Subgroups — #16016128

Order 3328.

734 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	C₂²×#88052	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic
4	#13116665	C₂	1	2	yes	maximal, complemented
5	#13116664	C₂	1	2	yes	maximal, complemented
6	#13116658	C₂	1	2	yes	maximal, complemented
7	#13116653	C₂	1	2	yes	maximal, complemented
8	#13116591	C₂	1	1	yes	maximal, characteristic, complemented
9	#13116446	C₂	1	1	yes	maximal, characteristic, complemented
10	M₃₂×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2112	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₂²⋊D₁₃	C₄	1	1	yes	characteristic
14	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊#1055	C₄	1	1	yes	characteristic
18	C₈×C₂²⋊D₁₃	C₄	1	1	yes	characteristic
19	C₈×C₂²⋊D₁₃	C₄	1	1	yes	characteristic
20	C₈×C₂²⋊D₁₃	C₄	1	1	yes	characteristic
21	C₈×C₂²⋊D₁₃	C₄	1	1	yes	characteristic
22	C₈×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
23	C₈×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
24	C₈×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
25	C₈×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
26	C₂×#88060	C₄	1	1	yes	characteristic
27	C₂×#88054	C₄	1	1	yes	characteristic
28	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
29	C₂×#88052	—	2	4	no	—
30	C₂×#88052	C₂²	1	1	yes	characteristic
31	C₂×#88052	C₂²	1	1	yes	characteristic
32	C₂×#88052	C₂²	1	2	yes	complemented
33	C₂²×#6090	C₂²	1	2	yes	complemented
34	D₁₃×M₃₂	—	2	4	no	—
35	C₂×#88038	C₂²	1	2	yes	complemented
36	C₂×C₁₆×D₁₃	C₂²	1	2	yes	complemented
37	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
38	C₁₃×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
39	#11718099	C₂²	1	2	yes	complemented
40	#11718099	C₂²	1	2	yes	complemented
41	#11718094	C₂²	1	2	yes	complemented
42	#11718093	C₂²	1	2	yes	complemented
43	#11718093	C₂²	1	2	yes	complemented
44	C₁₆×Dic₁₃	C₂²	1	2	yes	complemented
45	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
47	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	—	2	2	no	—
49	C₂²×C₈×C₁₃	—	2	2	no	—
50	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₂²⋊Dic₁₃	C₈	1	1	yes	characteristic
57	C₄×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
58	C₄×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
59	C₄×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
60	C₄×C₂²⋊D₁₃	C₈	1	1	yes	characteristic
61	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
63	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
64	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×#6103	C₈	1	1	yes	characteristic
66	C₂×#6101	C₈	1	1	yes	characteristic
67	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
69	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₁₃	—	2	2	no	—
71	C₂×C₈×D₁₃	—	2	2	no	—
72	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
75	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×M₃₂	—	2	2	no	—
77	C₁₃×M₃₂	—	2	2	no	—
78	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
79	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
80	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
81	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
82	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
83	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
84	#88060	C₂×C₄	1	1	yes	characteristic
85	#88060	C₂×C₄	1	1	yes	characteristic
86	#88060	C₂×C₄	1	1	yes	characteristic
87	#88060	C₂×C₄	1	1	yes	characteristic
88	#88054	C₂×C₄	1	1	yes	characteristic
89	#88054	C₂×C₄	1	1	yes	characteristic
90	#88054	C₂×C₄	1	1	yes	characteristic
91	#88054	C₂×C₄	1	1	yes	characteristic
92	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
93	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
94	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
95	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
96	#88052	—	2	2	no	—
97	#88052	—	2	4	no	—
98	#88052	D₄	1	4	yes	complemented
99	C₂×#6090	—	2	4	no	—
100	C₂×#6090	C₂³	1	2	yes	—
101	C₂×#6090	C₂³	1	2	yes	—
