Subgroups — #13129117

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×#537	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719536	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719533	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719530	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719529	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719351	C₂	1	2	yes	maximal, complemented
7	#11719346	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719341	C₂	1	2	yes	maximal, complemented
9	#11719337	C₂	1	1	yes	maximal, characteristic, complemented
10	D₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719330	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719326	C₂	1	2	yes	maximal, complemented
13	#11719319	C₂	1	2	yes	maximal, complemented
14	#11719319	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719318	C₂	1	2	yes	maximal, complemented
16	#11719318	C₂	1	2	yes	maximal, complemented
17	#11719311	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719308	C₂	1	2	yes	maximal, complemented
19	#11719308	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719307	C₂	1	2	yes	maximal, complemented
21	#11719303	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719218	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719216	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
26	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic
27	C₂×#6129	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
29	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₁₃×#121	C₂²	1	2	yes	—
34	C₁₃×#121	C₂²	1	1	yes	characteristic
35	C₁₃×#121	C₂²	1	2	yes	—
36	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#121	C₂²	1	2	yes	complemented
38	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
39	#88200	C₂²	1	1	yes	characteristic
40	#88200	C₂²	1	1	yes	characteristic
41	#88200	C₂²	1	1	yes	characteristic
42	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
43	#88198	C₂²	1	1	yes	characteristic, complemented
44	#88198	C₂²	1	2	yes	complemented
45	#88193	C₂²	1	2	yes	—
46	#88193	C₂²	1	2	yes	—
47	#88192	C₂²	1	1	yes	characteristic
48	#88192	C₂²	1	1	yes	characteristic
49	#88192	C₂²	1	1	yes	characteristic
50	#88192	C₂²	1	2	yes	—
51	#88192	C₂²	1	2	yes	—
52	#88191	C₂²	1	1	yes	characteristic
53	#88191	C₂²	1	1	yes	characteristic
54	#88191	C₂²	1	2	yes	—
55	#88190	C₂²	1	2	yes	—
56	#88190	C₂²	1	2	yes	—
57	#88190	C₂²	1	1	yes	characteristic, complemented
58	#88190	C₂²	1	2	yes	complemented
59	#88189	C₂²	1	2	yes	—
60	#88189	C₂²	1	1	yes	characteristic
61	#88189	C₂²	1	1	yes	characteristic
62	#88189	C₂²	1	2	yes	—
63	#88189	C₂²	1	2	yes	complemented
64	#88189	C₂²	1	2	yes	complemented
65	#88189	C₂²	1	2	yes	complemented
66	D₄×Dic₁₃	C₂²	1	2	yes	—
67	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
68	D₄×Dic₁₃	C₂²	1	2	yes	complemented
69	#88183	C₂²	1	2	yes	—
70	#88183	C₂²	1	2	yes	—
71	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
72	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
