Subgroups — C₁₃×#60818 #15747157

Order 3328.

2138 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3509	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3498	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#3222	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3210	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3208	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3138	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3043	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3009	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×H(5,𝔽₂)	C₂²	1	2	yes	—
14	C₂×C₁₃×#137	C₂²	1	4	yes	complemented
15	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
16	C₁₃×#557	—	2	2	no	—
17	C₁₃×#556	—	2	2	no	—
18	C₁₃×#552	—	2	4	no	—
19	C₁₃×#550	—	2	2	no	—
20	D₄²×C₁₃	—	2	4	no	—
21	D₄²×C₁₃	—	2	2	no	—
22	C₁₃×#541	C₂²	1	4	yes	complemented
23	C₁₃×#536	C₂²	1	2	yes	—
24	C₁₃×#535	C₂²	1	2	yes	—
25	C₁₃×#535	C₂²	1	4	yes	—
26	C₁₃×#533	C₂²	1	4	yes	complemented
27	C₁₃×#533	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#532	C₂²	1	1	yes	characteristic
29	C₁₃×#532	C₂²	1	2	yes	—
30	C₂×C₁₃×C₄⋊Q₈	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×#519	C₂²	1	2	yes	complemented
34	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
35	C₁₃×#497	C₂²	1	4	yes	complemented
36	C₁₃×#494	C₂²	1	2	yes	complemented
37	C₁₃×#492	C₂²	1	4	yes	complemented
38	C₁₃×#492	C₂²	1	4	yes	complemented
39	C₁₃×#492	C₂²	1	2	yes	complemented
40	C₁₃×#490	C₂²	1	4	yes	complemented
41	C₁₃×#488	C₂²	1	4	yes	complemented
42	C₁₃×#487	C₂²	1	2	yes	complemented
43	C₁₃×#486	C₂²	1	2	yes	complemented
44	C₁₃×#486	C₂²	1	4	yes	complemented
45	C₁₃×#464	C₂²	1	16	yes	complemented
46	C₁₃×#460	C₂²	1	16	yes	complemented
47	C₁₃×#452	C₂²	1	16	yes	complemented
48	C₁₃×#450	C₂²	1	16	yes	complemented
49	C₁₃×#433	C₂²	1	4	yes	complemented
50	C₁₃×#431	C₂²	1	4	yes	complemented
51	C₁₃×#424	C₂²	1	2	yes	complemented
52	C₁₃×#418	C₂²	1	4	yes	complemented
53	C₁₃×#416	C₂²	1	4	yes	complemented
54	C₁₃×#408	C₂²	1	2	yes	—
55	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
57	C₁₃×H(5,𝔽₂)	—	4	8	no	—
58	C₂×C₁₃×#41	—	2	2	no	—
59	C₂×C₁₃×#41	C₂³	1	2	yes	—
60	C₂×C₁₃×#41	C₂³	1	4	yes	—
61	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
63	C₂²×D₄×C₁₃	—	2	4	no	—
64	C₂²×D₄×C₁₃	—	2	2	no	—
65	C₂²×D₄×C₁₃	—	2	2	no	—
66	C₂²×D₄×C₁₃	—	2	4	no	—
67	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
69	C₁₃×#137	—	4	8	no	—
70	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
71	C₂×C₁₃×SD₁₆	—	4	8	no	—
72	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
73	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
74	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
75	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
76	C₁₃×C₄⋊Q₈	—	2	2	no	—
77	C₁₃×C₄⋊Q₈	—	2	2	no	—
78	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
80	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
81	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
82	C₁₃×#127	—	2	4	no	—
83	C₁₃×#127	—	2	2	no	—
84	C₁₃×#127	C₂³	1	4	yes	—
85	C₁₃×#127	C₂³	1	1	yes	characteristic
86	C₁₃×#127	C₂³	1	2	yes	—
87	C₁₃×#127	C₂³	1	2	yes	—
88	C₁₃×#126	—	2	8	no	—
89	C₁₃×#125	—	2	8	no	—
90	C₁₃×#125	—	2	4	no	—
91	C₁₃×#125	C₂³	1	2	yes	—
