Subgroups — #13128587

Order 1664.

1022 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719410	C₂	1	2	yes	maximal, complemented
3	#11719406	C₂	1	2	yes	maximal, complemented
4	#11719399	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719398	C₂	1	2	yes	maximal, complemented
6	#11719394	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719393	C₂	1	2	yes	maximal, complemented
8	#11719367	C₂	1	2	yes	maximal, complemented
9	#11719364	C₂	1	2	yes	maximal, complemented
10	#11719346	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719344	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719333	C₂	1	1	yes	maximal, characteristic, complemented
13	D₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719284	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719277	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719252	C₂	1	1	yes	maximal, characteristic
17	#11719247	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719234	C₂	1	2	yes	maximal, complemented
19	#11719234	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719233	C₂	1	2	yes	maximal, complemented
21	D₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719216	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719209	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic
25	C₂×#6127	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#126	C₂²	1	2	yes	—
28	C₁₃×#125	C₂²	1	2	yes	complemented
29	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#123	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	1	yes	characteristic, complemented
34	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#117	C₂²	1	1	yes	characteristic
36	C₁₃×#117	C₂²	1	2	yes	complemented
37	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
38	#88200	C₂²	1	1	yes	characteristic
39	#88200	C₂²	1	1	yes	characteristic, complemented
40	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
41	#88193	C₂²	1	1	yes	characteristic
42	#88191	C₂²	1	1	yes	characteristic
43	#88190	C₂²	1	2	yes	—
44	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
45	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
46	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
47	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
49	#88180	C₂²	1	1	yes	characteristic
50	#88180	C₂²	1	1	yes	characteristic, complemented
51	#88178	C₂²	1	1	yes	characteristic
52	#88178	C₂²	1	2	yes	complemented
53	#88178	C₂²	1	1	yes	characteristic, complemented
54	#88152	C₂²	1	2	yes	complemented
55	#88152	C₂²	1	2	yes	complemented
56	#88151	C₂²	1	1	yes	characteristic
57	#88151	C₂²	1	2	yes	—
58	#88151	C₂²	1	1	yes	characteristic, complemented
59	#88150	C₂²	1	2	yes	—
60	#88150	C₂²	1	2	yes	—
61	#88150	C₂²	1	1	yes	characteristic
62	#88150	C₂²	1	2	yes	—
63	#88150	C₂²	1	2	yes	—
64	#88150	C₂²	1	2	yes	complemented
