Subgroups — C₁₃×#10070 #15696409

Order 3328.

790 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2541	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#331	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×#127	—	2	1	no	—
10	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#121	—	2	2	no	—
12	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#486	—	2	2	no	—
14	C₁₃×#486	—	2	2	no	—
15	C₁₃×#474	—	2	2	no	—
16	C₁₃×#474	—	2	2	no	—
17	C₂×C₁₃×#107	—	2	1	no	—
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#103	—	2	2	no	—
21	C₂×C₁₃×#102	—	2	1	no	—
22	C₂×C₁₃×#102	—	2	2	no	—
23	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₁₃×#392	—	2	2	no	—
25	C₁₃×#390	—	2	1	no	—
26	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₁₃×#331	—	2	2	no	—
28	C₁₃×D₄⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₁₃	—	2	1	no	—
30	C₂²×D₄×C₁₃	—	2	4	no	—
31	C₂²×D₄×C₁₃	—	2	1	no	—
32	C₂²×D₄×C₁₃	—	2	1	no	—
33	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
34	C₂²×D₄×C₁₃	D₄	1	2	yes	—
35	C₂³×C₄×C₁₃	—	2	1	no	—
36	C₂²×C₈×C₁₃	—	2	1	no	—
37	C₂²×C₈×C₁₃	—	2	1	no	—
38	C₂²×C₈×C₁₃	—	2	1	no	—
39	C₁₃×C₄⋊Q₈	—	2	1	no	—
40	C₁₃×C₄⋊Q₈	—	2	1	no	—
41	C₁₃×C₄⋊Q₈	—	2	1	no	—
42	C₁₃×C₄⋊Q₈	D₄	1	2	yes	complemented
43	C₁₃×#127	—	2	1	no	—
44	C₁₃×#127	—	2	1	no	—
45	C₁₃×#127	—	2	1	no	—
46	C₁₃×#127	—	2	1	no	—
47	C₁₃×#127	—	4	2	no	—
48	C₁₃×#127	—	4	2	no	—
49	C₁₃×#121	—	4	4	no	—
50	C₁₃×#121	—	4	4	no	—
51	C₄×D₄×C₁₃	—	2	1	no	—
52	C₄×D₄×C₁₃	—	2	1	no	—
53	C₄×D₄×C₁₃	—	2	1	no	—
54	C₄×D₄×C₁₃	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
58	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
59	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
60	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
61	C₂×C₄²×C₁₃	—	2	1	no	—
62	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×#107	—	2	4	no	—
64	C₁₃×C₄⋊C₈	—	2	1	no	—
65	C₁₃×C₄⋊C₈	—	2	1	no	—
66	C₁₃×C₄⋊C₈	—	2	1	no	—
67	C₁₃×C₄⋊C₈	D₄	1	2	yes	complemented
68	C₁₃×#103	—	4	4	no	—
69	C₁₃×#102	—	2	4	no	—
70	C₁₃×#102	—	2	8	no	—
71	C₄×C₈×C₁₃	—	2	1	no	—
72	C₄×C₈×C₁₃	D₄	1	2	yes	complemented
73	C₁₃×#95	—	2	1	no	—
74	#10070	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
75	C₂⁴×C₁₃	—	2	1	no	—
76	C₂⁴×C₁₃	—	2	2	no	—
77	C₂×Q₈×C₁₃	—	2	2	no	—
78	C₂×Q₈×C₁₃	—	4	1	no	—
79	C₂×Q₈×C₁₃	—	4	2	no	—
80	C₂×Q₈×C₁₃	—	4	2	no	—
81	C₂×D₄×C₁₃	—	2	1	no	—
82	C₂×D₄×C₁₃	—	2	2	no	—
83	C₂×D₄×C₁₃	—	2	1	no	—
84	C₂×D₄×C₁₃	—	2	2	no	—
85	C₂×D₄×C₁₃	—	2	1	no	—
86	C₂×D₄×C₁₃	—	2	1	no	—
87	C₂×D₄×C₁₃	—	2	1	no	—
88	C₂×D₄×C₁₃	—	4	4	no	—
89	C₂×D₄×C₁₃	—	4	8	no	—
90	C₂×D₄×C₁₃	—	4	8	no	—
91	C₂×D₄×C₁₃	—	4	1	no	—
92	C₂×D₄×C₁₃	—	4	1	no	—
93	C₂×D₄×C₁₃	—	4	1	no	—
94	C₂×D₄×C₁₃	—	4	1	no	—
95	C₂×D₄×C₁₃	—	4	2	no	—
96	C₂×D₄×C₁₃	—	4	1	no	—
97	C₂×D₄×C₁₃	—	4	1	no	—
98	C₂×D₄×C₁₃	—	4	2	no	—
99	C₂×D₄×C₁₃	—	4	1	no	—
100	C₂×D₄×C₁₃	—	4	1	no	—
101	C₂×D₄×C₁₃	—	8	4	no	—
102	C₂×D₄×C₁₃	SD₁₆	1	2	yes	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	4	1	no	—
106	C₂²×C₄×C₁₃	—	4	1	no	—
107	C₂²×C₄×C₁₃	—	4	1	no	—
108	C₂²×C₄×C₁₃	—	4	2	no	—
109	C₂²×C₄×C₁₃	—	4	2	no	—
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	4	2	no	—
116	C₂×C₈×C₁₃	—	4	1	no	—
117	C₂×C₈×C₁₃	—	4	1	no	—
118	C₂×C₈×C₁₃	—	4	1	no	—
