Subgroups — C₁₃×#26274 #15712613

Order 3328.

796 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×#3155	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#3096	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2952	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2051	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2037	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1978	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1975	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1972	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1951	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1883	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1773	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
13	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
15	C₁₃×#535	C₂²	1	2	yes	—
16	C₁₃×#520	C₂²	1	2	yes	—
17	C₁₃×#496	—	2	2	no	—
18	C₁₃×#495	—	2	1	no	—
19	C₁₃×#493	—	2	1	no	—
20	C₁₃×#482	—	2	2	no	—
21	C₁₃×#482	—	2	2	no	—
22	C₁₃×#481	—	2	2	no	—
23	C₁₃×#480	—	2	2	no	—
24	C₁₃×#442	—	2	1	no	—
25	C₁₃×#441	—	2	1	no	—
26	C₄×C₁₃×SD₁₆	—	2	2	no	—
27	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
29	C₁₃×#428	C₂²	1	2	yes	—
30	C₁₃×#427	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#104	C₂²	1	2	yes	—
33	C₁₃×#418	C₂²	1	2	yes	—
34	C₁₃×#417	C₂²	1	2	yes	—
35	C₂×C₁₃×#102	C₂²	1	2	yes	—
36	C₂×C₁₃×#100	C₂²	1	2	yes	—
37	C₁₃×#408	C₂²	1	2	yes	—
38	C₁₃×#405	C₂²	1	1	yes	characteristic
39	C₁₃×#405	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
41	C₁₃×#390	C₂²	1	2	yes	—
42	C₁₃×#343	C₂²	1	2	yes	—
43	C₁₃×#339	C₂²	1	1	yes	characteristic
44	C₁₃×#339	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#41	C₂³	1	2	yes	—
46	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
47	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
48	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
49	C₁₃×#135	—	2	2	no	—
50	C₁₃×#135	—	2	2	no	—
51	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic
52	C₂×C₁₃×SD₁₆	—	2	2	no	—
53	C₂×C₁₃×SD₁₆	D₄	1	2	yes	—
54	C₂×C₁₃×D₈	—	2	2	no	—
55	C₂×C₁₃×D₈	—	2	1	no	—
56	C₂×C₁₃×D₈	—	2	1	no	—
57	C₂×C₁₃×D₈	—	2	2	no	—
58	C₂×C₁₃×D₈	—	2	2	no	—
59	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic
60	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
62	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×#127	—	2	2	no	—
66	C₁₃×#124	—	2	2	no	—
67	C₁₃×#121	—	2	2	no	—
68	C₁₃×#121	—	2	2	no	—
69	C₁₃×#120	—	4	2	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	—	4	2	no	—
73	C₁₃×#117	—	2	2	no	—
74	C₁₃×#117	C₂³	1	1	yes	characteristic
75	C₁₃×#117	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
78	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×#108	—	2	2	no	—
81	C₁₃×#108	—	2	2	no	—
82	C₁₃×#107	—	2	2	no	—
83	C₁₃×#107	D₄	1	2	yes	—
84	C₁₃×#106	—	2	1	no	—
85	C₁₃×#106	—	2	1	no	—
86	C₁₃×#106	—	2	2	no	—
87	C₁₃×#106	D₄	1	2	yes	—
88	C₁₃×#104	—	4	2	no	—
89	C₁₃×#103	—	2	2	no	—
90	C₁₃×#102	—	2	2	no	—
91	C₁₃×#102	—	2	2	no	—
92	C₁₃×#102	—	2	2	no	—
93	C₁₃×#102	—	2	2	no	—
94	C₁₃×#102	—	2	2	no	—
95	C₁₃×#100	—	4	2	no	—
96	C₁₃×C₂²⋊C₈	—	2	2	no	—
97	C₁₃×C₂²⋊C₈	—	2	2	no	—
98	C₁₃×#97	—	2	1	no	—
99	C₁₃×#97	—	2	1	no	—
100	C₁₃×#97	—	2	2	no	—
101	C₄×C₈×C₁₃	—	2	1	no	—
102	C₄×C₈×C₁₃	—	2	1	no	—
