Subgroups — #13129185

Order 1664.

1060 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#534	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719511	C₂	1	2	yes	maximal, complemented
3	#11719509	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#88190	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719367	C₂	1	2	yes	maximal, complemented
6	#11719364	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719356	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719354	C₂	1	2	yes	maximal, complemented
9	#11719353	C₂	1	2	yes	maximal, complemented
10	#11719326	C₂	1	2	yes	maximal, complemented
11	#11719321	C₂	1	2	yes	maximal, complemented
12	#11719318	C₂	1	2	yes	maximal, complemented
13	#11719308	C₂	1	2	yes	maximal, complemented
14	#11719299	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719298	C₂	1	2	yes	maximal, complemented
16	#11719296	C₂	1	2	yes	maximal, complemented
17	#11719292	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719292	C₂	1	2	yes	maximal, complemented
19	#11719200	C₂	1	2	yes	maximal, complemented
20	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
23	C₂×#6129	C₂²	1	2	yes	—
24	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#123	C₂²	1	1	yes	characteristic
26	C₁₃×#123	C₂²	1	2	yes	complemented
27	C₁₃×#123	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#121	C₂²	1	2	yes	—
29	C₁₃×#121	C₂²	1	2	yes	complemented
30	C₁₃×#120	C₂²	1	2	yes	—
31	C₁₃×#120	C₂²	1	1	yes	characteristic
32	C₁₃×#120	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
34	#88207	C₂²	1	2	yes	—
35	#88207	C₂²	1	2	yes	complemented
36	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
37	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
38	C₂×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	complemented
40	#88193	C₂²	1	2	yes	—
41	#88193	C₂²	1	2	yes	—
42	#88193	C₂²	1	2	yes	complemented
43	#88193	C₂²	1	2	yes	complemented
44	#88193	C₂²	1	2	yes	complemented
45	#88192	C₂²	1	2	yes	complemented
46	#88192	C₂²	1	2	yes	complemented
47	#88191	C₂²	1	1	yes	characteristic
48	#88191	C₂²	1	1	yes	characteristic, complemented
49	#88191	C₂²	1	2	yes	complemented
50	#88190	C₂²	1	1	yes	characteristic
51	#88190	C₂²	1	1	yes	characteristic
52	#88190	C₂²	1	2	yes	complemented
53	#88190	C₂²	1	2	yes	complemented
54	#88190	C₂²	1	1	yes	characteristic, complemented
55	#88190	C₂²	1	1	yes	characteristic, complemented
56	#88190	C₂²	1	2	yes	complemented
57	#88190	C₂²	1	2	yes	complemented
58	#88189	C₂²	1	1	yes	characteristic
59	#88189	C₂²	1	1	yes	characteristic, complemented
60	#88189	C₂²	1	2	yes	complemented
61	#88189	C₂²	1	2	yes	complemented
62	#88189	C₂²	1	2	yes	complemented
63	#88189	C₂²	1	2	yes	complemented
64	D₄×Dic₁₃	C₂²	1	2	yes	complemented
65	D₄×Dic₁₃	C₂²	1	2	yes	complemented
66	D₄×Dic₁₃	C₂²	1	2	yes	complemented
67	#88183	C₂²	1	2	yes	complemented
68	#88183	C₂²	1	2	yes	complemented
69	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
