Subgroups — #13129244

Order 1664.

1002 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719432	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719427	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719417	C₂	1	2	yes	maximal, complemented
5	#11719407	C₂	1	2	yes	maximal, complemented
6	#11719386	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719380	C₂	1	2	yes	maximal, complemented
8	#11719376	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719374	C₂	1	2	yes	maximal, complemented
10	#11719367	C₂	1	2	yes	maximal, complemented
11	#11719353	C₂	1	2	yes	maximal, complemented
12	#11719351	C₂	1	2	yes	maximal, complemented
13	#11719348	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719337	C₂	1	2	yes	maximal, complemented
15	#11719327	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719308	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719301	C₂	1	1	yes	maximal, characteristic
18	#11719273	C₂	1	1	yes	maximal, characteristic, complemented
19	Q₈×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719264	C₂	1	1	yes	maximal, characteristic, complemented
21	D₄×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719239	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719222	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₁₃	C₂²	1	2	yes	—
25	C₂×#6129	C₂²	1	2	yes	—
26	C₂²×Dic₂₆	C₂²	1	2	yes	—
27	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₁₃×#126	C₂²	1	2	yes	—
29	C₁₃×#124	C₂²	1	2	yes	—
30	C₁₃×#124	C₂²	1	1	yes	characteristic
31	C₁₃×#123	C₂²	1	2	yes	—
32	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
34	C₁₃×#121	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#117	C₂²	1	1	yes	characteristic
38	#88201	C₂²	1	1	yes	characteristic
39	#88200	C₂²	1	2	yes	—
40	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic
41	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic
42	#88198	C₂²	1	2	yes	—
43	#88198	C₂²	1	2	yes	—
44	#88198	C₂²	1	1	yes	characteristic
45	#88194	C₂²	1	1	yes	characteristic
46	#88193	C₂²	1	2	yes	—
47	#88190	C₂²	1	1	yes	characteristic
48	#88190	C₂²	1	2	yes	—
49	#88189	C₂²	1	2	yes	—
50	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
51	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
52	#88184	C₂²	1	1	yes	characteristic
53	#88183	C₂²	1	2	yes	—
54	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
55	#88180	C₂²	1	1	yes	characteristic
56	#88178	C₂²	1	1	yes	characteristic
57	#88178	C₂²	1	2	yes	—
58	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
59	#88152	C₂²	1	2	yes	—
60	#88152	C₂²	1	2	yes	—
61	#88152	C₂²	1	2	yes	—
62	#88151	C₂²	1	2	yes	—
63	#88150	C₂²	1	2	yes	—
64	#88150	C₂²	1	2	yes	—
65	#88150	C₂²	1	2	yes	—
66	#88150	C₂²	1	2	yes	—
67	#88147	C₂²	1	1	yes	characteristic
68	#88147	C₂²	1	1	yes	characteristic
69	#88144	C₂²	1	1	yes	characteristic
70	#88144	C₂²	1	1	yes	characteristic
71	#88143	C₂²	1	2	yes	—
72	#88142	C₂²	1	1	yes	characteristic
73	#88142	C₂²	1	1	yes	characteristic
74	#88142	C₂²	1	2	yes	—
75	#88142	C₂²	1	1	yes	characteristic
76	#88142	C₂²	1	1	yes	characteristic
