Subgroups — #13128580

Order 1664.

1022 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719433	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719429	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719413	C₂	1	2	yes	maximal, complemented
5	#11719410	C₂	1	2	yes	maximal, complemented
6	#11719410	C₂	1	2	yes	maximal, complemented
7	#11719407	C₂	1	2	yes	maximal, complemented
8	#11719399	C₂	1	2	yes	maximal, complemented
9	#11719398	C₂	1	2	yes	maximal, complemented
10	#11719398	C₂	1	2	yes	maximal, complemented
11	#11719396	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719395	C₂	1	2	yes	maximal, complemented
13	#11719394	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719348	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719332	C₂	1	1	yes	maximal, characteristic
16	D₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719330	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719285	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719283	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719279	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719277	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719239	C₂	1	1	yes	maximal, characteristic, complemented
23	D₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#6131	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#126	C₂²	1	2	yes	—
29	C₁₃×#126	C₂²	1	2	yes	—
30	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#125	C₂²	1	2	yes	complemented
32	C₁₃×#125	C₂²	1	2	yes	complemented
33	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#117	C₂²	1	1	yes	characteristic
38	#88201	C₂²	1	1	yes	characteristic, complemented
39	#88200	C₂²	1	1	yes	characteristic
40	#88200	C₂²	1	1	yes	characteristic
41	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
42	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
43	#88198	C₂²	1	1	yes	characteristic, complemented
44	#88184	C₂²	1	1	yes	characteristic
45	#88180	C₂²	1	1	yes	characteristic
46	#88178	C₂²	1	1	yes	characteristic
47	#88152	C₂²	1	2	yes	complemented
48	#88152	C₂²	1	2	yes	complemented
49	#88152	C₂²	1	2	yes	complemented
50	#88152	C₂²	1	2	yes	complemented
51	#88151	C₂²	1	2	yes	—
52	#88151	C₂²	1	1	yes	characteristic
53	#88151	C₂²	1	2	yes	—
54	#88151	C₂²	1	2	yes	complemented
55	#88150	C₂²	1	2	yes	—
56	#88150	C₂²	1	2	yes	—
57	#88150	C₂²	1	2	yes	—
58	#88150	C₂²	1	2	yes	complemented
59	#88150	C₂²	1	2	yes	complemented
60	#88150	C₂²	1	2	yes	complemented
61	#88149	C₂²	1	1	yes	characteristic
62	#88148	C₂²	1	2	yes	—
63	#88148	C₂²	1	2	yes	—
64	#88148	C₂²	1	2	yes	—
65	#88148	C₂²	1	2	yes	—
66	#88148	C₂²	1	2	yes	—
67	#88147	C₂²	1	2	yes	—
68	#88147	C₂²	1	2	yes	—
69	#88147	C₂²	1	2	yes	—
70	#88147	C₂²	1	1	yes	characteristic, complemented
71	#88146	C₂²	1	2	yes	—
72	#88146	C₂²	1	1	yes	characteristic
73	#88146	C₂²	1	1	yes	characteristic
74	#88146	C₂²	1	1	yes	characteristic
75	#88146	C₂²	1	2	yes	—
76	#88146	C₂²	1	2	yes	complemented
77	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
78	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
79	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
80	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
81	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
