Subgroups — C₁₃×#19269 #15705608

Order 3328.

716 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3115	C₂	1	2	yes	maximal, complemented
3	C₈×C₁₃×#41	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#1670	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1669	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1668	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1667	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1666	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1665	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1568	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1553	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₃×#135	—	2	1	no	—
13	C₂×C₁₃×#135	—	2	1	no	—
14	C₁₃×#532	C₂²	1	2	yes	—
15	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
16	C₁₃×#495	—	2	1	no	—
17	C₁₃×#495	—	2	1	no	—
18	C₁₃×#494	C₂²	1	1	yes	characteristic
19	C₁₃×#493	C₂²	1	1	yes	characteristic
20	C₁₃×#492	C₂²	1	2	yes	—
21	C₁₃×#482	—	2	2	no	—
22	C₁₃×#475	C₂²	1	2	yes	—
23	C₁₃×#474	C₂²	1	2	yes	—
24	C₁₃×#460	C₂²	1	2	yes	—
25	C₁₃×#459	C₂²	1	2	yes	—
26	C₁₃×#449	—	2	2	no	—
27	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₈×Q₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#442	—	2	2	no	—
30	C₁₃×#440	—	2	2	no	—
31	C₈×D₄×C₁₃	—	2	1	no	—
32	C₈×D₄×C₁₃	—	2	1	no	—
33	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₁₃×#432	C₂²	1	2	yes	—
36	C₁₃×#431	—	2	1	no	—
37	C₁₃×#431	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₁₃	—	2	1	no	—
39	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#335	C₂²	1	1	yes	characteristic
41	C₁₃×#335	C₂²	1	1	yes	characteristic
42	C₁₃×#334	C₂²	1	2	yes	—
43	C₁₃×#332	C₂²	1	2	yes	—
44	C₁₃×#332	C₂²	1	2	yes	—
45	C₁₃×#331	C₂²	1	2	yes	—
46	C₁₃×#331	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	—	2	2	no	—
48	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
49	C₁₃×#135	—	4	4	no	—
50	C₁₃×#135	—	4	4	no	—
51	C₂×C₁₃×Q₁₆	—	2	1	no	—
52	C₂×C₁₃×Q₁₆	—	2	1	no	—
53	C₂×C₁₃×SD₁₆	—	2	2	no	—
54	C₂×C₁₃×SD₁₆	—	2	2	no	—
55	C₂×C₁₃×SD₁₆	—	2	2	no	—
56	C₂×C₁₃×D₈	—	2	2	no	—
57	C₂×C₁₃×D₈	—	2	1	no	—
58	C₂×C₁₃×D₈	—	2	1	no	—
59	C₂²×C₈×C₁₃	—	2	1	no	—
60	C₂²×C₈×C₁₃	—	2	1	no	—
61	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
63	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
64	C₁₃×#127	C₂³	1	2	yes	—
65	C₁₃×#124	—	2	2	no	—
66	C₁₃×#121	—	2	2	no	—
67	C₁₃×#121	—	2	2	no	—
68	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
69	C₄×Q₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₄×D₄×C₁₃	—	2	1	no	—
71	C₄×D₄×C₁₃	—	2	1	no	—
72	C₄×D₄×C₁₃	—	2	2	no	—
73	C₄×D₄×C₁₃	—	2	2	no	—
74	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
75	C₄×D₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#117	—	2	1	no	—
77	C₁₃×#117	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	—	2	1	no	—
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×#107	—	2	2	no	—
81	C₁₃×#106	—	2	2	no	—
82	C₁₃×C₄⋊C₈	—	2	1	no	—
83	C₁₃×C₄⋊C₈	—	2	1	no	—
84	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
87	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
88	C₁₃×#103	—	2	2	no	—
89	C₁₃×#102	—	2	2	no	—
90	C₁₃×#102	—	2	2	no	—
91	C₁₃×#102	—	2	2	no	—
92	C₁₃×C₂²⋊C₈	—	2	1	no	—
93	C₁₃×C₂²⋊C₈	—	2	2	no	—
94	C₁₃×C₂²⋊C₈	—	2	1	no	—
95	C₁₃×C₂²⋊C₈	—	2	1	no	—
96	C₁₃×#97	—	2	2	no	—
97	C₄×C₈×C₁₃	—	2	1	no	—
98	C₄×C₈×C₁₃	—	2	1	no	—
99	C₄×C₈×C₁₃	—	2	1	no	—
100	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
101	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
