Subgroups — C₁₃×#61084 #15747423

Order 3328.

2834 conjugacy classes of subgroups.

The subgroup lattice has 630 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×#3283	C₂	1	2	yes	maximal, complemented
4	C₁₃×#3280	C₂	1	4	yes	maximal, complemented
5	D₄×C₁₃×D₈	C₂	1	2	yes	maximal, complemented
6	C₁₃×#3273	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3272	C₂	1	4	yes	maximal, complemented
8	C₁₃×#3147	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3061	C₂	1	2	yes	maximal, complemented
10	C₁₃×#3036	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3012	C₂	1	4	yes	maximal, complemented
12	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2931	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	4	yes	complemented
15	C₁₃×#576	—	2	16	no	—
16	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
18	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
19	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
20	C₂×C₁₃×#135	C₂²	1	2	yes	complemented
21	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×D₈	C₂²	1	4	yes	complemented
23	C₂×C₁₃×#131	C₂²	1	2	yes	complemented
24	C₁₃×#547	—	2	2	no	—
25	C₁₃×#547	C₂²	1	4	yes	complemented
26	C₁₃×#546	—	2	4	no	—
27	C₁₃×#546	C₂²	1	8	yes	complemented
28	D₄²×C₁₃	—	2	2	no	—
29	D₄²×C₁₃	C₂²	1	4	yes	complemented
30	C₁₃×#537	C₂²	1	4	yes	complemented
31	C₁₃×#534	—	2	4	no	—
32	C₁₃×#532	C₂²	1	1	yes	characteristic
33	C₁₃×#532	C₂²	1	2	yes	complemented
34	C₂×C₁₃×#121	—	2	4	no	—
35	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
36	C₁₃×#495	C₂²	1	2	yes	complemented
37	C₁₃×#495	C₂²	1	2	yes	complemented
38	C₁₃×#494	C₂²	1	1	yes	characteristic, complemented
39	C₁₃×#493	C₂²	1	1	yes	characteristic, complemented
40	C₁₃×#492	C₂²	1	2	yes	complemented
41	C₁₃×#468	C₂²	1	8	yes	complemented
42	C₁₃×#467	C₂²	1	4	yes	complemented
43	C₁₃×#466	C₂²	1	4	yes	complemented
44	C₁₃×#463	C₂²	1	8	yes	complemented
45	C₁₃×#461	C₂²	1	4	yes	complemented
46	C₁₃×#459	C₂²	1	4	yes	complemented
47	C₁₃×#452	C₂²	1	8	yes	complemented
48	C₁₃×#450	C₂²	1	8	yes	complemented
49	C₁₃×#449	C₂²	1	8	yes	complemented
50	C₁₃×#447	C₂²	1	8	yes	complemented
51	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
52	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
53	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
54	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
55	C₁₃×#436	C₂²	1	2	yes	complemented
56	C₁₃×#436	C₂²	1	2	yes	complemented
57	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
58	C₈×D₄×C₁₃	C₂²	1	2	yes	complemented
59	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic, complemented
60	C₁₃×#423	C₂²	1	1	yes	characteristic, complemented
61	C₁₃×#417	C₂²	1	4	yes	complemented
62	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
63	C₁₃×#408	C₂²	1	2	yes	complemented
64	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×H(5,𝔽₂)	—	2	16	no	—
66	C₁₃×H(5,𝔽₂)	—	4	8	no	—
67	C₂×C₁₃×#41	—	2	4	no	—
68	C₂×C₁₃×#41	C₂³	1	4	yes	—
69	C₂×C₁₃×#41	C₂³	1	8	yes	—
70	C₂×C₁₃×#41	C₂³	1	2	yes	—
71	C₂²×D₄×C₁₃	—	2	8	no	—
72	C₂²×D₄×C₁₃	—	2	4	no	—
73	C₂²×D₄×C₁₃	—	2	4	no	—
74	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
75	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₃	—	2	2	no	—
