Subgroups — #13129130

Order 1664.

1032 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719438	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719437	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719404	C₂	1	2	yes	maximal, complemented
5	#11719397	C₂	1	2	yes	maximal, complemented
6	#11719352	C₂	1	2	yes	maximal, complemented
7	#11719349	C₂	1	2	yes	maximal, complemented
8	#11719348	C₂	1	2	yes	maximal, complemented
9	#11719340	C₂	1	2	yes	maximal, complemented
10	#11719337	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719336	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719333	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719332	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719288	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719281	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719270	C₂	1	2	yes	maximal, complemented
17	#11719265	C₂	1	2	yes	maximal, complemented
18	#11719257	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719252	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719219	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719218	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719215	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#88151	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#6131	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×#6127	C₂²	1	1	yes	characteristic
27	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
29	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic
30	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#125	C₂²	1	2	yes	complemented
32	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
38	C₄×D₄×C₁₃	C₂²	1	2	yes	—
39	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
41	#88201	C₂²	1	2	yes	—
42	#88201	C₂²	1	2	yes	—
43	#88200	C₂²	1	1	yes	characteristic
44	#88200	C₂²	1	2	yes	complemented
45	Q₈×Dic₁₃	C₂²	1	2	yes	complemented
46	#88198	C₂²	1	1	yes	characteristic, complemented
47	#88193	C₂²	1	1	yes	characteristic
48	#88193	C₂²	1	2	yes	—
49	#88191	C₂²	1	1	yes	characteristic
50	#88184	C₂²	1	2	yes	—
51	#88184	C₂²	1	1	yes	characteristic
52	#88184	C₂²	1	2	yes	—
53	#88184	C₂²	1	2	yes	complemented
54	#88183	C₂²	1	2	yes	—
55	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
58	C₂×#6103	C₂²	1	2	yes	—
59	#88180	C₂²	1	2	yes	complemented
60	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
61	#88178	C₂²	1	1	yes	characteristic, complemented
62	#88152	C₂²	1	2	yes	—
63	#88152	C₂²	1	2	yes	—
64	#88152	C₂²	1	2	yes	—
65	#88152	C₂²	1	2	yes	complemented
66	#88152	C₂²	1	2	yes	complemented
67	#88152	C₂²	1	2	yes	complemented
68	#88151	C₂²	1	1	yes	characteristic
69	#88151	C₂²	1	1	yes	characteristic
70	#88151	C₂²	1	1	yes	characteristic
71	#88151	C₂²	1	1	yes	characteristic
