Subgroups — C₂×D₁₃×#518 #16769496

Order 3328.

14590 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#11719503	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11719226	C₂	1	2	yes	maximal, complemented
4	C₂×#11719191	C₂	1	4	yes	maximal, complemented
5	C₂×#11719250	C₂	1	8	yes	maximal, complemented
6	D₁₃×#518	C₂	1	32	yes	maximal, direct product factor
7	C₂×C₄×D₄×D₁₃	C₂	1	8	yes	maximal, complemented
8	C₂×D₁₃×#117	C₂	1	2	yes	maximal, complemented
9	C₂²×C₂²⋊C₄×D₁₃	C₂	1	4	yes	maximal, complemented
10	C₂×C₁₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁵×D₁₃	C₂²	1	2	yes	—
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	—
14	C₂²×D₄×D₁₃	C₄	1	32	yes	complemented
15	C₂²×D₄×D₁₃	C₂²	1	4	yes	—
16	C₂²×D₄×D₁₃	C₂²	1	16	yes	—
17	C₂²×D₄×D₁₃	C₂²	1	4	yes	—
18	C₂³×D₅₂	C₂²	1	1	yes	characteristic
19	C₂³×C₄×D₁₃	C₂²	1	1	yes	characteristic
20	C₂³×C₄×D₁₃	C₂²	1	8	yes	complemented
21	C₁₃×#518	C₂²	1	16	yes	complemented
22	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
23	C₂×C₁₃×#117	C₂²	1	2	yes	complemented
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	complemented
25	C₂²×C₂²⋊Dic₁₃	C₂²	1	4	yes	complemented
26	#11719503	C₂²	1	16	yes	complemented
27	C₂×D₄×Dic₁₃	C₂²	1	8	yes	complemented
28	C₂×C₄×C₂²⋊D₁₃	C₂²	1	16	yes	complemented
29	C₂²×#6103	C₂²	1	8	yes	complemented
30	C₂×#88180	C₂²	1	2	yes	complemented
31	#11719250	C₂²	1	128	yes	complemented
32	C₄×D₄×D₁₃	C₂²	1	128	yes	complemented
33	#11719226	C₂²	1	32	yes	complemented
34	D₁₃×#117	C₂²	1	32	yes	complemented
35	C₂×#88147	C₂²	1	8	yes	complemented
36	C₂×#88146	C₂²	1	4	yes	complemented
37	C₂×C₄⋊C₄×D₁₃	C₂²	1	4	yes	complemented
38	#11719191	C₂²	1	64	yes	complemented
39	C₂×#88135	C₂²	1	16	yes	complemented
40	C₂×C₂²⋊C₄×D₁₃	C₂²	1	4	yes	—
41	C₂×C₂²⋊C₄×D₁₃	C₂²	1	64	yes	complemented
42	C₂×C₂²⋊C₄×D₁₃	C₂²	1	8	yes	complemented
43	C₂×C₂²⋊C₄×D₁₃	C₂²	1	8	yes	complemented
44	C₂×C₂²⋊C₄×D₁₃	C₂²	1	8	yes	complemented
45	C₂×#88131	C₂²	1	4	yes	complemented
46	C₂×C₄×D₅₂	C₂²	1	8	yes	complemented
47	C₂×#88126	C₂²	1	4	yes	complemented
48	C₂×C₄²×D₁₃	C₂²	1	4	yes	complemented
49	C₂⁵×C₁₃	C₂³	1	2	yes	—
50	C₂⁴×D₁₃	—	4	16	no	—
51	C₂⁴×D₁₃	C₂×C₄	1	32	yes	complemented
52	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
53	C₂⁴×D₁₃	C₂³	1	4	yes	—
54	C₂⁴×D₁₃	C₂³	1	2	yes	—
55	C₂⁴×D₁₃	C₂³	1	16	yes	—
56	C₂⁴×D₁₃	C₂³	1	4	yes	—
57	C₂²×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
58	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
59	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	C₂³	1	8	yes	complemented
62	C₂²×C₂²⋊D₁₃	C₂×C₄	1	32	yes	complemented
63	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
64	C₂²×C₂²⋊D₁₃	C₂³	1	16	yes	—
65	C₂³×Dic₁₃	C₂³	1	1	yes	characteristic
66	C₂³×Dic₁₃	C₂³	1	8	yes	complemented
67	C₂×D₄×D₁₃	C₂×C₄	1	64	yes	complemented
68	C₂×D₄×D₁₃	C₂×C₄	1	256	yes	complemented
69	C₂×D₄×D₁₃	C₂×C₄	1	64	yes	complemented
70	C₂×D₄×D₁₃	C₂³	1	32	yes	—
