Subgroups — C₁₃×#61079 #15747418

Order 3328.

2826 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#576	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3496	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3267	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3264	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3150	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#3060	C₂	1	2	yes	maximal, complemented
7	C₁₃×#3036	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3012	C₂	1	4	yes	maximal, complemented
9	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2932	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	4	yes	complemented
12	C₁₃×#576	—	2	16	no	—
13	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
14	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
15	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
16	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
17	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
18	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×D₈	C₂²	1	4	yes	complemented
20	C₂×C₁₃×#131	C₂²	1	2	yes	complemented
21	C₁₃×#547	—	2	2	no	—
22	C₁₃×#547	C₂²	1	4	yes	complemented
23	C₁₃×#546	—	2	4	no	—
24	C₁₃×#546	C₂²	1	8	yes	complemented
25	D₄²×C₁₃	—	2	2	no	—
26	D₄²×C₁₃	C₂²	1	4	yes	complemented
27	C₁₃×#537	C₂²	1	4	yes	complemented
28	C₁₃×#534	—	2	4	no	—
29	C₁₃×#532	C₂²	1	1	yes	characteristic
30	C₁₃×#532	C₂²	1	2	yes	complemented
31	C₂×C₁₃×#121	—	2	4	no	—
32	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
33	C₁₃×#497	C₂²	1	4	yes	complemented
34	C₁₃×#496	C₂²	1	4	yes	complemented
35	C₁₃×#470	C₂²	1	4	yes	complemented
36	C₁₃×#469	C₂²	1	4	yes	complemented
37	C₁₃×#465	C₂²	1	8	yes	complemented
38	C₁₃×#463	C₂²	1	8	yes	complemented
39	C₁₃×#461	C₂²	1	4	yes	complemented
40	C₁₃×#459	C₂²	1	4	yes	complemented
41	C₁₃×#452	C₂²	1	8	yes	complemented
42	C₁₃×#450	C₂²	1	8	yes	complemented
43	C₁₃×#449	C₂²	1	8	yes	complemented
44	C₁₃×#447	C₂²	1	8	yes	complemented
45	C₁₃×#442	C₂²	1	8	yes	complemented
46	C₁₃×#435	C₂²	1	8	yes	complemented
47	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
48	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
49	C₁₃×#417	C₂²	1	4	yes	complemented
50	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
51	C₁₃×#408	C₂²	1	2	yes	complemented
52	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
53	C₁₃×H(5,𝔽₂)	—	2	16	no	—
54	C₁₃×H(5,𝔽₂)	—	4	8	no	—
55	C₂×C₁₃×#41	—	2	4	no	—
56	C₂×C₁₃×#41	C₂³	1	4	yes	—
57	C₂×C₁₃×#41	C₂³	1	8	yes	—
58	C₂×C₁₃×#41	C₂³	1	2	yes	—
59	C₂²×D₄×C₁₃	—	2	8	no	—
60	C₂²×D₄×C₁₃	—	2	4	no	—
61	C₂²×D₄×C₁₃	—	2	4	no	—
62	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
63	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃	—	2	2	no	—
65	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
66	C₁₃×AGL(1,ℤ/8)	—	2	32	no	—
67	C₁₃×#135	—	2	16	no	—
68	C₁₃×#135	—	2	8	no	—
69	C₁₃×#135	—	4	4	no	—
70	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
71	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
72	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
