Subgroups — C₁₃×#19200 #15705539

Order 3328.

660 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3245	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1703	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1701	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1679	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1677	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1550	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1547	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#131	—	2	1	no	—
13	C₁₃×#533	C₂²	1	1	yes	characteristic
14	C₁₃×#532	C₂²	1	1	yes	characteristic
15	C₁₃×#532	C₂²	1	1	yes	characteristic
16	C₁₃×#488	—	2	1	no	—
17	C₁₃×#488	—	2	1	no	—
18	C₁₃×#487	C₂²	1	1	yes	characteristic
19	C₁₃×#487	C₂²	1	1	yes	characteristic
20	C₁₃×#486	C₂²	1	1	yes	characteristic
21	C₁₃×#486	C₂²	1	1	yes	characteristic
22	C₁₃×#476	C₂²	1	2	yes	—
23	C₁₃×#475	—	2	1	no	—
24	C₁₃×#474	—	2	1	no	—
25	C₁₃×#474	C₂²	1	2	yes	—
26	C₁₃×#466	—	2	2	no	—
27	C₁₃×#465	—	2	2	no	—
28	C₁₃×#461	C₂²	1	2	yes	—
29	C₁₃×#460	—	2	1	no	—
30	C₁₃×#459	—	2	1	no	—
31	C₁₃×#459	C₂²	1	2	yes	—
32	C₁₃×#436	—	2	1	no	—
33	C₁₃×#436	C₂²	1	2	yes	—
34	C₈×D₄×C₁₃	—	2	1	no	—
35	C₈×D₄×C₁₃	C₂²	1	2	yes	—
36	C₁₃×#423	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
39	C₁₃×#416	—	2	1	no	—
40	C₁₃×#416	—	2	1	no	—
41	C₁₃×#408	—	2	1	no	—
42	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
43	C₁₃×#334	C₂²	1	2	yes	—
44	C₁₃×#334	C₂²	1	2	yes	—
45	C₁₃×#333	C₂²	1	2	yes	—
46	C₁₃×#332	C₂²	1	2	yes	—
47	C₁₃×#332	C₂²	1	2	yes	—
48	C₁₃×#331	C₂²	1	2	yes	—
49	C₂×C₁₃×#41	—	2	1	no	—
50	C₂×C₁₃×#41	—	2	1	no	—
51	C₂×C₁₃×SD₁₆	—	2	2	no	—
52	C₂×C₁₃×D₈	—	2	2	no	—
53	C₁₃×#131	—	4	4	no	—
54	C₂×C₁₃×M₁₆	—	2	1	no	—
55	C₂×C₁₃×M₁₆	—	2	2	no	—
56	C₂²×C₈×C₁₃	—	2	1	no	—
57	C₂²×C₈×C₁₃	—	2	1	no	—
58	C₂²×C₈×C₁₃	—	2	2	no	—
59	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
61	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
62	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₁₃×#127	D₄	1	1	yes	characteristic
66	C₁₃×#127	C₂³	1	1	yes	characteristic
67	C₁₃×#125	—	2	1	no	—
68	C₁₃×#124	—	2	1	no	—
69	C₁₃×#124	—	2	1	no	—
70	C₁₃×C₂²⋊Q₈	—	2	1	no	—
71	C₁₃×C₂²⋊Q₈	—	2	1	no	—
72	C₁₃×#121	—	2	1	no	—
73	C₁₃×#121	—	2	1	no	—
74	C₁₃×#121	—	2	1	no	—
75	C₁₃×#121	D₄	1	2	yes	—
76	C₄×Q₈×C₁₃	—	2	1	no	—
77	C₄×Q₈×C₁₃	—	2	1	no	—
78	C₄×D₄×C₁₃	—	2	1	no	—
79	C₄×D₄×C₁₃	—	2	1	no	—
80	C₄×D₄×C₁₃	—	2	1	no	—
81	C₄×D₄×C₁₃	C₂³	1	2	yes	—
82	C₁₃×#117	—	2	1	no	—
83	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×#107	—	2	2	no	—
85	C₁₃×#106	—	2	2	no	—
86	C₁₃×C₄⋊C₈	—	2	1	no	—
87	C₁₃×C₄⋊C₈	—	2	1	no	—
88	C₁₃×C₄⋊C₈	—	2	1	no	—
89	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
90	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
91	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