119	C₂×C₈×C₁₃	—	4	2	no	—
120	C₁₃×C₄⋊C₄	—	2	2	no	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	2	no	—
123	C₁₃×C₄⋊C₄	—	2	1	no	—
124	C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₁₃×C₄⋊C₄	—	4	1	no	—
126	C₁₃×C₄⋊C₄	—	4	1	no	—
127	C₁₃×C₄⋊C₄	D₈	1	4	yes	—
128	C₁₃×C₂²⋊C₄	—	4	8	no	—
129	C₁₃×C₂²⋊C₄	—	4	1	no	—
130	C₁₃×C₂²⋊C₄	—	4	1	no	—
131	C₄²×C₁₃	—	4	1	no	—
132	C₄²×C₁₃	—	4	1	no	—
133	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₃	#41	1	1	yes	characteristic
137	C₂×#486	C₂×C₁₃	1	1	yes	characteristic, complemented
138	C₂×#474	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#2541	C₂×C₁₃	1	1	yes	characteristic
140	#1981	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₂×#331	C₂×C₁₃	1	1	yes	characteristic, complemented
142	C₂×D₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#1279	C₂×C₁₃	1	1	yes	characteristic, complemented
144	C₂³×C₁₃	—	2	2	no	—
145	C₂³×C₁₃	—	4	1	no	—
146	C₂³×C₁₃	—	4	2	no	—
147	C₂³×C₁₃	—	4	1	no	—
148	C₂³×C₁₃	—	4	2	no	—
149	C₂³×C₁₃	—	4	2	no	—
150	C₂³×C₁₃	—	4	4	no	—
151	C₂³×C₁₃	—	4	2	no	—
152	C₂³×C₁₃	—	4	2	no	—
153	C₂³×C₁₃	—	4	4	no	—
154	C₂³×C₁₃	#120	1	1	yes	characteristic
155	Q₈×C₁₃	—	4	4	no	—
156	Q₈×C₁₃	—	8	1	no	—
157	Q₈×C₁₃	—	8	1	no	—
158	D₄×C₁₃	—	2	2	no	—
159	D₄×C₁₃	—	2	2	no	—
160	D₄×C₁₃	—	4	4	no	—
161	D₄×C₁₃	—	4	1	no	—
162	D₄×C₁₃	—	4	1	no	—
163	D₄×C₁₃	—	8	2	no	—
164	D₄×C₁₃	—	8	16	no	—
165	D₄×C₁₃	—	8	1	no	—
166	D₄×C₁₃	—	8	1	no	—
167	D₄×C₁₃	—	8	2	no	—
168	D₄×C₁₃	—	8	1	no	—
169	D₄×C₁₃	—	8	1	no	—
170	D₄×C₁₃	—	8	1	no	—
171	D₄×C₁₃	—	8	1	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	2	4	no	—
174	C₂×C₄×C₁₃	—	4	2	no	—
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	8	2	no	—
180	C₂×C₄×C₁₃	—	8	2	no	—
181	C₂×C₄×C₁₃	—	8	1	no	—
182	C₂×C₄×C₁₃	—	8	1	no	—
183	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
184	C₂×C₄×C₁₃	#120	1	1	yes	characteristic
185	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
186	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
187	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
188	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
190	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
191	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
192	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
193	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
194	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
195	C₈×C₁₃	—	4	2	no	—
196	C₈×C₁₃	—	4	2	no	—
197	C₈×C₁₃	—	8	1	no	—
198	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
199	C₂×#127	—	2	1	no	—
200	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
201	C₂×#121	—	2	2	no	—
202	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
203	#486	—	2	2	no	—
204	#486	—	2	2	no	—
205	#474	—	2	2	no	—
206	#474	—	2	2	no	—
207	C₂×#107	—	2	1	no	—
208	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
210	C₂×#103	—	2	2	no	—
211	C₂×#102	—	2	2	no	—
212	C₂×#102	—	2	1	no	—
213	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
214	#392	—	2	2	no	—
215	#390	—	2	1	no	—
216	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
217	#331	—	2	2	no	—
218	D₄⋊C₈	—	2	2	no	—
219	C₂²×C₁₃	—	4	4	no	—
220	C₂²×C₁₃	—	4	2	no	—
221	C₂²×C₁₃	—	8	2	no	—
