Subgroups — #13128986

Order 1664.

1336 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719511	C₂	1	2	yes	maximal, complemented
3	#11719509	C₂	1	2	yes	maximal, complemented
4	D₄×C₂²⋊D₁₃	C₂	1	2	yes	maximal, complemented
5	C₂×#88191	C₂	1	2	yes	maximal, complemented
6	#11719425	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719420	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719325	C₂	1	2	yes	maximal, complemented
9	#11719322	C₂	1	2	yes	maximal, complemented
10	#11719318	C₂	1	2	yes	maximal, complemented
11	#11719315	C₂	1	2	yes	maximal, complemented
12	#11719299	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719297	C₂	1	2	yes	maximal, complemented
14	#11719296	C₂	1	2	yes	maximal, complemented
15	#11719294	C₂	1	1	yes	maximal, characteristic, complemented
16	D₁₃×#120	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719292	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719265	C₂	1	2	yes	maximal, complemented
19	#11719261	C₂	1	2	yes	maximal, complemented
20	C₂⁴×D₁₃	C₂²	1	1	yes	characteristic, complemented
21	C₂²×D₄×C₁₃	C₂²	1	2	yes	complemented
22	C₂²×D₄×C₁₃	C₂²	1	2	yes	complemented
23	C₂²×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
24	C₂²×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
25	C₂²×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×#6129	C₂²	1	1	yes	characteristic, complemented
27	C₂×#6129	C₂²	1	2	yes	complemented
28	C₂×D₄×D₁₃	C₂²	1	2	yes	complemented
29	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#121	C₂²	1	2	yes	complemented
32	C₁₃×#121	C₂²	1	2	yes	complemented
33	C₁₃×#120	C₂²	1	1	yes	characteristic
34	C₁₃×#120	C₂²	1	2	yes	complemented
35	C₁₃×#120	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
37	#88207	C₂²	1	1	yes	characteristic, complemented
38	#88207	C₂²	1	2	yes	complemented
39	#88207	C₂²	1	2	yes	complemented
40	#88207	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
42	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
43	#88194	C₂²	1	2	yes	complemented
44	#88194	C₂²	1	1	yes	characteristic, complemented
45	#88193	C₂²	1	2	yes	complemented
46	#88193	C₂²	1	2	yes	complemented
47	#88193	C₂²	1	2	yes	complemented
48	#88193	C₂²	1	2	yes	complemented
49	#88193	C₂²	1	2	yes	complemented
50	#88193	C₂²	1	2	yes	complemented
51	#88193	C₂²	1	2	yes	complemented
52	#88193	C₂²	1	2	yes	complemented
53	#88192	C₂²	1	2	yes	complemented
54	#88192	C₂²	1	2	yes	complemented
55	#88191	C₂²	1	2	yes	—
56	#88191	C₂²	1	2	yes	complemented
57	#88191	C₂²	1	1	yes	characteristic, complemented
58	#88191	C₂²	1	2	yes	complemented
59	#88191	C₂²	1	2	yes	complemented
60	#88191	C₂²	1	2	yes	complemented
61	#88191	C₂²	1	2	yes	complemented
62	#88191	C₂²	1	2	yes	complemented
63	#88191	C₂²	1	2	yes	complemented
64	#88191	C₂²	1	2	yes	complemented
65	#88191	C₂²	1	2	yes	complemented
66	#88190	C₂²	1	2	yes	complemented
67	#88190	C₂²	1	1	yes	characteristic, complemented
68	#88189	C₂²	1	2	yes	complemented
69	#88189	C₂²	1	1	yes	characteristic, complemented