92	C₁₃×#103	—	2	1	no	—
93	C₁₃×#103	—	2	1	no	—
94	C₁₃×#103	—	2	1	no	—
95	C₁₃×#103	—	2	1	no	—
96	C₁₃×#103	—	2	2	no	—
97	C₁₃×#102	—	2	2	no	—
98	C₁₃×#102	—	2	2	no	—
99	C₁₃×#102	—	2	1	no	—
100	C₁₃×#102	—	2	1	no	—
101	C₁₃×#102	—	2	1	no	—
102	C₁₃×#102	—	2	1	no	—
103	C₁₃×#102	—	2	2	no	—
104	C₁₃×C₂²⋊C₈	—	2	2	no	—
105	C₁₃×C₂²⋊C₈	—	2	2	no	—
106	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
107	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
108	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
110	#19200	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₁₃×#41	—	4	2	no	—
112	C₁₃×#41	—	4	2	no	—
113	C₁₃×#41	—	4	2	no	—
114	C₁₃×#41	—	4	2	no	—
115	C₂×Q₈×C₁₃	—	2	1	no	—
116	C₂×Q₈×C₁₃	—	2	1	no	—
117	C₂×Q₈×C₁₃	—	2	1	no	—
118	C₂×Q₈×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	—	2	2	no	—
120	C₂×D₄×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	—	2	1	no	—
125	C₂×D₄×C₁₃	—	4	1	no	—
126	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	4	1	no	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
132	C₁₃×SD₁₆	—	8	2	no	—
133	C₁₃×D₈	—	8	2	no	—
134	C₁₃×M₁₆	—	4	4	no	—
135	C₁₃×M₁₆	—	4	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	—	4	4	no	—
142	C₂×C₈×C₁₃	—	8	1	no	—
143	C₂×C₈×C₁₃	—	8	1	no	—
144	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₁₃×C₄⋊C₄	—	2	1	no	—
149	C₁₃×C₄⋊C₄	—	2	1	no	—
150	C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₁₃×C₄⋊C₄	—	2	1	no	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₁₃×C₄⋊C₄	—	4	1	no	—
156	C₁₃×C₄⋊C₄	—	4	1	no	—
157	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
158	C₁₃×C₂²⋊C₄	—	2	2	no	—
159	C₁₃×C₂²⋊C₄	—	2	2	no	—
160	C₁₃×C₂²⋊C₄	—	4	1	no	—
161	C₁₃×C₂²⋊C₄	—	4	1	no	—
162	C₁₃×C₂²⋊C₄	—	4	1	no	—
163	C₄²×C₁₃	—	4	1	no	—
164	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₁₃	#41	1	1	yes	characteristic
167	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
168	#3246	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#3245	C₂×C₁₃	1	1	yes	characteristic
170	#3131	C₂×C₁₃	1	1	yes	characteristic, complemented
171	#2931	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#1703	C₂×C₁₃	1	2	yes	complemented
173	#1701	C₂×C₁₃	1	2	yes	complemented
174	#1679	C₂×C₁₃	1	2	yes	complemented
175	#1677	C₂×C₁₃	1	2	yes	complemented
176	C₂×#334	C₂×C₁₃	1	1	yes	characteristic, complemented
177	#1550	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#1547	C₂×C₁₃	1	1	yes	characteristic, complemented
179	C₂³×C₁₃	—	2	2	no	—
180	C₂³×C₁₃	—	4	1	no	—
181	C₂³×C₁₃	#121	1	1	yes	characteristic
182	Q₈×C₁₃	—	4	2	no	—
183	Q₈×C₁₃	—	4	1	no	—
184	Q₈×C₁₃	—	4	1	no	—
185	Q₈×C₁₃	—	4	1	no	—
186	Q₈×C₁₃	—	4	1	no	—
187	Q₈×C₁₃	—	8	1	no	—
188	D₄×C₁₃	—	2	2	no	—
189	D₄×C₁₃	—	2	2	no	—
190	D₄×C₁₃	—	4	2	no	—
191	D₄×C₁₃	—	4	4	no	—
192	D₄×C₁₃	—	4	1	no	—