70	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
71	#88180	C₂²	1	2	yes	complemented
72	#88178	C₂²	1	2	yes	complemented
73	#88178	C₂²	1	2	yes	complemented
74	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
75	#88152	C₂²	1	2	yes	complemented
76	#88150	C₂²	1	2	yes	complemented
77	#88150	C₂²	1	2	yes	complemented
78	#88146	C₂²	1	2	yes	complemented
79	#88143	C₂²	1	2	yes	complemented
80	#88142	C₂²	1	2	yes	complemented
81	#88142	C₂²	1	2	yes	complemented
82	#88141	C₂²	1	2	yes	complemented
83	#88140	C₂²	1	2	yes	complemented
84	#88139	C₂²	1	2	yes	complemented
85	#88139	C₂²	1	2	yes	complemented
86	#88139	C₂²	1	2	yes	complemented
87	#88139	C₂²	1	2	yes	complemented
88	#88139	C₂²	1	2	yes	complemented
89	#88137	C₂²	1	2	yes	complemented
90	#88137	C₂²	1	2	yes	complemented
91	#88135	C₂²	1	2	yes	complemented
92	#88135	C₂²	1	2	yes	complemented
93	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	complemented
94	#88133	C₂²	1	2	yes	complemented
95	#88133	C₂²	1	2	yes	complemented
96	#88133	C₂²	1	2	yes	complemented
97	#88133	C₂²	1	2	yes	complemented
98	#88133	C₂²	1	2	yes	complemented
99	#88132	C₂²	1	2	yes	complemented
100	#88132	C₂²	1	2	yes	complemented
101	#88132	C₂²	1	2	yes	complemented
102	#88132	C₂²	1	2	yes	complemented
103	#88132	C₂²	1	2	yes	complemented
104	#88131	C₂²	1	2	yes	complemented
105	#88131	C₂²	1	2	yes	complemented
106	#88131	C₂²	1	2	yes	complemented
107	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
108	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
109	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
110	C₂³×D₁₃	C₂³	1	1	yes	characteristic
111	C₂×D₄×C₁₃	—	4	2	no	—
112	C₂×D₄×C₁₃	—	4	2	no	—
113	C₂×D₄×C₁₃	C₂³	1	2	yes	—
114	C₂×D₄×C₁₃	C₂³	1	2	yes	—
115	C₂×D₄×C₁₃	C₂³	1	2	yes	—
116	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
117	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
118	C₂×D₄×C₁₃	C₂³	1	2	yes	—
119	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
120	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
124	C₂×C₂²⋊D₁₃	—	4	2	no	—
125	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
131	C₂²×Dic₁₃	C₂³	1	2	yes	—
132	C₂²×Dic₁₃	C₂³	1	2	yes	—
133	C₂²×Dic₁₃	C₂³	1	2	yes	—
134	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
135	C₂²×Dic₁₃	C₂³	1	2	yes	—
136	C₂²×Dic₁₃	C₂³	1	2	yes	—
137	#6129	—	4	4	no	—
138	C₂×C₄×D₁₃	C₂³	1	2	yes	—
139	C₂×C₄×D₁₃	C₂³	1	2	yes	—
140	C₂×Dic₂₆	—	4	2	no	—
141	C₂×Dic₂₆	C₂³	1	2	yes	—
142	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
143	C₂×Dic₂₆	C₂³	1	2	yes	—
144	C₂×Dic₂₆	C₂³	1	2	yes	—
145	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
146	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
154	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
155	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
156	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
157	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
158	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