77	#88142	C₂²	1	1	yes	characteristic
78	#88142	C₂²	1	1	yes	characteristic
79	#88142	C₂²	1	2	yes	—
80	#88142	C₂²	1	2	yes	—
81	#88141	C₂²	1	1	yes	characteristic
82	#88141	C₂²	1	1	yes	characteristic
83	#88141	C₂²	1	2	yes	—
84	#88141	C₂²	1	2	yes	—
85	#88140	C₂²	1	2	yes	—
86	#88139	C₂²	1	2	yes	—
87	#88139	C₂²	1	2	yes	—
88	#88139	C₂²	1	2	yes	—
89	#88139	C₂²	1	2	yes	—
90	#88139	C₂²	1	2	yes	—
91	#88137	C₂²	1	2	yes	—
92	#88137	C₂²	1	2	yes	—
93	#88137	C₂²	1	2	yes	—
94	#88137	C₂²	1	2	yes	—
95	#88135	C₂²	1	2	yes	—
96	#88135	C₂²	1	2	yes	—
97	#88133	C₂²	1	2	yes	—
98	#88133	C₂²	1	2	yes	—
99	#88133	C₂²	1	2	yes	—
100	#88132	C₂²	1	1	yes	characteristic
101	#88132	C₂²	1	1	yes	characteristic
102	#88132	C₂²	1	1	yes	characteristic
103	#88132	C₂²	1	1	yes	characteristic
104	#88132	C₂²	1	2	yes	—
105	#88132	C₂²	1	2	yes	—
106	#88132	C₂²	1	2	yes	—
107	#88132	C₂²	1	2	yes	—
108	#88132	C₂²	1	2	yes	—
109	#88131	C₂²	1	2	yes	—
110	#88131	C₂²	1	2	yes	—
111	#88130	C₂²	1	2	yes	—
112	#88129	C₂²	1	1	yes	characteristic
113	C₄×D₅₂	C₂²	1	1	yes	characteristic
114	#88126	C₂²	1	2	yes	—
115	#88123	C₂²	1	1	yes	characteristic
116	#88123	C₂²	1	2	yes	—
117	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
118	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
119	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
120	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
121	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
122	C₄×Dic₂₆	C₂²	1	2	yes	—
123	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
125	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₃	C₂³	1	2	yes	—
127	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
132	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
133	C₂²×Dic₁₃	C₂³	1	2	yes	—
134	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
135	C₂²×Dic₁₃	C₂³	1	2	yes	—
136	Q₈×D₁₃	—	4	4	no	—
137	#6129	—	4	4	no	—
138	C₂×D₅₂	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₁₃	C₂³	1	2	yes	—
140	C₂×C₄×D₁₃	C₂³	1	2	yes	—
141	C₂×C₄×D₁₃	C₂³	1	2	yes	—
142	C₂×Dic₂₆	—	4	4	no	—
143	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
144	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
145	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
146	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
147	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
148	C₂×Dic₂₆	C₂³	1	2	yes	—
149	C₂×Dic₂₆	C₂³	1	2	yes	—
150	C₂×Dic₂₆	C₂³	1	2	yes	—
151	C₂×Dic₂₆	C₂³	1	2	yes	—
152	C₂×Dic₂₆	C₂³	1	2	yes	—
153	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
154	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
163	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₄²×C₁₃	C₂³	1	1	yes	characteristic
168	C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₄²×C₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
174	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
177	#6103	C₂³	1	2	yes	—
178	#6103	C₂³	1	2	yes	—
179	#6103	C₂³	1	2	yes	—
180	#6103	C₂³	1	2	yes	—
181	#6103	C₂³	1	2	yes	—
182	#6103	C₂³	1	2	yes	—
183	#6103	C₂³	1	2	yes	—
184	#6103	C₂³	1	2	yes	—
185	C₄⋊Dic₁₃	C₂³	1	2	yes	—
