Subgroups — C₁₃×#60801 #15747140

Order 3328.

2186 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3219	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3210	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3207	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3040	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3005	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	—
14	C₂×C₁₃×#137	C₂²	1	4	yes	—
15	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	—
16	C₁₃×#533	C₂²	1	1	yes	characteristic
17	C₁₃×#533	C₂²	1	2	yes	complemented
18	C₁₃×#532	—	2	2	no	—
19	C₁₃×#532	—	2	2	no	—
20	C₁₃×#532	C₂²	1	1	yes	characteristic
21	C₁₃×#532	C₂²	1	4	yes	—
22	C₁₃×#532	C₂²	1	4	yes	—
23	C₁₃×#532	C₂²	1	2	yes	complemented
24	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
26	C₁₃×#529	—	2	2	no	—
27	C₁₃×#529	—	2	2	no	—
28	C₁₃×#529	C₂²	1	4	yes	complemented
29	C₂×C₁₃×#124	C₂²	1	2	yes	—
30	C₁₃×#525	—	2	2	no	—
31	C₁₃×#525	C₂²	1	2	yes	—
32	C₂×C₁₃×#121	—	2	2	no	—
33	C₄×C₁₃×#41	—	2	2	no	—
34	C₄×C₁₃×#41	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₃	—	2	2	no	—
36	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#497	C₂²	1	4	yes	complemented
38	C₁₃×#496	C₂²	1	4	yes	complemented
39	C₁₃×#494	C₂²	1	2	yes	complemented
40	C₁₃×#493	C₂²	1	2	yes	complemented
41	C₁₃×#492	C₂²	1	2	yes	complemented
42	C₁₃×#492	C₂²	1	2	yes	complemented
43	C₁₃×#491	C₂²	1	4	yes	complemented
44	C₁₃×#490	C₂²	1	4	yes	complemented
45	C₁₃×#487	C₂²	1	4	yes	complemented
46	C₁₃×#486	C₂²	1	4	yes	complemented
47	C₁₃×#464	C₂²	1	16	yes	complemented
48	C₁₃×#463	C₂²	1	16	yes	complemented
49	C₁₃×#452	C₂²	1	16	yes	complemented
50	C₁₃×#449	C₂²	1	16	yes	complemented
51	C₁₃×#432	C₂²	1	4	yes	complemented
52	C₁₃×#431	C₂²	1	4	yes	complemented
53	C₁₃×#423	C₂²	1	2	yes	—
54	C₁₃×#419	C₂²	1	4	yes	—
55	C₁₃×#418	C₂²	1	4	yes	—
56	C₁₃×#407	C₂²	1	2	yes	—
57	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
58	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
59	C₂×C₁₃×#41	—	2	2	no	—
60	C₂×C₁₃×#41	—	2	4	no	—
61	C₂×C₁₃×#41	—	4	8	no	—
62	C₂×C₁₃×#41	C₂³	1	2	yes	—
63	C₂×C₁₃×#41	C₂³	1	8	yes	—
64	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
65	C₂²×D₄×C₁₃	—	2	2	no	—
66	C₂²×D₄×C₁₃	—	2	2	no	—
67	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₃	—	2	2	no	—
69	C₂³×C₄×C₁₃	D₄	1	2	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#137	—	4	8	no	—
72	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
73	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
74	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
75	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
76	C₂×C₁₃×D₈	C₂³	1	8	yes	—
77	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
78	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
79	C₁₃×C₄⋊Q₈	—	2	2	no	—
80	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
81	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