73	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
74	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
75	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
77	#88180	C₂²	1	1	yes	characteristic
78	#88180	C₂²	1	2	yes	complemented
79	#88180	C₂²	1	1	yes	characteristic, complemented
80	#88178	C₂²	1	1	yes	characteristic
81	#88178	C₂²	1	1	yes	characteristic
82	#88178	C₂²	1	1	yes	characteristic, complemented
83	#88178	C₂²	1	2	yes	complemented
84	#88178	C₂²	1	1	yes	characteristic, complemented
85	#88178	C₂²	1	2	yes	complemented
86	C₂×#6101	C₂²	1	2	yes	complemented
87	#88152	C₂²	1	2	yes	—
88	#88152	C₂²	1	2	yes	—
89	#88151	C₂²	1	1	yes	characteristic
90	#88151	C₂²	1	1	yes	characteristic
91	#88150	C₂²	1	2	yes	—
92	#88150	C₂²	1	2	yes	—
93	#88150	C₂²	1	2	yes	—
94	#88146	C₂²	1	1	yes	characteristic
95	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
96	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
97	#88144	C₂²	1	1	yes	characteristic, complemented
98	#88144	C₂²	1	2	yes	complemented
99	#88143	C₂²	1	2	yes	complemented
100	#88143	C₂²	1	2	yes	complemented
101	#88143	C₂²	1	2	yes	complemented
102	#88142	C₂²	1	1	yes	characteristic, complemented
103	#88142	C₂²	1	2	yes	complemented
104	#88141	C₂²	1	1	yes	characteristic, complemented
105	#88141	C₂²	1	1	yes	characteristic, complemented
106	#88141	C₂²	1	2	yes	complemented
107	#88139	C₂²	1	2	yes	—
108	#88139	C₂²	1	2	yes	—
109	#88137	C₂²	1	2	yes	—
110	#88135	C₂²	1	2	yes	—
111	#88135	C₂²	1	2	yes	—
112	#88135	C₂²	1	2	yes	—
113	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
114	#88133	C₂²	1	2	yes	—
115	#88133	C₂²	1	2	yes	—
116	#88133	C₂²	1	2	yes	complemented
117	#88133	C₂²	1	2	yes	complemented
118	#88133	C₂²	1	2	yes	complemented
119	#88132	C₂²	1	2	yes	—
120	#88132	C₂²	1	2	yes	complemented
121	#88132	C₂²	1	2	yes	complemented
122	#88132	C₂²	1	2	yes	complemented
123	C₂³×D₁₃	C₂³	1	1	yes	characteristic
124	C₁₃×#41	—	4	2	no	—
125	C₁₃×#41	—	4	2	no	—
126	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₃	C₂³	1	2	yes	—
130	C₂×D₄×C₁₃	C₂³	1	2	yes	—
131	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
134	C₂×D₄×C₁₃	C₂³	1	2	yes	—
135	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
139	C₂²×C₄×C₁₃	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	1	yes	characteristic
143	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
146	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
147	C₂²×Dic₁₃	C₂³	1	2	yes	—
148	C₂²×Dic₁₃	C₂³	1	2	yes	—
149	C₂²×Dic₁₃	C₂³	1	2	yes	—
150	Q₈×D₁₃	—	4	2	no	—
151	#6129	—	4	2	no	—
152	C₂×C₄×D₁₃	—	4	2	no	—
153	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₁₃	C₂³	1	2	yes	—
156	C₂×C₄×D₁₃	C₂³	1	2	yes	—
157	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
168	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
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	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
179	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
188	C₂²⋊Dic₁₃	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	1	yes	characteristic