102	#88038	—	2	4	no	—
103	C₁₆×D₁₃	—	2	4	no	—
104	D₄×M₃₂	—	13	1	no	maximal, Sylow
105	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
106	C₂³×D₁₃	C₂×C₈	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₂²⋊D₁₃	—	2	4	no	—
116	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
117	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
118	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
119	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
120	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
121	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
122	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
123	C₂×C₄×D₁₃	—	2	2	no	—
124	C₂×C₄×D₁₃	—	2	2	no	—
125	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
126	C₂×C₄×D₁₃	C₂×C₈	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	—	2	2	no	—
132	C₂×C₈×C₁₃	—	2	1	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	1	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₁₃	#41	1	2	yes	—
141	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
143	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
144	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
145	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
146	#6103	C₂×C₈	1	1	yes	characteristic
147	#6103	C₂×C₈	1	1	yes	characteristic
148	#6103	C₂×C₈	1	1	yes	characteristic
149	#6103	C₂×C₈	1	1	yes	characteristic
150	#6101	C₂×C₈	1	1	yes	characteristic
151	#6101	C₂×C₈	1	1	yes	characteristic
152	#6101	C₂×C₈	1	1	yes	characteristic
153	#6101	C₂×C₈	1	1	yes	characteristic
154	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
155	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
156	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
157	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₂×#1055	—	2	2	no	—
159	C₂×#1055	—	2	2	no	—
160	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
161	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
162	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
163	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
164	C₈×D₁₃	—	2	2	no	—
165	C₈×D₁₃	—	2	2	no	—
166	C₈×D₁₃	—	2	1	no	—
167	C₈×D₁₃	—	2	1	no	—
168	C₈×D₁₃	—	2	1	no	—
169	C₈×D₁₃	—	2	1	no	—
170	C₁₃×C₁₆	—	2	2	no	—
171	C₁₃×C₁₆	—	2	2	no	—
172	#6090	—	2	2	no	—
173	#6090	C₂×D₄	1	4	yes	complemented
174	C₂²×M₃₂	—	13	1	no	—
175	C₂²×M₃₂	—	13	1	no	—
176	C₂×C₈×D₄	—	13	1	no	—
177	#2169	—	13	2	no	—
178	#2168	—	13	2	no	—
179	#2168	—	13	2	no	—
180	D₄×C₁₆	—	13	2	no	—
181	#2150	—	13	1	no	—
182	#2112	—	13	1	no	—
183	#2112	D₁₃	1	1	yes	characteristic, complemented
184	C₄×M₃₂	—	13	1	no	—
185	C₂³×C₁₃	—	2	2	no	—
186	C₂³×C₁₃	—	2	2	no	—
187	C₂³×C₁₃	—	4	1	no	—
188	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
189	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
190	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
191	C₂²×D₁₃	—	2	2	no	—
192	C₂²×D₁₃	—	2	2	no	—
193	C₂²×D₁₃	—	4	1	no	—
194	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
195	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
196	C₂×C₄×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	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
204	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
207	C₂×C₄×C₁₃	#131	1	2	yes	—
208	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
209	C₂²⋊D₁₃	—	2	2	no	—
210	C₂²⋊D₁₃	—	2	2	no	—
211	C₂²⋊D₁₃	—	2	2	no	—
212	C₂²⋊D₁₃	M₃₂	1	4	yes	complemented
213	C₂×Dic₁₃	—	2	2	no	—
214	C₂×Dic₁₃	—	2	2	no	—
215	C₂×Dic₁₃	—	4	1	no	—
216	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
217	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
218	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
219	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
220	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
221	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
222	C₄×D₁₃	—	2	1	no	—
223	C₄×D₁₃	—	2	1	no	—
224	C₄×D₁₃	—	2	1	no	—
225	C₄×D₁₃	—	2	1	no	—
226	C₄×D₁₃	—	2	2	no	—
227	C₄×D₁₃	—	2	2	no	—