82	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
84	C₁₃×#127	—	2	2	no	—
85	C₁₃×#127	C₂³	1	2	yes	—
86	C₁₃×#127	C₂³	1	2	yes	—
87	C₁₃×#127	C₂³	1	1	yes	characteristic
88	C₁₃×#126	—	2	4	no	—
89	C₁₃×#125	—	2	2	no	—
90	C₁₃×#125	C₂³	1	2	yes	—
91	C₁₃×#124	—	2	2	no	—
92	C₁₃×#124	—	2	2	no	—
93	C₁₃×#124	—	2	2	no	—
94	C₁₃×#124	C₂³	1	8	yes	—
95	C₁₃×#124	C₂³	1	2	yes	—
96	C₁₃×#123	—	2	4	no	—
97	C₁₃×#123	—	2	2	no	—
98	C₁₃×C₂²⋊Q₈	—	2	2	no	—
99	C₁₃×C₂²⋊Q₈	—	2	2	no	—
100	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
101	C₁₃×#121	—	2	4	no	—
102	C₁₃×#121	—	2	4	no	—
103	C₁₃×#121	—	2	4	no	—
104	C₁₃×#121	—	2	4	no	—
105	C₁₃×#121	—	2	2	no	—
106	C₁₃×#121	—	2	2	no	—
107	C₁₃×#121	C₂³	1	4	yes	—
108	C₁₃×#120	—	2	2	no	—
109	C₄×Q₈×C₁₃	—	2	2	no	—
110	C₄×Q₈×C₁₃	—	2	2	no	—
111	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
112	C₄×D₄×C₁₃	—	2	4	no	—
113	C₄×D₄×C₁₃	—	2	4	no	—
114	C₄×D₄×C₁₃	—	2	4	no	—
115	C₄×D₄×C₁₃	—	2	4	no	—
116	C₄×D₄×C₁₃	—	2	4	no	—
117	C₄×D₄×C₁₃	—	2	4	no	—
118	C₄×D₄×C₁₃	—	2	4	no	—
119	C₄×D₄×C₁₃	—	2	2	no	—
120	C₄×D₄×C₁₃	—	2	2	no	—
121	C₄×D₄×C₁₃	C₂³	1	4	yes	—
122	C₁₃×#117	—	2	2	no	—
123	C₁₃×#117	—	2	4	no	—
124	C₁₃×#117	—	2	2	no	—
125	C₁₃×#117	C₂³	1	2	yes	—
126	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
128	C₂×C₄²×C₁₃	—	2	2	no	—
129	C₂×C₄²×C₁₃	D₄	1	2	yes	—
130	C₂×C₄²×C₁₃	D₄	1	2	yes	—
131	C₂×C₄²×C₁₃	D₄	1	2	yes	—
132	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
135	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
136	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
137	C₁₃×#103	C₂³	1	16	yes	—
138	C₁₃×#102	C₂³	1	16	yes	—
139	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
140	C₁₃×#97	C₂³	1	2	yes	—
141	C₁₃×#97	C₂³	1	2	yes	—
142	C₄×C₈×C₁₃	C₂³	1	2	yes	—
143	C₄×C₈×C₁₃	C₂³	1	2	yes	—
144	#60801	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂⁴×C₁₃	—	2	2	no	—
146	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₁₃×#41	—	2	8	no	—
148	C₁₃×#41	—	4	16	no	—
149	C₁₃×#41	—	4	8	no	—
150	C₁₃×#41	—	4	16	no	—
151	C₂×Q₈×C₁₃	—	2	2	no	—
152	C₂×Q₈×C₁₃	—	2	2	no	—
153	C₂×Q₈×C₁₃	—	2	8	no	—
154	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
155	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
156	C₂×D₄×C₁₃	—	2	2	no	—
157	C₂×D₄×C₁₃	—	2	4	no	—
158	C₂×D₄×C₁₃	—	2	8	no	—
159	C₂×D₄×C₁₃	—	2	2	no	—
160	C₂×D₄×C₁₃	—	2	4	no	—
161	C₂×D₄×C₁₃	—	2	4	no	—
162	C₂×D₄×C₁₃	—	2	2	no	—
163	C₂×D₄×C₁₃	—	2	8	no	—
164	C₂×D₄×C₁₃	—	4	8	no	—
165	C₂×D₄×C₁₃	—	4	8	no	—
166	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
167	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₃	—	2	4	no	—
169	C₂²×C₄×C₁₃	—	2	2	no	—
170	C₂²×C₄×C₁₃	—	2	2	no	—
171	C₂²×C₄×C₁₃	—	2	4	no	—
172	C₂²×C₄×C₁₃	—	2	8	no	—
173	C₂²×C₄×C₁₃	—	4	4	no	—
174	C₂²×C₄×C₁₃	—	4	8	no	—
175	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
178	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