92	C₁₃×#124	—	2	2	no	—
93	C₁₃×#124	C₂³	1	4	yes	—
94	C₁₃×#124	C₂³	1	2	yes	—
95	C₁₃×#123	—	2	4	no	—
96	C₁₃×C₂²⋊Q₈	—	2	2	no	—
97	C₁₃×C₂²⋊Q₈	—	2	4	no	—
98	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	—
99	C₁₃×#121	—	2	2	no	—
100	C₁₃×#121	—	2	4	no	—
101	C₁₃×#121	—	2	4	no	—
102	C₁₃×#121	—	2	8	no	—
103	C₁₃×#120	—	2	4	no	—
104	C₁₃×#120	—	2	8	no	—
105	C₄×Q₈×C₁₃	—	2	4	no	—
106	C₄×Q₈×C₁₃	—	2	4	no	—
107	C₄×Q₈×C₁₃	—	2	2	no	—
108	C₄×Q₈×C₁₃	D₄	1	2	yes	—
109	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
110	C₄×D₄×C₁₃	—	2	4	no	—
111	C₄×D₄×C₁₃	—	2	2	no	—
112	C₄×D₄×C₁₃	D₄	1	4	yes	—
113	C₄×D₄×C₁₃	D₄	1	2	yes	—
114	C₁₃×#117	—	2	4	no	—
115	C₁₃×#117	—	2	4	no	—
116	C₁₃×#117	C₂³	1	2	yes	—
117	C₁₃×#117	C₂³	1	1	yes	characteristic
118	C₁₃×#117	C₂³	1	2	yes	—
119	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
122	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
123	C₁₃×#103	C₂³	1	8	yes	—
124	C₁₃×#102	C₂³	1	8	yes	—
125	C₁₃×#102	C₂³	1	16	yes	—
126	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
127	C₁₃×#97	C₂³	1	2	yes	—
128	C₄×C₈×C₁₃	C₂³	1	2	yes	—
129	C₄×C₈×C₁₃	C₂³	1	2	yes	—
130	C₄×C₈×C₁₃	C₂³	1	2	yes	—
131	#60818	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂⁴×C₁₃	—	2	4	no	—
133	C₂⁴×C₁₃	—	2	2	no	—
134	C₁₃×#41	—	2	4	no	—
135	C₁₃×#41	—	2	8	no	—
136	C₁₃×#41	—	4	8	no	—
137	C₁₃×#41	—	4	8	no	—
138	C₂×Q₈×C₁₃	—	2	2	no	—
139	C₂×Q₈×C₁₃	—	2	2	no	—
140	C₂×Q₈×C₁₃	—	2	8	no	—
141	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
143	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
144	C₂×D₄×C₁₃	—	2	4	no	—
145	C₂×D₄×C₁₃	—	2	2	no	—
146	C₂×D₄×C₁₃	—	2	4	no	—
147	C₂×D₄×C₁₃	—	2	2	no	—
148	C₂×D₄×C₁₃	—	2	4	no	—
149	C₂×D₄×C₁₃	—	2	2	no	—
150	C₂×D₄×C₁₃	—	2	8	no	—
151	C₂×D₄×C₁₃	—	2	4	no	—
152	C₂×D₄×C₁₃	—	2	8	no	—
153	C₂×D₄×C₁₃	—	4	8	no	—
154	C₂×D₄×C₁₃	—	4	16	no	—
155	C₂×D₄×C₁₃	—	4	8	no	—
156	C₂×D₄×C₁₃	—	8	4	no	—
157	C₂×D₄×C₁₃	—	8	8	no	—
158	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
159	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
161	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	2	2	no	—
165	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
169	C₁₃×Q₁₆	—	4	8	no	—
170	C₁₃×SD₁₆	—	4	16	no	—
171	C₁₃×SD₁₆	—	4	8	no	—
172	C₁₃×M₁₆	—	2	4	no	—
173	C₂×C₈×C₁₃	—	2	4	no	—
174	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
175	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
176	C₁₃×C₄⋊C₄	—	2	4	no	—
177	C₁₃×C₄⋊C₄	—	2	4	no	—
178	C₁₃×C₄⋊C₄	—	2	2	no	—
179	C₁₃×C₄⋊C₄	—	2	8	no	—
180	C₁₃×C₄⋊C₄	—	2	2	no	—
181	C₁₃×C₄⋊C₄	—	2	4	no	—
182	C₁₃×C₄⋊C₄	—	2	8	no	—
183	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
184	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
185	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
186	C₁₃×C₂²⋊C₄	—	2	2	no	—
187	C₁₃×C₂²⋊C₄	—	2	8	no	—
188	C₁₃×C₂²⋊C₄	—	2	8	no	—
189	C₁₃×C₂²⋊C₄	—	2	4	no	—
190	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
191	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
192	C₄²×C₁₃	—	2	8	no	—
193	C₄²×C₁₃	—	2	2	no	—
194	C₄²×C₁₃	C₂×D₄	1	4	yes	—
195	C₄²×C₁₃	C₂×D₄	1	2	yes	—
196	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
197	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
198	C₄²×C₁₃	C₂⁴	1	2	yes	—