228	C₈×C₁₃	—	2	1	no	—
229	C₈×C₁₃	—	2	1	no	—
230	C₈×C₁₃	C₄×D₄	1	2	yes	—
231	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
232	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
233	#1055	—	2	1	no	—
234	#1055	—	2	1	no	—
235	#1055	—	2	1	no	—
236	#1055	—	2	1	no	—
237	C₂³×C₈	—	13	1	no	—
238	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
239	C₂×C₄×D₄	—	13	1	no	—
240	C₂×M₃₂	—	13	1	no	—
241	C₂×M₃₂	—	13	1	no	—
242	C₂×M₃₂	—	13	2	no	—
243	C₂×M₃₂	—	13	2	no	—
244	C₂×M₃₂	—	26	4	no	—
245	C₂×M₃₂	—	26	4	no	—
246	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
247	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
248	C₂²×C₁₆	—	13	2	no	—
249	C₂²×C₁₆	—	13	2	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	—	13	1	no	—
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	C₂×D₁₃	1	2	yes	complemented
267	C₂²⋊C₁₆	C₂×D₁₃	1	2	yes	complemented
268	#346	—	13	2	no	—
269	C₄×C₁₆	—	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	—	2	1	no	—
276	C₂²×C₁₃	—	2	1	no	—
277	C₂²×C₁₃	—	4	4	no	—
278	C₂²×C₁₃	C₈×D₄	1	2	yes	—
279	C₂²×C₁₃	C₂×M₃₂	1	2	yes	complemented
280	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
281	C₂×D₁₃	—	2	1	no	—
282	C₂×D₁₃	—	2	1	no	—
283	C₂×D₁₃	—	2	1	no	—
284	C₂×D₁₃	—	2	1	no	—
285	C₂×D₁₃	—	2	1	no	—
286	C₂×D₁₃	—	4	4	no	—
287	C₂×D₁₃	C₂×M₃₂	1	2	yes	complemented
288	C₄×C₁₃	—	2	1	no	—
289	C₄×C₁₃	—	2	1	no	—
290	C₄×C₁₃	C₈×D₄	1	2	yes	—
291	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
292	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
293	Dic₁₃	—	2	1	no	—
294	Dic₁₃	—	2	1	no	—
295	Dic₁₃	—	2	1	no	—
296	Dic₁₃	—	2	1	no	—
297	Dic₁₃	—	2	1	no	—
298	Dic₁₃	C₂×M₃₂	1	2	yes	complemented
299	C₂²×D₄	—	13	1	no	—
300	C₂³×C₄	—	13	1	no	—
301	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
302	C₂²×C₈	—	2	2	no	—
303	C₂²×C₈	—	2	2	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	—	26	2	no	—
311	C₂²×C₈	—	26	2	no	—
312	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
313	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
314	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
315	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
316	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
317	C₂²×C₈	C₂²×D₁₃	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	—	13	1	no	—
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	—	2	2	no	—
331	M₃₂	—	2	2	no	—
332	M₃₂	—	13	4	no	—
333	M₃₂	—	26	4	no	—
334	M₃₂	—	26	4	no	—
335	M₃₂	—	26	2	no	—
336	C₂×C₁₆	—	13	2	no	—
337	C₂×C₁₆	—	13	2	no	—
338	C₂×C₁₆	—	26	4	no	—
339	C₂×C₁₆	—	26	4	no	—
340	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
341	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
342	C₄⋊C₈	—	13	1	no	—
343	C₄⋊C₈	—	13	1	no	—
344	C₄⋊C₈	—	13	1	no	—
345	C₄⋊C₈	—	13	1	no	—
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	—	13	1	no	—
353	C₂²⋊C₈	—	13	1	no	—
354	C₄×C₈	—	13	1	no	—
355	C₄×C₈	—	13	1	no	—
356	C₄×C₈	—	13	1	no	—
357	C₄×C₈	—	13	1	no	—
358	C₂×C₁₃	—	2	2	no	—
359	C₂×C₁₃	—	2	2	no	—
360	C₂×C₁₃	—	4	1	no	—
361	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
362	C₂×C₁₃	C₂²×M₃₂	1	1	yes	characteristic
363	C₂×C₁₃	#3407	1	1	yes	characteristic
364	D₁₃	—	2	2	no	—
365	D₁₃	—	4	1	no	—
366	C₂⁴	—	13	1	no	—
367	C₂⁴	C₈×D₁₃	1	1	yes	characteristic
368	C₂×D₄	—	13	1	no	—
369	C₂×D₄	—	13	1	no	—
370	C₂×D₄	—	13	1	no	—
371	C₂×D₄	—	13	1	no	—
372	C₂×D₄	—	26	4	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	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	—	26	2	no	—
383	C₂²×C₄	—	26	2	no	—
384	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
385	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
386	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
387	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	13	1	no	—
398	C₂×C₈	—	13	1	no	—
399	C₂×C₈	—	13	1	no	—
400	C₂×C₈	—	13	1	no	—
401	C₂×C₈	—	26	2	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	C₂×C₄×D₁₃	1	1	yes	characteristic
410	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