159	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
160	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
161	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
162	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
163	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
164	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
165	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
166	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
167	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
168	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
169	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
170	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
172	#6103	C₂³	1	2	yes	—
173	#6103	C₂³	1	2	yes	—
174	#6103	C₂³	1	2	yes	—
175	#6103	C₂³	1	2	yes	—
176	#6103	C₂³	1	2	yes	—
177	#6103	C₂³	1	2	yes	—
178	C₄⋊Dic₁₃	C₂³	1	2	yes	—
179	C₄⋊Dic₁₃	C₂³	1	2	yes	—
180	C₄⋊Dic₁₃	C₂³	1	2	yes	—
181	C₄⋊Dic₁₃	C₂³	1	2	yes	—
182	#6101	C₂³	1	2	yes	—
183	#6101	C₂³	1	2	yes	—
184	#6101	C₂³	1	2	yes	—
185	#6101	C₂³	1	2	yes	—
186	#6101	C₂³	1	2	yes	—
187	#6101	C₂³	1	2	yes	—
188	#6101	C₂³	1	2	yes	—
189	#6101	C₂³	1	2	yes	—
190	#6101	C₂³	1	2	yes	—
191	#6101	C₂³	1	2	yes	—
192	C₄×Dic₁₃	C₂³	1	2	yes	—
193	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
194	C₄×Dic₁₃	C₂³	1	2	yes	—
195	C₄×Dic₁₃	C₂³	1	2	yes	—
196	C₄×Dic₁₃	C₂³	1	2	yes	—
197	C₄×Dic₁₃	C₂³	1	2	yes	—
198	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
199	#3545	—	13	1	no	maximal, Sylow
200	C₂³×C₁₃	—	2	2	no	—
201	C₂³×C₁₃	—	2	2	no	—
202	C₂³×C₁₃	—	4	1	no	—
203	C₂³×C₁₃	—	4	2	no	—
204	C₂³×C₁₃	—	4	2	no	—
205	C₂³×C₁₃	—	4	2	no	—
206	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
207	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
208	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
209	C₂³×C₁₃	C₂⁴	1	2	yes	—
210	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
211	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
212	C₂²×D₁₃	—	4	1	no	—
213	C₂²×D₁₃	—	4	2	no	—
214	C₂²×D₁₃	C₂⁴	1	2	yes	—
215	D₄×C₁₃	—	2	4	no	—
216	D₄×C₁₃	—	4	1	no	—
217	D₄×C₁₃	—	4	1	no	—
218	D₄×C₁₃	—	4	1	no	—
219	D₄×C₁₃	—	4	1	no	—
220	D₄×C₁₃	—	4	2	no	—
221	D₄×C₁₃	—	4	2	no	—
222	D₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
227	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
230	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
231	C₂²⋊D₁₃	—	2	4	no	—
232	C₂²⋊D₁₃	—	4	2	no	—
233	C₂²⋊D₁₃	—	4	2	no	—
234	C₂²⋊D₁₃	—	4	2	no	—
235	C₂²⋊D₁₃	—	4	2	no	—
236	C₂²⋊D₁₃	—	4	2	no	—
237	C₂×Dic₁₃	—	2	4	no	—
238	C₂×Dic₁₃	—	4	2	no	—
239	C₂×Dic₁₃	—	4	2	no	—
240	C₂×Dic₁₃	—	4	2	no	—
241	C₂×Dic₁₃	—	4	2	no	—
242	C₂×Dic₁₃	—	4	1	no	—
243	C₂×Dic₁₃	C₂⁴	1	2	yes	—
244	C₂×Dic₁₃	C₂⁴	1	2	yes	—
245	C₂×Dic₁₃	C₂⁴	1	2	yes	—
246	C₂×Dic₁₃	C₂⁴	1	2	yes	—
247	C₂×Dic₁₃	C₂⁴	1	2	yes	—
248	C₂×Dic₁₃	C₂⁴	1	2	yes	—
249	C₂×Dic₁₃	C₂⁴	1	2	yes	—
250	C₄×D₁₃	—	4	2	no	—
251	C₄×D₁₃	—	4	2	no	—
252	Dic₂₆	—	4	1	no	—
253	Dic₂₆	—	4	2	no	—
254	Dic₂₆	—	4	1	no	—
