Subgroups — C₁₃×#61412 #15747751

Order 3328.

1886 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3510	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3403	C₂	1	4	yes	maximal, complemented
3	C₁₃×#3402	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3394	C₂	1	8	yes	maximal, complemented
5	C₁₃×#3154	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3044	C₂	1	2	yes	maximal, complemented
8	C₁₃×#3041	C₂	1	2	yes	maximal, complemented
9	C₁₃×#3040	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2949	C₂	1	2	yes	maximal, complemented
12	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×#137	C₂²	1	2	yes	—
14	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
15	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
18	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
19	C₁₃×#559	C₂²	1	8	yes	complemented
20	C₁₃×#556	C₂²	1	8	yes	complemented
21	C₁₃×#551	—	2	8	no	—
22	C₁₃×#542	—	2	4	no	—
23	C₁₃×#536	C₂²	1	2	yes	—
24	C₁₃×#535	C₂²	1	2	yes	—
25	C₁₃×#533	C₂²	1	1	yes	characteristic
26	C₁₃×#529	—	2	4	no	—
27	C₂×C₁₃×#124	C₂²	1	2	yes	—
28	C₁₃×#519	C₂²	1	2	yes	—
29	C₁₃×#518	C₂²	1	2	yes	—
30	C₄×C₁₃×#41	C₂²	1	2	yes	—
31	C₁₃×#497	C₂²	1	4	yes	complemented
32	C₁₃×#496	C₂²	1	4	yes	complemented
33	C₁₃×#495	C₂²	1	4	yes	—
34	C₁₃×#495	C₂²	1	4	yes	—
35	C₁₃×#495	C₂²	1	4	yes	complemented
36	C₁₃×#492	C₂²	1	4	yes	complemented
37	C₁₃×#464	C₂²	1	8	yes	complemented
38	C₁₃×#464	C₂²	1	8	yes	complemented
39	C₁₃×#463	C₂²	1	8	yes	—
40	C₁₃×#463	C₂²	1	8	yes	complemented
41	C₁₃×#462	C₂²	1	8	yes	complemented
42	C₁₃×#459	C₂²	1	8	yes	—
43	C₁₃×#446	C₂²	1	4	yes	complemented
44	C₈×Q₈×C₁₃	C₂²	1	4	yes	complemented
45	C₁₃×#440	C₂²	1	8	yes	complemented
46	C₄×C₁₃×Q₁₆	C₂²	1	2	yes	complemented
47	C₄×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
48	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
49	C₄×C₁₃×D₈	C₂²	1	2	yes	complemented
50	C₁₃×#427	C₂²	1	1	yes	characteristic
51	C₁₃×#424	C₂²	1	2	yes	—
52	C₁₃×#423	C₂²	1	1	yes	characteristic
53	C₁₃×#419	C₂²	1	2	yes	—
54	C₁₃×#418	C₂²	1	2	yes	—
55	C₁₃×#416	C₂²	1	2	yes	—
56	C₁₃×#405	C₂²	1	2	yes	—
57	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
58	C₂×C₁₃×#41	C₂³	1	2	yes	—
59	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
60	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
61	C₁₃×#137	—	4	4	no	—
62	C₁₃×AGL(1,ℤ/8)	—	4	4	no	—
63	C₁₃×#135	—	2	4	no	—
64	C₂×C₁₃×Q₁₆	—	4	2	no	—
65	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
67	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
68	C₂×C₁₃×SD₁₆	—	2	8	no	—
69	C₂×C₁₃×SD₁₆	C₂³	1	2	yes	—
70	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
71	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
72	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
73	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
74	C₂×C₁₃×D₈	—	4	2	no	—
75	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×D₈	C₂³	1	4	yes	—
77	C₂×C₁₃×D₈	C₂³	1	4	yes	—
78	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊Q₈	D₄	1	2	yes	—
82	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
