Subgroups — #13129059

Order 1664.

1134 conjugacy classes of subgroups.

The subgroup lattice has 704 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	#11719538	C₂	1	2	yes	maximal, complemented
3	#11719534	C₂	1	2	yes	maximal, complemented
4	#11719438	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719435	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719372	C₂	1	2	yes	maximal, complemented
7	#11719370	C₂	1	2	yes	maximal, complemented
8	#11719362	C₂	1	2	yes	maximal, complemented
9	#11719359	C₂	1	2	yes	maximal, complemented
10	#11719352	C₂	1	2	yes	maximal, complemented
11	#11719339	C₂	1	2	yes	maximal, complemented
12	#11719317	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719313	C₂	1	1	yes	maximal, characteristic, complemented
14	D₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719303	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719266	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719259	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719257	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719252	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719216	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719215	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#88151	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719212	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#41	C₂²	1	2	yes	complemented
25	C₂×#6129	C₂²	1	1	yes	characteristic, complemented
26	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
27	C₂×D₄×D₁₃	C₂²	1	2	yes	—
28	C₂×#6127	C₂²	1	2	yes	complemented
29	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
30	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
32	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#123	C₂²	1	2	yes	complemented
35	C₁₃×#123	C₂²	1	2	yes	complemented
36	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
37	C₁₃×#121	C₂²	1	1	yes	characteristic
38	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
43	#88201	C₂²	1	2	yes	complemented
44	#88200	C₂²	1	2	yes	—
45	#88200	C₂²	1	2	yes	complemented
46	#88200	C₂²	1	2	yes	complemented
47	#88193	C₂²	1	2	yes	—
48	#88193	C₂²	1	1	yes	characteristic, complemented
49	#88193	C₂²	1	2	yes	complemented
50	#88193	C₂²	1	2	yes	complemented
51	#88193	C₂²	1	2	yes	complemented
52	#88192	C₂²	1	1	yes	characteristic
53	#88192	C₂²	1	2	yes	complemented
54	#88192	C₂²	1	2	yes	complemented
55	#88191	C₂²	1	1	yes	characteristic
56	#88191	C₂²	1	2	yes	—
57	#88190	C₂²	1	1	yes	characteristic, complemented
58	D₄×Dic₁₃	C₂²	1	2	yes	complemented
59	#88184	C₂²	1	1	yes	characteristic
60	#88184	C₂²	1	2	yes	complemented
61	#88184	C₂²	1	2	yes	complemented
62	#88184	C₂²	1	2	yes	complemented
63	#88183	C₂²	1	2	yes	complemented
64	#88183	C₂²	1	2	yes	complemented
65	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
67	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
68	C₂×#6103	C₂²	1	2	yes	—
69	C₂×#6103	C₂²	1	2	yes	—
70	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	complemented