193	D₄×C₁₃	—	4	1	no	—
194	D₄×C₁₃	—	4	1	no	—
195	D₄×C₁₃	—	4	1	no	—
196	D₄×C₁₃	—	4	2	no	—
197	D₄×C₁₃	—	8	1	no	—
198	D₄×C₁₃	—	8	2	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	4	1	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	1	no	—
208	C₂×C₄×C₁₃	—	8	2	no	—
209	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
210	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
211	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
212	C₂×C₄×C₁₃	#135	1	2	yes	—
213	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
214	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
217	C₈×C₁₃	—	2	1	no	—
218	C₈×C₁₃	—	2	1	no	—
219	C₈×C₁₃	—	2	1	no	—
220	C₈×C₁₃	—	2	1	no	—
221	C₈×C₁₃	—	4	2	no	—
222	C₈×C₁₃	—	4	2	no	—
223	C₈×C₁₃	—	4	2	no	—
224	C₂×#131	—	2	1	no	—
225	#533	C₂²×C₁₃	1	1	yes	characteristic
226	#532	C₂²×C₁₃	1	1	yes	characteristic
227	#532	C₂²×C₁₃	1	1	yes	characteristic
228	#488	—	2	1	no	—
229	#488	—	2	1	no	—
230	#487	C₂²×C₁₃	1	1	yes	characteristic
231	#487	C₂²×C₁₃	1	1	yes	characteristic
232	#486	C₂²×C₁₃	1	1	yes	characteristic
233	#486	C₂²×C₁₃	1	1	yes	characteristic
234	#476	C₂²×C₁₃	1	2	yes	—
235	#475	—	2	1	no	—
236	#474	—	2	1	no	—
237	#474	C₂²×C₁₃	1	2	yes	—
238	#466	—	2	2	no	—
239	#465	—	2	2	no	—
240	#461	C₂²×C₁₃	1	2	yes	—
241	#460	—	2	1	no	—
242	#459	—	2	1	no	—
243	#459	C₂²×C₁₃	1	2	yes	—
244	#436	—	2	1	no	—
245	#436	C₂²×C₁₃	1	2	yes	—
246	C₈×D₄	—	2	1	no	—
247	C₈×D₄	C₂²×C₁₃	1	2	yes	—
248	#423	C₂²×C₁₃	1	1	yes	characteristic
249	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
251	#416	—	2	1	no	—
252	#416	—	2	1	no	—
253	#408	—	2	1	no	—
254	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
255	#334	C₂²×C₁₃	1	2	yes	—
256	#334	C₂²×C₁₃	1	2	yes	—
257	#333	C₂²×C₁₃	1	2	yes	—
258	#332	C₂²×C₁₃	1	2	yes	—
259	#332	C₂²×C₁₃	1	2	yes	—
260	#331	C₂²×C₁₃	1	2	yes	—
261	C₂²×C₁₃	—	2	1	no	—
262	C₂²×C₁₃	—	2	1	no	—
263	C₂²×C₁₃	—	4	2	no	—
264	C₂²×C₁₃	—	4	2	no	—
265	C₂²×C₁₃	—	4	2	no	—
266	C₂²×C₁₃	—	8	1	no	—
267	C₂²×C₁₃	—	8	1	no	—
268	C₂²×C₁₃	—	8	1	no	—
269	C₂²×C₁₃	#463	1	2	yes	—
270	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
271	C₄×C₁₃	—	2	1	no	—
272	C₄×C₁₃	—	2	1	no	—
273	C₄×C₁₃	—	2	1	no	—
274	C₄×C₁₃	—	4	2	no	—
275	C₄×C₁₃	—	8	1	no	—
276	C₄×C₁₃	—	8	1	no	—
277	C₄×C₁₃	—	8	1	no	—
278	C₄×C₁₃	#463	1	2	yes	—
279	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
280	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
281	C₄×C₁₃	#577	1	1	yes	characteristic
282	C₄×C₁₃	#577	1	1	yes	characteristic
283	C₂×#41	—	2	1	no	—
284	C₂×#41	—	2	1	no	—
285	C₂×SD₁₆	—	2	2	no	—
286	C₂×D₈	—	2	2	no	—
287	#131	—	4	4	no	—
288	C₂×M₁₆	—	2	1	no	—
289	C₂×M₁₆	—	2	2	no	—
290	C₂²×C₈	—	2	1	no	—
291	C₂²×C₈	—	2	1	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
294	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
