Subgroups — C₁₃×#61088 #15747427

Order 3328.

2714 conjugacy classes of subgroups.

The subgroup lattice has 622 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	2	yes	maximal, complemented
2	C₁₃×#3500	C₂	1	2	yes	maximal, complemented
3	C₁₃×#3282	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3277	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3273	C₂	1	4	yes	maximal, complemented
6	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3057	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3040	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3011	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3008	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
14	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
15	C₁₃×#577	—	2	16	no	—
16	C₂×C₁₃×#137	C₂²	1	2	yes	complemented
17	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
18	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
19	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
20	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
22	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
24	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
25	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#131	C₂²	1	2	yes	complemented
27	C₁₃×#548	C₂²	1	8	yes	complemented
28	C₁₃×#546	—	2	8	no	—
29	C₁₃×#546	C₂²	1	8	yes	complemented
30	C₁₃×#536	—	2	2	no	—
31	C₁₃×#536	C₂²	1	2	yes	complemented
32	C₁₃×#535	—	2	2	no	—
33	C₁₃×#535	C₂²	1	2	yes	—
34	C₁₃×#532	—	2	2	no	—
35	C₁₃×#532	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#124	—	2	2	no	—
37	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
38	C₄×C₁₃×#41	C₂²	1	2	yes	complemented
39	C₁₃×#495	C₂²	1	4	yes	complemented
40	C₁₃×#495	C₂²	1	4	yes	complemented
41	C₁₃×#468	C₂²	1	8	yes	complemented
42	C₁₃×#465	C₂²	1	8	yes	complemented
43	C₁₃×#464	C₂²	1	8	yes	complemented
44	C₁₃×#463	C₂²	1	8	yes	complemented
45	C₁₃×#452	C₂²	1	8	yes	complemented
46	C₁₃×#451	C₂²	1	8	yes	complemented
47	C₁₃×#449	C₂²	1	8	yes	complemented
48	C₁₃×#447	C₂²	1	8	yes	complemented
49	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
50	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
51	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
52	C₁₃×#436	C₂²	1	4	yes	complemented
53	C₈×D₄×C₁₃	C₂²	1	4	yes	complemented
54	C₁₃×#427	C₂²	1	1	yes	characteristic, complemented
55	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
56	C₁₃×#419	C₂²	1	2	yes	complemented
57	C₁₃×#418	C₂²	1	2	yes	complemented
58	C₁₃×#416	C₂²	1	2	yes	complemented
59	C₁₃×#408	C₂²	1	2	yes	complemented
60	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×2₋¹⁺⁴	—	2	8	no	—
62	C₁₃×2₋¹⁺⁴	—	4	4	no	—
63	C₁₃×H(5,𝔽₂)	—	2	8	no	—
64	C₁₃×H(5,𝔽₂)	—	4	4	no	—
65	C₂×C₁₃×#41	—	2	2	no	—
66	C₂×C₁₃×#41	—	2	2	no	—
67	C₂×C₁₃×#41	—	2	4	no	—
68	C₂×C₁₃×#41	C₂³	1	4	yes	—
69	C₂×C₁₃×#41	C₂³	1	4	yes	—
70	C₂×C₁₃×#41	C₂³	1	2	yes	—
71	C₂×C₁₃×#41	C₂³	1	2	yes	—
72	C₂²×Q₈×C₁₃	—	2	2	no	—
73	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
74	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
75	C₂²×D₄×C₁₃	—	2	2	no	—