71	#88178	C₂²	1	1	yes	characteristic, complemented
72	#88178	C₂²	1	2	yes	complemented
73	#88178	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
77	#88151	C₂²	1	2	yes	—
78	#88151	C₂²	1	1	yes	characteristic, complemented
79	#88151	C₂²	1	1	yes	characteristic, complemented
80	#88151	C₂²	1	1	yes	characteristic, complemented
81	#88151	C₂²	1	2	yes	complemented
82	#88151	C₂²	1	2	yes	complemented
83	#88150	C₂²	1	2	yes	—
84	#88150	C₂²	1	1	yes	characteristic
85	#88150	C₂²	1	2	yes	complemented
86	#88150	C₂²	1	2	yes	complemented
87	#88149	C₂²	1	1	yes	characteristic
88	#88149	C₂²	1	1	yes	characteristic, complemented
89	#88149	C₂²	1	2	yes	complemented
90	#88148	C₂²	1	2	yes	complemented
91	#88148	C₂²	1	2	yes	complemented
92	#88148	C₂²	1	1	yes	characteristic, complemented
93	#88147	C₂²	1	2	yes	—
94	#88147	C₂²	1	1	yes	characteristic, complemented
95	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
96	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
97	#88144	C₂²	1	2	yes	complemented
98	#88143	C₂²	1	2	yes	complemented
99	#88142	C₂²	1	1	yes	characteristic, complemented
100	#88141	C₂²	1	1	yes	characteristic, complemented
101	#88140	C₂²	1	2	yes	complemented
102	#88139	C₂²	1	2	yes	complemented
103	#88139	C₂²	1	2	yes	complemented
104	#88139	C₂²	1	2	yes	complemented
105	#88138	C₂²	1	1	yes	characteristic
106	#88138	C₂²	1	2	yes	—
107	#88138	C₂²	1	2	yes	complemented
108	#88137	C₂²	1	1	yes	characteristic, complemented
109	#88137	C₂²	1	2	yes	complemented
110	#88136	C₂²	1	1	yes	characteristic
111	#88136	C₂²	1	2	yes	—
112	#88135	C₂²	1	2	yes	complemented
113	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
114	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
115	#88133	C₂²	1	2	yes	complemented
116	#88132	C₂²	1	1	yes	characteristic, complemented
117	#88132	C₂²	1	2	yes	complemented
118	#88132	C₂²	1	2	yes	complemented
119	#88129	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₅₂	C₂²	1	1	yes	characteristic
121	#88126	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃	C₂³	1	1	yes	characteristic
124	C₂³×D₁₃	C₂³	1	2	yes	—
125	C₁₃×#41	—	4	4	no	—
126	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
127	C₂×D₄×C₁₃	C₂³	1	2	yes	—
128	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₃	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₃	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	2	yes	—
140	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
145	C₂²×Dic₁₃	C₂³	1	2	yes	—
146	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
147	C₂²×Dic₁₃	C₂³	1	2	yes	—
148	#6129	—	4	2	no	—
149	D₄×D₁₃	—	4	2	no	—
150	D₄×D₁₃	—	4	4	no	—
151	#6127	—	4	2	no	—
152	#6127	—	4	2	no	—
153	#6127	—	4	4	no	—
154	C₂×D₅₂	C₂³	1	1	yes	characteristic
155	C₂×D₅₂	C₂³	1	1	yes	characteristic
156	C₂×D₅₂	C₂³	1	1	yes	characteristic
157	C₂×D₅₂	C₂³	1	2	yes	—
158	C₂×D₅₂	C₂³	1	2	yes	—
159	C₂×C₄×D₁₃	—	4	2	no	—
160	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
