Subgroups — C₁₃×#60646 #15746985

Order 3328.

3250 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#577	C₂	1	4	yes	maximal, complemented
2	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#3154	C₂	1	12	yes	maximal, complemented
5	C₁₃×#3152	C₂	1	3	yes	maximal, complemented
6	C₁₃×#3151	C₂	1	3	yes	maximal, complemented
7	C₁₃×#3147	C₂	1	3	yes	maximal, complemented
8	C₂×C₁₃×#492	C₂	1	3	yes	maximal, complemented
9	C₄×C₁₃×#131	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
11	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
12	C₁₃×#577	—	2	32	no	—
13	C₂×C₁₃×#137	C₂²	1	12	yes	complemented
14	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	12	yes	complemented
15	C₂×C₁₃×#135	C₂²	1	12	yes	complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	12	yes	complemented
17	C₂×C₁₃×#131	C₂²	1	2	yes	—
18	C₁₃×#550	—	2	2	no	—
19	D₄×Q₈×C₁₃	—	2	2	no	—
20	C₁₃×#547	—	2	6	no	—
21	D₄²×C₁₃	—	2	6	no	—
22	C₁₃×#536	C₂²	1	6	yes	complemented
23	C₁₃×#535	C₂²	1	6	yes	—
24	C₁₃×#532	C₂²	1	3	yes	—
25	C₁₃×#532	C₂²	1	3	yes	complemented
26	C₂×C₁₃×C₄⋊Q₈	C₂²	1	3	yes	complemented
27	C₂×C₁₃×#127	C₂²	1	3	yes	—
28	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
29	C₁₃×#497	C₂²	1	12	yes	complemented
30	C₁₃×#496	C₂²	1	12	yes	complemented
31	C₁₃×#495	C₂²	1	12	yes	complemented
32	C₁₃×#494	C₂²	1	3	yes	complemented
33	C₁₃×#493	C₂²	1	3	yes	complemented
34	C₁₃×#492	C₂²	1	3	yes	complemented
35	C₁₃×#492	C₂²	1	6	yes	complemented
36	C₁₃×#492	C₂²	1	12	yes	complemented
37	C₁₃×#492	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#405	C₂²	1	6	yes	complemented
39	C₄×C₁₃×M₁₆	C₂²	1	3	yes	complemented
40	C₂×C₄×C₈×C₁₃	C₂²	1	3	yes	complemented
41	C₁₃×2₋¹⁺⁴	—	2	16	no	—
42	C₁₃×H(5,𝔽₂)	—	2	16	no	—
43	C₂×C₁₃×#41	—	2	2	no	—
44	C₂×C₁₃×#41	—	2	6	no	—
45	C₂×C₁₃×#41	C₂³	1	6	yes	—
46	C₂×C₁₃×#41	C₂³	1	6	yes	—
47	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₁₃	—	2	2	no	—
49	C₂²×Q₈×C₁₃	C₂³	1	6	yes	—
50	C₂²×D₄×C₁₃	—	2	6	no	—
51	C₂²×D₄×C₁₃	—	2	6	no	—
52	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
53	C₁₃×#137	—	2	48	no	—
54	C₁₃×AGL(1,ℤ/8)	—	2	48	no	—
55	C₁₃×#135	—	2	48	no	—
56	C₂×C₁₃×Q₁₆	C₂³	1	12	yes	—
57	C₂×C₁₃×SD₁₆	—	2	48	no	—
58	C₂×C₁₃×SD₁₆	C₂³	1	12	yes	—
59	C₂×C₁₃×SD₁₆	C₂³	1	24	yes	—
60	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
61	C₂×C₁₃×D₈	C₂³	1	12	yes	—
62	C₁₃×#131	D₄	1	16	yes	complemented
63	C₂×C₁₃×M₁₆	C₂³	1	6	yes	—
64	C₂²×C₈×C₁₃	C₂³	1	6	yes	—
