Subgroups — C₁₃×#60830 #15747169

Order 3328.

2150 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3222	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3220	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3219	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3217	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3150	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3142	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#490	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3045	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3012	C₂	1	4	yes	maximal, complemented
13	C₁₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
15	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
16	C₂×C₁₃×#135	C₂²	1	4	yes	complemented
17	C₁₃×#553	—	2	4	no	—
18	C₁₃×#553	—	2	2	no	—
19	C₁₃×#552	—	2	2	no	—
20	C₁₃×#550	—	2	2	no	—
21	D₄²×C₁₃	—	2	4	no	—
22	D₄²×C₁₃	—	2	2	no	—
23	C₁₃×#541	C₂²	1	2	yes	complemented
24	C₁₃×#540	C₂²	1	2	yes	complemented
25	C₁₃×#537	C₂²	1	2	yes	—
26	C₁₃×#535	C₂²	1	2	yes	—
27	C₁₃×#535	C₂²	1	4	yes	—
28	C₁₃×#532	C₂²	1	1	yes	characteristic
29	C₁₃×#532	C₂²	1	2	yes	—
30	C₁₃×#532	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#127	C₂²	1	2	yes	—
33	C₁₃×#529	C₂²	1	4	yes	complemented
34	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#520	C₂²	1	2	yes	complemented
36	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
37	C₁₃×#497	C₂²	1	2	yes	complemented
38	C₁₃×#497	C₂²	1	2	yes	complemented
39	C₁₃×#496	C₂²	1	2	yes	complemented
40	C₁₃×#496	C₂²	1	2	yes	complemented
41	C₁₃×#496	C₂²	1	4	yes	complemented
42	C₁₃×#493	C₂²	1	2	yes	complemented
43	C₁₃×#492	C₂²	1	2	yes	complemented
44	C₁₃×#491	C₂²	1	2	yes	complemented
45	C₁₃×#490	C₂²	1	4	yes	complemented
46	C₁₃×#490	C₂²	1	4	yes	complemented
47	C₁₃×#490	C₂²	1	2	yes	complemented
48	C₁₃×#488	C₂²	1	4	yes	complemented
49	C₁₃×#464	C₂²	1	8	yes	complemented
50	C₁₃×#463	C₂²	1	8	yes	complemented
51	C₁₃×#460	C₂²	1	8	yes	complemented
52	C₁₃×#459	C₂²	1	8	yes	complemented
53	C₁₃×#452	C₂²	1	8	yes	complemented
54	C₁₃×#450	C₂²	1	8	yes	complemented
55	C₁₃×#449	C₂²	1	8	yes	complemented
56	C₁₃×#447	C₂²	1	8	yes	complemented
57	C₁₃×#433	C₂²	1	4	yes	complemented
58	C₁₃×#432	C₂²	1	4	yes	complemented
59	C₁₃×#424	C₂²	1	2	yes	complemented
60	C₁₃×#417	C₂²	1	4	yes	complemented
61	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
62	C₁₃×#408	C₂²	1	2	yes	—
63	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
65	C₁₃×H(5,𝔽₂)	—	4	8	no	—
66	C₂×C₁₃×#41	—	2	2	no	—
67	C₂×C₁₃×#41	C₂³	1	2	yes	—
68	C₂×C₁₃×#41	C₂³	1	2	yes	—
69	C₂×C₁₃×#41	C₂³	1	4	yes	—
70	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₁₃	—	2	4	no	—
72	C₂²×D₄×C₁₃	—	2	2	no	—
73	C₂²×D₄×C₁₃	—	2	2	no	—
74	C₂²×D₄×C₁₃	—	2	4	no	—
75	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