161	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₁₃	C₂³	1	2	yes	—
165	C₂×C₄×D₁₃	C₂³	1	2	yes	—
166	C₂×C₄×D₁₃	C₂³	1	2	yes	—
167	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
168	C₂×C₄×D₁₃	C₂³	1	2	yes	—
169	C₂×Dic₂₆	—	4	2	no	—
170	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
171	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
172	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
173	C₂×Dic₂₆	C₂³	1	2	yes	—
174	C₂×Dic₂₆	C₂³	1	2	yes	—
175	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
182	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
183	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
185	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
187	C₄²×C₁₃	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
189	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
190	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
191	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
192	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
193	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
194	#6103	C₂³	1	1	yes	characteristic
195	#6103	C₂³	1	1	yes	characteristic
196	#6103	C₂³	1	1	yes	characteristic
197	#6103	C₂³	1	1	yes	characteristic
198	#6103	C₂³	1	2	yes	—
199	#6103	C₂³	1	2	yes	—
200	#6103	C₂³	1	1	yes	characteristic
201	#6103	C₂³	1	2	yes	—
202	#6103	C₂³	1	2	yes	—
203	#6103	C₂³	1	2	yes	—
204	#6103	C₂³	1	2	yes	—
205	#6103	C₂³	1	2	yes	—
206	#6103	C₂³	1	1	yes	characteristic
207	#6103	C₂³	1	2	yes	—
208	#6103	C₂³	1	2	yes	—
209	#6103	C₂³	1	2	yes	—
210	#6103	C₂³	1	2	yes	—
211	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
213	C₄⋊Dic₁₃	C₂³	1	2	yes	—
214	C₄⋊Dic₁₃	C₂³	1	2	yes	—
215	C₄⋊Dic₁₃	C₂³	1	2	yes	—
216	C₄⋊Dic₁₃	C₂³	1	2	yes	—
217	C₄⋊Dic₁₃	C₂³	1	2	yes	—
218	#6101	C₂³	1	2	yes	—
219	#6101	C₂³	1	1	yes	characteristic
220	#6101	C₂³	1	1	yes	characteristic
221	#6101	C₂³	1	1	yes	characteristic
222	#6101	C₂³	1	2	yes	—
223	#6101	C₂³	1	1	yes	characteristic
224	#6101	C₂³	1	2	yes	—
225	#6101	C₂³	1	2	yes	—
226	#6101	C₂³	1	2	yes	—
227	#6101	C₂³	1	2	yes	—
228	C₄×Dic₁₃	C₂³	1	2	yes	—
229	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
230	C₄×Dic₁₃	C₂³	1	2	yes	—
231	#3536	—	13	1	no	maximal, Sylow
232	C₂³×C₁₃	C₂⁴	1	2	yes	—
233	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₂²×D₁₃	—	2	2	no	—
236	C₂²×D₁₃	—	2	2	no	—
237	C₂²×D₁₃	—	2	4	no	—
238	C₂²×D₁₃	—	4	1	no	—
239	C₂²×D₁₃	—	4	2	no	—
240	C₂²×D₁₃	—	4	2	no	—
241	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
242	C₂²×D₁₃	C₂⁴	1	2	yes	—
243	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
244	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
245	Q₈×C₁₃	—	4	2	no	—
246	D₄×C₁₃	—	2	4	no	—
247	D₄×C₁₃	—	2	2	no	—
248	D₄×C₁₃	—	2	2	no	—
249	D₄×C₁₃	—	4	2	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	4	2	no	—
254	C₂×C₄×C₁₃	—	4	2	no	—
255	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
257	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
260	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