179	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
181	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
182	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
185	C₁₃×Q₁₆	—	4	8	no	—
186	C₁₃×SD₁₆	—	4	8	no	—
187	C₁₃×SD₁₆	—	4	8	no	—
188	C₁₃×D₈	—	4	8	no	—
189	C₁₃×M₁₆	—	2	4	no	—
190	C₁₃×M₁₆	—	2	4	no	—
191	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
192	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
193	C₁₃×C₄⋊C₄	—	2	4	no	—
194	C₁₃×C₄⋊C₄	—	2	4	no	—
195	C₁₃×C₄⋊C₄	—	2	2	no	—
196	C₁₃×C₄⋊C₄	—	2	2	no	—
197	C₁₃×C₄⋊C₄	—	2	4	no	—
198	C₁₃×C₄⋊C₄	—	2	4	no	—
199	C₁₃×C₄⋊C₄	—	2	4	no	—
200	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
201	C₁₃×C₂²⋊C₄	—	2	4	no	—
202	C₁₃×C₂²⋊C₄	—	2	2	no	—
203	C₁₃×C₂²⋊C₄	—	2	8	no	—
204	C₁₃×C₂²⋊C₄	—	2	8	no	—
205	C₁₃×C₂²⋊C₄	—	2	4	no	—
206	C₁₃×C₂²⋊C₄	—	2	4	no	—
207	C₁₃×C₂²⋊C₄	—	2	4	no	—
208	C₄²×C₁₃	—	2	4	no	—
209	C₄²×C₁₃	—	2	2	no	—
210	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₁₃	C₂×D₄	1	2	yes	—
212	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
213	C₄²×C₁₃	C₂×D₄	1	2	yes	—
214	C₄²×C₁₃	C₂×D₄	1	2	yes	—
215	C₄²×C₁₃	C₂×D₄	1	2	yes	—
216	C₄²×C₁₃	C₂×D₄	1	2	yes	—
217	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
218	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
219	C₄²×C₁₃	C₂⁴	1	2	yes	—
220	#3444	C₂×C₁₃	1	1	yes	characteristic, complemented
221	C₂×#532	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#3219	C₂×C₁₃	1	8	yes	complemented
223	#3210	C₂×C₁₃	1	4	yes	complemented
224	#3207	C₂×C₁₃	1	4	yes	complemented
225	#3152	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#3151	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#3139	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#3138	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#3040	C₂×C₁₃	1	4	yes	complemented
230	#3005	C₂×C₁₃	1	4	yes	complemented
231	#2920	C₂×C₁₃	1	1	yes	characteristic, complemented
232	C₂³×C₁₃	—	2	2	no	—
233	C₂³×C₁₃	—	2	2	no	—
234	C₂³×C₁₃	—	2	4	no	—
235	C₂³×C₁₃	—	4	2	no	—
236	C₂³×C₁₃	—	4	8	no	—
237	C₂³×C₁₃	—	4	4	no	—
238	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
239	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
240	Q₈×C₁₃	—	2	4	no	—
241	Q₈×C₁₃	—	2	8	no	—
242	Q₈×C₁₃	—	4	4	no	—
243	Q₈×C₁₃	—	4	4	no	—
244	D₄×C₁₃	—	2	4	no	—
245	D₄×C₁₃	—	2	8	no	—
246	D₄×C₁₃	—	4	8	no	—
247	D₄×C₁₃	—	4	16	no	—
248	D₄×C₁₃	—	4	8	no	—
249	D₄×C₁₃	—	4	4	no	—
250	D₄×C₁₃	—	4	4	no	—
251	D₄×C₁₃	—	4	8	no	—
252	D₄×C₁₃	—	4	4	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	4	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	2	4	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	4	no	—
261	C₂×C₄×C₁₃	—	2	4	no	—
262	C₂×C₄×C₁₃	—	4	2	no	—
263	C₂×C₄×C₁₃	—	4	2	no	—
264	C₂×C₄×C₁₃	—	4	2	no	—
265	C₂×C₄×C₁₃	—	4	16	no	—
266	C₂×C₄×C₁₃	—	4	8	no	—
267	C₂×C₄×C₁₃	—	4	4	no	—
268	C₂×C₄×C₁₃	—	4	4	no	—
269	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
