Subgroups — #16016449

Order 3328.

526 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123804	C₂	1	1	yes	maximal, characteristic
2	#13116742	C₂	1	1	yes	maximal, characteristic, complemented
3	#13116738	C₂	1	1	yes	maximal, characteristic, complemented
4	#13116666	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116661	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×#6090	C₂	1	1	yes	maximal, characteristic, complemented
7	#13116653	C₂	1	1	yes	maximal, characteristic, complemented
8	#13116653	C₂	1	1	yes	maximal, characteristic, complemented
9	#13116642	C₂	1	1	yes	maximal, characteristic, complemented
10	#13116640	C₂	1	1	yes	maximal, characteristic, complemented
11	#13116636	C₂	1	1	yes	maximal, characteristic, complemented
12	#13116435	C₂	1	1	yes	maximal, characteristic, complemented
13	#13116434	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719243	C₄	1	1	yes	characteristic
17	C₂×C₁₃×M₃₂	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
19	C₈×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₈×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
21	C₈×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
22	#11718762	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
24	C₂²×#6090	C₂²	1	1	yes	characteristic
25	C₂²×#6090	C₂²	1	1	yes	characteristic
26	#11718672	C₄	1	1	yes	characteristic
27	C₂×#88038	C₂²	1	1	yes	characteristic
28	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
29	#11718501	C₄	1	1	yes	characteristic
30	#11718489	C₄	1	1	yes	characteristic
31	#11718391	C₄	1	1	yes	characteristic
32	#11718390	C₄	1	1	yes	characteristic
33	#11718381	C₄	1	1	yes	characteristic
34	#11718380	C₄	1	1	yes	characteristic
35	#11718350	C₂²	1	1	yes	characteristic
36	C₈×Dic₂₆	C₂²	1	1	yes	characteristic
37	C₁₃×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₁₃×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
40	C₁₃×#346	C₂²	1	1	yes	characteristic
41	C₂²⋊#6090	C₂²	1	1	yes	characteristic
42	C₂²⋊#6090	C₂²	1	1	yes	characteristic
43	#11718099	C₂²	1	1	yes	characteristic
44	#11718099	C₂²	1	1	yes	characteristic
45	#11718094	C₂²	1	1	yes	characteristic
46	#11718094	C₂²	1	1	yes	characteristic
47	#11718094	C₂²	1	1	yes	characteristic
48	#11718093	C₂²	1	1	yes	characteristic
49	#11718093	C₂²	1	1	yes	characteristic
50	#11718093	C₂²	1	1	yes	characteristic
51	#11718093	C₂²	1	1	yes	characteristic
52	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
53	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
54	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
55	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
56	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
57	C₄⋊#6090	C₂²	1	1	yes	characteristic
58	C₄×#6090	C₂²	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
62	#88193	C₈	1	1	yes	characteristic
63	#88189	C₈	1	1	yes	characteristic
64	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
65	C₄×C₂²⋊D₁₃	C₂×C₄	1	1	yes	characteristic
66	#88180	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂×#6099	C₂×C₄	1	1	yes	characteristic
69	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
70	C₂×#6094	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
72	#88152	C₈	1	1	yes	characteristic