103	#26274	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂⁴×C₁₃	—	2	2	no	—
105	C₁₃×#41	—	2	2	no	—
106	C₁₃×#41	—	2	2	no	—
107	C₁₃×#41	—	2	2	no	—
108	C₁₃×#41	—	2	2	no	—
109	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
110	C₂×D₄×C₁₃	—	2	2	no	—
111	C₂×D₄×C₁₃	—	2	2	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	—	2	2	no	—
116	C₂×D₄×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	—	4	2	no	—
118	C₂×D₄×C₁₃	—	4	2	no	—
119	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	4	2	no	—
124	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
125	C₁₃×Q₁₆	—	2	2	no	—
126	C₁₃×SD₁₆	—	2	4	no	—
127	C₁₃×SD₁₆	—	4	4	no	—
128	C₁₃×D₈	—	2	2	no	—
129	C₁₃×D₈	—	4	4	no	—
130	C₁₃×D₈	—	4	2	no	—
131	C₁₃×D₈	—	4	2	no	—
132	C₁₃×M₁₆	—	2	1	no	—
133	C₁₃×M₁₆	—	2	1	no	—
134	C₁₃×M₁₆	—	2	2	no	—
135	C₁₃×M₁₆	—	2	1	no	—
136	C₁₃×M₁₆	—	2	2	no	—
137	C₁₃×M₁₆	#41	1	2	yes	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	#41	1	2	yes	—
148	C₂×C₈×C₁₃	#41	1	2	yes	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	4	2	no	—
152	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
153	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
154	C₁₃×C₂²⋊C₄	—	2	1	no	—
155	C₁₃×C₂²⋊C₄	—	2	1	no	—
156	C₁₃×C₂²⋊C₄	—	4	2	no	—
157	C₁₃×C₂²⋊C₄	—	4	2	no	—
158	C₁₃×C₂²⋊C₄	—	4	2	no	—
159	C₁₃×C₂²⋊C₄	—	8	4	no	—
160	C₄²×C₁₃	—	2	1	no	—
161	C₄²×C₁₃	—	2	1	no	—
162	C₄²×C₁₃	—	2	1	no	—
163	C₄²×C₁₃	—	2	1	no	—
164	C₄²×C₁₃	—	4	2	no	—
165	#3155	C₂×C₁₃	1	1	yes	characteristic
166	#3096	C₂×C₁₃	1	2	yes	complemented
167	#2952	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#2051	C₂×C₁₃	1	2	yes	complemented
169	#2037	C₂×C₁₃	1	2	yes	complemented
170	#1978	C₂×C₁₃	1	1	yes	characteristic, complemented
171	#1975	C₂×C₁₃	1	1	yes	characteristic, complemented
172	#1972	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#1951	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#1883	C₂×C₁₃	1	2	yes	complemented
175	#1773	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂³×C₁₃	—	2	2	no	—
177	C₂³×C₁₃	—	4	2	no	—
178	C₂³×C₁₃	—	4	2	no	—
179	C₂³×C₁₃	—	4	2	no	—
180	C₂³×C₁₃	—	8	2	no	—
181	C₂³×C₁₃	—	8	2	no	—
182	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
183	Q₈×C₁₃	—	2	2	no	—
184	Q₈×C₁₃	—	2	2	no	—
185	D₄×C₁₃	—	2	2	no	—
186	D₄×C₁₃	—	2	2	no	—
187	D₄×C₁₃	—	4	2	no	—
188	D₄×C₁₃	—	4	2	no	—
189	D₄×C₁₃	—	4	2	no	—
190	D₄×C₁₃	—	4	2	no	—
191	D₄×C₁₃	—	4	2	no	—
192	D₄×C₁₃	—	4	2	no	—
193	D₄×C₁₃	—	16	2	no	—
194	D₄×C₁₃	—	16	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	8	2	no	—
204	C₂×C₄×C₁₃	—	16	2	no	—
205	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
211	C₈×C₁₃	—	2	1	no	—
212	C₈×C₁₃	—	2	1	no	—
213	C₈×C₁₃	—	2	2	no	—
214	C₈×C₁₃	—	4	1	no	—
215	C₈×C₁₃	—	4	2	no	—
216	C₈×C₁₃	#123	1	2	yes	—
217	C₈×C₁₃	#123	1	2	yes	—
218	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
219	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
220	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
221	#535	C₂²×C₁₃	1	2	yes	—
222	#520	C₂²×C₁₃	1	2	yes	—
223	#496	—	2	2	no	—
224	#495	—	2	1	no	—
225	#493	—	2	1	no	—
226	#482	—	2	2	no	—
227	#482	—	2	2	no	—
228	#481	—	2	2	no	—
229	#480	—	2	2	no	—
230	#442	—	2	1	no	—
231	#441	—	2	1	no	—
232	C₄×SD₁₆	—	2	2	no	—
233	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
235	#428	C₂²×C₁₃	1	2	yes	—