83	C₁₃×#127	C₂³	1	4	yes	—
84	C₁₃×#126	—	2	8	no	—
85	C₁₃×#126	—	2	8	no	—
86	C₁₃×#125	D₄	1	2	yes	—
87	C₁₃×#124	—	2	8	no	—
88	C₁₃×#124	—	2	2	no	—
89	C₁₃×#124	—	2	2	no	—
90	C₁₃×#124	C₂³	1	4	yes	—
91	C₁₃×#124	C₂³	1	8	yes	—
92	C₁₃×#124	C₂³	1	4	yes	—
93	C₁₃×#123	—	2	8	no	—
94	C₁₃×#123	—	2	8	no	—
95	C₁₃×#123	—	2	4	no	—
96	C₁₃×C₂²⋊Q₈	—	2	8	no	—
97	C₁₃×C₂²⋊Q₈	—	2	4	no	—
98	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	—
99	C₁₃×#121	—	2	4	no	—
100	C₁₃×#120	—	2	4	no	—
101	C₄×Q₈×C₁₃	—	2	4	no	—
102	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
103	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
104	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
105	C₄×D₄×C₁₃	—	2	4	no	—
106	C₄×D₄×C₁₃	—	2	4	no	—
107	C₄×D₄×C₁₃	—	2	8	no	—
108	C₄×D₄×C₁₃	C₂³	1	4	yes	—
109	C₄×D₄×C₁₃	C₂³	1	8	yes	—
110	C₁₃×#117	—	2	8	no	—
111	C₁₃×#117	—	2	4	no	—
112	C₁₃×#117	—	2	2	no	—
113	C₁₃×#117	C₂³	1	2	yes	—
114	C₁₃×#117	C₂³	1	2	yes	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
117	C₂×C₄²×C₁₃	—	2	2	no	—
118	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
119	C₁₃×#107	C₂³	1	2	yes	—
120	C₁₃×#106	C₂³	1	2	yes	—
121	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
122	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
123	C₁₃×#103	C₂³	1	4	yes	—
124	C₁₃×#103	C₂³	1	8	yes	—
125	C₁₃×#102	C₂³	1	4	yes	—
126	C₁₃×#102	C₂³	1	8	yes	—
127	C₁₃×#97	C₂³	1	4	yes	—
128	C₄×C₈×C₁₃	C₂³	1	2	yes	—
129	C₄×C₈×C₁₃	C₂³	1	2	yes	—
130	C₄×C₈×C₁₃	C₂³	1	4	yes	—
131	#61412	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂⁴×C₁₃	—	2	2	no	—
133	C₁₃×#41	—	2	4	no	—
134	C₁₃×#41	—	2	4	no	—
135	C₂×Q₈×C₁₃	—	2	2	no	—
136	C₂×Q₈×C₁₃	—	2	4	no	—
137	C₂×Q₈×C₁₃	—	2	4	no	—
138	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
139	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
140	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
141	C₂×D₄×C₁₃	—	2	2	no	—
142	C₂×D₄×C₁₃	—	2	2	no	—
143	C₂×D₄×C₁₃	—	2	8	no	—
144	C₂×D₄×C₁₃	—	2	4	no	—
145	C₂×D₄×C₁₃	—	2	4	no	—
146	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
147	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₁₃	—	2	2	no	—
149	C₂²×C₄×C₁₃	—	2	2	no	—
150	C₂²×C₄×C₁₃	—	2	4	no	—
151	C₂²×C₄×C₁₃	—	2	8	no	—
152	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
154	C₁₃×Q₁₆	—	2	2	no	—
155	C₁₃×Q₁₆	—	4	4	no	—
156	C₁₃×Q₁₆	—	4	4	no	—
157	C₁₃×SD₁₆	—	2	8	no	—
158	C₁₃×SD₁₆	—	2	8	no	—
159	C₁₃×SD₁₆	—	2	4	no	—
160	C₁₃×SD₁₆	—	4	4	no	—
161	C₁₃×SD₁₆	—	4	4	no	—
162	C₁₃×D₈	—	2	2	no	—
163	C₁₃×D₈	—	4	4	no	—
164	C₁₃×D₈	—	4	4	no	—
165	C₁₃×M₁₆	—	2	4	no	—
166	C₂×C₈×C₁₃	—	2	2	no	—
167	C₂×C₈×C₁₃	#41	1	4	yes	—
168	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
169	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
170	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₁₃×C₄⋊C₄	—	2	4	no	—
173	C₁₃×C₄⋊C₄	—	2	8	no	—
174	C₁₃×C₄⋊C₄	—	2	8	no	—
175	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
176	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
177	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
178	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