73	#88143	C₈	1	1	yes	characteristic
74	#88140	C₈	1	1	yes	characteristic
75	#88139	C₈	1	1	yes	characteristic
76	#88133	C₈	1	1	yes	characteristic
77	#88132	C₈	1	1	yes	characteristic
78	#88126	C₂×C₄	1	1	yes	characteristic
79	C₄×Dic₂₆	C₂×C₄	1	1	yes	characteristic
80	C₁₃×M₃₂	—	2	2	no	—
81	C₂×C₁₃×C₁₆	—	2	2	no	—
82	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
86	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
87	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
88	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
89	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
91	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
92	#88060	C₂×C₄	1	1	yes	characteristic
93	#88060	C₂×C₄	1	1	yes	characteristic
94	#88055	C₂×C₄	1	1	yes	characteristic
95	#88055	C₂×C₄	1	1	yes	characteristic
96	#88055	C₂×C₄	1	1	yes	characteristic
97	#88054	C₂×C₄	1	1	yes	characteristic
98	#88054	C₂×C₄	1	1	yes	characteristic
99	#88054	C₂×C₄	1	1	yes	characteristic
100	#88054	C₂×C₄	1	1	yes	characteristic
101	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
102	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
103	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
104	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
105	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
106	C₂×#6090	—	2	2	no	—
107	C₂×#6090	—	2	2	no	—
108	C₂×#6090	C₂³	1	1	yes	characteristic
109	C₂×#6090	C₂³	1	1	yes	characteristic
110	C₂×#6090	C₂³	1	1	yes	characteristic
111	C₂×#6090	C₂³	1	1	yes	characteristic
112	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
113	#88043	C₂×C₄	1	1	yes	characteristic
114	#88038	—	2	2	no	—
115	C₁₆×D₁₃	—	2	2	no	—
116	#33480	—	13	1	no	maximal, Sylow
117	C₂×D₄×C₁₃	C₂×C₈	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
121	C₂×C₂²⋊D₁₃	C₂×C₈	1	1	yes	characteristic
122	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
123	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
124	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×Dic₂₆	C₂×C₈	1	1	yes	characteristic
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	—	2	1	no	—
130	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
135	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
136	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
137	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
139	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
140	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
141	C₂²⋊Dic₁₃	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	#6103	C₂×C₈	1	1	yes	characteristic
146	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
147	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
148	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
149	#6101	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	#6101	C₂×C₈	1	1	yes	characteristic
155	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
156	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
157	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
158	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
160	#6099	—	2	2	no	—
161	C₂×#1055	—	2	2	no	—
162	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
163	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