199	#3509	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#3498	C₂×C₁₃	1	1	yes	characteristic
201	#3222	C₂×C₁₃	1	8	yes	complemented
202	#3210	C₂×C₁₃	1	4	yes	complemented
203	#3208	C₂×C₁₃	1	4	yes	complemented
204	#3152	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₂×#492	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#3138	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#3131	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#3043	C₂×C₁₃	1	4	yes	complemented
209	#3009	C₂×C₁₃	1	4	yes	complemented
210	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
211	C₂³×C₁₃	—	2	4	no	—
212	C₂³×C₁₃	—	2	2	no	—
213	C₂³×C₁₃	—	4	8	no	—
214	C₂³×C₁₃	—	4	4	no	—
215	C₂³×C₁₃	—	8	4	no	—
216	C₂³×C₁₃	—	8	8	no	—
217	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
218	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
219	Q₈×C₁₃	—	2	2	no	—
220	Q₈×C₁₃	—	2	8	no	—
221	Q₈×C₁₃	—	2	4	no	—
222	Q₈×C₁₃	—	4	4	no	—
223	Q₈×C₁₃	—	4	4	no	—
224	D₄×C₁₃	—	2	4	no	—
225	D₄×C₁₃	—	2	2	no	—
226	D₄×C₁₃	—	2	8	no	—
227	D₄×C₁₃	—	2	4	no	—
228	D₄×C₁₃	—	4	8	no	—
229	D₄×C₁₃	—	4	8	no	—
230	D₄×C₁₃	—	4	4	no	—
231	D₄×C₁₃	—	4	4	no	—
232	D₄×C₁₃	—	4	8	no	—
233	D₄×C₁₃	—	4	4	no	—
234	D₄×C₁₃	—	8	8	no	—
235	D₄×C₁₃	—	8	4	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	8	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	4	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	4	8	no	—
243	C₂×C₄×C₁₃	—	4	4	no	—
244	C₂×C₄×C₁₃	—	4	4	no	—
245	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
246	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
251	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
252	C₈×C₁₃	—	2	4	no	—
253	C₈×C₁₃	—	2	4	no	—
254	C₂×H(5,𝔽₂)	C₂²×C₁₃	1	2	yes	—
255	C₂×#137	C₂²×C₁₃	1	4	yes	complemented
256	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
257	#557	—	2	2	no	—
258	#556	—	2	2	no	—
259	#552	—	2	4	no	—
260	#550	—	2	2	no	—
261	D₄²	—	2	4	no	—
262	D₄²	—	2	2	no	—
263	#541	C₂²×C₁₃	1	4	yes	complemented
264	#536	C₂²×C₁₃	1	2	yes	—
265	#535	C₂²×C₁₃	1	4	yes	—
266	#535	C₂²×C₁₃	1	2	yes	—
267	#533	C₂²×C₁₃	1	4	yes	complemented
268	#533	C₂²×C₁₃	1	1	yes	characteristic, complemented
269	#532	C₂²×C₁₃	1	1	yes	characteristic
270	#532	C₂²×C₁₃	1	2	yes	—
271	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
272	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×#127	C₂²×C₁₃	1	2	yes	—
274	#519	C₂²×C₁₃	1	2	yes	complemented
275	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
276	#497	C₂²×C₁₃	1	4	yes	complemented
277	#494	C₂²×C₁₃	1	2	yes	complemented
278	#492	C₂²×C₁₃	1	4	yes	complemented
279	#492	C₂²×C₁₃	1	4	yes	complemented
280	#492	C₂²×C₁₃	1	2	yes	complemented
281	#490	C₂²×C₁₃	1	4	yes	complemented
282	#488	C₂²×C₁₃	1	4	yes	complemented
283	#487	C₂²×C₁₃	1	2	yes	complemented
284	#486	C₂²×C₁₃	1	2	yes	complemented
285	#486	C₂²×C₁₃	1	4	yes	complemented
286	#464	C₂²×C₁₃	1	16	yes	complemented
287	#460	C₂²×C₁₃	1	16	yes	complemented
288	#452	C₂²×C₁₃	1	16	yes	complemented
289	#450	C₂²×C₁₃	1	16	yes	complemented
290	#433	C₂²×C₁₃	1	4	yes	complemented
291	#431	C₂²×C₁₃	1	4	yes	complemented
292	#424	C₂²×C₁₃	1	2	yes	complemented
293	#418	C₂²×C₁₃	1	4	yes	complemented
294	#416	C₂²×C₁₃	1	4	yes	complemented
295	#408	C₂²×C₁₃	1	2	yes	—
296	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic, complemented
