Subgroups — #13128550

Order 1664.

1040 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719439	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719434	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719414	C₂	1	2	yes	maximal, complemented
5	#11719413	C₂	1	2	yes	maximal, complemented
6	#11719411	C₂	1	2	yes	maximal, complemented
7	#11719409	C₂	1	2	yes	maximal, complemented
8	#11719383	C₂	1	2	yes	maximal, complemented
9	#11719375	C₂	1	2	yes	maximal, complemented
10	#11719347	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719346	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719334	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719332	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719286	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719285	C₂	1	2	yes	maximal, complemented
16	#11719279	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719273	C₂	1	2	yes	maximal, complemented
18	#11719270	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719252	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719237	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719235	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719228	C₂	1	1	yes	maximal, characteristic, complemented
23	D₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#6131	C₂²	1	1	yes	characteristic
25	C₂×#6127	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#126	C₂²	1	2	yes	—
29	C₁₃×#126	C₂²	1	2	yes	complemented
30	C₁₃×#124	C₂²	1	2	yes	—
31	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
33	C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
34	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
35	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#117	C₂²	1	1	yes	characteristic
37	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
38	#88201	C₂²	1	2	yes	—
39	#88201	C₂²	1	2	yes	complemented
40	#88200	C₂²	1	2	yes	—
41	#88200	C₂²	1	1	yes	characteristic
42	#88200	C₂²	1	1	yes	characteristic, complemented
43	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
44	#88198	C₂²	1	2	yes	complemented
45	#88193	C₂²	1	1	yes	characteristic
46	#88193	C₂²	1	2	yes	—
47	#88191	C₂²	1	1	yes	characteristic
48	#88184	C₂²	1	1	yes	characteristic
49	#88184	C₂²	1	1	yes	characteristic, complemented
50	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
51	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
52	#88180	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
54	#88152	C₂²	1	2	yes	—
55	#88152	C₂²	1	2	yes	complemented
56	#88152	C₂²	1	2	yes	complemented
57	#88150	C₂²	1	2	yes	—
58	#88150	C₂²	1	1	yes	characteristic
59	#88150	C₂²	1	2	yes	complemented
60	#88149	C₂²	1	1	yes	characteristic
61	#88149	C₂²	1	2	yes	—
62	#88149	C₂²	1	2	yes	—
63	#88149	C₂²	1	1	yes	characteristic, complemented
64	#88148	C₂²	1	1	yes	characteristic
65	#88148	C₂²	1	2	yes	—