255	Dic₂₆	—	4	2	no	—
256	Dic₂₆	—	4	2	no	—
257	#563	—	13	1	no	—
258	#562	—	13	2	no	—
259	H(3,𝔽₄)	—	13	1	no	—
260	#555	—	13	2	no	—
261	#551	—	13	1	no	—
262	#551	—	13	2	no	—
263	#551	—	13	1	no	—
264	#551	—	13	2	no	—
265	#546	—	13	2	no	—
266	#546	—	13	2	no	—
267	#542	—	13	2	no	—
268	#542	—	13	2	no	—
269	#538	—	13	2	no	—
270	#538	—	13	2	no	—
271	#536	—	13	2	no	—
272	#534	—	13	1	no	—
273	#534	D₁₃	1	1	yes	characteristic, complemented
274	#529	—	13	2	no	—
275	C₂×#124	—	13	1	no	—
276	C₂²×C₁₃	—	2	2	no	—
277	C₂²×C₁₃	—	2	2	no	—
278	C₂²×C₁₃	—	2	1	no	—
279	C₂²×C₁₃	—	2	1	no	—
280	C₂²×C₁₃	—	2	1	no	—
281	C₂²×C₁₃	—	2	1	no	—
282	C₂²×C₁₃	—	2	2	no	—
283	C₂²×C₁₃	—	2	2	no	—
284	C₂²×C₁₃	—	2	2	no	—
285	C₂²×C₁₃	—	2	2	no	—
286	C₂²×C₁₃	—	2	2	no	—
287	C₂²×C₁₃	—	2	2	no	—
288	C₂²×C₁₃	—	8	2	no	—
289	C₂²×C₁₃	—	8	2	no	—
290	C₂²×C₁₃	—	8	2	no	—
291	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
292	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
293	C₂×D₁₃	—	2	2	no	—
294	C₂×D₁₃	—	2	2	no	—
295	C₂×D₁₃	—	2	2	no	—
296	C₂×D₁₃	—	8	2	no	—
297	C₄×C₁₃	—	2	1	no	—
298	C₄×C₁₃	—	2	1	no	—
299	C₄×C₁₃	—	2	2	no	—
300	C₄×C₁₃	—	2	2	no	—
301	C₄×C₁₃	—	2	2	no	—
302	Dic₁₃	—	2	2	no	—
303	Dic₁₃	—	2	2	no	—
304	Dic₁₃	—	2	2	no	—
305	Dic₁₃	—	2	2	no	—
306	Dic₁₃	—	2	2	no	—
307	Dic₁₃	—	2	2	no	—
308	Dic₁₃	—	2	2	no	—
309	C₂×#41	—	13	2	no	—
310	C₂²×Q₈	—	13	1	no	—
311	C₂²×D₄	—	13	1	no	—
312	C₂²×D₄	C₂×D₁₃	1	1	yes	characteristic
313	C₂²×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
314	C₄⋊Q₈	—	13	2	no	—
315	C₄⋊Q₈	—	13	2	no	—
316	#126	—	13	2	no	—
317	#126	—	13	2	no	—
318	#126	—	13	2	no	—
319	#126	—	13	2	no	—
320	#126	—	13	2	no	—
321	#126	—	13	2	no	—
322	#125	—	13	2	no	—
323	#124	—	13	2	no	—
324	#124	—	13	2	no	—
325	#124	—	13	1	no	—
326	#124	—	13	1	no	—
327	#124	—	13	1	no	—
328	#124	—	13	1	no	—
329	#124	—	13	2	no	—
330	#124	—	13	2	no	—
331	#124	—	13	2	no	—
332	#124	—	13	2	no	—
333	#124	—	13	2	no	—
334	#124	—	13	2	no	—
335	#124	—	13	2	no	—
336	#123	—	13	1	no	—
337	#123	—	13	1	no	—
338	#123	—	13	2	no	—
339	#123	—	13	2	no	—
340	#123	—	13	2	no	—
341	#123	—	13	2	no	—
342	#123	—	13	2	no	—
343	#123	—	13	2	no	—
344	#123	—	13	2	no	—
345	#123	—	13	2	no	—
346	#123	—	13	2	no	—
347	#123	C₂×D₁₃	1	1	yes	characteristic
348	#123	C₂×D₁₃	1	2	yes	complemented
349	#123	C₂×D₁₃	1	1	yes	characteristic, complemented
350	C₂²⋊Q₈	—	13	2	no	—
351	C₂²⋊Q₈	—	13	2	no	—
352	C₂²⋊Q₈	—	13	2	no	—
353	C₂²⋊Q₈	—	13	2	no	—
354	C₂²⋊Q₈	—	13	2	no	—
355	C₂²⋊Q₈	—	13	2	no	—
356	C₂²⋊Q₈	—	13	2	no	—
357	C₂²⋊Q₈	—	13	2	no	—
358	C₂²⋊Q₈	—	13	2	no	—
359	#121	—	13	2	no	—
360	#121	—	13	2	no	—
361	#121	—	13	2	no	—
362	#121	—	13	2	no	—
363	#121	—	13	2	no	—
364	#121	—	13	2	no	—
365	#121	—	13	2	no	—
366	#121	C₂×D₁₃	1	2	yes	—
367	#121	C₂×D₁₃	1	2	yes	complemented
368	#120	—	13	2	no	—
369	#120	—	13	2	no	—
370	#120	—	13	1	no	—
371	#120	—	13	1	no	—
372	#120	—	13	2	no	—
373	#120	C₂×D₁₃	1	2	yes	—
374	#120	C₂×D₁₃	1	1	yes	characteristic