76	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
77	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
78	C₁₃×#135	—	4	8	no	—
79	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
80	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
81	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
82	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
83	C₂×C₁₃×D₈	C₂³	1	4	yes	—
84	C₂×C₁₃×D₈	C₂³	1	8	yes	—
85	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
86	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
87	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₁₃×#127	—	2	4	no	—
90	C₁₃×#127	—	2	2	no	—
91	C₁₃×#127	C₂³	1	4	yes	—
92	C₁₃×#127	C₂³	1	2	yes	—
93	C₁₃×#127	C₂³	1	2	yes	—
94	C₁₃×#127	C₂³	1	1	yes	characteristic
95	C₁₃×#127	C₂³	1	1	yes	characteristic
96	C₁₃×#126	—	2	4	no	—
97	C₁₃×#126	—	2	4	no	—
98	C₁₃×#125	—	2	4	no	—
99	C₁₃×#125	—	2	2	no	—
100	C₁₃×#125	C₂³	1	2	yes	—
101	C₁₃×#125	C₂³	1	2	yes	—
102	C₁₃×#124	C₂³	1	4	yes	—
103	C₁₃×#124	C₂³	1	2	yes	—
104	C₁₃×#124	C₂³	1	2	yes	—
105	C₁₃×#123	—	2	4	no	—
106	C₁₃×#123	—	2	4	no	—
107	C₁₃×C₂²⋊Q₈	—	2	2	no	—
108	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
109	C₁₃×#121	—	2	2	no	—
110	C₁₃×#121	—	2	4	no	—
111	C₁₃×#121	—	2	2	no	—
112	C₁₃×#121	—	2	4	no	—
113	C₁₃×#121	—	2	2	no	—
114	C₁₃×#121	—	2	4	no	—
115	C₁₃×#121	—	2	8	no	—
116	C₁₃×#121	—	2	4	no	—
117	C₁₃×#121	C₂³	1	4	yes	—
118	C₁₃×#120	—	2	4	no	—
119	C₁₃×#120	—	2	8	no	—
120	C₄×Q₈×C₁₃	D₄	1	2	yes	—
121	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
122	C₄×D₄×C₁₃	—	2	4	no	—
123	C₄×D₄×C₁₃	—	2	4	no	—
124	C₄×D₄×C₁₃	—	2	4	no	—
125	C₄×D₄×C₁₃	—	2	2	no	—
126	C₄×D₄×C₁₃	—	2	2	no	—
127	C₄×D₄×C₁₃	D₄	1	4	yes	—
128	C₄×D₄×C₁₃	D₄	1	2	yes	—
129	C₄×D₄×C₁₃	C₂³	1	4	yes	—
130	C₁₃×#117	—	2	2	no	—
131	C₁₃×#117	—	2	4	no	—
132	C₁₃×#117	C₂³	1	1	yes	characteristic
133	C₁₃×#117	C₂³	1	2	yes	—
134	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
139	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
140	C₁₃×#103	C₂³	1	8	yes	—
141	C₁₃×#102	C₂³	1	8	yes	—
142	C₁₃×#102	C₂³	1	8	yes	—
143	C₁₃×#102	C₂³	1	8	yes	—
144	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
145	C₁₃×#97	C₂³	1	2	yes	—
146	C₁₃×#97	C₂³	1	2	yes	—
147	C₁₃×#97	C₂³	1	2	yes	—
148	C₄×C₈×C₁₃	C₂³	1	2	yes	—
149	#60830	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₂⁴×C₁₃	—	2	4	no	—
151	C₂⁴×C₁₃	—	2	2	no	—
152	C₁₃×#41	—	2	4	no	—
153	C₁₃×#41	—	2	8	no	—
154	C₁₃×#41	—	2	8	no	—
155	C₁₃×#41	—	4	8	no	—
156	C₁₃×#41	—	4	8	no	—
157	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
159	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
160	C₂×D₄×C₁₃	—	2	2	no	—
161	C₂×D₄×C₁₃	—	2	4	no	—
162	C₂×D₄×C₁₃	—	2	2	no	—
163	C₂×D₄×C₁₃	—	2	4	no	—
164	C₂×D₄×C₁₃	—	2	4	no	—
165	C₂×D₄×C₁₃	—	2	2	no	—
166	C₂×D₄×C₁₃	—	2	4	no	—
167	C₂×D₄×C₁₃	—	2	2	no	—
168	C₂×D₄×C₁₃	—	2	2	no	—