186	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
187	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
188	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
189	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
190	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₁₃	C₂³	1	2	yes	—
193	C₄⋊Dic₁₃	C₂³	1	2	yes	—
194	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
195	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
196	#6101	C₂³	1	1	yes	characteristic
197	#6101	C₂³	1	1	yes	characteristic
198	#6101	C₂³	1	1	yes	characteristic
199	#6101	C₂³	1	1	yes	characteristic
200	#6101	C₂³	1	2	yes	—
201	#6101	C₂³	1	1	yes	characteristic
202	#6101	C₂³	1	1	yes	characteristic
203	#6101	C₂³	1	1	yes	characteristic
204	#6101	C₂³	1	1	yes	characteristic
205	#6101	C₂³	1	2	yes	—
206	#6101	C₂³	1	2	yes	—
207	#6101	C₂³	1	2	yes	—
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	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
215	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
216	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
217	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
218	C₄×Dic₁₃	C₂³	1	2	yes	—
219	C₄×Dic₁₃	C₂³	1	2	yes	—
220	C₄×Dic₁₃	C₂³	1	2	yes	—
221	C₄×Dic₁₃	C₂³	1	2	yes	—
222	C₄×Dic₁₃	C₂³	1	2	yes	—
223	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
225	#3550	—	13	1	no	maximal, Sylow
226	C₂³×C₁₃	C₂⁴	1	2	yes	—
227	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
228	C₂²×D₁₃	C₂⁴	1	2	yes	—
229	Q₈×C₁₃	—	2	2	no	—
230	Q₈×C₁₃	—	4	2	no	—
231	D₄×C₁₃	—	2	2	no	—
232	D₄×C₁₃	—	4	2	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
236	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
239	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
240	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂²⋊D₁₃	—	2	4	no	—
245	C₂²⋊D₁₃	—	4	2	no	—
246	C₂²⋊D₁₃	—	4	2	no	—
247	C₂×Dic₁₃	—	2	4	no	—
248	C₂×Dic₁₃	—	2	2	no	—
249	C₂×Dic₁₃	—	2	2	no	—
250	C₂×Dic₁₃	—	4	2	no	—
251	C₂×Dic₁₃	C₂⁴	1	2	yes	—
252	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₁₃	C₂⁴	1	2	yes	—
257	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₃	C₂⁴	1	2	yes	—
259	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
262	D₅₂	—	2	2	no	—
263	C₄×D₁₃	—	2	4	no	—
264	C₄×D₁₃	—	4	2	no	—
265	C₄×D₁₃	—	4	2	no	—
266	Dic₂₆	—	2	2	no	—
267	Dic₂₆	—	2	2	no	—
268	Dic₂₆	—	2	4	no	—
269	Dic₂₆	—	2	2	no	—
270	Dic₂₆	—	2	2	no	—
271	Dic₂₆	—	2	2	no	—
272	Dic₂₆	—	4	2	no	—
273	Dic₂₆	—	4	2	no	—
274	Dic₂₆	—	4	2	no	—
275	Dic₂₆	—	4	2	no	—
276	#563	—	13	2	no	—
277	#563	—	13	2	no	—
278	#559	—	13	1	no	—
279	#559	—	13	1	no	—
280	Q₈²	—	13	1	no	—
281	Q₈²	—	13	1	no	—
282	#556	—	13	2	no	—
283	#556	—	13	1	no	—
284	#556	—	13	1	no	—
285	D₄×Q₈	—	13	1	no	—
286	D₄×Q₈	—	13	2	no	—
287	D₄×Q₈	—	13	1	no	—
288	#542	—	13	2	no	—
289	#542	—	13	2	no	—
290	#542	—	13	1	no	—
291	#542	—	13	1	no	—
292	#542	—	13	1	no	—
293	#542	D₁₃	1	1	yes	characteristic, complemented
294	#536	—	13	2	no	—
295	#536	—	13	2	no	—
296	#533	—	13	1	no	—
297	#533	—	13	1	no	—
298	#532	—	13	1	no	—
299	C₂²×C₁₃	—	2	2	no	—
300	C₂²×C₁₃	—	2	1	no	—