65	C₁₃×C₄⋊Q₈	—	2	6	no	—
66	C₁₃×C₄⋊Q₈	C₂³	1	3	yes	—
67	C₁₃×C₄⋊Q₈	C₂³	1	6	yes	—
68	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
69	C₁₃×#127	—	2	6	no	—
70	C₁₃×#127	C₂³	1	3	yes	—
71	C₁₃×#127	C₂³	1	6	yes	—
72	C₁₃×#127	C₂³	1	1	yes	characteristic
73	C₁₃×#124	C₂³	1	6	yes	—
74	C₁₃×#124	C₂³	1	6	yes	—
75	C₁₃×#123	—	2	12	no	—
76	C₁₃×C₂²⋊Q₈	—	2	12	no	—
77	C₁₃×#121	—	2	6	no	—
78	C₁₃×#121	—	2	6	no	—
79	C₁₃×#121	—	2	12	no	—
80	C₁₃×#120	—	2	12	no	—
81	C₄×Q₈×C₁₃	D₄	1	2	yes	—
82	C₄×D₄×C₁₃	—	2	6	no	—
83	C₄×D₄×C₁₃	—	2	6	no	—
84	C₄×D₄×C₁₃	D₄	1	6	yes	—
85	C₁₃×#117	C₂³	1	3	yes	—
86	C₂×C₁₃×C₄⋊C₄	—	2	6	no	—
87	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
88	C₁₃×#97	C₂³	1	6	yes	—
89	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₁₃	C₂³	1	3	yes	—
91	C₄×C₈×C₁₃	C₂³	1	6	yes	—
92	#60646	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	—	2	6	no	—
94	C₁₃×#41	—	2	24	no	—
95	C₁₃×#41	—	2	24	no	—
96	C₁₃×#41	—	4	8	no	—
97	C₁₃×#41	—	4	24	no	—
98	C₁₃×#41	C₂×D₄	1	8	yes	—
99	C₂×Q₈×C₁₃	—	2	6	no	—
100	C₂×Q₈×C₁₃	—	2	24	no	—
101	C₂×Q₈×C₁₃	—	4	8	no	—
102	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
104	C₂×Q₈×C₁₃	C₂⁴	1	6	yes	—
105	C₂×D₄×C₁₃	—	2	6	no	—
106	C₂×D₄×C₁₃	—	2	6	no	—
107	C₂×D₄×C₁₃	—	2	24	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	—	2	6	no	—
110	C₂×D₄×C₁₃	—	2	6	no	—
111	C₂×D₄×C₁₃	—	2	12	no	—
112	C₂×D₄×C₁₃	—	4	24	no	—
113	C₂×D₄×C₁₃	—	8	12	no	—
114	C₂×D₄×C₁₃	C₂×D₄	1	3	yes	—
115	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
116	C₂×D₄×C₁₃	C₂⁴	1	6	yes	—
117	C₂²×C₄×C₁₃	—	2	6	no	—
118	C₂²×C₄×C₁₃	—	2	6	no	—
119	C₂²×C₄×C₁₃	—	2	6	no	—
120	C₂²×C₄×C₁₃	C₂×D₄	1	6	yes	—
121	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
122	C₁₃×Q₁₆	—	2	24	no	—
123	C₁₃×SD₁₆	—	2	24	no	—
124	C₁₃×SD₁₆	—	2	48	no	—
125	C₁₃×SD₁₆	—	2	8	no	—
126	C₁₃×D₈	—	2	24	no	—
127	C₁₃×M₁₆	C₂×D₄	1	24	yes	complemented
128	C₂×C₈×C₁₃	C₂×D₄	1	24	yes	complemented
129	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
130	C₂×C₈×C₁₃	C₂⁴	1	6	yes	—
131	C₁₃×C₄⋊C₄	—	2	6	no	—
132	C₁₃×C₄⋊C₄	—	2	12	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	C₂×D₄	1	6	yes	—
135	C₁₃×C₂²⋊C₄	—	2	12	no	—
136	C₁₃×C₂²⋊C₄	—	2	12	no	—
137	C₁₃×C₂²⋊C₄	C₂×D₄	1	6	yes	—
138	C₄²×C₁₃	C₂×D₄	1	6	yes	—
139	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
140	C₄²×C₁₃	C₂⁴	1	3	yes	—
141	C₂×#577	C₂×C₁₃	1	4	yes	complemented
142	#3499	C₂×C₁₃	1	1	yes	characteristic, complemented