169	C₂×D₄×C₁₃	—	2	8	no	—
170	C₂×D₄×C₁₃	—	2	4	no	—
171	C₂×D₄×C₁₃	—	2	8	no	—
172	C₂×D₄×C₁₃	—	4	8	no	—
173	C₂×D₄×C₁₃	—	4	16	no	—
174	C₂×D₄×C₁₃	—	4	8	no	—
175	C₂×D₄×C₁₃	—	8	8	no	—
176	C₂×D₄×C₁₃	—	8	4	no	—
177	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
178	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
179	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
180	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
181	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₁₃	—	2	2	no	—
183	C₂²×C₄×C₁₃	—	2	2	no	—
184	C₂²×C₄×C₁₃	—	2	4	no	—
185	C₂²×C₄×C₁₃	—	2	2	no	—
186	C₂²×C₄×C₁₃	—	2	4	no	—
187	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₁₃×Q₁₆	—	4	4	no	—
192	C₁₃×SD₁₆	—	4	4	no	—
193	C₁₃×SD₁₆	—	4	4	no	—
194	C₁₃×SD₁₆	—	4	8	no	—
195	C₁₃×D₈	—	4	4	no	—
196	C₁₃×D₈	—	4	8	no	—
197	C₁₃×M₁₆	—	2	4	no	—
198	C₂×C₈×C₁₃	—	2	4	no	—
199	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
200	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
201	C₁₃×C₄⋊C₄	—	2	2	no	—
202	C₁₃×C₄⋊C₄	—	2	4	no	—
203	C₁₃×C₄⋊C₄	—	2	4	no	—
204	C₁₃×C₄⋊C₄	—	2	4	no	—
205	C₁₃×C₄⋊C₄	—	2	4	no	—
206	C₁₃×C₄⋊C₄	—	2	2	no	—
207	C₁₃×C₄⋊C₄	—	2	2	no	—
208	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
209	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
210	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
211	C₁₃×C₂²⋊C₄	—	2	4	no	—
212	C₁₃×C₂²⋊C₄	—	2	2	no	—
213	C₁₃×C₂²⋊C₄	—	2	4	no	—
214	C₁₃×C₂²⋊C₄	—	2	4	no	—
215	C₁₃×C₂²⋊C₄	—	2	2	no	—
216	C₁₃×C₂²⋊C₄	—	2	8	no	—
217	C₁₃×C₂²⋊C₄	—	2	4	no	—
218	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
219	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
220	C₄²×C₁₃	—	2	4	no	—
221	C₄²×C₁₃	C₂×D₄	1	4	yes	—
222	C₄²×C₁₃	C₂×D₄	1	2	yes	—
223	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₄²×C₁₃	C₂⁴	1	2	yes	—
226	#3512	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#3498	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#3222	C₂×C₁₃	1	4	yes	complemented
229	#3220	C₂×C₁₃	1	4	yes	complemented
230	#3219	C₂×C₁₃	1	4	yes	complemented
231	#3217	C₂×C₁₃	1	4	yes	complemented
232	#3151	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#3150	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#3142	C₂×C₁₃	1	1	yes	characteristic, complemented
235	C₂×#490	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#3045	C₂×C₁₃	1	4	yes	complemented
237	#3012	C₂×C₁₃	1	4	yes	complemented
238	#2923	C₂×C₁₃	1	1	yes	characteristic, complemented
239	C₂³×C₁₃	—	2	2	no	—
240	C₂³×C₁₃	—	2	4	no	—
241	C₂³×C₁₃	—	2	2	no	—
242	C₂³×C₁₃	—	4	8	no	—
243	C₂³×C₁₃	—	4	4	no	—
244	C₂³×C₁₃	—	8	4	no	—
245	C₂³×C₁₃	—	8	8	no	—
246	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
247	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
248	Q₈×C₁₃	—	2	2	no	—
249	Q₈×C₁₃	—	2	4	no	—
250	Q₈×C₁₃	—	2	4	no	—
