Subgroups — #13129082

Order 1664.

1014 conjugacy classes of subgroups.

The subgroup lattice has 656 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	#11719417	C₂	1	2	yes	maximal, complemented
3	#11719412	C₂	1	2	yes	maximal, complemented
4	#11719404	C₂	1	2	yes	maximal, complemented
5	#11719402	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719399	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719394	C₂	1	2	yes	maximal, complemented
8	#11719370	C₂	1	2	yes	maximal, complemented
9	#11719363	C₂	1	2	yes	maximal, complemented
10	#11719337	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719337	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	#11719288	C₂	1	1	yes	maximal, characteristic, complemented
15	Q₈×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719252	C₂	1	1	yes	maximal, characteristic
17	D₄×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719234	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719232	C₂	1	2	yes	maximal, complemented
20	#11719231	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719224	C₂	1	2	yes	maximal, complemented
22	#11719218	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#88151	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×#6127	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
28	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic
29	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#126	C₂²	1	2	yes	complemented
31	C₁₃×#125	C₂²	1	2	yes	complemented
32	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#123	C₂²	1	2	yes	—
34	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
36	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#117	C₂²	1	2	yes	—
39	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	#88200	C₂²	1	1	yes	characteristic
42	#88198	C₂²	1	1	yes	characteristic, complemented
43	#88193	C₂²	1	1	yes	characteristic
44	#88191	C₂²	1	1	yes	characteristic
45	D₄×Dic₁₃	C₂²	1	2	yes	—
46	#88183	C₂²	1	2	yes	—
47	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
49	C₂×#6103	C₂²	1	2	yes	—
50	#88180	C₂²	1	2	yes	—
51	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
52	#88178	C₂²	1	1	yes	characteristic
53	#88178	C₂²	1	1	yes	characteristic, complemented
54	#88152	C₂²	1	2	yes	—
55	#88152	C₂²	1	2	yes	—
56	#88152	C₂²	1	2	yes	—
57	#88152	C₂²	1	2	yes	complemented
58	#88152	C₂²	1	2	yes	complemented
59	#88151	C₂²	1	1	yes	characteristic
60	#88151	C₂²	1	1	yes	characteristic
61	#88151	C₂²	1	1	yes	characteristic
62	#88151	C₂²	1	1	yes	characteristic
63	#88151	C₂²	1	2	yes	—
64	#88151	C₂²	1	2	yes	—
65	#88151	C₂²	1	1	yes	characteristic
66	#88151	C₂²	1	2	yes	—
67	#88151	C₂²	1	1	yes	characteristic, complemented
68	#88151	C₂²	1	1	yes	characteristic, complemented
69	#88151	C₂²	1	2	yes	complemented