73	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
74	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
75	C₂×C₁₃×D₈	—	2	16	no	—
76	C₂×C₁₃×D₈	D₄	1	8	yes	complemented
77	C₂×C₁₃×D₈	C₂³	1	8	yes	—
78	C₂×C₁₃×D₈	C₂³	1	2	yes	—
79	C₂×C₁₃×D₈	C₂³	1	2	yes	—
80	C₂×C₁₃×D₈	C₂³	1	4	yes	—
81	C₁₃×#131	—	2	8	no	—
82	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
83	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
84	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
86	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
88	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
89	C₁₃×#127	D₄	1	1	yes	characteristic
90	C₁₃×#127	C₂³	1	2	yes	—
91	C₁₃×#124	D₄	1	2	yes	—
92	C₁₃×#124	C₂³	1	4	yes	—
93	C₁₃×#123	—	2	8	no	—
94	C₁₃×#123	—	2	8	no	—
95	C₁₃×C₂²⋊Q₈	—	2	4	no	—
96	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
97	C₁₃×#121	—	2	8	no	—
98	C₁₃×#121	—	2	4	no	—
99	C₁₃×#121	—	2	4	no	—
100	C₁₃×#121	—	2	2	no	—
101	C₁₃×#121	—	2	2	no	—
102	C₁₃×#121	—	2	4	no	—
103	C₁₃×#121	—	2	8	no	—
104	C₁₃×#121	D₄	1	4	yes	—
105	C₁₃×#121	C₂³	1	8	yes	—
106	C₁₃×#120	—	2	8	no	—
107	C₁₃×#120	—	2	8	no	—
108	C₄×D₄×C₁₃	—	2	2	no	—
109	C₄×D₄×C₁₃	—	2	2	no	—
110	C₄×D₄×C₁₃	—	2	2	no	—
111	C₄×D₄×C₁₃	—	2	2	no	—
112	C₄×D₄×C₁₃	C₂³	1	4	yes	—
113	C₄×D₄×C₁₃	C₂³	1	4	yes	—
114	C₄×D₄×C₁₃	C₂³	1	4	yes	—
115	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
116	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
119	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
120	C₁₃×#106	C₂³	1	4	yes	—
121	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
122	C₁₃×#103	C₂³	1	8	yes	—
123	C₁₃×#102	C₂³	1	8	yes	—
124	C₁₃×#102	C₂³	1	8	yes	—
125	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
126	C₁₃×#97	C₂³	1	4	yes	—
127	#61079	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
128	C₂⁴×C₁₃	—	2	2	no	—
129	C₂⁴×C₁₃	—	2	8	no	—
130	C₁₃×#41	—	2	4	no	—
131	C₁₃×#41	—	2	4	no	—
132	C₁₃×#41	—	2	16	no	—
133	C₁₃×#41	—	2	8	no	—
134	C₁₃×#41	—	2	8	no	—
135	C₁₃×#41	—	4	8	no	—
136	C₁₃×#41	—	4	16	no	—
137	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
138	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
139	C₂×D₄×C₁₃	—	2	16	no	—
140	C₂×D₄×C₁₃	—	2	8	no	—
141	C₂×D₄×C₁₃	—	2	4	no	—
142	C₂×D₄×C₁₃	—	2	8	no	—
143	C₂×D₄×C₁₃	—	2	2	no	—
144	C₂×D₄×C₁₃	—	2	2	no	—
145	C₂×D₄×C₁₃	—	2	8	no	—
146	C₂×D₄×C₁₃	—	2	2	no	—
147	C₂×D₄×C₁₃	—	2	4	no	—
148	C₂×D₄×C₁₃	—	4	8	no	—
149	C₂×D₄×C₁₃	—	4	16	no	—
150	C₂×D₄×C₁₃	—	4	32	no	—
151	C₂×D₄×C₁₃	—	8	8	no	—
152	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
153	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
154	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
155	C₂×D₄×C₁₃	C₂×D₄	1	8	yes	complemented
156	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
157	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃	—	2	2	no	—
159	C₂²×C₄×C₁₃	—	2	8	no	—
160	C₂²×C₄×C₁₃	—	2	4	no	—
161	C₂²×C₄×C₁₃	—	2	4	no	—
162	C₂²×C₄×C₁₃	—	2	4	no	—
163	C₂²×C₄×C₁₃	—	8	4	no	—
164	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
167	C₁₃×Q₁₆	—	2	4	no	—
