Subgroups — #13128748

Order 1664.

1104 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719433	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719430	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719430	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719400	C₂	1	2	yes	maximal, complemented
7	#11719395	C₂	1	2	yes	maximal, complemented
8	#11719348	C₂	1	2	yes	maximal, complemented
9	#11719338	C₂	1	2	yes	maximal, complemented
10	#11719336	C₂	1	2	yes	maximal, complemented
11	#11719334	C₂	1	2	yes	maximal, complemented
12	#11719287	C₂	1	2	yes	maximal, complemented
13	#11719281	C₂	1	2	yes	maximal, complemented
14	#11719279	C₂	1	2	yes	maximal, complemented
15	#11719273	C₂	1	2	yes	maximal, complemented
16	#11719237	C₂	1	2	yes	maximal, complemented
17	#11719235	C₂	1	2	yes	maximal, complemented
18	#11719182	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#6127	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#6131	C₂²	1	2	yes	—
21	C₂×#6131	C₂²	1	2	yes	—
22	C₂×Q₈×D₁₃	C₂²	1	2	yes	—
23	C₂×#6127	C₂²	1	1	yes	characteristic
24	C₂×#6127	C₂²	1	2	yes	—
25	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₁₃×#125	C₂²	1	2	yes	—
28	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
31	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
32	C₁₃×#117	C₂²	1	2	yes	—
33	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
34	#88201	C₂²	1	2	yes	—
35	#88201	C₂²	1	2	yes	—
36	#88200	C₂²	1	2	yes	—
37	Q₈×Dic₁₃	C₂²	1	2	yes	—
38	#88198	C₂²	1	2	yes	—
39	#88184	C₂²	1	2	yes	—
40	#88184	C₂²	1	2	yes	—
41	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
42	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
43	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
44	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
45	#88180	C₂²	1	1	yes	characteristic
46	#88152	C₂²	1	4	yes	—
47	#88151	C₂²	1	2	yes	—
48	#88151	C₂²	1	4	yes	—
49	#88150	C₂²	1	4	yes	—
50	#88150	C₂²	1	4	yes	—
51	#88149	C₂²	1	2	yes	—
52	#88149	C₂²	1	2	yes	—
53	#88149	C₂²	1	2	yes	—
54	#88149	C₂²	1	2	yes	—
55	#88149	C₂²	1	4	yes	—
56	#88148	C₂²	1	4	yes	—
57	#88147	C₂²	1	2	yes	—
58	#88147	C₂²	1	2	yes	—
59	#88147	C₂²	1	2	yes	—
60	#88147	C₂²	1	2	yes	—
61	#88147	C₂²	1	4	yes	—
62	#88146	C₂²	1	2	yes	—
63	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
64	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
65	C₄⋊C₄×D₁₃	C₂²	1	4	yes	—
66	#88144	C₂²	1	2	yes	—
67	#88142	C₂²	1	2	yes	—
68	#88142	C₂²	1	2	yes	—
69	#88141	C₂²	1	2	yes	—
70	#88139	C₂²	1	4	yes	—
71	#88138	C₂²	1	4	yes	—
72	#88138	C₂²	1	4	yes	—
73	#88137	C₂²	1	4	yes	—
74	#88130	C₂²	1	4	yes	—
75	#88129	C₂²	1	2	yes	—
76	#88129	C₂²	1	4	yes	—
77	#88128	C₂²	1	1	yes	characteristic
78	C₄×D₅₂	C₂²	1	1	yes	characteristic
79	C₄×D₅₂	C₂²	1	1	yes	characteristic
80	C₄×D₅₂	C₂²	1	2	yes	—
81	C₄×D₅₂	C₂²	1	2	yes	—
82	C₄×D₅₂	C₂²	1	4	yes	—
83	#88126	C₂²	1	1	yes	characteristic
84	#88126	C₂²	1	1	yes	characteristic
85	#88126	C₂²	1	4	yes	—
86	C₄²×D₁₃	C₂²	1	1	yes	characteristic
87	C₄²×D₁₃	C₂²	1	1	yes	characteristic
88	#88123	C₂²	1	1	yes	characteristic
89	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
90	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