193	#6103	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	C₄⋊Dic₁₃	C₂³	1	2	yes	—
198	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₃	C₂³	1	2	yes	—
200	C₄⋊Dic₁₃	C₂³	1	2	yes	—
201	C₄⋊Dic₁₃	C₂³	1	2	yes	—
202	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
205	#6101	C₂³	1	2	yes	—
206	#6101	C₂³	1	2	yes	—
207	#6101	C₂³	1	1	yes	characteristic
208	#6101	C₂³	1	2	yes	—
209	#6101	C₂³	1	2	yes	—
210	#6101	C₂³	1	2	yes	—
211	#6101	C₂³	1	2	yes	—
212	#6101	C₂³	1	2	yes	—
213	#6101	C₂³	1	2	yes	—
214	#6101	C₂³	1	1	yes	characteristic
215	#6101	C₂³	1	2	yes	—
216	#6101	C₂³	1	2	yes	—
217	#6101	C₂³	1	1	yes	characteristic
218	#6101	C₂³	1	1	yes	characteristic
219	#6101	C₂³	1	2	yes	—
220	#6101	C₂³	1	2	yes	—
221	C₄×Dic₁₃	C₂³	1	2	yes	—
222	C₄×Dic₁₃	C₂³	1	2	yes	—
223	C₄×Dic₁₃	C₂³	1	2	yes	—
224	C₄×Dic₁₃	C₂³	1	2	yes	—
225	C₄×Dic₁₃	C₂³	1	2	yes	—
226	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
228	#3541	—	13	1	no	maximal, Sylow
229	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂³×C₁₃	C₂⁴	1	2	yes	—
233	C₂²×D₁₃	—	2	2	no	—
234	C₂²×D₁₃	—	4	1	no	—
235	C₂²×D₁₃	—	4	1	no	—
236	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
237	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
238	Q₈×C₁₃	—	2	2	no	—
239	Q₈×C₁₃	—	4	1	no	—
240	D₄×C₁₃	—	2	2	no	—
241	D₄×C₁₃	—	4	2	no	—
242	D₄×C₁₃	—	4	2	no	—
243	D₄×C₁₃	—	4	1	no	—
244	D₄×C₁₃	—	4	2	no	—
245	D₄×C₁₃	—	4	1	no	—
246	D₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	4	2	no	—
251	C₂×C₄×C₁₃	—	4	2	no	—
252	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂²⋊D₁₃	—	2	4	no	—
260	C₂²⋊D₁₃	—	2	2	no	—
261	C₂²⋊D₁₃	—	2	2	no	—
262	C₂²⋊D₁₃	—	4	2	no	—
263	C₂²⋊D₁₃	—	4	1	no	—
264	C₂²⋊D₁₃	—	4	1	no	—
265	C₂×Dic₁₃	—	4	2	no	—
266	C₂×Dic₁₃	—	4	1	no	—
267	C₂×Dic₁₃	—	4	2	no	—
268	C₂×Dic₁₃	—	4	2	no	—
269	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₃	C₂⁴	1	2	yes	—
271	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
275	C₂×Dic₁₃	C₂⁴	1	2	yes	—
276	C₂×Dic₁₃	C₂⁴	1	2	yes	—
277	C₂×Dic₁₃	C₂⁴	1	2	yes	—
278	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
279	C₄×D₁₃	—	2	2	no	—
280	C₄×D₁₃	—	2	2	no	—
281	C₄×D₁₃	—	4	1	no	—
282	C₄×D₁₃	—	4	1	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	2	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	—	13	1	no	—
295	#553	—	13	1	no	—
296	#553	—	13	2	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	D₁₃	1	1	yes	characteristic, complemented
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	2	no	—
315	C₂²×C₁₃	—	2	1	no	—
316	C₂²×C₁₃	—	2	1	no	—
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	—	2	1	no	—
319	C₂²×C₁₃	—	2	2	no	—
320	C₂²×C₁₃	—	2	1	no	—
321	C₂²×C₁₃	—	2	2	no	—
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	—	2	1	no	—
324	C₂²×C₁₃	—	2	1	no	—
325	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
326	C₂×D₁₃	—	2	1	no	—
327	C₂×D₁₃	—	2	1	no	—
328	C₂×D₁₃	—	2	1	no	—
329	C₂×D₁₃	—	2	1	no	—
330	C₂×D₁₃	—	2	1	no	—
331	C₂×D₁₃	—	4	4	no	—
332	C₂×D₁₃	2₋¹⁺⁴	1	2	yes	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	2	2	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
