	—	4	1	no	—
236	D₄×C₁₃	—	2	4	no	—
237	D₄×C₁₃	—	4	1	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	4	2	no	—
240	C₂×C₄×C₁₃	—	4	1	no	—
241	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
243	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
244	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
246	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂²⋊D₁₃	—	2	4	no	—
248	C₂²⋊D₁₃	—	2	4	no	—
249	C₂²⋊D₁₃	—	2	4	no	—
250	C₂²⋊D₁₃	—	4	2	no	—
251	C₂²⋊D₁₃	—	4	1	no	—
252	C₂²⋊D₁₃	—	4	1	no	—
253	C₂²⋊D₁₃	—	4	2	no	—
254	C₂²⋊D₁₃	—	4	2	no	—
255	C₂²⋊D₁₃	—	4	2	no	—
256	C₂×Dic₁₃	—	4	2	no	—
257	C₂×Dic₁₃	C₂⁴	1	2	yes	—
258	C₂×Dic₁₃	C₂⁴	1	2	yes	—
259	C₂×Dic₁₃	C₂⁴	1	2	yes	—
260	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
261	D₅₂	—	2	4	no	—
262	D₅₂	—	2	4	no	—
263	D₅₂	—	4	2	no	—
264	D₅₂	—	4	2	no	—
265	D₅₂	—	4	2	no	—
266	D₅₂	—	4	2	no	—
267	D₅₂	—	4	2	no	—
268	D₅₂	—	4	2	no	—
269	D₅₂	—	4	2	no	—
270	D₅₂	—	4	1	no	—
271	D₅₂	—	4	2	no	—
272	D₅₂	—	4	2	no	—
273	D₅₂	—	4	2	no	—
274	D₅₂	—	4	1	no	—
275	C₄×D₁₃	—	2	2	no	—
276	C₄×D₁₃	—	4	2	no	—
277	C₄×D₁₃	—	4	2	no	—
278	C₄×D₁₃	—	4	2	no	—
279	C₄×D₁₃	—	4	2	no	—
280	C₄×D₁₃	—	4	2	no	—
281	Dic₂₆	—	4	2	no	—
282	H(3,𝔽₄)	—	13	1	no	—
283	#560	—	13	2	no	—
284	#560	—	13	1	no	—
285	#551	—	13	2	no	—
286	#551	D₁₃	1	1	yes	characteristic, complemented
287	#546	—	13	2	no	—
288	#546	—	13	2	no	—
289	#546	—	13	2	no	—
290	D₄²	—	13	1	no	—
291	D₄²	—	13	2	no	—
292	#538	—	13	2	no	—
293	#538	—	13	2	no	—
294	#538	—	13	2	no	—
295	#535	—	13	1	no	—
296	#535	—	13	2	no	—
297	#534	—	13	2	no	—
298	#534	—	13	1	no	—
299	C₂×#120	—	13	1	no	—
300	C₂×#120	—	13	2	no	—
301	C₂²×C₁₃	—	2	2	no	—
302	C₂²×C₁₃	—	2	2	no	—
303	C₂²×C₁₃	—	2	2	no	—
304	C₂²×C₁₃	—	2	2	no	—
305	C₂²×C₁₃	—	2	1	no	—
306	C₂²×C₁₃	—	2	1	no	—
307	C₂²×C₁₃	—	4	4	no	—
308	C₂²×C₁₃	H(5,𝔽₂)	1	4	yes	—
309	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
310	C₂×D₁₃	—	2	2	no	—
311	C₂×D₁₃	—	2	2	no	—
312	C₂×D₁₃	—	2	2	no	—
313	C₂×D₁₃	—	2	2	no	—
314	C₂×D₁₃	—	2	2	no	—
315	C₂×D₁₃	—	2	2	no	—
316	C₂×D₁₃	—	2	2	no	—
317	C₂×D₁₃	—	2	1	no	—
318	C₂×D₁₃	—	2	2	no	—
319	C₂×D₁₃	—	2	2	no	—
320	C₂×D₁₃	—	2	2	no	—
321	C₂×D₁₃	—	2	2	no	—
322	C₂×D₁₃	—	2	2	no	—
323	C₂×D₁₃	—	2	1	no	—