375	#120	C₂×D₁₃	1	1	yes	characteristic, complemented
376	C₄×Q₈	—	13	2	no	—
377	C₄×D₄	—	13	2	no	—
378	C₄×D₄	—	13	2	no	—
379	C₄×D₄	—	13	2	no	—
380	C₄×D₄	—	13	2	no	—
381	C₄×D₄	—	13	2	no	—
382	C₄×D₄	—	13	2	no	—
383	C₄×D₄	—	13	2	no	—
384	#117	—	13	2	no	—
385	#117	—	13	2	no	—
386	#117	—	13	2	no	—
387	#117	—	13	2	no	—
388	#117	—	13	2	no	—
389	C₂×C₂²⋊C₄	—	13	2	no	—
390	C₂×C₂²⋊C₄	—	13	2	no	—
391	C₂×C₂²⋊C₄	—	13	1	no	—
392	C₂×C₂²⋊C₄	—	13	2	no	—
393	C₂×C₂²⋊C₄	—	13	2	no	—
394	C₂×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
395	C₂×C₄²	—	13	1	no	—
396	C₂×C₁₃	—	2	2	no	—
397	C₂×C₁₃	—	4	1	no	—
398	C₂×C₁₃	—	4	2	no	—
399	C₂×C₁₃	—	4	1	no	—
400	C₂×C₁₃	—	4	1	no	—
401	C₂×C₁₃	—	4	1	no	—
402	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
403	C₂×C₁₃	#585	1	2	yes	—
404	D₁₃	—	4	2	no	—
405	C₂⁴	—	13	1	no	—
406	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
407	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
408	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
409	#41	—	52	4	no	—
410	C₂×Q₈	—	13	2	no	—
411	C₂×Q₈	—	13	1	no	—
412	C₂×Q₈	—	13	2	no	—
413	C₂×Q₈	—	13	2	no	—
414	C₂×Q₈	—	13	1	no	—
415	C₂×Q₈	—	52	2	no	—
416	C₂×D₄	—	4	2	no	—
417	C₂×D₄	—	4	2	no	—
418	C₂×D₄	—	13	2	no	—
419	C₂×D₄	—	13	2	no	—
420	C₂×D₄	—	13	2	no	—
421	C₂×D₄	—	13	2	no	—
422	C₂×D₄	—	13	2	no	—
423	C₂×D₄	—	13	2	no	—
424	C₂×D₄	—	52	2	no	—
425	C₂×D₄	C₂²×D₁₃	1	2	yes	—
426	C₂×D₄	C₂²×D₁₃	1	2	yes	—
427	C₂×D₄	C₂²×D₁₃	1	2	yes	—
428	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
429	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
430	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
431	C₂×D₄	C₂²×D₁₃	1	2	yes	—
432	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
433	C₂²×C₄	—	13	2	no	—
434	C₂²×C₄	—	13	2	no	—
435	C₂²×C₄	—	13	2	no	—
436	C₂²×C₄	—	13	2	no	—
437	C₂²×C₄	—	13	2	no	—
438	C₂²×C₄	—	13	1	no	—
439	C₂²×C₄	—	13	2	no	—
440	C₂²×C₄	—	13	2	no	—
441	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
442	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
443	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
444	C₄⋊C₄	—	13	2	no	—
445	C₄⋊C₄	—	13	2	no	—
446	C₄⋊C₄	—	13	2	no	—
447	C₄⋊C₄	—	13	2	no	—
448	C₄⋊C₄	—	13	2	no	—
449	C₄⋊C₄	—	13	2	no	—
450	C₄⋊C₄	—	13	2	no	—
451	C₄⋊C₄	—	13	2	no	—
452	C₄⋊C₄	—	13	2	no	—
453	C₄⋊C₄	—	13	2	no	—
454	C₄⋊C₄	—	13	2	no	—
455	C₄⋊C₄	—	13	2	no	—
456	C₄⋊C₄	—	13	2	no	—
457	C₄⋊C₄	—	13	2	no	—
458	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
459	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
460	C₂²⋊C₄	—	13	2	no	—
461	C₂²⋊C₄	—	13	2	no	—
462	C₂²⋊C₄	—	13	2	no	—
463	C₂²⋊C₄	—	13	2	no	—
464	C₂²⋊C₄	—	13	2	no	—
465	C₂²⋊C₄	—	13	2	no	—
466	C₂²⋊C₄	—	13	2	no	—
467	C₂²⋊C₄	—	13	2	no	—
468	C₂²⋊C₄	—	13	2	no	—
469	C₂²⋊C₄	—	13	1	no	—
470	C₂²⋊C₄	—	13	1	no	—
471	C₂²⋊C₄	—	13	2	no	—
472	C₂²⋊C₄	—	13	2	no	—
473	C₂²⋊C₄	—	13	2	no	—
474	C₂²⋊C₄	—	13	2	no	—
475	C₂²⋊C₄	—	13	2	no	—
476	C₂²⋊C₄	—	13	2	no	—
477	C₂²⋊C₄	—	13	2	no	—
478	C₂²⋊C₄	—	13	2	no	—
479	C₂²⋊C₄	—	13	2	no	—
480	C₂²⋊C₄	—	13	2	no	—