297	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
298	C₂²×C₁₃	—	2	2	no	—
299	C₂²×C₁₃	—	2	2	no	—
300	C₂²×C₁₃	—	2	4	no	—
301	C₂²×C₁₃	—	4	4	no	—
302	C₂²×C₁₃	—	4	2	no	—
303	C₂²×C₁₃	—	4	8	no	—
304	C₂²×C₁₃	—	4	4	no	—
305	C₂²×C₁₃	—	16	4	no	—
306	C₂²×C₁₃	—	16	8	no	—
307	C₂²×C₁₃	#535	1	2	yes	—
308	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
309	C₄×C₁₃	—	2	2	no	—
310	C₄×C₁₃	—	2	4	no	—
311	C₄×C₁₃	—	2	2	no	—
312	C₄×C₁₃	—	4	2	no	—
313	C₄×C₁₃	—	4	4	no	—
314	C₄×C₁₃	—	4	4	no	—
315	C₄×C₁₃	#535	1	2	yes	—
316	C₄×C₁₃	#577	1	4	yes	—
317	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
318	H(5,𝔽₂)	—	4	8	no	—
319	C₂×#41	—	2	2	no	—
320	C₂×#41	C₂³×C₁₃	1	2	yes	—
321	C₂×#41	C₂³×C₁₃	1	4	yes	—
322	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
323	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
324	C₂²×D₄	—	2	4	no	—
325	C₂²×D₄	—	2	2	no	—
326	C₂²×D₄	—	2	2	no	—
327	C₂²×D₄	—	2	4	no	—
328	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
329	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
330	#137	—	4	8	no	—
331	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
332	C₂×SD₁₆	—	4	8	no	—
333	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
334	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
335	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
336	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
337	C₄⋊Q₈	—	2	2	no	—
338	C₄⋊Q₈	—	2	2	no	—
339	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
340	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
341	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
342	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
343	#127	—	2	4	no	—
344	#127	—	2	2	no	—
345	#127	C₂³×C₁₃	1	2	yes	—
346	#127	C₂³×C₁₃	1	1	yes	characteristic
347	#127	C₂³×C₁₃	1	4	yes	—
348	#127	C₂³×C₁₃	1	2	yes	—
349	#126	—	2	8	no	—
350	#125	—	2	8	no	—
351	#125	—	2	4	no	—
352	#125	C₂³×C₁₃	1	2	yes	—
353	#124	—	2	2	no	—
354	#124	C₂³×C₁₃	1	4	yes	—
355	#124	C₂³×C₁₃	1	2	yes	—
356	#123	—	2	4	no	—
357	C₂²⋊Q₈	—	2	2	no	—
358	C₂²⋊Q₈	—	2	4	no	—
359	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	—
360	#121	—	2	2	no	—
361	#121	—	2	4	no	—
362	#121	—	2	4	no	—
363	#121	—	2	8	no	—
364	#120	—	2	4	no	—
365	#120	—	2	8	no	—
366	C₄×Q₈	—	2	4	no	—
367	C₄×Q₈	—	2	4	no	—
368	C₄×Q₈	—	2	2	no	—
369	C₄×Q₈	D₄×C₁₃	1	2	yes	—
370	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
371	C₄×D₄	—	2	4	no	—
372	C₄×D₄	—	2	2	no	—
373	C₄×D₄	D₄×C₁₃	1	4	yes	—
374	C₄×D₄	D₄×C₁₃	1	2	yes	—
375	#117	—	2	4	no	—
376	#117	—	2	4	no	—
377	#117	C₂³×C₁₃	1	2	yes	—
378	#117	C₂³×C₁₃	1	1	yes	characteristic
379	#117	C₂³×C₁₃	1	2	yes	—
380	C₂×C₄⋊C₄	—	2	2	no	—
381	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
383	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
384	#103	C₂³×C₁₃	1	8	yes	—
385	#102	C₂³×C₁₃	1	8	yes	—
386	#102	C₂³×C₁₃	1	16	yes	—
387	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
388	#97	C₂³×C₁₃	1	2	yes	—
389	C₄×C₈	C₂³×C₁₃	1	2	yes	—
390	C₄×C₈	C₂³×C₁₃	1	2	yes	—
391	C₄×C₈	C₂³×C₁₃	1	2	yes	—
392	C₂×C₁₃	—	2	2	no	—
393	C₂×C₁₃	—	4	2	no	—
394	C₂×C₁₃	—	8	4	no	—
395	C₂×C₁₃	—	8	2	no	—
396	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
397	C₂×C₁₃	C₂×#577	1	2	yes	—
398	C₂⁴	—	2	4	no	—