324	C₂×D₁₃	—	4	8	no	—
325	C₂×D₁₃	—	4	4	no	—
326	C₂×D₁₃	—	4	8	no	—
327	C₂×D₁₃	—	4	4	no	—
328	C₂×D₁₃	—	8	2	no	—
329	C₂×D₁₃	—	8	4	no	—
330	C₂×D₁₃	—	8	2	no	—
331	C₂×D₁₃	H(5,𝔽₂)	1	2	yes	—
332	C₄×C₁₃	—	2	2	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	2	2	no	—
335	C₄×C₁₃	—	2	2	no	—
336	C₄×C₁₃	—	2	2	no	—
337	C₄×C₁₃	—	2	2	no	—
338	Dic₁₃	—	2	2	no	—
339	Dic₁₃	—	2	2	no	—
340	Dic₁₃	—	2	1	no	—
341	Dic₁₃	—	2	2	no	—
342	C₂⁵	—	13	1	no	—
343	C₂×#41	—	13	1	no	—
344	C₂×#41	—	13	2	no	—
345	C₂²×D₄	—	13	2	no	—
346	C₂²×D₄	—	13	1	no	—
347	C₂²×D₄	—	13	2	no	—
348	C₂²×D₄	—	13	2	no	—
349	C₂²×D₄	—	13	2	no	—
350	C₂²×D₄	—	13	2	no	—
351	C₂²×D₄	—	13	1	no	—
352	#127	—	13	1	no	—
353	#127	—	13	1	no	—
354	#127	—	13	2	no	—
355	#126	—	13	2	no	—
356	#126	—	13	2	no	—
357	#126	—	13	2	no	—
358	#126	C₂×D₁₃	1	2	yes	complemented
359	#124	—	13	1	no	—
360	#124	—	13	2	no	—
361	#124	—	13	2	no	—
362	#124	—	13	2	no	—
363	#124	—	13	2	no	—
364	#124	—	13	2	no	—
365	#124	C₂×D₁₃	1	1	yes	characteristic, complemented
366	#123	—	13	2	no	—
367	#123	—	13	1	no	—
368	#123	—	13	2	no	—
369	#123	—	13	2	no	—
370	#123	—	13	2	no	—
371	#123	—	13	2	no	—
372	#123	—	13	2	no	—
373	#123	—	13	2	no	—
374	#123	C₂×D₁₃	1	1	yes	characteristic, complemented
375	#123	C₂×D₁₃	1	2	yes	complemented
376	C₂²⋊Q₈	—	13	2	no	—
377	C₂²⋊Q₈	—	13	2	no	—
378	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
379	#121	—	13	2	no	—
380	#121	—	13	2	no	—
381	#121	—	13	2	no	—
382	#121	—	13	2	no	—
383	#121	—	13	2	no	—
384	#121	—	13	2	no	—
385	#121	—	13	2	no	—
386	#121	—	13	2	no	—
387	#121	—	13	2	no	—
388	#121	—	13	2	no	—
389	#121	—	13	2	no	—
390	#121	—	13	2	no	—
391	#121	—	13	2	no	—
392	#121	—	13	2	no	—
393	#121	—	13	2	no	—
394	#120	—	13	1	no	—
395	#120	—	13	2	no	—
396	#120	—	13	1	no	—
397	#120	—	13	1	no	—
398	#120	—	13	2	no	—
399	#120	—	13	2	no	—
400	#120	—	13	2	no	—
401	#120	—	13	2	no	—
402	#120	—	13	2	no	—
403	#120	—	13	2	no	—
404	#120	—	13	2	no	—
405	#120	—	13	2	no	—
406	#120	—	13	1	no	—
407	#120	—	13	2	no	—
408	#120	—	13	2	no	—
409	#120	—	13	2	no	—
410	#120	—	13	1	no	—
411	#120	—	13	2	no	—
412	#120	—	13	2	no	—
413	#120	C₂×D₁₃	1	1	yes	characteristic
