Subgroups — C₁₃×#60831 #15747170

Order 3328.

2014 conjugacy classes of subgroups.

The subgroup lattice has 586 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×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3223	C₂	1	4	yes	maximal, complemented
4	C₁₃×#3221	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3219	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3218	C₂	1	4	yes	maximal, complemented
7	C₁₃×#3152	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×#491	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3046	C₂	1	4	yes	maximal, complemented
12	C₁₃×#3013	C₂	1	4	yes	maximal, complemented
13	C₁₃×#2923	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
15	C₂×C₁₃×#137	C₂²	1	4	yes	—
16	C₂×C₁₃×#135	C₂²	1	4	yes	—
17	C₁₃×#553	—	2	4	no	—
18	C₁₃×#553	—	2	2	no	—
19	C₁₃×#552	—	2	2	no	—
20	D₄×Q₈×C₁₃	—	2	2	no	—
21	C₁₃×#547	—	2	4	no	—
22	C₁₃×#547	—	2	2	no	—
23	C₁₃×#541	C₂²	1	2	yes	—
24	C₁₃×#540	C₂²	1	2	yes	—
25	C₁₃×#537	C₂²	1	2	yes	—
26	C₁₃×#536	C₂²	1	2	yes	—
27	C₁₃×#536	C₂²	1	4	yes	—
28	C₁₃×#532	C₂²	1	1	yes	characteristic
29	C₁₃×#532	C₂²	1	1	yes	characteristic
30	C₁₃×#532	C₂²	1	2	yes	—
31	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
33	C₁₃×#529	C₂²	1	4	yes	—
34	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
35	C₁₃×#520	C₂²	1	2	yes	—
36	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
37	C₁₃×#497	C₂²	1	2	yes	—
38	C₁₃×#497	C₂²	1	2	yes	—
39	C₁₃×#497	C₂²	1	4	yes	—
40	C₁₃×#496	C₂²	1	2	yes	—
41	C₁₃×#496	C₂²	1	2	yes	—
42	C₁₃×#494	C₂²	1	2	yes	—
43	C₁₃×#492	C₂²	1	2	yes	—
44	C₁₃×#491	C₂²	1	4	yes	—
45	C₁₃×#491	C₂²	1	4	yes	—
46	C₁₃×#491	C₂²	1	2	yes	—
47	C₁₃×#490	C₂²	1	2	yes	—
48	C₁₃×#488	C₂²	1	4	yes	—
49	C₁₃×#464	C₂²	1	8	yes	—
50	C₁₃×#463	C₂²	1	8	yes	—
51	C₁₃×#462	C₂²	1	8	yes	—
52	C₁₃×#461	C₂²	1	8	yes	—
53	C₁₃×#452	C₂²	1	8	yes	—
54	C₁₃×#451	C₂²	1	8	yes	—
55	C₁₃×#449	C₂²	1	8	yes	—
56	C₁₃×#448	C₂²	1	8	yes	—
57	C₁₃×#433	C₂²	1	4	yes	—
58	C₁₃×#432	C₂²	1	4	yes	—
59	C₁₃×#424	C₂²	1	2	yes	—
60	C₁₃×#417	C₂²	1	4	yes	—
61	C₂×C₁₃×#103	C₂²	1	4	yes	—
62	C₁₃×#408	C₂²	1	2	yes	—
63	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
64	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
65	C₁₃×2₋¹⁺⁴	—	4	8	no	—
66	C₂×C₁₃×#41	—	2	2	no	—
67	C₂×C₁₃×#41	—	2	4	no	—
68	C₂×C₁₃×#41	C₂³	1	2	yes	—
69	C₂×C₁₃×#41	C₂³	1	2	yes	—
70	C₂×C₁₃×#41	C₂³	1	4	yes	—
71	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
72	C₂²×Q₈×C₁₃	—	2	2	no	—
73	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
74	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
75	C₁₃×#137	—	4	8	no	—
76	C₁₃×#135	—	4	8	no	—
77	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
78	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
79	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
80	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
81	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
82	C₂×C₁₃×D₈	C₂³	1	4	yes	—
83	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
84	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
85	C₁₃×C₄⋊Q₈	—	2	4	no	—
86	C₁₃×C₄⋊Q₈	—	2	2	no	—
87	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