82	#88144	C₂²	1	2	yes	complemented
83	#88144	C₂²	1	1	yes	characteristic, complemented
84	#88144	C₂²	1	2	yes	complemented
85	#88143	C₂²	1	2	yes	complemented
86	#88143	C₂²	1	2	yes	complemented
87	#88143	C₂²	1	2	yes	complemented
88	#88142	C₂²	1	1	yes	characteristic, complemented
89	#88142	C₂²	1	2	yes	complemented
90	#88141	C₂²	1	2	yes	complemented
91	#88141	C₂²	1	1	yes	characteristic, complemented
92	#88141	C₂²	1	2	yes	complemented
93	#88139	C₂²	1	2	yes	—
94	#88139	C₂²	1	2	yes	—
95	#88137	C₂²	1	2	yes	—
96	#88137	C₂²	1	2	yes	—
97	#88136	C₂²	1	2	yes	—
98	#88135	C₂²	1	2	yes	—
99	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
100	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
101	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
102	#88133	C₂²	1	2	yes	—
103	#88133	C₂²	1	2	yes	—
104	#88132	C₂²	1	2	yes	—
105	#88131	C₂²	1	1	yes	characteristic
106	#88131	C₂²	1	1	yes	characteristic
107	#88129	C₂²	1	1	yes	characteristic, complemented
108	C₄×D₅₂	C₂²	1	2	yes	—
109	C₄×D₅₂	C₂²	1	2	yes	—
110	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
111	#88126	C₂²	1	1	yes	characteristic
112	#88126	C₂²	1	1	yes	characteristic
113	#88126	C₂²	1	2	yes	—
114	#88126	C₂²	1	2	yes	—
115	#88126	C₂²	1	2	yes	complemented
116	#88126	C₂²	1	2	yes	complemented
117	C₄²×D₁₃	C₂²	1	1	yes	characteristic
118	C₄²×D₁₃	C₂²	1	1	yes	characteristic
119	#88123	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₂₆	C₂²	1	2	yes	complemented
122	C₄×Dic₂₆	C₂²	1	2	yes	complemented
123	C₂³×D₁₃	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
128	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
129	#6131	—	2	4	no	—
130	Q₈×D₁₃	—	2	4	no	—
131	C₂×D₅₂	C₂³	1	2	yes	—
132	C₂×D₅₂	C₂³	1	2	yes	—
133	C₂×D₅₂	C₂³	1	1	yes	characteristic
134	C₂×C₄×D₁₃	—	2	4	no	—
135	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₁₃	C₂³	1	2	yes	—
139	C₂×C₄×D₁₃	C₂³	1	2	yes	—
140	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₃	C₂³	1	2	yes	—
145	C₂×C₄×D₁₃	C₂³	1	2	yes	—
146	C₂×C₄×D₁₃	C₂³	1	2	yes	—
147	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
148	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
149	C₂×Dic₂₆	C₂³	1	2	yes	—
150	C₂×Dic₂₆	C₂³	1	2	yes	—
151	C₂×Dic₂₆	C₂³	1	2	yes	—
152	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
155	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
161	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
166	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₄²×C₁₃	C₂³	1	2	yes	—
170	C₄²×C₁₃	C₂³	1	2	yes	—
171	C₄²×C₁₃	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
173	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
174	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
175	#6103	C₂³	1	1	yes	characteristic
176	#6103	C₂³	1	1	yes	characteristic
177	#6103	C₂³	1	1	yes	characteristic
178	#6103	C₂³	1	1	yes	characteristic
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	#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	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	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	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
200	#6101	C₂³	1	1	yes	characteristic
201	#6101	C₂³	1	2	yes	—
202	#6101	C₂³	1	2	yes	—