71	C₂×D₄×D₁₃	C₂³	1	32	yes	—
72	C₂²×D₅₂	C₂×C₄	1	16	yes	complemented
73	C₂²×D₅₂	C₂³	1	4	yes	—
74	C₂²×D₅₂	C₂³	1	8	yes	—
75	C₂²×C₄×D₁₃	—	4	32	no	—
76	C₂²×C₄×D₁₃	C₂×C₄	1	16	yes	complemented
77	C₂²×C₄×D₁₃	C₂³	1	8	yes	—
78	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
79	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
80	C₂²×C₄×D₁₃	C₂³	1	8	yes	—
81	C₂²×C₄×D₁₃	C₂³	1	64	yes	complemented
82	C₂²×C₄×D₁₃	C₂³	1	16	yes	complemented
83	C₄×D₄×C₁₃	C₂³	1	64	yes	complemented
84	C₁₃×#117	C₂³	1	16	yes	complemented
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	32	yes	complemented
88	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
89	C₂×C₄²×C₁₃	C₂³	1	4	yes	complemented
90	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
91	C₂×C₂²⋊Dic₁₃	C₂³	1	32	yes	complemented
92	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	complemented
93	D₄×Dic₁₃	C₂³	1	64	yes	complemented
94	C₄×C₂²⋊D₁₃	C₂³	1	128	yes	complemented
95	C₂×#6103	C₂³	1	8	yes	—
96	C₂×#6103	C₂³	1	64	yes	complemented
97	C₂×#6103	C₂³	1	16	yes	complemented
98	#88180	C₂³	1	16	yes	complemented
99	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	complemented
100	C₂×#6101	C₂³	1	8	yes	complemented
101	C₂×C₄×Dic₁₃	C₂³	1	4	yes	complemented
102	C₂×C₄×Dic₁₃	C₂³	1	8	yes	complemented
103	#88147	C₂³	1	64	yes	complemented
104	#88146	C₂³	1	32	yes	complemented
105	C₄⋊C₄×D₁₃	C₂³	1	32	yes	complemented
106	#88135	C₂³	1	128	yes	complemented
107	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	—
108	C₂²⋊C₄×D₁₃	C₂³	1	64	yes	complemented
109	C₂²⋊C₄×D₁₃	C₂³	1	64	yes	complemented
110	C₂²⋊C₄×D₁₃	C₂³	1	64	yes	complemented
111	#88131	C₂³	1	32	yes	complemented
112	C₄×D₅₂	C₂³	1	64	yes	complemented
113	#88126	C₂³	1	32	yes	complemented
114	C₄²×D₁₃	C₂³	1	32	yes	complemented
115	C₂²×#518	—	13	1	no	maximal, Sylow
116	C₂⁴×C₁₃	—	4	8	no	—
117	C₂⁴×C₁₃	C₂²×C₄	1	16	yes	complemented
118	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
120	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
121	C₂³×D₁₃	—	2	32	no	—
122	C₂³×D₁₃	—	2	8	no	—
123	C₂³×D₁₃	—	4	128	no	—
124	C₂³×D₁₃	—	4	64	no	—
125	C₂³×D₁₃	—	4	8	no	—
126	C₂³×D₁₃	—	4	16	no	—
127	C₂³×D₁₃	C₂²×C₄	1	8	yes	—
128	C₂³×D₁₃	C₂²×C₄	1	32	yes	—
129	C₂³×D₁₃	C₂²×C₄	1	128	yes	complemented
130	C₂³×D₁₃	C₂²×C₄	1	16	yes	complemented
131	C₂³×D₁₃	C₂²×C₄	1	32	yes	complemented
132	C₂³×D₁₃	C₂⁴	1	4	yes	—
133	C₂³×D₁₃	C₂⁴	1	16	yes	—
134	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
135	C₂³×D₁₃	C₂⁴	1	4	yes	—
136	C₂³×D₁₃	C₂⁴	1	8	yes	—
137	C₂³×D₁₃	C₂⁴	1	16	yes	—
138	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
139	C₂×D₄×C₁₃	C₂²×C₄	1	32	yes	complemented
140	C₂×D₄×C₁₃	C₂²×C₄	1	64	yes	complemented
141	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
142	C₂²×C₄×C₁₃	—	4	16	no	—
143	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	complemented
144	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