66	#88148	C₂²	1	2	yes	—
67	#88147	C₂²	1	2	yes	—
68	#88147	C₂²	1	2	yes	—
69	#88147	C₂²	1	1	yes	characteristic, complemented
70	#88146	C₂²	1	1	yes	characteristic
71	#88146	C₂²	1	1	yes	characteristic
72	#88146	C₂²	1	1	yes	characteristic
73	#88146	C₂²	1	1	yes	characteristic, complemented
74	#88146	C₂²	1	2	yes	complemented
75	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
76	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
77	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
78	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
79	#88144	C₂²	1	1	yes	characteristic, complemented
80	#88144	C₂²	1	2	yes	complemented
81	#88143	C₂²	1	2	yes	complemented
82	#88143	C₂²	1	2	yes	complemented
83	#88142	C₂²	1	1	yes	characteristic, complemented
84	#88141	C₂²	1	2	yes	complemented
85	#88140	C₂²	1	2	yes	—
86	#88139	C₂²	1	2	yes	—
87	#88139	C₂²	1	2	yes	complemented
88	#88138	C₂²	1	2	yes	—
89	#88138	C₂²	1	2	yes	—
90	#88138	C₂²	1	1	yes	characteristic
91	#88138	C₂²	1	2	yes	—
92	#88138	C₂²	1	2	yes	complemented
93	#88137	C₂²	1	2	yes	—
94	#88137	C₂²	1	1	yes	characteristic
95	#88137	C₂²	1	2	yes	—
96	#88136	C₂²	1	1	yes	characteristic
97	#88136	C₂²	1	2	yes	—
98	#88135	C₂²	1	2	yes	—
99	#88135	C₂²	1	2	yes	—
100	#88135	C₂²	1	2	yes	complemented
101	#88135	C₂²	1	2	yes	complemented
102	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
103	#88133	C₂²	1	2	yes	—
104	#88132	C₂²	1	1	yes	characteristic
105	#88131	C₂²	1	2	yes	—
106	#88131	C₂²	1	2	yes	complemented
107	#88130	C₂²	1	2	yes	—
108	#88130	C₂²	1	2	yes	complemented
109	#88129	C₂²	1	2	yes	—
110	C₄×D₅₂	C₂²	1	1	yes	characteristic
111	C₄×D₅₂	C₂²	1	2	yes	—
112	C₄×D₅₂	C₂²	1	2	yes	—
113	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
114	C₄×D₅₂	C₂²	1	2	yes	complemented
115	#88126	C₂²	1	1	yes	characteristic
116	#88126	C₂²	1	2	yes	—
117	#88126	C₂²	1	2	yes	complemented
118	#88126	C₂²	1	2	yes	complemented
119	#88126	C₂²	1	2	yes	complemented
120	C₄²×D₁₃	C₂²	1	2	yes	—
121	#88124	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₆	C₂²	1	2	yes	complemented
123	C₂³×D₁₃	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
126	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
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	—
133	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
135	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
136	C₂²×Dic₁₃	C₂³	1	2	yes	—
137	#6131	—	2	4	no	—
138	#6127	—	2	4	no	—
139	C₂×D₅₂	C₂³	1	1	yes	characteristic
140	C₂×D₅₂	C₂³	1	2	yes	—
141	C₂×D₅₂	C₂³	1	1	yes	characteristic
142	C₂×D₅₂	C₂³	1	1	yes	characteristic
143	C₂×D₅₂	C₂³	1	2	yes	—
144	C₂×D₅₂	C₂³	1	2	yes	—
145	C₂×C₄×D₁₃	—	2	4	no	—
146	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₃	C₂³	1	2	yes	—
149	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₃	C₂³	1	2	yes	—
152	C₂×C₄×D₁₃	C₂³	1	2	yes	—
153	C₂×C₄×D₁₃	C₂³	1	2	yes	—
154	C₂×C₄×D₁₃	C₂³	1	2	yes	—