251	D₄×C₁₃	—	2	4	no	—
252	D₄×C₁₃	—	2	2	no	—
253	D₄×C₁₃	—	2	4	no	—
254	D₄×C₁₃	—	2	8	no	—
255	D₄×C₁₃	—	2	4	no	—
256	D₄×C₁₃	—	4	8	no	—
257	D₄×C₁₃	—	4	8	no	—
258	D₄×C₁₃	—	4	4	no	—
259	D₄×C₁₃	—	4	8	no	—
260	D₄×C₁₃	—	4	4	no	—
261	D₄×C₁₃	—	4	4	no	—
262	D₄×C₁₃	—	4	4	no	—
263	D₄×C₁₃	—	8	2	no	—
264	D₄×C₁₃	—	8	8	no	—
265	D₄×C₁₃	—	8	4	no	—
266	D₄×C₁₃	—	8	4	no	—
267	C₂×C₄×C₁₃	—	2	4	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	4	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	4	4	no	—
272	C₂×C₄×C₁₃	—	4	2	no	—
273	C₂×C₄×C₁₃	—	4	8	no	—
274	C₂×C₄×C₁₃	—	4	4	no	—
275	C₂×C₄×C₁₃	—	4	4	no	—
276	C₂×C₄×C₁₃	—	8	4	no	—
277	C₂×C₄×C₁₃	—	8	2	no	—
278	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
279	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
280	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
281	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
282	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
283	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
284	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
285	C₈×C₁₃	—	2	4	no	—
286	C₈×C₁₃	—	2	4	no	—
287	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
288	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	complemented
289	C₂×#135	C₂²×C₁₃	1	4	yes	complemented
290	#553	—	2	4	no	—
291	#553	—	2	2	no	—
292	#552	—	2	2	no	—
293	#550	—	2	2	no	—
294	D₄²	—	2	4	no	—
295	D₄²	—	2	2	no	—
296	#541	C₂²×C₁₃	1	2	yes	complemented
297	#540	C₂²×C₁₃	1	2	yes	complemented
298	#537	C₂²×C₁₃	1	2	yes	—
299	#535	C₂²×C₁₃	1	4	yes	—
300	#535	C₂²×C₁₃	1	2	yes	—
301	#532	C₂²×C₁₃	1	1	yes	characteristic
302	#532	C₂²×C₁₃	1	2	yes	—
303	#532	C₂²×C₁₃	1	1	yes	characteristic, complemented
304	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×#127	C₂²×C₁₃	1	2	yes	—
306	#529	C₂²×C₁₃	1	4	yes	complemented
307	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic, complemented
308	#520	C₂²×C₁₃	1	2	yes	complemented
309	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
310	#497	C₂²×C₁₃	1	2	yes	complemented
311	#497	C₂²×C₁₃	1	2	yes	complemented
312	#496	C₂²×C₁₃	1	2	yes	complemented
313	#496	C₂²×C₁₃	1	2	yes	complemented
314	#496	C₂²×C₁₃	1	4	yes	complemented
315	#493	C₂²×C₁₃	1	2	yes	complemented
316	#492	C₂²×C₁₃	1	2	yes	complemented
317	#491	C₂²×C₁₃	1	2	yes	complemented
318	#490	C₂²×C₁₃	1	4	yes	complemented
319	#490	C₂²×C₁₃	1	4	yes	complemented
320	#490	C₂²×C₁₃	1	2	yes	complemented
321	#488	C₂²×C₁₃	1	4	yes	complemented
322	#464	C₂²×C₁₃	1	8	yes	complemented
323	#463	C₂²×C₁₃	1	8	yes	complemented
324	#460	C₂²×C₁₃	1	8	yes	complemented
325	#459	C₂²×C₁₃	1	8	yes	complemented
326	#452	C₂²×C₁₃	1	8	yes	complemented
327	#450	C₂²×C₁₃	1	8	yes	complemented
328	#449	C₂²×C₁₃	1	8	yes	complemented
329	#447	C₂²×C₁₃	1	8	yes	complemented
330	#433	C₂²×C₁₃	1	4	yes	complemented
331	#432	C₂²×C₁₃	1	4	yes	complemented