145	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	32	yes	complemented
148	C₂×C₂²⋊D₁₃	C₂²×C₄	1	64	yes	complemented
149	C₂×C₂²⋊D₁₃	C₂²×C₄	1	128	yes	complemented
150	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
151	C₂²×Dic₁₃	—	4	16	no	—
152	C₂²×Dic₁₃	C₂²×C₄	1	8	yes	complemented
153	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
154	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
155	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
156	C₂²×Dic₁₃	C₂⁴	1	32	yes	complemented
157	D₄×D₁₃	C₂²×C₄	1	256	yes	complemented
158	D₄×D₁₃	C₂²×C₄	1	256	yes	complemented
159	C₂×D₅₂	C₂²×C₄	1	32	yes	complemented
160	C₂×D₅₂	C₂²×C₄	1	64	yes	complemented
161	C₂×D₅₂	C₂⁴	1	16	yes	—
162	C₂×C₄×D₁₃	—	2	32	no	—
163	C₂×C₄×D₁₃	—	4	128	no	—
164	C₂×C₄×D₁₃	—	4	32	no	—
165	C₂×C₄×D₁₃	C₂²×C₄	1	16	yes	—
166	C₂×C₄×D₁₃	C₂²×C₄	1	64	yes	complemented
167	C₂×C₄×D₁₃	C₂²×C₄	1	16	yes	complemented
168	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
169	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
170	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
171	C₂×C₄×D₁₃	C₂⁴	1	64	yes	complemented
172	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	complemented
173	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
174	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	complemented
175	C₄²×C₁₃	C₂⁴	1	16	yes	complemented
176	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
177	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	complemented
178	#6103	C₂⁴	1	32	yes	—
179	#6103	C₂⁴	1	64	yes	complemented
180	C₄⋊Dic₁₃	C₂⁴	1	16	yes	complemented
181	#6101	C₂⁴	1	32	yes	complemented
182	C₄×Dic₁₃	C₂⁴	1	16	yes	complemented
183	C₄×Dic₁₃	C₂⁴	1	32	yes	complemented
184	C₂⁴×D₄	—	13	1	no	—
185	C₂×#518	—	13	1	no	—
186	C₂×#518	—	13	32	no	—
187	C₂×#518	—	13	8	no	—
188	C₂×#518	—	13	2	no	—
189	C₂×#518	—	13	4	no	—
190	C₂×#518	D₁₃	1	1	yes	characteristic, direct product factor
191	C₂²×C₄×D₄	—	13	8	no	—
192	C₂²×#117	—	13	2	no	—
193	C₂³×C₂²⋊C₄	—	13	4	no	—
194	C₂³×C₁₃	—	2	16	no	—
195	C₂³×C₁₃	—	2	4	no	—
196	C₂³×C₁₃	—	4	32	no	—
197	C₂³×C₁₃	—	4	16	no	—
198	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
199	C₂³×C₁₃	C₂³×C₄	1	16	yes	—
200	C₂³×C₁₃	C₂³×C₄	1	32	yes	complemented
201	C₂³×C₁₃	C₂⁵	1	2	yes	—
202	C₂³×C₁₃	C₂⁵	1	8	yes	—
203	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
204	C₂²×D₁₃	—	2	16	no	—
205	C₂²×D₁₃	—	2	4	no	—
206	C₂²×D₁₃	—	2	32	no	—
207	C₂²×D₁₃	—	2	128	no	—
208	C₂²×D₁₃	—	2	64	no	—
209	C₂²×D₁₃	—	2	16	no	—
210	C₂²×D₁₃	—	4	256	no	—
211	C₂²×D₁₃	—	4	64	no	—
212	C₂²×D₁₃	—	4	32	no	—
213	C₂²×D₁₃	—	4	16	no	—
214	C₂²×D₁₃	—	4	32	no	—
215	C₂²×D₁₃	C₂³×C₄	1	4	yes	—
216	C₂²×D₁₃	C₂³×C₄	1	16	yes	—
217	C₂²×D₁₃	C₂³×C₄	1	16	yes	—
218	C₂²×D₁₃	C₂³×C₄	1	64	yes	—
219	C₂²×D₁₃	C₂³×C₄	1	4	yes	—
220	C₂²×D₁₃	C₂³×C₄	1	32	yes	complemented
221	C₂²×D₁₃	C₂³×C₄	1	64	yes	complemented
222	C₂²×D₁₃	H(5,𝔽₂)	1	8	yes	—
223	C₂²×D₁₃	C₂⁵	1	2	yes	—
224	C₂²×D₁₃	C₂⁵	1	8	yes	—