179	C₁₃×C₂²⋊C₄	—	2	2	no	—
180	C₁₃×C₂²⋊C₄	—	2	8	no	—
181	C₁₃×C₂²⋊C₄	—	2	8	no	—
182	C₁₃×C₂²⋊C₄	—	2	8	no	—
183	C₁₃×C₂²⋊C₄	—	2	4	no	—
184	C₁₃×C₂²⋊C₄	—	2	8	no	—
185	C₁₃×C₂²⋊C₄	—	2	8	no	—
186	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
187	C₄²×C₁₃	—	2	4	no	—
188	C₄²×C₁₃	—	2	2	no	—
189	C₄²×C₁₃	—	2	8	no	—
190	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₁₃	C₂⁴	1	2	yes	—
193	C₄²×C₁₃	C₂⁴	1	4	yes	—
194	#3510	C₂×C₁₃	1	2	yes	complemented
195	#3403	C₂×C₁₃	1	4	yes	complemented
196	#3402	C₂×C₁₃	1	4	yes	complemented
197	#3394	C₂×C₁₃	1	8	yes	complemented
198	#3154	C₂×C₁₃	1	2	yes	complemented
199	C₂×#495	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#3044	C₂×C₁₃	1	2	yes	complemented
201	#3041	C₂×C₁₃	1	2	yes	complemented
202	#3040	C₂×C₁₃	1	2	yes	complemented
203	#2960	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#2949	C₂×C₁₃	1	2	yes	complemented
205	C₄×#135	C₂×C₁₃	1	1	yes	characteristic, complemented
206	C₂³×C₁₃	—	2	4	no	—
207	C₂³×C₁₃	—	2	2	no	—
208	C₂³×C₁₃	—	4	4	no	—
209	C₂³×C₁₃	—	8	4	no	—
210	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	Q₈×C₁₃	—	2	4	no	—
212	Q₈×C₁₃	—	2	2	no	—
213	Q₈×C₁₃	—	2	2	no	—
214	Q₈×C₁₃	—	2	4	no	—
215	Q₈×C₁₃	—	4	4	no	—
216	Q₈×C₁₃	—	4	4	no	—
217	D₄×C₁₃	—	2	2	no	—
218	D₄×C₁₃	—	2	4	no	—
219	D₄×C₁₃	—	2	4	no	—
220	D₄×C₁₃	—	2	2	no	—
221	D₄×C₁₃	—	4	4	no	—
222	D₄×C₁₃	—	4	4	no	—
223	D₄×C₁₃	—	8	8	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	4	4	no	—
229	C₂×C₄×C₁₃	—	4	4	no	—
230	C₂×C₄×C₁₃	—	8	4	no	—
231	C₂×C₄×C₁₃	—	8	8	no	—
232	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
234	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
235	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
237	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
238	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
239	C₈×C₁₃	—	2	2	no	—
240	C₈×C₁₃	—	2	4	no	—
241	C₈×C₁₃	C₂×#41	1	2	yes	—
242	C₈×C₁₃	C₂×#41	1	2	yes	—
243	C₂×#137	C₂²×C₁₃	1	2	yes	—
244	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
245	C₂×#135	C₂²×C₁₃	1	1	yes	characteristic
246	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
247	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
248	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
249	#559	C₂²×C₁₃	1	8	yes	complemented
250	#556	C₂²×C₁₃	1	8	yes	complemented
251	#551	—	2	8	no	—
252	#542	—	2	4	no	—
253	#536	C₂²×C₁₃	1	2	yes	—
254	#535	C₂²×C₁₃	1	2	yes	—
255	#533	C₂²×C₁₃	1	1	yes	characteristic
256	#529	—	2	4	no	—
257	C₂×#124	C₂²×C₁₃	1	2	yes	—
258	#519	C₂²×C₁₃	1	2	yes	—
259	#518	C₂²×C₁₃	1	2	yes	—
260	C₄×#41	C₂²×C₁₃	1	2	yes	—
261	#497	C₂²×C₁₃	1	4	yes	complemented
262	#496	C₂²×C₁₃	1	4	yes	complemented
263	#495	C₂²×C₁₃	1	4	yes	—
264	#495	C₂²×C₁₃	1	4	yes	—
265	#495	C₂²×C₁₃	1	4	yes	complemented
266	#492	C₂²×C₁₃	1	4	yes	complemented
267	#464	C₂²×C₁₃	1	8	yes	complemented
268	#464	C₂²×C₁₃	1	8	yes	complemented
269	#463	C₂²×C₁₃	1	8	yes	—
270	#463	C₂²×C₁₃	1	8	yes	complemented
271	#462	C₂²×C₁₃	1	8	yes	complemented
272	#459	C₂²×C₁₃	1	8	yes	—
273	#446	C₂²×C₁₃	1	4	yes	complemented
274	C₈×Q₈	C₂²×C₁₃	1	4	yes	complemented