91	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
92	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
93	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
99	#6131	—	2	8	no	—
100	#6131	—	4	4	no	—
101	Q₈×D₁₃	—	4	4	no	—
102	#6127	—	2	4	no	—
103	#6127	—	4	4	no	—
104	C₂×D₅₂	C₂³	1	1	yes	characteristic
105	C₂×D₅₂	C₂³	1	2	yes	—
106	C₂×D₅₂	C₂³	1	2	yes	—
107	C₂×D₅₂	C₂³	1	4	yes	—
108	C₂×D₅₂	C₂³	1	2	yes	—
109	C₂×D₅₂	C₂³	1	4	yes	—
110	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
114	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
115	C₂×C₄×D₁₃	C₂³	1	4	yes	—
116	C₂×C₄×D₁₃	C₂³	1	4	yes	—
117	C₂×C₄×D₁₃	C₂³	1	4	yes	—
118	C₂×C₄×D₁₃	C₂³	1	4	yes	—
119	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
120	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
121	C₂×Dic₂₆	C₂³	1	2	yes	—
122	C₂×Dic₂₆	C₂³	1	4	yes	—
123	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
124	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
125	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
126	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
127	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
128	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
129	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
130	C₄²×C₁₃	C₂³	1	1	yes	characteristic
131	C₄²×C₁₃	C₂³	1	1	yes	characteristic
132	C₄²×C₁₃	C₂³	1	1	yes	characteristic
133	C₄²×C₁₃	C₂³	1	1	yes	characteristic
134	C₄²×C₁₃	C₂³	1	4	yes	—
135	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
136	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
137	#6103	C₂³	1	1	yes	characteristic
138	#6103	C₂³	1	4	yes	—
139	#6103	C₂³	1	1	yes	characteristic
140	#6103	C₂³	1	1	yes	characteristic
141	#6103	C₂³	1	1	yes	characteristic
142	#6103	C₂³	1	4	yes	—
143	#6103	C₂³	1	4	yes	—
144	#6103	C₂³	1	4	yes	—
145	#6103	C₂³	1	4	yes	—
146	#6103	C₂³	1	4	yes	—
147	#6103	C₂³	1	4	yes	—
148	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
149	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
150	C₄⋊Dic₁₃	C₂³	1	2	yes	—
151	C₄⋊Dic₁₃	C₂³	1	2	yes	—
152	C₄⋊Dic₁₃	C₂³	1	4	yes	—
153	#6101	C₂³	1	1	yes	characteristic
154	#6101	C₂³	1	1	yes	characteristic
155	#6101	C₂³	1	1	yes	characteristic
156	#6101	C₂³	1	1	yes	characteristic
157	#6101	C₂³	1	4	yes	—
158	#6101	C₂³	1	4	yes	—
159	#6101	C₂³	1	4	yes	—
160	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
161	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
162	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
163	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
164	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
165	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
166	C₄×Dic₁₃	C₂³	1	4	yes	—
167	#3511	—	13	1	no	maximal, Sylow
168	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
169	C₂²×D₁₃	C₂⁴	1	4	yes	—
170	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
171	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
172	Q₈×C₁₃	—	2	4	no	—
173	Q₈×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
178	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
181	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