222	C₂²×C₁₃	—	8	1	no	—
223	C₂²×C₁₃	—	8	1	no	—
224	C₂²×C₁₃	—	8	4	no	—
225	C₂²×C₁₃	—	8	4	no	—
226	C₂²×C₁₃	—	8	2	no	—
227	C₂²×C₁₃	—	8	2	no	—
228	C₂²×C₁₃	—	8	2	no	—
229	C₂²×C₁₃	#392	1	1	yes	characteristic
230	C₂²×C₁₃	#447	1	2	yes	—
231	C₂²×C₁₃	#450	1	1	yes	characteristic
232	C₂²×C₁₃	#452	1	1	yes	characteristic
233	C₂²×C₁₃	#455	1	2	yes	—
234	C₄×C₁₃	—	2	1	no	—
235	C₄×C₁₃	—	2	1	no	—
236	C₄×C₁₃	—	4	4	no	—
237	C₄×C₁₃	—	8	1	no	—
238	C₄×C₁₃	—	8	2	no	—
239	C₄×C₁₃	#448	1	1	yes	characteristic
240	C₄×C₁₃	#449	1	1	yes	characteristic
241	C₄×C₁₃	#459	1	2	yes	—
242	C₄×C₁₃	#465	1	1	yes	characteristic
243	C₄×C₁₃	#468	1	1	yes	characteristic
244	C₄×C₁₃	#493	1	1	yes	characteristic
245	C₄×C₁₃	#496	1	1	yes	characteristic
246	C₂²×Q₈	—	2	1	no	—
247	C₂²×D₄	—	2	4	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	—	2	1	no	—
250	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
251	C₂²×D₄	D₄×C₁₃	1	2	yes	—
252	C₂³×C₄	—	2	1	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₂²×C₈	—	2	1	no	—
256	C₄⋊Q₈	—	2	1	no	—
257	C₄⋊Q₈	—	2	1	no	—
258	C₄⋊Q₈	—	2	1	no	—
259	C₄⋊Q₈	D₄×C₁₃	1	2	yes	complemented
260	#127	—	2	1	no	—
261	#127	—	2	1	no	—
262	#127	—	2	1	no	—
263	#127	—	2	1	no	—
264	#127	—	4	2	no	—
265	#127	—	4	2	no	—
266	#121	—	4	4	no	—
267	#121	—	4	4	no	—
268	C₄×D₄	—	2	1	no	—
269	C₄×D₄	—	2	1	no	—
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
275	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
276	C₂×C₂²⋊C₄	—	2	4	no	—
277	C₂×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
280	#107	—	2	4	no	—
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	—	2	1	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	D₄×C₁₃	1	2	yes	complemented
285	#103	—	4	4	no	—
286	#102	—	2	4	no	—
287	#102	—	2	8	no	—
288	C₄×C₈	—	2	1	no	—
289	C₄×C₈	D₄×C₁₃	1	2	yes	complemented
290	#95	—	2	1	no	—
291	C₂×C₁₃	—	8	2	no	—
292	C₂×C₁₃	—	16	2	no	—
293	C₂×C₁₃	#1639	1	2	yes	—
294	C₂×C₁₃	#1641	1	2	yes	—
295	C₂×C₁₃	#2000	1	1	yes	characteristic
296	C₂×C₁₃	#2004	1	1	yes	characteristic
297	C₂×C₁₃	#2011	1	1	yes	characteristic
298	C₂⁴	—	2	1	no	—
299	C₂⁴	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	4	1	no	—
302	C₂×Q₈	—	4	2	no	—
303	C₂×Q₈	—	4	2	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	1	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	4	4	no	—
312	C₂×D₄	—	4	8	no	—
313	C₂×D₄	—	4	8	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂×D₄	—	4	1	no	—
316	C₂×D₄	—	4	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	2	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂×D₄	—	8	4	no	—
325	C₂×D₄	C₁₃×SD₁₆	1	2	yes	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	4	2	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	C₁₃×D₈	1	4	yes	—
351	C₂²⋊C₄	—	4	8	no	—
352	C₂²⋊C₄	—	4	1	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₄²	—	4	1	no	—
355	C₄²	—	4	1	no	—
356	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
357	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
358	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
359	C₄²	C₁₃×#41	1	1	yes	characteristic
360	C₁₃	#10070	1	1	yes	characteristic, direct product factor, Sylow
361	C₂³	—	2	2	no	—
362	C₂³	—	4	1	no	—