77	C₁₃×AGL(1,ℤ/8)	—	2	16	no	—
78	C₁₃×AGL(1,ℤ/8)	—	2	32	no	—
79	C₁₃×#135	—	2	16	no	—
80	C₁₃×#135	—	2	8	no	—
81	C₁₃×#135	—	4	4	no	—
82	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
83	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
84	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
85	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
86	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
87	C₂×C₁₃×D₈	—	2	16	no	—
88	C₂×C₁₃×D₈	D₄	1	8	yes	complemented
89	C₂×C₁₃×D₈	C₂³	1	8	yes	—
90	C₂×C₁₃×D₈	C₂³	1	2	yes	—
91	C₂×C₁₃×D₈	C₂³	1	2	yes	—
92	C₂×C₁₃×D₈	C₂³	1	2	yes	—
93	C₂×C₁₃×D₈	C₂³	1	2	yes	—
94	C₁₃×#131	—	2	8	no	—
95	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
96	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
97	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
99	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
101	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
102	C₁₃×#127	D₄	1	1	yes	characteristic
103	C₁₃×#127	C₂³	1	2	yes	—
104	C₁₃×#124	D₄	1	2	yes	—
105	C₁₃×#124	C₂³	1	4	yes	—
106	C₁₃×#123	—	2	8	no	—
107	C₁₃×#123	—	2	8	no	—
108	C₁₃×C₂²⋊Q₈	—	2	4	no	—
109	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
110	C₁₃×#121	—	2	8	no	—
111	C₁₃×#121	—	2	4	no	—
112	C₁₃×#121	—	2	4	no	—
113	C₁₃×#121	—	2	2	no	—
114	C₁₃×#121	—	2	2	no	—
115	C₁₃×#121	—	2	4	no	—
116	C₁₃×#121	—	2	8	no	—
117	C₁₃×#121	D₄	1	2	yes	—
118	C₁₃×#121	D₄	1	2	yes	—
119	C₁₃×#121	C₂³	1	8	yes	—
120	C₁₃×#120	—	2	8	no	—
121	C₁₃×#120	—	2	8	no	—
122	C₄×D₄×C₁₃	—	2	2	no	—
123	C₄×D₄×C₁₃	—	2	2	no	—
124	C₄×D₄×C₁₃	—	2	2	no	—
125	C₄×D₄×C₁₃	—	2	2	no	—
126	C₄×D₄×C₁₃	C₂³	1	4	yes	—
127	C₄×D₄×C₁₃	C₂³	1	4	yes	—
128	C₄×D₄×C₁₃	C₂³	1	2	yes	—
129	C₄×D₄×C₁₃	C₂³	1	2	yes	—
130	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
131	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
133	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
134	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
135	C₁₃×#107	C₂³	1	2	yes	—
136	C₁₃×#107	C₂³	1	2	yes	—
137	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
138	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
139	C₁₃×#103	C₂³	1	8	yes	—
140	C₁₃×#102	C₂³	1	4	yes	—
141	C₁₃×#102	C₂³	1	4	yes	—
142	C₁₃×#102	C₂³	1	8	yes	—
143	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
144	C₁₃×C₂²⋊C₈	C₂³	1	4	yes	—
145	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
146	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
147	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
148	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
149	#61084	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂⁴×C₁₃	—	2	2	no	—
151	C₂⁴×C₁₃	—	2	8	no	—
152	C₁₃×#41	—	2	4	no	—
153	C₁₃×#41	—	2	4	no	—
154	C₁₃×#41	—	2	16	no	—
155	C₁₃×#41	—	2	8	no	—
156	C₁₃×#41	—	2	8	no	—
157	C₁₃×#41	—	4	8	no	—
158	C₁₃×#41	—	4	16	no	—
159	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
160	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
161	C₂×D₄×C₁₃	—	2	16	no	—
162	C₂×D₄×C₁₃	—	2	8	no	—
163	C₂×D₄×C₁₃	—	2	4	no	—
164	C₂×D₄×C₁₃	—	2	8	no	—
165	C₂×D₄×C₁₃	—	2	2	no	—
166	C₂×D₄×C₁₃	—	2	2	no	—
167	C₂×D₄×C₁₃	—	2	8	no	—
168	C₂×D₄×C₁₃	—	2	2	no	—
169	C₂×D₄×C₁₃	—	2	4	no	—
170	C₂×D₄×C₁₃	—	4	8	no	—
171	C₂×D₄×C₁₃	—	4	16	no	—