261	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
263	C₂²⋊D₁₃	—	2	2	no	—
264	C₂²⋊D₁₃	—	2	4	no	—
265	C₂²⋊D₁₃	—	2	2	no	—
266	C₂²⋊D₁₃	—	4	2	no	—
267	C₂²⋊D₁₃	—	4	1	no	—
268	C₂²⋊D₁₃	—	4	1	no	—
269	C₂²⋊D₁₃	—	4	2	no	—
270	C₂²⋊D₁₃	—	4	2	no	—
271	C₂²⋊D₁₃	—	4	2	no	—
272	C₂×Dic₁₃	—	4	2	no	—
273	C₂×Dic₁₃	—	4	1	no	—
274	C₂×Dic₁₃	—	4	2	no	—
275	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₃	C₂⁴	1	2	yes	—
277	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
278	C₂×Dic₁₃	C₂⁴	1	2	yes	—
279	C₂×Dic₁₃	C₂⁴	1	2	yes	—
280	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
282	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
283	D₅₂	—	2	2	no	—
284	D₅₂	—	2	2	no	—
285	D₅₂	—	4	1	no	—
286	D₅₂	—	4	2	no	—
287	D₅₂	—	4	2	no	—
288	C₄×D₁₃	—	2	2	no	—
289	C₄×D₁₃	—	2	2	no	—
290	C₄×D₁₃	—	2	2	no	—
291	C₄×D₁₃	—	4	1	no	—
292	C₄×D₁₃	—	4	1	no	—
293	C₄×D₁₃	—	4	2	no	—
294	C₄×D₁₃	—	4	2	no	—
295	C₄×D₁₃	—	4	2	no	—
296	C₄×D₁₃	—	4	2	no	—
297	Dic₂₆	—	2	2	no	—
298	Dic₂₆	—	2	2	no	—
299	Dic₂₆	—	4	2	no	—
300	Dic₂₆	—	4	2	no	—
301	Dic₂₆	—	4	1	no	—
302	#562	—	13	2	no	—
303	#562	—	13	2	no	—
304	#554	—	13	1	no	—
305	#554	—	13	1	no	—
306	#548	—	13	1	no	—
307	#548	—	13	1	no	—
308	#547	—	13	1	no	—
309	#547	D₁₃	1	1	yes	characteristic, complemented
310	#546	—	13	2	no	—
311	#546	—	13	2	no	—
312	#546	—	13	1	no	—
313	#546	—	13	1	no	—
314	#543	—	13	2	no	—
315	#542	—	13	1	no	—
316	#542	—	13	1	no	—
317	#539	—	13	2	no	—
318	#538	—	13	2	no	—
319	#537	—	13	2	no	—
320	#537	—	13	1	no	—
321	#537	—	13	1	no	—
322	#525	—	13	1	no	—
323	C₂×C₂²⋊Q₈	—	13	1	no	—
324	C₂×#121	—	13	1	no	—
325	C₂²×C₁₃	—	2	1	no	—
326	C₂²×C₁₃	—	2	1	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	1	no	—
329	C₂²×C₁₃	—	2	2	no	—
330	C₂²×C₁₃	—	2	1	no	—
331	C₂²×C₁₃	—	2	1	no	—
332	C₂²×C₁₃	—	2	2	no	—
333	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
334	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
335	C₂×D₁₃	—	2	1	no	—
336	C₂×D₁₃	—	2	1	no	—
337	C₂×D₁₃	—	2	1	no	—
338	C₂×D₁₃	—	2	1	no	—
339	C₂×D₁₃	—	2	1	no	—
340	C₂×D₁₃	—	2	2	no	—
341	C₂×D₁₃	—	2	2	no	—
342	C₂×D₁₃	—	2	1	no	—
343	C₂×D₁₃	—	2	1	no	—
344	C₂×D₁₃	—	2	1	no	—
345	C₂×D₁₃	—	2	2	no	—
346	C₂×D₁₃	—	4	4	no	—
347	C₂×D₁₃	—	8	4	no	—
348	C₂×D₁₃	2₋¹⁺⁴	1	2	yes	—
349	C₄×C₁₃	—	2	1	no	—
350	C₄×C₁₃	—	2	1	no	—
351	C₄×C₁₃	—	2	2	no	—
352	C₄×C₁₃	—	2	2	no	—
353	C₄×C₁₃	—	2	2	no	—
354	C₄×C₁₃	—	2	1	no	—
355	C₄×C₁₃	—	2	1	no	—
356	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
357	Dic₁₃	—	2	2	no	—
358	Dic₁₃	—	2	2	no	—
359	Dic₁₃	—	2	1	no	—
360	Dic₁₃	—	2	1	no	—
361	Dic₁₃	—	2	1	no	—
362	Dic₁₃	—	2	2	no	—
363	Dic₁₃	—	2	1	no	—
364	Dic₁₃	—	2	1	no	—
365	C₂×#41	—	13	1	no	—
366	C₂×#41	—	13	1	no	—
367	C₂×#41	—	13	2	no	—
368	C₂×#41	—	13	1	no	—
369	C₂×#41	C₂×D₁₃	1	2	yes	complemented
370	C₂²×Q₈	—	13	1	no	—
371	C₂²×D₄	—	13	1	no	—
372	C₂²×D₄	—	13	2	no	—
373	C₂³×C₄	—	13	1	no	—
374	C₄⋊Q₈	—	13	1	no	—
375	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
376	#126	—	13	2	no	—
377	#126	—	13	2	no	—
378	#125	—	13	2	no	—
379	#125	—	13	2	no	—