301	C₂²×C₁₃	—	2	1	no	—
302	C₂²×C₁₃	—	2	2	no	—
303	C₂²×C₁₃	—	2	1	no	—
304	C₂²×C₁₃	—	2	2	no	—
305	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
306	C₂×D₁₃	—	2	2	no	—
307	C₂×D₁₃	—	2	2	no	—
308	C₂×D₁₃	—	2	2	no	—
309	C₄×C₁₃	—	2	1	no	—
310	C₄×C₁₃	—	2	2	no	—
311	C₄×C₁₃	—	2	1	no	—
312	C₄×C₁₃	—	2	2	no	—
313	C₄×C₁₃	—	2	1	no	—
314	C₄×C₁₃	—	2	1	no	—
315	C₄×C₁₃	—	2	1	no	—
316	C₄×C₁₃	—	2	2	no	—
317	C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
318	Dic₁₃	—	2	1	no	—
319	Dic₁₃	—	2	2	no	—
320	Dic₁₃	—	2	1	no	—
321	Dic₁₃	—	2	2	no	—
322	Dic₁₃	—	2	1	no	—
323	Dic₁₃	—	2	2	no	—
324	Dic₁₃	—	2	1	no	—
325	Dic₁₃	—	2	1	no	—
326	Dic₁₃	—	2	1	no	—
327	Dic₁₃	H(5,𝔽₂)	1	2	yes	—
328	Dic₁₃	2₋¹⁺⁴	1	2	yes	—
329	C₂×#41	—	13	2	no	—
330	C₂²×Q₈	—	13	2	no	—
331	C₂²×Q₈	—	13	2	no	—
332	C₄⋊Q₈	—	13	1	no	—
333	C₄⋊Q₈	—	13	2	no	—
334	C₄⋊Q₈	—	13	2	no	—
335	C₄⋊Q₈	—	13	1	no	—
336	C₄⋊Q₈	—	13	1	no	—
337	C₄⋊Q₈	—	13	1	no	—
338	C₄⋊Q₈	—	13	1	no	—
339	C₄⋊Q₈	—	13	2	no	—
340	C₄⋊Q₈	—	13	2	no	—
341	C₄⋊Q₈	—	13	2	no	—
342	C₄⋊Q₈	—	13	1	no	—
343	C₄⋊Q₈	—	13	1	no	—
344	C₄⋊Q₈	—	13	2	no	—
345	C₄⋊Q₈	—	13	1	no	—
346	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
347	#127	—	13	1	no	—
348	#126	—	13	2	no	—
349	#126	—	13	2	no	—
350	#126	—	13	2	no	—
351	#126	—	13	2	no	—
352	#126	—	13	2	no	—
353	#126	—	13	2	no	—
354	#126	—	13	2	no	—
355	#126	C₂×D₁₃	1	2	yes	—
356	#125	—	13	2	no	—
357	#125	—	13	1	no	—
358	#125	—	13	1	no	—
359	#124	—	13	1	no	—
360	#124	—	13	2	no	—
361	#124	—	13	1	no	—
362	#124	—	13	2	no	—
363	#124	—	13	2	no	—
364	#124	—	13	2	no	—
365	#124	—	13	2	no	—
366	#124	—	13	2	no	—
367	#124	—	13	1	no	—
368	#124	C₂×D₁₃	1	2	yes	—
369	#124	C₂×D₁₃	1	1	yes	characteristic
370	#123	—	13	2	no	—
371	#123	—	13	2	no	—
372	#123	—	13	2	no	—
373	#123	—	13	2	no	—
374	#123	—	13	2	no	—
375	#123	—	13	2	no	—
376	#123	—	13	2	no	—
377	#123	C₂×D₁₃	1	2	yes	—
378	C₂²⋊Q₈	—	13	2	no	—
379	C₂²⋊Q₈	—	13	1	no	—
380	C₂²⋊Q₈	—	13	2	no	—
381	C₂²⋊Q₈	—	13	2	no	—
382	C₂²⋊Q₈	—	13	2	no	—
383	C₂²⋊Q₈	—	13	2	no	—
384	C₂²⋊Q₈	—	13	2	no	—
385	C₂²⋊Q₈	—	13	2	no	—
386	C₂²⋊Q₈	—	13	2	no	—
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	2	no	—
392	C₂²⋊Q₈	—	13	2	no	—
393	C₂²⋊Q₈	—	13	2	no	—
394	C₂²⋊Q₈	—	13	2	no	—
395	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
396	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
397	#121	—	13	2	no	—
398	#121	—	13	1	no	—
399	#121	C₂×D₁₃	1	1	yes	characteristic
400	C₄×Q₈	—	13	1	no	—
401	C₄×Q₈	—	13	1	no	—
402	C₄×Q₈	—	13	2	no	—
403	C₄×Q₈	—	13	1	no	—
404	C₄×Q₈	—	13	2	no	—
405	C₄×Q₈	—	13	1	no	—
406	C₄×Q₈	—	13	1	no	—
407	C₄×Q₈	—	13	1	no	—
408	C₄×Q₈	—	13	1	no	—
409	C₄×Q₈	—	13	1	no	—
410	C₄×Q₈	—	13	2	no	—
411	C₄×Q₈	—	13	1	no	—
412	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
413	C₄×D₄	—	13	1	no	—
414	C₄×D₄	—	13	1	no	—
415	C₄×D₄	—	13	2	no	—
416	C₄×D₄	—	13	1	no	—
417	C₄×D₄	—	13	1	no	—
418	C₄×D₄	—	13	2	no	—
419	C₄×D₄	—	13	2	no	—
420	C₄×D₄	—	13	1	no	—
421	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
422	#117	—	13	1	no	—
423	#117	—	13	2	no	—
424	#117	—	13	2	no	—
425	#117	—	13	2	no	—
426	#117	C₂×D₁₃	1	1	yes	characteristic