88	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
89	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
90	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
91	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
92	C₁₃×#127	C₂³	1	1	yes	characteristic
93	C₁₃×#127	C₂³	1	1	yes	characteristic
94	C₁₃×#126	—	2	4	no	—
95	C₁₃×#126	—	2	4	no	—
96	C₁₃×#125	—	2	4	no	—
97	C₁₃×#125	—	2	2	no	—
98	C₁₃×#125	C₂³	1	2	yes	—
99	C₁₃×#125	C₂³	1	2	yes	—
100	C₁₃×#124	C₂³	1	4	yes	—
101	C₁₃×#124	C₂³	1	2	yes	—
102	C₁₃×#124	C₂³	1	2	yes	—
103	C₁₃×#123	—	2	4	no	—
104	C₁₃×#123	—	2	4	no	—
105	C₁₃×#123	—	2	4	no	—
106	C₁₃×#123	—	2	8	no	—
107	C₁₃×C₂²⋊Q₈	—	2	2	no	—
108	C₁₃×C₂²⋊Q₈	—	2	4	no	—
109	C₁₃×C₂²⋊Q₈	—	2	8	no	—
110	C₁₃×C₂²⋊Q₈	C₂³	1	4	yes	—
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	2	no	—
116	C₁₃×#121	—	2	4	no	—
117	C₁₃×#121	C₂³	1	4	yes	—
118	C₄×Q₈×C₁₃	D₄	1	2	yes	—
119	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
120	C₄×D₄×C₁₃	—	2	4	no	—
121	C₄×D₄×C₁₃	—	2	4	no	—
122	C₄×D₄×C₁₃	—	2	4	no	—
123	C₄×D₄×C₁₃	—	2	2	no	—
124	C₄×D₄×C₁₃	—	2	2	no	—
125	C₄×D₄×C₁₃	D₄	1	4	yes	—
126	C₄×D₄×C₁₃	D₄	1	2	yes	—
127	C₄×D₄×C₁₃	C₂³	1	4	yes	—
128	C₁₃×#117	—	2	2	no	—
129	C₁₃×#117	—	2	4	no	—
130	C₁₃×#117	C₂³	1	1	yes	characteristic
131	C₁₃×#117	C₂³	1	2	yes	—
132	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
133	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₂×C₁₃×C₄⋊C₄	—	2	4	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×#103	C₂³	1	8	yes	—
142	C₁₃×#103	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	#60831	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
150	C₁₃×#41	—	2	4	no	—
151	C₁₃×#41	—	2	8	no	—
152	C₁₃×#41	—	2	8	no	—
153	C₁₃×#41	—	4	8	no	—
154	C₁₃×#41	—	4	16	no	—
155	C₁₃×#41	—	4	8	no	—
156	C₂×Q₈×C₁₃	—	2	4	no	—
157	C₂×Q₈×C₁₃	—	2	2	no	—
158	C₂×Q₈×C₁₃	—	2	8	no	—
159	C₂×Q₈×C₁₃	—	4	8	no	—
160	C₂×Q₈×C₁₃	—	4	8	no	—
161	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
163	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
164	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
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	4	no	—
169	C₂×D₄×C₁₃	—	2	2	no	—
170	C₂×D₄×C₁₃	—	2	2	no	—
171	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
172	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
174	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₁₃	—	2	4	no	—
176	C₂²×C₄×C₁₃	—	2	2	no	—
177	C₂²×C₄×C₁₃	—	2	2	no	—
178	C₂²×C₄×C₁₃	—	2	2	no	—
179	C₂²×C₄×C₁₃	—	2	4	no	—
180	C₂²×C₄×C₁₃	—	2	2	no	—
181	C₂²×C₄×C₁₃	—	2	4	no	—
182	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
183	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
184	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₁₃×Q₁₆	—	4	4	no	—
187	C₁₃×Q₁₆	—	4	8	no	—
188	C₁₃×SD₁₆	—	4	4	no	—
189	C₁₃×SD₁₆	—	4	4	no	—
190	C₁₃×SD₁₆	—	4	8	no	—
191	C₁₃×D₈	—	4	4	no	—
192	C₁₃×M₁₆	—	2	4	no	—
193	C₂×C₈×C₁₃	—	2	4	no	—
194	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
195	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
196	C₁₃×C₄⋊C₄	—	2	4	no	—
197	C₁₃×C₄⋊C₄	—	2	2	no	—
198	C₁₃×C₄⋊C₄	—	2	2	no	—
199	C₁₃×C₄⋊C₄	—	2	4	no	—