65	#88148	C₂²	1	2	yes	—
66	#88148	C₂²	1	1	yes	characteristic
67	#88148	C₂²	1	2	yes	—
68	#88147	C₂²	1	2	yes	—
69	#88146	C₂²	1	1	yes	characteristic
70	#88146	C₂²	1	1	yes	characteristic
71	#88146	C₂²	1	2	yes	—
72	#88146	C₂²	1	2	yes	—
73	#88146	C₂²	1	2	yes	—
74	#88146	C₂²	1	1	yes	characteristic, 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
78	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
79	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
80	#88144	C₂²	1	1	yes	characteristic, complemented
81	#88144	C₂²	1	2	yes	complemented
82	#88143	C₂²	1	2	yes	complemented
83	#88143	C₂²	1	2	yes	complemented
84	#88143	C₂²	1	2	yes	complemented
85	#88142	C₂²	1	1	yes	characteristic, complemented
86	#88142	C₂²	1	2	yes	complemented
87	#88142	C₂²	1	2	yes	complemented
88	#88141	C₂²	1	2	yes	complemented
89	#88141	C₂²	1	1	yes	characteristic, complemented
90	#88141	C₂²	1	2	yes	complemented
91	#88141	C₂²	1	2	yes	complemented
92	#88141	C₂²	1	2	yes	complemented
93	#88139	C₂²	1	2	yes	—
94	#88139	C₂²	1	2	yes	complemented
95	#88138	C₂²	1	1	yes	characteristic
96	#88137	C₂²	1	2	yes	—
97	#88137	C₂²	1	1	yes	characteristic
98	#88137	C₂²	1	2	yes	—
99	#88137	C₂²	1	2	yes	—
100	#88136	C₂²	1	1	yes	characteristic
101	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
102	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
103	#88133	C₂²	1	2	yes	—
104	#88133	C₂²	1	2	yes	—
105	#88133	C₂²	1	2	yes	—
106	#88133	C₂²	1	2	yes	complemented
107	#88133	C₂²	1	2	yes	complemented
108	#88132	C₂²	1	1	yes	characteristic
109	#88132	C₂²	1	2	yes	—
110	#88131	C₂²	1	2	yes	—
111	C₄×D₅₂	C₂²	1	2	yes	—
112	C₄×D₅₂	C₂²	1	1	yes	characteristic
113	#88126	C₂²	1	2	yes	—
114	#88126	C₂²	1	2	yes	—
115	#88126	C₂²	1	1	yes	characteristic
116	#88126	C₂²	1	2	yes	complemented
117	C₄²×D₁₃	C₂²	1	2	yes	—
118	#88124	C₂²	1	2	yes	complemented
119	#88124	C₂²	1	2	yes	complemented
120	#88123	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₂₆	C₂²	1	2	yes	complemented
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	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	1	yes	characteristic
132	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
133	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
134	Q₈×D₁₃	—	2	4	no	—
135	#6127	—	2	4	no	—
136	C₂×D₅₂	C₂³	1	1	yes	characteristic
137	C₂×D₅₂	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₁₃	—	2	4	no	—
139	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₁₃	C₂³	1	2	yes	—
141	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₃	C₂³	1	2	yes	—
143	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₃	C₂³	1	2	yes	—
146	C₂×C₄×D₁₃	C₂³	1	2	yes	—
147	C₂×C₄×D₁₃	C₂³	1	2	yes	—
148	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
149	C₂×Dic₂₆	C₂³	1	2	yes	—
150	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