275	#440	C₂²×C₁₃	1	8	yes	complemented
276	C₄×Q₁₆	C₂²×C₁₃	1	2	yes	complemented
277	C₄×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
278	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
279	C₄×D₈	C₂²×C₁₃	1	2	yes	complemented
280	#427	C₂²×C₁₃	1	1	yes	characteristic
281	#424	C₂²×C₁₃	1	2	yes	—
282	#423	C₂²×C₁₃	1	1	yes	characteristic
283	#419	C₂²×C₁₃	1	2	yes	—
284	#418	C₂²×C₁₃	1	2	yes	—
285	#416	C₂²×C₁₃	1	2	yes	—
286	#405	C₂²×C₁₃	1	2	yes	—
287	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
288	C₂²×C₁₃	—	2	2	no	—
289	C₂²×C₁₃	—	4	4	no	—
290	C₂²×C₁₃	—	4	8	no	—
291	C₂²×C₁₃	—	4	2	no	—
292	C₂²×C₁₃	—	4	4	no	—
293	C₂²×C₁₃	—	16	4	no	—
294	C₂²×C₁₃	#550	1	2	yes	—
295	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
296	C₄×C₁₃	—	2	2	no	—
297	C₄×C₁₃	—	2	2	no	—
298	C₄×C₁₃	—	2	8	no	—
299	C₄×C₁₃	—	4	4	no	—
300	C₄×C₁₃	—	4	2	no	—
301	C₄×C₁₃	—	4	4	no	—
302	C₄×C₁₃	#550	1	2	yes	—
303	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
304	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
305	C₂×#41	C₂³×C₁₃	1	2	yes	—
306	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
307	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
308	#137	—	4	4	no	—
309	AGL(1,ℤ/8)	—	4	4	no	—
310	#135	—	2	4	no	—
311	C₂×Q₁₆	—	4	2	no	—
312	C₂×Q₁₆	C₂³×C₁₃	1	1	yes	characteristic
313	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
314	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
315	C₂×SD₁₆	—	2	8	no	—
316	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
317	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
318	C₂×SD₁₆	C₂³×C₁₃	1	2	yes	—
319	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
320	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
321	C₂×D₈	—	4	2	no	—
322	C₂×D₈	C₂³×C₁₃	1	1	yes	characteristic
323	C₂×D₈	C₂³×C₁₃	1	4	yes	—
324	C₂×D₈	C₂³×C₁₃	1	4	yes	—
325	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
326	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
328	C₄⋊Q₈	D₄×C₁₃	1	2	yes	—
329	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
330	#127	C₂³×C₁₃	1	4	yes	—
331	#126	—	2	8	no	—
332	#126	—	2	8	no	—
333	#125	D₄×C₁₃	1	2	yes	—
334	#124	—	2	8	no	—
335	#124	—	2	2	no	—
336	#124	—	2	2	no	—
337	#124	C₂³×C₁₃	1	8	yes	—
338	#124	C₂³×C₁₃	1	4	yes	—
339	#124	C₂³×C₁₃	1	4	yes	—
340	#123	—	2	8	no	—
341	#123	—	2	8	no	—
342	#123	—	2	4	no	—
343	C₂²⋊Q₈	—	2	8	no	—
344	C₂²⋊Q₈	—	2	4	no	—
345	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	—
346	#121	—	2	4	no	—
347	#120	—	2	4	no	—
348	C₄×Q₈	—	2	4	no	—
349	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
350	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
351	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
352	C₄×D₄	—	2	4	no	—
353	C₄×D₄	—	2	4	no	—
354	C₄×D₄	—	2	8	no	—
355	C₄×D₄	C₂³×C₁₃	1	4	yes	—
356	C₄×D₄	C₂³×C₁₃	1	8	yes	—
357	#117	—	2	8	no	—
358	#117	—	2	4	no	—
359	#117	—	2	2	no	—
360	#117	C₂³×C₁₃	1	2	yes	—
361	#117	C₂³×C₁₃	1	2	yes	—
362	C₂×C₂²⋊C₄	—	2	4	no	—
363	C₂×C₂²⋊C₄	—	2	4	no	—
364	C₂×C₄²	—	2	2	no	—
365	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