172	C₂×D₄×C₁₃	—	4	32	no	—
173	C₂×D₄×C₁₃	—	8	8	no	—
174	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
175	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
176	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
177	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
178	C₂×D₄×C₁₃	C₂×D₄	1	8	yes	complemented
179	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
180	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₁₃	—	2	2	no	—
182	C₂²×C₄×C₁₃	—	2	8	no	—
183	C₂²×C₄×C₁₃	—	2	4	no	—
184	C₂²×C₄×C₁₃	—	2	4	no	—
185	C₂²×C₄×C₁₃	—	2	4	no	—
186	C₂²×C₄×C₁₃	—	8	4	no	—
187	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₁₃×Q₁₆	—	2	4	no	—
192	C₁₃×Q₁₆	—	4	2	no	—
193	C₁₃×SD₁₆	—	2	16	no	—
194	C₁₃×SD₁₆	—	2	8	no	—
195	C₁₃×SD₁₆	—	4	4	no	—
196	C₁₃×D₈	—	2	16	no	—
197	C₁₃×D₈	—	2	4	no	—
198	C₁₃×D₈	—	4	2	no	—
199	C₁₃×D₈	C₂×D₄	1	8	yes	complemented
200	C₁₃×D₈	C₂×D₄	1	8	yes	complemented
201	C₁₃×M₁₆	—	2	4	no	—
202	C₁₃×M₁₆	—	2	8	no	—
203	C₂×C₈×C₁₃	—	2	2	no	—
204	C₂×C₈×C₁₃	—	2	8	no	—
205	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	complemented
206	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
207	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
208	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
209	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
210	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
211	C₁₃×C₄⋊C₄	—	2	2	no	—
212	C₁₃×C₄⋊C₄	—	2	8	no	—
213	C₁₃×C₄⋊C₄	—	2	2	no	—
214	C₁₃×C₄⋊C₄	—	2	2	no	—
215	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
216	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
217	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
218	C₁₃×C₂²⋊C₄	—	2	8	no	—
219	C₁₃×C₂²⋊C₄	—	2	4	no	—
220	C₁₃×C₂²⋊C₄	—	2	4	no	—
221	C₁₃×C₂²⋊C₄	—	2	4	no	—
222	C₁₃×C₂²⋊C₄	—	2	8	no	—
223	C₁₃×C₂²⋊C₄	—	2	4	no	—
224	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
225	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
226	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
227	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
228	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
229	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂×#576	C₂×C₁₃	1	2	yes	complemented
231	#3496	C₂×C₁₃	1	2	yes	complemented
232	#3283	C₂×C₁₃	1	2	yes	complemented
233	#3280	C₂×C₁₃	1	4	yes	complemented
234	D₄×D₈	C₂×C₁₃	1	2	yes	complemented
235	#3273	C₂×C₁₃	1	4	yes	complemented
236	#3272	C₂×C₁₃	1	4	yes	complemented
237	#3147	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#3061	C₂×C₁₃	1	2	yes	complemented
239	#3036	C₂×C₁₃	1	2	yes	complemented
240	#3012	C₂×C₁₃	1	4	yes	complemented
241	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#2931	C₂×C₁₃	1	1	yes	characteristic, complemented
243	C₂³×C₁₃	—	2	4	no	—
244	C₂³×C₁₃	—	2	8	no	—
245	C₂³×C₁₃	—	2	4	no	—
246	C₂³×C₁₃	—	4	16	no	—
247	C₂³×C₁₃	—	8	2	no	—
248	C₂³×C₁₃	—	8	2	no	—
249	C₂³×C₁₃	—	8	8	no	—
250	C₂³×C₁₃	—	8	8	no	—
251	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
252	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
253	Q₈×C₁₃	—	2	4	no	—
254	Q₈×C₁₃	—	2	4	no	—
255	Q₈×C₁₃	—	2	4	no	—
256	D₄×C₁₃	—	2	8	no	—
257	D₄×C₁₃	—	2	8	no	—
258	D₄×C₁₃	—	2	4	no	—
259	D₄×C₁₃	—	2	4	no	—
260	D₄×C₁₃	—	2	4	no	—