203	#6101	C₂³	1	2	yes	—
204	#6101	C₂³	1	1	yes	characteristic
205	#6101	C₂³	1	1	yes	characteristic
206	#6101	C₂³	1	1	yes	characteristic
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	2	yes	—
216	C₄×Dic₁₃	C₂³	1	2	yes	—
217	C₄×Dic₁₃	C₂³	1	2	yes	—
218	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
219	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
220	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₃	C₂³	1	2	yes	—
224	C₄×Dic₁₃	C₂³	1	2	yes	—
225	#3495	—	13	1	no	maximal, Sylow
226	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₂²×D₁₃	—	2	2	no	—
228	C₂²×D₁₃	—	2	2	no	—
229	C₂²×D₁₃	—	4	1	no	—
230	C₂²×D₁₃	C₂⁴	1	2	yes	—
231	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
233	Q₈×C₁₃	—	2	2	no	—
234	Q₈×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	2	no	—
236	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
238	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
239	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
242	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂²⋊D₁₃	—	4	2	no	—
247	C₂×Dic₁₃	—	2	2	no	—
248	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
250	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₃	C₂⁴	1	2	yes	—
252	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₃	C₂⁴	1	2	yes	—
254	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₃	C₂⁴	1	2	yes	—
256	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
257	D₅₂	—	2	4	no	—
258	D₅₂	—	2	4	no	—
259	D₅₂	—	2	2	no	—
260	C₄×D₁₃	—	2	2	no	—
261	C₄×D₁₃	—	2	4	no	—
262	C₄×D₁₃	—	2	2	no	—
263	C₄×D₁₃	—	2	2	no	—
264	C₄×D₁₃	—	2	2	no	—
265	C₄×D₁₃	—	2	2	no	—
266	C₄×D₁₃	—	2	4	no	—
267	C₄×D₁₃	—	4	1	no	—
268	C₄×D₁₃	—	4	2	no	—
269	C₄×D₁₃	—	4	2	no	—
270	C₄×D₁₃	—	4	1	no	—
271	C₄×D₁₃	—	4	2	no	—
272	C₄×D₁₃	#41	1	4	yes	—
273	Dic₂₆	—	2	2	no	—
274	Dic₂₆	—	2	4	no	—
275	Dic₂₆	—	4	2	no	—
276	Dic₂₆	—	4	2	no	—
277	#556	—	13	2	no	—
278	#554	—	13	2	no	—
279	#552	—	13	2	no	—
280	#552	—	13	2	no	—
281	#552	—	13	2	no	—
282	#552	—	13	2	no	—
283	#551	—	13	2	no	—
284	#551	—	13	2	no	—
285	#544	—	13	1	no	—
286	#542	—	13	1	no	—
287	#542	—	13	1	no	—
288	#541	—	13	1	no	—
289	#541	D₁₃	1	1	yes	characteristic, complemented
290	#536	—	13	1	no	—
291	#533	—	13	1	no	—
292	#533	—	13	1	no	—
293	#529	—	13	1	no	—
294	#529	—	13	1	no	—
295	#525	—	13	1	no	—
296	C₂×C₂²⋊Q₈	—	13	1	no	—
297	#520	—	13	1	no	—
298	#519	—	13	1	no	—
299	C₂×#117	—	13	1	no	—
300	C₂²×C₁₃	—	2	1	no	—
301	C₂²×C₁₃	—	2	1	no	—
302	C₂²×C₁₃	—	2	1	no	—
303	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
304	C₂×D₁₃	—	2	1	no	—
305	C₂×D₁₃	—	2	1	no	—
306	C₂×D₁₃	—	2	1	no	—
307	C₂×D₁₃	—	2	1	no	—
308	C₂×D₁₃	—	2	2	no	—
309	C₂×D₁₃	—	2	2	no	—
310	C₂×D₁₃	—	2	2	no	—
311	C₂×D₁₃	—	4	4	no	—
312	C₂×D₁₃	C₂×#41	1	2	yes	—
313	C₂×D₁₃	2₋¹⁺⁴	1	2	yes	—
314	C₄×C₁₃	—	2	2	no	—
315	C₄×C₁₃	—	2	1	no	—
316	C₄×C₁₃	—	2	2	no	—
317	C₄×C₁₃	—	2	1	no	—
318	C₄×C₁₃	—	2	1	no	—
319	C₄×C₁₃	—	2	2	no	—
320	C₄×C₁₃	—	2	1	no	—
321	C₄×C₁₃	—	2	2	no	—
322	C₄×C₁₃	—	2	1	no	—
323	C₄×C₁₃	C₂×#41	1	2	yes	—
324	Dic₁₃	—	2	2	no	—
325	Dic₁₃	—	2	1	no	—
326	Dic₁₃	—	2	1	no	—
327	Dic₁₃	—	2	1	no	—
328	Dic₁₃	—	2	1	no	—
329	Dic₁₃	—	2	2	no	—
330	Dic₁₃	—	2	2	no	—
331	Dic₁₃	—	2	1	no	—
332	Dic₁₃	C₂×#41	1	2	yes	—
333	C₂×#41	—	13	1	no	—
334	C₂²×Q₈	—	13	1	no	—