366	#107	C₂³×C₁₃	1	2	yes	—
367	#106	C₂³×C₁₃	1	2	yes	—
368	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
369	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
370	#103	C₂³×C₁₃	1	4	yes	—
371	#103	C₂³×C₁₃	1	8	yes	—
372	#102	C₂³×C₁₃	1	4	yes	—
373	#102	C₂³×C₁₃	1	8	yes	—
374	#97	C₂³×C₁₃	1	4	yes	—
375	C₄×C₈	C₂³×C₁₃	1	2	yes	—
376	C₄×C₈	C₂³×C₁₃	1	2	yes	—
377	C₄×C₈	C₂³×C₁₃	1	4	yes	—
378	C₂×C₁₃	—	2	2	no	—
379	C₂×C₁₃	—	8	2	no	—
380	C₂×C₁₃	—	8	4	no	—
381	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
382	C₂×C₁₃	#3584	1	2	yes	—
383	C₂⁴	—	2	2	no	—
384	#41	—	2	4	no	—
385	#41	—	2	4	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	4	no	—
388	C₂×Q₈	—	2	4	no	—
389	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
390	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
391	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	8	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	2	4	no	—
397	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
398	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	8	no	—
403	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
404	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
405	Q₁₆	—	2	2	no	—
406	Q₁₆	—	4	4	no	—
407	Q₁₆	—	4	4	no	—
408	SD₁₆	—	2	8	no	—
409	SD₁₆	—	2	8	no	—
410	SD₁₆	—	2	4	no	—
411	SD₁₆	—	4	4	no	—
412	SD₁₆	—	4	4	no	—
413	D₈	—	2	2	no	—
414	D₈	—	4	4	no	—
415	D₈	—	4	4	no	—
416	M₁₆	—	2	4	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	C₁₃×#41	1	4	yes	—
419	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
420	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
421	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
422	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	8	no	—
425	C₄⋊C₄	—	2	8	no	—
426	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
427	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
428	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
429	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	8	no	—
432	C₂²⋊C₄	—	2	8	no	—
433	C₂²⋊C₄	—	2	8	no	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₂²⋊C₄	—	2	8	no	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
438	C₄²	—	2	4	no	—
439	C₄²	—	2	2	no	—
440	C₄²	—	2	8	no	—
441	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
442	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
443	C₄²	C₂⁴×C₁₃	1	2	yes	—
444	C₄²	C₂⁴×C₁₃	1	4	yes	—
445	C₁₃	#61412	1	1	yes	characteristic, direct product factor, Sylow
446	C₂³	—	2	4	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	4	4	no	—
449	C₂³	—	8	4	no	—
450	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
451	Q₈	—	2	4	no	—
452	Q₈	—	2	2	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	2	4	no	—
455	Q₈	—	4	4	no	—
456	Q₈	—	4	4	no	—
457	D₄	—	2	2	no	—
458	D₄	—	2	4	no	—
459	D₄	—	2	4	no	—
460	D₄	—	2	2	no	—
461	D₄	—	4	4	no	—
462	D₄	—	4	4	no	—
463	D₄	—	8	8	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	4	no	—
469	C₂×C₄	—	4	4	no	—
470	C₂×C₄	—	8	4	no	—
471	C₂×C₄	—	8	8	no	—
472	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
474	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