151	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
152	C₂×Dic₂₆	C₂³	1	2	yes	—
153	C₂×Dic₂₆	C₂³	1	2	yes	—
154	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₁₃×C₄⋊C₄	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×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
168	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₄²×C₁₃	C₂³	1	1	yes	characteristic
170	C₄²×C₁₃	C₂³	1	2	yes	—
171	C₄²×C₁₃	C₂³	1	2	yes	—
172	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
178	#6103	C₂³	1	1	yes	characteristic
179	#6103	C₂³	1	2	yes	—
180	#6103	C₂³	1	2	yes	—
181	#6103	C₂³	1	1	yes	characteristic
182	#6103	C₂³	1	1	yes	characteristic
183	#6103	C₂³	1	2	yes	—
184	#6103	C₂³	1	2	yes	—
185	#6103	C₂³	1	2	yes	—
186	#6103	C₂³	1	1	yes	characteristic
187	#6103	C₂³	1	1	yes	characteristic
188	#6103	C₂³	1	2	yes	—
189	#6103	C₂³	1	1	yes	characteristic
190	#6103	C₂³	1	2	yes	—
191	C₄⋊Dic₁₃	C₂³	1	2	yes	—
192	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₁₃	C₂³	1	2	yes	—
194	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
195	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₁₃	C₂³	1	2	yes	—
198	C₄⋊Dic₁₃	C₂³	1	2	yes	—
199	C₄⋊Dic₁₃	C₂³	1	2	yes	—
200	#6101	C₂³	1	1	yes	characteristic
201	#6101	C₂³	1	2	yes	—
202	#6101	C₂³	1	2	yes	—
203	#6101	C₂³	1	1	yes	characteristic
204	#6101	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	2	yes	—
209	#6101	C₂³	1	2	yes	—
210	#6101	C₂³	1	1	yes	characteristic
211	#6101	C₂³	1	2	yes	—
212	#6101	C₂³	1	2	yes	—
213	#6101	C₂³	1	1	yes	characteristic
214	#6101	C₂³	1	2	yes	—
215	#6101	C₂³	1	2	yes	—
216	C₄×Dic₁₃	C₂³	1	2	yes	—
217	C₄×Dic₁₃	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	1	yes	characteristic
223	C₄×Dic₁₃	C₂³	1	2	yes	—
224	C₄×Dic₁₃	C₂³	1	2	yes	—
225	#3495	—	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	—	2	2	no	—
230	C₂²×D₁₃	—	4	1	no	—
231	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
233	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
234	Q₈×C₁₃	—	2	2	no	—
235	D₄×C₁₃	—	4	1	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
241	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂²⋊D₁₃	—	2	2	no	—
249	C₂²⋊D₁₃	—	2	2	no	—
250	C₂²⋊D₁₃	—	2	2	no	—
251	C₂²⋊D₁₃	—	4	1	no	—
252	C₂×Dic₁₃	—	2	2	no	—
253	C₂×Dic₁₃	C₂⁴	1	2	yes	—
254	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
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	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
262	D₅₂	—	2	2	no	—
263	D₅₂	—	2	2	no	—
264	C₄×D₁₃	—	2	2	no	—
265	C₄×D₁₃	—	2	4	no	—
266	C₄×D₁₃	—	2	4	no	—
267	C₄×D₁₃	—	2	2	no	—
268	C₄×D₁₃	—	2	2	no	—
269	C₄×D₁₃	—	2	2	no	—
270	C₄×D₁₃	—	4	2	no	—
271	C₄×D₁₃	—	4	2	no	—
272	C₄×D₁₃	—	4	2	no	—
273	C₄×D₁₃	#41	1	4	yes	—
274	Dic₂₆	—	2	2	no	—
275	Dic₂₆	—	2	2	no	—
276	Dic₂₆	—	2	4	no	—
277	Dic₂₆	—	4	2	no	—