340	Dic₁₃	—	2	2	no	—
341	Dic₁₃	—	2	2	no	—
342	Dic₁₃	—	2	1	no	—
343	Dic₁₃	—	2	1	no	—
344	Dic₁₃	—	2	1	no	—
345	Dic₁₃	—	2	2	no	—
346	Dic₁₃	—	2	1	no	—
347	Dic₁₃	—	2	1	no	—
348	Dic₁₃	—	2	2	no	—
349	Dic₁₃	—	2	1	no	—
350	C₂×#41	—	13	1	no	—
351	C₂×#41	C₂×D₁₃	1	1	yes	characteristic
352	C₂×#41	C₂×D₁₃	1	1	yes	characteristic, complemented
353	C₂²×Q₈	—	13	1	no	—
354	C₂²×Q₈	—	13	1	no	—
355	C₂³×C₄	—	13	1	no	—
356	C₄⋊Q₈	—	13	2	no	—
357	C₄⋊Q₈	—	13	1	no	—
358	C₄⋊Q₈	—	13	2	no	—
359	C₄⋊Q₈	—	13	1	no	—
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	2	no	—
369	#125	—	13	1	no	—
370	#125	—	13	2	no	—
371	#125	—	13	2	no	—
372	#124	—	13	2	no	—
373	#124	—	13	2	no	—
374	#124	—	13	1	no	—
375	#124	—	13	2	no	—
376	#124	—	13	2	no	—
377	#124	—	13	2	no	—
378	#123	—	13	1	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	2	no	—
386	#123	—	13	2	no	—
387	#123	—	13	2	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	1	no	—
394	C₂²⋊Q₈	—	13	1	no	—
395	C₂²⋊Q₈	—	13	2	no	—
396	C₂²⋊Q₈	—	13	2	no	—
397	C₂²⋊Q₈	—	13	1	no	—
398	C₂²⋊Q₈	—	13	2	no	—
399	C₂²⋊Q₈	—	13	1	no	—
400	C₂²⋊Q₈	—	13	2	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	C₂×D₁₃	1	1	yes	characteristic
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	1	no	—
411	#121	—	13	1	no	—
412	#121	—	13	2	no	—
413	#121	—	13	2	no	—
414	#121	—	13	2	no	—
415	#121	—	13	2	no	—
416	#121	C₂×D₁₃	1	1	yes	characteristic
417	#121	C₂×D₁₃	1	2	yes	—
418	#121	C₂×D₁₃	1	2	yes	—
419	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
420	#121	C₂×D₁₃	1	2	yes	complemented
421	#120	—	13	1	no	—
422	#120	—	13	1	no	—
423	#120	—	13	2	no	—
424	C₄×Q₈	—	13	1	no	—
425	C₄×Q₈	—	13	1	no	—
426	C₄×Q₈	—	13	1	no	—
427	C₄×Q₈	—	13	2	no	—
428	C₄×D₄	—	13	2	no	—
429	C₄×D₄	—	13	2	no	—
430	C₄×D₄	—	13	1	no	—
431	C₄×D₄	—	13	1	no	—
432	C₄×D₄	—	13	1	no	—
433	C₄×D₄	—	13	1	no	—
434	C₄×D₄	—	13	1	no	—
435	C₄×D₄	—	13	2	no	—
436	C₄×D₄	—	13	2	no	—
437	C₄×D₄	—	13	2	no	—
438	C₄×D₄	—	13	2	no	—
439	C₄×D₄	—	13	2	no	—
440	#117	—	13	1	no	—
441	#117	—	13	1	no	—
442	#117	—	13	2	no	—
443	#117	—	13	1	no	—
444	C₂×C₄⋊C₄	—	13	2	no	—
445	C₂×C₄⋊C₄	—	13	2	no	—
446	C₂×C₄⋊C₄	—	13	1	no	—
447	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
448	C₂×C₂²⋊C₄	—	13	2	no	—
449	C₂×C₁₃	—	4	1	no	—
450	C₂×C₁₃	—	4	1	no	—
451	C₂×C₁₃	—	4	2	no	—
452	C₂×C₁₃	—	4	1	no	—
453	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
454	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
455	C₂×C₁₃	#585	1	1	yes	characteristic
456	D₁₃	—	2	2	no	—
457	D₁₃	—	4	1	no	—
458	C₂⁴	—	13	1	no	—
459	#41	—	4	2	no	—
460	#41	—	4	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	2	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	1	yes	characteristic
471	C₂×D₄	—	13	1	no	—
472	C₂×D₄	—	13	1	no	—
473	C₂×D₄	—	13	2	no	—
474	C₂×D₄	—	13	1	no	—
475	C₂×D₄	—	13	1	no	—
476	C₂×D₄	—	13	2	no	—
477	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
478	C₂×D₄	C₂²×D₁₃	1	2	yes	—
479	C₂×D₄	C₂²×D₁₃	1	2	yes	—
480	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