270	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
271	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
272	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
273	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
275	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
276	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
277	C₈×C₁₃	—	2	4	no	—
278	C₈×C₁₃	—	2	4	no	—
279	C₂²×#41	C₂²×C₁₃	1	2	yes	—
280	C₂×#137	C₂²×C₁₃	1	4	yes	—
281	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	—
282	#533	C₂²×C₁₃	1	1	yes	characteristic
283	#533	C₂²×C₁₃	1	2	yes	complemented
284	#532	—	2	2	no	—
285	#532	—	2	2	no	—
286	#532	C₂²×C₁₃	1	1	yes	characteristic
287	#532	C₂²×C₁₃	1	4	yes	—
288	#532	C₂²×C₁₃	1	4	yes	—
289	#532	C₂²×C₁₃	1	2	yes	complemented
290	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
292	#529	—	2	2	no	—
293	#529	—	2	2	no	—
294	#529	C₂²×C₁₃	1	4	yes	complemented
295	C₂×#124	C₂²×C₁₃	1	2	yes	—
296	#525	—	2	2	no	—
297	#525	C₂²×C₁₃	1	2	yes	—
298	C₂×#121	—	2	2	no	—
299	C₄×#41	—	2	2	no	—
300	C₄×#41	C₂²×C₁₃	1	2	yes	—
301	C₂×C₄×D₄	—	2	2	no	—
302	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
303	#497	C₂²×C₁₃	1	4	yes	complemented
304	#496	C₂²×C₁₃	1	4	yes	complemented
305	#494	C₂²×C₁₃	1	2	yes	complemented
306	#493	C₂²×C₁₃	1	2	yes	complemented
307	#492	C₂²×C₁₃	1	2	yes	complemented
308	#492	C₂²×C₁₃	1	2	yes	complemented
309	#491	C₂²×C₁₃	1	4	yes	complemented
310	#490	C₂²×C₁₃	1	4	yes	complemented
311	#487	C₂²×C₁₃	1	4	yes	complemented
312	#486	C₂²×C₁₃	1	4	yes	complemented
313	#464	C₂²×C₁₃	1	16	yes	complemented
314	#463	C₂²×C₁₃	1	16	yes	complemented
315	#452	C₂²×C₁₃	1	16	yes	complemented
316	#449	C₂²×C₁₃	1	16	yes	complemented
317	#432	C₂²×C₁₃	1	4	yes	complemented
318	#431	C₂²×C₁₃	1	4	yes	complemented
319	#423	C₂²×C₁₃	1	2	yes	—
320	#419	C₂²×C₁₃	1	4	yes	—
321	#418	C₂²×C₁₃	1	4	yes	—
322	#407	C₂²×C₁₃	1	2	yes	—
323	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
324	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
325	C₂²×C₁₃	—	2	2	no	—
326	C₂²×C₁₃	—	2	2	no	—
327	C₂²×C₁₃	—	2	2	no	—
328	C₂²×C₁₃	—	2	2	no	—
329	C₂²×C₁₃	—	4	4	no	—
330	C₂²×C₁₃	—	4	4	no	—
331	C₂²×C₁₃	—	4	2	no	—
332	C₂²×C₁₃	—	4	4	no	—
333	C₂²×C₁₃	—	4	8	no	—
334	C₂²×C₁₃	—	8	8	no	—
335	C₂²×C₁₃	#535	1	2	yes	—
336	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	2	2	no	—
340	C₄×C₁₃	—	2	2	no	—
341	C₄×C₁₃	—	4	4	no	—
342	C₄×C₁₃	—	4	2	no	—
343	C₄×C₁₃	—	4	4	no	—
344	C₄×C₁₃	#535	1	2	yes	—
345	C₄×C₁₃	#575	1	4	yes	—
346	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
347	C₂×#41	—	2	2	no	—
348	C₂×#41	—	2	4	no	—
349	C₂×#41	—	4	8	no	—
350	C₂×#41	C₂³×C₁₃	1	2	yes	—
351	C₂×#41	C₂³×C₁₃	1	8	yes	—
352	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
353	C₂²×D₄	—	2	2	no	—
354	C₂²×D₄	—	2	2	no	—
355	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
356	C₂³×C₄	—	2	2	no	—
357	C₂³×C₄	D₄×C₁₃	1	2	yes	—