72	#88151	C₂²	1	2	yes	—
73	#88151	C₂²	1	2	yes	—
74	#88151	C₂²	1	1	yes	characteristic, complemented
75	#88151	C₂²	1	2	yes	complemented
76	#88151	C₂²	1	2	yes	complemented
77	#88150	C₂²	1	1	yes	characteristic
78	#88150	C₂²	1	2	yes	complemented
79	#88150	C₂²	1	2	yes	complemented
80	#88149	C₂²	1	1	yes	characteristic
81	#88149	C₂²	1	2	yes	—
82	#88149	C₂²	1	2	yes	—
83	#88149	C₂²	1	1	yes	characteristic, complemented
84	#88148	C₂²	1	2	yes	—
85	#88148	C₂²	1	1	yes	characteristic
86	#88148	C₂²	1	2	yes	—
87	#88148	C₂²	1	2	yes	—
88	#88148	C₂²	1	2	yes	—
89	#88148	C₂²	1	2	yes	complemented
90	#88147	C₂²	1	2	yes	—
91	#88147	C₂²	1	1	yes	characteristic, complemented
92	#88146	C₂²	1	1	yes	characteristic
93	#88146	C₂²	1	1	yes	characteristic, complemented
94	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
95	#88144	C₂²	1	1	yes	characteristic, complemented
96	#88143	C₂²	1	2	yes	complemented
97	#88143	C₂²	1	2	yes	complemented
98	#88142	C₂²	1	2	yes	complemented
99	#88142	C₂²	1	2	yes	complemented
100	#88141	C₂²	1	1	yes	characteristic, complemented
101	#88139	C₂²	1	2	yes	—
102	#88139	C₂²	1	2	yes	complemented
103	#88138	C₂²	1	1	yes	characteristic
104	#88138	C₂²	1	2	yes	—
105	#88137	C₂²	1	1	yes	characteristic
106	#88137	C₂²	1	2	yes	complemented
107	#88137	C₂²	1	2	yes	complemented
108	#88136	C₂²	1	1	yes	characteristic
109	#88136	C₂²	1	2	yes	—
110	#88135	C₂²	1	2	yes	—
111	#88135	C₂²	1	2	yes	—
112	#88135	C₂²	1	2	yes	—
113	#88132	C₂²	1	1	yes	characteristic
114	#88132	C₂²	1	2	yes	—
115	#88130	C₂²	1	2	yes	—
116	#88129	C₂²	1	2	yes	—
117	#88129	C₂²	1	1	yes	characteristic, complemented
118	C₄×D₅₂	C₂²	1	1	yes	characteristic
119	C₄×D₅₂	C₂²	1	2	yes	complemented
120	#88126	C₂²	1	1	yes	characteristic
121	#88124	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×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	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
137	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
138	C₂²×Dic₁₃	C₂³	1	2	yes	—
139	#6131	—	4	2	no	—
140	Q₈×D₁₃	—	4	2	no	—
141	#6127	—	4	2	no	—
142	#6127	—	4	2	no	—
143	C₂×D₅₂	C₂³	1	1	yes	characteristic
144	C₂×D₅₂	C₂³	1	1	yes	characteristic
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×C₄×D₁₃	—	4	2	no	—
150	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
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×C₄×D₁₃	C₂³	1	2	yes	—
158	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
159	C₂×Dic₂₆	—	4	2	no	—
160	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
161	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
162	C₂×Dic₂₆	C₂³	1	2	yes	—
163	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
164	C₂×Dic₂₆	C₂³	1	2	yes	—
165	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
170	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
