Subgroups — D₁₃⋊#2168 #16807125

Order 3328.

754 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃⋊M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₁₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#13131219	C₂	1	2	yes	maximal, complemented
4	#13131218	C₂	1	2	yes	maximal, complemented
5	#13131217	C₂	1	2	yes	maximal, complemented
6	#13131216	C₂	1	2	yes	maximal, complemented
7	D₁₃⋊(C₄⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
8	D₁₃⋊(C₂²⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
9	D₁₃⋊(C₂²⋊C₁₆)	C₂	1	1	yes	maximal, characteristic, complemented
10	#13131037	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
14	C₄×D₄×D₁₃	C₄	1	1	yes	characteristic
15	C₂×#88106	C₂²	1	2	yes	complemented
16	C₂²×#6092	C₂²	1	2	yes	complemented
17	D₁₃⋊M₃₂	—	2	4	no	—
18	C₂×#88098	C₂²	1	2	yes	complemented
19	C₂×D₁₃⋊C₁₆	—	2	4	no	—
20	C₂×D₁₃⋊C₁₆	C₂²	1	1	yes	characteristic
21	C₂×D₁₃⋊C₁₆	C₂²	1	1	yes	characteristic
22	C₂×D₁₃⋊C₁₆	C₂²	1	1	yes	characteristic
23	C₂×D₁₃⋊C₁₆	C₂²	1	1	yes	characteristic
24	C₂×D₁₃⋊C₁₆	C₂²	1	2	yes	complemented
25	C₈×D₄×C₁₃	C₄	1	1	yes	characteristic
26	C₈×C₂²⋊D₁₃	C₄	1	1	yes	characteristic
27	C₈×C₂²⋊D₁₃	C₄	1	1	yes	characteristic
28	D₄×#1055	C₂²	1	1	yes	characteristic
29	#11718495	C₂²	1	1	yes	characteristic
30	D₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic
31	#11718386	C₂²	1	1	yes	characteristic
32	#11718386	C₂²	1	1	yes	characteristic
33	D₁₃×C₂²⋊C₈	C₄	1	1	yes	characteristic
34	D₁₃×C₂²⋊C₈	C₄	1	1	yes	characteristic
35	C₈×D₅₂	C₄	1	1	yes	characteristic
36	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
37	C₂²⋊#6092	C₂²	1	2	yes	complemented
38	C₂²⋊#6092	C₂²	1	2	yes	complemented
39	#11718260	C₂²	1	2	yes	complemented
40	#11718259	C₂²	1	2	yes	complemented
41	#11718259	C₂²	1	2	yes	complemented
42	#11718258	C₂²	1	2	yes	complemented
43	#11718231	C₂²	1	2	yes	complemented
44	C₄⋊#6092	C₂²	1	2	yes	complemented
45	C₂×D₄×D₁₃	C₈	1	1	yes	characteristic
46	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
50	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
51	D₄×Dic₁₃	C₈	1	1	yes	characteristic
52	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
53	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂²×#1055	C₂³	1	1	yes	characteristic
55	C₂²×#1055	C₂³	1	1	yes	characteristic
56	C₂×C₈×D₁₃	—	2	2	no	—
57	C₂×C₈×D₁₃	—	2	2	no	—
58	C₂×C₈×D₁₃	—	2	2	no	—
59	C₂×C₈×D₁₃	—	2	2	no	—
60	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
68	#88147	C₈	1	1	yes	characteristic
69	C₄⋊C₄×D₁₃	C₈	1	1	yes	characteristic
70	#88135	C₈	1	1	yes	characteristic
71	#88135	C₈	1	1	yes	characteristic
72	C₂²⋊C₄×D₁₃	C₈	1	1	yes	characteristic
73	C₂²⋊C₄×D₁₃	C₈	1	1	yes	characteristic
74	C₄×D₅₂	C₂×C₄	1	1	yes	characteristic
75	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