168	C₁₃×Q₁₆	—	4	2	no	—
169	C₁₃×SD₁₆	—	2	16	no	—
170	C₁₃×SD₁₆	—	2	8	no	—
171	C₁₃×SD₁₆	—	4	4	no	—
172	C₁₃×D₈	—	2	16	no	—
173	C₁₃×D₈	—	2	4	no	—
174	C₁₃×D₈	—	4	2	no	—
175	C₁₃×D₈	C₂×D₄	1	16	yes	complemented
176	C₁₃×M₁₆	—	2	4	no	—
177	C₁₃×M₁₆	—	2	8	no	—
178	C₂×C₈×C₁₃	—	2	2	no	—
179	C₂×C₈×C₁₃	—	2	8	no	—
180	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	complemented
181	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
182	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
183	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
184	C₁₃×C₄⋊C₄	—	2	2	no	—
185	C₁₃×C₄⋊C₄	—	2	8	no	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	—	2	2	no	—
188	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
189	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
190	C₁₃×C₂²⋊C₄	—	2	8	no	—
191	C₁₃×C₂²⋊C₄	—	2	4	no	—
192	C₁₃×C₂²⋊C₄	—	2	4	no	—
193	C₁₃×C₂²⋊C₄	—	2	4	no	—
194	C₁₃×C₂²⋊C₄	—	2	8	no	—
195	C₁₃×C₂²⋊C₄	—	2	4	no	—
196	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
197	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₁₃	C₂⁴	1	2	yes	—
200	C₂×#576	C₂×C₁₃	1	2	yes	complemented
201	#3496	C₂×C₁₃	1	2	yes	complemented
202	#3267	C₂×C₁₃	1	8	yes	complemented
203	#3264	C₂×C₁₃	1	8	yes	complemented
204	#3150	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#3060	C₂×C₁₃	1	2	yes	complemented
206	#3036	C₂×C₁₃	1	2	yes	complemented
207	#3012	C₂×C₁₃	1	4	yes	complemented
208	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#2932	C₂×C₁₃	1	1	yes	characteristic, complemented
210	C₂³×C₁₃	—	2	4	no	—
211	C₂³×C₁₃	—	2	8	no	—
212	C₂³×C₁₃	—	2	4	no	—
213	C₂³×C₁₃	—	4	16	no	—
214	C₂³×C₁₃	—	8	2	no	—
215	C₂³×C₁₃	—	8	2	no	—
216	C₂³×C₁₃	—	8	8	no	—
217	C₂³×C₁₃	—	8	8	no	—
218	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
219	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
220	Q₈×C₁₃	—	2	4	no	—
221	Q₈×C₁₃	—	2	4	no	—
222	Q₈×C₁₃	—	2	4	no	—
223	D₄×C₁₃	—	2	8	no	—
224	D₄×C₁₃	—	2	8	no	—
225	D₄×C₁₃	—	2	4	no	—
226	D₄×C₁₃	—	2	4	no	—
227	D₄×C₁₃	—	2	4	no	—
228	D₄×C₁₃	—	2	4	no	—
229	D₄×C₁₃	—	4	4	no	—
230	D₄×C₁₃	—	4	16	no	—
231	D₄×C₁₃	—	4	4	no	—
232	D₄×C₁₃	—	4	16	no	—
233	D₄×C₁₃	—	4	8	no	—
234	D₄×C₁₃	—	8	2	no	—
235	D₄×C₁₃	—	8	8	no	—
236	D₄×C₁₃	C₂²×D₄	1	8	yes	—
237	C₂×C₄×C₁₃	—	2	4	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	4	2	no	—
242	C₂×C₄×C₁₃	—	4	16	no	—
243	C₂×C₄×C₁₃	—	4	8	no	—
244	C₂×C₄×C₁₃	—	4	8	no	—
245	C₂×C₄×C₁₃	—	8	4	no	—
246	C₂×C₄×C₁₃	—	8	2	no	—
247	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
250	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
252	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
253	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
254	C₈×C₁₃	—	2	4	no	—
255	C₈×C₁₃	—	2	2	no	—
256	C₈×C₁₃	C₂²×D₄	1	4	yes	—
257	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	4	yes	complemented
258	#576	—	2	16	no	—
259	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	8	yes	complemented
260	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
261	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