185	C₂²⋊D₁₃	—	2	2	no	—
186	C₂²⋊D₁₃	—	2	2	no	—
187	C₂²⋊D₁₃	—	4	4	no	—
188	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
189	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
190	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
191	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
192	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
193	C₂×Dic₁₃	C₂⁴	1	4	yes	—
194	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
195	D₅₂	—	2	2	no	—
196	D₅₂	—	2	8	no	—
197	D₅₂	—	2	4	no	—
198	D₅₂	—	2	4	no	—
199	D₅₂	—	2	4	no	—
200	D₅₂	—	4	4	no	—
201	C₄×D₁₃	—	2	2	no	—
202	C₄×D₁₃	—	2	2	no	—
203	C₄×D₁₃	—	2	2	no	—
204	C₄×D₁₃	—	2	2	no	—
205	C₄×D₁₃	—	2	2	no	—
206	C₄×D₁₃	—	2	8	no	—
207	C₄×D₁₃	—	4	4	no	—
208	C₄×D₁₃	—	4	4	no	—
209	C₄×D₁₃	—	4	4	no	—
210	C₄×D₁₃	#41	1	4	yes	complemented
211	Dic₂₆	—	2	4	no	—
212	Dic₂₆	—	2	2	no	—
213	Dic₂₆	—	4	4	no	—
214	#556	—	13	2	no	—
215	#555	—	13	2	no	—
216	#554	—	13	2	no	—
217	#553	—	13	2	no	—
218	#553	—	13	2	no	—
219	#548	—	13	2	no	—
220	#548	—	13	2	no	—
221	#547	—	13	2	no	—
222	#542	—	13	2	no	—
223	#542	—	13	2	no	—
224	#537	—	13	2	no	—
225	#533	—	13	1	no	—
226	#533	D₁₃	1	1	yes	characteristic, complemented
227	#532	—	13	1	no	—
228	#532	—	13	1	no	—
229	#532	—	13	1	no	—
230	C₂×C₄⋊Q₈	—	13	1	no	—
231	#520	—	13	2	no	—
232	C₄×#41	—	13	1	no	—
233	C₂²×C₁₃	—	2	1	no	—
234	C₂²×C₁₃	—	2	1	no	—
235	C₂²×C₁₃	—	2	1	no	—
236	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
237	C₂×D₁₃	—	2	1	no	—
238	C₂×D₁₃	—	2	1	no	—
239	C₂×D₁₃	—	2	4	no	—
240	C₂×D₁₃	—	2	1	no	—
241	C₂×D₁₃	—	2	1	no	—
242	C₂×D₁₃	—	2	4	no	—
243	C₂×D₁₃	—	2	1	no	—
244	C₂×D₁₃	—	2	4	no	—
245	C₂×D₁₃	C₂×#41	1	2	yes	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	—	2	4	no	—
248	C₄×C₁₃	—	2	4	no	—
249	C₄×C₁₃	—	2	1	no	—
250	C₄×C₁₃	—	2	1	no	—
251	C₄×C₁₃	C₂×#41	1	2	yes	—
252	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
253	C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
254	Dic₁₃	—	2	1	no	—
255	Dic₁₃	—	2	4	no	—
256	Dic₁₃	—	2	1	no	—
257	Dic₁₃	—	2	1	no	—
258	Dic₁₃	—	2	1	no	—
259	Dic₁₃	—	2	1	no	—
260	Dic₁₃	C₂×#41	1	2	yes	—
261	C₂×#41	—	13	2	no	—
262	C₂×#41	—	13	2	no	—
263	C₂×#41	—	13	1	no	—
264	C₂×#41	—	13	2	no	—
265	C₂²×Q₈	—	13	2	no	—
266	C₄⋊Q₈	—	13	2	no	—
267	C₄⋊Q₈	—	13	2	no	—
268	C₄⋊Q₈	—	13	2	no	—
269	C₄⋊Q₈	—	13	1	no	—
270	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
271	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
272	#127	—	13	1	no	—
273	#126	—	13	4	no	—
274	#126	—	13	4	no	—
275	#125	—	13	2	no	—
276	#125	C₂×D₁₃	1	2	yes	—
277	#124	—	13	2	no	—
278	#124	—	13	2	no	—
279	#124	—	13	4	no	—
280	#124	—	13	2	no	—
281	#124	—	13	4	no	—
282	#123	—	13	4	no	—
283	#123	—	13	4	no	—
284	C₂²⋊Q₈	—	13	2	no	—
285	C₂²⋊Q₈	—	13	2	no	—
286	C₂²⋊Q₈	—	13	4	no	—
287	C₂²⋊Q₈	—	13	4	no	—
288	C₂²⋊Q₈	—	13	4	no	—
289	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
290	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
291	#121	—	13	2	no	—
292	#121	—	13	2	no	—
293	#121	—	13	2	no	—
294	#121	—	13	2	no	—
295	#121	—	13	2	no	—
296	#121	—	13	2	no	—
297	#121	—	13	4	no	—
298	#121	—	13	4	no	—
299	#121	—	13	4	no	—
300	C₄×Q₈	—	13	2	no	—