236	#427	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
238	C₂×#104	C₂²×C₁₃	1	2	yes	—
239	#418	C₂²×C₁₃	1	2	yes	—
240	#417	C₂²×C₁₃	1	2	yes	—
241	C₂×#102	C₂²×C₁₃	1	2	yes	—
242	C₂×#100	C₂²×C₁₃	1	2	yes	—
243	#408	C₂²×C₁₃	1	2	yes	—
244	#405	C₂²×C₁₃	1	1	yes	characteristic
245	#405	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
247	#390	C₂²×C₁₃	1	2	yes	—
248	#343	C₂²×C₁₃	1	2	yes	—
249	#339	C₂²×C₁₃	1	1	yes	characteristic
250	#339	C₂²×C₁₃	1	1	yes	characteristic
251	C₂²×C₁₃	—	2	2	no	—
252	C₂²×C₁₃	—	4	2	no	—
253	C₂²×C₁₃	—	4	2	no	—
254	C₂²×C₁₃	—	4	2	no	—
255	C₂²×C₁₃	—	8	4	no	—
256	C₂²×C₁₃	—	8	2	no	—
257	C₂²×C₁₃	—	8	2	no	—
258	C₂²×C₁₃	—	8	2	no	—
259	C₂²×C₁₃	—	16	2	no	—
260	C₂²×C₁₃	#540	1	1	yes	characteristic
261	C₂²×C₁₃	D₄²	1	1	yes	characteristic
262	C₂²×C₁₃	#559	1	1	yes	characteristic
263	C₄×C₁₃	—	4	2	no	—
264	C₄×C₁₃	—	4	2	no	—
265	C₄×C₁₃	—	4	2	no	—
266	C₄×C₁₃	—	8	1	no	—
267	C₄×C₁₃	—	8	2	no	—
268	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
269	C₄×C₁₃	#532	1	1	yes	characteristic
270	C₄×C₁₃	#546	1	1	yes	characteristic
271	C₄×C₁₃	#550	1	1	yes	characteristic
272	C₂×#41	C₂³×C₁₃	1	2	yes	—
273	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
274	AGL(1,ℤ/8)	—	2	4	no	—
275	AGL(1,ℤ/8)	—	4	2	no	—
276	#135	—	2	2	no	—
277	#135	—	2	2	no	—
278	C₂×Q₁₆	D₄×C₁₃	1	1	yes	characteristic
279	C₂×SD₁₆	—	2	2	no	—
280	C₂×SD₁₆	D₄×C₁₃	1	2	yes	—
281	C₂×D₈	—	2	2	no	—
282	C₂×D₈	—	2	1	no	—
283	C₂×D₈	—	2	1	no	—
284	C₂×D₈	—	2	2	no	—
285	C₂×D₈	—	2	2	no	—
286	C₂×D₈	D₄×C₁₃	1	1	yes	characteristic
287	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
288	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
289	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
292	#127	—	2	2	no	—
293	#124	—	2	2	no	—
294	#121	—	2	2	no	—
295	#121	—	2	2	no	—
296	#120	—	4	2	no	—
297	C₄×Q₈	—	2	2	no	—
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	—	4	2	no	—
300	#117	—	2	2	no	—
301	#117	C₂³×C₁₃	1	1	yes	characteristic
302	#117	C₂³×C₁₃	1	1	yes	characteristic
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
305	C₂×C₂²⋊C₄	—	4	2	no	—
306	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
307	#108	—	2	2	no	—
308	#108	—	2	2	no	—
309	#107	—	2	2	no	—
310	#107	D₄×C₁₃	1	2	yes	—
311	#106	—	2	1	no	—
312	#106	—	2	1	no	—
313	#106	—	2	2	no	—
314	#106	D₄×C₁₃	1	2	yes	—
315	#104	—	4	2	no	—
316	#103	—	2	2	no	—
317	#102	—	2	2	no	—
318	#102	—	2	2	no	—
319	#102	—	2	2	no	—
320	#102	—	2	2	no	—
321	#102	—	2	2	no	—
322	#100	—	4	2	no	—
323	C₂²⋊C₈	—	2	2	no	—
324	C₂²⋊C₈	—	2	2	no	—
325	#97	—	2	1	no	—
326	#97	—	2	1	no	—
327	#97	—	2	2	no	—
328	C₄×C₈	—	2	1	no	—
329	C₄×C₈	—	2	1	no	—
330	C₂×C₁₃	—	2	1	no	—
331	C₂×C₁₃	—	2	1	no	—
332	C₂×C₁₃	—	8	2	no	—
333	C₂×C₁₃	—	16	2	no	—
334	C₂×C₁₃	#2445	1	1	yes	characteristic
335	C₂×C₁₃	#3288	1	2	yes	—
336	C₂⁴	—	2	2	no	—
337	#41	—	2	2	no	—
338	#41	—	2	2	no	—
339	#41	—	2	2	no	—
340	#41	—	2	2	no	—
341	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	4	2	no	—
350	C₂×D₄	—	4	2	no	—
351	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	4	2	no	—
356	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
357	Q₁₆	—	2	2	no	—
358	SD₁₆	—	2	4	no	—
359	SD₁₆	—	4	4	no	—
360	D₈	—	2	2	no	—
361	D₈	—	4	4	no	—
362	D₈	—	4	2	no	—
363	D₈	—	4	2	no	—
364	M₁₆	—	2	1	no	—
365	M₁₆	—	2	1	no	—
366	M₁₆	—	2	2	no	—
367	M₁₆	—	2	1	no	—