278	Dic₂₆	—	4	2	no	—
279	#556	—	13	1	no	—
280	#556	—	13	1	no	—
281	#554	—	13	1	no	—
282	#554	—	13	1	no	—
283	#552	—	13	2	no	—
284	#552	—	13	1	no	—
285	#552	—	13	1	no	—
286	#552	—	13	1	no	—
287	#552	—	13	2	no	—
288	#552	D₁₃	1	1	yes	characteristic, complemented
289	#551	—	13	2	no	—
290	#551	—	13	2	no	—
291	#544	—	13	1	no	—
292	#542	—	13	2	no	—
293	#541	—	13	2	no	—
294	#536	—	13	1	no	—
295	#533	—	13	2	no	—
296	#529	—	13	2	no	—
297	#525	—	13	1	no	—
298	C₂×C₂²⋊Q₈	—	13	1	no	—
299	#520	—	13	1	no	—
300	#519	—	13	1	no	—
301	C₂×#117	—	13	1	no	—
302	C₂²×C₁₃	—	2	1	no	—
303	C₂²×C₁₃	—	2	1	no	—
304	C₂²×C₁₃	—	2	1	no	—
305	C₂²×C₁₃	—	2	1	no	—
306	C₂²×C₁₃	—	2	1	no	—
307	C₂²×C₁₃	—	2	1	no	—
308	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
309	C₂×D₁₃	—	2	1	no	—
310	C₂×D₁₃	—	2	1	no	—
311	C₂×D₁₃	—	2	1	no	—
312	C₂×D₁₃	—	2	1	no	—
313	C₂×D₁₃	—	2	1	no	—
314	C₂×D₁₃	—	2	1	no	—
315	C₂×D₁₃	—	2	1	no	—
316	C₂×D₁₃	—	4	4	no	—
317	C₂×D₁₃	C₂×#41	1	2	yes	—
318	C₂×D₁₃	2₋¹⁺⁴	1	2	yes	—
319	C₄×C₁₃	—	2	2	no	—
320	C₄×C₁₃	—	2	1	no	—
321	C₄×C₁₃	—	2	1	no	—
322	C₄×C₁₃	—	2	2	no	—
323	C₄×C₁₃	—	2	1	no	—
324	C₄×C₁₃	—	2	1	no	—
325	C₄×C₁₃	—	2	2	no	—
326	C₄×C₁₃	—	2	2	no	—
327	C₄×C₁₃	C₂×#41	1	2	yes	—
328	Dic₁₃	—	2	2	no	—
329	Dic₁₃	—	2	1	no	—
330	Dic₁₃	—	2	1	no	—
331	Dic₁₃	—	2	2	no	—
332	Dic₁₃	—	2	1	no	—
333	Dic₁₃	—	2	2	no	—
334	Dic₁₃	—	2	1	no	—
335	Dic₁₃	—	2	2	no	—
336	Dic₁₃	C₂×#41	1	2	yes	—
337	C₂×#41	—	13	1	no	—
338	C₂²×Q₈	—	13	1	no	—
339	C₂³×C₄	—	13	1	no	—
340	C₄⋊Q₈	—	13	2	no	—
341	C₄⋊Q₈	—	13	2	no	—
342	C₄⋊Q₈	—	13	1	no	—
343	C₄⋊Q₈	—	13	1	no	—
344	#126	—	13	2	no	—
345	#126	—	13	2	no	—
346	#126	—	13	2	no	—
347	#126	—	13	2	no	—
348	#126	—	13	2	no	—
349	#126	—	13	2	no	—
350	#126	—	13	2	no	—
351	#126	C₂×D₁₃	1	2	yes	—
352	#125	—	13	2	no	—
353	#125	—	13	2	no	—
354	#125	—	13	2	no	—
355	#125	—	13	2	no	—
356	#125	—	13	1	no	—
357	#125	—	13	2	no	—
358	#125	—	13	2	no	—
359	#125	C₂×D₁₃	1	2	yes	complemented
360	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
361	#124	—	13	2	no	—
362	#124	—	13	2	no	—
363	#124	—	13	2	no	—
364	#123	—	13	1	no	—
365	#123	—	13	2	no	—
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	C₂×D₁₃	1	2	yes	—
372	C₂²⋊Q₈	—	13	1	no	—
373	C₂²⋊Q₈	—	13	1	no	—
374	C₂²⋊Q₈	—	13	1	no	—
375	C₂²⋊Q₈	—	13	1	no	—
376	C₂²⋊Q₈	—	13	2	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	—	13	2	no	—
384	C₂²⋊Q₈	—	13	2	no	—
385	C₂²⋊Q₈	—	13	2	no	—
386	C₂²⋊Q₈	—	13	2	no	—
387	C₂²⋊Q₈	—	13	1	no	—
388	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
389	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
390	#121	—	13	1	no	—
391	#121	—	13	1	no	—
392	#120	—	13	1	no	—
393	#120	—	13	1	no	—
394	C₄×Q₈	—	13	1	no	—
395	C₄×Q₈	—	13	2	no	—
396	C₄×Q₈	—	13	1	no	—
397	C₄×Q₈	—	13	2	no	—
398	C₄×Q₈	—	13	2	no	—
399	C₄×Q₈	—	13	2	no	—
400	C₄×Q₈	—	13	2	no	—