225	C₂²×D₁₃	C₂⁵	1	2	yes	—
226	D₄×C₁₃	C₂³×C₄	1	64	yes	complemented
227	C₂×C₄×C₁₃	—	2	16	no	—
228	C₂×C₄×C₁₃	—	4	32	no	—
229	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
230	C₂×C₄×C₁₃	C₂³×C₄	1	16	yes	complemented
231	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
232	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
233	C₂²⋊D₁₃	C₂³×C₄	1	128	yes	complemented
234	C₂×Dic₁₃	—	2	16	no	—
235	C₂×Dic₁₃	—	4	32	no	—
236	C₂×Dic₁₃	C₂³×C₄	1	8	yes	—
237	C₂×Dic₁₃	C₂³×C₄	1	16	yes	complemented
238	C₂×Dic₁₃	C₂⁵	1	16	yes	—
239	C₂×Dic₁₃	C₂⁵	1	4	yes	—
240	D₅₂	C₂³×C₄	1	64	yes	complemented
241	C₄×D₁₃	—	2	64	no	—
242	C₄×D₁₃	—	4	64	no	—
243	C₄×D₁₃	C₂³×C₄	1	32	yes	—
244	C₄×D₁₃	C₂³×C₄	1	32	yes	complemented
245	C₂⁶	—	13	2	no	—
246	C₂³×D₄	—	13	2	no	—
247	C₂³×D₄	—	13	32	no	—
248	C₂³×D₄	—	13	4	no	—
249	C₂³×D₄	—	13	4	no	—
250	C₂³×D₄	—	13	16	no	—
251	C₂³×D₄	—	13	1	no	—
252	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
253	C₂⁴×C₄	—	13	1	no	—
254	C₂⁴×C₄	—	13	8	no	—
255	#518	—	13	16	no	—
256	#518	—	13	128	no	—
257	#518	—	13	32	no	—
258	#518	—	13	64	no	—
259	#518	C₂×D₁₃	1	16	yes	direct product factor
260	C₂×C₄×D₄	—	13	8	no	—
261	C₂×C₄×D₄	—	13	16	no	—
262	C₂×C₄×D₄	—	13	128	no	—
263	C₂×C₄×D₄	—	13	8	no	—
264	C₂×C₄×D₄	—	13	16	no	—
265	C₂×C₄×D₄	—	13	8	no	—
266	C₂×C₄×D₄	C₂×D₁₃	1	8	yes	complemented
267	C₂×#117	—	13	2	no	—
268	C₂×#117	—	13	32	no	—
269	C₂×#117	—	13	4	no	—
270	C₂×#117	—	13	4	no	—
271	C₂×#117	—	13	4	no	—
272	C₂×#117	C₂×D₁₃	1	2	yes	complemented
273	C₂²×C₄⋊C₄	—	13	4	no	—
274	C₂²×C₂²⋊C₄	—	13	4	no	—
275	C₂²×C₂²⋊C₄	—	13	8	no	—
276	C₂²×C₂²⋊C₄	—	13	4	no	—
277	C₂²×C₂²⋊C₄	—	13	8	no	—
278	C₂²×C₂²⋊C₄	—	13	8	no	—
279	C₂²×C₂²⋊C₄	—	13	8	no	—
280	C₂²×C₂²⋊C₄	—	13	64	no	—
281	C₂²×C₂²⋊C₄	C₂×D₁₃	1	4	yes	complemented
282	C₂²×C₄²	—	13	4	no	—
283	C₂²×C₁₃	—	2	16	no	—
284	C₂²×C₁₃	—	2	4	no	—
285	C₂²×C₁₃	—	2	8	no	—
286	C₂²×C₁₃	—	2	32	no	—
287	C₂²×C₁₃	—	4	32	no	—
288	C₂²×C₁₃	C₂⁴×C₄	1	4	yes	—
289	C₂²×C₁₃	C₂⁴×C₄	1	16	yes	—
290	C₂²×C₁₃	C₂⁴×C₄	1	2	yes	—
291	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
292	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
293	C₂×D₁₃	—	2	16	no	—
294	C₂×D₁₃	—	2	4	no	—
295	C₂×D₁₃	—	2	8	no	—
296	C₂×D₁₃	—	2	32	no	—
297	C₂×D₁₃	—	2	32	no	—
298	C₂×D₁₃	—	2	128	no	—
299	C₂×D₁₃	—	4	64	no	—
300	C₂×D₁₃	—	4	32	no	—
301	C₂×D₁₃	#518	1	16	yes	direct product factor
302	C₂×D₁₃	C₂⁴×C₄	1	4	yes	—
303	C₂×D₁₃	C₂⁴×C₄	1	16	yes	—
304	C₂×D₁₃	C₂⁴×C₄	1	4	yes	—
305	C₂×D₁₃	C₂×H(5,𝔽₂)	1	8	yes	—
306	C₄×C₁₃	—	2	16	no	—
307	C₄×C₁₃	C₂⁴×C₄	1	8	yes	—
308	Dic₁₃	—	2	16	no	—
309	Dic₁₃	C₂⁴×C₄	1	8	yes	—
310	C₂⁵	—	13	1	no	—
311	C₂⁵	—	13	4	no	—
312	C₂⁵	—	13	32	no	—
313	C₂⁵	—	13	16	no	—
314	C₂⁵	—	13	4	no	—
315	C₂⁵	—	13	2	no	—
316	C₂⁵	—	52	16	no	—
317	C₂⁵	C₂²×D₁₃	1	2	yes	—
318	C₂²×D₄	—	13	32	no	—
319	C₂²×D₄	—	13	8	no	—
320	C₂²×D₄	—	13	16	no	—
321	C₂²×D₄	—	13	64	no	—
322	C₂²×D₄	—	13	64	no	—
323	C₂²×D₄	—	13	256	no	—
324	C₂²×D₄	—	13	32	no	—