414	C₄×D₄	—	13	2	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	C₂×D₁₃	1	2	yes	complemented
420	#117	—	13	1	no	—
421	#117	C₂×D₁₃	1	2	yes	complemented
422	C₂×C₂²⋊C₄	—	13	2	no	—
423	C₂×C₂²⋊C₄	—	13	2	no	—
424	C₂×C₂²⋊C₄	—	13	1	no	—
425	C₂×C₂²⋊C₄	—	13	2	no	—
426	C₂×C₂²⋊C₄	—	13	2	no	—
427	C₂×C₂²⋊C₄	—	13	1	no	—
428	C₂×C₂²⋊C₄	C₂×D₁₃	1	2	yes	complemented
429	C₂×C₁₃	—	2	4	no	—
430	C₂×C₁₃	—	4	1	no	—
431	C₂×C₁₃	—	4	1	no	—
432	C₂×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
433	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
434	D₁₃	—	2	2	no	—
435	D₁₃	—	4	2	no	—
436	D₁₃	—	4	1	no	—
437	D₁₃	—	4	2	no	—
438	D₁₃	—	4	1	no	—
439	D₁₃	—	4	2	no	—
440	C₂⁴	—	13	2	no	—
441	C₂⁴	—	13	1	no	—
442	C₂⁴	—	13	2	no	—
443	C₂⁴	—	13	1	no	—
444	C₂⁴	—	13	2	no	—
445	C₂⁴	—	13	1	no	—
446	C₂⁴	—	13	1	no	—
447	C₂⁴	—	52	4	no	—
448	C₂⁴	—	52	2	no	—
449	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
450	#41	—	52	4	no	—
451	#41	—	52	2	no	—
452	C₂×Q₈	—	13	2	no	—
453	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic, complemented
454	C₂×D₄	—	13	2	no	—
455	C₂×D₄	—	13	2	no	—
456	C₂×D₄	—	13	2	no	—
457	C₂×D₄	—	13	1	no	—
458	C₂×D₄	—	13	2	no	—
459	C₂×D₄	—	13	2	no	—
460	C₂×D₄	—	13	1	no	—
461	C₂×D₄	—	13	2	no	—
462	C₂×D₄	—	13	2	no	—
463	C₂×D₄	—	13	2	no	—
464	C₂×D₄	—	13	2	no	—
465	C₂×D₄	—	13	2	no	—
466	C₂×D₄	—	13	2	no	—
467	C₂×D₄	—	13	2	no	—
468	C₂×D₄	—	13	2	no	—
469	C₂×D₄	—	13	2	no	—
470	C₂×D₄	—	13	2	no	—
471	C₂×D₄	—	13	1	no	—
472	C₂×D₄	—	13	2	no	—
473	C₂×D₄	—	13	1	no	—
474	C₂×D₄	—	13	2	no	—
475	C₂×D₄	—	13	2	no	—
476	C₂×D₄	—	13	2	no	—
477	C₂×D₄	—	52	4	no	—
478	C₂×D₄	—	52	4	no	—
479	C₂×D₄	—	52	2	no	—
480	C₂×D₄	—	52	2	no	—
481	C₂×D₄	—	52	4	no	—
482	C₂×D₄	—	52	4	no	—
483	C₂×D₄	—	52	4	no	—
484	C₂×D₄	C₂²×D₁₃	1	2	yes	—
485	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
486	C₂²×C₄	—	13	2	no	—
487	C₂²×C₄	—	13	1	no	—
488	C₂²×C₄	—	13	2	no	—
489	C₂²×C₄	—	13	2	no	—
490	C₂²×C₄	—	13	2	no	—
491	C₂²×C₄	—	13	2	no	—
492	C₂²×C₄	—	13	2	no	—
493	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
494	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
495	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic, complemented
496	C₄⋊C₄	—	13	2	no	—
497	C₄⋊C₄	—	13	2	no	—