70	#88189	C₂²	1	2	yes	complemented
71	#88189	C₂²	1	2	yes	complemented
72	D₄×Dic₁₃	C₂²	1	2	yes	complemented
73	D₄×Dic₁₃	C₂²	1	2	yes	complemented
74	#88184	C₂²	1	2	yes	complemented
75	#88183	C₂²	1	2	yes	complemented
76	#88183	C₂²	1	2	yes	complemented
77	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
78	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
79	C₂×#6103	C₂²	1	2	yes	complemented
80	C₂×#6103	C₂²	1	2	yes	complemented
81	#88178	C₂²	1	2	yes	complemented
82	#88152	C₂²	1	2	yes	complemented
83	#88152	C₂²	1	2	yes	complemented
84	#88150	C₂²	1	2	yes	complemented
85	#88148	C₂²	1	2	yes	complemented
86	#88140	C₂²	1	1	yes	characteristic, complemented
87	#88140	C₂²	1	2	yes	complemented
88	#88139	C₂²	1	2	yes	complemented
89	#88139	C₂²	1	2	yes	complemented
90	#88139	C₂²	1	2	yes	complemented
91	#88139	C₂²	1	2	yes	complemented
92	#88138	C₂²	1	2	yes	complemented
93	#88138	C₂²	1	2	yes	complemented
94	#88137	C₂²	1	2	yes	complemented
95	#88136	C₂²	1	2	yes	complemented
96	#88136	C₂²	1	1	yes	characteristic, complemented
97	#88135	C₂²	1	2	yes	complemented
98	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
99	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
100	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
101	#88133	C₂²	1	2	yes	complemented
102	#88132	C₂²	1	2	yes	complemented
103	#88131	C₂²	1	2	yes	complemented
104	#88130	C₂²	1	2	yes	complemented
105	#88129	C₂²	1	1	yes	characteristic, complemented
106	#88126	C₂²	1	1	yes	characteristic, complemented
107	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
108	C₂⁴×C₁₃	C₂³	1	2	yes	—
109	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic, complemented
110	C₂³×D₁₃	—	4	2	no	—
111	C₂³×D₁₃	—	4	4	no	—
112	C₂³×D₁₃	C₂³	1	2	yes	—
113	C₂³×D₁₃	C₂³	1	1	yes	characteristic
114	C₂³×D₁₃	C₂³	1	1	yes	characteristic
115	C₂³×D₁₃	C₂³	1	2	yes	—
116	C₂³×D₁₃	C₂³	1	1	yes	characteristic
117	C₂×D₄×C₁₃	—	4	4	no	—
118	C₂×D₄×C₁₃	—	4	4	no	—
119	C₂×D₄×C₁₃	C₂³	1	2	yes	—
120	C₂×D₄×C₁₃	C₂³	1	2	yes	—
121	C₂×D₄×C₁₃	C₂³	1	2	yes	—
122	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
123	C₂×D₄×C₁₃	C₂³	1	2	yes	—
124	C₂×D₄×C₁₃	C₂³	1	2	yes	—
125	C₂×D₄×C₁₃	C₂³	1	2	yes	complemented
126	C₂×D₄×C₁₃	C₂³	1	2	yes	complemented
127	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic, complemented
128	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂³	1	2	yes	complemented
130	C₂×C₂²⋊D₁₃	—	4	4	no	—
131	C₂×C₂²⋊D₁₃	—	4	4	no	—
132	C₂×C₂²⋊D₁₃	—	4	2	no	—
133	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
135	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
136	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
138	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
139	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
143	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	complemented
146	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	complemented
147	C₂²×Dic₁₃	C₂³	1	2	yes	—
148	C₂²×Dic₁₃	C₂³	1	2	yes	—