481	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
482	C₂×D₄	C₂²×D₁₃	1	2	yes	—
483	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
484	C₂²×C₄	—	13	2	no	—
485	C₂²×C₄	—	13	2	no	—
486	C₂²×C₄	—	13	2	no	—
487	C₂²×C₄	—	13	1	no	—
488	C₂²×C₄	—	13	1	no	—
489	C₂²×C₄	—	13	1	no	—
490	C₂²×C₄	—	13	2	no	—
491	C₂²×C₄	—	13	2	no	—
492	C₂²×C₄	—	13	1	no	—
493	C₂²×C₄	—	13	1	no	—
494	C₂²×C₄	—	52	2	no	—
495	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
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	1	no	—
504	C₄⋊C₄	—	13	2	no	—
505	C₄⋊C₄	—	13	2	no	—
506	C₄⋊C₄	—	13	2	no	—
507	C₄⋊C₄	—	13	2	no	—
508	C₄⋊C₄	—	13	1	no	—
509	C₄⋊C₄	—	13	1	no	—
510	C₄⋊C₄	—	13	1	no	—
511	C₄⋊C₄	—	13	2	no	—
512	C₄⋊C₄	—	13	1	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	1	no	—
518	C₄⋊C₄	—	13	2	no	—
519	C₄⋊C₄	—	13	2	no	—
520	C₄⋊C₄	—	13	2	no	—
521	C₄⋊C₄	—	13	2	no	—
522	C₄⋊C₄	—	13	2	no	—
523	C₄⋊C₄	—	13	2	no	—
524	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
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	2	no	—
530	C₂²⋊C₄	—	13	1	no	—
531	C₂²⋊C₄	—	13	1	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	2	no	—
537	C₂²⋊C₄	—	13	1	no	—
538	C₂²⋊C₄	—	13	2	no	—
539	C₂²⋊C₄	—	13	1	no	—
540	C₂²⋊C₄	—	13	2	no	—
541	C₂²⋊C₄	—	13	2	no	—
542	C₂²⋊C₄	—	13	2	no	—
543	C₂²⋊C₄	—	13	2	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	1	no	—
549	C₂²⋊C₄	—	13	2	no	—
550	C₂²⋊C₄	—	13	1	no	—
551	C₂²⋊C₄	—	13	1	no	—
552	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
556	C₄²	—	13	2	no	—
557	C₄²	—	13	1	no	—
558	C₄²	—	13	1	no	—
559	C₄²	—	13	2	no	—
560	C₄²	—	13	2	no	—
561	C₄²	—	13	2	no	—
562	C₄²	—	13	2	no	—
563	C₁₃	#3541	1	1	yes	characteristic, complemented, Sylow
564	C₂³	—	13	1	no	—
565	C₂³	—	13	1	no	—
566	C₂³	—	26	2	no	—
567	C₂³	—	52	1	no	—
568	C₂³	—	52	1	no	—
569	C₂³	C₂³×D₁₃	1	1	yes	characteristic
570	C₂³	C₂³×D₁₃	1	1	yes	characteristic
571	C₂³	C₂³×D₁₃	1	1	yes	characteristic
572	C₂³	C₂³×D₁₃	1	2	yes	—
573	Q₈	—	2	2	no	—
574	Q₈	—	4	1	no	—
575	Q₈	—	26	2	no	—
576	Q₈	—	26	2	no	—
577	Q₈	—	52	2	no	—
578	Q₈	—	52	2	no	—
579	Q₈	—	52	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	4	1	no	—
584	D₄	—	4	1	no	—
585	D₄	—	4	1	no	—
586	D₄	—	4	2	no	—
587	D₄	—	26	2	no	—
588	D₄	—	26	2	no	—
589	D₄	—	26	4	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	—	2	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	13	2	no	—
599	C₂×C₄	—	13	1	no	—
600	C₂×C₄	—	13	1	no	—
601	C₂×C₄	—	13	1	no	—
602	C₂×C₄	—	13	1	no	—
603	C₂×C₄	—	13	2	no	—
604	C₂×C₄	—	13	2	no	—
605	C₂×C₄	—	13	1	no	—
606	C₂×C₄	—	13	2	no	—
607	C₂×C₄	—	13	1	no	—
608	C₂×C₄	—	26	2	no	—
609	C₂×C₄	—	26	2	no	—
610	C₂×C₄	—	52	2	no	—
611	C₂×C₄	—	52	1	no	—
612	C₂×C₄	—	52	1	no	—
613	C₂×C₄	—	52	2	no	—
614	C₂×C₄	—	52	2	no	—
615	C₂×C₄	—	52	1	no	—
616	C₂×C₄	—	52	2	no	—
617	C₂×C₄	—	52	2	no	—
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	2	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	1	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	1	no	—
637	C₂²	—	13	2	no	—
638	C₂²	—	26	1	no	—
639	C₂²	—	26	1	no	—