70	#88150	C₂²	1	2	yes	—
71	#88150	C₂²	1	1	yes	characteristic
72	#88150	C₂²	1	2	yes	—
73	#88150	C₂²	1	2	yes	complemented
74	#88148	C₂²	1	2	yes	—
75	#88148	C₂²	1	2	yes	—
76	#88148	C₂²	1	1	yes	characteristic
77	#88146	C₂²	1	2	yes	—
78	#88146	C₂²	1	1	yes	characteristic, complemented
79	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
80	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
81	#88144	C₂²	1	1	yes	characteristic, complemented
82	#88144	C₂²	1	2	yes	complemented
83	#88144	C₂²	1	2	yes	complemented
84	#88144	C₂²	1	2	yes	complemented
85	#88143	C₂²	1	2	yes	complemented
86	#88143	C₂²	1	2	yes	complemented
87	#88142	C₂²	1	2	yes	complemented
88	#88142	C₂²	1	2	yes	complemented
89	#88142	C₂²	1	2	yes	complemented
90	#88142	C₂²	1	2	yes	complemented
91	#88141	C₂²	1	1	yes	characteristic, complemented
92	#88141	C₂²	1	1	yes	characteristic, complemented
93	#88140	C₂²	1	2	yes	—
94	#88140	C₂²	1	2	yes	complemented
95	#88139	C₂²	1	2	yes	—
96	#88138	C₂²	1	1	yes	characteristic
97	#88137	C₂²	1	2	yes	—
98	#88137	C₂²	1	1	yes	characteristic
99	#88137	C₂²	1	2	yes	complemented
100	#88136	C₂²	1	1	yes	characteristic
101	#88135	C₂²	1	2	yes	—
102	#88135	C₂²	1	2	yes	—
103	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
104	#88133	C₂²	1	2	yes	complemented
105	#88132	C₂²	1	1	yes	characteristic
106	#88132	C₂²	1	2	yes	—
107	#88132	C₂²	1	2	yes	—
108	#88132	C₂²	1	2	yes	—
109	#88132	C₂²	1	2	yes	complemented
110	#88132	C₂²	1	2	yes	complemented
111	#88130	C₂²	1	2	yes	—
112	#88129	C₂²	1	2	yes	—
113	C₄×D₅₂	C₂²	1	2	yes	—
114	C₄×D₅₂	C₂²	1	1	yes	characteristic
115	#88126	C₂²	1	2	yes	—
116	#88126	C₂²	1	1	yes	characteristic
117	#88124	C₂²	1	2	yes	complemented
118	#88124	C₂²	1	2	yes	complemented
119	#88123	C₂²	1	2	yes	complemented
120	#88123	C₂²	1	2	yes	complemented
121	#88123	C₂²	1	1	yes	characteristic, 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	C₂²×Dic₁₃	C₂³	1	2	yes	—
135	C₂²×Dic₁₃	C₂³	1	2	yes	—
136	Q₈×D₁₃	—	4	2	no	—
137	Q₈×D₁₃	—	4	2	no	—
138	#6127	—	4	2	no	—
139	C₂×D₅₂	C₂³	1	1	yes	characteristic
140	C₂×D₅₂	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₃	—	4	2	no	—
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	1	yes	characteristic
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×C₄×D₁₃	C₂³	1	1	yes	characteristic
150	C₂×Dic₂₆	—	4	2	no	—
151	C₂×Dic₂₆	—	4	2	no	—
152	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
153	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
154	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
155	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
156	C₂×Dic₂₆	C₂³	1	2	yes	—
157	C₂×Dic₂₆	C₂³	1	2	yes	—
158	C₂×Dic₂₆	C₂³	1	2	yes	—
159	C₂×Dic₂₆	C₂³	1	2	yes	—
160	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
166	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₄²×C₁₃	C₂³	1	1	yes	characteristic