76	#88106	—	2	4	no	—
77	C₂×#6092	—	2	4	no	—
78	C₂×#6092	C₂³	1	2	yes	—
79	C₂×#6092	C₂³	1	2	yes	—
80	C₂×#6092	C₂³	1	2	yes	—
81	C₂×#6092	C₂³	1	2	yes	—
82	#88098	—	2	4	no	—
83	D₁₃⋊C₁₆	—	2	2	no	—
84	D₁₃⋊C₁₆	—	2	2	no	—
85	D₁₃⋊C₁₆	—	2	2	no	—
86	D₁₃⋊C₁₆	—	2	4	no	—
87	D₁₃⋊C₁₆	D₄	1	4	yes	complemented
88	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
89	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
90	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
92	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
94	#88060	C₂×C₄	1	1	yes	characteristic
95	#88060	C₂×C₄	1	1	yes	characteristic
96	#88060	C₂×C₄	1	1	yes	characteristic
97	#88060	C₂×C₄	1	1	yes	characteristic
98	#88054	C₂×C₄	1	1	yes	characteristic
99	#88054	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
101	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
102	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
103	C₄×#1055	C₂³	1	1	yes	characteristic
104	C₂×#2168	—	13	1	no	maximal, Sylow
105	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
106	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
107	C₂×D₄×C₁₃	C₂×C₈	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
111	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
112	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
113	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
114	D₄×D₁₃	—	2	4	no	—
115	C₂×D₅₂	C₂×C₈	1	1	yes	characteristic
116	C₂×C₄×D₁₃	—	2	2	no	—
117	C₂×C₄×D₁₃	—	2	2	no	—
118	C₂×C₄×D₁₃	—	2	2	no	—
119	C₂×C₄×D₁₃	—	2	2	no	—
120	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
121	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
122	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
123	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
124	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
125	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
126	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
136	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
137	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
138	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
140	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
141	#6103	C₂×C₈	1	1	yes	characteristic
142	#6103	C₂×C₈	1	1	yes	characteristic
143	#6103	C₂×C₈	1	1	yes	characteristic
144	#6103	C₂×C₈	1	1	yes	characteristic
145	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
146	#6101	C₂×C₈	1	1	yes	characteristic
147	#6101	C₂×C₈	1	1	yes	characteristic
148	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
149	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
150	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₂×#1055	—	2	1	no	—
152	C₂×#1055	—	2	1	no	—
153	C₂×#1055	—	2	1	no	—
154	C₂×#1055	—	2	1	no	—
155	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