76	C₂²×D₄×C₁₃	—	2	4	no	—
77	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
78	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
79	C₁₃×#137	—	2	8	no	—
80	C₁₃×#137	—	2	16	no	—
81	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
82	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
83	C₁₃×#135	—	2	16	no	—
84	C₁₃×#135	D₄	1	8	yes	complemented
85	C₂×C₁₃×Q₁₆	—	4	2	no	—
86	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
87	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
88	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×SD₁₆	—	2	16	no	—
90	C₂×C₁₃×SD₁₆	—	2	8	no	—
91	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
92	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
93	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
94	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
95	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
96	C₂×C₁₃×D₈	—	4	2	no	—
97	C₂×C₁₃×D₈	C₂³	1	4	yes	—
98	C₂×C₁₃×D₈	C₂³	1	4	yes	—
99	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
100	C₁₃×#131	—	2	8	no	—
101	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
102	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
103	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
105	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
106	C₁₃×C₄⋊Q₈	—	2	2	no	—
107	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
108	C₁₃×#127	—	2	2	no	—
109	C₁₃×#127	D₄	1	1	yes	characteristic
110	C₁₃×#124	—	2	2	no	—
111	C₁₃×#124	—	2	2	no	—
112	C₁₃×#124	—	2	8	no	—
113	C₁₃×#124	—	2	2	no	—
114	C₁₃×#124	—	2	2	no	—
115	C₁₃×#124	D₄	1	2	yes	—
116	C₁₃×#124	C₂³	1	8	yes	—
117	C₁₃×#123	—	2	4	no	—
118	C₁₃×#123	—	2	8	no	—
119	C₁₃×C₂²⋊Q₈	—	2	8	no	—
120	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
121	C₁₃×#121	—	2	8	no	—
122	C₁₃×#121	—	2	8	no	—
123	C₁₃×#121	D₄	1	4	yes	—
124	C₁₃×#121	C₂³	1	8	yes	—
125	C₁₃×#120	—	2	8	no	—
126	C₁₃×#120	—	2	4	no	—
127	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
128	C₄×D₄×C₁₃	—	2	4	no	—
129	C₄×D₄×C₁₃	—	2	8	no	—
130	C₄×D₄×C₁₃	C₂³	1	4	yes	—
131	C₄×D₄×C₁₃	C₂³	1	4	yes	—
132	C₁₃×#117	—	2	2	no	—
133	C₁₃×#117	C₂³	1	2	yes	—
134	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
135	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
136	C₂×C₄²×C₁₃	—	2	2	no	—
137	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
138	C₁₃×#107	C₂³	1	2	yes	—
139	C₁₃×#106	C₂³	1	2	yes	—
140	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
141	C₁₃×#103	C₂³	1	4	yes	—
142	C₁₃×#103	C₂³	1	8	yes	—
143	C₁₃×#102	C₂³	1	4	yes	—
144	C₁₃×#102	C₂³	1	8	yes	—
145	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
146	C₄×C₈×C₁₃	C₂³	1	2	yes	—
147	C₄×C₈×C₁₃	C₂³	1	2	yes	—
148	#61088	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
149	C₂⁴×C₁₃	—	2	4	no	—
150	C₂⁴×C₁₃	—	2	2	no	—
151	C₁₃×#41	—	2	4	no	—
152	C₁₃×#41	—	2	4	no	—
153	C₁₃×#41	—	2	4	no	—
154	C₁₃×#41	—	2	8	no	—
155	C₁₃×#41	—	2	8	no	—
156	C₁₃×#41	—	4	4	no	—
157	C₁₃×#41	—	4	4	no	—
158	C₁₃×#41	—	4	8	no	—
159	C₁₃×#41	—	4	8	no	—
160	C₁₃×#41	—	4	16	no	—
161	C₁₃×#41	C₂×D₄	1	8	yes	—
162	C₂×Q₈×C₁₃	—	2	4	no	—