176	C₄²×C₁₃	C₂³	1	2	yes	—
177	C₄²×C₁₃	C₂³	1	2	yes	—
178	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
182	#6103	C₂³	1	1	yes	characteristic
183	#6103	C₂³	1	2	yes	—
184	#6103	C₂³	1	1	yes	characteristic
185	#6103	C₂³	1	1	yes	characteristic
186	#6103	C₂³	1	2	yes	—
187	#6103	C₂³	1	1	yes	characteristic
188	#6103	C₂³	1	1	yes	characteristic
189	#6103	C₂³	1	2	yes	—
190	#6103	C₂³	1	2	yes	—
191	#6103	C₂³	1	2	yes	—
192	#6103	C₂³	1	2	yes	—
193	#6103	C₂³	1	2	yes	—
194	#6103	C₂³	1	2	yes	—
195	#6103	C₂³	1	1	yes	characteristic
196	#6103	C₂³	1	2	yes	—
197	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₁₃	C₂³	1	2	yes	—
199	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₁₃	C₂³	1	2	yes	—
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	C₄⋊Dic₁₃	C₂³	1	2	yes	—
206	C₄⋊Dic₁₃	C₂³	1	2	yes	—
207	C₄⋊Dic₁₃	C₂³	1	2	yes	—
208	C₄⋊Dic₁₃	C₂³	1	2	yes	—
209	#6101	C₂³	1	2	yes	—
210	#6101	C₂³	1	1	yes	characteristic
211	#6101	C₂³	1	1	yes	characteristic
212	#6101	C₂³	1	2	yes	—
213	#6101	C₂³	1	2	yes	—
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	1	yes	characteristic
219	#6101	C₂³	1	2	yes	—
220	#6101	C₂³	1	2	yes	—
221	#6101	C₂³	1	2	yes	—
222	#6101	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₃	C₂³	1	2	yes	—
224	C₄×Dic₁₃	C₂³	1	2	yes	—
225	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₃	C₂³	1	2	yes	—
227	C₄×Dic₁₃	C₂³	1	2	yes	—
228	#3538	—	13	1	no	maximal, Sylow
229	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₃	—	2	2	no	—
232	C₂²×D₁₃	—	2	2	no	—
233	C₂²×D₁₃	—	4	1	no	—
234	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
235	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
236	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
237	Q₈×C₁₃	—	2	2	no	—
238	D₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
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	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
248	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂²⋊D₁₃	—	2	2	no	—
252	C₂²⋊D₁₃	—	2	2	no	—
253	C₂²⋊D₁₃	—	4	1	no	—
254	C₂²⋊D₁₃	—	4	1	no	—
255	C₂×Dic₁₃	—	4	2	no	—
256	C₂×Dic₁₃	—	4	2	no	—
257	C₂×Dic₁₃	—	4	1	no	—
258	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₃	C₂⁴	1	2	yes	—
261	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₃	C₂⁴	1	2	yes	—
263	C₂×Dic₁₃	C₂⁴	1	2	yes	—
264	C₂×Dic₁₃	C₂⁴	1	2	yes	—
265	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
267	D₅₂	—	2	2	no	—
268	D₅₂	—	4	1	no	—
269	C₄×D₁₃	—	2	4	no	—
270	C₄×D₁₃	—	2	2	no	—
271	C₄×D₁₃	—	2	2	no	—
272	C₄×D₁₃	—	2	2	no	—
273	C₄×D₁₃	—	4	1	no	—
274	C₄×D₁₃	—	4	1	no	—
275	C₄×D₁₃	—	4	2	no	—
276	C₄×D₁₃	—	4	2	no	—
277	Dic₂₆	—	2	2	no	—
278	Dic₂₆	—	2	2	no	—
279	Dic₂₆	—	2	2	no	—
280	Dic₂₆	—	4	2	no	—
281	Dic₂₆	—	4	2	no	—
282	Dic₂₆	—	4	1	no	—
283	Dic₂₆	—	4	2	no	—