102	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
103	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
104	#19269	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
105	C₁₃×#41	—	2	2	no	—
106	C₁₃×#41	—	2	2	no	—
107	C₁₃×#41	—	4	4	no	—
108	C₁₃×#41	—	4	4	no	—
109	C₂×Q₈×C₁₃	—	2	2	no	—
110	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂×D₄×C₁₃	—	2	1	no	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	2	2	no	—
114	C₂×D₄×C₁₃	—	2	2	no	—
115	C₂×D₄×C₁₃	—	4	2	no	—
116	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	4	2	no	—
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
124	C₁₃×Q₁₆	—	4	2	no	—
125	C₁₃×Q₁₆	—	4	2	no	—
126	C₁₃×SD₁₆	—	4	4	no	—
127	C₁₃×SD₁₆	—	4	4	no	—
128	C₁₃×SD₁₆	—	4	4	no	—
129	C₁₃×D₈	—	4	2	no	—
130	C₁₃×D₈	—	4	4	no	—
131	C₁₃×D₈	—	4	2	no	—
132	C₂×C₈×C₁₃	—	2	2	no	—
133	C₂×C₈×C₁₃	—	2	2	no	—
134	C₂×C₈×C₁₃	—	2	1	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	4	2	no	—
139	C₂×C₈×C₁₃	—	4	2	no	—
140	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₁₃×C₄⋊C₄	—	2	1	no	—
145	C₁₃×C₄⋊C₄	—	2	1	no	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
149	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
150	C₁₃×C₂²⋊C₄	—	2	1	no	—
151	C₁₃×C₂²⋊C₄	—	2	1	no	—
152	C₁₃×C₂²⋊C₄	—	2	1	no	—
153	C₁₃×C₂²⋊C₄	—	4	2	no	—
154	C₁₃×C₂²⋊C₄	—	4	2	no	—
155	C₄²×C₁₃	—	2	1	no	—
156	C₄²×C₁₃	—	2	1	no	—
157	C₄²×C₁₃	—	2	1	no	—
158	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₁₃	#41	1	1	yes	characteristic
161	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
162	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#3115	C₂×C₁₃	1	2	yes	complemented
164	C₈×#41	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#1670	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#1669	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#1668	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#1667	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#1666	C₂×C₁₃	1	2	yes	complemented
170	#1665	C₂×C₁₃	1	2	yes	complemented
171	#1568	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#1553	C₂×C₁₃	1	2	yes	complemented
173	C₂³×C₁₃	—	2	1	no	—
174	C₂³×C₁₃	—	4	2	no	—
175	C₂³×C₁₃	#121	1	1	yes	characteristic
176	Q₈×C₁₃	—	2	1	no	—
177	Q₈×C₁₃	—	4	2	no	—
178	Q₈×C₁₃	—	4	2	no	—
179	Q₈×C₁₃	#135	1	2	yes	complemented
180	D₄×C₁₃	—	2	4	no	—
181	D₄×C₁₃	—	2	1	no	—
182	D₄×C₁₃	—	4	2	no	—
183	D₄×C₁₃	—	4	2	no	—
184	D₄×C₁₃	—	4	2	no	—
185	D₄×C₁₃	—	4	2	no	—
186	D₄×C₁₃	—	8	2	no	—
187	D₄×C₁₃	—	8	4	no	—
188	D₄×C₁₃	#135	1	2	yes	complemented
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	1	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	8	4	no	—
203	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
204	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
205	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
209	C₈×C₁₃	—	2	1	no	—
210	C₈×C₁₃	—	2	1	no	—
211	C₈×C₁₃	—	4	2	no	—
212	C₈×C₁₃	—	4	2	no	—
213	C₈×C₁₃	—	4	1	no	—
214	C₈×C₁₃	—	4	1	no	—
215	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
216	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
217	C₂×#135	—	2	1	no	—
218	C₂×#135	—	2	1	no	—
219	#532	C₂²×C₁₃	1	2	yes	—
220	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
221	#495	—	2	1	no	—
222	#495	—	2	1	no	—
223	#494	C₂²×C₁₃	1	1	yes	characteristic
224	#493	C₂²×C₁₃	1	1	yes	characteristic
225	#492	C₂²×C₁₃	1	2	yes	—
226	#482	—	2	2	no	—
227	#475	C₂²×C₁₃	1	2	yes	—
228	#474	C₂²×C₁₃	1	2	yes	—
229	#460	C₂²×C₁₃	1	2	yes	—
230	#459	C₂²×C₁₃	1	2	yes	—
231	#449	—	2	2	no	—