200	C₁₃×C₄⋊C₄	—	2	4	no	—
201	C₁₃×C₄⋊C₄	—	2	4	no	—
202	C₁₃×C₄⋊C₄	—	2	8	no	—
203	C₁₃×C₄⋊C₄	—	2	4	no	—
204	C₁₃×C₄⋊C₄	—	2	4	no	—
205	C₁₃×C₄⋊C₄	—	2	2	no	—
206	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
207	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
208	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
209	C₁₃×C₂²⋊C₄	—	2	4	no	—
210	C₁₃×C₂²⋊C₄	—	2	2	no	—
211	C₁₃×C₂²⋊C₄	—	2	4	no	—
212	C₁₃×C₂²⋊C₄	—	2	4	no	—
213	C₁₃×C₂²⋊C₄	—	2	2	no	—
214	C₁₃×C₂²⋊C₄	—	2	8	no	—
215	C₁₃×C₂²⋊C₄	—	2	4	no	—
216	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
217	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
218	C₄²×C₁₃	—	2	4	no	—
219	C₄²×C₁₃	C₂×D₄	1	4	yes	—
220	C₄²×C₁₃	C₂×D₄	1	2	yes	—
221	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
222	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
223	C₄²×C₁₃	C₂⁴	1	2	yes	—
224	#3512	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#3499	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#3223	C₂×C₁₃	1	4	yes	complemented
227	#3221	C₂×C₁₃	1	4	yes	complemented
228	#3219	C₂×C₁₃	1	4	yes	complemented
229	#3218	C₂×C₁₃	1	4	yes	complemented
230	#3152	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#3150	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#3142	C₂×C₁₃	1	1	yes	characteristic, complemented
233	C₂×#491	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#3046	C₂×C₁₃	1	4	yes	complemented
235	#3013	C₂×C₁₃	1	4	yes	complemented
236	#2923	C₂×C₁₃	1	1	yes	characteristic, complemented
237	C₂³×C₁₃	—	2	2	no	—
238	C₂³×C₁₃	—	2	2	no	—
239	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
240	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
241	Q₈×C₁₃	—	2	2	no	—
242	Q₈×C₁₃	—	2	4	no	—
243	Q₈×C₁₃	—	2	8	no	—
244	Q₈×C₁₃	—	2	4	no	—
245	Q₈×C₁₃	—	4	8	no	—
246	Q₈×C₁₃	—	4	4	no	—
247	D₄×C₁₃	—	2	4	no	—
248	D₄×C₁₃	—	2	2	no	—
249	D₄×C₁₃	—	2	4	no	—
250	D₄×C₁₃	—	2	4	no	—
251	D₄×C₁₃	—	4	4	no	—
252	D₄×C₁₃	—	4	8	no	—
253	D₄×C₁₃	—	4	4	no	—
254	D₄×C₁₃	—	4	4	no	—
255	D₄×C₁₃	—	8	2	no	—
256	D₄×C₁₃	—	8	4	no	—
257	C₂×C₄×C₁₃	—	2	4	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	4	no	—
260	C₂×C₄×C₁₃	—	2	4	no	—
261	C₂×C₄×C₁₃	—	2	2	no	—
262	C₂×C₄×C₁₃	—	4	4	no	—
263	C₂×C₄×C₁₃	—	4	2	no	—
264	C₂×C₄×C₁₃	—	4	8	no	—
265	C₂×C₄×C₁₃	—	4	8	no	—
266	C₂×C₄×C₁₃	—	4	4	no	—
267	C₂×C₄×C₁₃	—	4	4	no	—
268	C₂×C₄×C₁₃	—	4	4	no	—
269	C₂×C₄×C₁₃	—	8	4	no	—
270	C₂×C₄×C₁₃	—	8	2	no	—
271	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
272	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
273	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
274	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
275	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
277	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
278	C₈×C₁₃	—	2	4	no	—
279	C₈×C₁₃	—	2	4	no	—
280	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
281	C₂×#137	C₂²×C₁₃	1	4	yes	—
282	C₂×#135	C₂²×C₁₃	1	4	yes	—
283	#553	—	2	4	no	—
284	#553	—	2	2	no	—
285	#552	—	2	2	no	—
286	D₄×Q₈	—	2	2	no	—
287	#547	—	2	4	no	—
288	#547	—	2	2	no	—
289	#541	C₂²×C₁₃	1	2	yes	—
290	#540	C₂²×C₁₃	1	2	yes	—
291	#537	C₂²×C₁₃	1	2	yes	—