284	Dic₂₆	—	4	2	no	—
285	#563	—	13	2	no	—
286	#563	—	13	2	no	—
287	#552	—	13	1	no	—
288	#552	—	13	1	no	—
289	#552	—	13	1	no	—
290	#552	D₁₃	1	1	yes	characteristic, complemented
291	#551	—	13	2	no	—
292	#551	—	13	2	no	—
293	D₄×Q₈	—	13	1	no	—
294	D₄×Q₈	—	13	1	no	—
295	D₄×Q₈	—	13	1	no	—
296	D₄×Q₈	—	13	1	no	—
297	#544	—	13	2	no	—
298	#544	—	13	2	no	—
299	#541	—	13	1	no	—
300	#541	—	13	1	no	—
301	#539	—	13	2	no	—
302	#539	—	13	2	no	—
303	#536	—	13	1	no	—
304	#536	—	13	1	no	—
305	#525	—	13	1	no	—
306	C₂×C₂²⋊Q₈	—	13	1	no	—
307	C₂×C₂²⋊Q₈	—	13	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	2₋¹⁺⁴	1	2	yes	—
314	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
315	C₂×D₁₃	—	2	1	no	—
316	C₂×D₁₃	—	2	1	no	—
317	C₂×D₁₃	—	2	1	no	—
318	C₂×D₁₃	—	2	1	no	—
319	C₂×D₁₃	—	2	1	no	—
320	C₂×D₁₃	—	2	1	no	—
321	C₂×D₁₃	—	2	1	no	—
322	C₂×D₁₃	—	2	1	no	—
323	C₂×D₁₃	—	4	4	no	—
324	C₂×D₁₃	2₋¹⁺⁴	1	2	yes	—
325	C₄×C₁₃	—	2	1	no	—
326	C₄×C₁₃	—	2	1	no	—
327	C₄×C₁₃	—	2	2	no	—
328	C₄×C₁₃	—	2	2	no	—
329	C₄×C₁₃	—	2	1	no	—
330	C₄×C₁₃	—	2	2	no	—
331	C₄×C₁₃	—	2	2	no	—
332	C₄×C₁₃	—	2	1	no	—
333	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
334	Dic₁₃	—	2	2	no	—
335	Dic₁₃	—	2	2	no	—
336	Dic₁₃	—	2	2	no	—
337	Dic₁₃	—	2	1	no	—
338	Dic₁₃	—	2	1	no	—
339	Dic₁₃	—	2	1	no	—
340	Dic₁₃	—	2	2	no	—
341	Dic₁₃	—	2	1	no	—
342	Dic₁₃	—	2	1	no	—
343	C₂×#41	—	13	1	no	—
344	C₂²×Q₈	—	13	1	no	—
345	C₂²×Q₈	—	13	1	no	—
346	C₂²×Q₈	—	13	1	no	—
347	C₂²×Q₈	—	13	1	no	—
348	C₂³×C₄	—	13	1	no	—
349	C₄⋊Q₈	—	13	1	no	—
350	C₄⋊Q₈	—	13	2	no	—
351	C₄⋊Q₈	—	13	2	no	—
352	C₄⋊Q₈	—	13	2	no	—
353	C₄⋊Q₈	—	13	2	no	—
354	C₄⋊Q₈	—	13	2	no	—
355	C₄⋊Q₈	—	13	1	no	—
356	C₄⋊Q₈	—	13	2	no	—
357	#126	—	13	2	no	—
358	#126	—	13	2	no	—
359	#126	—	13	2	no	—
360	#126	—	13	2	no	—
361	#126	—	13	2	no	—
362	#126	—	13	2	no	—
363	#126	—	13	2	no	—
364	#126	C₂×D₁₃	1	2	yes	complemented
365	#125	—	13	2	no	—
366	#125	—	13	2	no	—
367	#125	—	13	2	no	—
368	#125	—	13	1	no	—
369	#125	—	13	2	no	—
370	#125	—	13	2	no	—
371	#125	—	13	2	no	—
372	#125	—	13	2	no	—
373	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
374	#125	C₂×D₁₃	1	2	yes	complemented
375	#124	—	13	2	no	—
376	#124	—	13	2	no	—
377	#123	—	13	2	no	—
378	#123	—	13	1	no	—
379	#123	—	13	2	no	—
380	#123	—	13	2	no	—
381	#123	—	13	1	no	—
382	#123	—	13	2	no	—
383	#123	—	13	2	no	—
384	#123	—	13	2	no	—
385	#123	—	13	2	no	—
386	#123	C₂×D₁₃	1	2	yes	—
387	C₂²⋊Q₈	—	13	1	no	—
388	C₂²⋊Q₈	—	13	1	no	—
389	C₂²⋊Q₈	—	13	1	no	—
390	C₂²⋊Q₈	—	13	1	no	—
391	C₂²⋊Q₈	—	13	1	no	—
392	C₂²⋊Q₈	—	13	1	no	—
393	C₂²⋊Q₈	—	13	2	no	—
394	C₂²⋊Q₈	—	13	1	no	—
395	C₂²⋊Q₈	—	13	1	no	—
396	C₂²⋊Q₈	—	13	2	no	—
397	C₂²⋊Q₈	—	13	2	no	—
398	C₂²⋊Q₈	—	13	1	no	—
399	C₂²⋊Q₈	—	13	1	no	—
400	C₂²⋊Q₈	—	13	1	no	—
401	C₂²⋊Q₈	—	13	2	no	—
402	C₂²⋊Q₈	—	13	2	no	—
403	C₂²⋊Q₈	—	13	2	no	—