155	C₂×C₄×D₁₃	C₂³	1	2	yes	—
156	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
157	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
158	C₂×Dic₂₆	C₂³	1	2	yes	—
159	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₄²×C₁₃	C₂³	1	2	yes	—
174	C₄²×C₁₃	C₂³	1	1	yes	characteristic
175	C₄²×C₁₃	C₂³	1	2	yes	—
176	C₄²×C₁₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
180	#6103	C₂³	1	1	yes	characteristic
181	#6103	C₂³	1	2	yes	—
182	#6103	C₂³	1	2	yes	—
183	#6103	C₂³	1	1	yes	characteristic
184	#6103	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
191	#6103	C₂³	1	2	yes	—
192	#6103	C₂³	1	2	yes	—
193	#6103	C₂³	1	1	yes	characteristic
194	#6103	C₂³	1	2	yes	—
195	#6103	C₂³	1	1	yes	characteristic
196	#6103	C₂³	1	2	yes	—
197	#6103	C₂³	1	2	yes	—
198	C₄⋊Dic₁₃	C₂³	1	2	yes	—
199	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₁₃	C₂³	1	2	yes	—
203	C₄⋊Dic₁₃	C₂³	1	2	yes	—
204	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
205	#6101	C₂³	1	2	yes	—
206	#6101	C₂³	1	2	yes	—
207	#6101	C₂³	1	2	yes	—
208	#6101	C₂³	1	2	yes	—
209	#6101	C₂³	1	1	yes	characteristic
210	#6101	C₂³	1	2	yes	—
211	#6101	C₂³	1	1	yes	characteristic
212	#6101	C₂³	1	1	yes	characteristic
213	#6101	C₂³	1	2	yes	—
214	#6101	C₂³	1	2	yes	—
215	#6101	C₂³	1	2	yes	—
216	#6101	C₂³	1	1	yes	characteristic
217	#6101	C₂³	1	2	yes	—
218	C₄×Dic₁₃	C₂³	1	2	yes	—
219	C₄×Dic₁₃	C₂³	1	2	yes	—
220	C₄×Dic₁₃	C₂³	1	2	yes	—
221	C₄×Dic₁₃	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	#3493	—	13	1	no	maximal, Sylow
226	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₂²×D₁₃	—	2	2	no	—
229	C₂²×D₁₃	—	4	1	no	—
230	C₂²×D₁₃	—	4	1	no	—
231	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
236	Q₈×C₁₃	—	4	2	no	—
237	D₄×C₁₃	—	4	1	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
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	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂²⋊D₁₃	—	2	2	no	—
250	C₂²⋊D₁₃	—	2	2	no	—
251	C₂²⋊D₁₃	—	4	1	no	—
252	C₂²⋊D₁₃	—	4	2	no	—
253	C₂²⋊D₁₃	—	4	1	no	—
254	C₂²⋊D₁₃	—	4	2	no	—
255	C₂×Dic₁₃	—	2	2	no	—
256	C₂×Dic₁₃	—	4	2	no	—
257	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₃	C₂⁴	1	2	yes	—
259	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₃	C₂⁴	1	2	yes	—
262	C₂×Dic₁₃	C₂⁴	1	2	yes	—
263	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
265	D₅₂	—	2	2	no	—
266	D₅₂	—	2	4	no	—
267	D₅₂	—	2	2	no	—
268	D₅₂	—	4	2	no	—
269	D₅₂	—	4	1	no	—
270	D₅₂	—	4	2	no	—
271	C₄×D₁₃	—	2	2	no	—
272	C₄×D₁₃	—	2	2	no	—
273	C₄×D₁₃	—	2	2	no	—
274	C₄×D₁₃	—	2	2	no	—
275	C₄×D₁₃	—	2	4	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	C₄×D₁₃	#41	1	4	yes	—
282	Dic₂₆	—	2	2	no	—
283	Dic₂₆	—	4	2	no	—
284	#556	—	13	1	no	—
285	#556	—	13	2	no	—
286	#556	D₁₃	1	1	yes	characteristic, complemented
287	#555	—	13	1	no	—
288	#555	—	13	2	no	—
289	#555	—	13	1	no	—
290	#553	—	13	2	no	—
291	#553	—	13	1	no	—
