Subgroups — #13129323

Order 1664.

910 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719436	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719426	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719417	C₂	1	2	yes	maximal, complemented
5	#11719407	C₂	1	2	yes	maximal, complemented
6	#11719406	C₂	1	2	yes	maximal, complemented
7	#11719406	C₂	1	2	yes	maximal, complemented
8	#11719387	C₂	1	1	yes	maximal, characteristic
9	#11719385	C₂	1	1	yes	maximal, characteristic
10	#11719376	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719376	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719351	C₂	1	2	yes	maximal, complemented
13	#11719328	C₂	1	2	yes	maximal, complemented
14	#11719288	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719283	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719283	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719274	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719272	C₂	1	1	yes	maximal, characteristic, complemented
19	Q₈×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719266	C₂	1	1	yes	maximal, characteristic
21	#11719244	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719236	C₂	1	2	yes	maximal, complemented
23	#11719223	C₂	1	2	yes	maximal, complemented
24	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₃×#126	C₂²	1	2	yes	—
26	C₁₃×#126	C₂²	1	2	yes	—
27	C₁₃×#124	C₂²	1	1	yes	characteristic
28	C₁₃×#124	C₂²	1	1	yes	characteristic
29	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#117	C₂²	1	2	yes	—
35	#88200	C₂²	1	1	yes	characteristic
36	#88200	C₂²	1	1	yes	characteristic
37	#88200	C₂²	1	1	yes	characteristic
38	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic
39	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic
40	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic
41	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic
42	#88198	C₂²	1	1	yes	characteristic
43	#88198	C₂²	1	1	yes	characteristic
44	#88198	C₂²	1	2	yes	—
45	#88198	C₂²	1	1	yes	characteristic
46	#88192	C₂²	1	1	yes	characteristic
47	#88190	C₂²	1	1	yes	characteristic
48	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
49	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
50	#88183	C₂²	1	2	yes	—
51	#88178	C₂²	1	2	yes	—
52	#88178	C₂²	1	2	yes	—
53	C₂×#6101	C₂²	1	2	yes	—
54	#88152	C₂²	1	2	yes	—
55	#88152	C₂²	1	2	yes	—
56	#88152	C₂²	1	2	yes	—
57	#88151	C₂²	1	1	yes	characteristic
58	#88151	C₂²	1	1	yes	characteristic
59	#88150	C₂²	1	1	yes	characteristic
60	#88150	C₂²	1	2	yes	—
61	#88150	C₂²	1	1	yes	characteristic
62	#88144	C₂²	1	2	yes	—
63	#88144	C₂²	1	1	yes	characteristic
64	#88144	C₂²	1	2	yes	—
65	#88143	C₂²	1	2	yes	—
66	#88143	C₂²	1	2	yes	—
67	#88143	C₂²	1	2	yes	—
68	#88143	C₂²	1	2	yes	—
69	#88143	C₂²	1	1	yes	characteristic
70	#88143	C₂²	1	2	yes	—
71	#88143	C₂²	1	2	yes	—
72	#88143	C₂²	1	2	yes	—
73	#88143	C₂²	1	1	yes	characteristic
74	#88143	C₂²	1	2	yes	—
75	#88142	C₂²	1	1	yes	characteristic
76	#88142	C₂²	1	1	yes	characteristic