149	C₂²×Dic₁₃	C₂³	1	2	yes	complemented
150	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic, complemented
151	C₂²×Dic₁₃	C₂³	1	2	yes	complemented
152	#6129	—	4	2	no	—
153	#6129	—	4	4	no	—
154	D₄×D₁₃	—	4	2	no	—
155	D₄×D₁₃	—	4	4	no	—
156	C₂×D₅₂	C₂³	1	1	yes	characteristic
157	C₂×D₅₂	C₂³	1	2	yes	—
158	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₃	C₂³	1	2	yes	—
160	C₂×C₄×D₁₃	C₂³	1	2	yes	complemented
161	C₂×Dic₂₆	C₂³	1	1	yes	characteristic, complemented
162	C₂×Dic₂₆	C₂³	1	2	yes	complemented
163	C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
164	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic, complemented
167	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	complemented
168	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	complemented
169	C₄²×C₁₃	C₂³	1	1	yes	characteristic, complemented
170	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
172	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic, complemented
177	C₂²⋊Dic₁₃	C₂³	1	2	yes	complemented
178	C₂²⋊Dic₁₃	C₂³	1	2	yes	complemented
179	C₂²⋊Dic₁₃	C₂³	1	2	yes	complemented
180	C₂²⋊Dic₁₃	C₂³	1	2	yes	complemented
181	C₂²⋊Dic₁₃	C₂³	1	2	yes	complemented
182	#6103	C₂³	1	2	yes	—
183	#6103	C₂³	1	2	yes	—
184	#6103	C₂³	1	2	yes	—
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	2	yes	—
191	#6103	C₂³	1	2	yes	—
192	#6103	C₂³	1	2	yes	—
193	#6103	C₂³	1	2	yes	complemented
194	C₄⋊Dic₁₃	C₂³	1	2	yes	complemented
195	C₄⋊Dic₁₃	C₂³	1	2	yes	complemented
196	#6101	C₂³	1	2	yes	complemented
197	#6101	C₂³	1	2	yes	complemented
198	#6101	C₂³	1	2	yes	complemented
199	#6101	C₂³	1	2	yes	complemented
200	#6101	C₂³	1	2	yes	complemented
201	#6101	C₂³	1	2	yes	complemented
202	C₄×Dic₁₃	C₂³	1	1	yes	characteristic, complemented
203	C₄×Dic₁₃	C₂³	1	2	yes	complemented
204	C₄×Dic₁₃	C₂³	1	2	yes	complemented
205	#3532	—	13	1	no	maximal, Sylow
206	C₂³×C₁₃	—	2	4	no	—
207	C₂³×C₁₃	—	2	4	no	—
208	C₂³×C₁₃	—	4	1	no	—
209	C₂³×C₁₃	—	4	2	no	—
210	C₂³×C₁₃	—	4	1	no	—
211	C₂³×C₁₃	—	4	2	no	—
212	C₂³×C₁₃	—	4	2	no	—
213	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
214	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
215	C₂³×C₁₃	C₂⁴	1	2	yes	—
216	C₂³×C₁₃	C₂⁴	1	2	yes	—
217	C₂³×C₁₃	C₂⁴	1	2	yes	—
218	C₂²×D₁₃	—	2	4	no	—
219	C₂²×D₁₃	—	2	4	no	—
220	C₂²×D₁₃	—	2	2	no	—
221	C₂²×D₁₃	—	2	4	no	—
222	C₂²×D₁₃	—	2	2	no	—
223	C₂²×D₁₃	—	4	2	no	—
224	C₂²×D₁₃	—	4	2	no	—
225	C₂²×D₁₃	—	4	2	no	—
226	C₂²×D₁₃	—	4	2	no	—
227	C₂²×D₁₃	—	4	2	no	—
228	C₂²×D₁₃	—	4	1	no	—
229	C₂²×D₁₃	—	4	2	no	—
230	C₂²×D₁₃	—	4	16	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	D₄×C₁₃	—	2	4	no	—
236	D₄×C₁₃	—	2	4	no	—
237	D₄×C₁₃	—	2	4	no	—
238	D₄×C₁₃	—	4	1	no	—
239	D₄×C₁₃	—	4	1	no	—
240	D₄×C₁₃	—	4	2	no	—
241	D₄×C₁₃	—	4	2	no	—
242	D₄×C₁₃	—	4	2	no	—
243	D₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	—	4	2	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂²⋊D₁₃	—	2	4	no	—
251	C₂²⋊D₁₃	—	2	4	no	—
252	C₂²⋊D₁₃	—	2	4	no	—
253	C₂²⋊D₁₃	—	4	2	no	—
254	C₂²⋊D₁₃	—	4	1	no	—