380	#124	—	13	2	no	—
381	#124	—	13	1	no	—
382	#124	—	13	2	no	—
383	#124	—	13	2	no	—
384	#124	—	13	2	no	—
385	#124	—	13	1	no	—
386	#123	—	13	2	no	—
387	#123	—	13	2	no	—
388	#123	—	13	1	no	—
389	#123	—	13	2	no	—
390	#123	—	13	2	no	—
391	#123	—	13	1	no	—
392	#123	—	13	2	no	—
393	#123	—	13	2	no	—
394	#123	C₂×D₁₃	1	2	yes	complemented
395	#123	C₂×D₁₃	1	2	yes	complemented
396	C₂²⋊Q₈	—	13	2	no	—
397	C₂²⋊Q₈	—	13	2	no	—
398	C₂²⋊Q₈	—	13	2	no	—
399	C₂²⋊Q₈	—	13	2	no	—
400	C₂²⋊Q₈	—	13	1	no	—
401	C₂²⋊Q₈	—	13	2	no	—
402	C₂²⋊Q₈	—	13	1	no	—
403	C₂²⋊Q₈	—	13	1	no	—
404	C₂²⋊Q₈	—	13	2	no	—
405	C₂²⋊Q₈	—	13	1	no	—
406	C₂²⋊Q₈	—	13	1	no	—
407	C₂²⋊Q₈	—	13	2	no	—
408	C₂²⋊Q₈	—	13	1	no	—
409	C₂²⋊Q₈	—	13	2	no	—
410	C₂²⋊Q₈	—	13	1	no	—
411	C₂²⋊Q₈	—	13	2	no	—
412	C₂²⋊Q₈	—	13	2	no	—
413	C₂²⋊Q₈	—	13	2	no	—
414	C₂²⋊Q₈	—	13	1	no	—
415	C₂²⋊Q₈	—	13	2	no	—
416	C₂²⋊Q₈	—	13	2	no	—
417	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
418	#121	—	13	2	no	—
419	#121	—	13	1	no	—
420	#121	—	13	1	no	—
421	#121	—	13	2	no	—
422	#121	—	13	2	no	—
423	#121	—	13	2	no	—
424	#121	—	13	2	no	—
425	#121	—	13	2	no	—
426	#121	—	13	1	no	—
427	#121	—	13	2	no	—
428	#121	—	13	2	no	—
429	#121	—	13	2	no	—
430	#121	—	13	1	no	—
431	#121	—	13	1	no	—
432	#121	—	13	2	no	—
433	#121	—	13	2	no	—
434	#121	—	13	1	no	—
435	#121	—	13	2	no	—
436	#121	C₂×D₁₃	1	1	yes	characteristic
437	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
438	#120	—	13	1	no	—
439	#120	—	13	2	no	—
440	#120	—	13	1	no	—
441	#120	—	13	2	no	—
442	C₄×Q₈	—	13	1	no	—
443	C₄×Q₈	—	13	1	no	—
444	C₄×D₄	—	13	2	no	—
445	C₄×D₄	—	13	1	no	—
446	C₄×D₄	—	13	1	no	—
447	C₄×D₄	—	13	2	no	—
448	C₄×D₄	—	13	2	no	—
449	C₄×D₄	—	13	1	no	—
450	C₄×D₄	—	13	2	no	—
451	C₄×D₄	—	13	1	no	—
452	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
453	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
454	#117	—	13	1	no	—
455	C₂×C₄⋊C₄	—	13	2	no	—
456	C₂×C₄⋊C₄	—	13	1	no	—
457	C₂×C₄⋊C₄	—	13	1	no	—
458	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
459	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
460	C₂×C₂²⋊C₄	—	13	2	no	—
461	C₂×C₂²⋊C₄	—	13	2	no	—
462	C₂×C₂²⋊C₄	—	13	2	no	—
463	C₂×C₂²⋊C₄	—	13	2	no	—
464	C₂×C₁₃	—	2	2	no	—
465	C₂×C₁₃	—	4	2	no	—
466	C₂×C₁₃	—	4	1	no	—
467	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
468	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
469	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
470	D₁₃	—	2	2	no	—
471	D₁₃	—	4	1	no	—
472	D₁₃	—	4	1	no	—
473	D₁₃	—	4	2	no	—
474	C₂⁴	—	13	1	no	—
475	C₂⁴	—	13	2	no	—
476	#41	—	4	4	no	—
477	#41	—	52	2	no	—
478	#41	—	52	4	no	—
479	#41	—	52	2	no	—
480	#41	—	52	2	no	—
481	C₂×Q₈	—	13	1	no	—
482	C₂×Q₈	—	13	1	no	—
483	C₂×Q₈	—	13	1	no	—
484	C₂×Q₈	—	13	2	no	—
485	C₂×Q₈	—	13	2	no	—
486	C₂×Q₈	—	52	2	no	—
487	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
488	C₂×D₄	—	13	1	no	—
489	C₂×D₄	—	13	1	no	—
490	C₂×D₄	—	13	2	no	—
491	C₂×D₄	—	13	1	no	—
492	C₂×D₄	—	13	2	no	—
493	C₂×D₄	—	13	2	no	—
494	C₂×D₄	—	13	1	no	—
495	C₂×D₄	—	13	2	no	—