77	#88142	C₂²	1	2	yes	—
78	#88142	C₂²	1	2	yes	—
79	#88142	C₂²	1	2	yes	—
80	#88142	C₂²	1	1	yes	characteristic
81	#88141	C₂²	1	2	yes	—
82	#88141	C₂²	1	2	yes	—
83	#88140	C₂²	1	2	yes	—
84	#88139	C₂²	1	2	yes	—
85	#88139	C₂²	1	2	yes	—
86	#88137	C₂²	1	2	yes	—
87	#88135	C₂²	1	2	yes	—
88	#88133	C₂²	1	2	yes	—
89	#88133	C₂²	1	2	yes	—
90	#88133	C₂²	1	2	yes	—
91	#88133	C₂²	1	2	yes	—
92	#88133	C₂²	1	2	yes	—
93	#88133	C₂²	1	2	yes	—
94	#88133	C₂²	1	2	yes	—
95	#88132	C₂²	1	2	yes	—
96	#88132	C₂²	1	2	yes	—
97	#88132	C₂²	1	2	yes	—
98	#88132	C₂²	1	2	yes	—
99	#88132	C₂²	1	2	yes	—
100	#88131	C₂²	1	2	yes	—
101	#88131	C₂²	1	2	yes	—
102	#88131	C₂²	1	2	yes	—
103	#88130	C₂²	1	2	yes	—
104	#88126	C₂²	1	1	yes	characteristic
105	#88126	C₂²	1	2	yes	—
106	#88126	C₂²	1	1	yes	characteristic
107	C₄²×D₁₃	C₂²	1	1	yes	characteristic
108	#88124	C₂²	1	1	yes	characteristic
109	#88124	C₂²	1	2	yes	—
110	#88124	C₂²	1	2	yes	—
111	#88124	C₂²	1	1	yes	characteristic
112	#88123	C₂²	1	2	yes	—
113	#88123	C₂²	1	1	yes	characteristic
114	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
115	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
116	C₄×Dic₂₆	C₂²	1	2	yes	—
117	C₄×Dic₂₆	C₂²	1	2	yes	—
118	C₄×Dic₂₆	C₂²	1	2	yes	—
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	1	yes	characteristic
123	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
129	C₂²×Dic₁₃	C₂³	1	2	yes	—
130	C₂²×Dic₁₃	C₂³	1	2	yes	—
131	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
132	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
133	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
134	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
135	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
136	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
137	C₂×Dic₂₆	C₂³	1	2	yes	—
138	C₂×Dic₂₆	C₂³	1	2	yes	—
139	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
140	C₂×Dic₂₆	C₂³	1	2	yes	—
141	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
143	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
147	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₁₃×C₄⋊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	2	yes	—
154	C₄²×C₁₃	C₂³	1	1	yes	characteristic
155	C₄²×C₁₃	C₂³	1	1	yes	characteristic
156	C₄²×C₁₃	C₂³	1	2	yes	—
157	C₄²×C₁₃	C₂³	1	1	yes	characteristic
158	C₄²×C₁₃	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	2	yes	—
164	#6103	C₂³	1	1	yes	characteristic
165	#6103	C₂³	1	2	yes	—
166	#6103	C₂³	1	1	yes	characteristic
167	#6103	C₂³	1	1	yes	characteristic
168	#6103	C₂³	1	2	yes	—
169	#6103	C₂³	1	1	yes	characteristic
170	#6103	C₂³	1	2	yes	—
171	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
172	C₄⋊Dic₁₃	C₂³	1	2	yes	—
173	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
174	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
175	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
176	C₄⋊Dic₁₃	C₂³	1	2	yes	—
177	C₄⋊Dic₁₃	C₂³	1	2	yes	—
178	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