295	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
296	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
297	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
298	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
299	#127	D₄×C₁₃	1	1	yes	characteristic
300	#127	C₂³×C₁₃	1	1	yes	characteristic
301	#125	—	2	1	no	—
302	#124	—	2	1	no	—
303	#124	—	2	1	no	—
304	C₂²⋊Q₈	—	2	1	no	—
305	C₂²⋊Q₈	—	2	1	no	—
306	#121	—	2	1	no	—
307	#121	—	2	1	no	—
308	#121	—	2	1	no	—
309	#121	D₄×C₁₃	1	2	yes	—
310	C₄×Q₈	—	2	1	no	—
311	C₄×Q₈	—	2	1	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	C₂³×C₁₃	1	2	yes	—
316	#117	—	2	1	no	—
317	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
318	#107	—	2	2	no	—
319	#106	—	2	2	no	—
320	C₄⋊C₈	—	2	1	no	—
321	C₄⋊C₈	—	2	1	no	—
322	C₄⋊C₈	—	2	1	no	—
323	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
324	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
325	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
326	#103	—	2	1	no	—
327	#103	—	2	1	no	—
328	#103	—	2	1	no	—
329	#103	—	2	1	no	—
330	#103	—	2	2	no	—
331	#102	—	2	2	no	—
332	#102	—	2	2	no	—
333	#102	—	2	1	no	—
334	#102	—	2	1	no	—
335	#102	—	2	1	no	—
336	#102	—	2	1	no	—
337	#102	—	2	2	no	—
338	C₂²⋊C₈	—	2	2	no	—
339	C₂²⋊C₈	—	2	2	no	—
340	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
341	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
342	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
343	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
344	C₂×C₁₃	—	2	2	no	—
345	C₂×C₁₃	—	8	2	no	—
346	C₂×C₁₃	—	16	1	no	—
347	C₂×C₁₃	C₂×#463	1	1	yes	characteristic
348	C₂×C₁₃	#3060	1	1	yes	characteristic
349	C₂×C₁₃	#3067	1	1	yes	characteristic
350	#41	—	4	2	no	—
351	#41	—	4	2	no	—
352	#41	—	4	2	no	—
353	#41	—	4	2	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	4	1	no	—
365	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	4	1	no	—
368	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
370	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
371	SD₁₆	—	8	2	no	—
372	D₈	—	8	2	no	—
373	M₁₆	—	4	4	no	—
374	M₁₆	—	4	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	4	4	no	—
381	C₂×C₈	—	8	1	no	—
382	C₂×C₈	—	8	1	no	—
383	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
384	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
385	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
386	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	4	1	no	—
395	C₄⋊C₄	—	4	1	no	—
396	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	4	1	no	—
400	C₂²⋊C₄	—	4	1	no	—
401	C₂²⋊C₄	—	4	1	no	—
402	C₄²	—	4	1	no	—
403	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
404	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
405	C₄²	C₁₃×#41	1	1	yes	characteristic