255	C₂²⋊D₁₃	—	4	1	no	—
256	C₂²⋊D₁₃	—	4	2	no	—
257	C₂²⋊D₁₃	—	4	2	no	—
258	C₂²⋊D₁₃	—	4	2	no	—
259	C₂²⋊D₁₃	—	4	2	no	—
260	C₂²⋊D₁₃	—	4	2	no	—
261	C₂²⋊D₁₃	—	4	2	no	—
262	C₂²⋊D₁₃	—	4	2	no	—
263	C₂²⋊D₁₃	—	4	2	no	—
264	C₂×Dic₁₃	—	2	4	no	—
265	C₂×Dic₁₃	—	4	2	no	—
266	C₂×Dic₁₃	—	4	2	no	—
267	C₂×Dic₁₃	—	4	2	no	—
268	C₂×Dic₁₃	—	4	1	no	—
269	C₂×Dic₁₃	C₂⁴	1	2	yes	—
270	C₂×Dic₁₃	C₂⁴	1	2	yes	—
271	C₂×Dic₁₃	C₂⁴	1	2	yes	—
272	C₂×Dic₁₃	C₂⁴	1	2	yes	—
273	C₂×Dic₁₃	C₂⁴	1	2	yes	—
274	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
275	D₅₂	—	4	1	no	—
276	D₅₂	—	4	2	no	—
277	C₄×D₁₃	—	2	2	no	—
278	C₄×D₁₃	—	4	2	no	—
279	C₄×D₁₃	—	4	2	no	—
280	Dic₂₆	—	4	2	no	—
281	Dic₂₆	—	4	1	no	—
282	H(3,𝔽₄)	—	13	1	no	—
283	#560	—	13	1	no	—
284	#560	—	13	2	no	—
285	#551	—	13	1	no	—
286	#551	—	13	2	no	—
287	#546	—	13	2	no	—
288	#546	—	13	2	no	—
289	#546	—	13	2	no	—
290	D₄²	—	13	2	no	—
291	D₄²	D₁₃	1	1	yes	characteristic, complemented
292	#538	—	13	2	no	—
293	#538	—	13	2	no	—
294	#538	—	13	2	no	—
295	#535	—	13	1	no	—
296	#535	—	13	2	no	—
297	#534	—	13	2	no	—
298	#534	—	13	1	no	—
299	C₂×#120	—	13	2	no	—
300	C₂×#120	—	13	1	no	—
301	C₂²×C₁₃	—	2	2	no	—
302	C₂²×C₁₃	—	2	2	no	—
303	C₂²×C₁₃	—	2	2	no	—
304	C₂²×C₁₃	—	2	2	no	—
305	C₂²×C₁₃	—	2	1	no	—
306	C₂²×C₁₃	—	2	2	no	—
307	C₂²×C₁₃	—	2	2	no	—
308	C₂²×C₁₃	—	2	2	no	—
309	C₂²×C₁₃	—	2	2	no	—
310	C₂²×C₁₃	—	2	1	no	—
311	C₂²×C₁₃	—	2	2	no	—
312	C₂²×C₁₃	—	2	2	no	—
313	C₂²×C₁₃	—	4	4	no	—
314	C₂²×C₁₃	—	8	4	no	—
315	C₂²×C₁₃	—	8	2	no	—
316	C₂²×C₁₃	H(5,𝔽₂)	1	4	yes	—
317	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
318	C₂×D₁₃	—	2	2	no	—
319	C₂×D₁₃	—	2	2	no	—
320	C₂×D₁₃	—	2	1	no	—
321	C₂×D₁₃	—	2	2	no	—
322	C₂×D₁₃	—	2	1	no	—
323	C₂×D₁₃	—	2	2	no	—
324	C₂×D₁₃	—	2	2	no	—
325	C₂×D₁₃	—	2	2	no	—
326	C₂×D₁₃	—	4	8	no	—
327	C₂×D₁₃	—	4	4	no	—
328	C₂×D₁₃	—	4	8	no	—
329	C₂×D₁₃	—	4	4	no	—
330	C₂×D₁₃	—	8	2	no	—
331	C₂×D₁₃	H(5,𝔽₂)	1	2	yes	—
332	C₄×C₁₃	—	2	1	no	—
333	C₄×C₁₃	—	2	2	no	—
334	C₄×C₁₃	—	2	2	no	—
335	C₄×C₁₃	—	2	2	no	—
336	Dic₁₃	—	2	2	no	—
337	Dic₁₃	—	2	2	no	—
338	Dic₁₃	—	2	2	no	—
339	Dic₁₃	—	2	1	no	—
340	Dic₁₃	—	2	2	no	—
341	Dic₁₃	—	2	2	no	—
342	C₂⁵	—	13	1	no	—
343	C₂×#41	—	13	2	no	—
344	C₂×#41	—	13	1	no	—
345	C₂²×D₄	—	13	2	no	—
346	C₂²×D₄	—	13	2	no	—
347	C₂²×D₄	—	13	1	no	—
348	C₂²×D₄	—	13	1	no	—
349	C₂²×D₄	—	13	2	no	—
350	C₂²×D₄	C₂×D₁₃	1	2	yes	complemented
351	C₂²×D₄	C₂×D₁₃	1	2	yes	complemented
352	#127	—	13	1	no	—
353	#127	—	13	2	no	—
354	#127	C₂×D₁₃	1	1	yes	characteristic, complemented
355	#126	—	13	2	no	—
356	#126	—	13	2	no	—
357	#126	—	13	2	no	—
358	#126	—	13	2	no	—
359	#124	—	13	1	no	—
360	#124	—	13	2	no	—
361	#124	—	13	2	no	—
362	#124	—	13	2	no	—
363	#124	—	13	2	no	—
364	#124	—	13	2	no	—
365	#124	—	13	1	no	—
366	#123	—	13	2	no	—
367	#123	—	13	2	no	—
368	#123	—	13	1	no	—
369	#123	—	13	2	no	—
370	#123	—	13	2	no	—
371	#123	—	13	2	no	—
372	#123	—	13	2	no	—
373	#123	—	13	1	no	—
374	#123	—	13	2	no	—
375	#123	—	13	2	no	—
376	C₂²⋊Q₈	—	13	2	no	—
377	C₂²⋊Q₈	—	13	2	no	—