325	C₂²×D₄	—	13	32	no	—
326	C₂²×D₄	—	13	16	no	—
327	C₂²×D₄	—	13	4	no	—
328	C₂²×D₄	—	13	8	no	—
329	C₂²×D₄	C₄×D₁₃	1	16	yes	complemented
330	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
331	C₂²×D₄	C₂²×D₁₃	1	8	yes	—
332	C₂³×C₄	—	13	1	no	—
333	C₂³×C₄	—	13	16	no	—
334	C₂³×C₄	—	13	2	no	—
335	C₂³×C₄	—	13	8	no	—
336	C₂³×C₄	—	13	2	no	—
337	C₂³×C₄	—	13	8	no	—
338	C₂³×C₄	—	13	8	no	—
339	C₂³×C₄	—	13	16	no	—
340	C₂³×C₄	—	13	64	no	—
341	C₂³×C₄	—	52	32	no	—
342	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
343	C₂³×C₄	C₂²×D₁₃	1	8	yes	complemented
344	C₄×D₄	—	13	64	no	—
345	C₄×D₄	—	13	128	no	—
346	C₄×D₄	—	13	64	no	—
347	C₄×D₄	—	13	128	no	—
348	C₄×D₄	—	13	64	no	—
349	C₄×D₄	C₂²×D₁₃	1	64	yes	complemented
350	#117	—	13	16	no	—
351	#117	—	13	32	no	—
352	#117	—	13	32	no	—
353	#117	—	13	32	no	—
354	#117	C₂²×D₁₃	1	16	yes	complemented
355	C₂×C₄⋊C₄	—	13	8	no	—
356	C₂×C₄⋊C₄	—	13	4	no	—
357	C₂×C₄⋊C₄	—	13	32	no	—
358	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	complemented
359	C₂×C₂²⋊C₄	—	13	4	no	—
360	C₂×C₂²⋊C₄	—	13	8	no	—
361	C₂×C₂²⋊C₄	—	13	32	no	—
362	C₂×C₂²⋊C₄	—	13	8	no	—
363	C₂×C₂²⋊C₄	—	13	16	no	—
364	C₂×C₂²⋊C₄	—	13	64	no	—
365	C₂×C₂²⋊C₄	—	13	32	no	—
366	C₂×C₂²⋊C₄	—	13	64	no	—
367	C₂×C₂²⋊C₄	—	13	64	no	—
368	C₂×C₂²⋊C₄	—	13	64	no	—
369	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
370	C₂×C₂²⋊C₄	C₂²×D₁₃	1	32	yes	complemented
371	C₂×C₂²⋊C₄	C₂²×D₁₃	1	8	yes	complemented
372	C₂×C₄²	—	13	8	no	—
373	C₂×C₄²	—	13	4	no	—
374	C₂×C₄²	—	13	32	no	—
375	C₂×C₄²	C₂²×D₁₃	1	4	yes	complemented
376	C₂×C₁₃	—	2	4	no	—
377	C₂×C₁₃	—	2	16	no	—
378	C₂×C₁₃	C₂×#518	1	4	yes	complemented
379	C₂×C₁₃	C₂⁵×C₄	1	1	yes	characteristic
380	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
381	D₁₃	—	2	4	no	—
382	D₁₃	—	2	16	no	—
383	D₁₃	C₂×#518	1	8	yes	direct product factor
384	C₂⁴	—	4	8	no	—
385	C₂⁴	—	13	1	no	—
386	C₂⁴	—	13	8	no	—
387	C₂⁴	—	13	32	no	—
388	C₂⁴	—	13	4	no	—
389	C₂⁴	—	13	16	no	—
390	C₂⁴	—	13	1	no	—
391	C₂⁴	—	13	4	no	—
392	C₂⁴	—	13	32	no	—
393	C₂⁴	—	13	16	no	—
394	C₂⁴	—	13	128	no	—
395	C₂⁴	—	13	16	no	—
396	C₂⁴	—	13	8	no	—
397	C₂⁴	—	26	32	no	—
398	C₂⁴	—	26	8	no	—
399	C₂⁴	—	52	16	no	—
400	C₂⁴	—	52	8	no	—
401	C₂⁴	—	52	128	no	—
402	C₂⁴	—	52	64	no	—
403	C₂⁴	C₂×C₄×D₁₃	1	16	yes	complemented
404	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
405	C₂⁴	C₂³×D₁₃	1	4	yes	—
406	C₂⁴	C₂³×D₁₃	1	8	yes	—
407	C₂×D₄	—	13	64	no	—
408	C₂×D₄	—	13	128	no	—
409	C₂×D₄	—	13	32	no	—
410	C₂×D₄	—	13	256	no	—
411	C₂×D₄	—	13	256	no	—
412	C₂×D₄	—	13	32	no	—
413	C₂×D₄	—	13	64	no	—
414	C₂×D₄	—	13	16	no	—
415	C₂×D₄	C₂×C₄×D₁₃	1	32	yes	complemented
416	C₂×D₄	C₂×C₄×D₁₃	1	64	yes	complemented
417	C₂×D₄	C₂³×D₁₃	1	16	yes	—
418	C₂²×C₄	—	4	16	no	—
419	C₂²×C₄	—	13	8	no	—
420	C₂²×C₄	—	13	4	no	—
421	C₂²×C₄	—	13	2	no	—
422	C₂²×C₄	—	13	16	no	—
423	C₂²×C₄	—	13	16	no	—
424	C₂²×C₄	—	13	64	no	—
425	C₂²×C₄	—	13	8	no	—
426	C₂²×C₄	—	13	8	no	—
427	C₂²×C₄	—	13	8	no	—