401	C₄×Q₈	—	13	1	no	—
402	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
403	C₄×D₄	—	13	2	no	—
404	C₄×D₄	—	13	2	no	—
405	C₄×D₄	—	13	1	no	—
406	C₄×D₄	—	13	1	no	—
407	C₄×D₄	—	13	2	no	—
408	C₄×D₄	—	13	2	no	—
409	C₄×D₄	—	13	1	no	—
410	C₄×D₄	—	13	2	no	—
411	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
412	#117	—	13	1	no	—
413	#117	—	13	1	no	—
414	#117	—	13	1	no	—
415	#117	—	13	1	no	—
416	#117	—	13	2	no	—
417	#117	—	13	1	no	—
418	#117	—	13	2	no	—
419	#117	—	13	2	no	—
420	#117	—	13	2	no	—
421	#117	—	13	2	no	—
422	#117	—	13	1	no	—
423	#117	—	13	2	no	—
424	#117	—	13	2	no	—
425	#117	C₂×D₁₃	1	1	yes	characteristic
426	#117	C₂×D₁₃	1	2	yes	complemented
427	C₂×C₄⋊C₄	—	13	1	no	—
428	C₂×C₄⋊C₄	—	13	1	no	—
429	C₂×C₄⋊C₄	—	13	1	no	—
430	C₂×C₄⋊C₄	—	13	1	no	—
431	C₂×C₄⋊C₄	—	13	2	no	—
432	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
433	C₂×C₂²⋊C₄	—	13	2	no	—
434	C₂×C₂²⋊C₄	—	13	2	no	—
435	C₂×C₄²	—	13	2	no	—
436	C₂×C₁₃	—	4	1	no	—
437	C₂×C₁₃	—	4	1	no	—
438	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
439	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
440	C₂×C₁₃	#585	1	1	yes	characteristic
441	D₁₃	—	2	2	no	—
442	D₁₃	—	2	2	no	—
443	D₁₃	—	4	1	no	—
444	C₂⁴	—	13	1	no	—
445	#41	—	26	4	no	—
446	C₂×Q₈	—	13	1	no	—
447	C₂×Q₈	—	13	2	no	—
448	C₂×Q₈	—	13	1	no	—
449	C₂×Q₈	—	13	2	no	—
450	C₂×Q₈	—	13	2	no	—
451	C₂×Q₈	—	26	4	no	—
452	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
453	C₂×D₄	—	13	1	no	—
454	C₂×D₄	—	13	1	no	—
455	C₂×D₄	—	13	1	no	—
456	C₂×D₄	—	13	1	no	—
457	C₂×D₄	—	13	1	no	—
458	C₂×D₄	—	13	1	no	—
459	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
460	C₂²×C₄	—	13	1	no	—
461	C₂²×C₄	—	13	1	no	—
462	C₂²×C₄	—	13	1	no	—
463	C₂²×C₄	—	13	2	no	—
464	C₂²×C₄	—	13	2	no	—
465	C₂²×C₄	—	13	1	no	—
466	C₂²×C₄	—	13	1	no	—
467	C₂²×C₄	—	13	1	no	—
468	C₂²×C₄	—	13	2	no	—
469	C₂²×C₄	—	13	2	no	—
470	C₂²×C₄	—	13	2	no	—
471	C₂²×C₄	—	26	4	no	—
472	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
473	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
474	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
475	C₄⋊C₄	—	13	1	no	—
476	C₄⋊C₄	—	13	1	no	—
477	C₄⋊C₄	—	13	2	no	—
478	C₄⋊C₄	—	13	1	no	—
479	C₄⋊C₄	—	13	2	no	—
480	C₄⋊C₄	—	13	2	no	—
481	C₄⋊C₄	—	13	2	no	—
482	C₄⋊C₄	—	13	2	no	—
483	C₄⋊C₄	—	13	2	no	—
484	C₄⋊C₄	—	13	2	no	—
485	C₄⋊C₄	—	13	1	no	—
486	C₄⋊C₄	—	13	1	no	—
487	C₄⋊C₄	—	13	2	no	—
488	C₄⋊C₄	—	13	2	no	—
489	C₄⋊C₄	—	13	2	no	—
490	C₄⋊C₄	—	13	2	no	—
491	C₄⋊C₄	—	13	2	no	—
492	C₄⋊C₄	—	13	2	no	—
493	C₄⋊C₄	—	13	1	no	—
494	C₄⋊C₄	—	13	1	no	—
495	C₄⋊C₄	—	13	1	no	—
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	C₂²×D₁₃	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
503	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
504	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