292	#553	—	13	1	no	—
293	#552	—	13	2	no	—
294	#552	—	13	1	no	—
295	#552	—	13	1	no	—
296	#544	—	13	1	no	—
297	#538	—	13	2	no	—
298	#538	—	13	2	no	—
299	#537	—	13	1	no	—
300	#529	—	13	2	no	—
301	#529	—	13	2	no	—
302	#525	—	13	1	no	—
303	#525	—	13	1	no	—
304	#520	—	13	1	no	—
305	#520	—	13	1	no	—
306	C₂×#117	—	13	1	no	—
307	C₂²×C₁₃	—	2	1	no	—
308	C₂²×C₁₃	—	2	1	no	—
309	C₂²×C₁₃	—	2	1	no	—
310	C₂²×C₁₃	—	2	1	no	—
311	C₂²×C₁₃	—	2	1	no	—
312	C₂²×C₁₃	—	2	1	no	—
313	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
314	C₂×D₁₃	—	2	1	no	—
315	C₂×D₁₃	—	2	1	no	—
316	C₂×D₁₃	—	2	1	no	—
317	C₂×D₁₃	—	2	2	no	—
318	C₂×D₁₃	—	2	1	no	—
319	C₂×D₁₃	—	2	1	no	—
320	C₂×D₁₃	—	2	2	no	—
321	C₂×D₁₃	—	2	2	no	—
322	C₂×D₁₃	—	2	1	no	—
323	C₂×D₁₃	—	2	1	no	—
324	C₂×D₁₃	—	2	1	no	—
325	C₂×D₁₃	—	4	4	no	—
326	C₂×D₁₃	C₂×#41	1	2	yes	—
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	1	no	—
329	C₄×C₁₃	—	2	2	no	—
330	C₄×C₁₃	—	2	2	no	—
331	C₄×C₁₃	—	2	2	no	—
332	C₄×C₁₃	—	2	1	no	—
333	C₄×C₁₃	—	2	2	no	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	C₂×#41	1	2	yes	—
336	Dic₁₃	—	2	1	no	—
337	Dic₁₃	—	2	1	no	—
338	Dic₁₃	—	2	1	no	—
339	Dic₁₃	—	2	2	no	—
340	Dic₁₃	—	2	2	no	—
341	Dic₁₃	—	2	1	no	—
342	Dic₁₃	—	2	2	no	—
343	Dic₁₃	C₂×#41	1	2	yes	—
344	C₂×#41	—	13	1	no	—
345	C₂×#41	—	13	1	no	—
346	C₂³×C₄	—	13	1	no	—
347	C₄⋊Q₈	—	13	2	no	—
348	C₄⋊Q₈	—	13	1	no	—
349	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
350	#126	—	13	2	no	—
351	#126	—	13	2	no	—
352	#126	—	13	2	no	—
353	#126	—	13	2	no	—
354	#126	—	13	2	no	—
355	#126	—	13	2	no	—
356	#126	C₂×D₁₃	1	2	yes	—
357	#126	C₂×D₁₃	1	2	yes	complemented
358	#125	—	13	2	no	—
359	#125	—	13	2	no	—
360	#125	—	13	2	no	—
361	#125	—	13	1	no	—
362	#125	—	13	1	no	—
363	#124	—	13	2	no	—
364	#124	—	13	2	no	—
365	#124	—	13	2	no	—
366	#124	—	13	2	no	—
367	#124	—	13	2	no	—
368	#124	C₂×D₁₃	1	2	yes	—
369	#123	—	13	2	no	—
370	#123	—	13	1	no	—
371	#123	—	13	2	no	—
372	#123	—	13	1	no	—
373	#123	—	13	2	no	—
374	#123	—	13	2	no	—
375	#123	—	13	2	no	—
376	C₂²⋊Q₈	—	13	1	no	—
377	C₂²⋊Q₈	—	13	2	no	—
378	C₂²⋊Q₈	—	13	1	no	—
379	C₂²⋊Q₈	—	13	1	no	—
380	C₂²⋊Q₈	—	13	2	no	—
381	C₂²⋊Q₈	—	13	2	no	—
382	C₂²⋊Q₈	—	13	1	no	—
383	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
384	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
385	#121	—	13	1	no	—
386	#121	—	13	2	no	—
387	#121	—	13	1	no	—
388	#121	—	13	1	no	—
389	#121	—	13	1	no	—
390	#121	—	13	2	no	—
391	#121	—	13	1	no	—
392	#121	—	13	2	no	—
393	#121	—	13	1	no	—
394	#121	—	13	2	no	—
395	#121	—	13	2	no	—
396	#121	—	13	2	no	—
397	#121	—	13	2	no	—
398	#120	—	13	1	no	—
399	#120	—	13	2	no	—
400	#120	—	13	1	no	—
401	C₄×Q₈	—	13	1	no	—
402	C₄×Q₈	—	13	2	no	—
403	C₄×Q₈	—	13	2	no	—
404	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
405	C₄×Q₈	C₂×D₁₃	1	2	yes	complemented
406	C₄×D₄	—	13	1	no	—
407	C₄×D₄	—	13	1	no	—
408	C₄×D₄	—	13	2	no	—