428	C₂²×C₄	—	13	32	no	—
429	C₂²×C₄	—	13	32	no	—
430	C₂²×C₄	—	13	64	no	—
431	C₂²×C₄	—	26	32	no	—
432	C₂²×C₄	—	52	32	no	—
433	C₂²×C₄	—	52	128	no	—
434	C₂²×C₄	—	52	16	no	—
435	C₂²×C₄	C₂×C₄×D₁₃	1	8	yes	complemented
436	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
437	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
438	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
439	C₂²×C₄	C₂³×D₁₃	1	32	yes	complemented
440	C₄⋊C₄	—	13	32	no	—
441	C₄⋊C₄	—	13	16	no	—
442	C₄⋊C₄	C₂³×D₁₃	1	16	yes	complemented
443	C₂²⋊C₄	—	13	16	no	—
444	C₂²⋊C₄	—	13	32	no	—
445	C₂²⋊C₄	—	13	32	no	—
446	C₂²⋊C₄	—	13	64	no	—
447	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
448	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	complemented
449	C₄²	—	13	32	no	—
450	C₄²	—	13	16	no	—
451	C₄²	C₂³×D₁₃	1	16	yes	complemented
452	C₁₃	C₂²×#518	1	1	yes	characteristic, complemented, Sylow
453	C₂³	—	2	16	no	—
454	C₂³	—	2	4	no	—
455	C₂³	—	4	32	no	—
456	C₂³	—	4	16	no	—
457	C₂³	—	13	4	no	—
458	C₂³	—	13	8	no	—
459	C₂³	—	13	2	no	—
460	C₂³	—	13	16	no	—
461	C₂³	—	13	4	no	—
462	C₂³	—	13	64	no	—
463	C₂³	—	13	16	no	—
464	C₂³	—	13	2	no	—
465	C₂³	—	13	8	no	—
466	C₂³	—	13	64	no	—
467	C₂³	—	13	32	no	—
468	C₂³	—	26	64	no	—
469	C₂³	—	26	32	no	—
470	C₂³	—	26	16	no	—
471	C₂³	—	26	128	no	—
472	C₂³	—	26	16	no	—
473	C₂³	—	26	4	no	—
474	C₂³	—	52	32	no	—
475	C₂³	—	52	64	no	—
476	C₂³	—	52	32	no	—
477	C₂³	—	52	16	no	—
478	C₂³	—	52	256	no	—
479	C₂³	C₂²×C₄×D₁₃	1	4	yes	—
480	C₂³	C₂²×C₄×D₁₃	1	16	yes	—
481	C₂³	C₂²×C₄×D₁₃	1	32	yes	complemented
482	C₂³	C₂⁴×D₁₃	1	2	yes	—
483	C₂³	C₂⁴×D₁₃	1	8	yes	—
484	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
485	D₄	—	13	128	no	—
486	D₄	—	13	64	no	—
487	D₄	C₂²×C₄×D₁₃	1	64	yes	complemented
488	C₂×C₄	—	2	16	no	—
489	C₂×C₄	—	4	32	no	—
490	C₂×C₄	—	13	8	no	—
491	C₂×C₄	—	13	16	no	—
492	C₂×C₄	—	13	4	no	—
493	C₂×C₄	—	13	32	no	—
494	C₂×C₄	—	13	32	no	—
495	C₂×C₄	—	13	16	no	—
496	C₂×C₄	—	26	64	no	—
497	C₂×C₄	—	26	16	no	—
498	C₂×C₄	—	52	64	no	—
499	C₂×C₄	—	52	32	no	—
500	C₂×C₄	C₂²×C₄×D₁₃	1	8	yes	—
501	C₂×C₄	C₂²×C₄×D₁₃	1	16	yes	complemented
502	C₂×C₄	C₂⁴×D₁₃	1	16	yes	—
503	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
504	C₂²	—	2	8	no	—
505	C₂²	—	2	32	no	—
506	C₂²	—	2	16	no	—
507	C₂²	—	2	4	no	—
508	C₂²	—	4	32	no	—
509	C₂²	—	13	16	no	—
510	C₂²	—	13	4	no	—
511	C₂²	—	13	8	no	—
512	C₂²	—	13	4	no	—
513	C₂²	—	13	16	no	—
514	C₂²	—	26	128	no	—
515	C₂²	—	26	32	no	—
516	C₂²	—	26	32	no	—
517	C₂²	—	26	8	no	—
518	C₂²	—	26	16	no	—
519	C₂²	—	26	4	no	—
520	C₂²	—	52	32	no	—
521	C₂²	—	52	64	no	—
522	C₂²	C₂³×C₄×D₁₃	1	4	yes	—
523	C₂²	C₂³×C₄×D₁₃	1	16	yes	—
524	C₂²	C₂³×C₄×D₁₃	1	2	yes	—
525	C₂²	D₁₃×H(5,𝔽₂)	1	4	yes	—
526	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
527	C₄	—	2	16	no	—
528	C₄	—	13	8	no	—
529	C₄	—	26	16	no	—
530	C₄	C₂³×C₄×D₁₃	1	8	yes	—
531	C₂	—	2	4	no	—
532	C₂	—	2	16	no	—
533	C₂	—	13	8	no	—
534	C₂	—	26	4	no	—
535	C₂	—	26	16	no	—