301	C₄×Q₈	—	13	2	no	—
302	C₄×Q₈	—	13	1	no	—
303	C₄×Q₈	—	13	1	no	—
304	C₄×Q₈	C₂×D₁₃	1	2	yes	—
305	C₄×Q₈	C₂×D₁₃	1	2	yes	—
306	C₄×D₄	—	13	1	no	—
307	C₄×D₄	—	13	1	no	—
308	C₄×D₄	—	13	1	no	—
309	C₄×D₄	—	13	1	no	—
310	C₄×D₄	—	13	2	no	—
311	C₄×D₄	—	13	4	no	—
312	C₄×D₄	—	13	2	no	—
313	C₄×D₄	—	13	2	no	—
314	C₄×D₄	—	13	2	no	—
315	C₄×D₄	—	13	1	no	—
316	C₄×D₄	—	13	1	no	—
317	C₄×D₄	—	13	2	no	—
318	C₄×D₄	—	13	4	no	—
319	C₄×D₄	—	13	2	no	—
320	#117	—	13	1	no	—
321	#117	—	13	2	no	—
322	#117	—	13	1	no	—
323	#117	—	13	1	no	—
324	#117	—	13	4	no	—
325	#117	C₂×D₁₃	1	2	yes	—
326	C₂×C₄⋊C₄	—	13	2	no	—
327	C₂×C₄⋊C₄	—	13	4	no	—
328	C₂×C₄⋊C₄	—	13	2	no	—
329	C₂×C₄²	—	13	1	no	—
330	C₂×C₄²	—	13	1	no	—
331	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
332	C₂×C₁₃	—	4	1	no	—
333	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
334	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
335	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
336	D₁₃	—	2	2	no	—
337	D₁₃	—	4	4	no	—
338	D₁₃	—	4	1	no	—
339	#41	—	26	4	no	—
340	#41	—	26	8	no	—
341	#41	—	52	4	no	—
342	#41	—	52	4	no	—
343	C₂×Q₈	—	13	1	no	—
344	C₂×Q₈	—	13	2	no	—
345	C₂×Q₈	—	13	4	no	—
346	C₂×Q₈	—	52	4	no	—
347	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
348	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
349	C₂×D₄	—	13	1	no	—
350	C₂×D₄	—	13	1	no	—
351	C₂×D₄	—	13	4	no	—
352	C₂×D₄	—	13	2	no	—
353	C₂×D₄	—	13	4	no	—
354	C₂×D₄	—	13	1	no	—
355	C₂×D₄	—	13	2	no	—
356	C₂×D₄	—	13	2	no	—
357	C₂×D₄	—	13	4	no	—
358	C₂²×C₄	—	13	1	no	—
359	C₂²×C₄	—	13	1	no	—
360	C₂²×C₄	—	13	1	no	—
361	C₂²×C₄	—	13	1	no	—
362	C₂²×C₄	—	13	1	no	—
363	C₂²×C₄	—	13	1	no	—
364	C₂²×C₄	—	13	4	no	—
365	C₂²×C₄	—	13	4	no	—
366	C₂²×C₄	—	13	4	no	—
367	C₂²×C₄	—	13	4	no	—
368	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
369	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
370	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
371	C₄⋊C₄	—	13	1	no	—
372	C₄⋊C₄	—	13	4	no	—
373	C₄⋊C₄	—	13	2	no	—
374	C₄⋊C₄	—	13	2	no	—
375	C₄⋊C₄	—	13	4	no	—
376	C₄⋊C₄	—	13	4	no	—
377	C₄⋊C₄	—	13	1	no	—
378	C₄⋊C₄	—	13	1	no	—
379	C₄⋊C₄	—	13	1	no	—
380	C₄⋊C₄	—	13	1	no	—
381	C₄⋊C₄	—	13	1	no	—
382	C₄⋊C₄	—	13	4	no	—
383	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
384	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
385	C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
386	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
387	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
388	C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
389	C₂²⋊C₄	—	13	1	no	—
390	C₂²⋊C₄	—	13	1	no	—
391	C₂²⋊C₄	—	13	1	no	—
392	C₂²⋊C₄	—	13	1	no	—
393	C₂²⋊C₄	—	13	4	no	—
394	C₂²⋊C₄	—	13	4	no	—
395	C₂²⋊C₄	—	13	1	no	—
396	C₂²⋊C₄	—	13	1	no	—
397	C₂²⋊C₄	—	13	4	no	—
398	C₂²⋊C₄	—	13	4	no	—
399	C₂²⋊C₄	—	13	4	no	—
400	C₂²⋊C₄	—	13	4	no	—
401	C₂²⋊C₄	—	13	4	no	—
402	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
403	C₄²	—	13	1	no	—
404	C₄²	—	13	1	no	—
405	C₄²	—	13	1	no	—
406	C₄²	—	13	1	no	—
407	C₄²	—	13	1	no	—
408	C₄²	—	13	1	no	—
409	C₄²	—	13	4	no	—
410	C₄²	C₂²×D₁₃	1	1	yes	characteristic
411	C₄²	C₂²×D₁₃	1	1	yes	characteristic
412	C₄²	C₂²×D₁₃	1	1	yes	characteristic