163	C₂×Q₈×C₁₃	—	2	2	no	—
164	C₂×Q₈×C₁₃	—	2	8	no	—
165	C₂×Q₈×C₁₃	—	2	4	no	—
166	C₂×Q₈×C₁₃	—	2	4	no	—
167	C₂×Q₈×C₁₃	—	4	4	no	—
168	C₂×Q₈×C₁₃	—	4	8	no	—
169	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
170	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
171	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
172	C₂×D₄×C₁₃	—	2	2	no	—
173	C₂×D₄×C₁₃	—	2	8	no	—
174	C₂×D₄×C₁₃	—	2	4	no	—
175	C₂×D₄×C₁₃	—	2	4	no	—
176	C₂×D₄×C₁₃	—	2	8	no	—
177	C₂×D₄×C₁₃	—	2	4	no	—
178	C₂×D₄×C₁₃	—	2	4	no	—
179	C₂×D₄×C₁₃	—	2	2	no	—
180	C₂×D₄×C₁₃	—	2	4	no	—
181	C₂×D₄×C₁₃	—	4	4	no	—
182	C₂×D₄×C₁₃	—	4	8	no	—
183	C₂×D₄×C₁₃	—	4	16	no	—
184	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
185	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
186	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
187	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
188	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₃	—	2	2	no	—
190	C₂²×C₄×C₁₃	—	2	2	no	—
191	C₂²×C₄×C₁₃	—	2	4	no	—
192	C₂²×C₄×C₁₃	—	2	4	no	—
193	C₂²×C₄×C₁₃	—	2	4	no	—
194	C₂²×C₄×C₁₃	—	2	4	no	—
195	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
196	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
198	C₁₃×Q₁₆	—	2	8	no	—
199	C₁₃×Q₁₆	—	4	4	no	—
200	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
201	C₁₃×SD₁₆	—	2	8	no	—
202	C₁₃×SD₁₆	—	2	8	no	—
203	C₁₃×SD₁₆	—	2	8	no	—
204	C₁₃×SD₁₆	—	2	8	no	—
205	C₁₃×SD₁₆	C₂×D₄	1	8	yes	—
206	C₁₃×D₈	—	2	8	no	—
207	C₁₃×D₈	—	4	4	no	—
208	C₁₃×D₈	C₂×D₄	1	4	yes	—
209	C₁₃×M₁₆	—	2	4	no	—
210	C₁₃×M₁₆	—	2	8	no	—
211	C₂×C₈×C₁₃	—	2	2	no	—
212	C₂×C₈×C₁₃	—	2	8	no	—
213	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
214	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
215	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
216	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
217	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
218	C₁₃×C₄⋊C₄	—	2	4	no	—
219	C₁₃×C₄⋊C₄	—	2	8	no	—
220	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
221	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
222	C₁₃×C₂²⋊C₄	—	2	8	no	—
223	C₁₃×C₂²⋊C₄	—	2	2	no	—
224	C₁₃×C₂²⋊C₄	—	2	8	no	—
225	C₁₃×C₂²⋊C₄	—	2	8	no	—
226	C₁₃×C₂²⋊C₄	—	2	8	no	—
227	C₁₃×C₂²⋊C₄	—	2	4	no	—
228	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
229	C₄²×C₁₃	—	2	2	no	—
230	C₄²×C₁₃	—	2	4	no	—
231	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
232	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
233	C₄²×C₁₃	C₂⁴	1	2	yes	—
234	C₂×#577	C₂×C₁₃	1	2	yes	complemented
235	#3500	C₂×C₁₃	1	2	yes	complemented
236	#3282	C₂×C₁₃	1	8	yes	complemented
237	#3277	C₂×C₁₃	1	4	yes	complemented
238	#3273	C₂×C₁₃	1	4	yes	complemented
239	C₂×#495	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#3057	C₂×C₁₃	1	2	yes	complemented
241	#3040	C₂×C₁₃	1	2	yes	complemented
242	#3011	C₂×C₁₃	1	2	yes	complemented
243	#3008	C₂×C₁₃	1	2	yes	complemented
244	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#2931	C₂×C₁₃	1	1	yes	characteristic, complemented
246	C₂³×C₁₃	—	2	2	no	—
247	C₂³×C₁₃	—	2	4	no	—
248	C₂³×C₁₃	—	4	8	no	—
249	C₂³×C₁₃	—	4	4	no	—