498	C₄⋊C₄	—	13	2	no	—
499	C₄⋊C₄	—	13	2	no	—
500	C₄⋊C₄	—	13	2	no	—
501	C₄⋊C₄	C₂²×D₁₃	1	2	yes	complemented
502	C₄⋊C₄	C₂²×D₁₃	1	2	yes	complemented
503	C₄⋊C₄	C₂²×D₁₃	1	2	yes	complemented
504	C₄⋊C₄	C₂²×D₁₃	1	2	yes	complemented
505	C₂²⋊C₄	—	13	2	no	—
506	C₂²⋊C₄	—	13	1	no	—
507	C₂²⋊C₄	—	13	1	no	—
508	C₂²⋊C₄	—	13	2	no	—
509	C₂²⋊C₄	—	13	2	no	—
510	C₂²⋊C₄	—	13	2	no	—
511	C₂²⋊C₄	—	13	2	no	—
512	C₂²⋊C₄	—	13	2	no	—
513	C₂²⋊C₄	—	13	2	no	—
514	C₂²⋊C₄	—	13	2	no	—
515	C₂²⋊C₄	—	13	2	no	—
516	C₂²⋊C₄	—	13	2	no	—
517	C₂²⋊C₄	—	13	2	no	—
518	C₂²⋊C₄	—	13	2	no	—
519	C₂²⋊C₄	—	13	2	no	—
520	C₂²⋊C₄	—	13	2	no	—
521	C₂²⋊C₄	—	13	2	no	—
522	C₂²⋊C₄	—	13	2	no	—
523	C₂²⋊C₄	—	13	2	no	—
524	C₂²⋊C₄	—	13	2	no	—
525	C₂²⋊C₄	—	13	2	no	—
526	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
529	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
530	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic, complemented
533	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	complemented
534	C₄²	—	13	1	no	—
535	C₄²	—	13	2	no	—
536	C₄²	C₂²×D₁₃	1	1	yes	characteristic, complemented
537	C₄²	C₂²×D₁₃	1	2	yes	complemented
538	C₁₃	#3532	1	1	yes	characteristic, complemented, Sylow
539	C₂³	—	2	4	no	—
540	C₂³	—	4	1	no	—
541	C₂³	—	13	1	no	—
542	C₂³	—	13	2	no	—
543	C₂³	—	13	1	no	—
544	C₂³	—	13	2	no	—
545	C₂³	—	13	1	no	—
546	C₂³	—	13	2	no	—
547	C₂³	—	26	4	no	—
548	C₂³	—	26	2	no	—
549	C₂³	—	26	2	no	—
550	C₂³	—	26	4	no	—
551	C₂³	—	26	4	no	—
552	C₂³	—	26	4	no	—
553	C₂³	—	52	2	no	—
554	C₂³	—	52	2	no	—
555	C₂³	—	52	2	no	—
556	C₂³	—	52	2	no	—
557	C₂³	—	52	2	no	—
558	C₂³	—	52	1	no	—
559	C₂³	—	52	2	no	—
560	C₂³	—	52	2	no	—
561	C₂³	—	52	2	no	—
562	C₂³	—	52	2	no	—
563	C₂³	—	52	1	no	—
564	C₂³	—	52	16	no	—
565	C₂³	C₂³×D₁₃	1	1	yes	characteristic
566	C₂³	C₂³×D₁₃	1	1	yes	characteristic
567	C₂³	C₂³×D₁₃	1	2	yes	—
568	Q₈	—	4	1	no	—
569	Q₈	—	52	2	no	—
570	D₄	—	2	4	no	—
571	D₄	—	4	1	no	—
572	D₄	—	26	4	no	—
573	D₄	—	26	4	no	—
574	D₄	—	26	4	no	—
575	D₄	—	26	4	no	—
576	D₄	—	26	4	no	—
577	D₄	—	52	2	no	—
578	D₄	—	52	2	no	—
579	D₄	—	52	2	no	—
580	D₄	—	52	2	no	—
581	D₄	—	52	2	no	—
582	D₄	—	52	2	no	—
583	D₄	—	52	2	no	—
584	D₄	—	52	2	no	—
585	D₄	—	52	2	no	—
586	D₄	—	52	1	no	—