481	C₂²⋊C₄	—	13	2	no	—
482	C₂²⋊C₄	—	13	2	no	—
483	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
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	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
488	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
489	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
490	C₄²	—	13	1	no	—
491	C₄²	—	13	2	no	—
492	C₄²	—	13	1	no	—
493	C₄²	—	13	2	no	—
494	C₄²	—	13	2	no	—
495	C₄²	—	13	2	no	—
496	C₄²	—	13	2	no	—
497	C₁₃	#3545	1	1	yes	characteristic, complemented, Sylow
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	13	2	no	—
505	C₂³	—	52	1	no	—
506	C₂³	—	52	2	no	—
507	C₂³	C₂³×D₁₃	1	1	yes	characteristic
508	C₂³	C₂³×D₁₃	1	1	yes	characteristic
509	C₂³	C₂³×D₁₃	1	1	yes	characteristic
510	C₂³	C₂³×D₁₃	1	2	yes	—
511	C₂³	C₂³×D₁₃	1	1	yes	characteristic
512	C₂³	C₂³×D₁₃	1	1	yes	characteristic
513	Q₈	—	52	2	no	—
514	Q₈	—	52	1	no	—
515	Q₈	—	52	2	no	—
516	Q₈	—	52	1	no	—
517	Q₈	—	52	2	no	—
518	D₄	—	2	4	no	—
519	D₄	—	4	1	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	1	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	26	4	no	—
527	D₄	—	52	2	no	—
528	D₄	—	52	2	no	—
529	D₄	—	52	2	no	—
530	D₄	—	52	2	no	—
531	D₄	—	52	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	13	2	no	—
536	C₂×C₄	—	13	2	no	—
537	C₂×C₄	—	13	2	no	—
538	C₂×C₄	—	13	2	no	—
539	C₂×C₄	—	13	2	no	—
540	C₂×C₄	—	13	2	no	—
541	C₂×C₄	—	13	2	no	—
542	C₂×C₄	—	26	4	no	—
543	C₂×C₄	—	52	2	no	—
544	C₂×C₄	—	52	2	no	—
545	C₂×C₄	—	52	2	no	—
546	C₂×C₄	—	52	2	no	—
547	C₂×C₄	—	52	2	no	—
548	C₂×C₄	—	52	1	no	—
549	C₂×C₄	—	52	2	no	—
550	C₂×C₄	C₂³×D₁₃	1	2	yes	—
551	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
552	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
553	C₂×C₄	C₂³×D₁₃	1	2	yes	—
554	C₂×C₄	C₂³×D₁₃	1	2	yes	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	8	2	no	—
568	C₂²	—	8	2	no	—
569	C₂²	—	8	2	no	—
570	C₂²	—	26	2	no	—
571	C₂²	—	26	2	no	—
572	C₂²	—	26	2	no	—
573	C₂²	—	104	2	no	—
574	C₂²	#88251	1	2	yes	—
575	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
576	C₄	—	2	1	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	2	no	—
581	C₄	—	26	2	no	—
582	C₄	—	26	2	no	—
583	C₄	—	26	2	no	—
584	C₄	—	26	2	no	—
585	C₄	—	26	2	no	—
586	C₄	—	26	2	no	—
587	C₄	—	26	2	no	—
588	C₂	—	2	2	no	—
589	C₂	—	4	1	no	—
590	C₂	—	4	1	no	—
591	C₂	—	4	2	no	—
592	C₂	—	4	1	no	—
593	C₂	—	4	1	no	—
594	C₂	—	52	2	no	—
595	C₂	C₂×#88251	1	1	yes	characteristic
596	C₂	#11719650	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#534	C₂
hypercenter	#534	D₁₃
hypocenter	C₁₃	#3545
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #534

Complements

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

N	H ≅ G/N	type
1. C₁₃×#534	C₂	semidirect
2. #11719511	C₂	semidirect
3. #11719509	C₂	semidirect
4. C₂×#88190	C₂	semidirect
5. #11719367	C₂	semidirect
6. #11719364	C₂	semidirect
7. #11719356	C₂	semidirect
8. #11719354	C₂	semidirect
9. #11719353	C₂	semidirect