505	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
506	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
507	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
508	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
509	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
510	C₂²⋊C₄	—	13	2	no	—
511	C₂²⋊C₄	—	13	2	no	—
512	C₂²⋊C₄	—	13	2	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	2	no	—
520	C₂²⋊C₄	—	13	1	no	—
521	C₂²⋊C₄	—	13	1	no	—
522	C₂²⋊C₄	—	13	1	no	—
523	C₂²⋊C₄	—	13	1	no	—
524	C₂²⋊C₄	—	13	1	no	—
525	C₂²⋊C₄	—	13	2	no	—
526	C₂²⋊C₄	—	13	2	no	—
527	C₂²⋊C₄	—	13	1	no	—
528	C₂²⋊C₄	—	13	2	no	—
529	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
530	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
532	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
533	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
534	C₄²	—	13	2	no	—
535	C₄²	—	13	2	no	—
536	C₄²	—	13	2	no	—
537	C₄²	—	13	2	no	—
538	C₄²	—	13	2	no	—
539	C₄²	—	13	2	no	—
540	C₄²	—	13	2	no	—
541	C₄²	—	13	2	no	—
542	C₄²	—	13	1	no	—
543	C₄²	C₂²×D₁₃	1	2	yes	—
544	C₄²	C₂²×D₁₃	1	2	yes	—
545	C₄²	C₂²×D₁₃	1	1	yes	characteristic
546	C₁₃	#3495	1	1	yes	characteristic, complemented, Sylow
547	C₂³	—	13	1	no	—
548	C₂³	—	13	1	no	—
549	C₂³	—	13	1	no	—
550	C₂³	—	26	2	no	—
551	C₂³	—	26	2	no	—
552	C₂³	—	52	1	no	—
553	C₂³	C₂³×D₁₃	1	1	yes	characteristic
554	C₂³	C₂³×D₁₃	1	1	yes	characteristic
555	Q₈	—	2	2	no	—
556	Q₈	—	26	4	no	—
557	Q₈	—	26	2	no	—
558	Q₈	—	26	2	no	—
559	Q₈	—	52	2	no	—
560	Q₈	—	52	2	no	—
561	D₄	—	4	1	no	—
562	D₄	—	26	2	no	—
563	D₄	—	26	2	no	—
564	D₄	—	26	2	no	—
565	D₄	—	26	2	no	—
566	D₄	—	26	2	no	—
567	D₄	—	52	1	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	13	1	no	—
572	C₂×C₄	—	13	4	no	—
573	C₂×C₄	—	13	2	no	—
574	C₂×C₄	—	13	1	no	—
575	C₂×C₄	—	13	1	no	—
576	C₂×C₄	—	13	2	no	—
577	C₂×C₄	—	13	2	no	—
578	C₂×C₄	—	13	1	no	—
579	C₂×C₄	—	13	2	no	—
580	C₂×C₄	—	13	1	no	—
581	C₂×C₄	—	26	2	no	—
582	C₂×C₄	—	26	4	no	—
583	C₂×C₄	—	26	2	no	—
584	C₂×C₄	—	26	4	no	—
585	C₂×C₄	—	26	2	no	—
586	C₂×C₄	—	26	2	no	—
587	C₂×C₄	—	26	2	no	—
588	C₂×C₄	—	52	2	no	—
589	C₂×C₄	—	52	2	no	—
590	C₂×C₄	—	52	2	no	—
591	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₁₃	1	2	yes	—
593	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
594	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₁₃	1	2	yes	—
596	C₂×C₄	C₂³×D₁₃	1	2	yes	—
597	C₂×C₄	C₂³×D₁₃	1	2	yes	—
598	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	13	2	no	—
607	C₂²	—	13	2	no	—
608	C₂²	—	26	1	no	—
609	C₂²	—	26	1	no	—
610	C₂²	—	26	1	no	—
611	C₂²	—	26	1	no	—
612	C₂²	—	26	1	no	—
613	C₂²	—	26	1	no	—
614	C₂²	—	26	1	no	—
615	C₂²	—	52	4	no	—
616	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	13	2	no	—
626	C₄	—	26	1	no	—
627	C₄	—	26	1	no	—
628	C₄	—	26	2	no	—
629	C₄	—	26	2	no	—
630	C₄	—	26	2	no	—
