Subgroups — C₁₃×#22668 #15709007

Order 3328.

868 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×C₁₃×M₁₆	C₂	1	2	yes	maximal
2	C₂×C₁₃×#435	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#430	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1950	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1855	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1855	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1849	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1811	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1810	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1778	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
13	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#436	—	2	2	no	—
18	C₁₃×#435	—	2	2	no	—
19	C₁₃×#435	—	2	2	no	—
20	C₁₃×#435	C₄	1	4	yes	—
21	C₁₃×#435	C₄	1	4	yes	—
22	C₈×D₄×C₁₃	—	2	2	no	—
23	C₁₃×#430	—	2	4	no	—
24	C₂×C₁₃×#108	—	2	4	no	—
25	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#108	C₂²	1	2	yes	—
29	C₂×C₁₃×#108	C₂²	1	2	yes	—
30	C₂×C₁₃×#108	C₂²	1	2	yes	—
31	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
32	C₁₃×#423	C₂²	1	2	yes	—
33	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₁₃×#407	C₂²	1	2	yes	—
35	C₁₃×#407	C₂²	1	2	yes	—
36	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×M₁₆	C₂²	1	2	yes	—
39	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
40	C₁₃×#341	C₂²	1	2	yes	—
41	C₁₃×#341	C₂²	1	2	yes	—
42	C₁₃×#341	C₂²	1	2	yes	—
43	C₂²×D₄×C₁₃	Q₈	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂×C₁₃×M₁₆	—	2	2	no	—
47	C₂×C₁₃×M₁₆	—	2	2	no	—
48	C₂×C₁₃×M₁₆	—	2	2	no	—
49	C₂×C₁₃×M₁₆	—	2	2	no	—
50	C₂×C₁₃×M₁₆	—	2	4	no	—
51	C₂×C₁₃×M₁₆	—	2	4	no	—
52	C₂×C₁₃×M₁₆	—	4	2	no	—
53	C₂×C₁₃×M₁₆	—	4	2	no	—
54	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
55	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
56	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
57	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
58	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₃	—	2	2	no	—
60	C₂²×C₈×C₁₃	—	2	2	no	—
61	C₂²×C₈×C₁₃	—	2	2	no	—
62	C₂²×C₈×C₁₃	—	2	2	no	—
63	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
64	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
70	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
71	C₄×D₄×C₁₃	D₄	1	2	yes	—
72	C₄×D₄×C₁₃	D₄	1	2	yes	—
73	C₂×C₁₃×C₄⋊C₄	Q₈	1	1	yes	characteristic
74	C₂×C₁₃×C₂²⋊C₄	Q₈	1	1	yes	characteristic
75	C₂×C₁₃×C₂²⋊C₄	Q₈	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×#108	—	2	4	no	—
78	C₁₃×#108	—	2	4	no	—
79	C₁₃×#108	—	2	2	no	—
80	C₁₃×#108	—	2	2	no	—
81	C₁₃×#108	—	2	2	no	—
82	C₁₃×#108	—	4	2	no	—
83	C₁₃×#108	D₄	1	4	yes	complemented
84	C₁₃×C₄⋊C₈	—	2	2	no	—
85	C₁₃×C₄⋊C₈	—	2	2	no	—
86	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
87	C₁₃×C₂²⋊C₈	—	2	2	no	—
88	C₁₃×C₂²⋊C₈	—	2	2	no	—
89	C₁₃×C₂²⋊C₈	—	2	2	no	—
90	C₁₃×C₂²⋊C₈	—	2	2	no	—
91	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
92	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
93	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
94	C₁₃×#97	—	2	2	no	—
95	C₁₃×#97	C₂×C₄	1	4	yes	—
96	C₄×C₈×C₁₃	—	2	2	no	—
97	#22668	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂⁴×C₁₃	C₂×Q₈	1	1	yes	characteristic
99	C₂⁴×C₁₃	C₂×Q₈	1	1	yes	characteristic
100	C₂×D₄×C₁₃	—	4	2	no	—
101	C₂×D₄×C₁₃	C₄⋊C₄	1	2	yes	—
102	C₂×D₄×C₁₃	C₄⋊C₄	1	2	yes	—
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
122	C₁₃×M₁₆	—	2	2	no	—
123	C₁₃×M₁₆	—	2	8	no	—
124	C₁₃×M₁₆	—	2	2	no	—
125	C₁₃×M₁₆	—	2	2	no	—
126	C₁₃×M₁₆	—	2	2	no	—
127	C₁₃×M₁₆	—	2	2	no	—
128	C₁₃×M₁₆	—	2	2	no	—
129	C₁₃×M₁₆	—	2	2	no	—
130	C₁₃×M₁₆	—	4	4	no	—
131	C₁₃×M₁₆	—	4	4	no	—