475	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
476	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
477	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
478	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
479	C₈	—	2	2	no	—
480	C₈	—	2	4	no	—
481	C₈	C₂×C₁₃×#41	1	2	yes	—
482	C₈	C₂×C₁₃×#41	1	2	yes	—
483	C₂²	—	2	2	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	4	8	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	16	4	no	—
489	C₂²	C₁₃×#550	1	2	yes	—
490	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
491	C₄	—	2	2	no	—
492	C₄	—	2	2	no	—
493	C₄	—	2	8	no	—
494	C₄	—	4	4	no	—
495	C₄	—	4	2	no	—
496	C₄	—	4	4	no	—
497	C₄	C₁₃×#550	1	2	yes	—
498	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
499	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
500	C₂	—	2	2	no	—
501	C₂	—	8	4	no	—
502	C₂	—	8	2	no	—
503	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
504	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3510	C₂	semidirect
2. C₁₃×#3403	C₂	semidirect
3. C₁₃×#3402	C₂	semidirect
4. C₁₃×#3394	C₂	semidirect
5. C₁₃×#3154	C₂	semidirect
6. C₂×C₁₃×#495	C₂	semidirect
7. C₁₃×#3044	C₂	semidirect
8. C₁₃×#3041	C₂	semidirect
9. C₁₃×#3040	C₂	semidirect
10. C₁₃×#2960	C₂	semidirect
11. C₁₃×#2949	C₂	semidirect
12. C₄×C₁₃×#135	C₂	semidirect
19. C₁₃×#559	C₂²	semidirect
20. C₁₃×#556	C₂²	semidirect
31. C₁₃×#497	C₂²	semidirect
32. C₁₃×#496	C₂²	semidirect
35. C₁₃×#495	C₂²	semidirect
36. C₁₃×#492	C₂²	semidirect
37. C₁₃×#464	C₂²	semidirect
38. C₁₃×#464	C₂²	semidirect
40. C₁₃×#463	C₂²	semidirect
41. C₁₃×#462	C₂²	semidirect
43. C₁₃×#446	C₂²	semidirect
44. C₈×Q₈×C₁₃	C₂²	semidirect
45. C₁₃×#440	C₂²	semidirect
46. C₄×C₁₃×Q₁₆	C₂²	semidirect
47. C₄×C₁₃×SD₁₆	C₂²	semidirect
48. C₄×C₁₃×SD₁₆	C₂²	semidirect
49. C₄×C₁₃×D₈	C₂²	semidirect
131. #61412	C₁₃	direct (N × H)
194. #3510	C₂×C₁₃	semidirect
195. #3403	C₂×C₁₃	semidirect
196. #3402	C₂×C₁₃	semidirect
197. #3394	C₂×C₁₃	semidirect
198. #3154	C₂×C₁₃	semidirect
199. C₂×#495	C₂×C₁₃	semidirect
200. #3044	C₂×C₁₃	semidirect
201. #3041	C₂×C₁₃	semidirect
202. #3040	C₂×C₁₃	semidirect
203. #2960	C₂×C₁₃	semidirect
204. #2949	C₂×C₁₃	semidirect
205. C₄×#135	C₂×C₁₃	semidirect
249. #559	C₂²×C₁₃	semidirect
250. #556	C₂²×C₁₃	semidirect
261. #497	C₂²×C₁₃	semidirect
262. #496	C₂²×C₁₃	semidirect
265. #495	C₂²×C₁₃	semidirect
266. #492	C₂²×C₁₃	semidirect
267. #464	C₂²×C₁₃	semidirect
268. #464	C₂²×C₁₃	semidirect
270. #463	C₂²×C₁₃	semidirect
271. #462	C₂²×C₁₃	semidirect
273. #446	C₂²×C₁₃	semidirect
274. C₈×Q₈	C₂²×C₁₃	semidirect
275. #440	C₂²×C₁₃	semidirect
276. C₄×Q₁₆	C₂²×C₁₃	semidirect
277. C₄×SD₁₆	C₂²×C₁₃	semidirect
278. C₄×SD₁₆	C₂²×C₁₃	semidirect
279. C₄×D₈	C₂²×C₁₃	semidirect
445. C₁₃	#61412	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×#3510	2
C₁₃×#3403	2
C₁₃×#3402	2
C₁₃×#3394	2
C₁₃×#3154	2
C₂×C₁₃×#495	2
C₁₃×#3044	2
C₁₃×#3041	2
C₁₃×#3040	2
C₁₃×#2960	2
C₁₃×#2949	2
C₄×C₁₃×#135	2
#61412	13

Subgroups — C13×#61412 #15747751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#61412 #15747751