404	C₂²⋊Q₈	—	13	2	no	—
405	C₂²⋊Q₈	—	13	2	no	—
406	C₂²⋊Q₈	—	13	1	no	—
407	C₂²⋊Q₈	—	13	2	no	—
408	C₂²⋊Q₈	—	13	2	no	—
409	C₂²⋊Q₈	—	13	2	no	—
410	C₂²⋊Q₈	—	13	2	no	—
411	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
412	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
413	#121	—	13	1	no	—
414	#121	—	13	1	no	—
415	#120	—	13	1	no	—
416	#120	—	13	1	no	—
417	C₄×Q₈	—	13	1	no	—
418	C₄×Q₈	—	13	1	no	—
419	C₄×Q₈	—	13	1	no	—
420	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
421	C₄×D₄	—	13	2	no	—
422	C₄×D₄	—	13	1	no	—
423	C₄×D₄	—	13	1	no	—
424	C₄×D₄	—	13	2	no	—
425	C₄×D₄	—	13	2	no	—
426	C₄×D₄	—	13	1	no	—
427	C₄×D₄	—	13	2	no	—
428	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
429	#117	—	13	2	no	—
430	#117	—	13	1	no	—
431	#117	—	13	2	no	—
432	#117	—	13	1	no	—
433	#117	—	13	2	no	—
434	#117	C₂×D₁₃	1	2	yes	—
435	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
436	C₂×C₄⋊C₄	—	13	2	no	—
437	C₂×C₄⋊C₄	—	13	2	no	—
438	C₂×C₄⋊C₄	—	13	1	no	—
439	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
440	C₂×C₂²⋊C₄	—	13	2	no	—
441	C₂×C₂²⋊C₄	—	13	2	no	—
442	C₂×C₁₃	—	2	2	no	—
443	C₂×C₁₃	—	4	1	no	—
444	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
445	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
446	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
447	D₁₃	—	2	2	no	—
448	D₁₃	—	4	1	no	—
449	D₁₃	—	4	1	no	—
450	C₂⁴	—	13	1	no	—
451	#41	—	52	2	no	—
452	C₂×Q₈	—	13	1	no	—
453	C₂×Q₈	—	13	1	no	—
454	C₂×Q₈	—	13	1	no	—
455	C₂×Q₈	—	13	2	no	—
456	C₂×Q₈	—	13	2	no	—
457	C₂×Q₈	—	13	2	no	—
458	C₂×Q₈	—	13	2	no	—
459	C₂×Q₈	—	13	1	no	—
460	C₂×Q₈	—	52	2	no	—
461	C₂×Q₈	—	52	2	no	—
462	C₂×Q₈	—	52	2	no	—
463	C₂×Q₈	—	52	2	no	—
464	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
465	C₂×D₄	—	13	1	no	—
466	C₂×D₄	—	13	1	no	—
467	C₂×D₄	—	13	1	no	—
468	C₂×D₄	—	13	1	no	—
469	C₂×D₄	—	13	1	no	—
470	C₂×D₄	—	13	1	no	—
471	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
472	C₂²×C₄	—	13	2	no	—
473	C₂²×C₄	—	13	1	no	—
474	C₂²×C₄	—	13	2	no	—
475	C₂²×C₄	—	13	2	no	—
476	C₂²×C₄	—	13	1	no	—
477	C₂²×C₄	—	13	1	no	—
478	C₂²×C₄	—	13	1	no	—
479	C₂²×C₄	—	13	2	no	—
480	C₂²×C₄	—	13	1	no	—
481	C₂²×C₄	—	13	2	no	—
482	C₂²×C₄	—	13	1	no	—
483	C₂²×C₄	—	52	2	no	—
484	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
485	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
486	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
487	C₄⋊C₄	—	13	1	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	2	no	—
494	C₄⋊C₄	—	13	2	no	—
495	C₄⋊C₄	—	13	2	no	—
496	C₄⋊C₄	—	13	1	no	—
497	C₄⋊C₄	—	13	1	no	—
498	C₄⋊C₄	—	13	2	no	—
499	C₄⋊C₄	—	13	2	no	—
500	C₄⋊C₄	—	13	2	no	—
501	C₄⋊C₄	—	13	2	no	—
502	C₄⋊C₄	—	13	2	no	—
503	C₄⋊C₄	—	13	2	no	—
504	C₄⋊C₄	—	13	2	no	—
505	C₄⋊C₄	—	13	2	no	—
506	C₄⋊C₄	—	13	2	no	—
507	C₄⋊C₄	—	13	1	no	—