143	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
144	#3154	C₂×C₁₃	1	12	yes	complemented
145	#3152	C₂×C₁₃	1	3	yes	complemented
146	#3151	C₂×C₁₃	1	3	yes	complemented
147	#3147	C₂×C₁₃	1	3	yes	complemented
148	C₂×#492	C₂×C₁₃	1	3	yes	complemented
149	C₄×#131	C₂×C₁₃	1	1	yes	characteristic, complemented
150	C₂³×C₁₃	—	2	2	no	—
151	C₂³×C₁₃	—	2	6	no	—
152	C₂³×C₁₃	—	4	12	no	—
153	C₂³×C₁₃	—	8	12	no	—
154	C₂³×C₁₃	C₂²×D₄	1	3	yes	—
155	Q₈×C₁₃	—	2	12	no	—
156	Q₈×C₁₃	—	2	4	no	—
157	Q₈×C₁₃	—	4	12	no	—
158	Q₈×C₁₃	#127	1	4	yes	—
159	D₄×C₁₃	—	2	4	no	—
160	D₄×C₁₃	—	2	12	no	—
161	D₄×C₁₃	—	4	12	no	—
162	D₄×C₁₃	—	4	12	no	—
163	D₄×C₁₃	—	4	12	no	—
164	D₄×C₁₃	—	4	4	no	—
165	D₄×C₁₃	—	4	12	no	—
166	D₄×C₁₃	—	8	12	no	—
167	D₄×C₁₃	#127	1	12	yes	—
168	C₂×C₄×C₁₃	—	2	12	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	6	no	—
171	C₂×C₄×C₁₃	—	4	12	no	—
172	C₂×C₄×C₁₃	—	4	12	no	—
173	C₂×C₄×C₁₃	—	4	12	no	—
174	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
175	C₂×C₄×C₁₃	C₂²×D₄	1	3	yes	—
176	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
177	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
178	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
179	C₈×C₁₃	C₂²×D₄	1	4	yes	—
180	C₈×C₁₃	C₂²×D₄	1	12	yes	—
181	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
182	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
183	#577	—	2	32	no	—
184	C₂×#137	C₂²×C₁₃	1	12	yes	complemented
185	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	12	yes	complemented
186	C₂×#135	C₂²×C₁₃	1	12	yes	complemented
187	C₂²×SD₁₆	C₂²×C₁₃	1	12	yes	complemented
188	C₂×#131	C₂²×C₁₃	1	2	yes	—
189	#550	—	2	2	no	—
190	D₄×Q₈	—	2	2	no	—
191	#547	—	2	6	no	—
192	D₄²	—	2	6	no	—
193	#536	C₂²×C₁₃	1	6	yes	complemented
194	#535	C₂²×C₁₃	1	6	yes	—
195	#532	C₂²×C₁₃	1	3	yes	—
196	#532	C₂²×C₁₃	1	3	yes	complemented
197	C₂×C₄⋊Q₈	C₂²×C₁₃	1	3	yes	complemented
198	C₂×#127	C₂²×C₁₃	1	3	yes	—
199	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
200	#497	C₂²×C₁₃	1	12	yes	complemented
201	#496	C₂²×C₁₃	1	12	yes	complemented
202	#495	C₂²×C₁₃	1	12	yes	complemented
203	#494	C₂²×C₁₃	1	3	yes	complemented
204	#493	C₂²×C₁₃	1	3	yes	complemented
205	#492	C₂²×C₁₃	1	3	yes	complemented
206	#492	C₂²×C₁₃	1	6	yes	complemented
207	#492	C₂²×C₁₃	1	12	yes	complemented
208	#492	C₂²×C₁₃	1	1	yes	characteristic, complemented
209	#405	C₂²×C₁₃	1	6	yes	complemented
210	C₄×M₁₆	C₂²×C₁₃	1	3	yes	complemented