156	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
157	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
158	C₂×#1055	C₂⁴	1	1	yes	characteristic
159	C₈×D₁₃	—	2	2	no	—
160	C₈×D₁₃	—	2	2	no	—
161	C₈×D₁₃	—	2	2	no	—
162	C₈×D₁₃	—	2	2	no	—
163	C₈×D₁₃	—	2	2	no	—
164	C₈×D₁₃	—	2	1	no	—
165	C₈×D₁₃	—	2	1	no	—
166	C₈×D₁₃	—	2	1	no	—
167	C₈×D₁₃	—	2	1	no	—
168	C₈×D₁₃	C₂×D₄	1	2	yes	—
169	C₈×D₁₃	#41	1	2	yes	—
170	#6092	—	2	2	no	—
171	#6092	—	2	2	no	—
172	#6092	—	2	2	no	—
173	#6092	C₂×D₄	1	4	yes	complemented
174	C₂²×M₃₂	—	13	1	no	—
175	C₂³×C₁₆	—	13	1	no	—
176	C₂×C₈×D₄	—	13	1	no	—
177	#2168	—	13	2	no	—
178	#2168	—	13	2	no	—
179	#2168	—	13	2	no	—
180	#2168	—	13	2	no	—
181	C₂×C₄⋊C₁₆	—	13	1	no	—
182	C₂×C₂²⋊C₁₆	—	13	1	no	—
183	C₂×C₂²⋊C₁₆	—	13	1	no	—
184	C₂×#346	—	13	1	no	—
185	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
186	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
187	C₂²×D₁₃	—	2	2	no	—
188	C₂²×D₁₃	—	2	2	no	—
189	C₂²×D₁₃	—	2	2	no	—
190	C₂²×D₁₃	—	2	2	no	—
191	C₂²×D₁₃	—	2	2	no	—
192	C₂²×D₁₃	M₃₂	1	4	yes	complemented
193	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
194	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
195	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
196	D₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	1	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	C₂²×C₈	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
206	C₂²⋊D₁₃	—	2	2	no	—
207	C₂²⋊D₁₃	—	2	2	no	—
208	C₂×Dic₁₃	—	2	2	no	—
209	C₂×Dic₁₃	—	2	2	no	—
210	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
211	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
212	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
213	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
214	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
215	D₅₂	—	2	2	no	—
216	C₄×D₁₃	—	2	2	no	—
217	C₄×D₁₃	—	2	2	no	—
218	C₄×D₁₃	—	2	2	no	—
219	C₄×D₁₃	—	2	2	no	—
220	C₄×D₁₃	—	2	1	no	—
221	C₄×D₁₃	—	2	1	no	—
222	C₄×D₁₃	—	2	1	no	—
223	C₄×D₁₃	—	2	1	no	—
224	C₄×D₁₃	—	2	2	no	—
225	C₄×D₁₃	—	2	2	no	—
226	C₄×D₁₃	C₄×D₄	1	2	yes	—
227	C₄×D₁₃	#131	1	2	yes	—
228	C₈×C₁₃	—	2	1	no	—
229	C₈×C₁₃	—	2	1	no	—
230	C₈×C₁₃	—	2	1	no	—
231	C₈×C₁₃	C₄×D₄	1	2	yes	—
232	#1055	—	2	1	no	—
233	#1055	—	2	1	no	—
234	#1055	—	2	1	no	—
235	#1055	C₂²×D₄	1	1	yes	characteristic
236	#1055	C₂×#41	1	1	yes	characteristic
237	C₂³×C₈	—	13	1	no	—
238	C₂³×C₈	—	13	1	no	—
239	C₂×C₄×D₄	—	13	1	no	—
240	C₂×M₃₂	—	13	2	no	—
241	C₂×M₃₂	—	13	2	no	—
242	C₂×M₃₂	—	26	4	no	—
243	C₂²×C₁₆	—	13	1	no	—
244	C₂²×C₁₆	—	13	1	no	—
245	C₂²×C₁₆	—	13	1	no	—
246	C₂²×C₁₆	—	13	1	no	—
247	C₂²×C₁₆	—	13	2	no	—
248	C₂²×C₁₆	—	13	2	no	—
249	C₂²×C₁₆	—	26	4	no	—
250	C₈×D₄	—	13	1	no	—
251	C₈×D₄	—	13	1	no	—
252	C₈×D₄	—	13	1	no	—
253	C₈×D₄	—	13	1	no	—
254	C₈×D₄	—	13	1	no	—