332	#424	C₂²×C₁₃	1	2	yes	complemented
333	#417	C₂²×C₁₃	1	4	yes	complemented
334	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
335	#408	C₂²×C₁₃	1	2	yes	—
336	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
337	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic, complemented
338	C₂²×C₁₃	—	2	2	no	—
339	C₂²×C₁₃	—	2	4	no	—
340	C₂²×C₁₃	—	2	2	no	—
341	C₂²×C₁₃	—	4	2	no	—
342	C₂²×C₁₃	—	4	8	no	—
343	C₂²×C₁₃	—	4	4	no	—
344	C₂²×C₁₃	—	4	2	no	—
345	C₂²×C₁₃	—	4	4	no	—
346	C₂²×C₁₃	—	4	2	no	—
347	C₂²×C₁₃	—	4	2	no	—
348	C₂²×C₁₃	—	16	4	no	—
349	C₂²×C₁₃	—	16	8	no	—
350	C₂²×C₁₃	#535	1	2	yes	—
351	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
352	C₄×C₁₃	—	2	2	no	—
353	C₄×C₁₃	—	2	4	no	—
354	C₄×C₁₃	—	2	2	no	—
355	C₄×C₁₃	—	2	2	no	—
356	C₄×C₁₃	—	4	4	no	—
357	C₄×C₁₃	—	4	2	no	—
358	C₄×C₁₃	—	4	2	no	—
359	C₄×C₁₃	#535	1	2	yes	—
360	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
361	H(5,𝔽₂)	—	4	8	no	—
362	C₂×#41	—	2	2	no	—
363	C₂×#41	C₂³×C₁₃	1	2	yes	—
364	C₂×#41	C₂³×C₁₃	1	2	yes	—
365	C₂×#41	C₂³×C₁₃	1	4	yes	—
366	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
367	C₂²×D₄	—	2	4	no	—
368	C₂²×D₄	—	2	2	no	—
369	C₂²×D₄	—	2	2	no	—
370	C₂²×D₄	—	2	4	no	—
371	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
372	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
373	AGL(1,ℤ/8)	—	4	8	no	—
374	#135	—	4	8	no	—
375	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
376	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
377	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
378	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
379	C₂×D₈	C₂³×C₁₃	1	4	yes	—
380	C₂×D₈	C₂³×C₁₃	1	8	yes	—
381	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
382	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
383	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
384	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
385	#127	—	2	4	no	—
386	#127	—	2	2	no	—
387	#127	C₂³×C₁₃	1	2	yes	—
388	#127	C₂³×C₁₃	1	1	yes	characteristic
389	#127	C₂³×C₁₃	1	4	yes	—
390	#127	C₂³×C₁₃	1	2	yes	—
391	#127	C₂³×C₁₃	1	1	yes	characteristic
392	#126	—	2	4	no	—
393	#126	—	2	4	no	—
394	#125	—	2	4	no	—
395	#125	—	2	2	no	—
396	#125	C₂³×C₁₃	1	2	yes	—
397	#125	C₂³×C₁₃	1	2	yes	—
398	#124	C₂³×C₁₃	1	2	yes	—
399	#124	C₂³×C₁₃	1	4	yes	—
400	#124	C₂³×C₁₃	1	2	yes	—
401	#123	—	2	4	no	—
402	#123	—	2	4	no	—
403	C₂²⋊Q₈	—	2	2	no	—
404	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
405	#121	—	2	2	no	—
406	#121	—	2	4	no	—
407	#121	—	2	2	no	—
408	#121	—	2	4	no	—
409	#121	—	2	2	no	—
410	#121	—	2	4	no	—
411	#121	—	2	8	no	—
412	#121	—	2	4	no	—
413	#121	C₂³×C₁₃	1	4	yes	—
414	#120	—	2	4	no	—
415	#120	—	2	8	no	—
416	C₄×Q₈	D₄×C₁₃	1	2	yes	—
417	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
418	C₄×D₄	—	2	4	no	—
419	C₄×D₄	—	2	4	no	—