427	C₂×C₄²	—	13	1	no	—
428	C₂×C₁₃	—	4	2	no	—
429	C₂×C₁₃	—	4	1	no	—
430	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
431	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
432	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
433	D₁₃	—	4	2	no	—
434	#41	—	52	4	no	—
435	C₂×Q₈	—	13	1	no	—
436	C₂×Q₈	—	13	1	no	—
437	C₂×Q₈	—	13	1	no	—
438	C₂×Q₈	—	13	2	no	—
439	C₂×Q₈	—	13	1	no	—
440	C₂×Q₈	—	13	1	no	—
441	C₂×Q₈	—	13	2	no	—
442	C₂×Q₈	—	13	2	no	—
443	C₂×Q₈	—	13	2	no	—
444	C₂×Q₈	—	13	2	no	—
445	C₂×Q₈	—	52	4	no	—
446	C₂×Q₈	—	52	4	no	—
447	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
448	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
449	C₂×D₄	—	13	2	no	—
450	C₂×D₄	—	13	2	no	—
451	C₂×D₄	—	13	2	no	—
452	C₂×D₄	—	13	1	no	—
453	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
454	C₂×D₄	C₂²×D₁₃	1	2	yes	—
455	C₂²×C₄	—	13	1	no	—
456	C₂²×C₄	—	13	1	no	—
457	C₂²×C₄	—	13	2	no	—
458	C₂²×C₄	—	13	2	no	—
459	C₂²×C₄	—	13	2	no	—
460	C₂²×C₄	—	13	2	no	—
461	C₂²×C₄	—	13	2	no	—
462	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
463	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
464	C₄⋊C₄	—	13	2	no	—
465	C₄⋊C₄	—	13	1	no	—
466	C₄⋊C₄	—	13	1	no	—
467	C₄⋊C₄	—	13	2	no	—
468	C₄⋊C₄	—	13	1	no	—
469	C₄⋊C₄	—	13	2	no	—
470	C₄⋊C₄	—	13	1	no	—
471	C₄⋊C₄	—	13	1	no	—
472	C₄⋊C₄	—	13	1	no	—
473	C₄⋊C₄	—	13	1	no	—
474	C₄⋊C₄	—	13	2	no	—
475	C₄⋊C₄	—	13	1	no	—
476	C₄⋊C₄	—	13	2	no	—
477	C₄⋊C₄	—	13	1	no	—
478	C₄⋊C₄	—	13	1	no	—
479	C₄⋊C₄	—	13	1	no	—
480	C₄⋊C₄	—	13	1	no	—
481	C₄⋊C₄	—	13	2	no	—
482	C₄⋊C₄	—	13	2	no	—
483	C₄⋊C₄	—	13	2	no	—
484	C₄⋊C₄	—	13	2	no	—
485	C₄⋊C₄	—	13	2	no	—
486	C₄⋊C₄	—	13	2	no	—
487	C₄⋊C₄	—	13	2	no	—
488	C₄⋊C₄	—	13	1	no	—
489	C₄⋊C₄	—	13	1	no	—
490	C₄⋊C₄	—	13	2	no	—
491	C₄⋊C₄	—	13	1	no	—
492	C₄⋊C₄	—	13	1	no	—
493	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
498	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
499	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
500	C₂²⋊C₄	—	13	1	no	—
501	C₂²⋊C₄	—	13	1	no	—
502	C₂²⋊C₄	—	13	2	no	—
503	C₂²⋊C₄	—	13	2	no	—
504	C₂²⋊C₄	—	13	2	no	—
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	2	no	—
511	C₂²⋊C₄	—	13	2	no	—
512	C₂²⋊C₄	—	13	2	no	—
513	C₂²⋊C₄	—	13	2	no	—
514	C₂²⋊C₄	—	13	2	no	—
515	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
516	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
517	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
518	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
519	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
520	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
521	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
522	C₄²	—	13	1	no	—
523	C₄²	—	13	1	no	—
524	C₄²	—	13	1	no	—
525	C₄²	—	13	1	no	—
526	C₄²	—	13	2	no	—
527	C₄²	—	13	2	no	—
528	C₄²	—	13	1	no	—
529	C₄²	—	13	1	no	—
530	C₄²	—	13	2	no	—
531	C₄²	—	13	2	no	—
532	C₄²	—	13	2	no	—
533	C₄²	C₂²×D₁₃	1	2	yes	—
534	C₄²	C₂²×D₁₃	1	1	yes	characteristic
535	C₄²	C₂²×D₁₃	1	1	yes	characteristic
536	C₁₃	#3550	1	1	yes	characteristic, complemented, Sylow
537	C₂³	—	13	2	no	—
538	C₂³	C₂³×D₁₃	1	1	yes	characteristic