378	C₂²⋊Q₈	—	13	2	no	—
379	#121	—	13	2	no	—
380	#121	—	13	2	no	—
381	#121	—	13	2	no	—
382	#121	—	13	2	no	—
383	#121	—	13	2	no	—
384	#121	—	13	2	no	—
385	#121	—	13	2	no	—
386	#121	—	13	2	no	—
387	#121	—	13	2	no	—
388	#121	—	13	2	no	—
389	#121	—	13	2	no	—
390	#121	—	13	2	no	—
391	#121	—	13	2	no	—
392	#121	C₂×D₁₃	1	2	yes	complemented
393	#121	C₂×D₁₃	1	2	yes	complemented
394	#120	—	13	1	no	—
395	#120	—	13	2	no	—
396	#120	—	13	1	no	—
397	#120	—	13	2	no	—
398	#120	—	13	2	no	—
399	#120	—	13	2	no	—
400	#120	—	13	2	no	—
401	#120	—	13	2	no	—
402	#120	—	13	2	no	—
403	#120	—	13	2	no	—
404	#120	—	13	2	no	—
405	#120	—	13	2	no	—
406	#120	—	13	2	no	—
407	#120	—	13	1	no	—
408	#120	—	13	2	no	—
409	#120	—	13	2	no	—
410	#120	—	13	1	no	—
411	#120	C₂×D₁₃	1	1	yes	characteristic
412	#120	C₂×D₁₃	1	2	yes	complemented
413	#120	C₂×D₁₃	1	1	yes	characteristic, complemented
414	C₄×D₄	—	13	2	no	—
415	C₄×D₄	—	13	2	no	—
416	C₄×D₄	—	13	2	no	—
417	C₄×D₄	—	13	2	no	—
418	C₄×D₄	—	13	2	no	—
419	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
420	#117	—	13	2	no	—
421	#117	—	13	1	no	—
422	C₂×C₂²⋊C₄	—	13	2	no	—
423	C₂×C₂²⋊C₄	—	13	2	no	—
424	C₂×C₂²⋊C₄	—	13	2	no	—
425	C₂×C₂²⋊C₄	—	13	2	no	—
426	C₂×C₂²⋊C₄	—	13	1	no	—
427	C₂×C₂²⋊C₄	—	13	2	no	—
428	C₂×C₂²⋊C₄	—	13	1	no	—
429	C₂×C₁₃	—	2	4	no	—
430	C₂×C₁₃	—	4	1	no	—
431	C₂×C₁₃	—	4	1	no	—
432	C₂×C₁₃	—	4	2	no	—
433	C₂×C₁₃	—	4	2	no	—
434	C₂×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
435	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
436	D₁₃	—	2	2	no	—
437	D₁₃	—	4	2	no	—
438	D₁₃	—	4	1	no	—
439	D₁₃	—	4	1	no	—
440	C₂⁴	—	13	2	no	—
441	C₂⁴	—	13	1	no	—
442	C₂⁴	—	13	2	no	—
443	C₂⁴	—	13	1	no	—
444	C₂⁴	—	13	1	no	—
445	C₂⁴	—	52	4	no	—
446	C₂⁴	—	52	2	no	—
447	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
448	C₂⁴	C₂²×D₁₃	1	2	yes	—
449	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic, complemented
450	#41	—	52	4	no	—
451	#41	—	52	2	no	—
452	C₂×Q₈	—	13	2	no	—
453	C₂×Q₈	—	13	1	no	—
454	C₂×D₄	—	4	4	no	—
455	C₂×D₄	—	4	4	no	—
456	C₂×D₄	—	13	2	no	—
457	C₂×D₄	—	13	2	no	—
458	C₂×D₄	—	13	2	no	—
459	C₂×D₄	—	13	1	no	—
460	C₂×D₄	—	13	2	no	—
461	C₂×D₄	—	13	2	no	—
462	C₂×D₄	—	13	2	no	—
463	C₂×D₄	—	13	2	no	—
464	C₂×D₄	—	13	2	no	—
465	C₂×D₄	—	13	1	no	—
466	C₂×D₄	—	13	2	no	—
467	C₂×D₄	—	13	2	no	—
468	C₂×D₄	—	13	2	no	—
469	C₂×D₄	—	13	2	no	—
470	C₂×D₄	—	13	2	no	—
471	C₂×D₄	—	13	1	no	—
472	C₂×D₄	—	52	2	no	—
473	C₂×D₄	—	52	4	no	—
474	C₂×D₄	—	52	4	no	—
475	C₂×D₄	—	52	2	no	—
476	C₂×D₄	—	52	4	no	—
477	C₂×D₄	C₂²×D₁₃	1	2	yes	—
478	C₂×D₄	C₂²×D₁₃	1	2	yes	—
479	C₂×D₄	C₂²×D₁₃	1	2	yes	—
480	C₂×D₄	C₂²×D₁₃	1	2	yes	—
481	C₂×D₄	C₂²×D₁₃	1	2	yes	—
482	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
483	C₂×D₄	C₂²×D₁₃	1	2	yes	complemented
484	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic, complemented
485	C₂×D₄	C₂²×D₁₃	1	2	yes	complemented
486	C₂²×C₄	—	13	2	no	—
487	C₂²×C₄	—	13	2	no	—
488	C₂²×C₄	—	13	2	no	—
489	C₂²×C₄	—	13	2	no	—
490	C₂²×C₄	—	13	1	no	—
491	C₂²×C₄	—	13	1	no	—