179	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
180	C₄⋊Dic₁₃	C₂³	1	2	yes	—
181	C₄⋊Dic₁₃	C₂³	1	2	yes	—
182	C₄⋊Dic₁₃	C₂³	1	2	yes	—
183	C₄⋊Dic₁₃	C₂³	1	2	yes	—
184	#6101	C₂³	1	1	yes	characteristic
185	#6101	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
191	#6101	C₂³	1	2	yes	—
192	#6101	C₂³	1	2	yes	—
193	#6101	C₂³	1	1	yes	characteristic
194	#6101	C₂³	1	2	yes	—
195	#6101	C₂³	1	1	yes	characteristic
196	#6101	C₂³	1	2	yes	—
197	#6101	C₂³	1	1	yes	characteristic
198	#6101	C₂³	1	1	yes	characteristic
199	#6101	C₂³	1	2	yes	—
200	#6101	C₂³	1	2	yes	—
201	#6101	C₂³	1	2	yes	—
202	#6101	C₂³	1	2	yes	—
203	#6101	C₂³	1	2	yes	—
204	#6101	C₂³	1	2	yes	—
205	#6101	C₂³	1	2	yes	—
206	#6101	C₂³	1	1	yes	characteristic
207	#6101	C₂³	1	1	yes	characteristic
208	#6101	C₂³	1	1	yes	characteristic
209	#6101	C₂³	1	2	yes	—
210	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
211	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
212	C₄×Dic₁₃	C₂³	1	2	yes	—
213	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
214	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
215	C₄×Dic₁₃	C₂³	1	2	yes	—
216	C₄×Dic₁₃	C₂³	1	2	yes	—
217	C₄×Dic₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
222	#3555	—	13	1	no	maximal, Sylow
223	C₂³×C₁₃	C₂⁴	1	2	yes	—
224	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
225	Q₈×C₁₃	—	2	2	no	—
226	Q₈×C₁₃	—	2	2	no	—
227	Q₈×C₁₃	—	4	1	no	—
228	D₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	4	2	no	—
230	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
232	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
233	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
240	C₂²⋊D₁₃	—	4	2	no	—
241	C₂×Dic₁₃	—	2	4	no	—
242	C₂×Dic₁₃	—	4	2	no	—
243	C₂×Dic₁₃	C₂⁴	1	2	yes	—
244	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
245	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×Dic₁₃	C₂⁴	1	2	yes	—
247	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₁₃	C₂⁴	1	2	yes	—
250	C₂×Dic₁₃	C₂⁴	1	2	yes	—
251	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
254	C₄×D₁₃	—	2	2	no	—
255	C₄×D₁₃	—	2	2	no	—
256	C₄×D₁₃	—	4	1	no	—
257	Dic₂₆	—	2	2	no	—
258	Dic₂₆	—	2	2	no	—
259	Dic₂₆	—	2	2	no	—
260	Dic₂₆	—	4	2	no	—
261	Dic₂₆	—	4	1	no	—
262	Dic₂₆	—	4	2	no	—
263	Dic₂₆	—	4	2	no	—
264	#563	—	13	2	no	—
265	#563	—	13	2	no	—
266	Q₈²	—	13	1	no	—
267	#557	—	13	1	no	—
268	#557	—	13	1	no	—
269	#557	—	13	1	no	—
270	#556	—	13	2	no	—
271	#556	—	13	1	no	—
272	#556	—	13	1	no	—
273	#556	D₁₃	1	1	yes	characteristic, complemented
274	#554	—	13	1	no	—
275	#552	—	13	2	no	—
276	#544	—	13	2	no	—
277	#542	—	13	1	no	—
278	#542	—	13	1	no	—
279	#541	—	13	1	no	—
280	#541	—	13	2	no	—
281	#541	—	13	2	no	—
282	#541	—	13	1	no	—
283	#541	—	13	2	no	—
284	#533	—	13	1	no	—
285	#533	—	13	1	no	—
286	#529	—	13	1	no	—
287	C₂²×C₁₃	—	2	2	no	—
288	C₂²×C₁₃	—	2	2	no	—
289	C₂²×C₁₃	—	2	2	no	—
290	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
291	C₂×D₁₃	—	2	1	no	—
292	C₂×D₁₃	—	2	1	no	—
293	C₂×D₁₃	—	2	1	no	—