539	C₂³	C₂³×D₁₃	1	2	yes	—
540	Q₈	—	2	2	no	—
541	Q₈	—	4	2	no	—
542	Q₈	—	26	2	no	—
543	Q₈	—	26	2	no	—
544	Q₈	—	26	2	no	—
545	Q₈	—	26	4	no	—
546	Q₈	—	26	2	no	—
547	Q₈	—	26	2	no	—
548	Q₈	—	52	2	no	—
549	Q₈	—	52	2	no	—
550	Q₈	—	52	2	no	—
551	Q₈	—	52	2	no	—
552	D₄	—	2	2	no	—
553	D₄	—	4	2	no	—
554	D₄	—	26	4	no	—
555	D₄	—	26	2	no	—
556	D₄	—	52	2	no	—
557	D₄	—	52	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	13	1	no	—
561	C₂×C₄	—	13	1	no	—
562	C₂×C₄	—	13	2	no	—
563	C₂×C₄	—	13	1	no	—
564	C₂×C₄	—	13	1	no	—
565	C₂×C₄	—	13	1	no	—
566	C₂×C₄	—	13	2	no	—
567	C₂×C₄	—	13	1	no	—
568	C₂×C₄	—	13	1	no	—
569	C₂×C₄	—	13	2	no	—
570	C₂×C₄	—	13	1	no	—
571	C₂×C₄	—	26	4	no	—
572	C₂×C₄	—	26	2	no	—
573	C₂×C₄	—	26	4	no	—
574	C₂×C₄	—	26	2	no	—
575	C₂×C₄	—	52	2	no	—
576	C₂×C₄	—	52	2	no	—
577	C₂×C₄	—	52	2	no	—
578	C₂×C₄	C₂³×D₁₃	1	2	yes	—
579	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
580	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
581	C₂×C₄	C₂³×D₁₃	1	2	yes	—
582	C₂×C₄	C₂³×D₁₃	1	2	yes	—
583	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
587	C₂²	—	2	1	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	2	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	2	no	—
593	C₂²	—	26	2	no	—
594	C₂²	—	26	2	no	—
595	C₂²	—	26	2	no	—
596	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
597	C₄	—	2	1	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	1	no	—
600	C₄	—	2	2	no	—
601	C₄	—	2	2	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	13	2	no	—
606	C₄	—	13	2	no	—
607	C₄	—	26	2	no	—
608	C₄	—	26	1	no	—
609	C₄	—	26	2	no	—
610	C₄	—	26	1	no	—
611	C₄	—	26	2	no	—
612	C₄	—	26	1	no	—
613	C₄	—	26	1	no	—
614	C₄	—	26	1	no	—
615	C₄	—	26	1	no	—
616	C₄	#88257	1	2	yes	—
617	C₂	—	4	1	no	—
618	C₂	—	4	2	no	—
619	C₂	—	52	2	no	—
620	C₂	C₂×#88257	1	1	yes	characteristic
621	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic
622	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×#542	C₂
prime radical	#11719301	C₂
hypercenter	#542	D₁₃
hypocenter	C₁₃	#3550
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
1. C₁₃×#542	C₂	semidirect
2. #11719432	C₂	semidirect
3. #11719427	C₂	semidirect
4. #11719417	C₂	semidirect
5. #11719407	C₂	semidirect
6. #11719386	C₂	semidirect
7. #11719380	C₂	semidirect
8. #11719376	C₂	semidirect
9. #11719374	C₂	semidirect
10. #11719367	C₂	semidirect
11. #11719353	C₂	semidirect
12. #11719351	C₂	semidirect
13. #11719348	C₂	semidirect
14. #11719337	C₂	semidirect
15. #11719327	C₂	semidirect
16. #11719308	C₂	semidirect
18. #11719273	C₂	semidirect
19. Q₈×Dic₂₆	C₂	semidirect
20. #11719264	C₂	semidirect
21. D₄×Dic₂₆	C₂	semidirect
22. #11719239	C₂	semidirect
23. #11719222	C₂	semidirect
293. #542	D₁₃	semidirect
536. C₁₃	#3550	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#542	2
#11719432	2
#11719427	2
#11719417	2
#11719407	2
#11719386	2
#11719380	2
#11719376	2
#11719374	2
#11719367	2
#11719353	2
#11719351	2
#11719348	2
#11719337	2
#11719327	2
#11719308	2
#11719301	2
#11719273	2
Q₈×Dic₂₆	2
#11719264	2
D₄×Dic₂₆	2
#11719239	2
#11719222	2
#3550	13