261	D₄×C₁₃	—	2	4	no	—
262	D₄×C₁₃	—	2	4	no	—
263	D₄×C₁₃	—	4	2	no	—
264	D₄×C₁₃	—	4	16	no	—
265	D₄×C₁₃	—	4	16	no	—
266	D₄×C₁₃	—	4	8	no	—
267	D₄×C₁₃	—	4	4	no	—
268	D₄×C₁₃	—	8	2	no	—
269	D₄×C₁₃	—	8	8	no	—
270	D₄×C₁₃	C₂²×D₄	1	8	yes	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	4	no	—
273	C₂×C₄×C₁₃	—	2	4	no	—
274	C₂×C₄×C₁₃	—	2	4	no	—
275	C₂×C₄×C₁₃	—	2	4	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	4	16	no	—
278	C₂×C₄×C₁₃	—	4	8	no	—
279	C₂×C₄×C₁₃	—	4	8	no	—
280	C₂×C₄×C₁₃	—	8	4	no	—
281	C₂×C₄×C₁₃	—	8	2	no	—
282	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
284	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
286	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
288	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
290	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
291	C₈×C₁₃	—	2	4	no	—
292	C₈×C₁₃	—	2	1	no	—
293	C₈×C₁₃	—	2	1	no	—
294	C₈×C₁₃	C₂²×D₄	1	2	yes	—
295	C₈×C₁₃	C₂²×D₄	1	2	yes	—
296	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	4	yes	complemented
297	#576	—	2	16	no	—
298	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
299	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	8	yes	complemented
300	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
301	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
302	C₂×#135	C₂²×C₁₃	1	2	yes	complemented
303	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
304	C₂²×D₈	C₂²×C₁₃	1	4	yes	complemented
305	C₂×#131	C₂²×C₁₃	1	2	yes	complemented
306	#547	—	2	2	no	—
307	#547	C₂²×C₁₃	1	4	yes	complemented
308	#546	—	2	4	no	—
309	#546	C₂²×C₁₃	1	8	yes	complemented
310	D₄²	—	2	2	no	—
311	D₄²	C₂²×C₁₃	1	4	yes	complemented
312	#537	C₂²×C₁₃	1	4	yes	complemented
313	#534	—	2	4	no	—
314	#532	C₂²×C₁₃	1	1	yes	characteristic
315	#532	C₂²×C₁₃	1	2	yes	complemented
316	C₂×#121	—	2	4	no	—
317	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	complemented
318	#495	C₂²×C₁₃	1	2	yes	complemented
319	#495	C₂²×C₁₃	1	2	yes	complemented
320	#494	C₂²×C₁₃	1	1	yes	characteristic, complemented
321	#493	C₂²×C₁₃	1	1	yes	characteristic, complemented
322	#492	C₂²×C₁₃	1	2	yes	complemented
323	#468	C₂²×C₁₃	1	8	yes	complemented
324	#467	C₂²×C₁₃	1	4	yes	complemented
325	#466	C₂²×C₁₃	1	4	yes	complemented
326	#463	C₂²×C₁₃	1	8	yes	complemented
327	#461	C₂²×C₁₃	1	4	yes	complemented
328	#459	C₂²×C₁₃	1	4	yes	complemented
329	#452	C₂²×C₁₃	1	8	yes	complemented
330	#450	C₂²×C₁₃	1	8	yes	complemented
331	#449	C₂²×C₁₃	1	8	yes	complemented
332	#447	C₂²×C₁₃	1	8	yes	complemented
333	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
334	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
335	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
336	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
337	#436	C₂²×C₁₃	1	2	yes	complemented
338	#436	C₂²×C₁₃	1	2	yes	complemented
339	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
340	C₈×D₄	C₂²×C₁₃	1	2	yes	complemented
341	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic, complemented
342	#423	C₂²×C₁₃	1	1	yes	characteristic, complemented
343	#417	C₂²×C₁₃	1	4	yes	complemented
344	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
345	#408	C₂²×C₁₃	1	2	yes	complemented
346	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