250	C₂³×C₁₃	—	8	4	no	—
251	C₂³×C₁₃	—	8	8	no	—
252	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
253	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
254	Q₈×C₁₃	—	2	4	no	—
255	Q₈×C₁₃	—	2	2	no	—
256	Q₈×C₁₃	—	2	4	no	—
257	Q₈×C₁₃	—	2	4	no	—
258	Q₈×C₁₃	—	4	8	no	—
259	Q₈×C₁₃	—	4	4	no	—
260	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
261	D₄×C₁₃	—	2	8	no	—
262	D₄×C₁₃	—	2	8	no	—
263	D₄×C₁₃	—	2	4	no	—
264	D₄×C₁₃	—	2	4	no	—
265	D₄×C₁₃	—	2	2	no	—
266	D₄×C₁₃	—	2	4	no	—
267	D₄×C₁₃	—	4	4	no	—
268	D₄×C₁₃	—	4	8	no	—
269	D₄×C₁₃	—	4	8	no	—
270	D₄×C₁₃	—	4	8	no	—
271	D₄×C₁₃	—	4	4	no	—
272	D₄×C₁₃	—	8	8	no	—
273	D₄×C₁₃	C₂²×D₄	1	4	yes	—
274	C₂×C₄×C₁₃	—	2	2	no	—
275	C₂×C₄×C₁₃	—	2	8	no	—
276	C₂×C₄×C₁₃	—	2	4	no	—
277	C₂×C₄×C₁₃	—	2	4	no	—
278	C₂×C₄×C₁₃	—	2	4	no	—
279	C₂×C₄×C₁₃	—	2	4	no	—
280	C₂×C₄×C₁₃	—	4	2	no	—
281	C₂×C₄×C₁₃	—	4	8	no	—
282	C₂×C₄×C₁₃	—	4	8	no	—
283	C₂×C₄×C₁₃	—	4	8	no	—
284	C₂×C₄×C₁₃	—	4	4	no	—
285	C₂×C₄×C₁₃	—	8	4	no	—
286	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
287	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
288	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
289	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
291	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
292	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
293	C₈×C₁₃	—	2	4	no	—
294	C₈×C₁₃	—	2	2	no	—
295	C₈×C₁₃	C₂²×D₄	1	2	yes	—
296	C₈×C₁₃	C₂²×D₄	1	2	yes	—
297	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
298	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	complemented
299	#577	—	2	16	no	—
300	C₂×#137	C₂²×C₁₃	1	2	yes	complemented
301	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
302	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
303	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
304	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
306	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
307	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
308	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
309	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×#131	C₂²×C₁₃	1	2	yes	complemented
311	#548	C₂²×C₁₃	1	8	yes	complemented
312	#546	—	2	8	no	—
313	#546	C₂²×C₁₃	1	8	yes	complemented
314	#536	—	2	2	no	—
315	#536	C₂²×C₁₃	1	2	yes	complemented
316	#535	—	2	2	no	—
317	#535	C₂²×C₁₃	1	2	yes	—
318	#532	—	2	2	no	—
319	#532	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×#124	—	2	2	no	—
321	C₂×#124	C₂²×C₁₃	1	2	yes	complemented
322	C₄×#41	C₂²×C₁₃	1	2	yes	complemented
323	#495	C₂²×C₁₃	1	4	yes	complemented
324	#495	C₂²×C₁₃	1	4	yes	complemented
325	#468	C₂²×C₁₃	1	8	yes	complemented
326	#465	C₂²×C₁₃	1	8	yes	complemented
327	#464	C₂²×C₁₃	1	8	yes	complemented
328	#463	C₂²×C₁₃	1	8	yes	complemented
329	#452	C₂²×C₁₃	1	8	yes	complemented
330	#451	C₂²×C₁₃	1	8	yes	complemented
331	#449	C₂²×C₁₃	1	8	yes	complemented
332	#447	C₂²×C₁₃	1	8	yes	complemented
333	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
334	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
335	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