262	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
263	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
264	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
265	C₂²×D₈	C₂²×C₁₃	1	4	yes	complemented
266	C₂×#131	C₂²×C₁₃	1	2	yes	complemented
267	#547	—	2	2	no	—
268	#547	C₂²×C₁₃	1	4	yes	complemented
269	#546	—	2	4	no	—
270	#546	C₂²×C₁₃	1	8	yes	complemented
271	D₄²	—	2	2	no	—
272	D₄²	C₂²×C₁₃	1	4	yes	complemented
273	#537	C₂²×C₁₃	1	4	yes	complemented
274	#534	—	2	4	no	—
275	#532	C₂²×C₁₃	1	1	yes	characteristic
276	#532	C₂²×C₁₃	1	2	yes	complemented
277	C₂×#121	—	2	4	no	—
278	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
279	#497	C₂²×C₁₃	1	4	yes	complemented
280	#496	C₂²×C₁₃	1	4	yes	complemented
281	#470	C₂²×C₁₃	1	4	yes	complemented
282	#469	C₂²×C₁₃	1	4	yes	complemented
283	#465	C₂²×C₁₃	1	8	yes	complemented
284	#463	C₂²×C₁₃	1	8	yes	complemented
285	#461	C₂²×C₁₃	1	4	yes	complemented
286	#459	C₂²×C₁₃	1	4	yes	complemented
287	#452	C₂²×C₁₃	1	8	yes	complemented
288	#450	C₂²×C₁₃	1	8	yes	complemented
289	#449	C₂²×C₁₃	1	8	yes	complemented
290	#447	C₂²×C₁₃	1	8	yes	complemented
291	#442	C₂²×C₁₃	1	8	yes	complemented
292	#435	C₂²×C₁₃	1	8	yes	complemented
293	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
294	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
295	#417	C₂²×C₁₃	1	4	yes	complemented
296	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
297	#408	C₂²×C₁₃	1	2	yes	complemented
298	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
299	C₂²×C₁₃	—	2	2	no	—
300	C₂²×C₁₃	—	2	8	no	—
301	C₂²×C₁₃	—	2	4	no	—
302	C₂²×C₁₃	—	2	8	no	—
303	C₂²×C₁₃	—	4	4	no	—
304	C₂²×C₁₃	—	4	4	no	—
305	C₂²×C₁₃	—	4	4	no	—
306	C₂²×C₁₃	—	4	4	no	—
307	C₂²×C₁₃	—	4	4	no	—
308	C₂²×C₁₃	—	8	8	no	—
309	C₂²×C₁₃	—	16	16	no	—
310	C₂²×C₁₃	D₄²	1	2	yes	—
311	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
312	C₄×C₁₃	—	2	2	no	—
313	C₄×C₁₃	—	2	2	no	—
314	C₄×C₁₃	—	2	4	no	—
315	C₄×C₁₃	—	4	4	no	—
316	C₄×C₁₃	—	4	4	no	—
317	C₄×C₁₃	D₄²	1	2	yes	—
318	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
319	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
320	H(5,𝔽₂)	—	2	16	no	—
321	H(5,𝔽₂)	—	4	8	no	—
322	C₂×#41	—	2	4	no	—
323	C₂×#41	C₂³×C₁₃	1	4	yes	—
324	C₂×#41	C₂³×C₁₃	1	8	yes	—
325	C₂×#41	C₂³×C₁₃	1	2	yes	—
326	C₂²×D₄	—	2	8	no	—
327	C₂²×D₄	—	2	4	no	—
328	C₂²×D₄	—	2	4	no	—
329	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
330	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
331	C₂³×C₄	—	2	2	no	—
332	AGL(1,ℤ/8)	—	2	16	no	—
333	AGL(1,ℤ/8)	—	2	32	no	—
334	#135	—	2	16	no	—
335	#135	—	2	8	no	—
336	#135	—	4	4	no	—
337	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
338	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
339	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
340	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
341	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
342	C₂×D₈	—	2	16	no	—
343	C₂×D₈	D₄×C₁₃	1	8	yes	complemented
344	C₂×D₈	C₂³×C₁₃	1	2	yes	—
345	C₂×D₈	C₂³×C₁₃	1	8	yes	—
346	C₂×D₈	C₂³×C₁₃	1	2	yes	—
347	C₂×D₈	C₂³×C₁₃	1	4	yes	—