347	C₂²×C₁₃	—	2	1	no	—
348	C₂²×C₁₃	—	2	1	no	—
349	C₂²×C₁₃	—	2	4	no	—
350	C₂²×C₁₃	—	2	4	no	—
351	C₂²×C₁₃	—	2	8	no	—
352	C₂²×C₁₃	—	2	4	no	—
353	C₂²×C₁₃	—	4	4	no	—
354	C₂²×C₁₃	—	4	4	no	—
355	C₂²×C₁₃	—	4	4	no	—
356	C₂²×C₁₃	—	4	4	no	—
357	C₂²×C₁₃	—	4	4	no	—
358	C₂²×C₁₃	—	8	8	no	—
359	C₂²×C₁₃	—	16	16	no	—
360	C₂²×C₁₃	D₄²	1	2	yes	—
361	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
362	C₄×C₁₃	—	2	1	no	—
363	C₄×C₁₃	—	2	1	no	—
364	C₄×C₁₃	—	2	4	no	—
365	C₄×C₁₃	—	2	1	no	—
366	C₄×C₁₃	—	4	4	no	—
367	C₄×C₁₃	—	4	4	no	—
368	C₄×C₁₃	D₄²	1	2	yes	—
369	C₄×C₁₃	#576	1	2	yes	complemented
370	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
371	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
372	H(5,𝔽₂)	—	2	16	no	—
373	H(5,𝔽₂)	—	4	8	no	—
374	C₂×#41	—	2	4	no	—
375	C₂×#41	C₂³×C₁₃	1	4	yes	—
376	C₂×#41	C₂³×C₁₃	1	8	yes	—
377	C₂×#41	C₂³×C₁₃	1	2	yes	—
378	C₂²×D₄	—	2	8	no	—
379	C₂²×D₄	—	2	4	no	—
380	C₂²×D₄	—	2	4	no	—
381	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
382	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
383	C₂³×C₄	—	2	2	no	—
384	AGL(1,ℤ/8)	—	2	16	no	—
385	AGL(1,ℤ/8)	—	2	32	no	—
386	#135	—	2	16	no	—
387	#135	—	2	8	no	—
388	#135	—	4	4	no	—
389	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
390	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
391	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
392	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
393	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
394	C₂×D₈	—	2	16	no	—
395	C₂×D₈	D₄×C₁₃	1	8	yes	complemented
396	C₂×D₈	C₂³×C₁₃	1	2	yes	—
397	C₂×D₈	C₂³×C₁₃	1	8	yes	—
398	C₂×D₈	C₂³×C₁₃	1	2	yes	—
399	C₂×D₈	C₂³×C₁₃	1	2	yes	—
400	C₂×D₈	C₂³×C₁₃	1	2	yes	—
401	#131	—	2	8	no	—
402	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
403	C₂×M₁₆	C₂³×C₁₃	1	4	yes	—
404	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
405	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
406	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
407	C₄⋊Q₈	D₄×C₁₃	1	1	yes	characteristic
408	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
409	#127	D₄×C₁₃	1	1	yes	characteristic
410	#127	C₂³×C₁₃	1	2	yes	—
411	#124	D₄×C₁₃	1	2	yes	—
412	#124	C₂³×C₁₃	1	4	yes	—
413	#123	—	2	8	no	—
414	#123	—	2	8	no	—
415	C₂²⋊Q₈	—	2	4	no	—
416	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
417	#121	—	2	8	no	—
418	#121	—	2	4	no	—
419	#121	—	2	4	no	—
420	#121	—	2	2	no	—
421	#121	—	2	2	no	—
422	#121	—	2	4	no	—
423	#121	—	2	8	no	—
424	#121	D₄×C₁₃	1	2	yes	—
425	#121	D₄×C₁₃	1	2	yes	—
426	#121	C₂³×C₁₃	1	8	yes	—
427	#120	—	2	8	no	—
428	#120	—	2	8	no	—
429	C₄×D₄	—	2	2	no	—
430	C₄×D₄	—	2	2	no	—
431	C₄×D₄	—	2	2	no	—
432	C₄×D₄	—	2	2	no	—
433	C₄×D₄	C₂³×C₁₃	1	4	yes	—
434	C₄×D₄	C₂³×C₁₃	1	4	yes	—
435	C₄×D₄	C₂³×C₁₃	1	2	yes	—
436	C₄×D₄	C₂³×C₁₃	1	2	yes	—
437	C₂×C₄⋊C₄	—	2	4	no	—
438	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
439	C₂×C₂²⋊C₄	—	2	2	no	—
440	C₂×C₂²⋊C₄	—	2	8	no	—
441	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
442	#107	C₂³×C₁₃	1	2	yes	—
443	#107	C₂³×C₁₃	1	2	yes	—
444	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
445	C₄⋊C₈	C₂³×C₁₃	1	2	yes	—
446	#103	C₂³×C₁₃	1	8	yes	—
447	#102	C₂³×C₁₃	1	4	yes	—
448	#102	C₂³×C₁₃	1	4	yes	—