294	C₄×C₁₃	—	2	1	no	—
295	C₄×C₁₃	—	2	1	no	—
296	C₄×C₁₃	—	2	1	no	—
297	C₄×C₁₃	—	2	2	no	—
298	C₄×C₁₃	—	2	2	no	—
299	C₄×C₁₃	—	2	2	no	—
300	C₄×C₁₃	—	2	1	no	—
301	C₄×C₁₃	—	2	1	no	—
302	C₄×C₁₃	—	2	1	no	—
303	C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
304	Dic₁₃	—	2	2	no	—
305	Dic₁₃	—	2	1	no	—
306	Dic₁₃	—	2	1	no	—
307	Dic₁₃	—	2	1	no	—
308	Dic₁₃	—	2	2	no	—
309	Dic₁₃	—	2	1	no	—
310	Dic₁₃	—	2	1	no	—
311	Dic₁₃	—	2	2	no	—
312	Dic₁₃	—	2	2	no	—
313	Dic₁₃	—	2	1	no	—
314	Dic₁₃	2₋¹⁺⁴	1	2	yes	—
315	C₄⋊Q₈	—	13	1	no	—
316	C₄⋊Q₈	—	13	1	no	—
317	C₄⋊Q₈	—	13	1	no	—
318	C₄⋊Q₈	—	13	2	no	—
319	C₄⋊Q₈	—	13	1	no	—
320	C₄⋊Q₈	—	13	1	no	—
321	C₄⋊Q₈	—	13	2	no	—
322	C₄⋊Q₈	—	13	1	no	—
323	C₄⋊Q₈	—	13	2	no	—
324	C₄⋊Q₈	—	13	2	no	—
325	C₄⋊Q₈	—	13	2	no	—
326	C₄⋊Q₈	—	13	1	no	—
327	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
328	#126	—	13	2	no	—
329	#126	—	13	2	no	—
330	#126	—	13	2	no	—
331	#126	—	13	2	no	—
332	#126	—	13	2	no	—
333	#126	—	13	2	no	—
334	#126	—	13	2	no	—
335	#126	—	13	2	no	—
336	#126	—	13	2	no	—
337	#126	—	13	2	no	—
338	#126	—	13	2	no	—
339	#126	C₂×D₁₃	1	2	yes	—
340	#126	C₂×D₁₃	1	2	yes	—
341	#125	—	13	1	no	—
342	#125	—	13	1	no	—
343	#125	—	13	2	no	—
344	#125	—	13	2	no	—
345	#125	—	13	2	no	—
346	#125	—	13	2	no	—
347	#125	—	13	2	no	—
348	#125	—	13	1	no	—
349	#125	—	13	2	no	—
350	#125	—	13	2	no	—
351	#125	—	13	2	no	—
352	#125	—	13	2	no	—
353	#125	—	13	2	no	—
354	#125	—	13	1	no	—
355	#125	—	13	2	no	—
356	#125	—	13	2	no	—
357	#125	—	13	1	no	—
358	#124	—	13	1	no	—
359	#124	—	13	2	no	—
360	#124	—	13	2	no	—
361	#124	C₂×D₁₃	1	1	yes	characteristic
362	#124	C₂×D₁₃	1	1	yes	characteristic
363	#123	—	13	2	no	—
364	#123	—	13	2	no	—
365	#123	—	13	2	no	—
366	C₂²⋊Q₈	—	13	1	no	—
367	C₂²⋊Q₈	—	13	1	no	—
368	C₂²⋊Q₈	—	13	1	no	—
369	C₂²⋊Q₈	—	13	2	no	—
370	C₂²⋊Q₈	—	13	2	no	—
371	C₂²⋊Q₈	—	13	1	no	—
372	C₂²⋊Q₈	—	13	1	no	—
373	C₂²⋊Q₈	—	13	1	no	—
374	C₂²⋊Q₈	—	13	2	no	—
375	C₂²⋊Q₈	—	13	1	no	—
376	C₂²⋊Q₈	—	13	2	no	—
377	C₂²⋊Q₈	—	13	2	no	—
378	C₂²⋊Q₈	—	13	2	no	—
379	C₂²⋊Q₈	—	13	2	no	—
380	C₂²⋊Q₈	—	13	2	no	—
381	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
382	#121	—	13	1	no	—
383	C₄×Q₈	—	13	1	no	—
384	C₄×Q₈	—	13	1	no	—
385	C₄×Q₈	—	13	1	no	—
386	C₄×Q₈	—	13	1	no	—
387	C₄×Q₈	—	13	2	no	—
388	C₄×Q₈	—	13	2	no	—
389	C₄×Q₈	—	13	2	no	—
390	C₄×Q₈	—	13	1	no	—
391	C₄×Q₈	—	13	1	no	—
392	C₄×Q₈	—	13	1	no	—
393	C₄×Q₈	—	13	1	no	—
394	C₄×Q₈	—	13	2	no	—
395	C₄×Q₈	—	13	1	no	—
396	C₄×Q₈	—	13	2	no	—
397	C₄×Q₈	—	13	1	no	—
398	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
399	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
400	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
401	C₄×D₄	—	13	1	no	—
402	C₄×D₄	—	13	1	no	—
403	C₄×D₄	—	13	2	no	—
404	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
405	#117	—	13	2	no	—
406	#117	—	13	2	no	—
407	#117	—	13	2	no	—
408	#117	—	13	1	no	—
409	#117	—	13	1	no	—
410	#117	—	13	2	no	—
411	#117	C₂×D₁₃	1	2	yes	—
412	C₂×C₄⋊C₄	—	13	2	no	—
413	C₂×C₄²	—	13	1	no	—
414	C₂×C₁₃	—	4	2	no	—