508	C₄⋊C₄	—	13	1	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	C₂²×D₁₃	1	1	yes	characteristic
514	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
515	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
518	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
519	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
520	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
521	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
523	C₂²⋊C₄	—	13	2	no	—
524	C₂²⋊C₄	—	13	1	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	2	no	—
533	C₂²⋊C₄	—	13	1	no	—
534	C₂²⋊C₄	—	13	1	no	—
535	C₂²⋊C₄	—	13	1	no	—
536	C₂²⋊C₄	—	13	1	no	—
537	C₂²⋊C₄	—	13	2	no	—
538	C₂²⋊C₄	—	13	1	no	—
539	C₂²⋊C₄	—	13	1	no	—
540	C₂²⋊C₄	—	13	2	no	—
541	C₂²⋊C₄	—	13	2	no	—
542	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
544	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
547	C₄²	—	13	2	no	—
548	C₄²	—	13	1	no	—
549	C₄²	—	13	2	no	—
550	C₄²	—	13	2	no	—
551	C₄²	—	13	2	no	—
552	C₄²	C₂²×D₁₃	1	2	yes	—
553	C₄²	C₂²×D₁₃	1	1	yes	characteristic
554	C₄²	C₂²×D₁₃	1	2	yes	—
555	C₁₃	#3538	1	1	yes	characteristic, complemented, Sylow
556	C₂³	—	13	1	no	—
557	C₂³	—	13	1	no	—
558	C₂³	—	13	1	no	—
559	C₂³	—	26	2	no	—
560	C₂³	—	26	2	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	—	26	2	no	—
566	Q₈	—	26	2	no	—
567	Q₈	—	26	2	no	—
568	Q₈	—	52	2	no	—
569	Q₈	—	52	2	no	—
570	Q₈	—	52	2	no	—
571	Q₈	—	52	2	no	—
572	Q₈	—	52	1	no	—
573	D₄	—	2	2	no	—
574	D₄	—	26	2	no	—
575	D₄	—	26	2	no	—
576	D₄	—	26	2	no	—
577	D₄	—	52	1	no	—
578	D₄	—	52	1	no	—
579	D₄	—	52	1	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	13	1	no	—
584	C₂×C₄	—	13	1	no	—
585	C₂×C₄	—	13	2	no	—
586	C₂×C₄	—	13	1	no	—
587	C₂×C₄	—	13	2	no	—
588	C₂×C₄	—	13	2	no	—
589	C₂×C₄	—	13	2	no	—
590	C₂×C₄	—	13	1	no	—
591	C₂×C₄	—	13	1	no	—
592	C₂×C₄	—	26	4	no	—
593	C₂×C₄	—	26	2	no	—
594	C₂×C₄	—	26	2	no	—
595	C₂×C₄	—	26	2	no	—
596	C₂×C₄	—	52	1	no	—
597	C₂×C₄	—	52	1	no	—
598	C₂×C₄	—	52	2	no	—
599	C₂×C₄	—	52	2	no	—
600	C₂×C₄	—	52	1	no	—
601	C₂×C₄	—	52	2	no	—
602	C₂×C₄	—	52	2	no	—
603	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
604	C₂×C₄	C₂³×D₁₃	1	2	yes	—
605	C₂×C₄	C₂³×D₁₃	1	2	yes	—
606	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₁₃	1	2	yes	—
608	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₁₃	1	2	yes	—
610	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	2	1	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	13	2	no	—
618	C₂²	—	26	1	no	—
619	C₂²	—	26	1	no	—
620	C₂²	—	26	1	no	—
621	C₂²	—	26	1	no	—
622	C₂²	—	26	1	no	—
623	C₂²	—	26	1	no	—
624	C₂²	—	26	1	no	—
625	C₂²	—	26	1	no	—
626	C₂²	—	52	4	no	—
627	C₂²	#88257	1	2	yes	—
628	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
629	C₄	—	2	1	no	—
630	C₄	—	2	1	no	—
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	2	no	—