640	C₂²	—	26	1	no	—
641	C₂²	—	26	1	no	—
642	C₂²	—	26	1	no	—
643	C₂²	—	52	4	no	—
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	—	26	1	no	—
652	C₄	—	26	1	no	—
653	C₄	—	26	2	no	—
654	C₄	—	26	2	no	—
655	C₄	—	26	1	no	—
656	C₄	—	26	2	no	—
657	C₄	—	26	1	no	—
658	C₄	—	26	2	no	—
659	C₄	—	26	1	no	—
660	C₄	—	26	1	no	—
661	C₄	#88251	1	2	yes	—
662	C₂	—	4	1	no	—
663	C₂	—	4	1	no	—
664	C₂	—	4	1	no	—
665	C₂	—	4	2	no	—
666	C₂	—	26	2	no	—
667	C₂	—	52	1	no	—
668	C₂	C₂×#88251	1	1	yes	characteristic
669	C₂	#11719650	1	1	yes	characteristic
670	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×#537	C₂
hypercenter	#537	D₁₃
hypocenter	C₁₃	#3541
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #537

Complements

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

N	H ≅ G/N	type
1. C₁₃×#537	C₂	semidirect
2. #11719536	C₂	semidirect
3. #11719533	C₂	semidirect
4. #11719530	C₂	semidirect
5. #11719529	C₂	semidirect
6. #11719351	C₂	semidirect
7. #11719346	C₂	semidirect
8. #11719341	C₂	semidirect
9. #11719337	C₂	semidirect
10. D₁₃×C₂²⋊Q₈	C₂	semidirect
11. #11719330	C₂	semidirect
12. #11719326	C₂	semidirect
13. #11719319	C₂	semidirect
14. #11719319	C₂	semidirect
15. #11719318	C₂	semidirect
16. #11719318	C₂	semidirect
17. #11719311	C₂	semidirect
18. #11719308	C₂	semidirect
19. #11719308	C₂	semidirect
20. #11719307	C₂	semidirect
21. #11719303	C₂	semidirect
22. #11719218	C₂	semidirect
23. #11719216	C₂	semidirect
25. C₂×C₁₃×#41	C₂²	semidirect
29. C₂²×Dic₂₆	C₂²	semidirect
31. C₁₃×C₂²⋊Q₈	C₂²	semidirect
32. C₁₃×C₂²⋊Q₈	C₂²	semidirect
36. C₁₃×#121	C₂²	semidirect
37. C₁₃×#121	C₂²	semidirect
38. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
42. Q₈×Dic₁₃	C₂²	semidirect
43. #88198	C₂²	semidirect
44. #88198	C₂²	semidirect
57. #88190	C₂²	semidirect
58. #88190	C₂²	semidirect
63. #88189	C₂²	semidirect
64. #88189	C₂²	semidirect
65. #88189	C₂²	semidirect
67. D₄×Dic₁₃	C₂²	semidirect
68. D₄×Dic₁₃	C₂²	semidirect
78. #88180	C₂²	semidirect
79. #88180	C₂²	semidirect
82. #88178	C₂²	semidirect
83. #88178	C₂²	semidirect
84. #88178	C₂²	semidirect
85. #88178	C₂²	semidirect
86. C₂×#6101	C₂²	semidirect
97. #88144	C₂²	semidirect
98. #88144	C₂²	semidirect
99. #88143	C₂²	semidirect
100. #88143	C₂²	semidirect
101. #88143	C₂²	semidirect
102. #88142	C₂²	semidirect
103. #88142	C₂²	semidirect
104. #88141	C₂²	semidirect
105. #88141	C₂²	semidirect
106. #88141	C₂²	semidirect
116. #88133	C₂²	semidirect
117. #88133	C₂²	semidirect
118. #88133	C₂²	semidirect
120. #88132	C₂²	semidirect
121. #88132	C₂²	semidirect
122. #88132	C₂²	semidirect
308. #537	D₁₃	semidirect
352. C₂×#41	C₂×D₁₃	semidirect
407. C₂²⋊Q₈	C₂×D₁₃	semidirect
408. C₂²⋊Q₈	C₂×D₁₃	semidirect
419. #121	C₂×D₁₃	semidirect
420. #121	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×#537	2
#11719536	2
#11719533	2
#11719530	2
#11719529	2
#11719351	2
#11719346	2
#11719341	2
#11719337	2
D₁₃×C₂²⋊Q₈	2
#11719330	2
#11719326	2
#11719319	2
#11719318	2
#11719311	2
#11719308	2
#11719307	2
#11719303	2
#11719218	2
#11719216	2
#3541	13