171	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
173	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
175	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
178	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₄²×C₁₃	C₂³	1	1	yes	characteristic
180	C₄²×C₁₃	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
184	#6103	C₂³	1	1	yes	characteristic
185	#6103	C₂³	1	1	yes	characteristic
186	#6103	C₂³	1	1	yes	characteristic
187	#6103	C₂³	1	1	yes	characteristic
188	#6103	C₂³	1	2	yes	—
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	2	yes	—
196	#6103	C₂³	1	2	yes	—
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	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₁₃	C₂³	1	2	yes	—
206	C₄⋊Dic₁₃	C₂³	1	2	yes	—
207	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₁₃	C₂³	1	2	yes	—
209	C₄⋊Dic₁₃	C₂³	1	2	yes	—
210	C₄⋊Dic₁₃	C₂³	1	2	yes	—
211	C₄⋊Dic₁₃	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	#6101	C₂³	1	1	yes	characteristic
217	#6101	C₂³	1	2	yes	—
218	#6101	C₂³	1	2	yes	—
219	#6101	C₂³	1	2	yes	—
220	#6101	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
225	C₄×Dic₁₃	C₂³	1	2	yes	—
226	C₄×Dic₁₃	C₂³	1	2	yes	—
227	C₄×Dic₁₃	C₂³	1	2	yes	—
228	#3541	—	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	—	4	1	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	C₂²×D₁₃	C₂⁴	1	2	yes	—
238	Q₈×C₁₃	—	2	2	no	—
239	Q₈×C₁₃	—	4	2	no	—
240	D₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	—	4	2	no	—
245	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
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	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂²⋊D₁₃	—	2	4	no	—
255	C₂²⋊D₁₃	—	2	2	no	—
256	C₂²⋊D₁₃	—	4	2	no	—
257	C₂²⋊D₁₃	—	4	1	no	—
258	C₂²⋊D₁₃	—	4	1	no	—
259	C₂²⋊D₁₃	—	4	1	no	—
260	C₂×Dic₁₃	—	4	2	no	—
261	C₂×Dic₁₃	—	4	1	no	—
262	C₂×Dic₁₃	C₂⁴	1	2	yes	—
263	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₃	C₂⁴	1	2	yes	—
268	C₂×Dic₁₃	C₂⁴	1	2	yes	—
269	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
270	D₅₂	—	2	2	no	—
271	D₅₂	—	4	2	no	—
272	D₅₂	—	4	2	no	—
273	D₅₂	—	4	1	no	—
274	D₅₂	—	4	1	no	—
275	D₅₂	—	4	2	no	—
276	C₄×D₁₃	—	2	2	no	—
277	C₄×D₁₃	—	2	2	no	—
278	C₄×D₁₃	—	2	2	no	—
279	C₄×D₁₃	—	4	1	no	—
280	C₄×D₁₃	—	4	1	no	—
281	C₄×D₁₃	—	4	2	no	—
282	C₄×D₁₃	—	4	2	no	—
283	C₄×D₁₃	—	4	2	no	—
284	C₄×D₁₃	—	4	2	no	—
285	Dic₂₆	—	2	2	no	—
286	Dic₂₆	—	2	2	no	—
287	Dic₂₆	—	4	2	no	—
288	Dic₂₆	—	4	1	no	—
289	Dic₂₆	—	4	2	no	—
290	#563	—	13	2	no	—
291	#562	—	13	2	no	—
292	#556	—	13	1	no	—
293	#554	—	13	2	no	—
294	#554	D₁₃	1	1	yes	characteristic, complemented
295	#553	—	13	2	no	—
296	#553	—	13	1	no	—
297	#552	—	13	1	no	—
298	D₄×Q₈	—	13	1	no	—
299	#548	—	13	1	no	—
300	#548	—	13	1	no	—
301	#547	—	13	1	no	—
302	#542	—	13	1	no	—
303	#542	—	13	2	no	—