587	D₄	—	52	2	no	—
588	D₄	—	52	1	no	—
589	D₄	—	52	2	no	—
590	D₄	—	52	2	no	—
591	D₄	—	52	2	no	—
592	D₄	—	52	2	no	—
593	D₄	—	52	1	no	—
594	D₄	—	52	1	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	13	2	no	—
599	C₂×C₄	—	13	2	no	—
600	C₂×C₄	—	13	2	no	—
601	C₂×C₄	—	13	1	no	—
602	C₂×C₄	—	26	2	no	—
603	C₂×C₄	—	52	2	no	—
604	C₂×C₄	—	52	2	no	—
605	C₂×C₄	—	52	2	no	—
606	C₂×C₄	—	52	2	no	—
607	C₂×C₄	—	52	2	no	—
608	C₂×C₄	—	52	2	no	—
609	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₁₃	1	2	yes	—
611	C₂×C₄	C₂³×D₁₃	1	2	yes	—
612	C₂×C₄	C₂³×D₁₃	1	2	yes	—
613	C₂×C₄	C₂³×D₁₃	1	2	yes	—
614	C₂×C₄	C₂³×D₁₃	1	2	yes	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	4	4	no	—
622	C₂²	—	13	2	no	—
623	C₂²	—	26	2	no	—
624	C₂²	—	26	2	no	—
625	C₂²	—	26	2	no	—
626	C₂²	—	26	2	no	—
627	C₂²	—	26	2	no	—
628	C₂²	—	26	2	no	—
629	C₂²	—	26	2	no	—
630	C₂²	—	26	2	no	—
631	C₂²	—	26	2	no	—
632	C₂²	—	26	2	no	—
633	C₂²	—	26	2	no	—
634	C₂²	—	26	1	no	—
635	C₂²	—	26	2	no	—
636	C₂²	—	26	1	no	—
637	C₂²	—	52	8	no	—
638	C₂²	—	52	8	no	—
639	C₂²	—	52	4	no	—
640	C₂²	—	52	4	no	—
641	C₂²	—	104	4	no	—
642	C₂²	—	104	2	no	—
643	C₂²	—	104	2	no	—
644	C₂²	#88256	1	4	yes	—
645	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	1	no	—
652	C₄	—	26	2	no	—
653	C₄	—	26	2	no	—
654	C₄	—	26	2	no	—
655	C₄	—	26	1	no	—
656	C₂	—	2	4	no	—
657	C₂	—	4	1	no	—
658	C₂	—	4	1	no	—
659	C₂	—	26	2	no	—
660	C₂	—	52	2	no	—
661	C₂	—	52	1	no	—
662	C₂	—	52	2	no	—
663	C₂	—	52	1	no	—
664	C₂	—	52	2	no	—
665	C₂	C₂×#88256	1	2	yes	—
666	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×#551	C₂
hypercenter	#551	D₁₃
hypocenter	C₁₃	#3532
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #551

Complements

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

N	H ≅ G/N	type
1. C₁₃×#551	C₂	semidirect
2. #11719416	C₂	semidirect
3. #11719409	C₂	semidirect
4. #11719388	C₂	semidirect
5. #11719379	C₂	semidirect
6. #11719371	C₂	semidirect
7. #11719359	C₂	semidirect
8. #11719358	C₂	semidirect
9. #11719358	C₂	semidirect
10. #11719349	C₂	semidirect
11. #11719335	C₂	semidirect
12. #11719295	C₂	semidirect
13. D₁₃×#120	C₂	semidirect
14. #11719265	C₂	semidirect
15. D₄×D₅₂	C₂	semidirect