358	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
359	#137	—	4	8	no	—
360	AGL(1,ℤ/8)	—	4	8	no	—
361	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
362	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
363	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
364	C₂×D₈	C₂³×C₁₃	1	8	yes	—
365	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
366	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
367	C₄⋊Q₈	—	2	2	no	—
368	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
369	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
370	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
371	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
372	#127	—	2	2	no	—
373	#127	C₂³×C₁₃	1	2	yes	—
374	#127	C₂³×C₁₃	1	2	yes	—
375	#127	C₂³×C₁₃	1	1	yes	characteristic
376	#126	—	2	4	no	—
377	#125	—	2	2	no	—
378	#125	C₂³×C₁₃	1	2	yes	—
379	#124	—	2	2	no	—
380	#124	—	2	2	no	—
381	#124	—	2	2	no	—
382	#124	C₂³×C₁₃	1	8	yes	—
383	#124	C₂³×C₁₃	1	2	yes	—
384	#123	—	2	4	no	—
385	#123	—	2	2	no	—
386	C₂²⋊Q₈	—	2	2	no	—
387	C₂²⋊Q₈	—	2	2	no	—
388	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
389	#121	—	2	4	no	—
390	#121	—	2	4	no	—
391	#121	—	2	4	no	—
392	#121	—	2	4	no	—
393	#121	—	2	2	no	—
394	#121	—	2	2	no	—
395	#121	C₂³×C₁₃	1	4	yes	—
396	#120	—	2	2	no	—
397	C₄×Q₈	—	2	2	no	—
398	C₄×Q₈	—	2	2	no	—
399	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
400	C₄×D₄	—	2	4	no	—
401	C₄×D₄	—	2	4	no	—
402	C₄×D₄	—	2	4	no	—
403	C₄×D₄	—	2	4	no	—
404	C₄×D₄	—	2	4	no	—
405	C₄×D₄	—	2	4	no	—
406	C₄×D₄	—	2	4	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	2	no	—
409	C₄×D₄	C₂³×C₁₃	1	4	yes	—
410	#117	—	2	2	no	—
411	#117	—	2	4	no	—
412	#117	—	2	2	no	—
413	#117	C₂³×C₁₃	1	2	yes	—
414	C₂×C₄⋊C₄	—	2	2	no	—
415	C₂×C₂²⋊C₄	—	2	4	no	—
416	C₂×C₄²	—	2	2	no	—
417	C₂×C₄²	D₄×C₁₃	1	2	yes	—
418	C₂×C₄²	D₄×C₁₃	1	2	yes	—
419	C₂×C₄²	D₄×C₁₃	1	2	yes	—
420	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
421	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
422	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
424	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
425	#103	C₂³×C₁₃	1	16	yes	—
426	#102	C₂³×C₁₃	1	16	yes	—
427	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
428	#97	C₂³×C₁₃	1	2	yes	—
429	#97	C₂³×C₁₃	1	2	yes	—
430	C₄×C₈	C₂³×C₁₃	1	2	yes	—
431	C₄×C₈	C₂³×C₁₃	1	2	yes	—
432	C₂×C₁₃	—	2	2	no	—
433	C₂×C₁₃	—	4	2	no	—
434	C₂×C₁₃	—	8	2	no	—
435	C₂×C₁₃	—	8	4	no	—
436	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
437	C₂×C₁₃	C₂×#575	1	2	yes	—
438	C₂⁴	—	2	2	no	—
439	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
440	#41	—	2	8	no	—
441	#41	—	4	16	no	—
442	#41	—	4	16	no	—
443	#41	—	4	8	no	—
444	C₂×Q₈	—	2	2	no	—
445	C₂×Q₈	—	2	2	no	—
446	C₂×Q₈	—	2	8	no	—
447	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
448	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	4	no	—