492	C₂²×C₄	—	13	2	no	—
493	C₂²×C₄	—	13	2	no	—
494	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
495	C₂²×C₄	C₂²×D₁₃	1	2	yes	complemented
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	—	13	2	no	—
501	C₄⋊C₄	—	13	2	no	—
502	C₄⋊C₄	—	13	2	no	—
503	C₄⋊C₄	—	13	2	no	—
504	C₄⋊C₄	C₂²×D₁₃	1	2	yes	complemented
505	C₂²⋊C₄	—	13	2	no	—
506	C₂²⋊C₄	—	13	2	no	—
507	C₂²⋊C₄	—	13	2	no	—
508	C₂²⋊C₄	—	13	2	no	—
509	C₂²⋊C₄	—	13	2	no	—
510	C₂²⋊C₄	—	13	1	no	—
511	C₂²⋊C₄	—	13	1	no	—
512	C₂²⋊C₄	—	13	2	no	—
513	C₂²⋊C₄	—	13	2	no	—
514	C₂²⋊C₄	—	13	2	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	2	no	—
521	C₂²⋊C₄	—	13	2	no	—
522	C₂²⋊C₄	—	13	2	no	—
523	C₂²⋊C₄	—	13	2	no	—
524	C₂²⋊C₄	—	13	2	no	—
525	C₂²⋊C₄	—	13	2	no	—
526	C₂²⋊C₄	—	13	2	no	—
527	C₂²⋊C₄	—	13	2	no	—
528	C₂²⋊C₄	—	13	2	no	—
529	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
530	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
531	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic, complemented
532	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	complemented
533	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	complemented
534	C₄²	—	13	1	no	—
535	C₄²	—	13	2	no	—
536	C₄²	—	13	2	no	—
537	C₄²	C₂²×D₁₃	1	1	yes	characteristic, complemented
538	C₁₃	#3532	1	1	yes	characteristic, complemented, Sylow
539	C₂³	—	2	4	no	—
540	C₂³	—	2	4	no	—
541	C₂³	—	4	1	no	—
542	C₂³	—	4	2	no	—
543	C₂³	—	4	2	no	—
544	C₂³	—	4	2	no	—
545	C₂³	—	4	1	no	—
546	C₂³	—	13	1	no	—
547	C₂³	—	13	2	no	—
548	C₂³	—	13	1	no	—
549	C₂³	—	13	1	no	—
550	C₂³	—	26	4	no	—
551	C₂³	—	26	2	no	—
552	C₂³	—	26	2	no	—
553	C₂³	—	26	4	no	—
554	C₂³	—	26	4	no	—
555	C₂³	—	52	2	no	—
556	C₂³	—	52	2	no	—
557	C₂³	—	52	2	no	—
558	C₂³	—	52	2	no	—
559	C₂³	—	52	2	no	—
560	C₂³	—	52	1	no	—
561	C₂³	—	52	2	no	—
562	C₂³	—	52	16	no	—
563	C₂³	C₂³×D₁₃	1	1	yes	characteristic
564	C₂³	C₂³×D₁₃	1	1	yes	characteristic
565	C₂³	C₂³×D₁₃	1	2	yes	—
566	C₂³	C₂³×D₁₃	1	2	yes	—
567	C₂³	C₂³×D₁₃	1	2	yes	—
568	Q₈	—	52	2	no	—
569	Q₈	—	52	1	no	—
570	D₄	—	2	4	no	—
571	D₄	—	2	4	no	—
572	D₄	—	2	4	no	—
573	D₄	—	4	2	no	—
574	D₄	—	4	2	no	—
575	D₄	—	4	2	no	—
576	D₄	—	4	2	no	—
577	D₄	—	4	1	no	—
578	D₄	—	4	1	no	—
579	D₄	—	26	4	no	—
580	D₄	—	26	4	no	—
581	D₄	—	26	4	no	—
582	D₄	—	52	2	no	—
583	D₄	—	52	1	no	—
584	D₄	—	52	2	no	—
585	D₄	—	52	2	no	—
586	D₄	—	52	2	no	—
587	D₄	—	52	2	no	—
588	D₄	—	52	2	no	—
589	D₄	—	52	1	no	—
590	D₄	—	52	1	no	—
591	D₄	—	52	2	no	—
592	D₄	—	52	2	no	—
593	D₄	—	52	2	no	—
594	D₄	—	52	2	no	—
595	C₂×C₄	—	4	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	13	2	no	—
598	C₂×C₄	—	13	2	no	—
599	C₂×C₄	—	13	2	no	—
600	C₂×C₄	—	13	2	no	—
601	C₂×C₄	—	13	2	no	—
602	C₂×C₄	—	13	1	no	—
603	C₂×C₄	—	26	2	no	—
604	C₂×C₄	—	26	4	no	—
605	C₂×C₄	—	52	2	no	—
606	C₂×C₄	—	52	2	no	—
607	C₂×C₄	—	52	1	no	—
608	C₂×C₄	—	52	2	no	—
609	C₂×C₄	—	52	2	no	—
610	C₂×C₄	—	52	2	no	—
611	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₁₃	1	2	yes	—
613	C₂×C₄	C₂³×D₁₃	1	2	yes	—