335	C₂³×C₄	—	13	1	no	—
336	C₄⋊Q₈	—	13	1	no	—
337	C₄⋊Q₈	—	13	1	no	—
338	C₄⋊Q₈	—	13	2	no	—
339	C₄⋊Q₈	—	13	1	no	—
340	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
341	#126	—	13	2	no	—
342	#126	—	13	2	no	—
343	#126	—	13	2	no	—
344	#126	—	13	2	no	—
345	#126	—	13	2	no	—
346	#126	—	13	2	no	—
347	#126	C₂×D₁₃	1	2	yes	—
348	#126	C₂×D₁₃	1	2	yes	—
349	#125	—	13	1	no	—
350	#125	—	13	2	no	—
351	#125	—	13	2	no	—
352	#125	—	13	2	no	—
353	#125	—	13	2	no	—
354	#125	—	13	2	no	—
355	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
356	#125	C₂×D₁₃	1	2	yes	complemented
357	#125	C₂×D₁₃	1	2	yes	complemented
358	#124	—	13	1	no	—
359	#124	—	13	2	no	—
360	#124	—	13	2	no	—
361	#124	—	13	1	no	—
362	#123	—	13	2	no	—
363	#123	—	13	2	no	—
364	#123	—	13	2	no	—
365	#123	—	13	2	no	—
366	#123	—	13	2	no	—
367	#123	—	13	2	no	—
368	#123	—	13	2	no	—
369	C₂²⋊Q₈	—	13	1	no	—
370	C₂²⋊Q₈	—	13	1	no	—
371	C₂²⋊Q₈	—	13	1	no	—
372	C₂²⋊Q₈	—	13	1	no	—
373	C₂²⋊Q₈	—	13	2	no	—
374	C₂²⋊Q₈	—	13	2	no	—
375	C₂²⋊Q₈	—	13	2	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	—	13	2	no	—
382	C₂²⋊Q₈	—	13	2	no	—
383	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
384	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
385	#121	—	13	1	no	—
386	#121	—	13	1	no	—
387	#120	—	13	2	no	—
388	C₄×Q₈	—	13	1	no	—
389	C₄×Q₈	—	13	1	no	—
390	C₄×Q₈	—	13	1	no	—
391	C₄×Q₈	—	13	2	no	—
392	C₄×Q₈	—	13	2	no	—
393	C₄×Q₈	—	13	1	no	—
394	C₄×Q₈	—	13	2	no	—
395	C₄×Q₈	—	13	2	no	—
396	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
397	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
398	C₄×D₄	—	13	1	no	—
399	C₄×D₄	—	13	2	no	—
400	C₄×D₄	—	13	2	no	—
401	C₄×D₄	—	13	2	no	—
402	C₄×D₄	—	13	2	no	—
403	C₄×D₄	—	13	1	no	—
404	C₄×D₄	—	13	2	no	—
405	C₄×D₄	—	13	2	no	—
406	#117	—	13	1	no	—
407	#117	—	13	1	no	—
408	#117	—	13	1	no	—
409	#117	—	13	1	no	—
410	#117	—	13	2	no	—
411	#117	—	13	2	no	—
412	#117	—	13	2	no	—
413	#117	—	13	1	no	—
414	#117	—	13	1	no	—
415	#117	—	13	1	no	—
416	#117	—	13	1	no	—
417	#117	—	13	2	no	—
418	#117	—	13	2	no	—
419	#117	—	13	2	no	—
420	#117	—	13	2	no	—
421	#117	C₂×D₁₃	1	1	yes	characteristic
422	C₂×C₄⋊C₄	—	13	1	no	—
423	C₂×C₄⋊C₄	—	13	1	no	—
424	C₂×C₄⋊C₄	—	13	1	no	—
425	C₂×C₄⋊C₄	—	13	2	no	—
426	C₂×C₄⋊C₄	—	13	2	no	—
427	C₂×C₂²⋊C₄	—	13	1	no	—
428	C₂×C₂²⋊C₄	—	13	1	no	—
429	C₂×C₂²⋊C₄	—	13	2	no	—
430	C₂×C₄²	—	13	1	no	—
431	C₂×C₄²	—	13	1	no	—
432	C₂×C₁₃	—	4	1	no	—
433	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
434	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
435	C₂×C₁₃	#585	1	1	yes	characteristic
436	D₁₃	—	2	2	no	—
437	D₁₃	—	2	2	no	—
438	D₁₃	—	4	2	no	—
439	C₂⁴	—	13	1	no	—
440	#41	—	26	4	no	—
441	C₂×Q₈	—	13	2	no	—
442	C₂×Q₈	—	13	1	no	—
443	C₂×Q₈	—	13	2	no	—
444	C₂×Q₈	—	13	2	no	—
445	C₂×Q₈	—	26	4	no	—
446	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
447	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
448	C₂×D₄	—	13	2	no	—
449	C₂×D₄	—	13	2	no	—
450	C₂×D₄	—	13	2	no	—
451	C₂×D₄	—	13	1	no	—
452	C₂²×C₄	—	13	1	no	—
453	C₂²×C₄	—	13	1	no	—
454	C₂²×C₄	—	13	1	no	—
455	C₂²×C₄	—	13	1	no	—
456	C₂²×C₄	—	13	1	no	—
457	C₂²×C₄	—	13	2	no	—
458	C₂²×C₄	—	13	1	no	—
459	C₂²×C₄	—	13	1	no	—
460	C₂²×C₄	—	13	2	no	—
461	C₂²×C₄	—	13	1	no	—