406	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
407	C₁₃	#19200	1	1	yes	characteristic, direct product factor, Sylow
408	C₂³	—	2	2	no	—
409	C₂³	—	4	1	no	—
410	C₂³	C₁₃×#121	1	1	yes	characteristic
411	Q₈	—	4	2	no	—
412	Q₈	—	4	1	no	—
413	Q₈	—	4	1	no	—
414	Q₈	—	4	1	no	—
415	Q₈	—	4	1	no	—
416	Q₈	—	8	1	no	—
417	D₄	—	2	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	4	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	1	no	—
423	D₄	—	4	1	no	—
424	D₄	—	4	1	no	—
425	D₄	—	4	1	no	—
426	D₄	—	8	1	no	—
427	D₄	—	8	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	8	2	no	—
438	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
439	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
440	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
441	C₂×C₄	C₁₃×#135	1	2	yes	—
442	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
443	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
444	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
445	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
446	C₈	—	2	1	no	—
447	C₈	—	2	1	no	—
448	C₈	—	2	1	no	—
449	C₈	—	2	1	no	—
450	C₈	—	4	2	no	—
451	C₈	—	4	2	no	—
452	C₈	—	4	2	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	8	1	no	—
459	C₂²	—	8	1	no	—
460	C₂²	—	8	1	no	—
461	C₂²	C₁₃×#463	1	2	yes	—
462	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	4	2	no	—
467	C₄	—	8	1	no	—
468	C₄	—	8	1	no	—
469	C₄	—	8	1	no	—
470	C₄	C₁₃×#463	1	2	yes	—
471	C₄	C₂×C₁₃×#135	1	1	yes	characteristic
472	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
473	C₄	C₁₃×#577	1	1	yes	characteristic
474	C₄	C₁₃×#577	1	1	yes	characteristic
475	C₂	—	2	2	no	—
476	C₂	—	8	2	no	—
477	C₂	—	16	1	no	—
478	C₂	C₂×C₁₃×#463	1	1	yes	characteristic
479	C₂	C₁₃×#3060	1	1	yes	characteristic
480	C₂	C₁₃×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₁₃×#3245	C₂
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×#3246	C₂	semidirect
3. C₁₃×#3131	C₂	semidirect
4. C₁₃×#2931	C₂	semidirect
5. C₁₃×#1703	C₂	semidirect
6. C₁₃×#1701	C₂	semidirect
7. C₁₃×#1679	C₂	semidirect
8. C₁₃×#1677	C₂	semidirect
9. C₂×C₁₃×#334	C₂	semidirect
10. C₁₃×#1550	C₂	semidirect
11. C₁₃×#1547	C₂	semidirect
110. #19200	C₁₃	direct (N × H)
168. #3246	C₂×C₁₃	semidirect
170. #3131	C₂×C₁₃	semidirect
171. #2931	C₂×C₁₃	semidirect
172. #1703	C₂×C₁₃	semidirect
173. #1701	C₂×C₁₃	semidirect
174. #1679	C₂×C₁₃	semidirect
175. #1677	C₂×C₁₃	semidirect
176. C₂×#334	C₂×C₁₃	semidirect
177. #1550	C₂×C₁₃	semidirect
178. #1547	C₂×C₁₃	semidirect
407. C₁₃	#19200	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3246	2
C₁₃×#3245	2
C₁₃×#3131	2
C₁₃×#2931	2
C₁₃×#1703	2
C₁₃×#1701	2
C₁₃×#1679	2
C₁₃×#1677	2
C₂×C₁₃×#334	2
C₁₃×#1550	2
C₁₃×#1547	2
#19200	13

Subgroups — C13×#19200 #15705539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#19200 #15705539