368	M₁₆	—	2	2	no	—
369	M₁₆	C₁₃×#41	1	2	yes	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
376	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
377	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
378	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
379	C₂×C₈	C₁₃×#41	1	2	yes	—
380	C₂×C₈	C₁₃×#41	1	2	yes	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
385	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
386	C₂²⋊C₄	—	2	1	no	—
387	C₂²⋊C₄	—	2	1	no	—
388	C₂²⋊C₄	—	4	2	no	—
389	C₂²⋊C₄	—	4	2	no	—
390	C₂²⋊C₄	—	4	2	no	—
391	C₂²⋊C₄	—	8	4	no	—
392	C₄²	—	2	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	4	2	no	—
397	C₁₃	#26274	1	1	yes	characteristic, direct product factor, Sylow
398	C₂³	—	2	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	8	2	no	—
403	C₂³	—	8	2	no	—
404	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
405	Q₈	—	2	2	no	—
406	Q₈	—	2	2	no	—
407	D₄	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	16	2	no	—
416	D₄	—	16	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	8	2	no	—
426	C₂×C₄	—	16	2	no	—
427	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
428	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
429	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
430	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
431	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
432	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
433	C₈	—	2	1	no	—
434	C₈	—	2	1	no	—
435	C₈	—	2	2	no	—
436	C₈	—	4	1	no	—
437	C₈	—	4	2	no	—
438	C₈	C₁₃×#123	1	2	yes	—
439	C₈	C₁₃×#123	1	2	yes	—
440	C₂²	—	2	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	8	4	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	16	2	no	—
449	C₂²	C₁₃×#540	1	1	yes	characteristic
450	C₂²	D₄²×C₁₃	1	1	yes	characteristic
451	C₂²	C₁₃×#559	1	1	yes	characteristic
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	8	1	no	—
456	C₄	—	8	2	no	—
457	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
458	C₄	C₁₃×#532	1	1	yes	characteristic
459	C₄	C₁₃×#546	1	1	yes	characteristic
460	C₄	C₁₃×#550	1	1	yes	characteristic
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	8	2	no	—
464	C₂	—	16	2	no	—
465	C₂	C₁₃×#2445	1	1	yes	characteristic
466	C₂	C₁₃×#3288	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#3155	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#3096	C₂	semidirect
3. C₁₃×#2952	C₂	semidirect
4. C₁₃×#2051	C₂	semidirect
5. C₁₃×#2037	C₂	semidirect
6. C₁₃×#1978	C₂	semidirect
7. C₁₃×#1975	C₂	semidirect
8. C₁₃×#1972	C₂	semidirect
9. C₁₃×#1951	C₂	semidirect
10. C₁₃×#1883	C₂	semidirect
11. C₁₃×#1773	C₂	semidirect
103. #26274	C₁₃	direct (N × H)
166. #3096	C₂×C₁₃	semidirect
167. #2952	C₂×C₁₃	semidirect
168. #2051	C₂×C₁₃	semidirect
169. #2037	C₂×C₁₃	semidirect
170. #1978	C₂×C₁₃	semidirect
171. #1975	C₂×C₁₃	semidirect
172. #1972	C₂×C₁₃	semidirect
173. #1951	C₂×C₁₃	semidirect
174. #1883	C₂×C₁₃	semidirect
175. #1773	C₂×C₁₃	semidirect
397. C₁₃	#26274	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×#3155	2
C₁₃×#3096	2
C₁₃×#2952	2
C₁₃×#2051	2
C₁₃×#2037	2
C₁₃×#1978	2
C₁₃×#1975	2
C₁₃×#1972	2
C₁₃×#1951	2
C₁₃×#1883	2
C₁₃×#1773	2
#26274	13

Subgroups — C13×#26274 #15712613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26274 #15712613