449	#102	C₂³×C₁₃	1	8	yes	—
450	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
451	C₂²⋊C₈	C₂³×C₁₃	1	4	yes	—
452	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
453	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
454	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
455	C₄×C₈	C₂³×C₁₃	1	1	yes	characteristic
456	C₂×C₁₃	—	2	2	no	—
457	C₂×C₁₃	—	4	4	no	—
458	C₂×C₁₃	—	4	8	no	—
459	C₂×C₁₃	—	8	4	no	—
460	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
461	C₂×C₁₃	C₂×#576	1	1	yes	characteristic
462	C₂×C₁₃	#3584	1	1	yes	characteristic
463	C₂⁴	—	2	2	no	—
464	C₂⁴	—	2	8	no	—
465	#41	—	2	4	no	—
466	#41	—	2	4	no	—
467	#41	—	2	16	no	—
468	#41	—	2	8	no	—
469	#41	—	2	8	no	—
470	#41	—	4	8	no	—
471	#41	—	4	16	no	—
472	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
473	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
474	C₂×D₄	—	2	16	no	—
475	C₂×D₄	—	2	8	no	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	2	8	no	—
478	C₂×D₄	—	2	2	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	8	no	—
481	C₂×D₄	—	2	2	no	—
482	C₂×D₄	—	2	4	no	—
483	C₂×D₄	—	4	8	no	—
484	C₂×D₄	—	4	16	no	—
485	C₂×D₄	—	4	32	no	—
486	C₂×D₄	—	8	8	no	—
487	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
488	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
489	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
490	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
491	C₂×D₄	C₂×D₄×C₁₃	1	8	yes	complemented
492	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
493	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	8	no	—
496	C₂²×C₄	—	2	4	no	—
497	C₂²×C₄	—	2	4	no	—
498	C₂²×C₄	—	2	4	no	—
499	C₂²×C₄	—	8	4	no	—
500	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
501	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
502	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
503	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
504	Q₁₆	—	2	4	no	—
505	Q₁₆	—	4	2	no	—
506	SD₁₆	—	2	16	no	—
507	SD₁₆	—	2	8	no	—
508	SD₁₆	—	4	4	no	—
509	D₈	—	2	16	no	—
510	D₈	—	2	4	no	—
511	D₈	—	4	2	no	—
512	D₈	C₂×D₄×C₁₃	1	8	yes	complemented
513	D₈	C₂×D₄×C₁₃	1	8	yes	complemented
514	M₁₆	—	2	4	no	—
515	M₁₆	—	2	8	no	—
516	C₂×C₈	—	2	2	no	—
517	C₂×C₈	—	2	8	no	—
518	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	complemented
519	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
520	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
521	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
522	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
523	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	2	8	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
529	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
530	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
531	C₂²⋊C₄	—	2	8	no	—
532	C₂²⋊C₄	—	2	4	no	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	8	no	—
536	C₂²⋊C₄	—	2	4	no	—
537	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
538	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
539	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
540	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
541	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