409	C₄×D₄	—	13	1	no	—
410	C₄×D₄	—	13	2	no	—
411	C₄×D₄	—	13	2	no	—
412	C₄×D₄	—	13	2	no	—
413	C₄×D₄	—	13	2	no	—
414	C₄×D₄	—	13	2	no	—
415	C₄×D₄	—	13	2	no	—
416	C₄×D₄	—	13	2	no	—
417	C₄×D₄	—	13	1	no	—
418	C₄×D₄	—	13	1	no	—
419	C₄×D₄	—	13	2	no	—
420	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
421	#117	—	13	1	no	—
422	#117	—	13	1	no	—
423	#117	—	13	1	no	—
424	#117	—	13	1	no	—
425	#117	—	13	1	no	—
426	#117	—	13	2	no	—
427	#117	—	13	2	no	—
428	#117	—	13	2	no	—
429	#117	—	13	2	no	—
430	#117	—	13	1	no	—
431	#117	—	13	2	no	—
432	#117	—	13	2	no	—
433	#117	—	13	2	no	—
434	#117	C₂×D₁₃	1	1	yes	characteristic
435	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
436	C₂×C₄⋊C₄	—	13	1	no	—
437	C₂×C₄⋊C₄	—	13	1	no	—
438	C₂×C₄⋊C₄	—	13	1	no	—
439	C₂×C₄⋊C₄	—	13	2	no	—
440	C₂×C₄⋊C₄	—	13	1	no	—
441	C₂×C₂²⋊C₄	—	13	2	no	—
442	C₂×C₄²	—	13	2	no	—
443	C₂×C₁₃	—	4	1	no	—
444	C₂×C₁₃	—	4	1	no	—
445	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
446	C₂×C₁₃	#585	1	1	yes	characteristic
447	C₂×C₁₃	#585	1	1	yes	characteristic
448	D₁₃	—	2	2	no	—
449	D₁₃	—	4	2	no	—
450	D₁₃	—	4	1	no	—
451	D₁₃	—	4	1	no	—
452	C₂⁴	—	13	1	no	—
453	#41	—	26	4	no	—
454	#41	—	26	4	no	—
455	C₂×Q₈	—	13	1	no	—
456	C₂×Q₈	—	13	2	no	—
457	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
458	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
459	C₂×D₄	—	13	1	no	—
460	C₂×D₄	—	13	1	no	—
461	C₂×D₄	—	13	1	no	—
462	C₂×D₄	—	13	2	no	—
463	C₂×D₄	—	13	1	no	—
464	C₂×D₄	—	13	2	no	—
465	C₂×D₄	—	13	2	no	—
466	C₂×D₄	—	13	1	no	—
467	C₂×D₄	—	13	1	no	—
468	C₂×D₄	—	13	1	no	—
469	C₂×D₄	—	13	2	no	—
470	C₂×D₄	—	13	2	no	—
471	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
472	C₂²×C₄	—	13	1	no	—
473	C₂²×C₄	—	13	1	no	—
474	C₂²×C₄	—	13	2	no	—
475	C₂²×C₄	—	13	1	no	—
476	C₂²×C₄	—	13	2	no	—
477	C₂²×C₄	—	13	1	no	—
478	C₂²×C₄	—	13	1	no	—
479	C₂²×C₄	—	13	1	no	—
480	C₂²×C₄	—	13	2	no	—
481	C₂²×C₄	—	13	2	no	—
482	C₂²×C₄	—	13	2	no	—
483	C₂²×C₄	—	13	2	no	—
484	C₂²×C₄	—	13	2	no	—
485	C₂²×C₄	—	26	4	no	—
486	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
487	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
488	C₄⋊C₄	—	13	2	no	—
489	C₄⋊C₄	—	13	1	no	—
490	C₄⋊C₄	—	13	1	no	—
491	C₄⋊C₄	—	13	1	no	—
492	C₄⋊C₄	—	13	2	no	—
493	C₄⋊C₄	—	13	1	no	—
494	C₄⋊C₄	—	13	2	no	—
495	C₄⋊C₄	—	13	2	no	—
496	C₄⋊C₄	—	13	2	no	—
497	C₄⋊C₄	—	13	1	no	—
498	C₄⋊C₄	—	13	2	no	—
499	C₄⋊C₄	—	13	1	no	—
500	C₄⋊C₄	—	13	1	no	—
501	C₄⋊C₄	—	13	2	no	—
502	C₄⋊C₄	—	13	2	no	—
503	C₄⋊C₄	—	13	2	no	—
504	C₄⋊C₄	—	13	1	no	—
505	C₄⋊C₄	—	13	2	no	—
506	C₄⋊C₄	—	13	2	no	—
507	C₄⋊C₄	—	13	2	no	—
508	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
511	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
512	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
513	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
514	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