292	#536	C₂²×C₁₃	1	4	yes	—
293	#536	C₂²×C₁₃	1	2	yes	—
294	#532	C₂²×C₁₃	1	1	yes	characteristic
295	#532	C₂²×C₁₃	1	1	yes	characteristic
296	#532	C₂²×C₁₃	1	2	yes	—
297	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
299	#529	C₂²×C₁₃	1	4	yes	—
300	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
301	#520	C₂²×C₁₃	1	2	yes	—
302	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
303	#497	C₂²×C₁₃	1	2	yes	—
304	#497	C₂²×C₁₃	1	2	yes	—
305	#497	C₂²×C₁₃	1	4	yes	—
306	#496	C₂²×C₁₃	1	2	yes	—
307	#496	C₂²×C₁₃	1	2	yes	—
308	#494	C₂²×C₁₃	1	2	yes	—
309	#492	C₂²×C₁₃	1	2	yes	—
310	#491	C₂²×C₁₃	1	4	yes	—
311	#491	C₂²×C₁₃	1	4	yes	—
312	#491	C₂²×C₁₃	1	2	yes	—
313	#490	C₂²×C₁₃	1	2	yes	—
314	#488	C₂²×C₁₃	1	4	yes	—
315	#464	C₂²×C₁₃	1	8	yes	—
316	#463	C₂²×C₁₃	1	8	yes	—
317	#462	C₂²×C₁₃	1	8	yes	—
318	#461	C₂²×C₁₃	1	8	yes	—
319	#452	C₂²×C₁₃	1	8	yes	—
320	#451	C₂²×C₁₃	1	8	yes	—
321	#449	C₂²×C₁₃	1	8	yes	—
322	#448	C₂²×C₁₃	1	8	yes	—
323	#433	C₂²×C₁₃	1	4	yes	—
324	#432	C₂²×C₁₃	1	4	yes	—
325	#424	C₂²×C₁₃	1	2	yes	—
326	#417	C₂²×C₁₃	1	4	yes	—
327	C₂×#103	C₂²×C₁₃	1	4	yes	—
328	#408	C₂²×C₁₃	1	2	yes	—
329	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
331	C₂²×C₁₃	—	2	2	no	—
332	C₂²×C₁₃	—	2	4	no	—
333	C₂²×C₁₃	—	2	2	no	—
334	C₂²×C₁₃	—	4	2	no	—
335	C₂²×C₁₃	—	4	4	no	—
336	C₂²×C₁₃	—	4	2	no	—
337	C₂²×C₁₃	—	4	2	no	—
338	C₂²×C₁₃	—	4	2	no	—
339	C₂²×C₁₃	#535	1	2	yes	—
340	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
341	C₄×C₁₃	—	2	2	no	—
342	C₄×C₁₃	—	2	4	no	—
343	C₄×C₁₃	—	2	2	no	—
344	C₄×C₁₃	—	2	2	no	—
345	C₄×C₁₃	—	4	4	no	—
346	C₄×C₁₃	—	4	4	no	—
347	C₄×C₁₃	—	4	2	no	—
348	C₄×C₁₃	—	4	2	no	—
349	C₄×C₁₃	#535	1	2	yes	—
350	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
351	2₋¹⁺⁴	—	4	8	no	—
352	C₂×#41	—	2	2	no	—
353	C₂×#41	—	2	4	no	—
354	C₂×#41	C₂³×C₁₃	1	2	yes	—
355	C₂×#41	C₂³×C₁₃	1	2	yes	—
356	C₂×#41	C₂³×C₁₃	1	4	yes	—
357	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
358	C₂²×Q₈	—	2	2	no	—
359	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
360	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
361	#137	—	4	8	no	—
362	#135	—	4	8	no	—
363	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
364	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
365	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
366	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
367	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
368	C₂×D₈	C₂³×C₁₃	1	4	yes	—
369	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
370	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
371	C₄⋊Q₈	—	2	4	no	—
372	C₄⋊Q₈	—	2	2	no	—
373	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
374	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
375	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
376	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
377	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
378	#127	C₂³×C₁₃	1	1	yes	characteristic
379	#127	C₂³×C₁₃	1	1	yes	characteristic
380	#126	—	2	4	no	—
381	#126	—	2	4	no	—
382	#125	—	2	4	no	—
383	#125	—	2	2	no	—
384	#125	C₂³×C₁₃	1	2	yes	—
385	#125	C₂³×C₁₃	1	2	yes	—
386	#124	C₂³×C₁₃	1	2	yes	—