634	C₄	—	2	1	no	—
635	C₄	—	2	2	no	—
636	C₄	—	2	1	no	—
637	C₄	—	26	1	no	—
638	C₄	—	26	1	no	—
639	C₄	—	26	1	no	—
640	C₄	—	26	2	no	—
641	C₄	—	26	2	no	—
642	C₄	—	26	2	no	—
643	C₄	—	26	1	no	—
644	C₄	—	26	2	no	—
645	C₄	—	26	1	no	—
646	C₄	#88256	1	2	yes	—
647	C₂	—	2	2	no	—
648	C₂	—	4	1	no	—
649	C₂	—	26	2	no	—
650	C₂	—	52	1	no	—
651	C₂	—	52	1	no	—
652	C₂	C₂×#88256	1	1	yes	characteristic
653	C₂	C₂×#88257	1	1	yes	characteristic
654	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	#3538
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. #11719417	C₂	semidirect
3. #11719412	C₂	semidirect
4. #11719404	C₂	semidirect
5. #11719402	C₂	semidirect
6. #11719399	C₂	semidirect
7. #11719394	C₂	semidirect
8. #11719370	C₂	semidirect
9. #11719363	C₂	semidirect
10. #11719337	C₂	semidirect
11. #11719337	C₂	semidirect
12. #11719333	C₂	semidirect
13. D₁₃×C₂²⋊Q₈	C₂	semidirect
14. #11719288	C₂	semidirect
15. Q₈×D₅₂	C₂	semidirect
17. D₄×Dic₂₆	C₂	semidirect
18. #11719234	C₂	semidirect
19. #11719232	C₂	semidirect
20. #11719231	C₂	semidirect
21. #11719224	C₂	semidirect
22. #11719218	C₂	semidirect
23. C₂×#88151	C₂	semidirect
25. C₂×Q₈×D₁₃	C₂²	semidirect
29. C₂²×Dic₂₆	C₂²	semidirect
30. C₁₃×#126	C₂²	semidirect
31. C₁₃×#125	C₂²	semidirect
32. C₁₃×#125	C₂²	semidirect
35. C₁₃×C₂²⋊Q₈	C₂²	semidirect
36. C₄×Q₈×C₁₃	C₂²	semidirect
39. C₁₃×#117	C₂²	semidirect
42. #88198	C₂²	semidirect
53. #88178	C₂²	semidirect
57. #88152	C₂²	semidirect
58. #88152	C₂²	semidirect
67. #88151	C₂²	semidirect
68. #88151	C₂²	semidirect
69. #88151	C₂²	semidirect
73. #88150	C₂²	semidirect
78. #88146	C₂²	semidirect
81. #88144	C₂²	semidirect
82. #88144	C₂²	semidirect
83. #88144	C₂²	semidirect
84. #88144	C₂²	semidirect
85. #88143	C₂²	semidirect
86. #88143	C₂²	semidirect
87. #88142	C₂²	semidirect
88. #88142	C₂²	semidirect
89. #88142	C₂²	semidirect
90. #88142	C₂²	semidirect
91. #88141	C₂²	semidirect
92. #88141	C₂²	semidirect
94. #88140	C₂²	semidirect
99. #88137	C₂²	semidirect
104. #88133	C₂²	semidirect
109. #88132	C₂²	semidirect
110. #88132	C₂²	semidirect
117. #88124	C₂²	semidirect
118. #88124	C₂²	semidirect
119. #88123	C₂²	semidirect
120. #88123	C₂²	semidirect
121. #88123	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
290. #552	D₁₃	semidirect
364. #126	C₂×D₁₃	semidirect
373. #125	C₂×D₁₃	semidirect
374. #125	C₂×D₁₃	semidirect
412. C₂²⋊Q₈	C₂×D₁₃	semidirect
420. C₄×Q₈	C₂×D₁₃	semidirect
435. #117	C₂×D₁₃	semidirect
555. C₁₃	#3538	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
#11719417	2
#11719412	2
#11719404	2
#11719402	2
#11719399	2
#11719394	2
#11719370	2
#11719363	2
#11719337	2
#11719333	2
D₁₃×C₂²⋊Q₈	2
#11719288	2
Q₈×D₅₂	2
#11719252	2
D₄×Dic₂₆	2
#11719234	2
#11719232	2
#11719231	2
#11719224	2
#11719218	2
C₂×#88151	2
#3538	13