255	C₈×D₄	—	13	1	no	—
256	C₈×D₄	—	13	1	no	—
257	C₈×D₄	#261	1	1	yes	characteristic
258	C₂×C₄⋊C₈	—	13	1	no	—
259	C₂×C₂²⋊C₈	—	13	1	no	—
260	C₂×C₂²⋊C₈	—	13	1	no	—
261	C₂×C₄×C₈	—	13	1	no	—
262	C₄⋊C₁₆	—	13	2	no	—
263	C₄⋊C₁₆	—	13	2	no	—
264	C₂²⋊C₁₆	—	13	2	no	—
265	C₂²⋊C₁₆	—	13	2	no	—
266	C₂²⋊C₁₆	—	13	2	no	—
267	C₂²⋊C₁₆	—	13	2	no	—
268	#346	—	13	2	no	—
269	#346	—	13	2	no	—
270	C₂²×C₁₃	—	2	1	no	—
271	C₂²×C₁₃	—	2	1	no	—
272	C₂²×C₁₃	—	2	1	no	—
273	C₂²×C₁₃	—	2	1	no	—
274	C₂²×C₁₃	—	2	1	no	—
275	C₂²×C₁₃	C₂×M₃₂	1	2	yes	complemented
276	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
277	C₂×D₁₃	—	2	1	no	—
278	C₂×D₁₃	—	2	1	no	—
279	C₂×D₁₃	—	2	8	no	—
280	C₂×D₁₃	—	2	1	no	—
281	C₂×D₁₃	—	2	1	no	—
282	C₂×D₁₃	—	2	1	no	—
283	C₂×D₁₃	—	4	4	no	—
284	C₂×D₁₃	C₈×D₄	1	2	yes	—
285	C₂×D₁₃	C₂×M₃₂	1	2	yes	—
286	C₂×D₁₃	C₂×M₃₂	1	2	yes	complemented
287	C₂×D₁₃	#504	1	2	yes	—
288	C₄×C₁₃	—	2	1	no	—
289	C₄×C₁₃	—	2	1	no	—
290	C₄×C₁₃	—	2	1	no	—
291	C₄×C₁₃	—	2	1	no	—
292	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
293	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
294	Dic₁₃	—	2	1	no	—
295	Dic₁₃	—	2	1	no	—
296	Dic₁₃	—	2	1	no	—
297	Dic₁₃	—	2	1	no	—
298	Dic₁₃	C₈×D₄	1	2	yes	—
299	C₂²×D₄	—	13	1	no	—
300	C₂³×C₄	—	13	1	no	—
301	C₂³×C₄	—	13	1	no	—
302	C₂²×C₈	—	13	1	no	—
303	C₂²×C₈	—	13	1	no	—
304	C₂²×C₈	—	13	1	no	—
305	C₂²×C₈	—	13	1	no	—
306	C₂²×C₈	—	13	1	no	—
307	C₂²×C₈	—	13	1	no	—
308	C₂²×C₈	—	13	1	no	—
309	C₂²×C₈	—	13	1	no	—
310	C₂²×C₈	—	13	1	no	—
311	C₂²×C₈	—	13	1	no	—
312	C₂²×C₈	—	26	2	no	—
313	C₂²×C₈	—	26	2	no	—
314	C₂²×C₈	—	26	2	no	—
315	C₂²×C₈	—	26	2	no	—
316	C₂²×C₈	C₂×#261	1	1	yes	characteristic
317	C₂²×C₈	C₂×#261	1	1	yes	characteristic
318	C₄×D₄	—	13	1	no	—
319	C₄×D₄	—	13	1	no	—
320	C₄×D₄	—	13	1	no	—
321	C₄×D₄	—	13	1	no	—
322	C₄×D₄	—	13	1	no	—
323	C₄×D₄	—	13	1	no	—
324	C₄×D₄	—	13	1	no	—
325	C₄×D₄	C₂×#261	1	1	yes	characteristic
326	C₂×C₄⋊C₄	—	13	1	no	—
327	C₂×C₂²⋊C₄	—	13	1	no	—
328	C₂×C₂²⋊C₄	—	13	1	no	—
329	C₂×C₄²	—	13	1	no	—
330	M₃₂	—	26	4	no	—
331	M₃₂	—	26	4	no	—
332	C₂×C₁₆	—	13	4	no	—
333	C₂×C₁₆	—	13	2	no	—
334	C₂×C₁₆	—	13	2	no	—
335	C₂×C₁₆	—	13	2	no	—
336	C₂×C₁₆	—	13	2	no	—
337	C₂×C₁₆	—	26	4	no	—
338	C₂×C₁₆	—	26	4	no	—
339	C₂×C₁₆	—	26	2	no	—
340	C₂×C₁₆	—	26	2	no	—
341	C₂×C₁₆	—	26	2	no	—
342	C₄⋊C₈	—	13	1	no	—
343	C₄⋊C₈	—	13	1	no	—
344	C₄⋊C₈	—	13	1	no	—
345	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
346	C₂²⋊C₈	—	13	1	no	—
347	C₂²⋊C₈	—	13	1	no	—
348	C₂²⋊C₈	—	13	1	no	—
349	C₂²⋊C₈	—	13	1	no	—
350	C₂²⋊C₈	—	13	1	no	—
351	C₂²⋊C₈	—	13	1	no	—
352	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
353	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
354	C₄×C₈	—	13	1	no	—
355	C₄×C₈	—	13	1	no	—
356	C₄×C₈	—	13	1	no	—
357	C₄×C₈	C₂×#261	1	1	yes	characteristic
358	C₂×C₁₃	—	2	2	no	—
359	C₂×C₁₃	—	4	1	no	—