10. #11719326	C₂	semidirect
11. #11719321	C₂	semidirect
12. #11719318	C₂	semidirect
13. #11719308	C₂	semidirect
14. #11719299	C₂	semidirect
15. #11719298	C₂	semidirect
16. #11719296	C₂	semidirect
17. #11719292	C₂	semidirect
18. #11719292	C₂	semidirect
19. #11719200	C₂	semidirect
21. C₂²×D₄×C₁₃	C₂²	semidirect
22. C₂²×C₂²⋊D₁₃	C₂²	semidirect
24. C₂²×Dic₂₆	C₂²	semidirect
26. C₁₃×#123	C₂²	semidirect
27. C₁₃×#123	C₂²	semidirect
29. C₁₃×#121	C₂²	semidirect
32. C₁₃×#120	C₂²	semidirect
33. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
35. #88207	C₂²	semidirect
36. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
37. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
38. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
39. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
42. #88193	C₂²	semidirect
43. #88193	C₂²	semidirect
44. #88193	C₂²	semidirect
45. #88192	C₂²	semidirect
46. #88192	C₂²	semidirect
48. #88191	C₂²	semidirect
49. #88191	C₂²	semidirect
52. #88190	C₂²	semidirect
53. #88190	C₂²	semidirect
54. #88190	C₂²	semidirect
55. #88190	C₂²	semidirect
56. #88190	C₂²	semidirect
57. #88190	C₂²	semidirect
59. #88189	C₂²	semidirect
60. #88189	C₂²	semidirect
61. #88189	C₂²	semidirect
62. #88189	C₂²	semidirect
63. #88189	C₂²	semidirect
64. D₄×Dic₁₃	C₂²	semidirect
65. D₄×Dic₁₃	C₂²	semidirect
66. D₄×Dic₁₃	C₂²	semidirect
67. #88183	C₂²	semidirect
68. #88183	C₂²	semidirect
69. C₄×C₂²⋊D₁₃	C₂²	semidirect
70. C₄×C₂²⋊D₁₃	C₂²	semidirect
71. #88180	C₂²	semidirect
72. #88178	C₂²	semidirect
73. #88178	C₂²	semidirect
74. C₂×C₄×Dic₁₃	C₂²	semidirect
75. #88152	C₂²	semidirect
76. #88150	C₂²	semidirect
77. #88150	C₂²	semidirect
78. #88146	C₂²	semidirect
79. #88143	C₂²	semidirect
80. #88142	C₂²	semidirect
81. #88142	C₂²	semidirect
82. #88141	C₂²	semidirect
83. #88140	C₂²	semidirect
84. #88139	C₂²	semidirect
85. #88139	C₂²	semidirect
86. #88139	C₂²	semidirect
87. #88139	C₂²	semidirect
88. #88139	C₂²	semidirect
89. #88137	C₂²	semidirect
90. #88137	C₂²	semidirect
91. #88135	C₂²	semidirect
92. #88135	C₂²	semidirect
93. C₂²⋊C₄×D₁₃	C₂²	semidirect
94. #88133	C₂²	semidirect
95. #88133	C₂²	semidirect
96. #88133	C₂²	semidirect
97. #88133	C₂²	semidirect
98. #88133	C₂²	semidirect
99. #88132	C₂²	semidirect
100. #88132	C₂²	semidirect
101. #88132	C₂²	semidirect
102. #88132	C₂²	semidirect
103. #88132	C₂²	semidirect
104. #88131	C₂²	semidirect
105. #88131	C₂²	semidirect
106. #88131	C₂²	semidirect
273. #534	D₁₃	semidirect
313. C₂²×D₄	C₂×D₁₃	semidirect
348. #123	C₂×D₁₃	semidirect
349. #123	C₂×D₁₃	semidirect
367. #121	C₂×D₁₃	semidirect
375. #120	C₂×D₁₃	semidirect
394. C₂×C₂²⋊C₄	C₂×D₁₃	semidirect
497. C₁₃	#3545	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#534	2
#11719511	2
#11719509	2
C₂×#88190	2
#11719367	2
#11719364	2
#11719356	2
#11719354	2
#11719353	2
#11719326	2
#11719321	2
#11719318	2
#11719308	2
#11719299	2
#11719298	2
#11719296	2
#11719292	2
#11719200	2
#3545	13