399	C₂⁴	—	2	2	no	—
400	#41	—	2	4	no	—
401	#41	—	2	8	no	—
402	#41	—	4	8	no	—
403	#41	—	4	8	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	8	no	—
407	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
408	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
409	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	4	no	—
418	C₂×D₄	—	2	8	no	—
419	C₂×D₄	—	4	8	no	—
420	C₂×D₄	—	4	16	no	—
421	C₂×D₄	—	4	8	no	—
422	C₂×D₄	—	8	4	no	—
423	C₂×D₄	—	8	8	no	—
424	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
425	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
426	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
427	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
432	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
433	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
434	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
435	Q₁₆	—	4	8	no	—
436	SD₁₆	—	4	16	no	—
437	SD₁₆	—	4	8	no	—
438	M₁₆	—	2	4	no	—
439	C₂×C₈	—	2	4	no	—
440	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
441	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	8	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	8	no	—
449	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
450	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
451	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	8	no	—
454	C₂²⋊C₄	—	2	8	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
457	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
458	C₄²	—	2	8	no	—
459	C₄²	—	2	2	no	—
460	C₄²	C₂×D₄×C₁₃	1	4	yes	—
461	C₄²	C₂×D₄×C₁₃	1	2	yes	—
462	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
463	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
464	C₄²	C₂⁴×C₁₃	1	2	yes	—
465	C₁₃	#60818	1	1	yes	characteristic, direct product factor, Sylow
466	C₂³	—	2	4	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	4	8	no	—
469	C₂³	—	4	4	no	—
470	C₂³	—	8	4	no	—
471	C₂³	—	8	8	no	—
472	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
473	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
474	Q₈	—	2	2	no	—
475	Q₈	—	2	8	no	—
476	Q₈	—	2	4	no	—
477	Q₈	—	4	4	no	—
478	Q₈	—	4	4	no	—
479	D₄	—	2	4	no	—
480	D₄	—	2	2	no	—
481	D₄	—	2	8	no	—
482	D₄	—	2	4	no	—
483	D₄	—	4	8	no	—
484	D₄	—	4	8	no	—
485	D₄	—	4	4	no	—
486	D₄	—	4	4	no	—
487	D₄	—	4	8	no	—
488	D₄	—	4	4	no	—
489	D₄	—	8	8	no	—
490	D₄	—	8	4	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	8	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	4	8	no	—
498	C₂×C₄	—	4	4	no	—
499	C₂×C₄	—	4	4	no	—
500	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
501	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
502	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
503	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
504	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
505	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
506	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
507	C₈	—	2	4	no	—
508	C₈	—	2	4	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	4	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	4	8	no	—
513	C₂²	—	4	4	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	16	4	no	—
517	C₂²	—	16	8	no	—
518	C₂²	C₁₃×#535	1	2	yes	—
519	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