211	C₂×C₄×C₈	C₂²×C₁₃	1	3	yes	complemented
212	C₂²×C₁₃	—	2	6	no	—
213	C₂²×C₁₃	—	4	2	no	—
214	C₂²×C₁₃	—	4	6	no	—
215	C₂²×C₁₃	—	4	12	no	—
216	C₂²×C₁₃	—	4	4	no	—
217	C₂²×C₁₃	—	16	12	no	—
218	C₂²×C₁₃	C₂×#127	1	6	yes	—
219	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
220	C₄×C₁₃	—	2	6	no	—
221	C₄×C₁₃	—	4	2	no	—
222	C₄×C₁₃	—	4	6	no	—
223	C₄×C₁₃	C₂×#127	1	6	yes	—
224	C₄×C₁₃	#577	1	4	yes	complemented
225	C₄×C₁₃	C₂³×D₄	1	2	yes	—
226	2₋¹⁺⁴	—	2	16	no	—
227	H(5,𝔽₂)	—	2	16	no	—
228	C₂×#41	—	2	2	no	—
229	C₂×#41	—	2	6	no	—
230	C₂×#41	C₂³×C₁₃	1	6	yes	—
231	C₂×#41	C₂³×C₁₃	1	6	yes	—
232	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
233	C₂²×Q₈	—	2	2	no	—
234	C₂²×Q₈	C₂³×C₁₃	1	6	yes	—
235	C₂²×D₄	—	2	6	no	—
236	C₂²×D₄	—	2	6	no	—
237	C₂²×D₄	C₂³×C₁₃	1	6	yes	—
238	#137	—	2	48	no	—
239	AGL(1,ℤ/8)	—	2	48	no	—
240	#135	—	2	48	no	—
241	C₂×Q₁₆	C₂³×C₁₃	1	12	yes	—
242	C₂×SD₁₆	—	2	48	no	—
243	C₂×SD₁₆	C₂³×C₁₃	1	12	yes	—
244	C₂×SD₁₆	C₂³×C₁₃	1	24	yes	—
245	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
246	C₂×D₈	C₂³×C₁₃	1	12	yes	—
247	#131	D₄×C₁₃	1	16	yes	complemented
248	C₂×M₁₆	C₂³×C₁₃	1	6	yes	—
249	C₂²×C₈	C₂³×C₁₃	1	6	yes	—
250	C₄⋊Q₈	—	2	6	no	—
251	C₄⋊Q₈	C₂³×C₁₃	1	3	yes	—
252	C₄⋊Q₈	C₂³×C₁₃	1	6	yes	—
253	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
254	#127	—	2	6	no	—
255	#127	C₂³×C₁₃	1	3	yes	—
256	#127	C₂³×C₁₃	1	6	yes	—
257	#127	C₂³×C₁₃	1	1	yes	characteristic
258	#124	C₂³×C₁₃	1	6	yes	—
259	#124	C₂³×C₁₃	1	6	yes	—
260	#123	—	2	12	no	—
261	C₂²⋊Q₈	—	2	12	no	—
262	#121	—	2	6	no	—
263	#121	—	2	6	no	—
264	#121	—	2	12	no	—
265	#120	—	2	12	no	—
266	C₄×Q₈	D₄×C₁₃	1	2	yes	—
267	C₄×D₄	—	2	6	no	—
268	C₄×D₄	—	2	6	no	—
269	C₄×D₄	D₄×C₁₃	1	6	yes	—
270	#117	C₂³×C₁₃	1	3	yes	—
271	C₂×C₄⋊C₄	—	2	6	no	—
272	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
273	#97	C₂³×C₁₃	1	6	yes	—
274	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
275	C₄×C₈	C₂³×C₁₃	1	3	yes	—
276	C₄×C₈	C₂³×C₁₃	1	6	yes	—
277	C₂×C₁₃	—	2	6	no	—
278	C₂×C₁₃	—	8	2	no	—
279	C₂×C₁₃	—	8	6	no	—
280	C₂×C₁₃	C₂²×#127	1	1	yes	characteristic
281	C₂×C₁₃	C₂×#577	1	2	yes	—
282	C₂⁴	—	2	6	no	—
283	#41	—	2	24	no	—
284	#41	—	2	24	no	—
285	#41	—	4	8	no	—
286	#41	—	4	24	no	—
287	#41	C₂×D₄×C₁₃	1	8	yes	—
288	C₂×Q₈	—	2	6	no	—
289	C₂×Q₈	—	2	24	no	—
290	C₂×Q₈	—	4	8	no	—
291	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
292	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
293	C₂×Q₈	C₂⁴×C₁₃	1	6	yes	—