387	#124	C₂³×C₁₃	1	4	yes	—
388	#124	C₂³×C₁₃	1	2	yes	—
389	#123	—	2	4	no	—
390	#123	—	2	4	no	—
391	#123	—	2	4	no	—
392	#123	—	2	8	no	—
393	C₂²⋊Q₈	—	2	2	no	—
394	C₂²⋊Q₈	—	2	4	no	—
395	C₂²⋊Q₈	—	2	8	no	—
396	C₂²⋊Q₈	C₂³×C₁₃	1	4	yes	—
397	#121	—	2	2	no	—
398	#121	—	2	4	no	—
399	#121	—	2	2	no	—
400	#121	—	2	4	no	—
401	#121	—	2	2	no	—
402	#121	—	2	4	no	—
403	#121	C₂³×C₁₃	1	4	yes	—
404	C₄×Q₈	D₄×C₁₃	1	2	yes	—
405	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
406	C₄×D₄	—	2	4	no	—
407	C₄×D₄	—	2	4	no	—
408	C₄×D₄	—	2	4	no	—
409	C₄×D₄	—	2	2	no	—
410	C₄×D₄	—	2	2	no	—
411	C₄×D₄	D₄×C₁₃	1	4	yes	—
412	C₄×D₄	D₄×C₁₃	1	2	yes	—
413	C₄×D₄	C₂³×C₁₃	1	4	yes	—
414	#117	—	2	2	no	—
415	#117	—	2	4	no	—
416	#117	C₂³×C₁₃	1	1	yes	characteristic
417	#117	C₂³×C₁₃	1	2	yes	—
418	C₂×C₄⋊C₄	—	2	2	no	—
419	C₂×C₄⋊C₄	—	2	2	no	—
420	C₂×C₄⋊C₄	—	2	4	no	—
421	C₂×C₄⋊C₄	—	2	2	no	—
422	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
423	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
425	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
426	#103	C₂³×C₁₃	1	8	yes	—
427	#103	C₂³×C₁₃	1	8	yes	—
428	#103	C₂³×C₁₃	1	8	yes	—
429	#102	C₂³×C₁₃	1	8	yes	—
430	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
431	#97	C₂³×C₁₃	1	2	yes	—
432	#97	C₂³×C₁₃	1	2	yes	—
433	#97	C₂³×C₁₃	1	2	yes	—
434	C₄×C₈	C₂³×C₁₃	1	2	yes	—
435	C₂×C₁₃	—	2	2	no	—
436	C₂×C₁₃	—	4	2	no	—
437	C₂×C₁₃	—	8	2	no	—
438	C₂×C₁₃	—	8	2	no	—
439	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
440	C₂×C₁₃	#3586	1	2	yes	—
441	#41	—	2	4	no	—
442	#41	—	2	8	no	—
443	#41	—	2	8	no	—
444	#41	—	4	8	no	—
445	#41	—	4	16	no	—
446	#41	—	4	8	no	—
447	C₂×Q₈	—	2	4	no	—
448	C₂×Q₈	—	2	2	no	—
449	C₂×Q₈	—	2	8	no	—
450	C₂×Q₈	—	4	8	no	—
451	C₂×Q₈	—	4	8	no	—
452	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
453	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
454	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
455	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	2	2	no	—
459	C₂×D₄	—	2	4	no	—
460	C₂×D₄	—	2	2	no	—
461	C₂×D₄	—	2	2	no	—
462	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
463	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
464	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
465	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
474	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
475	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
476	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
477	Q₁₆	—	4	4	no	—
478	Q₁₆	—	4	8	no	—
479	SD₁₆	—	4	4	no	—
480	SD₁₆	—	4	4	no	—
481	SD₁₆	—	4	8	no	—
482	D₈	—	4	4	no	—
483	M₁₆	—	2	4	no	—
484	C₂×C₈	—	2	4	no	—
485	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
486	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
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	—	2	8	no	—
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
498	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
499	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	4	no	—
503	C₂²⋊C₄	—	2	4	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	8	no	—
506	C₂²⋊C₄	—	2	4	no	—
507	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