363	C₂³	—	4	2	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	—	4	4	no	—
368	C₂³	—	4	2	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	4	4	no	—
371	C₂³	C₁₃×#120	1	1	yes	characteristic
372	Q₈	—	4	4	no	—
373	Q₈	—	8	1	no	—
374	Q₈	—	8	1	no	—
375	D₄	—	2	2	no	—
376	D₄	—	2	2	no	—
377	D₄	—	4	4	no	—
378	D₄	—	4	1	no	—
379	D₄	—	4	1	no	—
380	D₄	—	8	2	no	—
381	D₄	—	8	16	no	—
382	D₄	—	8	1	no	—
383	D₄	—	8	1	no	—
384	D₄	—	8	2	no	—
385	D₄	—	8	1	no	—
386	D₄	—	8	1	no	—
387	D₄	—	8	1	no	—
388	D₄	—	8	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	8	2	no	—
397	C₂×C₄	—	8	2	no	—
398	C₂×C₄	—	8	1	no	—
399	C₂×C₄	—	8	1	no	—
400	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
401	C₂×C₄	C₁₃×#120	1	1	yes	characteristic
402	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
403	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
404	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
405	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
406	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
407	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
408	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
409	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
410	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
411	C₂×C₄	C₁₃×#137	1	1	yes	characteristic
412	C₈	—	4	2	no	—
413	C₈	—	4	2	no	—
414	C₈	—	8	1	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	8	1	no	—
418	C₂²	—	8	1	no	—
419	C₂²	—	8	2	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	4	no	—
424	C₂²	—	8	4	no	—
425	C₂²	C₁₃×#392	1	1	yes	characteristic
426	C₂²	C₁₃×#447	1	2	yes	—
427	C₂²	C₁₃×#450	1	1	yes	characteristic
428	C₂²	C₁₃×#452	1	1	yes	characteristic
429	C₂²	C₁₃×#455	1	2	yes	—
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	4	4	no	—
433	C₄	—	8	1	no	—
434	C₄	—	8	2	no	—
435	C₄	C₁₃×#448	1	1	yes	characteristic
436	C₄	C₁₃×#449	1	1	yes	characteristic
437	C₄	C₁₃×#459	1	2	yes	—
438	C₄	C₁₃×#465	1	1	yes	characteristic
439	C₄	C₁₃×#468	1	1	yes	characteristic
440	C₄	C₁₃×#493	1	1	yes	characteristic
441	C₄	C₁₃×#496	1	1	yes	characteristic
442	C₂	—	8	2	no	—
443	C₂	—	16	2	no	—
444	C₂	C₁₃×#1639	1	2	yes	—
445	C₂	C₁₃×#1641	1	2	yes	—
446	C₂	C₁₃×#2000	1	1	yes	characteristic
447	C₂	C₁₃×#2004	1	1	yes	characteristic
448	C₂	C₁₃×#2011	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₁₃×#2541	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#486	C₂	semidirect
2. C₂×C₁₃×#474	C₂	semidirect
4. C₁₃×#1981	C₂	semidirect
5. C₂×C₁₃×#331	C₂	semidirect
6. C₂×C₁₃×D₄⋊C₈	C₂	semidirect
7. C₁₃×#1279	C₂	semidirect
42. C₁₃×C₄⋊Q₈	D₄	semidirect
67. C₁₃×C₄⋊C₈	D₄	semidirect
72. C₄×C₈×C₁₃	D₄	semidirect
74. #10070	C₁₃	direct (N × H)
137. C₂×#486	C₂×C₁₃	semidirect
138. C₂×#474	C₂×C₁₃	semidirect
140. #1981	C₂×C₁₃	semidirect
141. C₂×#331	C₂×C₁₃	semidirect
142. C₂×D₄⋊C₈	C₂×C₁₃	semidirect
143. #1279	C₂×C₁₃	semidirect
259. C₄⋊Q₈	D₄×C₁₃	semidirect
284. C₄⋊C₈	D₄×C₁₃	semidirect
289. C₄×C₈	D₄×C₁₃	semidirect
360. C₁₃	#10070	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#486	2
C₂×C₁₃×#474	2
C₁₃×#2541	2
C₁₃×#1981	2
C₂×C₁₃×#331	2
C₂×C₁₃×D₄⋊C₈	2
C₁₃×#1279	2
#10070	13

Subgroups — C13×#10070 #15696409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10070 #15696409