16. #11719232	C₂	semidirect
17. #11719230	C₂	semidirect
18. #11719195	C₂	semidirect
19. C₂×#88136	C₂	semidirect
20. C₂⁴×D₁₃	C₂²	semidirect
21. C₂²×C₂²⋊D₁₃	C₂²	semidirect
22. C₂×#6131	C₂²	semidirect
23. C₂×D₄×D₁₃	C₂²	semidirect
24. C₂×D₄×D₁₃	C₂²	semidirect
25. C₂×D₄×D₁₃	C₂²	semidirect
26. C₂×#6127	C₂²	semidirect
27. C₂²×D₅₂	C₂²	semidirect
28. C₂²×D₅₂	C₂²	semidirect
29. C₂²×D₅₂	C₂²	semidirect
30. C₁₃×#126	C₂²	semidirect
31. C₁₃×#124	C₂²	semidirect
32. C₁₃×#123	C₂²	semidirect
33. C₁₃×#123	C₂²	semidirect
34. C₁₃×C₂²⋊Q₈	C₂²	semidirect
36. C₄×D₄×C₁₃	C₂²	semidirect
37. C₁₃×#117	C₂²	semidirect
38. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
39. #88207	C₂²	semidirect
40. #88201	C₂²	semidirect
41. #88201	C₂²	semidirect
42. #88194	C₂²	semidirect
43. #88193	C₂²	semidirect
44. #88191	C₂²	semidirect
45. #88191	C₂²	semidirect
46. #88191	C₂²	semidirect
47. #88184	C₂²	semidirect
48. #88184	C₂²	semidirect
49. #88183	C₂²	semidirect
50. #88183	C₂²	semidirect
51. C₄×C₂²⋊D₁₃	C₂²	semidirect
52. C₂×#6103	C₂²	semidirect
53. C₂×#6103	C₂²	semidirect
54. #88152	C₂²	semidirect
55. #88152	C₂²	semidirect
56. #88150	C₂²	semidirect
57. #88149	C₂²	semidirect
58. #88149	C₂²	semidirect
59. #88149	C₂²	semidirect
60. #88149	C₂²	semidirect
61. #88149	C₂²	semidirect
62. #88149	C₂²	semidirect
63. #88149	C₂²	semidirect
64. #88148	C₂²	semidirect
65. #88148	C₂²	semidirect
66. #88148	C₂²	semidirect
67. #88148	C₂²	semidirect
68. #88148	C₂²	semidirect
69. #88147	C₂²	semidirect
70. #88139	C₂²	semidirect
71. #88139	C₂²	semidirect
72. #88138	C₂²	semidirect
73. #88138	C₂²	semidirect
74. #88138	C₂²	semidirect
75. #88138	C₂²	semidirect
76. #88138	C₂²	semidirect
77. #88137	C₂²	semidirect
79. #88136	C₂²	semidirect
80. #88136	C₂²	semidirect
81. #88136	C₂²	semidirect
82. #88136	C₂²	semidirect
83. #88136	C₂²	semidirect
84. #88136	C₂²	semidirect
85. #88136	C₂²	semidirect
86. #88136	C₂²	semidirect
87. #88136	C₂²	semidirect
88. #88136	C₂²	semidirect
89. #88136	C₂²	semidirect
90. #88136	C₂²	semidirect
91. #88136	C₂²	semidirect
92. #88136	C₂²	semidirect
93. #88135	C₂²	semidirect
94. #88135	C₂²	semidirect
95. C₂²⋊C₄×D₁₃	C₂²	semidirect
96. C₂²⋊C₄×D₁₃	C₂²	semidirect