411	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
412	C₂×C₈	D₄×D₁₃	1	2	yes	—
413	C₂×C₈	#6129	1	2	yes	—
414	C₂×C₈	C₂³×D₁₃	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	—	13	1	no	—
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	—	13	1	no	—
426	C₂²⋊C₄	—	13	1	no	—
427	C₄²	—	13	1	no	—
428	C₄²	—	13	1	no	—
429	C₄²	—	13	1	no	—
430	C₄²	—	13	1	no	—
431	C₁₆	—	2	2	no	—
432	C₁₆	—	2	2	no	—
433	C₁₆	—	13	4	no	—
434	C₁₆	—	26	2	no	—
435	C₁₃	D₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	13	1	no	—
440	C₂³	—	13	1	no	—
441	C₂³	—	26	2	no	—
442	C₂³	—	26	2	no	—
443	C₂³	—	52	1	no	—
444	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
445	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
446	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
447	D₄	—	13	4	no	—
448	D₄	—	26	2	no	—
449	D₄	—	26	2	no	—
450	D₄	—	26	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	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	—	13	1	no	—
463	C₂×C₄	—	13	1	no	—
464	C₂×C₄	—	26	2	no	—
465	C₂×C₄	—	26	2	no	—
466	C₂×C₄	—	26	1	no	—
467	C₂×C₄	—	26	1	no	—
468	C₂×C₄	—	26	1	no	—
469	C₂×C₄	—	26	1	no	—
470	C₂×C₄	—	26	2	no	—
471	C₂×C₄	—	26	2	no	—
472	C₂×C₄	—	52	1	no	—
473	C₂×C₄	#88135	1	2	yes	—
474	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
475	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
476	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
477	C₂×C₄	#88161	1	2	yes	—
478	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
479	C₈	—	2	1	no	—
480	C₈	—	2	1	no	—
481	C₈	—	26	1	no	—
482	C₈	—	26	1	no	—
483	C₈	—	26	1	no	—
484	C₈	—	26	1	no	—
485	C₈	#88135	1	2	yes	—
486	C₈	C₂×D₄×D₁₃	1	1	yes	characteristic
487	C₈	C₂×#6129	1	1	yes	characteristic
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	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	13	2	no	—
497	C₂²	—	26	1	no	—
498	C₂²	—	26	1	no	—
499	C₂²	—	26	1	no	—
500	C₂²	—	26	1	no	—
501	C₂²	—	26	1	no	—
502	C₂²	—	52	4	no	—
503	C₂²	#11718386	1	2	yes	—
504	C₂²	D₁₃×M₃₂	1	2	yes	complemented
505	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	13	2	no	—
509	C₄	—	26	1	no	—
510	C₄	—	26	1	no	—
511	C₄	—	26	1	no	—
512	C₄	—	26	1	no	—
513	C₄	—	26	1	no	—
514	C₄	#11718386	1	2	yes	—
515	C₄	C₂×#88135	1	1	yes	characteristic
516	C₄	C₂×#88161	1	1	yes	characteristic
517	C₂	—	2	2	no	—
518	C₂	—	2	2	no	—
519	C₂	—	4	1	no	—
520	C₂	—	26	2	no	—
521	C₂	—	52	1	no	—
522	C₂	C₂×#11718386	1	1	yes	characteristic
523	C₂	C₂×D₁₃×M₃₂	1	1	yes	characteristic
524	C₂	#13127938	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₁₃×#2112	C₂
prime radical	C₂²×C₂²⋊D₁₃	C₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	#2112	D₁₃
hypocenter	C₁₃	D₄×M₃₂
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ #2112

Complements

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

N	H ≅ G/N	type
1. C₂²×#88052	C₂	semidirect
2. C₂×D₁₃×M₃₂	C₂	semidirect
4. #13116665	C₂	semidirect
5. #13116664	C₂	semidirect
6. #13116658	C₂	semidirect
7. #13116653	C₂	semidirect
8. #13116591	C₂	semidirect
9. #13116446	C₂	semidirect
10. M₃₂×Dic₁₃	C₂	semidirect
11. C₁₃×#2112	C₂	semidirect
32. C₂×#88052	C₂²	semidirect
33. C₂²×#6090	C₂²	semidirect
35. C₂×#88038	C₂²	semidirect
36. C₂×C₁₆×D₁₃	C₂²	semidirect
37. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
38. C₁₃×C₂²⋊C₁₆	C₂²	semidirect
39. #11718099	C₂²	semidirect
40. #11718099	C₂²	semidirect
41. #11718094	C₂²	semidirect
42. #11718093	C₂²	semidirect
43. #11718093	C₂²	semidirect
44. C₁₆×Dic₁₃	C₂²	semidirect
98. #88052	D₄	semidirect
173. #6090	C₂×D₄	semidirect
183. #2112	D₁₃	semidirect
212. C₂²⋊D₁₃	M₃₂	semidirect
266. C₂²⋊C₁₆	C₂×D₁₃	semidirect
267. C₂²⋊C₁₆	C₂×D₁₃	semidirect
279. C₂²×C₁₃	C₂×M₃₂	semidirect
287. C₂×D₁₃	C₂×M₃₂	semidirect
298. Dic₁₃	C₂×M₃₂	semidirect
435. C₁₃	D₄×M₃₂	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
C₂²×#88052	2
C₂×D₁₃×M₃₂	2
C₂×C₈×C₂²⋊D₁₃	2
#13116665	2
#13116664	2
#13116658	2
#13116653	2
#13116591	2
#13116446	2
M₃₂×Dic₁₃	2
C₁₃×#2112	2
D₄×M₃₂	13