360	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
361	C₂×C₁₃	C₂²×M₃₂	1	1	yes	characteristic
362	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
363	D₁₃	—	2	2	no	—
364	D₁₃	—	4	1	no	—
365	D₁₃	#2168	1	4	yes	complemented
366	C₂⁴	—	13	1	no	—
367	C₂⁴	—	13	1	no	—
368	C₂×D₄	—	13	1	no	—
369	C₂×D₄	—	13	1	no	—
370	C₂×D₄	—	13	1	no	—
371	C₂×D₄	—	26	4	no	—
372	C₂×D₄	D₁₃⋊C₈	1	1	yes	characteristic
373	C₂²×C₄	—	13	1	no	—
374	C₂²×C₄	—	13	1	no	—
375	C₂²×C₄	—	13	1	no	—
376	C₂²×C₄	—	13	1	no	—
377	C₂²×C₄	—	13	1	no	—
378	C₂²×C₄	—	13	1	no	—
379	C₂²×C₄	—	13	1	no	—
380	C₂²×C₄	—	13	1	no	—
381	C₂²×C₄	—	13	1	no	—
382	C₂²×C₄	—	13	1	no	—
383	C₂²×C₄	—	13	1	no	—
384	C₂²×C₄	—	26	2	no	—
385	C₂²×C₄	—	26	2	no	—
386	C₂²×C₄	—	26	2	no	—
387	C₂²×C₄	—	26	2	no	—
388	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
389	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	13	1	no	—
393	C₂×C₈	—	13	2	no	—
394	C₂×C₈	—	13	2	no	—
395	C₂×C₈	—	13	1	no	—
396	C₂×C₈	—	13	1	no	—
397	C₂×C₈	—	13	1	no	—
398	C₂×C₈	—	26	1	no	—
399	C₂×C₈	—	26	1	no	—
400	C₂×C₈	—	26	1	no	—
401	C₂×C₈	—	26	1	no	—
402	C₂×C₈	—	26	2	no	—
403	C₂×C₈	—	26	2	no	—
404	C₂×C₈	—	26	2	no	—
405	C₂×C₈	—	26	1	no	—
406	C₂×C₈	—	26	1	no	—
407	C₂×C₈	—	26	1	no	—
408	C₂×C₈	—	26	1	no	—
409	C₂×C₈	—	26	2	no	—
410	C₂×C₈	—	26	2	no	—
411	C₂×C₈	C₂²×#261	1	1	yes	characteristic
412	C₂×C₈	C₂²×#261	1	1	yes	characteristic
413	C₂×C₈	C₂²×#261	1	1	yes	characteristic
414	C₂×C₈	C₂²×#261	1	1	yes	characteristic
415	C₄⋊C₄	—	13	1	no	—
416	C₄⋊C₄	—	13	1	no	—
417	C₄⋊C₄	—	13	1	no	—
418	C₄⋊C₄	D₁₃⋊C₈	1	1	yes	characteristic
419	C₂²⋊C₄	—	13	1	no	—
420	C₂²⋊C₄	—	13	1	no	—
421	C₂²⋊C₄	—	13	1	no	—
422	C₂²⋊C₄	—	13	1	no	—
423	C₂²⋊C₄	—	13	1	no	—
424	C₂²⋊C₄	—	13	1	no	—
425	C₂²⋊C₄	D₁₃⋊C₈	1	1	yes	characteristic
426	C₂²⋊C₄	D₁₃⋊C₈	1	1	yes	characteristic
427	C₄²	—	13	1	no	—
428	C₄²	—	13	1	no	—
429	C₄²	—	13	1	no	—
430	C₄²	C₂²×#261	1	1	yes	characteristic
431	C₁₆	—	13	4	no	—
432	C₁₆	—	26	2	no	—
433	C₁₆	—	26	2	no	—
434	C₁₆	—	26	2	no	—
435	C₁₃	C₂×#2168	1	1	yes	characteristic, complemented, Sylow
436	C₂³	—	13	1	no	—
437	C₂³	—	13	4	no	—
438	C₂³	—	13	1	no	—
439	C₂³	—	13	1	no	—
440	C₂³	—	26	2	no	—
441	C₂³	—	26	2	no	—
442	C₂³	—	26	2	no	—
443	C₂³	—	26	2	no	—
444	C₂³	—	26	2	no	—
445	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
446	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
447	D₄	—	2	2	no	—
448	D₄	—	26	2	no	—
449	D₄	—	26	2	no	—
450	D₄	—	26	2	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	13	1	no	—
456	C₂×C₄	—	13	2	no	—
457	C₂×C₄	—	13	2	no	—
458	C₂×C₄	—	13	1	no	—
459	C₂×C₄	—	13	1	no	—
460	C₂×C₄	—	13	1	no	—
461	C₂×C₄	—	13	1	no	—
462	C₂×C₄	—	26	2	no	—
463	C₂×C₄	—	26	2	no	—
464	C₂×C₄	—	26	2	no	—
465	C₂×C₄	—	26	2	no	—
466	C₂×C₄	—	26	2	no	—
467	C₂×C₄	—	26	2	no	—
468	C₂×C₄	—	26	2	no	—
469	C₂×C₄	—	26	2	no	—