97. C₂²⋊C₄×D₁₃	C₂²	semidirect
98. C₂²⋊C₄×D₁₃	C₂²	semidirect
99. #88132	C₂²	semidirect
100. #88130	C₂²	semidirect
101. #88129	C₂²	semidirect
102. #88129	C₂²	semidirect
103. #88128	C₂²	semidirect
104. #88128	C₂²	semidirect
105. C₄×D₅₂	C₂²	semidirect
106. #88126	C₂²	semidirect
116. C₂³×D₁₃	C₂³	semidirect
117. C₂×Q₈×C₁₃	C₂³	semidirect
122. C₂²×C₄×C₁₃	C₂³	semidirect
132. C₂×C₂²⋊D₁₃	C₂³	semidirect
152. C₂×D₅₂	C₂³	semidirect
153. C₂×D₅₂	C₂³	semidirect
154. C₂×D₅₂	C₂³	semidirect
155. C₂×D₅₂	C₂³	semidirect
158. C₂×C₄×D₁₃	C₂³	semidirect
159. C₂×C₄×D₁₃	C₂³	semidirect
160. C₂×C₄×D₁₃	C₂³	semidirect
161. C₂×C₄×D₁₃	C₂³	semidirect
162. C₂×Dic₂₆	C₂³	semidirect
163. C₁₃×C₄⋊C₄	C₂³	semidirect
164. C₁₃×C₄⋊C₄	C₂³	semidirect
165. C₁₃×C₄⋊C₄	C₂³	semidirect
166. C₁₃×C₄⋊C₄	C₂³	semidirect
173. C₁₃×C₂²⋊C₄	C₂³	semidirect
174. C₁₃×C₂²⋊C₄	C₂³	semidirect
175. C₄²×C₁₃	C₂³	semidirect
176. C₄²×C₁₃	C₂³	semidirect
179. C₂²⋊Dic₁₃	C₂³	semidirect
191. #6103	C₂³	semidirect
192. #6103	C₂³	semidirect
193. #6103	C₂³	semidirect
194. #6103	C₂³	semidirect
195. #6103	C₂³	semidirect
196. #6103	C₂³	semidirect
197. #6103	C₂³	semidirect
198. C₄⋊Dic₁₃	C₂³	semidirect
199. #6101	C₂³	semidirect
200. #6101	C₂³	semidirect
201. #6101	C₂³	semidirect
202. #6101	C₂³	semidirect
203. C₄×Dic₁₃	C₂³	semidirect
204. C₄×Dic₁₃	C₂³	semidirect
286. #551	D₁₃	semidirect
358. #126	C₂×D₁₃	semidirect
365. #124	C₂×D₁₃	semidirect
374. #123	C₂×D₁₃	semidirect
375. #123	C₂×D₁₃	semidirect
378. C₂²⋊Q₈	C₂×D₁₃	semidirect
419. C₄×D₄	C₂×D₁₃	semidirect
421. #117	C₂×D₁₃	semidirect
428. C₂×C₂²⋊C₄	C₂×D₁₃	semidirect
453. C₂×Q₈	C₂²×D₁₃	semidirect
495. C₂²×C₄	C₂²×D₁₃	semidirect
501. C₄⋊C₄	C₂²×D₁₃	semidirect
502. C₄⋊C₄	C₂²×D₁₃	semidirect
503. C₄⋊C₄	C₂²×D₁₃	semidirect
504. C₄⋊C₄	C₂²×D₁₃	semidirect
532. C₂²⋊C₄	C₂²×D₁₃	semidirect
533. C₂²⋊C₄	C₂²×D₁₃	semidirect
536. C₄²	C₂²×D₁₃	semidirect
537. C₄²	C₂²×D₁₃	semidirect
538. C₁₃	#3532	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#551	2
#11719416	2
#11719409	2
#11719388	2
#11719379	2
#11719371	2
#11719359	2
#11719358	2
#11719349	2
#11719335	2
#11719295	2
D₁₃×#120	2
#11719265	2
D₄×D₅₂	2
#11719232	2
#11719230	2
#11719195	2
C₂×#88136	2
#3532	13