496	C₂×D₄	—	13	2	no	—
497	C₂×D₄	—	13	1	no	—
498	C₂×D₄	—	13	1	no	—
499	C₂×D₄	—	13	2	no	—
500	C₂×D₄	—	13	1	no	—
501	C₂×D₄	—	13	2	no	—
502	C₂×D₄	—	52	2	no	—
503	C₂×D₄	—	52	4	no	—
504	C₂×D₄	C₂²×D₁₃	1	2	yes	—
505	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
506	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
507	C₂×D₄	C₂²×D₁₃	1	2	yes	—
508	C₂²×C₄	—	13	2	no	—
509	C₂²×C₄	—	13	2	no	—
510	C₂²×C₄	—	13	1	no	—
511	C₂²×C₄	—	13	1	no	—
512	C₂²×C₄	—	13	1	no	—
513	C₂²×C₄	—	13	1	no	—
514	C₂²×C₄	—	13	1	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	1	no	—
520	C₂²×C₄	—	52	2	no	—
521	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
522	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
523	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
524	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
525	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
526	C₄⋊C₄	—	13	1	no	—
527	C₄⋊C₄	—	13	2	no	—
528	C₄⋊C₄	—	13	2	no	—
529	C₄⋊C₄	—	13	2	no	—
530	C₄⋊C₄	—	13	2	no	—
531	C₄⋊C₄	—	13	2	no	—
532	C₄⋊C₄	—	13	2	no	—
533	C₄⋊C₄	—	13	1	no	—
534	C₄⋊C₄	—	13	1	no	—
535	C₄⋊C₄	—	13	2	no	—
536	C₄⋊C₄	—	13	2	no	—
537	C₄⋊C₄	—	13	1	no	—
538	C₄⋊C₄	—	13	1	no	—
539	C₄⋊C₄	—	13	1	no	—
540	C₄⋊C₄	—	13	2	no	—
541	C₄⋊C₄	—	13	2	no	—
542	C₄⋊C₄	—	13	2	no	—
543	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
544	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
545	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
546	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
547	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
548	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
549	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
550	C₂²⋊C₄	—	13	2	no	—
551	C₂²⋊C₄	—	13	2	no	—
552	C₂²⋊C₄	—	13	1	no	—
553	C₂²⋊C₄	—	13	2	no	—
554	C₂²⋊C₄	—	13	1	no	—
555	C₂²⋊C₄	—	13	2	no	—
556	C₂²⋊C₄	—	13	2	no	—
557	C₂²⋊C₄	—	13	2	no	—
558	C₂²⋊C₄	—	13	1	no	—
559	C₂²⋊C₄	—	13	1	no	—
560	C₂²⋊C₄	—	13	2	no	—
561	C₂²⋊C₄	—	13	2	no	—
562	C₂²⋊C₄	—	13	2	no	—
563	C₂²⋊C₄	—	13	2	no	—
564	C₂²⋊C₄	—	13	2	no	—
565	C₂²⋊C₄	—	13	2	no	—
566	C₂²⋊C₄	—	13	1	no	—
567	C₂²⋊C₄	—	13	1	no	—
568	C₂²⋊C₄	—	13	2	no	—
569	C₂²⋊C₄	—	13	2	no	—
570	C₂²⋊C₄	—	13	1	no	—
571	C₂²⋊C₄	—	13	2	no	—
572	C₂²⋊C₄	—	13	1	no	—
573	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
574	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
575	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
576	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
577	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
578	C₄²	—	13	1	no	—
579	C₄²	—	13	2	no	—
580	C₄²	—	13	2	no	—
581	C₄²	C₂²×D₁₃	1	1	yes	characteristic
582	C₁₃	#3536	1	1	yes	characteristic, complemented, Sylow
583	C₂³	—	13	1	no	—
584	C₂³	—	13	2	no	—
585	C₂³	—	13	1	no	—
586	C₂³	—	13	1	no	—
587	C₂³	—	26	2	no	—
588	C₂³	—	26	4	no	—
589	C₂³	—	26	2	no	—
590	C₂³	—	52	1	no	—
591	C₂³	—	52	2	no	—
592	C₂³	—	52	2	no	—
593	C₂³	C₂³×D₁₃	1	2	yes	—
594	C₂³	C₂³×D₁₃	1	1	yes	characteristic
595	C₂³	C₂³×D₁₃	1	1	yes	characteristic