614	C₂×C₄	C₂³×D₁₃	1	2	yes	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	4	4	no	—
628	C₂²	—	8	4	no	—
629	C₂²	—	8	2	no	—
630	C₂²	—	13	2	no	—
631	C₂²	—	26	2	no	—
632	C₂²	—	26	2	no	—
633	C₂²	—	26	2	no	—
634	C₂²	—	26	2	no	—
635	C₂²	—	26	2	no	—
636	C₂²	—	26	1	no	—
637	C₂²	—	26	1	no	—
638	C₂²	—	26	2	no	—
639	C₂²	—	52	8	no	—
640	C₂²	—	52	8	no	—
641	C₂²	—	52	4	no	—
642	C₂²	—	52	4	no	—
643	C₂²	—	104	2	no	—
644	C₂²	#88251	1	4	yes	—
645	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	1	no	—
650	C₄	—	26	2	no	—
651	C₄	—	26	2	no	—
652	C₄	—	26	2	no	—
653	C₄	—	26	1	no	—
654	C₄	—	26	2	no	—
655	C₄	—	26	2	no	—
656	C₂	—	2	4	no	—
657	C₂	—	4	1	no	—
658	C₂	—	4	2	no	—
659	C₂	—	4	1	no	—
660	C₂	—	4	2	no	—
661	C₂	—	26	2	no	—
662	C₂	—	52	2	no	—
663	C₂	—	52	1	no	—
664	C₂	—	52	1	no	—
665	C₂	C₂×#88251	1	2	yes	—
666	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	D₄²×C₁₃	C₂
hypercenter	D₄²	D₁₃
hypocenter	C₁₃	#3532
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ D₄²

Complements

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

N	H ≅ G/N	type
1. D₄²×C₁₃	C₂	semidirect
2. #11719511	C₂	semidirect
3. #11719509	C₂	semidirect
4. D₄×C₂²⋊D₁₃	C₂	semidirect
5. C₂×#88191	C₂	semidirect
6. #11719425	C₂	semidirect
7. #11719420	C₂	semidirect
8. #11719325	C₂	semidirect
9. #11719322	C₂	semidirect
10. #11719318	C₂	semidirect
11. #11719315	C₂	semidirect
12. #11719299	C₂	semidirect
13. #11719297	C₂	semidirect
14. #11719296	C₂	semidirect
15. #11719294	C₂	semidirect
16. D₁₃×#120	C₂	semidirect
17. #11719292	C₂	semidirect
18. #11719265	C₂	semidirect
19. #11719261	C₂	semidirect
20. C₂⁴×D₁₃	C₂²	semidirect
21. C₂²×D₄×C₁₃	C₂²	semidirect
22. C₂²×D₄×C₁₃	C₂²	semidirect
23. C₂²×C₂²⋊D₁₃	C₂²	semidirect
24. C₂²×C₂²⋊D₁₃	C₂²	semidirect
25. C₂²×C₂²⋊D₁₃	C₂²	semidirect
26. C₂×#6129	C₂²	semidirect
27. C₂×#6129	C₂²	semidirect
28. C₂×D₄×D₁₃	C₂²	semidirect
29. C₂×D₄×D₁₃	C₂²	semidirect
30. C₁₃×#127	C₂²	semidirect
31. C₁₃×#121	C₂²	semidirect
32. C₁₃×#121	C₂²	semidirect
34. C₁₃×#120	C₂²	semidirect
35. C₁₃×#120	C₂²	semidirect
36. C₄×D₄×C₁₃	C₂²	semidirect
37. #88207	C₂²	semidirect
38. #88207	C₂²	semidirect
39. #88207	C₂²	semidirect
40. #88207	C₂²	semidirect
41. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
42. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
43. #88194	C₂²	semidirect
44. #88194	C₂²	semidirect
45. #88193	C₂²	semidirect
46. #88193	C₂²	semidirect
47. #88193	C₂²	semidirect
48. #88193	C₂²	semidirect
49. #88193	C₂²	semidirect
50. #88193	C₂²	semidirect
51. #88193	C₂²	semidirect
52. #88193	C₂²	semidirect
53. #88192	C₂²	semidirect
54. #88192	C₂²	semidirect
56. #88191	C₂²	semidirect
57. #88191	C₂²	semidirect
58. #88191	C₂²	semidirect
59. #88191	C₂²	semidirect
60. #88191	C₂²	semidirect
61. #88191	C₂²	semidirect
62. #88191	C₂²	semidirect
63. #88191	C₂²	semidirect
64. #88191	C₂²	semidirect
65. #88191	C₂²	semidirect
66. #88190	C₂²	semidirect
67. #88190	C₂²	semidirect
68. #88189	C₂²	semidirect
69. #88189	C₂²	semidirect
70. #88189	C₂²	semidirect