304	#541	—	13	1	no	—
305	#539	—	13	2	no	—
306	#538	—	13	2	no	—
307	#538	—	13	2	no	—
308	#537	—	13	1	no	—
309	#536	—	13	1	no	—
310	#525	—	13	1	no	—
311	#525	—	13	1	no	—
312	C₂×C₂²⋊Q₈	—	13	1	no	—
313	C₂²×C₁₃	—	2	1	no	—
314	C₂²×C₁₃	—	2	1	no	—
315	C₂²×C₁₃	—	2	1	no	—
316	C₂²×C₁₃	—	2	1	no	—
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	2₋¹⁺⁴	1	2	yes	—
319	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
320	C₂×D₁₃	—	2	1	no	—
321	C₂×D₁₃	—	2	1	no	—
322	C₂×D₁₃	—	2	1	no	—
323	C₂×D₁₃	—	2	2	no	—
324	C₂×D₁₃	—	2	1	no	—
325	C₂×D₁₃	—	2	2	no	—
326	C₂×D₁₃	—	2	1	no	—
327	C₂×D₁₃	—	2	1	no	—
328	C₂×D₁₃	—	2	2	no	—
329	C₂×D₁₃	—	2	1	no	—
330	C₂×D₁₃	—	2	1	no	—
331	C₂×D₁₃	—	2	1	no	—
332	C₂×D₁₃	—	4	4	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	—	2	2	no	—
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	2	2	no	—
340	C₄×C₁₃	—	2	1	no	—
341	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
342	Dic₁₃	—	2	2	no	—
343	Dic₁₃	—	2	2	no	—
344	Dic₁₃	—	2	1	no	—
345	Dic₁₃	—	2	1	no	—
346	Dic₁₃	—	2	1	no	—
347	Dic₁₃	—	2	2	no	—
348	Dic₁₃	—	2	1	no	—
349	Dic₁₃	—	2	1	no	—
350	C₂×#41	—	13	1	no	—
351	C₂×#41	—	13	1	no	—
352	C₂×#41	—	13	1	no	—
353	C₂²×Q₈	—	13	1	no	—
354	C₂²×Q₈	—	13	1	no	—
355	C₂³×C₄	—	13	1	no	—
356	C₄⋊Q₈	—	13	1	no	—
357	C₄⋊Q₈	—	13	2	no	—
358	C₄⋊Q₈	—	13	2	no	—
359	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
360	#126	—	13	2	no	—
361	#126	—	13	2	no	—
362	#126	—	13	2	no	—
363	#126	—	13	2	no	—
364	#126	—	13	2	no	—
365	#126	—	13	2	no	—
366	#126	—	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	C₂×D₁₃	1	2	yes	complemented
372	#124	—	13	2	no	—
373	#124	—	13	2	no	—
374	#124	—	13	2	no	—
375	#124	—	13	2	no	—
376	#124	—	13	2	no	—
377	#124	—	13	1	no	—
378	#123	—	13	2	no	—
379	#123	—	13	1	no	—
380	#123	—	13	2	no	—
381	#123	—	13	2	no	—
382	#123	—	13	2	no	—
383	#123	—	13	2	no	—
384	#123	—	13	2	no	—
385	#123	—	13	1	no	—
386	#123	—	13	2	no	—
387	#123	—	13	2	no	—
388	C₂²⋊Q₈	—	13	1	no	—
389	C₂²⋊Q₈	—	13	2	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	1	no	—
398	C₂²⋊Q₈	—	13	1	no	—
399	C₂²⋊Q₈	—	13	2	no	—
400	C₂²⋊Q₈	—	13	2	no	—
401	C₂²⋊Q₈	—	13	2	no	—
402	C₂²⋊Q₈	—	13	2	no	—
403	C₂²⋊Q₈	—	13	1	no	—
404	C₂²⋊Q₈	—	13	2	no	—
405	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
406	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
407	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
408	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
409	#121	—	13	1	no	—
410	#121	—	13	2	no	—
411	#121	—	13	1	no	—
412	#121	—	13	2	no	—
413	#121	—	13	2	no	—
414	#121	—	13	2	no	—
415	#121	—	13	1	no	—
416	#121	—	13	2	no	—
417	#121	—	13	1	no	—
418	#121	—	13	2	no	—
419	#121	—	13	1	no	—
420	#121	—	13	2	no	—
421	#120	—	13	1	no	—
422	#120	—	13	2	no	—
423	#120	—	13	1	no	—
424	C₄×Q₈	—	13	2	no	—