516	C₂²⋊C₄	—	13	2	no	—
517	C₂²⋊C₄	—	13	1	no	—
518	C₂²⋊C₄	—	13	1	no	—
519	C₂²⋊C₄	—	13	2	no	—
520	C₂²⋊C₄	—	13	2	no	—
521	C₂²⋊C₄	—	13	2	no	—
522	C₂²⋊C₄	—	13	1	no	—
523	C₂²⋊C₄	—	13	1	no	—
524	C₂²⋊C₄	—	13	2	no	—
525	C₂²⋊C₄	—	13	1	no	—
526	C₂²⋊C₄	—	13	2	no	—
527	C₂²⋊C₄	—	13	2	no	—
528	C₂²⋊C₄	—	13	2	no	—
529	C₂²⋊C₄	—	13	2	no	—
530	C₂²⋊C₄	—	13	2	no	—
531	C₂²⋊C₄	—	13	2	no	—
532	C₂²⋊C₄	—	13	1	no	—
533	C₂²⋊C₄	—	13	2	no	—
534	C₂²⋊C₄	—	13	2	no	—
535	C₂²⋊C₄	—	13	1	no	—
536	C₂²⋊C₄	—	13	1	no	—
537	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
538	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
539	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
540	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
541	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
542	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
543	C₄²	—	13	2	no	—
544	C₄²	—	13	2	no	—
545	C₄²	—	13	2	no	—
546	C₄²	—	13	2	no	—
547	C₄²	—	13	2	no	—
548	C₄²	—	13	2	no	—
549	C₄²	—	13	1	no	—
550	C₄²	C₂²×D₁₃	1	2	yes	—
551	C₄²	C₂²×D₁₃	1	2	yes	—
552	C₄²	C₂²×D₁₃	1	2	yes	—
553	C₄²	C₂²×D₁₃	1	1	yes	characteristic
554	C₁₃	#3493	1	1	yes	characteristic, complemented, Sylow
555	C₂³	—	13	1	no	—
556	C₂³	—	13	1	no	—
557	C₂³	—	13	1	no	—
558	C₂³	—	13	2	no	—
559	C₂³	—	26	2	no	—
560	C₂³	—	52	1	no	—
561	C₂³	—	52	1	no	—
562	C₂³	C₂³×D₁₃	1	1	yes	characteristic
563	C₂³	C₂³×D₁₃	1	1	yes	characteristic
564	Q₈	—	2	2	no	—
565	Q₈	—	4	2	no	—
566	Q₈	—	26	2	no	—
567	Q₈	—	52	2	no	—
568	D₄	—	4	1	no	—
569	D₄	—	26	2	no	—
570	D₄	—	26	4	no	—
571	D₄	—	26	2	no	—
572	D₄	—	26	2	no	—
573	D₄	—	26	2	no	—
574	D₄	—	52	2	no	—
575	D₄	—	52	2	no	—
576	D₄	—	52	1	no	—
577	D₄	—	52	2	no	—
578	D₄	—	52	1	no	—
579	D₄	—	52	1	no	—
580	D₄	—	52	2	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	13	1	no	—
584	C₂×C₄	—	13	4	no	—
585	C₂×C₄	—	13	1	no	—
586	C₂×C₄	—	13	2	no	—
587	C₂×C₄	—	13	1	no	—
588	C₂×C₄	—	13	1	no	—
589	C₂×C₄	—	13	2	no	—
590	C₂×C₄	—	13	1	no	—
591	C₂×C₄	—	13	2	no	—
592	C₂×C₄	—	26	2	no	—
593	C₂×C₄	—	26	4	no	—
594	C₂×C₄	—	26	2	no	—
595	C₂×C₄	—	26	2	no	—
596	C₂×C₄	—	26	2	no	—
597	C₂×C₄	—	26	2	no	—
598	C₂×C₄	—	52	2	no	—
599	C₂×C₄	—	52	2	no	—
600	C₂×C₄	—	52	2	no	—
601	C₂×C₄	—	52	2	no	—
602	C₂×C₄	—	52	2	no	—
603	C₂×C₄	—	52	2	no	—
604	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₁₃	1	2	yes	—
606	C₂×C₄	C₂³×D₁₃	1	2	yes	—
607	C₂×C₄	C₂³×D₁₃	1	2	yes	—
608	C₂×C₄	C₂³×D₁₃	1	2	yes	—
609	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	13	2	no	—
620	C₂²	—	26	1	no	—
621	C₂²	—	26	1	no	—
622	C₂²	—	26	1	no	—
623	C₂²	—	26	2	no	—
624	C₂²	—	26	1	no	—
625	C₂²	—	26	1	no	—
626	C₂²	—	26	2	no	—
627	C₂²	—	26	1	no	—
628	C₂²	—	26	1	no	—
629	C₂²	—	26	2	no	—
630	C₂²	—	26	1	no	—
631	C₂²	—	52	4	no	—
632	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
633	C₄	—	2	1	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	2	no	—
640	C₄	—	2	1	no	—
641	C₄	—	13	2	no	—