596	Q₈	—	4	2	no	—
597	Q₈	—	26	2	no	—
598	Q₈	—	26	2	no	—
599	Q₈	—	52	2	no	—
600	Q₈	—	52	2	no	—
601	Q₈	—	52	1	no	—
602	D₄	—	2	4	no	—
603	D₄	—	2	2	no	—
604	D₄	—	2	2	no	—
605	D₄	—	4	2	no	—
606	D₄	—	26	2	no	—
607	D₄	—	26	2	no	—
608	D₄	—	26	4	no	—
609	D₄	—	26	2	no	—
610	D₄	—	26	2	no	—
611	D₄	—	52	2	no	—
612	D₄	—	52	2	no	—
613	D₄	—	52	1	no	—
614	D₄	—	52	2	no	—
615	D₄	—	52	2	no	—
616	D₄	—	52	1	no	—
617	D₄	—	52	1	no	—
618	D₄	—	52	2	no	—
619	D₄	—	52	2	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	4	2	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	—	13	1	no	—
626	C₂×C₄	—	13	1	no	—
627	C₂×C₄	—	13	2	no	—
628	C₂×C₄	—	13	2	no	—
629	C₂×C₄	—	13	2	no	—
630	C₂×C₄	—	13	1	no	—
631	C₂×C₄	—	13	1	no	—
632	C₂×C₄	—	13	1	no	—
633	C₂×C₄	—	26	2	no	—
634	C₂×C₄	—	26	2	no	—
635	C₂×C₄	—	26	2	no	—
636	C₂×C₄	—	52	1	no	—
637	C₂×C₄	—	52	1	no	—
638	C₂×C₄	—	52	2	no	—
639	C₂×C₄	—	52	2	no	—
640	C₂×C₄	—	52	2	no	—
641	C₂×C₄	—	52	2	no	—
642	C₂×C₄	—	52	1	no	—
643	C₂×C₄	—	52	2	no	—
644	C₂×C₄	—	52	2	no	—
645	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
646	C₂×C₄	C₂³×D₁₃	1	2	yes	—
647	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
648	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
649	C₂×C₄	C₂³×D₁₃	1	2	yes	—
650	C₂×C₄	C₂³×D₁₃	1	2	yes	—
651	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
652	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
653	C₂²	—	2	1	no	—
654	C₂²	—	2	1	no	—
655	C₂²	—	2	1	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	1	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	1	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	13	2	no	—
662	C₂²	—	26	1	no	—
663	C₂²	—	26	1	no	—
664	C₂²	—	26	1	no	—
665	C₂²	—	26	2	no	—
666	C₂²	—	26	1	no	—
667	C₂²	—	26	1	no	—
668	C₂²	—	26	1	no	—
669	C₂²	—	26	2	no	—
670	C₂²	—	26	1	no	—
671	C₂²	—	26	1	no	—
672	C₂²	—	26	2	no	—
673	C₂²	—	52	4	no	—
674	C₂²	—	104	4	no	—
675	C₂²	#88251	1	2	yes	—
676	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
677	C₄	—	2	2	no	—
678	C₄	—	2	2	no	—
679	C₄	—	2	1	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	1	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	26	2	no	—
685	C₄	—	26	1	no	—
686	C₄	—	26	1	no	—
687	C₄	—	26	1	no	—
688	C₄	—	26	1	no	—
689	C₄	—	26	2	no	—
690	C₄	—	26	2	no	—
691	C₄	—	26	1	no	—
692	C₄	#88256	1	2	yes	—
693	C₂	—	2	2	no	—
694	C₂	—	4	2	no	—
695	C₂	—	4	1	no	—
696	C₂	—	26	2	no	—
697	C₂	—	52	1	no	—
698	C₂	—	52	2	no	—
699	C₂	—	52	1	no	—
700	C₂	C₂×#88251	1	1	yes	characteristic
701	C₂	C₂×#88256	1	1	yes	characteristic
702	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	#3536
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. #11719538	C₂	semidirect
3. #11719534	C₂	semidirect
4. #11719438	C₂	semidirect
5. #11719435	C₂	semidirect
6. #11719372	C₂	semidirect
7. #11719370	C₂	semidirect
8. #11719362	C₂	semidirect
9. #11719359	C₂	semidirect
10. #11719352	C₂	semidirect
11. #11719339	C₂	semidirect
12. #11719317	C₂	semidirect
13. #11719313	C₂	semidirect