132	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	1	no	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	1	no	—
137	C₂×C₈×C₁₃	—	2	1	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	2	4	no	—
141	C₂×C₈×C₁₃	—	2	4	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	4	4	no	—
146	C₂×C₈×C₁₃	—	4	4	no	—
147	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
149	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
150	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₁₃	#41	1	2	yes	—
153	C₁₃×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
154	C₁₃×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
155	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
156	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
157	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
158	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
159	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
160	C₄²×C₁₃	C₂×D₄	1	2	yes	—
161	D₄×M₁₆	C₂×C₁₃	1	2	yes	—
162	C₂×#435	C₂×C₁₃	1	1	yes	characteristic
163	C₂×#430	C₂×C₁₃	1	1	yes	characteristic, complemented
164	C₂²×#108	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#1950	C₂×C₁₃	1	2	yes	complemented
166	#1855	C₂×C₁₃	1	2	yes	complemented
167	#1855	C₂×C₁₃	1	2	yes	complemented
168	#1849	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#1811	C₂×C₁₃	1	1	yes	characteristic, complemented
170	#1810	C₂×C₁₃	1	1	yes	characteristic, complemented
171	#1778	C₂×C₁₃	1	1	yes	characteristic, complemented
172	C₂³×C₁₃	—	2	1	no	—
173	C₂³×C₁₃	—	2	1	no	—
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	—	2	1	no	—
176	C₂³×C₁₃	—	2	1	no	—
177	C₂³×C₁₃	—	4	1	no	—
178	C₂³×C₁₃	—	4	1	no	—
179	C₂³×C₁₃	—	4	1	no	—
180	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
181	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
184	D₄×C₁₃	—	2	4	no	—
185	D₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	4	1	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
205	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
206	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
209	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
214	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
215	C₈×C₁₃	—	2	2	no	—
216	C₈×C₁₃	—	2	2	no	—
217	C₈×C₁₃	—	2	2	no	—
218	C₈×C₁₃	—	2	4	no	—
219	C₈×C₁₃	—	4	2	no	—
220	C₈×C₁₃	—	4	2	no	—
221	C₈×C₁₃	—	4	2	no	—
222	C₈×C₁₃	C₄×D₄	1	4	yes	—
223	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
224	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
225	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
226	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
228	#436	—	2	2	no	—
229	#435	—	2	2	no	—
230	#435	—	2	2	no	—
231	#435	C₄×C₁₃	1	4	yes	—
232	#435	C₄×C₁₃	1	4	yes	—
233	C₈×D₄	—	2	2	no	—
234	#430	—	2	4	no	—
235	C₂×#108	—	2	4	no	—
236	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
238	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×#108	C₂²×C₁₃	1	2	yes	—
240	C₂×#108	C₂²×C₁₃	1	2	yes	—
241	C₂×#108	C₂²×C₁₃	1	2	yes	—
242	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
243	#423	C₂²×C₁₃	1	2	yes	—
244	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
245	#407	C₂²×C₁₃	1	2	yes	—
246	#407	C₂²×C₁₃	1	2	yes	—
247	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
249	C₄×M₁₆	C₂²×C₁₃	1	2	yes	—
250	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
251	#341	C₂²×C₁₃	1	2	yes	—
252	#341	C₂²×C₁₃	1	2	yes	—
253	#341	C₂²×C₁₃	1	2	yes	—
254	C₂²×C₁₃	—	2	1	no	—
255	C₂²×C₁₃	—	2	1	no	—
256	C₂²×C₁₃	—	2	1	no	—
257	C₂²×C₁₃	—	2	1	no	—
258	C₂²×C₁₃	—	2	1	no	—
259	C₂²×C₁₃	—	2	2	no	—
260	C₂²×C₁₃	—	2	2	no	—
261	C₂²×C₁₃	—	2	1	no	—
262	C₂²×C₁₃	—	2	1	no	—
263	C₂²×C₁₃	—	2	2	no	—
264	C₂²×C₁₃	—	4	2	no	—