71. #88189	C₂²	semidirect
72. D₄×Dic₁₃	C₂²	semidirect
73. D₄×Dic₁₃	C₂²	semidirect
74. #88184	C₂²	semidirect
75. #88183	C₂²	semidirect
76. #88183	C₂²	semidirect
77. C₄×C₂²⋊D₁₃	C₂²	semidirect
78. C₄×C₂²⋊D₁₃	C₂²	semidirect
79. C₂×#6103	C₂²	semidirect
80. C₂×#6103	C₂²	semidirect
81. #88178	C₂²	semidirect
82. #88152	C₂²	semidirect
83. #88152	C₂²	semidirect
84. #88150	C₂²	semidirect
85. #88148	C₂²	semidirect
86. #88140	C₂²	semidirect
87. #88140	C₂²	semidirect
88. #88139	C₂²	semidirect
89. #88139	C₂²	semidirect
90. #88139	C₂²	semidirect
91. #88139	C₂²	semidirect
92. #88138	C₂²	semidirect
93. #88138	C₂²	semidirect
94. #88137	C₂²	semidirect
95. #88136	C₂²	semidirect
96. #88136	C₂²	semidirect
97. #88135	C₂²	semidirect
98. C₂²⋊C₄×D₁₃	C₂²	semidirect
99. C₂²⋊C₄×D₁₃	C₂²	semidirect
100. C₂²⋊C₄×D₁₃	C₂²	semidirect
101. #88133	C₂²	semidirect
102. #88132	C₂²	semidirect
103. #88131	C₂²	semidirect
104. #88130	C₂²	semidirect
105. #88129	C₂²	semidirect
106. #88126	C₂²	semidirect
109. C₂⁴×C₁₃	C₂³	semidirect
125. C₂×D₄×C₁₃	C₂³	semidirect
126. C₂×D₄×C₁₃	C₂³	semidirect
127. C₂×D₄×C₁₃	C₂³	semidirect
129. C₂²×C₄×C₁₃	C₂³	semidirect
145. C₂×C₂²⋊D₁₃	C₂³	semidirect
146. C₂×C₂²⋊D₁₃	C₂³	semidirect
149. C₂²×Dic₁₃	C₂³	semidirect
150. C₂²×Dic₁₃	C₂³	semidirect
151. C₂²×Dic₁₃	C₂³	semidirect
160. C₂×C₄×D₁₃	C₂³	semidirect
161. C₂×Dic₂₆	C₂³	semidirect
162. C₂×Dic₂₆	C₂³	semidirect
163. C₁₃×C₄⋊C₄	C₂³	semidirect
166. C₁₃×C₂²⋊C₄	C₂³	semidirect
167. C₁₃×C₂²⋊C₄	C₂³	semidirect
168. C₁₃×C₂²⋊C₄	C₂³	semidirect
169. C₄²×C₁₃	C₂³	semidirect
176. C₂²⋊Dic₁₃	C₂³	semidirect
177. C₂²⋊Dic₁₃	C₂³	semidirect
178. C₂²⋊Dic₁₃	C₂³	semidirect
179. C₂²⋊Dic₁₃	C₂³	semidirect
180. C₂²⋊Dic₁₃	C₂³	semidirect
181. C₂²⋊Dic₁₃	C₂³	semidirect
193. #6103	C₂³	semidirect
194. C₄⋊Dic₁₃	C₂³	semidirect
195. C₄⋊Dic₁₃	C₂³	semidirect
196. #6101	C₂³	semidirect
197. #6101	C₂³	semidirect
198. #6101	C₂³	semidirect
199. #6101	C₂³	semidirect
200. #6101	C₂³	semidirect
201. #6101	C₂³	semidirect
202. C₄×Dic₁₃	C₂³	semidirect
203. C₄×Dic₁₃	C₂³	semidirect
204. C₄×Dic₁₃	C₂³	semidirect
291. D₄²	D₁₃	semidirect
350. C₂²×D₄	C₂×D₁₃	semidirect
351. C₂²×D₄	C₂×D₁₃	semidirect
354. #127	C₂×D₁₃	semidirect
392. #121	C₂×D₁₃	semidirect
393. #121	C₂×D₁₃	semidirect
412. #120	C₂×D₁₃	semidirect
413. #120	C₂×D₁₃	semidirect
419. C₄×D₄	C₂×D₁₃	semidirect
449. C₂⁴	C₂²×D₁₃	semidirect
483. C₂×D₄	C₂²×D₁₃	semidirect
484. C₂×D₄	C₂²×D₁₃	semidirect
485. C₂×D₄	C₂²×D₁₃	semidirect
495. C₂²×C₄	C₂²×D₁₃	semidirect
504. C₄⋊C₄	C₂²×D₁₃	semidirect
531. C₂²⋊C₄	C₂²×D₁₃	semidirect
532. C₂²⋊C₄	C₂²×D₁₃	semidirect
533. C₂²⋊C₄	C₂²×D₁₃	semidirect
537. C₄²	C₂²×D₁₃	semidirect
538. C₁₃	#3532	semidirect

Maximal subgroups

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

subgroup	index
D₄²×C₁₃	2
#11719511	2
#11719509	2
D₄×C₂²⋊D₁₃	2
C₂×#88191	2
#11719425	2
#11719420	2
#11719325	2
#11719322	2
#11719318	2
#11719315	2
#11719299	2
#11719297	2
#11719296	2
#11719294	2
D₁₃×#120	2
#11719292	2
#11719265	2
#11719261	2
#3532	13