542	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
543	C₁₃	#61084	1	1	yes	characteristic, direct product factor, Sylow
544	C₂³	—	2	4	no	—
545	C₂³	—	2	8	no	—
546	C₂³	—	2	4	no	—
547	C₂³	—	4	16	no	—
548	C₂³	—	8	2	no	—
549	C₂³	—	8	2	no	—
550	C₂³	—	8	8	no	—
551	C₂³	—	8	8	no	—
552	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
553	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
554	Q₈	—	2	4	no	—
555	Q₈	—	2	4	no	—
556	Q₈	—	2	4	no	—
557	D₄	—	2	8	no	—
558	D₄	—	2	8	no	—
559	D₄	—	2	4	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	4	no	—
563	D₄	—	2	4	no	—
564	D₄	—	4	2	no	—
565	D₄	—	4	16	no	—
566	D₄	—	4	16	no	—
567	D₄	—	4	8	no	—
568	D₄	—	4	4	no	—
569	D₄	—	8	2	no	—
570	D₄	—	8	8	no	—
571	D₄	C₂²×D₄×C₁₃	1	8	yes	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	16	no	—
579	C₂×C₄	—	4	8	no	—
580	C₂×C₄	—	4	8	no	—
581	C₂×C₄	—	8	4	no	—
582	C₂×C₄	—	8	2	no	—
583	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
584	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
585	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
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	C₂²×D₄×C₁₃	1	1	yes	characteristic
590	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
591	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
592	C₈	—	2	4	no	—
593	C₈	—	2	1	no	—
594	C₈	—	2	1	no	—
595	C₈	C₂²×D₄×C₁₃	1	2	yes	—
596	C₈	C₂²×D₄×C₁₃	1	2	yes	—
597	C₂²	—	2	1	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	2	4	no	—
600	C₂²	—	2	4	no	—
601	C₂²	—	2	4	no	—
602	C₂²	—	2	8	no	—
603	C₂²	—	4	4	no	—
604	C₂²	—	4	4	no	—
605	C₂²	—	4	4	no	—
606	C₂²	—	4	4	no	—
607	C₂²	—	4	4	no	—
608	C₂²	—	8	8	no	—
609	C₂²	—	16	16	no	—
610	C₂²	D₄²×C₁₃	1	2	yes	—
611	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
612	C₄	—	2	1	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	4	no	—
616	C₄	—	4	4	no	—
617	C₄	—	4	4	no	—
618	C₄	D₄²×C₁₃	1	2	yes	—
619	C₄	C₁₃×#576	1	2	yes	complemented
620	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
621	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
622	C₂	—	2	2	no	—
623	C₂	—	4	4	no	—
624	C₂	—	4	8	no	—
625	C₂	—	8	4	no	—
626	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
627	C₂	C₂×C₁₃×#576	1	1	yes	characteristic
628	C₂	C₁₃×#3584	1	1	yes	characteristic

	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×#3283	C₂	semidirect
4. C₁₃×#3280	C₂	semidirect
5. D₄×C₁₃×D₈	C₂	semidirect
6. C₁₃×#3273	C₂	semidirect
7. C₁₃×#3272	C₂	semidirect
8. C₁₃×#3147	C₂	semidirect
9. C₁₃×#3061	C₂	semidirect
10. C₁₃×#3036	C₂	semidirect
11. C₁₃×#3012	C₂	semidirect
12. C₂×C₄×C₁₃×D₈	C₂	semidirect
13. C₁₃×#2931	C₂	semidirect
14. C₂×C₁₃×H(5,𝔽₂)	C₂²	semidirect
16. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
17. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
18. C₂×C₁₃×#135	C₂²	semidirect
19. C₂×C₁₃×#135	C₂²	semidirect
20. C₂×C₁₃×#135	C₂²	semidirect
22. C₂²×C₁₃×D₈	C₂²	semidirect
23. C₂×C₁₃×#131	C₂²	semidirect
25. C₁₃×#547	C₂²	semidirect
27. C₁₃×#546	C₂²	semidirect
29. D₄²×C₁₃	C₂²	semidirect
30. C₁₃×#537	C₂²	semidirect
33. C₁₃×#532	C₂²	semidirect
35. C₂×C₄×D₄×C₁₃	C₂²	semidirect
36. C₁₃×#495	C₂²	semidirect
37. C₁₃×#495	C₂²	semidirect
38. C₁₃×#494	C₂²	semidirect
39. C₁₃×#493	C₂²	semidirect
40. C₁₃×#492	C₂²	semidirect