451	C₂×D₄	—	2	8	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	4	no	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	8	no	—
457	C₂×D₄	—	4	8	no	—
458	C₂×D₄	—	4	8	no	—
459	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
460	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	8	no	—
466	C₂²×C₄	—	4	4	no	—
467	C₂²×C₄	—	4	8	no	—
468	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
469	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
471	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
472	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
473	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
474	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
475	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
476	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
477	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
478	Q₁₆	—	4	8	no	—
479	SD₁₆	—	4	8	no	—
480	SD₁₆	—	4	8	no	—
481	D₈	—	4	8	no	—
482	M₁₆	—	2	4	no	—
483	M₁₆	—	2	4	no	—
484	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
485	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	—	2	4	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	4	no	—
491	C₄⋊C₄	—	2	4	no	—
492	C₄⋊C₄	—	2	4	no	—
493	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	8	no	—
497	C₂²⋊C₄	—	2	8	no	—
498	C₂²⋊C₄	—	2	4	no	—
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₄²	—	2	4	no	—
502	C₄²	—	2	2	no	—
503	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
504	C₄²	C₂×D₄×C₁₃	1	2	yes	—
505	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
506	C₄²	C₂×D₄×C₁₃	1	2	yes	—
507	C₄²	C₂×D₄×C₁₃	1	2	yes	—
508	C₄²	C₂×D₄×C₁₃	1	2	yes	—
509	C₄²	C₂×D₄×C₁₃	1	2	yes	—
510	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
511	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
512	C₄²	C₂⁴×C₁₃	1	2	yes	—
513	C₁₃	#60801	1	1	yes	characteristic, direct product factor, Sylow
514	C₂³	—	2	2	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	4	2	no	—
518	C₂³	—	4	8	no	—
519	C₂³	—	4	4	no	—
520	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
521	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
522	Q₈	—	2	4	no	—
523	Q₈	—	2	8	no	—
524	Q₈	—	4	4	no	—
525	Q₈	—	4	4	no	—
526	D₄	—	2	4	no	—
527	D₄	—	2	8	no	—
528	D₄	—	4	8	no	—
529	D₄	—	4	16	no	—
530	D₄	—	4	8	no	—
531	D₄	—	4	4	no	—
532	D₄	—	4	4	no	—
533	D₄	—	4	8	no	—
534	D₄	—	4	4	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	16	no	—
548	C₂×C₄	—	4	8	no	—
549	C₂×C₄	—	4	4	no	—
550	C₂×C₄	—	4	4	no	—
551	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
552	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
553	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
554	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
555	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
556	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
557	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