420	C₄×D₄	—	2	4	no	—
421	C₄×D₄	—	2	2	no	—
422	C₄×D₄	—	2	2	no	—
423	C₄×D₄	D₄×C₁₃	1	4	yes	—
424	C₄×D₄	D₄×C₁₃	1	2	yes	—
425	C₄×D₄	C₂³×C₁₃	1	4	yes	—
426	#117	—	2	2	no	—
427	#117	—	2	4	no	—
428	#117	C₂³×C₁₃	1	1	yes	characteristic
429	#117	C₂³×C₁₃	1	2	yes	—
430	C₂×C₄⋊C₄	—	2	2	no	—
431	C₂×C₄⋊C₄	—	2	2	no	—
432	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
433	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
434	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
435	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
436	#103	C₂³×C₁₃	1	8	yes	—
437	#102	C₂³×C₁₃	1	8	yes	—
438	#102	C₂³×C₁₃	1	8	yes	—
439	#102	C₂³×C₁₃	1	8	yes	—
440	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
441	#97	C₂³×C₁₃	1	2	yes	—
442	#97	C₂³×C₁₃	1	2	yes	—
443	#97	C₂³×C₁₃	1	2	yes	—
444	C₄×C₈	C₂³×C₁₃	1	2	yes	—
445	C₂×C₁₃	—	2	2	no	—
446	C₂×C₁₃	—	4	2	no	—
447	C₂×C₁₃	—	8	2	no	—
448	C₂×C₁₃	—	8	4	no	—
449	C₂×C₁₃	—	8	2	no	—
450	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
451	C₂×C₁₃	#3585	1	2	yes	—
452	C₂⁴	—	2	4	no	—
453	C₂⁴	—	2	2	no	—
454	#41	—	2	4	no	—
455	#41	—	2	8	no	—
456	#41	—	2	8	no	—
457	#41	—	4	8	no	—
458	#41	—	4	8	no	—
459	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
460	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
461	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	4	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	4	no	—
466	C₂×D₄	—	2	4	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	4	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	8	no	—
472	C₂×D₄	—	2	4	no	—
473	C₂×D₄	—	2	8	no	—
474	C₂×D₄	—	4	8	no	—
475	C₂×D₄	—	4	16	no	—
476	C₂×D₄	—	4	8	no	—
477	C₂×D₄	—	8	8	no	—
478	C₂×D₄	—	8	4	no	—
479	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
480	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
481	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
482	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
483	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
490	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
491	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
492	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
493	Q₁₆	—	4	4	no	—
494	SD₁₆	—	4	4	no	—
495	SD₁₆	—	4	4	no	—
496	SD₁₆	—	4	8	no	—
497	D₈	—	4	4	no	—
498	D₈	—	4	8	no	—
499	M₁₆	—	2	4	no	—
500	C₂×C₈	—	2	4	no	—
501	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
502	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	4	no	—
506	C₄⋊C₄	—	2	4	no	—
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
511	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
512	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
513	C₂²⋊C₄	—	2	4	no	—
514	C₂²⋊C₄	—	2	2	no	—
515	C₂²⋊C₄	—	2	4	no	—
516	C₂²⋊C₄	—	2	4	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	8	no	—
519	C₂²⋊C₄	—	2	4	no	—