642	C₄	—	26	1	no	—
643	C₄	—	26	1	no	—
644	C₄	—	26	2	no	—
645	C₄	—	26	1	no	—
646	C₄	—	26	2	no	—
647	C₄	—	26	1	no	—
648	C₄	—	26	2	no	—
649	C₄	#41×D₁₃	1	2	yes	—
650	C₂	—	4	1	no	—
651	C₂	—	4	1	no	—
652	C₂	—	26	2	no	—
653	C₂	—	52	1	no	—
654	C₂	—	52	2	no	—
655	C₂	—	52	1	no	—
656	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
657	C₂	#11719648	1	1	yes	characteristic
658	C₂	#11719652	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#556	C₂
hypercenter	#556	D₁₃
hypocenter	C₁₃	#3493
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. C₁₃×#556	C₂	semidirect
2. #11719439	C₂	semidirect
3. #11719434	C₂	semidirect
4. #11719414	C₂	semidirect
5. #11719413	C₂	semidirect
6. #11719411	C₂	semidirect
7. #11719409	C₂	semidirect
8. #11719383	C₂	semidirect
9. #11719375	C₂	semidirect
10. #11719347	C₂	semidirect
11. #11719346	C₂	semidirect
12. #11719334	C₂	semidirect
13. #11719332	C₂	semidirect
14. #11719286	C₂	semidirect
15. #11719285	C₂	semidirect
16. #11719279	C₂	semidirect
17. #11719273	C₂	semidirect
18. #11719270	C₂	semidirect
19. #11719252	C₂	semidirect
20. #11719237	C₂	semidirect
21. #11719235	C₂	semidirect
22. #11719228	C₂	semidirect
23. D₁₃×#117	C₂	semidirect
27. C₁₃×C₄⋊Q₈	C₂²	semidirect
29. C₁₃×#126	C₂²	semidirect
32. C₁₃×C₂²⋊Q₈	C₂²	semidirect
33. C₄×Q₈×C₁₃	C₂²	semidirect
34. C₄×Q₈×C₁₃	C₂²	semidirect
37. C₁₃×#117	C₂²	semidirect
39. #88201	C₂²	semidirect
42. #88200	C₂²	semidirect
43. Q₈×Dic₁₃	C₂²	semidirect
44. #88198	C₂²	semidirect
49. #88184	C₂²	semidirect
53. C₂×C₄⋊Dic₁₃	C₂²	semidirect
55. #88152	C₂²	semidirect
56. #88152	C₂²	semidirect
59. #88150	C₂²	semidirect
63. #88149	C₂²	semidirect
69. #88147	C₂²	semidirect
73. #88146	C₂²	semidirect
74. #88146	C₂²	semidirect
77. C₄⋊C₄×D₁₃	C₂²	semidirect
78. C₄⋊C₄×D₁₃	C₂²	semidirect
79. #88144	C₂²	semidirect
80. #88144	C₂²	semidirect
81. #88143	C₂²	semidirect
82. #88143	C₂²	semidirect
83. #88142	C₂²	semidirect
84. #88141	C₂²	semidirect
87. #88139	C₂²	semidirect
92. #88138	C₂²	semidirect
100. #88135	C₂²	semidirect
101. #88135	C₂²	semidirect
106. #88131	C₂²	semidirect
108. #88130	C₂²	semidirect
113. C₄×D₅₂	C₂²	semidirect
114. C₄×D₅₂	C₂²	semidirect
117. #88126	C₂²	semidirect
118. #88126	C₂²	semidirect
119. #88126	C₂²	semidirect
121. #88124	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
286. #556	D₁₃	semidirect
349. C₄⋊Q₈	C₂×D₁₃	semidirect
357. #126	C₂×D₁₃	semidirect
384. C₂²⋊Q₈	C₂×D₁₃	semidirect
404. C₄×Q₈	C₂×D₁₃	semidirect
405. C₄×Q₈	C₂×D₁₃	semidirect
435. #117	C₂×D₁₃	semidirect
554. C₁₃	#3493	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#556	2
#11719439	2
#11719434	2
#11719414	2
#11719413	2
#11719411	2
#11719409	2
#11719383	2
#11719375	2
#11719347	2
#11719346	2
#11719334	2
#11719332	2
#11719286	2
#11719285	2
#11719279	2
#11719273	2
#11719270	2
#11719252	2
#11719237	2
#11719235	2
#11719228	2
D₁₃×#117	2
#3493	13