265	C₂²×C₁₃	—	4	2	no	—
266	C₂²×C₁₃	—	8	1	no	—
267	C₂²×C₁₃	—	8	1	no	—
268	C₂²×C₁₃	#430	1	2	yes	complemented
269	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
270	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
271	C₂²×C₁₃	#554	1	1	yes	characteristic
272	C₄×C₁₃	—	2	1	no	—
273	C₄×C₁₃	—	2	1	no	—
274	C₄×C₁₃	—	2	2	no	—
275	C₄×C₁₃	—	2	2	no	—
276	C₄×C₁₃	—	2	2	no	—
277	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
278	C₄×C₁₃	#520	1	1	yes	characteristic
279	C₄×C₁₃	D₄²	1	1	yes	characteristic
280	C₄×C₁₃	#547	1	1	yes	characteristic
281	C₂²×D₄	Q₈×C₁₃	1	1	yes	characteristic
282	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
283	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	—	2	2	no	—
286	C₂×M₁₆	—	2	2	no	—
287	C₂×M₁₆	—	2	2	no	—
288	C₂×M₁₆	—	2	4	no	—
289	C₂×M₁₆	—	2	4	no	—
290	C₂×M₁₆	—	4	2	no	—
291	C₂×M₁₆	—	4	2	no	—
292	C₂×M₁₆	C₂×C₄×C₁₃	1	4	yes	—
293	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
294	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
295	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
296	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
297	C₂²×C₈	—	2	2	no	—
298	C₂²×C₈	—	2	2	no	—
299	C₂²×C₈	—	2	2	no	—
300	C₂²×C₈	—	2	2	no	—
301	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
302	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
303	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
306	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
307	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
308	C₄×D₄	C₂×C₄×C₁₃	1	2	yes	—
309	C₄×D₄	D₄×C₁₃	1	2	yes	—
310	C₄×D₄	D₄×C₁₃	1	2	yes	—
311	C₂×C₄⋊C₄	Q₈×C₁₃	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	Q₈×C₁₃	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	Q₈×C₁₃	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
315	#108	—	2	4	no	—
316	#108	—	2	4	no	—
317	#108	—	2	2	no	—
318	#108	—	2	2	no	—
319	#108	—	2	2	no	—
320	#108	—	4	2	no	—
321	#108	D₄×C₁₃	1	4	yes	complemented
322	C₄⋊C₈	—	2	2	no	—
323	C₄⋊C₈	—	2	2	no	—
324	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	C₂²⋊C₈	—	2	2	no	—
328	C₂²⋊C₈	—	2	2	no	—
329	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
330	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
331	C₂²⋊C₈	C₂×C₄×C₁₃	1	2	yes	—
332	#97	—	2	2	no	—
333	#97	C₂×C₄×C₁₃	1	4	yes	—
334	C₄×C₈	—	2	2	no	—
335	C₂×C₁₃	—	2	1	no	—
336	C₂×C₁₃	—	2	1	no	—
337	C₂×C₁₃	—	2	2	no	—
338	C₂×C₁₃	—	4	1	no	—
339	C₂×C₁₃	—	4	2	no	—
340	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
341	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
342	C₂×C₁₃	#2916	1	1	yes	characteristic
343	C₂⁴	C₂×Q₈×C₁₃	1	1	yes	characteristic
344	C₂⁴	C₂×Q₈×C₁₃	1	1	yes	characteristic
345	C₂×D₄	—	4	2	no	—
346	C₂×D₄	C₁₃×C₄⋊C₄	1	2	yes	—
347	C₂×D₄	C₁₃×C₄⋊C₄	1	2	yes	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
357	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
358	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
359	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
362	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
363	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
364	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
365	C₂²×C₄	C₂×Q₈×C₁₃	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
367	M₁₆	—	2	2	no	—
368	M₁₆	—	2	8	no	—
369	M₁₆	—	2	2	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	2	2	no	—
372	M₁₆	—	2	2	no	—
373	M₁₆	—	2	2	no	—
374	M₁₆	—	2	2	no	—
375	M₁₆	—	4	4	no	—
376	M₁₆	—	4	4	no	—
377	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	4	no	—
386	C₂×C₈	—	2	4	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	4	4	no	—
391	C₂×C₈	—	4	4	no	—
392	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