520	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
521	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
522	C₄²	—	2	4	no	—
523	C₄²	C₂×D₄×C₁₃	1	4	yes	—
524	C₄²	C₂×D₄×C₁₃	1	2	yes	—
525	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
526	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
527	C₄²	C₂⁴×C₁₃	1	2	yes	—
528	C₁₃	#60830	1	1	yes	characteristic, direct product factor, Sylow
529	C₂³	—	2	2	no	—
530	C₂³	—	2	4	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	4	8	no	—
533	C₂³	—	4	4	no	—
534	C₂³	—	8	4	no	—
535	C₂³	—	8	8	no	—
536	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
537	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
538	Q₈	—	2	2	no	—
539	Q₈	—	2	4	no	—
540	Q₈	—	2	4	no	—
541	D₄	—	2	4	no	—
542	D₄	—	2	2	no	—
543	D₄	—	2	4	no	—
544	D₄	—	2	8	no	—
545	D₄	—	2	4	no	—
546	D₄	—	4	8	no	—
547	D₄	—	4	8	no	—
548	D₄	—	4	4	no	—
549	D₄	—	4	8	no	—
550	D₄	—	4	4	no	—
551	D₄	—	4	4	no	—
552	D₄	—	4	4	no	—
553	D₄	—	8	8	no	—
554	D₄	—	8	4	no	—
555	D₄	—	8	2	no	—
556	D₄	—	8	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	8	no	—
564	C₂×C₄	—	4	4	no	—
565	C₂×C₄	—	4	4	no	—
566	C₂×C₄	—	8	4	no	—
567	C₂×C₄	—	8	2	no	—
568	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
569	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
570	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
571	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
572	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
573	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
574	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
575	C₈	—	2	4	no	—
576	C₈	—	2	4	no	—
577	C₂²	—	2	2	no	—
578	C₂²	—	2	4	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	8	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	4	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	16	4	no	—
588	C₂²	—	16	8	no	—
589	C₂²	C₁₃×#535	1	2	yes	—
590	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
591	C₄	—	2	2	no	—
592	C₄	—	2	4	no	—
593	C₄	—	2	2	no	—
594	C₄	—	2	2	no	—
595	C₄	—	4	4	no	—
596	C₄	—	4	2	no	—
597	C₄	—	4	2	no	—
598	C₄	C₁₃×#535	1	2	yes	—
599	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
600	C₂	—	2	2	no	—
601	C₂	—	4	2	no	—
602	C₂	—	8	4	no	—
603	C₂	—	8	2	no	—
604	C₂	—	8	2	no	—
605	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
606	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 ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3512	C₂	semidirect
2. C₁₃×#3498	C₂	semidirect
3. C₁₃×#3222	C₂	semidirect
4. C₁₃×#3220	C₂	semidirect
5. C₁₃×#3219	C₂	semidirect
6. C₁₃×#3217	C₂	semidirect
7. C₁₃×#3151	C₂	semidirect
8. C₁₃×#3150	C₂	semidirect
9. C₁₃×#3142	C₂	semidirect
10. C₂×C₁₃×#490	C₂	semidirect
11. C₁₃×#3045	C₂	semidirect
12. C₁₃×#3012	C₂	semidirect
13. C₁₃×#2923	C₂	semidirect
15. C₂×C₁₃×AGL(1,ℤ/8)	C₂²	semidirect