536	C₂	D₁₃×#518	1	4	yes	direct product factor
537	C₂	C₂⁴×C₄×D₁₃	1	1	yes	characteristic
538	C₂	C₂×D₁₃×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator	C₂×C₁₃	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₁₃×#518	C₂
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂³×D₄×D₁₃	C₂
cosocle	C₂²×C₁₃	C₂⁶
hypercenter	C₂×#518	D₁₃
hypocenter	C₁₃	C₂²×#518
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#518

Complements

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

N	H ≅ G/N	type
2. C₂×#11719503	C₂	semidirect
3. C₂×#11719226	C₂	semidirect
4. C₂×#11719191	C₂	semidirect
5. C₂×#11719250	C₂	semidirect
6. D₁₃×#518	C₂	direct (N × H)
7. C₂×C₄×D₄×D₁₃	C₂	semidirect
8. C₂×D₁₃×#117	C₂	semidirect
9. C₂²×C₂²⋊C₄×D₁₃	C₂	semidirect
10. C₂×C₁₃×#518	C₂	semidirect
14. C₂²×D₄×D₁₃	C₄	semidirect
20. C₂³×C₄×D₁₃	C₂²	semidirect
21. C₁₃×#518	C₂²	semidirect
22. C₂×C₄×D₄×C₁₃	C₂²	semidirect
23. C₂×C₁₃×#117	C₂²	semidirect
24. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
25. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
26. #11719503	C₂²	semidirect
27. C₂×D₄×Dic₁₃	C₂²	semidirect
28. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
29. C₂²×#6103	C₂²	semidirect
30. C₂×#88180	C₂²	semidirect
31. #11719250	C₂²	semidirect
32. C₄×D₄×D₁₃	C₂²	semidirect
33. #11719226	C₂²	semidirect
34. D₁₃×#117	C₂²	semidirect
35. C₂×#88147	C₂²	semidirect
36. C₂×#88146	C₂²	semidirect
37. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
38. #11719191	C₂²	semidirect
39. C₂×#88135	C₂²	semidirect
41. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
42. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
43. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
44. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
45. C₂×#88131	C₂²	semidirect
46. C₂×C₄×D₅₂	C₂²	semidirect
47. C₂×#88126	C₂²	semidirect
48. C₂×C₄²×D₁₃	C₂²	semidirect
51. C₂⁴×D₁₃	C₂×C₄	semidirect
57. C₂²×D₄×C₁₃	C₂×C₄	semidirect
61. C₂³×C₄×C₁₃	C₂³	semidirect
62. C₂²×C₂²⋊D₁₃	C₂×C₄	semidirect
66. C₂³×Dic₁₃	C₂³	semidirect
67. C₂×D₄×D₁₃	C₂×C₄	semidirect
68. C₂×D₄×D₁₃	C₂×C₄	semidirect
69. C₂×D₄×D₁₃	C₂×C₄	semidirect
72. C₂²×D₅₂	C₂×C₄	semidirect
76. C₂²×C₄×D₁₃	C₂×C₄	semidirect
81. C₂²×C₄×D₁₃	C₂³	semidirect
82. C₂²×C₄×D₁₃	C₂³	semidirect
83. C₄×D₄×C₁₃	C₂³	semidirect
84. C₁₃×#117	C₂³	semidirect
85. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
87. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
88. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
89. C₂×C₄²×C₁₃	C₂³	semidirect
91. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
92. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
93. D₄×Dic₁₃	C₂³	semidirect
94. C₄×C₂²⋊D₁₃	C₂³	semidirect
96. C₂×#6103	C₂³	semidirect
97. C₂×#6103	C₂³	semidirect
98. #88180	C₂³	semidirect
99. C₂×C₄⋊Dic₁₃	C₂³	semidirect
100. C₂×#6101	C₂³	semidirect
101. C₂×C₄×Dic₁₃	C₂³	semidirect
102. C₂×C₄×Dic₁₃	C₂³	semidirect