14. D₁₃×#121	C₂	semidirect
15. #11719303	C₂	semidirect
16. #11719266	C₂	semidirect
17. #11719259	C₂	semidirect
18. #11719257	C₂	semidirect
19. #11719252	C₂	semidirect
20. #11719216	C₂	semidirect
21. #11719215	C₂	semidirect
22. C₂×#88151	C₂	semidirect
23. #11719212	C₂	semidirect
24. C₂×C₁₃×#41	C₂²	semidirect
25. C₂×#6129	C₂²	semidirect
28. C₂×#6127	C₂²	semidirect
29. C₂×#6127	C₂²	semidirect
30. C₂×#6127	C₂²	semidirect
32. C₂²×Dic₂₆	C₂²	semidirect
33. C₁₃×C₄⋊Q₈	C₂²	semidirect
34. C₁₃×#123	C₂²	semidirect
35. C₁₃×#123	C₂²	semidirect
36. C₁₃×C₂²⋊Q₈	C₂²	semidirect
38. C₁₃×#121	C₂²	semidirect
39. C₄×D₄×C₁₃	C₂²	semidirect
40. C₄×D₄×C₁₃	C₂²	semidirect
41. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
42. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
43. #88201	C₂²	semidirect
45. #88200	C₂²	semidirect
46. #88200	C₂²	semidirect
48. #88193	C₂²	semidirect
49. #88193	C₂²	semidirect
50. #88193	C₂²	semidirect
51. #88193	C₂²	semidirect
53. #88192	C₂²	semidirect
54. #88192	C₂²	semidirect
57. #88190	C₂²	semidirect
58. D₄×Dic₁₃	C₂²	semidirect
60. #88184	C₂²	semidirect
61. #88184	C₂²	semidirect
62. #88184	C₂²	semidirect
63. #88183	C₂²	semidirect
64. #88183	C₂²	semidirect
67. C₄×C₂²⋊D₁₃	C₂²	semidirect
70. C₂×C₄⋊Dic₁₃	C₂²	semidirect
71. #88178	C₂²	semidirect
72. #88178	C₂²	semidirect
73. #88178	C₂²	semidirect
74. #88152	C₂²	semidirect
78. #88151	C₂²	semidirect
79. #88151	C₂²	semidirect
80. #88151	C₂²	semidirect
81. #88151	C₂²	semidirect
82. #88151	C₂²	semidirect
85. #88150	C₂²	semidirect
86. #88150	C₂²	semidirect
88. #88149	C₂²	semidirect
89. #88149	C₂²	semidirect
90. #88148	C₂²	semidirect
91. #88148	C₂²	semidirect
92. #88148	C₂²	semidirect
94. #88147	C₂²	semidirect
96. C₄⋊C₄×D₁₃	C₂²	semidirect
97. #88144	C₂²	semidirect
98. #88143	C₂²	semidirect
99. #88142	C₂²	semidirect
100. #88141	C₂²	semidirect
101. #88140	C₂²	semidirect
102. #88139	C₂²	semidirect
103. #88139	C₂²	semidirect
104. #88139	C₂²	semidirect
107. #88138	C₂²	semidirect
108. #88137	C₂²	semidirect
109. #88137	C₂²	semidirect
112. #88135	C₂²	semidirect
115. #88133	C₂²	semidirect
116. #88132	C₂²	semidirect
117. #88132	C₂²	semidirect
118. #88132	C₂²	semidirect
119. #88129	C₂²	semidirect
121. #88126	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
309. #547	D₁₃	semidirect
369. C₂×#41	C₂×D₁₃	semidirect
375. C₄⋊Q₈	C₂×D₁₃	semidirect
394. #123	C₂×D₁₃	semidirect
395. #123	C₂×D₁₃	semidirect
417. C₂²⋊Q₈	C₂×D₁₃	semidirect
437. #121	C₂×D₁₃	semidirect
452. C₄×D₄	C₂×D₁₃	semidirect
453. C₄×D₄	C₂×D₁₃	semidirect
458. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
459. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
582. C₁₃	#3536	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
#11719538	2
#11719534	2
#11719438	2
#11719435	2
#11719372	2
#11719370	2
#11719362	2
#11719359	2
#11719352	2
#11719339	2
#11719317	2
#11719313	2
D₁₃×#121	2
#11719303	2
#11719266	2
#11719259	2
#11719257	2
#11719252	2
#11719216	2
#11719215	2
C₂×#88151	2
#11719212	2
#3536	13