16. C₂×C₁₃×#135	C₂²	semidirect
23. C₁₃×#541	C₂²	semidirect
24. C₁₃×#540	C₂²	semidirect
30. C₁₃×#532	C₂²	semidirect
33. C₁₃×#529	C₂²	semidirect
34. C₂×C₁₃×#125	C₂²	semidirect
35. C₁₃×#520	C₂²	semidirect
37. C₁₃×#497	C₂²	semidirect
38. C₁₃×#497	C₂²	semidirect
39. C₁₃×#496	C₂²	semidirect
40. C₁₃×#496	C₂²	semidirect
41. C₁₃×#496	C₂²	semidirect
42. C₁₃×#493	C₂²	semidirect
43. C₁₃×#492	C₂²	semidirect
44. C₁₃×#491	C₂²	semidirect
45. C₁₃×#490	C₂²	semidirect
46. C₁₃×#490	C₂²	semidirect
47. C₁₃×#490	C₂²	semidirect
48. C₁₃×#488	C₂²	semidirect
49. C₁₃×#464	C₂²	semidirect
50. C₁₃×#463	C₂²	semidirect
51. C₁₃×#460	C₂²	semidirect
52. C₁₃×#459	C₂²	semidirect
53. C₁₃×#452	C₂²	semidirect
54. C₁₃×#450	C₂²	semidirect
55. C₁₃×#449	C₂²	semidirect
56. C₁₃×#447	C₂²	semidirect
57. C₁₃×#433	C₂²	semidirect
58. C₁₃×#432	C₂²	semidirect
59. C₁₃×#424	C₂²	semidirect
60. C₁₃×#417	C₂²	semidirect
61. C₂×C₁₃×#102	C₂²	semidirect
63. C₄×C₁₃×M₁₆	C₂²	semidirect
64. C₂×C₁₃×#97	C₂²	semidirect
149. #60830	C₁₃	direct (N × H)
226. #3512	C₂×C₁₃	semidirect
227. #3498	C₂×C₁₃	semidirect
228. #3222	C₂×C₁₃	semidirect
229. #3220	C₂×C₁₃	semidirect
230. #3219	C₂×C₁₃	semidirect
231. #3217	C₂×C₁₃	semidirect
232. #3151	C₂×C₁₃	semidirect
233. #3150	C₂×C₁₃	semidirect
234. #3142	C₂×C₁₃	semidirect
235. C₂×#490	C₂×C₁₃	semidirect
236. #3045	C₂×C₁₃	semidirect
237. #3012	C₂×C₁₃	semidirect
238. #2923	C₂×C₁₃	semidirect
288. C₂×AGL(1,ℤ/8)	C₂²×C₁₃	semidirect
289. C₂×#135	C₂²×C₁₃	semidirect
296. #541	C₂²×C₁₃	semidirect
297. #540	C₂²×C₁₃	semidirect
303. #532	C₂²×C₁₃	semidirect
306. #529	C₂²×C₁₃	semidirect
307. C₂×#125	C₂²×C₁₃	semidirect
308. #520	C₂²×C₁₃	semidirect
310. #497	C₂²×C₁₃	semidirect
311. #497	C₂²×C₁₃	semidirect
312. #496	C₂²×C₁₃	semidirect
313. #496	C₂²×C₁₃	semidirect
314. #496	C₂²×C₁₃	semidirect
315. #493	C₂²×C₁₃	semidirect
316. #492	C₂²×C₁₃	semidirect
317. #491	C₂²×C₁₃	semidirect
318. #490	C₂²×C₁₃	semidirect
319. #490	C₂²×C₁₃	semidirect
320. #490	C₂²×C₁₃	semidirect
321. #488	C₂²×C₁₃	semidirect
322. #464	C₂²×C₁₃	semidirect
323. #463	C₂²×C₁₃	semidirect
324. #460	C₂²×C₁₃	semidirect
325. #459	C₂²×C₁₃	semidirect
326. #452	C₂²×C₁₃	semidirect
327. #450	C₂²×C₁₃	semidirect
328. #449	C₂²×C₁₃	semidirect
329. #447	C₂²×C₁₃	semidirect
330. #433	C₂²×C₁₃	semidirect
331. #432	C₂²×C₁₃	semidirect
332. #424	C₂²×C₁₃	semidirect
333. #417	C₂²×C₁₃	semidirect
334. C₂×#102	C₂²×C₁₃	semidirect
336. C₄×M₁₆	C₂²×C₁₃	semidirect
337. C₂×#97	C₂²×C₁₃	semidirect
528. C₁₃	#60830	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×#3512	2
C₁₃×#3498	2
C₁₃×#3222	2
C₁₃×#3220	2
C₁₃×#3219	2
C₁₃×#3217	2
C₁₃×#3151	2
C₁₃×#3150	2
C₁₃×#3142	2
C₂×C₁₃×#490	2
C₁₃×#3045	2
C₁₃×#3012	2
C₁₃×#2923	2
#60830	13

Subgroups — C13×#60830 #15747169

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60830 #15747169