470	C₂×C₄	—	26	1	no	—
471	C₂×C₄	—	26	1	no	—
472	C₂×C₄	—	26	1	no	—
473	C₂×C₄	—	26	1	no	—
474	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
475	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
476	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
477	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
478	C₂×C₄	C₂³×#261	1	1	yes	characteristic
479	C₈	—	2	1	no	—
480	C₈	—	2	1	no	—
481	C₈	—	2	1	no	—
482	C₈	—	13	1	no	—
483	C₈	—	13	1	no	—
484	C₈	—	26	1	no	—
485	C₈	—	26	1	no	—
486	C₈	—	26	1	no	—
487	C₈	D₄×#261	1	2	yes	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	13	2	no	—
494	C₂²	—	13	2	no	—
495	C₂²	—	13	2	no	—
496	C₂²	—	13	2	no	—
497	C₂²	—	26	8	no	—
498	C₂²	—	26	1	no	—
499	C₂²	—	26	1	no	—
500	C₂²	—	26	1	no	—
501	C₂²	—	26	1	no	—
502	C₂²	—	26	1	no	—
503	C₂²	—	52	4	no	—
504	C₂²	D₁₃⋊M₃₂	1	2	yes	complemented
505	C₂²	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	2	1	no	—
510	C₄	—	13	2	no	—
511	C₄	—	26	1	no	—
512	C₄	—	26	1	no	—
513	C₄	—	26	1	no	—
514	C₄	—	26	1	no	—
515	C₄	C₂×D₄×#261	1	1	yes	characteristic
516	C₄	D₁₃⋊#131	1	1	yes	characteristic
517	C₂	—	2	2	no	—
518	C₂	—	4	1	no	—
519	C₂	—	13	4	no	—
520	C₂	—	26	2	no	—
521	C₂	—	52	1	no	—
522	C₂	D₄×D₁₃⋊C₈	1	1	yes	characteristic
523	C₂	C₂×D₁₃⋊M₃₂	1	1	yes	characteristic
524	C₂	D₁₃⋊#504	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²×#261
commutator, socle	C₂²×C₁₃	C₂³×C₈
Frattini	C₂×C₄	C₂³×#261
Fitting	C₈×D₄×C₁₃	C₄
prime radical	C₂×D₄×D₁₃	C₈
cosocle	C₂×#1055	C₂⁴
hypercenter	C₈×D₄	#261
hypocenter	C₁₃	C₂×#2168
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₈×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₃⋊M₃₂	C₂	semidirect
2. C₂²×D₁₃⋊C₁₆	C₂	semidirect
3. #13131219	C₂	semidirect
4. #13131218	C₂	semidirect
5. #13131217	C₂	semidirect
6. #13131216	C₂	semidirect
7. D₁₃⋊(C₄⋊C₁₆)	C₂	semidirect
8. D₁₃⋊(C₂²⋊C₁₆)	C₂	semidirect
9. D₁₃⋊(C₂²⋊C₁₆)	C₂	semidirect
10. #13131037	C₂	semidirect
15. C₂×#88106	C₂²	semidirect
16. C₂²×#6092	C₂²	semidirect
18. C₂×#88098	C₂²	semidirect
24. C₂×D₁₃⋊C₁₆	C₂²	semidirect
37. C₂²⋊#6092	C₂²	semidirect
38. C₂²⋊#6092	C₂²	semidirect
39. #11718260	C₂²	semidirect
40. #11718259	C₂²	semidirect
41. #11718259	C₂²	semidirect
42. #11718258	C₂²	semidirect
43. #11718231	C₂²	semidirect
44. C₄⋊#6092	C₂²	semidirect
87. D₁₃⋊C₁₆	D₄	semidirect
173. #6092	C₂×D₄	semidirect
192. C₂²×D₁₃	M₃₂	semidirect
275. C₂²×C₁₃	C₂×M₃₂	semidirect
286. C₂×D₁₃	C₂×M₃₂	semidirect
365. D₁₃	#2168	semidirect
435. C₁₃	C₂×#2168	semidirect
504. C₂²	D₁₃⋊M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃⋊M₃₂	2
C₂²×D₁₃⋊C₁₆	2
#13131219	2
#13131218	2
#13131217	2
#13131216	2
D₁₃⋊(C₄⋊C₁₆)	2
D₁₃⋊(C₂²⋊C₁₆)	2
#13131037	2
C₈×D₄×D₁₃	2
C₂×#2168	13

Subgroups — D13⋊#2168 #16807125

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃⋊#2168 #16807125