508	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
509	C₄²	—	2	4	no	—
510	C₄²	C₂×D₄×C₁₃	1	4	yes	—
511	C₄²	C₂×D₄×C₁₃	1	2	yes	—
512	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
513	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
514	C₄²	C₂⁴×C₁₃	1	2	yes	—
515	C₁₃	#60831	1	1	yes	characteristic, direct product factor, Sylow
516	C₂³	—	2	2	no	—
517	C₂³	—	2	2	no	—
518	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
519	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
520	Q₈	—	2	2	no	—
521	Q₈	—	2	4	no	—
522	Q₈	—	2	8	no	—
523	Q₈	—	2	4	no	—
524	Q₈	—	4	8	no	—
525	Q₈	—	4	4	no	—
526	D₄	—	2	4	no	—
527	D₄	—	2	2	no	—
528	D₄	—	2	4	no	—
529	D₄	—	2	4	no	—
530	D₄	—	4	4	no	—
531	D₄	—	4	8	no	—
532	D₄	—	4	4	no	—
533	D₄	—	4	4	no	—
534	D₄	—	8	2	no	—
535	D₄	—	8	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	4	4	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	8	no	—
544	C₂×C₄	—	4	8	no	—
545	C₂×C₄	—	4	4	no	—
546	C₂×C₄	—	4	4	no	—
547	C₂×C₄	—	4	4	no	—
548	C₂×C₄	—	8	4	no	—
549	C₂×C₄	—	8	2	no	—
550	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
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	1	yes	characteristic
555	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
556	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
557	C₈	—	2	4	no	—
558	C₈	—	2	4	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	4	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	4	4	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	C₁₃×#535	1	2	yes	—
568	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
569	C₄	—	2	2	no	—
570	C₄	—	2	4	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	4	4	no	—
574	C₄	—	4	4	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	2	no	—
577	C₄	C₁₃×#535	1	2	yes	—
578	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
579	C₂	—	2	2	no	—
580	C₂	—	4	2	no	—
581	C₂	—	8	2	no	—
582	C₂	—	8	2	no	—
583	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
584	C₂	C₁₃×#3586	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×#3499	C₂	semidirect
3. C₁₃×#3223	C₂	semidirect
4. C₁₃×#3221	C₂	semidirect
5. C₁₃×#3219	C₂	semidirect
6. C₁₃×#3218	C₂	semidirect
7. C₁₃×#3152	C₂	semidirect
8. C₁₃×#3150	C₂	semidirect
9. C₁₃×#3142	C₂	semidirect
10. C₂×C₁₃×#491	C₂	semidirect
11. C₁₃×#3046	C₂	semidirect
12. C₁₃×#3013	C₂	semidirect
13. C₁₃×#2923	C₂	semidirect
149. #60831	C₁₃	direct (N × H)
224. #3512	C₂×C₁₃	semidirect
225. #3499	C₂×C₁₃	semidirect
226. #3223	C₂×C₁₃	semidirect
227. #3221	C₂×C₁₃	semidirect
228. #3219	C₂×C₁₃	semidirect
229. #3218	C₂×C₁₃	semidirect
230. #3152	C₂×C₁₃	semidirect
231. #3150	C₂×C₁₃	semidirect
232. #3142	C₂×C₁₃	semidirect
233. C₂×#491	C₂×C₁₃	semidirect
234. #3046	C₂×C₁₃	semidirect
235. #3013	C₂×C₁₃	semidirect
236. #2923	C₂×C₁₃	semidirect
515. C₁₃	#60831	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×#3499	2
C₁₃×#3223	2
C₁₃×#3221	2
C₁₃×#3219	2
C₁₃×#3218	2
C₁₃×#3152	2
C₁₃×#3150	2
C₁₃×#3142	2
C₂×C₁₃×#491	2
C₁₃×#3046	2
C₁₃×#3013	2
C₁₃×#2923	2
#60831	13

Subgroups — C13×#60831 #15747170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60831 #15747170