294	C₂×D₄	—	2	6	no	—
295	C₂×D₄	—	2	6	no	—
296	C₂×D₄	—	2	24	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	2	6	no	—
299	C₂×D₄	—	2	6	no	—
300	C₂×D₄	—	2	12	no	—
301	C₂×D₄	—	4	24	no	—
302	C₂×D₄	—	8	12	no	—
303	C₂×D₄	C₂×D₄×C₁₃	1	3	yes	—
304	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
305	C₂×D₄	C₂⁴×C₁₃	1	6	yes	—
306	C₂²×C₄	—	2	6	no	—
307	C₂²×C₄	—	2	6	no	—
308	C₂²×C₄	—	2	6	no	—
309	C₂²×C₄	C₂×D₄×C₁₃	1	6	yes	—
310	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
311	Q₁₆	—	2	24	no	—
312	SD₁₆	—	2	24	no	—
313	SD₁₆	—	2	48	no	—
314	SD₁₆	—	2	8	no	—
315	D₈	—	2	24	no	—
316	M₁₆	C₂×D₄×C₁₃	1	24	yes	complemented
317	C₂×C₈	C₂×D₄×C₁₃	1	24	yes	complemented
318	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
319	C₂×C₈	C₂⁴×C₁₃	1	6	yes	—
320	C₄⋊C₄	—	2	6	no	—
321	C₄⋊C₄	—	2	12	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
324	C₂²⋊C₄	—	2	12	no	—
325	C₂²⋊C₄	—	2	12	no	—
326	C₂²⋊C₄	C₂×D₄×C₁₃	1	6	yes	—
327	C₄²	C₂×D₄×C₁₃	1	6	yes	—
328	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
329	C₄²	C₂⁴×C₁₃	1	3	yes	—
330	C₁₃	#60646	1	1	yes	characteristic, direct product factor, Sylow
331	C₂³	—	2	2	no	—
332	C₂³	—	2	6	no	—
333	C₂³	—	4	12	no	—
334	C₂³	—	8	12	no	—
335	C₂³	C₂²×D₄×C₁₃	1	3	yes	—
336	Q₈	—	2	12	no	—
337	Q₈	—	2	4	no	—
338	Q₈	—	4	12	no	—
339	Q₈	C₁₃×#127	1	4	yes	—
340	D₄	—	2	4	no	—
341	D₄	—	2	12	no	—
342	D₄	—	4	12	no	—
343	D₄	—	4	12	no	—
344	D₄	—	4	12	no	—
345	D₄	—	4	12	no	—
346	D₄	—	4	4	no	—
347	D₄	—	8	12	no	—
348	D₄	C₁₃×#127	1	12	yes	—
349	C₂×C₄	—	2	12	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	6	no	—
352	C₂×C₄	—	4	12	no	—
353	C₂×C₄	—	4	12	no	—
354	C₂×C₄	—	4	12	no	—
355	C₂×C₄	C₂²×D₄×C₁₃	1	6	yes	—
356	C₂×C₄	C₂²×D₄×C₁₃	1	3	yes	—
357	C₂×C₄	C₂²×D₄×C₁₃	1	12	yes	—
358	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
359	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
360	C₈	C₂²×D₄×C₁₃	1	4	yes	—
361	C₈	C₂²×D₄×C₁₃	1	12	yes	—
362	C₂²	—	2	6	no	—
363	C₂²	—	4	12	no	—
364	C₂²	—	4	4	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	6	no	—
367	C₂²	—	16	12	no	—
368	C₂²	C₂×C₁₃×#127	1	6	yes	—
369	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
370	C₄	—	2	6	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	6	no	—
373	C₄	C₂×C₁₃×#127	1	6	yes	—
374	C₄	C₁₃×#577	1	4	yes	complemented
375	C₄	C₂³×D₄×C₁₃	1	2	yes	—
376	C₂	—	2	6	no	—
377	C₂	—	8	6	no	—
378	C₂	—	8	2	no	—
379	C₂	C₂²×C₁₃×#127	1	1	yes	characteristic