164	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
165	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
166	#6094	—	2	2	no	—
167	C₈×D₁₃	—	2	1	no	—
168	C₈×D₁₃	—	2	1	no	—
169	C₁₃×C₁₆	—	2	1	no	—
170	C₁₃×C₁₆	—	2	1	no	—
171	C₁₃×C₁₆	—	2	1	no	—
172	C₁₃×C₁₆	#41	1	2	yes	—
173	#6090	—	2	1	no	—
174	#6090	—	2	1	no	—
175	#6090	—	2	1	no	—
176	#6090	#41	1	2	yes	—
177	#2966	—	13	1	no	—
178	#2183	—	13	1	no	—
179	Q₈×C₁₆	—	13	1	no	—
180	#2169	—	13	1	no	—
181	#2168	—	13	1	no	—
182	#2168	D₁₃	1	1	yes	characteristic, complemented
183	D₄×C₁₆	—	13	1	no	—
184	D₄×C₁₆	—	13	1	no	—
185	D₄×C₁₆	—	13	1	no	—
186	#2164	—	13	1	no	—
187	#2164	—	13	1	no	—
188	#2163	—	13	1	no	—
189	#2108	—	13	1	no	—
190	#2108	—	13	1	no	—
191	C₂×C₄×C₁₆	—	13	1	no	—
192	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
193	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
194	C₂²×D₁₃	C₂²×C₈	1	1	yes	characteristic
195	D₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	1	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	C₂²×C₈	1	1	yes	characteristic
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	C₂³×C₄	1	1	yes	characteristic
205	C₂²⋊D₁₃	—	2	2	no	—
206	C₂²⋊D₁₃	—	2	2	no	—
207	C₂×Dic₁₃	—	2	2	no	—
208	C₂×Dic₁₃	—	2	2	no	—
209	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
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	C₂×Dic₁₃	C₂²×C₈	1	1	yes	characteristic
216	C₄×D₁₃	—	2	1	no	—
217	C₄×D₁₃	—	2	1	no	—
218	Dic₂₆	—	2	2	no	—
219	C₈×C₁₃	—	2	1	no	—
220	C₈×C₁₃	—	2	1	no	—
221	C₈×C₁₃	—	2	1	no	—
222	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
223	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
224	#1055	—	2	1	no	—
225	#1055	—	2	1	no	—
226	#1055	—	2	1	no	—
227	#1055	#131	1	2	yes	—
228	#529	—	13	1	no	—
229	C₂×M₃₂	—	13	1	no	—
230	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
231	C₂²×C₁₆	—	13	1	no	—
232	C₂²×C₁₆	—	13	1	no	—
233	C₂²×C₁₆	—	13	1	no	—
234	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
235	#446	—	13	1	no	—
236	C₈×Q₈	—	13	1	no	—
237	#436	—	13	1	no	—
238	#435	—	13	1	no	—
239	#435	—	13	1	no	—
240	C₈×D₄	—	13	1	no	—
241	C₈×D₄	—	13	1	no	—
242	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
243	#433	—	13	1	no	—
244	#433	—	13	1	no	—
245	#432	—	13	1	no	—
246	#405	—	13	1	no	—
247	#405	—	13	1	no	—
248	C₂×C₄×C₈	—	13	1	no	—
249	C₄⋊C₁₆	—	13	1	no	—
250	C₄⋊C₁₆	—	13	1	no	—
251	C₄⋊C₁₆	—	13	1	no	—
252	C₄⋊C₁₆	—	13	1	no	—
253	C₄⋊C₁₆	—	13	1	no	—
254	C₄⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic
255	C₂²⋊C₁₆	—	13	1	no	—
256	C₂²⋊C₁₆	—	13	1	no	—
257	C₂²⋊C₁₆	—	13	1	no	—
258	C₂²⋊C₁₆	—	13	1	no	—
259	C₂²⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic
260	C₂²⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic
261	#346	—	13	1	no	—
262	#346	—	13	1	no	—
263	#346	—	13	1	no	—
264	#346	C₂×D₁₃	1	1	yes	characteristic
265	C₄×C₁₆	—	13	1	no	—
266	C₄×C₁₆	—	13	1	no	—
267	C₄×C₁₆	—	13	1	no	—
268	C₄×C₁₆	—	13	1	no	—
269	C₄×C₁₆	—	13	1	no	—
270	C₄×C₁₆	—	13	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	#504	1	2	yes	—
277	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
278	C₂×D₁₃	—	2	1	no	—
279	C₂×D₁₃	—	2	1	no	—
280	C₂×D₁₃	—	2	1	no	—
281	C₄×C₁₃	—	2	1	no	—
282	C₄×C₁₃	—	2	1	no	—
283	C₄×C₁₃	—	2	1	no	—
284	C₄×C₁₃	—	2	1	no	—