336	#436	C₂²×C₁₃	1	4	yes	complemented
337	C₈×D₄	C₂²×C₁₃	1	4	yes	complemented
338	#427	C₂²×C₁₃	1	1	yes	characteristic, complemented
339	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
340	#419	C₂²×C₁₃	1	2	yes	complemented
341	#418	C₂²×C₁₃	1	2	yes	complemented
342	#416	C₂²×C₁₃	1	2	yes	complemented
343	#408	C₂²×C₁₃	1	2	yes	complemented
344	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
345	C₂²×C₁₃	—	2	2	no	—
346	C₂²×C₁₃	—	2	8	no	—
347	C₂²×C₁₃	—	2	4	no	—
348	C₂²×C₁₃	—	2	4	no	—
349	C₂²×C₁₃	—	4	4	no	—
350	C₂²×C₁₃	—	4	8	no	—
351	C₂²×C₁₃	—	4	4	no	—
352	C₂²×C₁₃	—	16	4	no	—
353	C₂²×C₁₃	—	16	8	no	—
354	C₂²×C₁₃	D₄²	1	2	yes	—
355	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
356	C₄×C₁₃	—	2	2	no	—
357	C₄×C₁₃	—	2	2	no	—
358	C₄×C₁₃	—	2	4	no	—
359	C₄×C₁₃	—	2	4	no	—
360	C₄×C₁₃	—	4	4	no	—
361	C₄×C₁₃	—	4	4	no	—
362	C₄×C₁₃	D₄²	1	2	yes	—
363	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
364	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
365	2₋¹⁺⁴	—	2	8	no	—
366	2₋¹⁺⁴	—	4	4	no	—
367	H(5,𝔽₂)	—	2	8	no	—
368	H(5,𝔽₂)	—	4	4	no	—
369	C₂×#41	—	2	2	no	—
370	C₂×#41	—	2	2	no	—
371	C₂×#41	—	2	4	no	—
372	C₂×#41	C₂³×C₁₃	1	4	yes	—
373	C₂×#41	C₂³×C₁₃	1	4	yes	—
374	C₂×#41	C₂³×C₁₃	1	2	yes	—
375	C₂×#41	C₂³×C₁₃	1	2	yes	—
376	C₂²×Q₈	—	2	2	no	—
377	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
378	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
379	C₂²×D₄	—	2	2	no	—
380	C₂²×D₄	—	2	4	no	—
381	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
382	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
383	#137	—	2	8	no	—
384	#137	—	2	16	no	—
385	AGL(1,ℤ/8)	—	2	8	no	—
386	AGL(1,ℤ/8)	—	2	16	no	—
387	#135	—	2	16	no	—
388	#135	D₄×C₁₃	1	8	yes	complemented
389	C₂×Q₁₆	—	4	2	no	—
390	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
391	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
392	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
393	C₂×SD₁₆	—	2	16	no	—
394	C₂×SD₁₆	—	2	8	no	—
395	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
396	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
397	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
398	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
399	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
400	C₂×D₈	—	4	2	no	—
401	C₂×D₈	C₂³×C₁₃	1	4	yes	—
402	C₂×D₈	C₂³×C₁₃	1	4	yes	—
403	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
404	#131	—	2	8	no	—
405	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
406	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
407	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
408	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
409	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
410	C₄⋊Q₈	—	2	2	no	—
411	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
412	#127	—	2	2	no	—
413	#127	D₄×C₁₃	1	1	yes	characteristic
414	#124	—	2	2	no	—
415	#124	—	2	2	no	—
416	#124	—	2	8	no	—
417	#124	—	2	2	no	—
418	#124	—	2	2	no	—
419	#124	D₄×C₁₃	1	2	yes	—
420	#124	C₂³×C₁₃	1	8	yes	—
421	#123	—	2	4	no	—
422	#123	—	2	8	no	—
423	C₂²⋊Q₈	—	2	8	no	—