232	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
233	C₈×Q₈	C₂²×C₁₃	1	1	yes	characteristic
234	#442	—	2	2	no	—
235	#440	—	2	2	no	—
236	C₈×D₄	—	2	1	no	—
237	C₈×D₄	—	2	1	no	—
238	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
239	C₈×D₄	C₂²×C₁₃	1	1	yes	characteristic
240	#432	C₂²×C₁₃	1	2	yes	—
241	#431	—	2	1	no	—
242	#431	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×C₄×C₈	—	2	1	no	—
244	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
245	#335	C₂²×C₁₃	1	1	yes	characteristic
246	#335	C₂²×C₁₃	1	1	yes	characteristic
247	#334	C₂²×C₁₃	1	2	yes	—
248	#332	C₂²×C₁₃	1	2	yes	—
249	#332	C₂²×C₁₃	1	2	yes	—
250	#331	C₂²×C₁₃	1	2	yes	—
251	#331	C₂²×C₁₃	1	2	yes	—
252	C₂²×C₁₃	—	2	1	no	—
253	C₂²×C₁₃	—	2	1	no	—
254	C₂²×C₁₃	—	2	2	no	—
255	C₂²×C₁₃	—	2	1	no	—
256	C₂²×C₁₃	—	4	1	no	—
257	C₂²×C₁₃	—	4	1	no	—
258	C₂²×C₁₃	—	8	2	no	—
259	C₂²×C₁₃	—	8	2	no	—
260	C₂²×C₁₃	—	8	2	no	—
261	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
262	C₄×C₁₃	—	2	1	no	—
263	C₄×C₁₃	—	2	1	no	—
264	C₄×C₁₃	—	2	2	no	—
265	C₄×C₁₃	—	2	1	no	—
266	C₄×C₁₃	—	2	1	no	—
267	C₄×C₁₃	—	4	1	no	—
268	C₄×C₁₃	—	4	1	no	—
269	C₄×C₁₃	—	8	2	no	—
270	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
271	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
272	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
273	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
274	C₂×#41	—	2	2	no	—
275	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
276	#135	—	4	4	no	—
277	#135	—	4	4	no	—
278	C₂×Q₁₆	—	2	1	no	—
279	C₂×Q₁₆	—	2	1	no	—
280	C₂×SD₁₆	—	2	2	no	—
281	C₂×SD₁₆	—	2	2	no	—
282	C₂×SD₁₆	—	2	2	no	—
283	C₂×D₈	—	2	2	no	—
284	C₂×D₈	—	2	1	no	—
285	C₂×D₈	—	2	1	no	—
286	C₂²×C₈	—	2	1	no	—
287	C₂²×C₈	—	2	1	no	—
288	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
289	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
290	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
291	#127	C₂³×C₁₃	1	2	yes	—
292	#124	—	2	2	no	—
293	#121	—	2	2	no	—
294	#121	—	2	2	no	—
295	C₄×Q₈	D₄×C₁₃	1	1	yes	characteristic
296	C₄×Q₈	C₂³×C₁₃	1	1	yes	characteristic
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	2	2	no	—
300	C₄×D₄	—	2	2	no	—
301	C₄×D₄	D₄×C₁₃	1	1	yes	characteristic
302	C₄×D₄	C₂³×C₁₃	1	1	yes	characteristic
303	#117	—	2	1	no	—
304	#117	D₄×C₁₃	1	1	yes	characteristic
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
307	#107	—	2	2	no	—
308	#106	—	2	2	no	—
309	C₄⋊C₈	—	2	1	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
312	C₄⋊C₈	C₂³×C₁₃	1	1	yes	characteristic
313	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
314	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
315	#103	—	2	2	no	—
316	#102	—	2	2	no	—
317	#102	—	2	2	no	—
318	#102	—	2	2	no	—
319	C₂²⋊C₈	—	2	1	no	—
320	C₂²⋊C₈	—	2	2	no	—
321	C₂²⋊C₈	—	2	1	no	—
322	C₂²⋊C₈	—	2	1	no	—
323	#97	—	2	2	no	—
324	C₄×C₈	—	2	1	no	—
325	C₄×C₈	—	2	1	no	—
326	C₄×C₈	—	2	1	no	—
327	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
328	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
329	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
330	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
331	C₂×C₁₃	—	4	1	no	—
332	C₂×C₁₃	—	4	2	no	—
333	C₂×C₁₃	—	16	2	no	—
334	C₂×C₁₃	#3038	1	1	yes	characteristic
335	C₂×C₁₃	#3050	1	1	yes	characteristic
336	C₂×C₁₃	#3067	1	1	yes	characteristic
337	#41	—	2	2	no	—
338	#41	—	2	2	no	—
339	#41	—	4	4	no	—
340	#41	—	4	4	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	4	2	no	—
348	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	4	2	no	—