425	C₄×Q₈	—	13	1	no	—
426	C₄×Q₈	—	13	1	no	—
427	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
428	C₄×D₄	—	13	1	no	—
429	C₄×D₄	—	13	1	no	—
430	C₄×D₄	—	13	2	no	—
431	C₄×D₄	—	13	2	no	—
432	C₄×D₄	—	13	1	no	—
433	C₄×D₄	—	13	2	no	—
434	C₄×D₄	—	13	2	no	—
435	C₄×D₄	—	13	2	no	—
436	C₄×D₄	—	13	1	no	—
437	C₄×D₄	—	13	2	no	—
438	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
439	C₄×D₄	C₂×D₁₃	1	2	yes	—
440	#117	—	13	2	no	—
441	#117	—	13	1	no	—
442	#117	—	13	1	no	—
443	#117	—	13	1	no	—
444	C₂×C₄⋊C₄	—	13	2	no	—
445	C₂×C₄⋊C₄	—	13	2	no	—
446	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
448	C₂×C₂²⋊C₄	—	13	2	no	—
449	C₂×C₁₃	—	2	2	no	—
450	C₂×C₁₃	—	4	1	no	—
451	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
452	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
453	C₂×C₁₃	#585	1	1	yes	characteristic
454	D₁₃	—	4	1	no	—
455	D₁₃	—	4	2	no	—
456	D₁₃	—	4	1	no	—
457	D₁₃	—	4	1	no	—
458	C₂⁴	—	13	1	no	—
459	#41	—	52	2	no	—
460	#41	—	52	2	no	—
461	#41	—	52	2	no	—
462	C₂×Q₈	—	13	1	no	—
463	C₂×Q₈	—	13	1	no	—
464	C₂×Q₈	—	13	2	no	—
465	C₂×Q₈	—	13	1	no	—
466	C₂×Q₈	—	13	2	no	—
467	C₂×Q₈	—	52	2	no	—
468	C₂×Q₈	—	52	2	no	—
469	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
470	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
471	C₂×D₄	—	13	1	no	—
472	C₂×D₄	—	13	2	no	—
473	C₂×D₄	—	13	1	no	—
474	C₂×D₄	—	13	1	no	—
475	C₂×D₄	—	13	1	no	—
476	C₂×D₄	—	13	2	no	—
477	C₂×D₄	—	13	1	no	—
478	C₂×D₄	—	13	2	no	—
479	C₂×D₄	—	13	1	no	—
480	C₂×D₄	—	13	2	no	—
481	C₂×D₄	—	13	1	no	—
482	C₂×D₄	—	13	2	no	—
483	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
484	C₂²×C₄	—	13	2	no	—
485	C₂²×C₄	—	13	1	no	—
486	C₂²×C₄	—	13	1	no	—
487	C₂²×C₄	—	13	1	no	—
488	C₂²×C₄	—	13	1	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	—	13	1	no	—
494	C₂²×C₄	—	13	1	no	—
495	C₂²×C₄	—	52	2	no	—
496	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
497	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
498	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
499	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
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	2	no	—
505	C₄⋊C₄	—	13	2	no	—
506	C₄⋊C₄	—	13	1	no	—
507	C₄⋊C₄	—	13	1	no	—
508	C₄⋊C₄	—	13	1	no	—
509	C₄⋊C₄	—	13	2	no	—
510	C₄⋊C₄	—	13	1	no	—
511	C₄⋊C₄	—	13	2	no	—
512	C₄⋊C₄	—	13	2	no	—
513	C₄⋊C₄	—	13	1	no	—
514	C₄⋊C₄	—	13	2	no	—
515	C₄⋊C₄	—	13	2	no	—
516	C₄⋊C₄	—	13	2	no	—
517	C₄⋊C₄	—	13	2	no	—
518	C₄⋊C₄	—	13	2	no	—
519	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
520	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
521	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
523	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
525	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
526	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