462	C₂²×C₄	—	13	1	no	—
463	C₂²×C₄	—	13	2	no	—
464	C₂²×C₄	—	13	2	no	—
465	C₂²×C₄	—	13	2	no	—
466	C₂²×C₄	—	26	4	no	—
467	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
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	1	no	—
475	C₄⋊C₄	—	13	2	no	—
476	C₄⋊C₄	—	13	2	no	—
477	C₄⋊C₄	—	13	1	no	—
478	C₄⋊C₄	—	13	2	no	—
479	C₄⋊C₄	—	13	2	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	2	no	—
489	C₄⋊C₄	—	13	2	no	—
490	C₄⋊C₄	—	13	2	no	—
491	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
492	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
493	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
495	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
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	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
501	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
502	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
503	C₂²⋊C₄	—	13	1	no	—
504	C₂²⋊C₄	—	13	1	no	—
505	C₂²⋊C₄	—	13	2	no	—
506	C₂²⋊C₄	—	13	1	no	—
507	C₂²⋊C₄	—	13	1	no	—
508	C₂²⋊C₄	—	13	1	no	—
509	C₂²⋊C₄	—	13	1	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	—	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	C₂²×D₁₃	1	1	yes	characteristic
523	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
524	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
525	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
526	C₄²	—	13	1	no	—
527	C₄²	—	13	1	no	—
528	C₄²	—	13	1	no	—
529	C₄²	—	13	1	no	—
530	C₄²	—	13	1	no	—
531	C₄²	—	13	1	no	—
532	C₄²	—	13	2	no	—
533	C₄²	—	13	2	no	—
534	C₄²	—	13	2	no	—
535	C₄²	—	13	2	no	—
536	C₄²	—	13	2	no	—
537	C₄²	C₂²×D₁₃	1	1	yes	characteristic
538	C₄²	C₂²×D₁₃	1	1	yes	characteristic
539	C₄²	C₂²×D₁₃	1	2	yes	—
540	C₄²	C₂²×D₁₃	1	2	yes	—
541	C₁₃	#3495	1	1	yes	characteristic, complemented, Sylow
542	C₂³	—	13	1	no	—
543	C₂³	—	13	1	no	—
544	C₂³	—	13	2	no	—
545	C₂³	—	26	2	no	—
546	C₂³	—	26	2	no	—
547	C₂³	—	52	1	no	—
548	C₂³	C₂³×D₁₃	1	1	yes	characteristic
549	Q₈	—	2	2	no	—
550	Q₈	—	2	2	no	—
551	Q₈	—	26	4	no	—
552	Q₈	—	26	2	no	—
553	Q₈	—	52	2	no	—
554	Q₈	—	52	2	no	—
555	D₄	—	26	4	no	—
556	D₄	—	26	4	no	—
557	D₄	—	26	2	no	—
558	D₄	—	52	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	13	1	no	—
561	C₂×C₄	—	13	4	no	—
562	C₂×C₄	—	13	1	no	—
563	C₂×C₄	—	13	1	no	—
564	C₂×C₄	—	13	1	no	—
565	C₂×C₄	—	13	2	no	—
566	C₂×C₄	—	13	1	no	—
567	C₂×C₄	—	13	2	no	—
568	C₂×C₄	—	13	1	no	—
569	C₂×C₄	—	13	2	no	—
570	C₂×C₄	—	26	2	no	—
571	C₂×C₄	—	26	4	no	—
572	C₂×C₄	—	26	2	no	—
573	C₂×C₄	—	26	2	no	—
574	C₂×C₄	—	26	2	no	—
575	C₂×C₄	—	26	4	no	—
576	C₂×C₄	—	26	2	no	—
577	C₂×C₄	—	26	2	no	—
578	C₂×C₄	—	52	2	no	—
579	C₂×C₄	—	52	1	no	—
580	C₂×C₄	—	52	2	no	—
581	C₂×C₄	—	52	2	no	—
582	C₂×C₄	—	52	1	no	—
583	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₁₃	1	2	yes	—
585	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
587	C₂×C₄	C₂³×D₁₃	1	2	yes	—
588	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
589	C₂×C₄	C₂³×D₁₃	1	2	yes	—
590	C₂×C₄	C₂³×D₁₃	1	2	yes	—
591	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	1	no	—
596	C₂²	—	13	2	no	—
597	C₂²	—	13	2	no	—
598	C₂²	—	26	1	no	—
599	C₂²	—	26	1	no	—
600	C₂²	—	26	1	no	—
601	C₂²	—	26	1	no	—
602	C₂²	—	26	2	no	—
603	C₂²	—	26	2	no	—