424	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
425	#121	—	2	8	no	—
426	#121	—	2	8	no	—
427	#121	D₄×C₁₃	1	4	yes	—
428	#121	C₂³×C₁₃	1	8	yes	—
429	#120	—	2	8	no	—
430	#120	—	2	4	no	—
431	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
432	C₄×D₄	—	2	4	no	—
433	C₄×D₄	—	2	8	no	—
434	C₄×D₄	C₂³×C₁₃	1	4	yes	—
435	C₄×D₄	C₂³×C₁₃	1	4	yes	—
436	#117	—	2	2	no	—
437	#117	C₂³×C₁₃	1	2	yes	—
438	C₂×C₂²⋊C₄	—	2	4	no	—
439	C₂×C₂²⋊C₄	—	2	8	no	—
440	C₂×C₄²	—	2	2	no	—
441	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
442	#107	C₂³×C₁₃	1	2	yes	—
443	#106	C₂³×C₁₃	1	2	yes	—
444	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
445	#103	C₂³×C₁₃	1	4	yes	—
446	#103	C₂³×C₁₃	1	8	yes	—
447	#102	C₂³×C₁₃	1	4	yes	—
448	#102	C₂³×C₁₃	1	8	yes	—
449	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
450	C₄×C₈	C₂³×C₁₃	1	2	yes	—
451	C₄×C₈	C₂³×C₁₃	1	2	yes	—
452	C₂×C₁₃	—	2	2	no	—
453	C₂×C₁₃	—	4	4	no	—
454	C₂×C₁₃	—	4	4	no	—
455	C₂×C₁₃	—	8	4	no	—
456	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
457	C₂×C₁₃	#3584	1	2	yes	—
458	C₂⁴	—	2	4	no	—
459	C₂⁴	—	2	2	no	—
460	#41	—	2	4	no	—
461	#41	—	2	4	no	—
462	#41	—	2	4	no	—
463	#41	—	2	8	no	—
464	#41	—	2	8	no	—
465	#41	—	4	4	no	—
466	#41	—	4	4	no	—
467	#41	—	4	8	no	—
468	#41	—	4	8	no	—
469	#41	—	4	16	no	—
470	#41	C₂×D₄×C₁₃	1	8	yes	—
471	C₂×Q₈	—	2	4	no	—
472	C₂×Q₈	—	2	2	no	—
473	C₂×Q₈	—	2	8	no	—
474	C₂×Q₈	—	2	4	no	—
475	C₂×Q₈	—	2	4	no	—
476	C₂×Q₈	—	4	4	no	—
477	C₂×Q₈	—	4	8	no	—
478	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
479	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
480	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
481	C₂×D₄	—	2	2	no	—
482	C₂×D₄	—	2	8	no	—
483	C₂×D₄	—	2	4	no	—
484	C₂×D₄	—	2	4	no	—
485	C₂×D₄	—	2	8	no	—
486	C₂×D₄	—	2	4	no	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	2	2	no	—
489	C₂×D₄	—	2	4	no	—
490	C₂×D₄	—	4	4	no	—
491	C₂×D₄	—	4	8	no	—
492	C₂×D₄	—	4	16	no	—
493	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
494	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
495	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
496	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
497	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	—	2	4	no	—
501	C₂²×C₄	—	2	4	no	—
502	C₂²×C₄	—	2	4	no	—
503	C₂²×C₄	—	2	4	no	—
504	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
505	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
506	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
507	Q₁₆	—	2	8	no	—
508	Q₁₆	—	4	4	no	—
509	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
510	SD₁₆	—	2	8	no	—
511	SD₁₆	—	2	8	no	—
512	SD₁₆	—	2	8	no	—
513	SD₁₆	—	2	8	no	—
514	SD₁₆	C₂×D₄×C₁₃	1	8	yes	—
515	D₈	—	2	8	no	—
516	D₈	—	4	4	no	—
517	D₈	C₂×D₄×C₁₃	1	4	yes	—
518	M₁₆	—	2	4	no	—
519	M₁₆	—	2	8	no	—
520	C₂×C₈	—	2	2	no	—
521	C₂×C₈	—	2	8	no	—
522	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
523	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
524	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
525	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