41. C₁₃×#468	C₂²	semidirect
42. C₁₃×#467	C₂²	semidirect
43. C₁₃×#466	C₂²	semidirect
44. C₁₃×#463	C₂²	semidirect
45. C₁₃×#461	C₂²	semidirect
46. C₁₃×#459	C₂²	semidirect
47. C₁₃×#452	C₂²	semidirect
48. C₁₃×#450	C₂²	semidirect
49. C₁₃×#449	C₂²	semidirect
50. C₁₃×#447	C₂²	semidirect
51. C₄×C₁₃×D₈	C₂²	semidirect
52. C₄×C₁₃×D₈	C₂²	semidirect
53. C₄×C₁₃×D₈	C₂²	semidirect
54. C₄×C₁₃×D₈	C₂²	semidirect
55. C₁₃×#436	C₂²	semidirect
56. C₁₃×#436	C₂²	semidirect
57. C₈×D₄×C₁₃	C₂²	semidirect
58. C₈×D₄×C₁₃	C₂²	semidirect
59. C₂×C₁₃×#107	C₂²	semidirect
60. C₁₃×#423	C₂²	semidirect
61. C₁₃×#417	C₂²	semidirect
62. C₂×C₁₃×#102	C₂²	semidirect
63. C₁₃×#408	C₂²	semidirect
64. C₂×C₄×C₈×C₁₃	C₂²	semidirect
88. C₂×C₁₃×D₈	D₄	semidirect
149. #61084	C₁₃	direct (N × H)
178. C₂×D₄×C₁₃	C₂×D₄	semidirect
199. C₁₃×D₈	C₂×D₄	semidirect
200. C₁₃×D₈	C₂×D₄	semidirect
205. C₂×C₈×C₁₃	C₂×D₄	semidirect
230. C₂×#576	C₂×C₁₃	semidirect
231. #3496	C₂×C₁₃	semidirect
232. #3283	C₂×C₁₃	semidirect
233. #3280	C₂×C₁₃	semidirect
234. D₄×D₈	C₂×C₁₃	semidirect
235. #3273	C₂×C₁₃	semidirect
236. #3272	C₂×C₁₃	semidirect
237. #3147	C₂×C₁₃	semidirect
238. #3061	C₂×C₁₃	semidirect
239. #3036	C₂×C₁₃	semidirect
240. #3012	C₂×C₁₃	semidirect
241. C₂×C₄×D₈	C₂×C₁₃	semidirect
242. #2931	C₂×C₁₃	semidirect
296. C₂×H(5,𝔽₂)	C₂²×C₁₃	semidirect
298. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
299. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
300. C₂×#135	C₂²×C₁₃	semidirect
301. C₂×#135	C₂²×C₁₃	semidirect
302. C₂×#135	C₂²×C₁₃	semidirect
304. C₂²×D₈	C₂²×C₁₃	semidirect
305. C₂×#131	C₂²×C₁₃	semidirect
307. #547	C₂²×C₁₃	semidirect
309. #546	C₂²×C₁₃	semidirect
311. D₄²	C₂²×C₁₃	semidirect
312. #537	C₂²×C₁₃	semidirect
315. #532	C₂²×C₁₃	semidirect
317. C₂×C₄×D₄	C₂²×C₁₃	semidirect
318. #495	C₂²×C₁₃	semidirect
319. #495	C₂²×C₁₃	semidirect
320. #494	C₂²×C₁₃	semidirect
321. #493	C₂²×C₁₃	semidirect
322. #492	C₂²×C₁₃	semidirect
323. #468	C₂²×C₁₃	semidirect
324. #467	C₂²×C₁₃	semidirect
325. #466	C₂²×C₁₃	semidirect
326. #463	C₂²×C₁₃	semidirect
327. #461	C₂²×C₁₃	semidirect
328. #459	C₂²×C₁₃	semidirect
329. #452	C₂²×C₁₃	semidirect
330. #450	C₂²×C₁₃	semidirect
331. #449	C₂²×C₁₃	semidirect
332. #447	C₂²×C₁₃	semidirect
333. C₄×D₈	C₂²×C₁₃	semidirect
334. C₄×D₈	C₂²×C₁₃	semidirect
335. C₄×D₈	C₂²×C₁₃	semidirect
336. C₄×D₈	C₂²×C₁₃	semidirect
337. #436	C₂²×C₁₃	semidirect
338. #436	C₂²×C₁₃	semidirect
339. C₈×D₄	C₂²×C₁₃	semidirect
340. C₈×D₄	C₂²×C₁₃	semidirect
341. C₂×#107	C₂²×C₁₃	semidirect
342. #423	C₂²×C₁₃	semidirect
343. #417	C₂²×C₁₃	semidirect
344. C₂×#102	C₂²×C₁₃	semidirect
345. #408	C₂²×C₁₃	semidirect
346. C₂×C₄×C₈	C₂²×C₁₃	semidirect
369. C₄×C₁₃	#576	semidirect
395. C₂×D₈	D₄×C₁₃	semidirect
491. C₂×D₄	C₂×D₄×C₁₃	semidirect
512. D₈	C₂×D₄×C₁₃	semidirect
513. D₈	C₂×D₄×C₁₃	semidirect
518. C₂×C₈	C₂×D₄×C₁₃	semidirect
543. C₁₃	#61084	direct (N × H)
619. C₄	C₁₃×#576	semidirect

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×#3283	2
C₁₃×#3280	2
D₄×C₁₃×D₈	2
C₁₃×#3273	2
C₁₃×#3272	2
C₁₃×#3147	2
C₁₃×#3061	2
C₁₃×#3036	2
C₁₃×#3012	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2931	2
#61084	13

Subgroups — C13×#61084 #15747423

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61084 #15747423