285	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
286	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
287	Dic₁₃	—	2	1	no	—
288	Dic₁₃	—	2	1	no	—
289	Dic₁₃	—	2	1	no	—
290	Dic₁₃	—	2	1	no	—
291	Dic₁₃	—	2	1	no	—
292	Dic₁₃	—	2	1	no	—
293	Dic₁₃	#504	1	2	yes	—
294	C₂×M₁₆	—	13	1	no	—
295	C₂×M₁₆	—	13	1	no	—
296	C₂²×C₈	—	13	1	no	—
297	C₂²×C₈	—	13	1	no	—
298	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
299	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
300	#126	—	13	1	no	—
301	#126	—	13	1	no	—
302	#125	—	13	1	no	—
303	#124	—	13	1	no	—
304	#123	—	13	1	no	—
305	#123	—	13	1	no	—
306	C₂²⋊Q₈	—	13	1	no	—
307	#121	—	13	1	no	—
308	C₄×Q₈	—	13	1	no	—
309	C₄×D₄	—	13	1	no	—
310	C₄×D₄	—	13	1	no	—
311	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
312	#117	—	13	1	no	—
313	#117	—	13	1	no	—
314	C₂×C₄²	—	13	1	no	—
315	M₃₂	—	2	2	no	—
316	M₃₂	—	26	2	no	—
317	C₂×C₁₆	—	2	2	no	—
318	C₂×C₁₆	—	13	1	no	—
319	C₂×C₁₆	—	13	1	no	—
320	C₂×C₁₆	—	13	1	no	—
321	C₂×C₁₆	—	13	1	no	—
322	C₂×C₁₆	—	26	2	no	—
323	C₂×C₁₆	—	26	2	no	—
324	C₂×C₁₆	—	26	2	no	—
325	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
326	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
327	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
328	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
329	C₄⋊C₈	—	13	1	no	—
330	C₄⋊C₈	—	13	1	no	—
331	C₄⋊C₈	—	13	1	no	—
332	C₄⋊C₈	—	13	1	no	—
333	C₄⋊C₈	—	13	1	no	—
334	C₄⋊C₈	C₄×D₁₃	1	1	yes	characteristic
335	C₂²⋊C₈	—	13	1	no	—
336	C₂²⋊C₈	—	13	1	no	—
337	C₂²⋊C₈	—	13	1	no	—
338	C₂²⋊C₈	—	13	1	no	—
339	C₂²⋊C₈	C₄×D₁₃	1	1	yes	characteristic
340	C₂²⋊C₈	C₄×D₁₃	1	1	yes	characteristic
341	#97	—	13	1	no	—
342	#97	—	13	1	no	—
343	#97	—	13	1	no	—
344	#97	—	13	1	no	—
345	C₄×C₈	—	13	1	no	—
346	C₄×C₈	—	13	1	no	—
347	C₄×C₈	—	13	1	no	—
348	C₄×C₈	—	13	1	no	—
349	C₄×C₈	—	13	1	no	—
350	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
351	C₂×C₁₃	—	2	2	no	—
352	C₂×C₁₃	—	4	1	no	—
353	C₂×C₁₃	C₈×#41	1	1	yes	characteristic
354	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
355	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
356	D₁₃	—	4	1	no	—
357	C₂×Q₈	—	13	1	no	—
358	C₂×D₄	—	13	1	no	—
359	C₂×D₄	—	13	1	no	—
360	C₂×D₄	C₈×D₁₃	1	1	yes	characteristic
361	C₂²×C₄	—	13	1	no	—
362	C₂²×C₄	—	13	1	no	—
363	C₂²×C₄	—	13	1	no	—
364	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
365	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
366	M₁₆	—	26	2	no	—
367	M₁₆	—	26	2	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	13	1	no	—
373	C₂×C₈	—	13	1	no	—
374	C₂×C₈	—	13	1	no	—
375	C₂×C₈	—	13	1	no	—
376	C₂×C₈	—	26	2	no	—
377	C₂×C₈	—	26	1	no	—
378	C₂×C₈	—	26	1	no	—
379	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
380	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
381	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
382	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
383	C₄⋊C₄	—	13	1	no	—
384	C₄⋊C₄	—	13	1	no	—
385	C₄⋊C₄	—	13	1	no	—
386	C₄⋊C₄	—	13	1	no	—
387	C₄⋊C₄	—	13	1	no	—
388	C₄⋊C₄	—	13	1	no	—
389	C₄⋊C₄	—	13	1	no	—
390	C₄⋊C₄	—	13	1	no	—
391	C₄⋊C₄	—	13	1	no	—
392	C₄⋊C₄	C₈×D₁₃	1	1	yes	characteristic
393	C₂²⋊C₄	—	13	1	no	—
394	C₂²⋊C₄	—	13	1	no	—
395	C₂²⋊C₄	—	13	1	no	—
396	C₂²⋊C₄	—	13	1	no	—
397	C₂²⋊C₄	—	13	1	no	—