528	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
529	C₂²⋊C₄	—	13	1	no	—
530	C₂²⋊C₄	—	13	2	no	—
531	C₂²⋊C₄	—	13	1	no	—
532	C₂²⋊C₄	—	13	2	no	—
533	C₂²⋊C₄	—	13	2	no	—
534	C₂²⋊C₄	—	13	2	no	—
535	C₂²⋊C₄	—	13	2	no	—
536	C₂²⋊C₄	—	13	1	no	—
537	C₂²⋊C₄	—	13	2	no	—
538	C₂²⋊C₄	—	13	1	no	—
539	C₂²⋊C₄	—	13	2	no	—
540	C₂²⋊C₄	—	13	1	no	—
541	C₂²⋊C₄	—	13	1	no	—
542	C₂²⋊C₄	—	13	2	no	—
543	C₂²⋊C₄	—	13	1	no	—
544	C₂²⋊C₄	—	13	2	no	—
545	C₂²⋊C₄	—	13	2	no	—
546	C₂²⋊C₄	—	13	2	no	—
547	C₂²⋊C₄	—	13	1	no	—
548	C₂²⋊C₄	—	13	2	no	—
549	C₂²⋊C₄	—	13	2	no	—
550	C₂²⋊C₄	—	13	2	no	—
551	C₂²⋊C₄	—	13	2	no	—
552	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
553	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
556	C₄²	—	13	2	no	—
557	C₄²	—	13	1	no	—
558	C₄²	—	13	2	no	—
559	C₄²	—	13	2	no	—
560	C₄²	—	13	2	no	—
561	C₄²	C₂²×D₁₃	1	1	yes	characteristic
562	C₄²	C₂²×D₁₃	1	2	yes	—
563	C₁₃	#3541	1	1	yes	characteristic, complemented, Sylow
564	C₂³	—	13	1	no	—
565	C₂³	—	13	1	no	—
566	C₂³	—	13	1	no	—
567	C₂³	—	13	2	no	—
568	C₂³	—	26	2	no	—
569	C₂³	—	52	1	no	—
570	C₂³	—	52	1	no	—
571	C₂³	C₂³×D₁₃	1	1	yes	characteristic
572	C₂³	C₂³×D₁₃	1	1	yes	characteristic
573	Q₈	—	2	2	no	—
574	Q₈	—	4	2	no	—
575	Q₈	—	26	2	no	—
576	Q₈	—	26	2	no	—
577	Q₈	—	52	2	no	—
578	Q₈	—	52	2	no	—
579	Q₈	—	52	1	no	—
580	D₄	—	2	2	no	—
581	D₄	—	26	2	no	—
582	D₄	—	26	4	no	—
583	D₄	—	26	2	no	—
584	D₄	—	52	2	no	—
585	D₄	—	52	2	no	—
586	D₄	—	52	1	no	—
587	D₄	—	52	1	no	—
588	D₄	—	52	2	no	—
589	D₄	—	52	1	no	—
590	D₄	—	52	1	no	—
591	D₄	—	52	1	no	—
592	D₄	—	52	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	13	2	no	—
598	C₂×C₄	—	13	1	no	—
599	C₂×C₄	—	13	1	no	—
600	C₂×C₄	—	13	1	no	—
601	C₂×C₄	—	13	2	no	—
602	C₂×C₄	—	13	1	no	—
603	C₂×C₄	—	13	2	no	—
604	C₂×C₄	—	13	1	no	—
605	C₂×C₄	—	26	2	no	—
606	C₂×C₄	—	26	2	no	—
607	C₂×C₄	—	26	2	no	—
608	C₂×C₄	—	52	2	no	—
609	C₂×C₄	—	52	1	no	—
610	C₂×C₄	—	52	1	no	—
611	C₂×C₄	—	52	2	no	—
612	C₂×C₄	—	52	2	no	—
613	C₂×C₄	—	52	2	no	—
614	C₂×C₄	—	52	1	no	—
615	C₂×C₄	—	52	2	no	—
616	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
617	C₂×C₄	C₂³×D₁₃	1	2	yes	—
618	C₂×C₄	C₂³×D₁₃	1	2	yes	—
619	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₁₃	1	2	yes	—
621	C₂×C₄	C₂³×D₁₃	1	2	yes	—
622	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	26	1	no	—
631	C₂²	—	26	2	no	—
632	C₂²	—	26	1	no	—
633	C₂²	—	26	1	no	—
634	C₂²	—	26	1	no	—
635	C₂²	—	26	1	no	—
636	C₂²	—	26	1	no	—
637	C₂²	—	26	2	no	—
638	C₂²	—	26	2	no	—
639	C₂²	—	26	1	no	—
640	C₂²	—	26	1	no	—
641	C₂²	—	26	1	no	—
642	C₂²	—	52	4	no	—
643	C₂²	#88254	1	2	yes	—
644	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	1	no	—
653	C₄	—	26	2	no	—
654	C₄	—	26	1	no	—
655	C₄	—	26	1	no	—
656	C₄	—	26	1	no	—
657	C₄	—	26	1	no	—
658	C₄	—	26	2	no	—
659	C₄	—	26	2	no	—