415	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
416	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
417	C₂×C₁₃	#585	1	1	yes	characteristic
418	D₁₃	—	4	1	no	—
419	C₂×Q₈	—	13	1	no	—
420	C₂×Q₈	—	13	1	no	—
421	C₂×Q₈	—	13	1	no	—
422	C₂×Q₈	—	13	1	no	—
423	C₂×Q₈	—	13	2	no	—
424	C₂×Q₈	—	13	2	no	—
425	C₂×Q₈	—	13	2	no	—
426	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
427	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
428	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
429	C₂×D₄	—	13	2	no	—
430	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
431	C₂²×C₄	—	13	2	no	—
432	C₂²×C₄	—	13	2	no	—
433	C₂²×C₄	—	13	1	no	—
434	C₂²×C₄	—	13	1	no	—
435	C₂²×C₄	—	13	1	no	—
436	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
437	C₄⋊C₄	—	13	1	no	—
438	C₄⋊C₄	—	13	2	no	—
439	C₄⋊C₄	—	13	2	no	—
440	C₄⋊C₄	—	13	2	no	—
441	C₄⋊C₄	—	13	1	no	—
442	C₄⋊C₄	—	13	2	no	—
443	C₄⋊C₄	—	13	1	no	—
444	C₄⋊C₄	—	13	1	no	—
445	C₄⋊C₄	—	13	1	no	—
446	C₄⋊C₄	—	13	2	no	—
447	C₄⋊C₄	—	13	2	no	—
448	C₄⋊C₄	—	13	2	no	—
449	C₄⋊C₄	—	13	1	no	—
450	C₄⋊C₄	—	13	1	no	—
451	C₄⋊C₄	—	13	1	no	—
452	C₄⋊C₄	—	13	1	no	—
453	C₄⋊C₄	—	13	2	no	—
454	C₄⋊C₄	—	13	1	no	—
455	C₄⋊C₄	—	13	1	no	—
456	C₄⋊C₄	—	13	1	no	—
457	C₄⋊C₄	—	13	1	no	—
458	C₄⋊C₄	—	13	2	no	—
459	C₄⋊C₄	—	13	2	no	—
460	C₄⋊C₄	—	13	2	no	—
461	C₄⋊C₄	—	13	2	no	—
462	C₄⋊C₄	—	13	2	no	—
463	C₄⋊C₄	—	13	2	no	—
464	C₄⋊C₄	—	13	2	no	—
465	C₄⋊C₄	—	13	2	no	—
466	C₄⋊C₄	—	13	2	no	—
467	C₄⋊C₄	—	13	2	no	—
468	C₄⋊C₄	—	13	1	no	—
469	C₄⋊C₄	—	13	1	no	—
470	C₄⋊C₄	—	13	2	no	—
471	C₄⋊C₄	—	13	1	no	—
472	C₄⋊C₄	—	13	2	no	—
473	C₄⋊C₄	—	13	2	no	—
474	C₄⋊C₄	—	13	2	no	—
475	C₄⋊C₄	—	13	2	no	—
476	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
477	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
478	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
479	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
481	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
482	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
483	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
484	C₂²⋊C₄	—	13	2	no	—
485	C₂²⋊C₄	—	13	2	no	—
486	C₂²⋊C₄	—	13	2	no	—
487	C₂²⋊C₄	—	13	2	no	—
488	C₂²⋊C₄	—	13	2	no	—
489	C₂²⋊C₄	—	13	1	no	—
490	C₂²⋊C₄	—	13	1	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	—	13	2	no	—
496	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
497	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
498	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
499	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
500	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
501	C₄²	—	13	1	no	—
502	C₄²	—	13	1	no	—
503	C₄²	—	13	1	no	—
504	C₄²	—	13	2	no	—
505	C₄²	—	13	2	no	—
506	C₄²	—	13	1	no	—
507	C₄²	—	13	1	no	—
508	C₄²	—	13	2	no	—
509	C₄²	—	13	2	no	—
510	C₄²	—	13	2	no	—
511	C₄²	—	13	2	no	—
512	C₄²	—	13	2	no	—
513	C₄²	C₂²×D₁₃	1	1	yes	characteristic
514	C₄²	C₂²×D₁₃	1	2	yes	—
515	C₄²	C₂²×D₁₃	1	1	yes	characteristic
516	C₄²	C₂²×D₁₃	1	1	yes	characteristic
517	C₄²	C₂²×D₁₃	1	2	yes	—