398	C₂²⋊C₄	—	13	1	no	—
399	C₂²⋊C₄	—	13	1	no	—
400	C₂²⋊C₄	—	13	1	no	—
401	C₂²⋊C₄	C₈×D₁₃	1	1	yes	characteristic
402	C₂²⋊C₄	C₈×D₁₃	1	1	yes	characteristic
403	C₄²	—	13	1	no	—
404	C₄²	—	13	1	no	—
405	C₄²	—	13	1	no	—
406	C₄²	—	13	1	no	—
407	C₄²	—	13	1	no	—
408	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
409	C₁₆	—	2	1	no	—
410	C₁₆	—	2	1	no	—
411	C₁₆	—	2	1	no	—
412	C₁₆	—	13	2	no	—
413	C₁₆	—	26	1	no	—
414	C₁₆	—	26	1	no	—
415	C₁₆	—	26	1	no	—
416	C₁₆	#6129	1	2	yes	—
417	C₁₃	#33480	1	1	yes	characteristic, complemented, Sylow
418	C₂³	—	13	1	no	—
419	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
420	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
421	Q₈	—	26	2	no	—
422	D₄	—	2	2	no	—
423	D₄	—	26	2	no	—
424	D₄	—	26	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	13	1	no	—
430	C₂×C₄	—	13	1	no	—
431	C₂×C₄	—	13	1	no	—
432	C₂×C₄	—	13	1	no	—
433	C₂×C₄	—	13	1	no	—
434	C₂×C₄	—	13	1	no	—
435	C₂×C₄	—	13	1	no	—
436	C₂×C₄	—	26	2	no	—
437	C₂×C₄	—	26	2	no	—
438	C₂×C₄	—	26	1	no	—
439	C₂×C₄	—	26	1	no	—
440	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
441	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
442	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
443	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
444	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
445	C₈	—	2	1	no	—
446	C₈	—	2	1	no	—
447	C₈	—	2	1	no	—
448	C₈	—	13	2	no	—
449	C₈	—	26	1	no	—
450	C₈	—	26	1	no	—
451	C₈	—	26	1	no	—
452	C₈	C₂×#6129	1	1	yes	characteristic
453	C₈	#41×D₁₃	1	1	yes	characteristic
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	1	no	—
459	C₂²	—	26	1	no	—
460	C₂²	—	26	1	no	—
461	C₂²	—	26	1	no	—
462	C₂²	#11718568	1	2	yes	—
463	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	2	1	no	—
468	C₄	—	13	2	no	—
469	C₄	—	26	1	no	—
470	C₄	—	26	1	no	—
471	C₄	—	26	1	no	—
472	C₄	—	26	1	no	—
473	C₄	—	26	1	no	—
474	C₄	—	26	1	no	—
475	C₄	C₄×#6129	1	1	yes	characteristic
476	C₄	D₁₃×#131	1	1	yes	characteristic
477	C₂	—	2	2	no	—
478	C₂	—	4	1	no	—
479	C₂	—	52	1	no	—
480	C₂	C₈×#6129	1	1	yes	characteristic
481	C₂	D₁₃×#504	1	1	yes	characteristic
482	C₂	C₂×#11718568	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₃
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₁₃×#2168	C₂
prime radical	#88193	C₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	#2168	D₁₃
hypocenter	C₁₃	#33480
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ #2168

Complements

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

N	H ≅ G/N	type
2. #13116742	C₂	semidirect
3. #13116738	C₂	semidirect
4. #13116666	C₂	semidirect
5. #13116661	C₂	semidirect
6. D₄×#6090	C₂	semidirect
7. #13116653	C₂	semidirect
8. #13116653	C₂	semidirect
9. #13116642	C₂	semidirect
10. #13116640	C₂	semidirect
11. #13116636	C₂	semidirect
12. #13116435	C₂	semidirect
13. #13116434	C₂	semidirect
14. C₂×C₁₆×Dic₁₃	C₂	semidirect
15. C₁₃×#2168	C₂	semidirect
182. #2168	D₁₃	semidirect
417. C₁₃	#33480	semidirect

Maximal subgroups

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

subgroup	index
#13123804	2
#13116742	2
#13116738	2
#13116666	2
#13116661	2
D₄×#6090	2
#13116653	2
#13116642	2
#13116640	2
#13116636	2
#13116435	2
#13116434	2
C₂×C₁₆×Dic₁₃	2
C₁₃×#2168	2
#33480	13