660	C₄	—	26	1	no	—
661	C₄	#88256	1	2	yes	—
662	C₂	—	2	2	no	—
663	C₂	—	4	1	no	—
664	C₂	—	52	1	no	—
665	C₂	—	52	1	no	—
666	C₂	—	52	1	no	—
667	C₂	—	52	2	no	—
668	C₂	C₂×#88254	1	1	yes	characteristic
669	C₂	C₂×#88256	1	1	yes	characteristic
670	C₂	#11719650	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#554	C₂
hypercenter	#554	D₁₃
hypocenter	C₁₃	#3541
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. C₁₃×#554	C₂	semidirect
2. #11719438	C₂	semidirect
3. #11719437	C₂	semidirect
4. #11719404	C₂	semidirect
5. #11719397	C₂	semidirect
6. #11719352	C₂	semidirect
7. #11719349	C₂	semidirect
8. #11719348	C₂	semidirect
9. #11719340	C₂	semidirect
10. #11719337	C₂	semidirect
11. #11719336	C₂	semidirect
12. #11719333	C₂	semidirect
13. #11719332	C₂	semidirect
14. #11719288	C₂	semidirect
15. #11719281	C₂	semidirect
16. #11719270	C₂	semidirect
17. #11719265	C₂	semidirect
18. #11719257	C₂	semidirect
19. #11719252	C₂	semidirect
20. #11719219	C₂	semidirect
21. #11719218	C₂	semidirect
22. #11719215	C₂	semidirect
23. C₂×#88151	C₂	semidirect
25. C₂×Q₈×D₁₃	C₂²	semidirect
27. C₂×#6127	C₂²	semidirect
30. C₁₃×C₄⋊Q₈	C₂²	semidirect
31. C₁₃×#125	C₂²	semidirect
34. C₁₃×C₂²⋊Q₈	C₂²	semidirect
35. C₁₃×C₂²⋊Q₈	C₂²	semidirect
36. C₄×Q₈×C₁₃	C₂²	semidirect
40. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
44. #88200	C₂²	semidirect
45. Q₈×Dic₁₃	C₂²	semidirect
46. #88198	C₂²	semidirect
53. #88184	C₂²	semidirect
59. #88180	C₂²	semidirect
61. #88178	C₂²	semidirect
65. #88152	C₂²	semidirect
66. #88152	C₂²	semidirect
67. #88152	C₂²	semidirect
74. #88151	C₂²	semidirect
75. #88151	C₂²	semidirect
76. #88151	C₂²	semidirect
78. #88150	C₂²	semidirect
79. #88150	C₂²	semidirect
83. #88149	C₂²	semidirect
89. #88148	C₂²	semidirect
91. #88147	C₂²	semidirect
93. #88146	C₂²	semidirect
94. C₄⋊C₄×D₁₃	C₂²	semidirect
95. #88144	C₂²	semidirect
96. #88143	C₂²	semidirect
97. #88143	C₂²	semidirect
98. #88142	C₂²	semidirect
99. #88142	C₂²	semidirect
100. #88141	C₂²	semidirect
102. #88139	C₂²	semidirect
106. #88137	C₂²	semidirect
107. #88137	C₂²	semidirect
117. #88129	C₂²	semidirect
119. C₄×D₅₂	C₂²	semidirect
121. #88124	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
294. #554	D₁₃	semidirect
359. C₄⋊Q₈	C₂×D₁₃	semidirect
371. #125	C₂×D₁₃	semidirect
407. C₂²⋊Q₈	C₂×D₁₃	semidirect
408. C₂²⋊Q₈	C₂×D₁₃	semidirect
427. C₄×Q₈	C₂×D₁₃	semidirect
447. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
563. C₁₃	#3541	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#554	2
#11719438	2
#11719437	2
#11719404	2
#11719397	2
#11719352	2
#11719349	2
#11719348	2
#11719340	2
#11719337	2
#11719336	2
#11719333	2
#11719332	2
#11719288	2
#11719281	2
#11719270	2
#11719265	2
#11719257	2
#11719252	2
#11719219	2
#11719218	2
#11719215	2
C₂×#88151	2
#3541	13