353	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
355	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
356	Q₁₆	—	4	2	no	—
357	Q₁₆	—	4	2	no	—
358	SD₁₆	—	4	4	no	—
359	SD₁₆	—	4	4	no	—
360	SD₁₆	—	4	4	no	—
361	D₈	—	4	2	no	—
362	D₈	—	4	4	no	—
363	D₈	—	4	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	4	2	no	—
371	C₂×C₈	—	4	2	no	—
372	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
373	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
374	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
375	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
381	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	2	1	no	—
385	C₂²⋊C₄	—	4	2	no	—
386	C₂²⋊C₄	—	4	2	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
391	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
392	C₄²	C₁₃×#41	1	1	yes	characteristic
393	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
394	C₁₃	#19269	1	1	yes	characteristic, direct product factor, Sylow
395	C₂³	—	2	1	no	—
396	C₂³	—	4	2	no	—
397	C₂³	C₁₃×#121	1	1	yes	characteristic
398	Q₈	—	2	1	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	C₁₃×#135	1	2	yes	complemented
402	D₄	—	2	4	no	—
403	D₄	—	2	1	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	2	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	2	no	—
408	D₄	—	8	2	no	—
409	D₄	—	8	4	no	—
410	D₄	C₁₃×#135	1	2	yes	complemented
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	8	4	no	—
425	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
426	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
427	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
430	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	4	2	no	—
434	C₈	—	4	2	no	—
435	C₈	—	4	1	no	—
436	C₈	—	4	1	no	—
437	C₈	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
438	C₈	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	2	no	—
448	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	4	1	no	—
455	C₄	—	4	1	no	—
456	C₄	—	8	2	no	—
457	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
458	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
459	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
460	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
461	C₂	—	4	1	no	—
462	C₂	—	4	2	no	—
463	C₂	—	16	2	no	—
464	C₂	C₁₃×#3038	1	1	yes	characteristic
465	C₂	C₁₃×#3050	1	1	yes	characteristic
466	C₂	C₁₃×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3147	C₂	semidirect
2. C₁₃×#3115	C₂	semidirect
3. C₈×C₁₃×#41	C₂	semidirect
4. C₁₃×#1670	C₂	semidirect
5. C₁₃×#1669	C₂	semidirect
6. C₁₃×#1668	C₂	semidirect
7. C₁₃×#1667	C₂	semidirect
8. C₁₃×#1666	C₂	semidirect
9. C₁₃×#1665	C₂	semidirect
10. C₁₃×#1568	C₂	semidirect
11. C₁₃×#1553	C₂	semidirect
104. #19269	C₁₃	direct (N × H)
162. #3147	C₂×C₁₃	semidirect
163. #3115	C₂×C₁₃	semidirect
164. C₈×#41	C₂×C₁₃	semidirect
165. #1670	C₂×C₁₃	semidirect
166. #1669	C₂×C₁₃	semidirect
167. #1668	C₂×C₁₃	semidirect
168. #1667	C₂×C₁₃	semidirect
169. #1666	C₂×C₁₃	semidirect
170. #1665	C₂×C₁₃	semidirect
171. #1568	C₂×C₁₃	semidirect
172. #1553	C₂×C₁₃	semidirect
179. Q₈×C₁₃	#135	semidirect
188. D₄×C₁₃	#135	semidirect
394. C₁₃	#19269	direct (N × H)
401. Q₈	C₁₃×#135	semidirect
410. D₄	C₁₃×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#3147	2
C₁₃×#3115	2
C₈×C₁₃×#41	2
C₁₃×#1670	2
C₁₃×#1669	2
C₁₃×#1668	2
C₁₃×#1667	2
C₁₃×#1666	2
C₁₃×#1665	2
C₁₃×#1568	2
C₁₃×#1553	2
#19269	13

Subgroups — C13×#19269 #15705608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19269 #15705608