520	C₄	—	2	4	no	—
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	4	4	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	4	no	—
526	C₄	C₁₃×#535	1	2	yes	—
527	C₄	C₁₃×#577	1	4	yes	—
528	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
529	C₂	—	2	2	no	—
530	C₂	—	4	2	no	—
531	C₂	—	8	4	no	—
532	C₂	—	8	2	no	—
533	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
534	C₂	C₂×C₁₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₁₃×#3498	C₂
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×#3509	C₂	semidirect
3. C₁₃×#3222	C₂	semidirect
4. C₁₃×#3210	C₂	semidirect
5. C₁₃×#3208	C₂	semidirect
6. C₁₃×#3152	C₂	semidirect
7. C₂×C₁₃×#492	C₂	semidirect
8. C₁₃×#3138	C₂	semidirect
9. C₁₃×#3131	C₂	semidirect
10. C₁₃×#3043	C₂	semidirect
11. C₁₃×#3009	C₂	semidirect
12. C₁₃×#2922	C₂	semidirect
14. C₂×C₁₃×#137	C₂²	semidirect
15. C₂²×C₁₃×SD₁₆	C₂²	semidirect
22. C₁₃×#541	C₂²	semidirect
26. C₁₃×#533	C₂²	semidirect
27. C₁₃×#533	C₂²	semidirect
30. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
33. C₁₃×#519	C₂²	semidirect
35. C₁₃×#497	C₂²	semidirect
36. C₁₃×#494	C₂²	semidirect
37. C₁₃×#492	C₂²	semidirect
38. C₁₃×#492	C₂²	semidirect
39. C₁₃×#492	C₂²	semidirect
40. C₁₃×#490	C₂²	semidirect
41. C₁₃×#488	C₂²	semidirect
42. C₁₃×#487	C₂²	semidirect
43. C₁₃×#486	C₂²	semidirect
44. C₁₃×#486	C₂²	semidirect
45. C₁₃×#464	C₂²	semidirect
46. C₁₃×#460	C₂²	semidirect
47. C₁₃×#452	C₂²	semidirect
48. C₁₃×#450	C₂²	semidirect
49. C₁₃×#433	C₂²	semidirect
50. C₁₃×#431	C₂²	semidirect
51. C₁₃×#424	C₂²	semidirect
52. C₁₃×#418	C₂²	semidirect
53. C₁₃×#416	C₂²	semidirect
55. C₄×C₁₃×M₁₆	C₂²	semidirect
56. C₂×C₄×C₈×C₁₃	C₂²	semidirect
131. #60818	C₁₃	direct (N × H)
199. #3509	C₂×C₁₃	semidirect
201. #3222	C₂×C₁₃	semidirect
202. #3210	C₂×C₁₃	semidirect
203. #3208	C₂×C₁₃	semidirect
204. #3152	C₂×C₁₃	semidirect
205. C₂×#492	C₂×C₁₃	semidirect
206. #3138	C₂×C₁₃	semidirect
207. #3131	C₂×C₁₃	semidirect
208. #3043	C₂×C₁₃	semidirect
209. #3009	C₂×C₁₃	semidirect
210. #2922	C₂×C₁₃	semidirect
255. C₂×#137	C₂²×C₁₃	semidirect
256. C₂²×SD₁₆	C₂²×C₁₃	semidirect
263. #541	C₂²×C₁₃	semidirect
267. #533	C₂²×C₁₃	semidirect
268. #533	C₂²×C₁₃	semidirect
271. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
274. #519	C₂²×C₁₃	semidirect
276. #497	C₂²×C₁₃	semidirect
277. #494	C₂²×C₁₃	semidirect
278. #492	C₂²×C₁₃	semidirect
279. #492	C₂²×C₁₃	semidirect
280. #492	C₂²×C₁₃	semidirect
281. #490	C₂²×C₁₃	semidirect
282. #488	C₂²×C₁₃	semidirect
283. #487	C₂²×C₁₃	semidirect
284. #486	C₂²×C₁₃	semidirect
285. #486	C₂²×C₁₃	semidirect
286. #464	C₂²×C₁₃	semidirect
287. #460	C₂²×C₁₃	semidirect
288. #452	C₂²×C₁₃	semidirect
289. #450	C₂²×C₁₃	semidirect
290. #433	C₂²×C₁₃	semidirect
291. #431	C₂²×C₁₃	semidirect
292. #424	C₂²×C₁₃	semidirect
293. #418	C₂²×C₁₃	semidirect
294. #416	C₂²×C₁₃	semidirect
296. C₄×M₁₆	C₂²×C₁₃	semidirect
297. C₂×C₄×C₈	C₂²×C₁₃	semidirect
465. C₁₃	#60818	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×#3509	2
C₁₃×#3498	2
C₁₃×#3222	2
C₁₃×#3210	2
C₁₃×#3208	2
C₁₃×#3152	2
C₂×C₁₃×#492	2
C₁₃×#3138	2
C₁₃×#3131	2
C₁₃×#3043	2
C₁₃×#3009	2
C₁₃×#2922	2
#60818	13

Subgroups — C13×#60818 #15747157

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60818 #15747157