348	#131	—	2	8	no	—
349	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
350	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
351	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
352	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
354	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
355	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
356	#127	D₄×C₁₃	1	1	yes	characteristic
357	#127	C₂³×C₁₃	1	2	yes	—
358	#124	D₄×C₁₃	1	2	yes	—
359	#124	C₂³×C₁₃	1	4	yes	—
360	#123	—	2	8	no	—
361	#123	—	2	8	no	—
362	C₂²⋊Q₈	—	2	4	no	—
363	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
364	#121	—	2	8	no	—
365	#121	—	2	4	no	—
366	#121	—	2	4	no	—
367	#121	—	2	2	no	—
368	#121	—	2	2	no	—
369	#121	—	2	4	no	—
370	#121	—	2	8	no	—
371	#121	D₄×C₁₃	1	4	yes	—
372	#121	C₂³×C₁₃	1	8	yes	—
373	#120	—	2	8	no	—
374	#120	—	2	8	no	—
375	C₄×D₄	—	2	2	no	—
376	C₄×D₄	—	2	2	no	—
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	—	2	2	no	—
379	C₄×D₄	C₂³×C₁₃	1	4	yes	—
380	C₄×D₄	C₂³×C₁₃	1	4	yes	—
381	C₄×D₄	C₂³×C₁₃	1	4	yes	—
382	C₂×C₄⋊C₄	—	2	4	no	—
383	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
384	C₂×C₂²⋊C₄	—	2	2	no	—
385	C₂×C₂²⋊C₄	—	2	8	no	—
386	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
387	#106	C₂³×C₁₃	1	4	yes	—
388	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
389	#103	C₂³×C₁₃	1	8	yes	—
390	#102	C₂³×C₁₃	1	8	yes	—
391	#102	C₂³×C₁₃	1	8	yes	—
392	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
393	#97	C₂³×C₁₃	1	4	yes	—
394	C₂×C₁₃	—	2	2	no	—
395	C₂×C₁₃	—	4	4	no	—
396	C₂×C₁₃	—	4	8	no	—
397	C₂×C₁₃	—	8	4	no	—
398	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
399	C₂×C₁₃	#3585	1	2	yes	—
400	C₂⁴	—	2	2	no	—
401	C₂⁴	—	2	8	no	—
402	#41	—	2	4	no	—
403	#41	—	2	4	no	—
404	#41	—	2	16	no	—
405	#41	—	2	8	no	—
406	#41	—	2	8	no	—
407	#41	—	4	8	no	—
408	#41	—	4	16	no	—
409	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
410	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
411	C₂×D₄	—	2	16	no	—
412	C₂×D₄	—	2	8	no	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	2	8	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	8	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	4	8	no	—
421	C₂×D₄	—	4	16	no	—
422	C₂×D₄	—	4	32	no	—
423	C₂×D₄	—	8	8	no	—
424	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
425	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
426	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
427	C₂×D₄	C₂×D₄×C₁₃	1	8	yes	complemented
428	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
429	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	8	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	4	no	—
435	C₂²×C₄	—	8	4	no	—
436	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
437	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
438	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
439	Q₁₆	—	2	4	no	—
440	Q₁₆	—	4	2	no	—
441	SD₁₆	—	2	16	no	—
442	SD₁₆	—	2	8	no	—
443	SD₁₆	—	4	4	no	—
444	D₈	—	2	16	no	—
445	D₈	—	2	4	no	—
446	D₈	—	4	2	no	—
447	D₈	C₂×D₄×C₁₃	1	16	yes	complemented