526	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
527	C₄⋊C₄	—	2	4	no	—
528	C₄⋊C₄	—	2	8	no	—
529	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
530	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
531	C₂²⋊C₄	—	2	8	no	—
532	C₂²⋊C₄	—	2	2	no	—
533	C₂²⋊C₄	—	2	8	no	—
534	C₂²⋊C₄	—	2	8	no	—
535	C₂²⋊C₄	—	2	8	no	—
536	C₂²⋊C₄	—	2	4	no	—
537	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
538	C₄²	—	2	2	no	—
539	C₄²	—	2	4	no	—
540	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
541	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
542	C₄²	C₂⁴×C₁₃	1	2	yes	—
543	C₁₃	#61088	1	1	yes	characteristic, direct product factor, Sylow
544	C₂³	—	2	2	no	—
545	C₂³	—	2	4	no	—
546	C₂³	—	4	8	no	—
547	C₂³	—	4	4	no	—
548	C₂³	—	8	4	no	—
549	C₂³	—	8	8	no	—
550	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
551	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
552	Q₈	—	2	4	no	—
553	Q₈	—	2	2	no	—
554	Q₈	—	2	4	no	—
555	Q₈	—	2	4	no	—
556	Q₈	—	4	8	no	—
557	Q₈	—	4	4	no	—
558	Q₈	C₂²×D₄×C₁₃	1	4	yes	—
559	D₄	—	2	8	no	—
560	D₄	—	2	8	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	4	no	—
563	D₄	—	2	2	no	—
564	D₄	—	2	4	no	—
565	D₄	—	4	4	no	—
566	D₄	—	4	8	no	—
567	D₄	—	4	8	no	—
568	D₄	—	4	8	no	—
569	D₄	—	4	4	no	—
570	D₄	—	8	8	no	—
571	D₄	C₂²×D₄×C₁₃	1	4	yes	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	8	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	4	2	no	—
579	C₂×C₄	—	4	8	no	—
580	C₂×C₄	—	4	8	no	—
581	C₂×C₄	—	4	8	no	—
582	C₂×C₄	—	4	4	no	—
583	C₂×C₄	—	8	4	no	—
584	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
585	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
586	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
587	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
588	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
589	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
590	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
591	C₈	—	2	4	no	—
592	C₈	—	2	2	no	—
593	C₈	C₂²×D₄×C₁₃	1	2	yes	—
594	C₈	C₂²×D₄×C₁₃	1	2	yes	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	8	no	—
597	C₂²	—	2	4	no	—
598	C₂²	—	2	4	no	—
599	C₂²	—	4	4	no	—
600	C₂²	—	4	8	no	—
601	C₂²	—	4	4	no	—
602	C₂²	—	16	4	no	—
603	C₂²	—	16	8	no	—
604	C₂²	D₄²×C₁₃	1	2	yes	—
605	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
606	C₄	—	2	2	no	—
607	C₄	—	2	2	no	—
608	C₄	—	2	4	no	—
609	C₄	—	2	4	no	—
610	C₄	—	4	4	no	—
611	C₄	—	4	4	no	—
612	C₄	D₄²×C₁₃	1	2	yes	—
613	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
614	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
615	C₂	—	2	2	no	—
616	C₂	—	4	4	no	—
617	C₂	—	4	4	no	—
618	C₂	—	8	4	no	—
619	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
620	C₂	C₁₃×#3584	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×#577	C₂	semidirect
2. C₁₃×#3500	C₂	semidirect
3. C₁₃×#3282	C₂	semidirect
4. C₁₃×#3277	C₂	semidirect
5. C₁₃×#3273	C₂	semidirect
6. C₂×C₁₃×#495	C₂	semidirect
7. C₁₃×#3057	C₂	semidirect
8. C₁₃×#3040	C₂	semidirect
9. C₁₃×#3011	C₂	semidirect
10. C₁₃×#3008	C₂	semidirect
11. C₄×C₁₃×#135	C₂	semidirect