631	C₄	—	26	1	no	—
632	C₄	—	26	2	no	—
633	C₄	—	26	1	no	—
634	C₄	#41×D₁₃	1	2	yes	—
635	C₂	—	4	1	no	—
636	C₂	—	4	1	no	—
637	C₂	—	26	2	no	—
638	C₂	—	26	2	no	—
639	C₂	—	52	1	no	—
640	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
641	C₂	#11719648	1	1	yes	characteristic
642	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×#552	C₂
prime radical	#11719252	C₂
hypercenter	#552	D₁₃
hypocenter	C₁₃	#3495
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. C₁₃×#552	C₂	semidirect
2. #11719410	C₂	semidirect
3. #11719406	C₂	semidirect
4. #11719399	C₂	semidirect
5. #11719398	C₂	semidirect
6. #11719394	C₂	semidirect
7. #11719393	C₂	semidirect
8. #11719367	C₂	semidirect
9. #11719364	C₂	semidirect
10. #11719346	C₂	semidirect
11. #11719344	C₂	semidirect
12. #11719333	C₂	semidirect
13. D₁₃×C₂²⋊Q₈	C₂	semidirect
14. #11719284	C₂	semidirect
15. #11719277	C₂	semidirect
17. #11719247	C₂	semidirect
18. #11719234	C₂	semidirect
19. #11719234	C₂	semidirect
20. #11719233	C₂	semidirect
21. D₁₃×#117	C₂	semidirect
22. #11719216	C₂	semidirect
23. #11719209	C₂	semidirect
28. C₁₃×#125	C₂²	semidirect
29. C₁₃×#125	C₂²	semidirect
32. C₁₃×C₂²⋊Q₈	C₂²	semidirect
33. C₄×Q₈×C₁₃	C₂²	semidirect
36. C₁₃×#117	C₂²	semidirect
37. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
39. #88200	C₂²	semidirect
40. Q₈×Dic₁₃	C₂²	semidirect
48. C₄×C₂²⋊D₁₃	C₂²	semidirect
50. #88180	C₂²	semidirect
52. #88178	C₂²	semidirect
53. #88178	C₂²	semidirect
54. #88152	C₂²	semidirect
55. #88152	C₂²	semidirect
58. #88151	C₂²	semidirect
64. #88150	C₂²	semidirect
74. #88146	C₂²	semidirect
79. C₄⋊C₄×D₁₃	C₂²	semidirect
80. #88144	C₂²	semidirect
81. #88144	C₂²	semidirect
82. #88143	C₂²	semidirect
83. #88143	C₂²	semidirect
84. #88143	C₂²	semidirect
85. #88142	C₂²	semidirect
86. #88142	C₂²	semidirect
87. #88142	C₂²	semidirect
88. #88141	C₂²	semidirect
89. #88141	C₂²	semidirect
90. #88141	C₂²	semidirect
91. #88141	C₂²	semidirect
92. #88141	C₂²	semidirect
94. #88139	C₂²	semidirect
106. #88133	C₂²	semidirect
107. #88133	C₂²	semidirect
116. #88126	C₂²	semidirect
118. #88124	C₂²	semidirect
119. #88124	C₂²	semidirect
120. #88123	C₂²	semidirect
121. C₄×Dic₂₆	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
288. #552	D₁₃	semidirect
359. #125	C₂×D₁₃	semidirect
360. #125	C₂×D₁₃	semidirect
389. C₂²⋊Q₈	C₂×D₁₃	semidirect
402. C₄×Q₈	C₂×D₁₃	semidirect
426. #117	C₂×D₁₃	semidirect
432. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
546. C₁₃	#3495	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#552	2
#11719410	2
#11719406	2
#11719399	2
#11719398	2
#11719394	2
#11719393	2
#11719367	2
#11719364	2
#11719346	2
#11719344	2
#11719333	2
D₁₃×C₂²⋊Q₈	2
#11719284	2
#11719277	2
#11719252	2
#11719247	2
#11719234	2
#11719233	2
D₁₃×#117	2
#11719216	2
#11719209	2
#3495	13