558	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
559	C₈	—	2	4	no	—
560	C₈	—	2	4	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	4	8	no	—
568	C₂²	—	4	4	no	—
569	C₂²	—	4	2	no	—
570	C₂²	—	8	8	no	—
571	C₂²	C₁₃×#535	1	2	yes	—
572	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	4	4	no	—
578	C₄	—	4	4	no	—
579	C₄	—	4	2	no	—
580	C₄	C₁₃×#535	1	2	yes	—
581	C₄	C₁₃×#575	1	4	yes	—
582	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
583	C₂	—	2	2	no	—
584	C₂	—	4	2	no	—
585	C₂	—	8	4	no	—
586	C₂	—	8	2	no	—
587	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
588	C₂	C₂×C₁₃×#575	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 ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3444	C₂	semidirect
2. C₂×C₁₃×#532	C₂	semidirect
3. C₁₃×#3219	C₂	semidirect
4. C₁₃×#3210	C₂	semidirect
5. C₁₃×#3207	C₂	semidirect
6. C₁₃×#3152	C₂	semidirect
7. C₁₃×#3151	C₂	semidirect
8. C₁₃×#3139	C₂	semidirect
9. C₁₃×#3138	C₂	semidirect
10. C₁₃×#3040	C₂	semidirect
11. C₁₃×#3005	C₂	semidirect
12. C₁₃×#2920	C₂	semidirect
17. C₁₃×#533	C₂²	semidirect
23. C₁₃×#532	C₂²	semidirect
28. C₁₃×#529	C₂²	semidirect
37. C₁₃×#497	C₂²	semidirect
38. C₁₃×#496	C₂²	semidirect
39. C₁₃×#494	C₂²	semidirect
40. C₁₃×#493	C₂²	semidirect
41. C₁₃×#492	C₂²	semidirect
42. C₁₃×#492	C₂²	semidirect
43. C₁₃×#491	C₂²	semidirect
44. C₁₃×#490	C₂²	semidirect
45. C₁₃×#487	C₂²	semidirect
46. C₁₃×#486	C₂²	semidirect
47. C₁₃×#464	C₂²	semidirect
48. C₁₃×#463	C₂²	semidirect
49. C₁₃×#452	C₂²	semidirect
50. C₁₃×#449	C₂²	semidirect
51. C₁₃×#432	C₂²	semidirect
52. C₁₃×#431	C₂²	semidirect
144. #60801	C₁₃	direct (N × H)
220. #3444	C₂×C₁₃	semidirect
221. C₂×#532	C₂×C₁₃	semidirect
222. #3219	C₂×C₁₃	semidirect
223. #3210	C₂×C₁₃	semidirect
224. #3207	C₂×C₁₃	semidirect
225. #3152	C₂×C₁₃	semidirect
226. #3151	C₂×C₁₃	semidirect
227. #3139	C₂×C₁₃	semidirect
228. #3138	C₂×C₁₃	semidirect
229. #3040	C₂×C₁₃	semidirect
230. #3005	C₂×C₁₃	semidirect
231. #2920	C₂×C₁₃	semidirect
283. #533	C₂²×C₁₃	semidirect
289. #532	C₂²×C₁₃	semidirect
294. #529	C₂²×C₁₃	semidirect
303. #497	C₂²×C₁₃	semidirect
304. #496	C₂²×C₁₃	semidirect
305. #494	C₂²×C₁₃	semidirect
306. #493	C₂²×C₁₃	semidirect
307. #492	C₂²×C₁₃	semidirect
308. #492	C₂²×C₁₃	semidirect
309. #491	C₂²×C₁₃	semidirect
310. #490	C₂²×C₁₃	semidirect
311. #487	C₂²×C₁₃	semidirect
312. #486	C₂²×C₁₃	semidirect
313. #464	C₂²×C₁₃	semidirect
314. #463	C₂²×C₁₃	semidirect
315. #452	C₂²×C₁₃	semidirect
316. #449	C₂²×C₁₃	semidirect
317. #432	C₂²×C₁₃	semidirect
318. #431	C₂²×C₁₃	semidirect
513. C₁₃	#60801	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×#3444	2
C₂×C₁₃×#532	2
C₁₃×#3219	2
C₁₃×#3210	2
C₁₃×#3207	2
C₁₃×#3152	2
C₁₃×#3151	2
C₁₃×#3139	2
C₁₃×#3138	2
C₁₃×#3040	2
C₁₃×#3005	2
C₁₃×#2920	2
#60801	13

Subgroups — C13×#60801 #15747140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60801 #15747140