12. C₁₃×#2931	C₂	semidirect
14. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
16. C₂×C₁₃×#137	C₂²	semidirect
17. C₂×C₁₃×#137	C₂²	semidirect
19. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₁₃×#135	C₂²	semidirect
22. C₂²×C₁₃×Q₁₆	C₂²	semidirect
23. C₂²×C₁₃×SD₁₆	C₂²	semidirect
24. C₂²×C₁₃×SD₁₆	C₂²	semidirect
26. C₂×C₁₃×#131	C₂²	semidirect
27. C₁₃×#548	C₂²	semidirect
29. C₁₃×#546	C₂²	semidirect
31. C₁₃×#536	C₂²	semidirect
37. C₂×C₁₃×#124	C₂²	semidirect
38. C₄×C₁₃×#41	C₂²	semidirect
39. C₁₃×#495	C₂²	semidirect
40. C₁₃×#495	C₂²	semidirect
41. C₁₃×#468	C₂²	semidirect
42. C₁₃×#465	C₂²	semidirect
43. C₁₃×#464	C₂²	semidirect
44. C₁₃×#463	C₂²	semidirect
45. C₁₃×#452	C₂²	semidirect
46. C₁₃×#451	C₂²	semidirect
47. C₁₃×#449	C₂²	semidirect
48. C₁₃×#447	C₂²	semidirect
49. C₄×C₁₃×Q₁₆	C₂²	semidirect
50. C₄×C₁₃×SD₁₆	C₂²	semidirect
51. C₄×C₁₃×D₈	C₂²	semidirect
52. C₁₃×#436	C₂²	semidirect
53. C₈×D₄×C₁₃	C₂²	semidirect
54. C₁₃×#427	C₂²	semidirect
55. C₁₃×#423	C₂²	semidirect
56. C₁₃×#419	C₂²	semidirect
57. C₁₃×#418	C₂²	semidirect
58. C₁₃×#416	C₂²	semidirect
59. C₁₃×#408	C₂²	semidirect
60. C₂×C₄×C₈×C₁₃	C₂²	semidirect
84. C₁₃×#135	D₄	semidirect
148. #61088	C₁₃	direct (N × H)
234. C₂×#577	C₂×C₁₃	semidirect
235. #3500	C₂×C₁₃	semidirect
236. #3282	C₂×C₁₃	semidirect
237. #3277	C₂×C₁₃	semidirect
238. #3273	C₂×C₁₃	semidirect
239. C₂×#495	C₂×C₁₃	semidirect
240. #3057	C₂×C₁₃	semidirect
241. #3040	C₂×C₁₃	semidirect
242. #3011	C₂×C₁₃	semidirect
243. #3008	C₂×C₁₃	semidirect
244. C₄×#135	C₂×C₁₃	semidirect
245. #2931	C₂×C₁₃	semidirect
298. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
300. C₂×#137	C₂²×C₁₃	semidirect
301. C₂×#137	C₂²×C₁₃	semidirect
303. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
305. C₂×#135	C₂²×C₁₃	semidirect
306. C₂²×Q₁₆	C₂²×C₁₃	semidirect
307. C₂²×SD₁₆	C₂²×C₁₃	semidirect
308. C₂²×SD₁₆	C₂²×C₁₃	semidirect
310. C₂×#131	C₂²×C₁₃	semidirect
311. #548	C₂²×C₁₃	semidirect
313. #546	C₂²×C₁₃	semidirect
315. #536	C₂²×C₁₃	semidirect
321. C₂×#124	C₂²×C₁₃	semidirect
322. C₄×#41	C₂²×C₁₃	semidirect
323. #495	C₂²×C₁₃	semidirect
324. #495	C₂²×C₁₃	semidirect
325. #468	C₂²×C₁₃	semidirect
326. #465	C₂²×C₁₃	semidirect
327. #464	C₂²×C₁₃	semidirect
328. #463	C₂²×C₁₃	semidirect
329. #452	C₂²×C₁₃	semidirect
330. #451	C₂²×C₁₃	semidirect
331. #449	C₂²×C₁₃	semidirect
332. #447	C₂²×C₁₃	semidirect
333. C₄×Q₁₆	C₂²×C₁₃	semidirect
334. C₄×SD₁₆	C₂²×C₁₃	semidirect
335. C₄×D₈	C₂²×C₁₃	semidirect
336. #436	C₂²×C₁₃	semidirect
337. C₈×D₄	C₂²×C₁₃	semidirect
338. #427	C₂²×C₁₃	semidirect
339. #423	C₂²×C₁₃	semidirect
340. #419	C₂²×C₁₃	semidirect
341. #418	C₂²×C₁₃	semidirect
342. #416	C₂²×C₁₃	semidirect
343. #408	C₂²×C₁₃	semidirect
344. C₂×C₄×C₈	C₂²×C₁₃	semidirect
388. #135	D₄×C₁₃	semidirect
543. C₁₃	#61088	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×#577	2
C₁₃×#3500	2
C₁₃×#3282	2
C₁₃×#3277	2
C₁₃×#3273	2
C₂×C₁₃×#495	2
C₁₃×#3057	2
C₁₃×#3040	2
C₁₃×#3011	2
C₁₃×#3008	2
C₄×C₁₃×#135	2
C₁₃×#2931	2
#61088	13

Subgroups — C13×#61088 #15747427

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61088 #15747427