448	M₁₆	—	2	4	no	—
449	M₁₆	—	2	8	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	8	no	—
452	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	complemented
453	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
454	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
455	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	8	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
461	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
462	C₂²⋊C₄	—	2	8	no	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	2	8	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
469	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₄²	C₂⁴×C₁₃	1	2	yes	—
472	C₁₃	#61079	1	1	yes	characteristic, direct product factor, Sylow
473	C₂³	—	2	4	no	—
474	C₂³	—	2	8	no	—
475	C₂³	—	2	4	no	—
476	C₂³	—	4	16	no	—
477	C₂³	—	8	2	no	—
478	C₂³	—	8	2	no	—
479	C₂³	—	8	8	no	—
480	C₂³	—	8	8	no	—
481	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
482	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
483	Q₈	—	2	4	no	—
484	Q₈	—	2	4	no	—
485	Q₈	—	2	4	no	—
486	D₄	—	2	8	no	—
487	D₄	—	2	8	no	—
488	D₄	—	2	4	no	—
489	D₄	—	2	4	no	—
490	D₄	—	2	4	no	—
491	D₄	—	2	4	no	—
492	D₄	—	4	4	no	—
493	D₄	—	4	16	no	—
494	D₄	—	4	4	no	—
495	D₄	—	4	16	no	—
496	D₄	—	4	8	no	—
497	D₄	—	8	2	no	—
498	D₄	—	8	8	no	—
499	D₄	C₂²×D₄×C₁₃	1	8	yes	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	16	no	—
506	C₂×C₄	—	4	8	no	—
507	C₂×C₄	—	4	8	no	—
508	C₂×C₄	—	8	4	no	—
509	C₂×C₄	—	8	2	no	—
510	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
511	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
512	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
513	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
515	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
516	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
517	C₈	—	2	4	no	—
518	C₈	—	2	2	no	—
519	C₈	C₂²×D₄×C₁₃	1	4	yes	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	8	no	—
522	C₂²	—	2	4	no	—
523	C₂²	—	2	8	no	—
524	C₂²	—	4	4	no	—
525	C₂²	—	4	4	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	4	4	no	—
528	C₂²	—	4	4	no	—
529	C₂²	—	8	8	no	—
530	C₂²	—	16	16	no	—
531	C₂²	D₄²×C₁₃	1	2	yes	—
532	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
533	C₄	—	2	2	no	—
534	C₄	—	2	2	no	—
535	C₄	—	2	4	no	—
536	C₄	—	4	4	no	—
537	C₄	—	4	4	no	—
538	C₄	D₄²×C₁₃	1	2	yes	—
539	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
540	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
541	C₂	—	2	2	no	—
542	C₂	—	4	4	no	—
543	C₂	—	4	8	no	—
544	C₂	—	8	4	no	—
545	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
546	C₂	C₁₃×#3585	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 ◁ C₁₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#576	C₂	semidirect
2. C₁₃×#3496	C₂	semidirect
3. C₁₃×#3267	C₂	semidirect
4. C₁₃×#3264	C₂	semidirect
5. C₁₃×#3150	C₂	semidirect
6. C₁₃×#3060	C₂	semidirect
7. C₁₃×#3036	C₂	semidirect
8. C₁₃×#3012	C₂	semidirect
9. C₂×C₁₃×#442	C₂	semidirect
10. C₁₃×#2932	C₂	semidirect
11. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
13. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
14. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
15. C₂×C₁₃×#135	C₂²	semidirect
16. C₂×C₁₃×#135	C₂²	semidirect
17. C₂×C₁₃×#135	C₂²	semidirect
19. C₂²×C₁₃×D₈	C₂²	semidirect
20. C₂×C₁₃×#131	C₂²	semidirect
22. C₁₃×#547	C₂²	semidirect
24. C₁₃×#546	C₂²	semidirect
26. D₄²×C₁₃	C₂²	semidirect
27. C₁₃×#537	C₂²	semidirect
30. C₁₃×#532	C₂²	semidirect
32. C₂×C₄×D₄×C₁₃	C₂²	semidirect
33. C₁₃×#497	C₂²	semidirect
34. C₁₃×#496	C₂²	semidirect
35. C₁₃×#470	C₂²	semidirect
36. C₁₃×#469	C₂²	semidirect
37. C₁₃×#465	C₂²	semidirect
38. C₁₃×#463	C₂²	semidirect
39. C₁₃×#461	C₂²	semidirect
40. C₁₃×#459	C₂²	semidirect
41. C₁₃×#452	C₂²	semidirect
42. C₁₃×#450	C₂²	semidirect
43. C₁₃×#449	C₂²	semidirect
44. C₁₃×#447	C₂²	semidirect
45. C₁₃×#442	C₂²	semidirect
46. C₁₃×#435	C₂²	semidirect
47. C₂×C₁₃×#106	C₂²	semidirect
48. C₁₃×#423	C₂²	semidirect
49. C₁₃×#417	C₂²	semidirect
50. C₂×C₁₃×#102	C₂²	semidirect
51. C₁₃×#408	C₂²	semidirect
52. C₂×C₁₃×#97	C₂²	semidirect
76. C₂×C₁₃×D₈	D₄	semidirect
127. #61079	C₁₃	direct (N × H)
155. C₂×D₄×C₁₃	C₂×D₄	semidirect
175. C₁₃×D₈	C₂×D₄	semidirect
180. C₂×C₈×C₁₃	C₂×D₄	semidirect
200. C₂×#576	C₂×C₁₃	semidirect
201. #3496	C₂×C₁₃	semidirect
202. #3267	C₂×C₁₃	semidirect
203. #3264	C₂×C₁₃	semidirect
204. #3150	C₂×C₁₃	semidirect
205. #3060	C₂×C₁₃	semidirect
206. #3036	C₂×C₁₃	semidirect
207. #3012	C₂×C₁₃	semidirect
208. C₂×#442	C₂×C₁₃	semidirect
209. #2932	C₂×C₁₃	semidirect
257. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
259. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
260. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
261. C₂×#135	C₂²×C₁₃	semidirect
262. C₂×#135	C₂²×C₁₃	semidirect
263. C₂×#135	C₂²×C₁₃	semidirect
265. C₂²×D₈	C₂²×C₁₃	semidirect
266. C₂×#131	C₂²×C₁₃	semidirect
268. #547	C₂²×C₁₃	semidirect
270. #546	C₂²×C₁₃	semidirect
272. D₄²	C₂²×C₁₃	semidirect
273. #537	C₂²×C₁₃	semidirect
276. #532	C₂²×C₁₃	semidirect
278. C₂×C₄×D₄	C₂²×C₁₃	semidirect
279. #497	C₂²×C₁₃	semidirect
280. #496	C₂²×C₁₃	semidirect
281. #470	C₂²×C₁₃	semidirect
282. #469	C₂²×C₁₃	semidirect
283. #465	C₂²×C₁₃	semidirect
284. #463	C₂²×C₁₃	semidirect
285. #461	C₂²×C₁₃	semidirect
286. #459	C₂²×C₁₃	semidirect
287. #452	C₂²×C₁₃	semidirect
288. #450	C₂²×C₁₃	semidirect
289. #449	C₂²×C₁₃	semidirect
290. #447	C₂²×C₁₃	semidirect
291. #442	C₂²×C₁₃	semidirect
292. #435	C₂²×C₁₃	semidirect
293. C₂×#106	C₂²×C₁₃	semidirect
294. #423	C₂²×C₁₃	semidirect
295. #417	C₂²×C₁₃	semidirect
296. C₂×#102	C₂²×C₁₃	semidirect
297. #408	C₂²×C₁₃	semidirect
298. C₂×#97	C₂²×C₁₃	semidirect
343. C₂×D₈	D₄×C₁₃	semidirect
427. C₂×D₄	C₂×D₄×C₁₃	semidirect
447. D₈	C₂×D₄×C₁₃	semidirect
452. C₂×C₈	C₂×D₄×C₁₃	semidirect
472. C₁₃	#61079	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×#576	2
C₁₃×#3496	2
C₁₃×#3267	2
C₁₃×#3264	2
C₁₃×#3150	2
C₁₃×#3060	2
C₁₃×#3036	2
C₁₃×#3012	2
C₂×C₁₃×#442	2
C₁₃×#2932	2
#61079	13

Subgroups — C13×#61079 #15747418

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61079 #15747418