103. #88147	C₂³	semidirect
104. #88146	C₂³	semidirect
105. C₄⋊C₄×D₁₃	C₂³	semidirect
106. #88135	C₂³	semidirect
108. C₂²⋊C₄×D₁₃	C₂³	semidirect
109. C₂²⋊C₄×D₁₃	C₂³	semidirect
110. C₂²⋊C₄×D₁₃	C₂³	semidirect
111. #88131	C₂³	semidirect
112. C₄×D₅₂	C₂³	semidirect
113. #88126	C₂³	semidirect
114. C₄²×D₁₃	C₂³	semidirect
117. C₂⁴×C₁₃	C₂²×C₄	semidirect
129. C₂³×D₁₃	C₂²×C₄	semidirect
130. C₂³×D₁₃	C₂²×C₄	semidirect
131. C₂³×D₁₃	C₂²×C₄	semidirect
139. C₂×D₄×C₁₃	C₂²×C₄	semidirect
140. C₂×D₄×C₁₃	C₂²×C₄	semidirect
143. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
147. C₂²×C₄×C₁₃	C₂⁴	semidirect
148. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
149. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
152. C₂²×Dic₁₃	C₂²×C₄	semidirect
156. C₂²×Dic₁₃	C₂⁴	semidirect
157. D₄×D₁₃	C₂²×C₄	semidirect
158. D₄×D₁₃	C₂²×C₄	semidirect
159. C₂×D₅₂	C₂²×C₄	semidirect
160. C₂×D₅₂	C₂²×C₄	semidirect
166. C₂×C₄×D₁₃	C₂²×C₄	semidirect
167. C₂×C₄×D₁₃	C₂²×C₄	semidirect
171. C₂×C₄×D₁₃	C₂⁴	semidirect
172. C₁₃×C₄⋊C₄	C₂⁴	semidirect
174. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
175. C₄²×C₁₃	C₂⁴	semidirect
177. C₂²⋊Dic₁₃	C₂⁴	semidirect
179. #6103	C₂⁴	semidirect
180. C₄⋊Dic₁₃	C₂⁴	semidirect
181. #6101	C₂⁴	semidirect
182. C₄×Dic₁₃	C₂⁴	semidirect
183. C₄×Dic₁₃	C₂⁴	semidirect
190. C₂×#518	D₁₃	direct (N × H)
200. C₂³×C₁₃	C₂³×C₄	semidirect
220. C₂²×D₁₃	C₂³×C₄	semidirect
221. C₂²×D₁₃	C₂³×C₄	semidirect
226. D₄×C₁₃	C₂³×C₄	semidirect
230. C₂×C₄×C₁₃	C₂³×C₄	semidirect
233. C₂²⋊D₁₃	C₂³×C₄	semidirect
237. C₂×Dic₁₃	C₂³×C₄	semidirect
240. D₅₂	C₂³×C₄	semidirect
244. C₄×D₁₃	C₂³×C₄	semidirect
259. #518	C₂×D₁₃	direct (N × H)
266. C₂×C₄×D₄	C₂×D₁₃	semidirect
272. C₂×#117	C₂×D₁₃	semidirect
281. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
301. C₂×D₁₃	#518	direct (N × H)
329. C₂²×D₄	C₄×D₁₃	semidirect
343. C₂³×C₄	C₂²×D₁₃	semidirect
349. C₄×D₄	C₂²×D₁₃	semidirect
354. #117	C₂²×D₁₃	semidirect
358. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
370. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
371. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
375. C₂×C₄²	C₂²×D₁₃	semidirect
378. C₂×C₁₃	C₂×#518	semidirect
383. D₁₃	C₂×#518	direct (N × H)
403. C₂⁴	C₂×C₄×D₁₃	semidirect
415. C₂×D₄	C₂×C₄×D₁₃	semidirect
416. C₂×D₄	C₂×C₄×D₁₃	semidirect
435. C₂²×C₄	C₂×C₄×D₁₃	semidirect
439. C₂²×C₄	C₂³×D₁₃	semidirect
442. C₄⋊C₄	C₂³×D₁₃	semidirect
448. C₂²⋊C₄	C₂³×D₁₃	semidirect
451. C₄²	C₂³×D₁₃	semidirect
452. C₁₃	C₂²×#518	semidirect
481. C₂³	C₂²×C₄×D₁₃	semidirect
487. D₄	C₂²×C₄×D₁₃	semidirect
501. C₂×C₄	C₂²×C₄×D₁₃	semidirect
536. C₂	D₁₃×#518	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₄×D₁₃	2
C₂×#11719503	2
C₂×#11719226	2
C₂×#11719191	2
C₂×#11719250	2
D₁₃×#518	2
C₂×C₄×D₄×D₁₃	2
C₂×D₁₃×#117	2
C₂²×C₂²⋊C₄×D₁₃	2
C₂×C₁₃×#518	2
C₂²×#518	13

Subgroups — C2×D13×#518 #16769496

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃×#518 #16769496