380	C₂	C₂×C₁₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#577	C₂	semidirect
2. C₁₃×#3499	C₂	semidirect
3. C₁₃×#3498	C₂	semidirect
4. C₁₃×#3154	C₂	semidirect
5. C₁₃×#3152	C₂	semidirect
6. C₁₃×#3151	C₂	semidirect
7. C₁₃×#3147	C₂	semidirect
8. C₂×C₁₃×#492	C₂	semidirect
9. C₄×C₁₃×#131	C₂	semidirect
13. C₂×C₁₃×#137	C₂²	semidirect
14. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
15. C₂×C₁₃×#135	C₂²	semidirect
16. C₂²×C₁₃×SD₁₆	C₂²	semidirect
22. C₁₃×#536	C₂²	semidirect
25. C₁₃×#532	C₂²	semidirect
26. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
29. C₁₃×#497	C₂²	semidirect
30. C₁₃×#496	C₂²	semidirect
31. C₁₃×#495	C₂²	semidirect
32. C₁₃×#494	C₂²	semidirect
33. C₁₃×#493	C₂²	semidirect
34. C₁₃×#492	C₂²	semidirect
35. C₁₃×#492	C₂²	semidirect
36. C₁₃×#492	C₂²	semidirect
37. C₁₃×#492	C₂²	semidirect
38. C₁₃×#405	C₂²	semidirect
39. C₄×C₁₃×M₁₆	C₂²	semidirect
40. C₂×C₄×C₈×C₁₃	C₂²	semidirect
62. C₁₃×#131	D₄	semidirect
92. #60646	C₁₃	direct (N × H)
127. C₁₃×M₁₆	C₂×D₄	semidirect
128. C₂×C₈×C₁₃	C₂×D₄	semidirect
141. C₂×#577	C₂×C₁₃	semidirect
142. #3499	C₂×C₁₃	semidirect
143. #3498	C₂×C₁₃	semidirect
144. #3154	C₂×C₁₃	semidirect
145. #3152	C₂×C₁₃	semidirect
146. #3151	C₂×C₁₃	semidirect
147. #3147	C₂×C₁₃	semidirect
148. C₂×#492	C₂×C₁₃	semidirect
149. C₄×#131	C₂×C₁₃	semidirect
184. C₂×#137	C₂²×C₁₃	semidirect
185. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
186. C₂×#135	C₂²×C₁₃	semidirect
187. C₂²×SD₁₆	C₂²×C₁₃	semidirect
193. #536	C₂²×C₁₃	semidirect
196. #532	C₂²×C₁₃	semidirect
197. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
200. #497	C₂²×C₁₃	semidirect
201. #496	C₂²×C₁₃	semidirect
202. #495	C₂²×C₁₃	semidirect
203. #494	C₂²×C₁₃	semidirect
204. #493	C₂²×C₁₃	semidirect
205. #492	C₂²×C₁₃	semidirect
206. #492	C₂²×C₁₃	semidirect
207. #492	C₂²×C₁₃	semidirect
208. #492	C₂²×C₁₃	semidirect
209. #405	C₂²×C₁₃	semidirect
210. C₄×M₁₆	C₂²×C₁₃	semidirect
211. C₂×C₄×C₈	C₂²×C₁₃	semidirect
224. C₄×C₁₃	#577	semidirect
247. #131	D₄×C₁₃	semidirect
316. M₁₆	C₂×D₄×C₁₃	semidirect
317. C₂×C₈	C₂×D₄×C₁₃	semidirect
330. C₁₃	#60646	direct (N × H)
374. C₄	C₁₃×#577	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#577	2
C₁₃×#3499	2
C₁₃×#3498	2
C₁₃×#3154	2
C₁₃×#3152	2
C₁₃×#3151	2
C₁₃×#3147	2
C₂×C₁₃×#492	2
C₄×C₁₃×#131	2
#60646	13

Subgroups — C13×#60646 #15746985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60646 #15746985