413	C₄²	C₂²×D₁₃	1	1	yes	characteristic
414	C₄²	C₂²×D₁₃	1	4	yes	—
415	C₁₃	#3511	1	1	yes	characteristic, complemented, Sylow
416	C₂³	—	13	1	no	—
417	C₂³	—	13	1	no	—
418	C₂³	—	13	4	no	—
419	C₂³	C₂³×D₁₃	1	1	yes	characteristic
420	Q₈	—	2	4	no	—
421	Q₈	—	2	4	no	—
422	Q₈	—	26	2	no	—
423	Q₈	—	26	4	no	—
424	Q₈	—	52	4	no	—
425	D₄	—	26	2	no	—
426	D₄	—	26	8	no	—
427	D₄	—	26	2	no	—
428	D₄	—	26	2	no	—
429	D₄	—	26	4	no	—
430	D₄	—	26	4	no	—
431	D₄	—	26	4	no	—
432	D₄	—	52	4	no	—
433	D₄	—	52	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	13	1	no	—
438	C₂×C₄	—	13	4	no	—
439	C₂×C₄	—	13	1	no	—
440	C₂×C₄	—	13	1	no	—
441	C₂×C₄	—	13	1	no	—
442	C₂×C₄	—	13	1	no	—
443	C₂×C₄	—	13	1	no	—
444	C₂×C₄	—	13	4	no	—
445	C₂×C₄	—	26	8	no	—
446	C₂×C₄	—	26	2	no	—
447	C₂×C₄	—	26	2	no	—
448	C₂×C₄	—	26	2	no	—
449	C₂×C₄	—	26	2	no	—
450	C₂×C₄	—	26	2	no	—
451	C₂×C₄	—	52	4	no	—
452	C₂×C₄	—	52	4	no	—
453	C₂×C₄	—	52	4	no	—
454	C₂×C₄	C₂³×D₁₃	1	4	yes	—
455	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
456	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
457	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
458	C₂×C₄	C₂³×D₁₃	1	4	yes	—
459	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
460	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
461	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	13	2	no	—
466	C₂²	—	26	1	no	—
467	C₂²	—	26	1	no	—
468	C₂²	—	26	1	no	—
469	C₂²	—	26	4	no	—
470	C₂²	—	26	4	no	—
471	C₂²	—	26	1	no	—
472	C₂²	—	26	1	no	—
473	C₂²	—	26	4	no	—
474	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	4	no	—
478	C₄	—	2	1	no	—
479	C₄	—	2	4	no	—
480	C₄	—	13	2	no	—
481	C₄	—	26	1	no	—
482	C₄	—	26	1	no	—
483	C₄	—	26	1	no	—
484	C₄	—	26	1	no	—
485	C₄	—	26	1	no	—
486	C₄	—	26	4	no	—
487	C₄	#88254	1	2	yes	—
488	C₄	#41×D₁₃	1	2	yes	—
489	C₄	#88256	1	2	yes	—
490	C₂	—	4	1	no	—
491	C₂	—	26	2	no	—
492	C₂	—	52	1	no	—
493	C₂	—	52	4	no	—
494	C₂	C₂×#88254	1	1	yes	characteristic
495	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
496	C₂	C₂×#88256	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#533	C₂
hypercenter	#533	D₁₃
hypocenter	C₁₃	#3511
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #533

Complements

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

N	H ≅ G/N	type
1. C₁₃×#533	C₂	semidirect
2. #11719433	C₂	semidirect
3. #11719430	C₂	semidirect
4. #11719430	C₂	semidirect
5. D₁₃×C₄⋊Q₈	C₂	semidirect
6. #11719400	C₂	semidirect
7. #11719395	C₂	semidirect
8. #11719348	C₂	semidirect
9. #11719338	C₂	semidirect
10. #11719336	C₂	semidirect
11. #11719334	C₂	semidirect
12. #11719287	C₂	semidirect
13. #11719281	C₂	semidirect
14. #11719279	C₂	semidirect
15. #11719273	C₂	semidirect
16. #11719237	C₂	semidirect
17. #11719235	C₂	semidirect
18. #11719182	C₂	semidirect
19. C₄×#6127	C₂	semidirect
210. C₄×D₁₃	#41	semidirect
226. #533	D₁₃	semidirect
415. C₁₃	#3511	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#533	2
#11719433	2
#11719430	2
D₁₃×C₄⋊Q₈	2
#11719400	2
#11719395	2
#11719348	2
#11719338	2
#11719336	2
#11719334	2
#11719287	2
#11719281	2
#11719279	2
#11719273	2
#11719237	2
#11719235	2
#11719182	2
C₄×#6127	2
#3511	13