393	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
394	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
395	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
396	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
397	C₂×C₈	C₁₃×#41	1	2	yes	—
398	C₄⋊C₄	C₁₃×C₄⋊C₄	1	2	yes	—
399	C₄⋊C₄	C₁₃×C₄⋊C₄	1	2	yes	—
400	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	2	yes	—
401	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	2	yes	—
402	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	2	yes	—
403	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	2	yes	—
404	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
405	C₄²	C₂×D₄×C₁₃	1	2	yes	—
406	C₁₃	#22668	1	1	yes	characteristic, direct product factor, Sylow
407	C₂³	—	2	2	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
416	C₂³	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
417	C₂³	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
418	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
419	D₄	—	2	4	no	—
420	D₄	—	4	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
440	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
441	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
442	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
443	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
444	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
445	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
446	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
447	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
448	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
449	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
450	C₈	—	2	2	no	—
451	C₈	—	2	2	no	—
452	C₈	—	2	2	no	—
453	C₈	—	2	4	no	—
454	C₈	—	4	2	no	—
455	C₈	—	4	2	no	—
456	C₈	—	4	2	no	—
457	C₈	C₄×D₄×C₁₃	1	4	yes	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	8	1	no	—
471	C₂²	—	8	1	no	—
472	C₂²	C₁₃×#430	1	2	yes	complemented
473	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
474	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
475	C₂²	C₁₃×#554	1	1	yes	characteristic
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	2	no	—
481	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
482	C₄	C₁₃×#520	1	1	yes	characteristic
483	C₄	D₄²×C₁₃	1	1	yes	characteristic
484	C₄	C₁₃×#547	1	1	yes	characteristic
485	C₂	—	2	1	no	—
486	C₂	—	2	1	no	—
487	C₂	—	2	2	no	—
488	C₂	—	4	1	no	—
489	C₂	—	4	2	no	—
490	C₂	D₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
491	C₂	C₂×C₁₃×#430	1	1	yes	characteristic
492	C₂	C₁₃×#2916	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂²×D₄×C₁₃	Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₃×#430	C₂	semidirect
4. C₂²×C₁₃×#108	C₂	semidirect
5. C₁₃×#1950	C₂	semidirect
6. C₁₃×#1855	C₂	semidirect
7. C₁₃×#1855	C₂	semidirect
8. C₁₃×#1849	C₂	semidirect
9. C₁₃×#1811	C₂	semidirect
10. C₁₃×#1810	C₂	semidirect
11. C₁₃×#1778	C₂	semidirect
83. C₁₃×#108	D₄	semidirect
97. #22668	C₁₃	direct (N × H)
163. C₂×#430	C₂×C₁₃	semidirect
164. C₂²×#108	C₂×C₁₃	semidirect
165. #1950	C₂×C₁₃	semidirect
166. #1855	C₂×C₁₃	semidirect
167. #1855	C₂×C₁₃	semidirect
168. #1849	C₂×C₁₃	semidirect
169. #1811	C₂×C₁₃	semidirect
170. #1810	C₂×C₁₃	semidirect
171. #1778	C₂×C₁₃	semidirect
268. C₂²×C₁₃	#430	semidirect
321. #108	D₄×C₁₃	semidirect
406. C₁₃	#22668	direct (N × H)
472. C₂²	C₁₃×#430	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
D₄×C₁₃×M₁₆	2
C₂×C₁₃×#435	2
C₂×C₁₃×#430	2
C₂²×C₁₃×#108	2
C₁₃×#1950	2
C₁₃×#1855	2
C₁₃×#1849	2
C₁₃×#1811	2
C₁₃×#1810	2
C₁₃×#1778	2
#22668	13

Subgroups — C13×#22668 #15709007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22668 #15709007