518	C₁₃	#3555	1	1	yes	characteristic, complemented, Sylow
519	C₂³	—	13	1	no	—
520	C₂³	C₂³×D₁₃	1	2	yes	—
521	Q₈	—	2	2	no	—
522	Q₈	—	2	2	no	—
523	Q₈	—	4	1	no	—
524	Q₈	—	26	2	no	—
525	Q₈	—	26	2	no	—
526	Q₈	—	26	2	no	—
527	Q₈	—	52	2	no	—
528	Q₈	—	52	2	no	—
529	Q₈	—	52	1	no	—
530	Q₈	—	52	2	no	—
531	D₄	—	2	2	no	—
532	D₄	—	52	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	13	1	no	—
535	C₂×C₄	—	13	2	no	—
536	C₂×C₄	—	13	1	no	—
537	C₂×C₄	—	13	1	no	—
538	C₂×C₄	—	13	1	no	—
539	C₂×C₄	—	13	2	no	—
540	C₂×C₄	—	13	1	no	—
541	C₂×C₄	—	13	2	no	—
542	C₂×C₄	—	13	1	no	—
543	C₂×C₄	—	13	2	no	—
544	C₂×C₄	—	13	1	no	—
545	C₂×C₄	—	26	2	no	—
546	C₂×C₄	—	26	4	no	—
547	C₂×C₄	—	26	2	no	—
548	C₂×C₄	—	52	1	no	—
549	C₂×C₄	—	52	2	no	—
550	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
551	C₂×C₄	C₂³×D₁₃	1	2	yes	—
552	C₂×C₄	C₂³×D₁₃	1	2	yes	—
553	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
554	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
555	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
556	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
557	C₂×C₄	C₂³×D₁₃	1	2	yes	—
558	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
559	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
560	C₂²	—	2	2	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	26	1	no	—
564	C₂²	—	26	1	no	—
565	C₂²	—	26	1	no	—
566	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
567	C₄	—	2	2	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	1	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	1	no	—
576	C₄	—	13	2	no	—
577	C₄	—	26	1	no	—
578	C₄	—	26	2	no	—
579	C₄	—	26	1	no	—
580	C₄	—	26	1	no	—
581	C₄	—	26	2	no	—
582	C₄	—	26	2	no	—
583	C₄	—	26	1	no	—
584	C₄	—	26	2	no	—
585	C₄	—	26	1	no	—
586	C₄	—	26	1	no	—
587	C₄	#88257	1	2	yes	—
588	C₂	—	4	2	no	—
589	C₂	—	52	1	no	—
590	C₂	C₂×#88257	1	1	yes	characteristic
591	C₂	#11719648	1	1	yes	characteristic
592	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×#556	C₂
prime radical	#88192	C₂²
hypercenter	#556	D₁₃
hypocenter	C₁₃	#3555
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. C₁₃×#556	C₂	semidirect
2. #11719436	C₂	semidirect
3. #11719426	C₂	semidirect
4. #11719417	C₂	semidirect
5. #11719407	C₂	semidirect
6. #11719406	C₂	semidirect
7. #11719406	C₂	semidirect
10. #11719376	C₂	semidirect
11. #11719376	C₂	semidirect
12. #11719351	C₂	semidirect
13. #11719328	C₂	semidirect
14. #11719288	C₂	semidirect
15. #11719283	C₂	semidirect
16. #11719283	C₂	semidirect
17. #11719274	C₂	semidirect
18. #11719272	C₂	semidirect
19. Q₈×Dic₂₆	C₂	semidirect
21. #11719244	C₂	semidirect
22. #11719236	C₂	semidirect
23. #11719223	C₂	semidirect
273. #556	D₁₃	semidirect
518. C₁₃	#3555	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#556	2
#11719436	2
#11719426	2
#11719417	2
#11719407	2
#11719406	2
#11719387	2
#11719385	2
#11719376	2
#11719351	2
#11719328	2
#11719288	2
#11719283	2
#11719274	2
#11719272	2
Q₈×Dic₂₆	2
#11719266	2
#11719244	2
#11719236	2
#11719223	2
#3555	13