604	C₂²	—	26	2	no	—
605	C₂²	—	52	4	no	—
606	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
607	C₄	—	2	1	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	2	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	2	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	2	no	—
615	C₄	—	2	1	no	—
616	C₄	—	13	2	no	—
617	C₄	—	26	1	no	—
618	C₄	—	26	2	no	—
619	C₄	—	26	1	no	—
620	C₄	—	26	1	no	—
621	C₄	—	26	1	no	—
622	C₄	—	26	2	no	—
623	C₄	—	26	1	no	—
624	C₄	—	26	2	no	—
625	C₄	#41×D₁₃	1	2	yes	—
626	C₂	—	4	1	no	—
627	C₂	—	26	2	no	—
628	C₂	—	26	2	no	—
629	C₂	—	52	2	no	—
630	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
631	C₂	D₁₃×2₋¹⁺⁴	1	1	yes	characteristic
632	C₂	#11719652	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#541	C₂
prime radical	#11719332	C₂
hypercenter	#541	D₁₃
hypocenter	C₁₃	#3495
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #541

Complements

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

N	H ≅ G/N	type
1. C₁₃×#541	C₂	semidirect
2. #11719433	C₂	semidirect
3. #11719429	C₂	semidirect
4. #11719413	C₂	semidirect
5. #11719410	C₂	semidirect
6. #11719410	C₂	semidirect
7. #11719407	C₂	semidirect
8. #11719399	C₂	semidirect
9. #11719398	C₂	semidirect
10. #11719398	C₂	semidirect
11. #11719396	C₂	semidirect
12. #11719395	C₂	semidirect
13. #11719394	C₂	semidirect
14. #11719348	C₂	semidirect
16. D₁₃×C₂²⋊Q₈	C₂	semidirect
17. #11719330	C₂	semidirect
18. #11719285	C₂	semidirect
19. #11719283	C₂	semidirect
20. #11719279	C₂	semidirect
21. #11719277	C₂	semidirect
22. #11719239	C₂	semidirect
23. D₁₃×#117	C₂	semidirect
27. C₁₃×C₄⋊Q₈	C₂²	semidirect
30. C₁₃×#125	C₂²	semidirect
31. C₁₃×#125	C₂²	semidirect
32. C₁₃×#125	C₂²	semidirect
35. C₄×Q₈×C₁₃	C₂²	semidirect
36. C₄×Q₈×C₁₃	C₂²	semidirect
38. #88201	C₂²	semidirect
41. Q₈×Dic₁₃	C₂²	semidirect
42. Q₈×Dic₁₃	C₂²	semidirect
43. #88198	C₂²	semidirect
47. #88152	C₂²	semidirect
48. #88152	C₂²	semidirect
49. #88152	C₂²	semidirect
50. #88152	C₂²	semidirect
54. #88151	C₂²	semidirect
58. #88150	C₂²	semidirect
59. #88150	C₂²	semidirect
60. #88150	C₂²	semidirect
70. #88147	C₂²	semidirect
76. #88146	C₂²	semidirect
81. C₄⋊C₄×D₁₃	C₂²	semidirect
82. #88144	C₂²	semidirect
83. #88144	C₂²	semidirect
84. #88144	C₂²	semidirect
85. #88143	C₂²	semidirect
86. #88143	C₂²	semidirect
87. #88143	C₂²	semidirect
88. #88142	C₂²	semidirect
89. #88142	C₂²	semidirect
90. #88141	C₂²	semidirect
91. #88141	C₂²	semidirect
92. #88141	C₂²	semidirect
107. #88129	C₂²	semidirect
110. C₄×D₅₂	C₂²	semidirect
115. #88126	C₂²	semidirect
116. #88126	C₂²	semidirect
119. #88123	C₂²	semidirect
120. C₄×Dic₂₆	C₂²	semidirect
121. C₄×Dic₂₆	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
289. #541	D₁₃	semidirect
340. C₄⋊Q₈	C₂×D₁₃	semidirect
355. #125	C₂×D₁₃	semidirect
356. #125	C₂×D₁₃	semidirect
357. #125	C₂×D₁₃	semidirect
396. C₄×Q₈	C₂×D₁₃	semidirect
397. C₄×Q₈	C₂×D₁₃	semidirect
541. C₁₃	#3495	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#541	2
#11719433	2
#11719429	2
#11719413	2
#11719410	2
#11719407	2
#11719399	2
#11719398	2
#11719396	2
#11719395	2
#11719394	2
#11719348	2
#11719332	2
D₁₃×C₂²⋊Q₈	2
#11719330	2
#11719285	2
#11719283	2
#11719279	2
#11719277	2
#11719239	2
D₁₃×#117	2
#3495	13