Subgroups — #16016439

Order 3328.

558 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	C₈×#6129	C₂	1	1	yes	maximal, characteristic
2	#13116743	C₂	1	1	yes	maximal, characteristic, complemented
3	#13116742	C₂	1	1	yes	maximal, characteristic, complemented
4	#13116666	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116665	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116662	C₂	1	1	yes	maximal, characteristic, complemented
7	#13116661	C₂	1	1	yes	maximal, characteristic, complemented
8	#13116658	C₂	1	1	yes	maximal, characteristic, complemented
9	#13116634	C₂	1	1	yes	maximal, characteristic, complemented
10	#13116632	C₂	1	1	yes	maximal, characteristic, complemented
11	#13116632	C₂	1	1	yes	maximal, characteristic, complemented
12	#13116429	C₂	1	1	yes	maximal, characteristic, complemented
13	M₃₂×Dic₁₃	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	C₄×#6129	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	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
24	C₂×#88052	C₂²	1	1	yes	characteristic
25	C₂²×#6090	C₂²	1	1	yes	characteristic
26	D₄×#1055	C₄	1	1	yes	characteristic
27	C₂×#88038	C₂²	1	1	yes	characteristic
28	C₂×#88038	C₂²	1	1	yes	characteristic
29	#11718494	C₄	1	1	yes	characteristic
30	#11718491	C₄	1	1	yes	characteristic
31	#11718386	C₄	1	1	yes	characteristic
32	#11718386	C₄	1	1	yes	characteristic
33	#11718379	C₄	1	1	yes	characteristic
34	#11718379	C₄	1	1	yes	characteristic
35	C₄×C₈×D₁₃	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	#11718093	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	C₁₆×Dic₁₃	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	#11718053	C₂²	1	1	yes	characteristic
59	C₂×#6129	C₈	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
63	D₄×Dic₁₃	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	C₂×C₄×Dic₁₃	C₂×C₄	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	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
72	#88146	C₈	1	1	yes	characteristic
73	#88141	C₈	1	1	yes	characteristic
74	#88135	C₈	1	1	yes	characteristic
75	#88135	C₈	1	1	yes	characteristic
76	#88131	C₈	1	1	yes	characteristic
77	#88131	C₈	1	1	yes	characteristic
78	C₄²×D₁₃	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	#88054	C₂×C₄	1	1	yes	characteristic
95	#88054	C₂×C₄	1	1	yes	characteristic
96	#88054	C₂×C₄	1	1	yes	characteristic
97	#88054	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₁₃	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	#88052	—	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	C₄×#1055	C₂×C₄	1	1	yes	characteristic
114	#88038	—	2	2	no	—
115	#88038	—	2	2	no	—
116	#33479	—	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	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
125	C₂²×Dic₁₃	C₂×C₈	1	1	yes	characteristic
126	#6129	—	2	4	no	—
127	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
128	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
129	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂×Dic₂₆	C₂×C₈	1	1	yes	characteristic
131	C₂×C₈×C₁₃	—	2	1	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	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₁₃×C₄⋊C₄	C₂×C₈	1	1	yes	characteristic
140	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
141	C₁₃×C₂²⋊C₄	C₂×C₈	1	1	yes	characteristic
142	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
143	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
144	C₂²⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
145	#6103	C₂×C₈	1	1	yes	characteristic
146	#6103	C₂×C₈	1	1	yes	characteristic
147	C₄⋊Dic₁₃	C₂×C₈	1	1	yes	characteristic
148	#6101	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	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
153	C₄×Dic₁₃	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	C₂×C₈	1	1	yes	characteristic
157	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
158	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
159	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
160	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₂×#1055	—	2	2	no	—
162	C₂×#1055	—	2	2	no	—
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	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
167	C₈×D₁₃	—	2	1	no	—
168	C₈×D₁₃	—	2	1	no	—
169	C₈×D₁₃	—	2	2	no	—
170	C₁₃×C₁₆	—	2	1	no	—
171	C₁₃×C₁₆	—	2	1	no	—
172	C₁₃×C₁₆	—	2	1	no	—
173	C₁₃×C₁₆	#41	1	2	yes	complemented
174	#6090	—	2	1	no	—
175	#6090	—	2	1	no	—
176	#6090	—	2	1	no	—
177	#6090	#41	1	2	yes	complemented
178	C₈×#41	—	13	1	no	—
179	#2183	—	13	1	no	—
180	#2183	—	13	1	no	—
181	#2169	—	13	1	no	—
182	#2169	—	13	1	no	—
183	#2168	—	13	1	no	—
184	#2168	—	13	1	no	—
185	#2168	—	13	1	no	—
186	#2168	D₁₃	1	1	yes	characteristic, complemented
187	#2162	—	13	1	no	—
188	#2162	—	13	1	no	—
189	#2162	—	13	1	no	—
190	C₄×M₃₂	—	13	1	no	—
191	C₄×M₃₂	—	13	1	no	—
192	C₂×C₄×C₁₆	—	13	1	no	—
193	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
194	C₂³×C₁₃	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	—	2	2	no	—
211	C₂×Dic₁₃	M₃₂	1	4	yes	complemented
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	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	C₄×D₁₃	—	2	1	no	—
220	C₄×D₁₃	—	2	1	no	—
221	C₄×D₁₃	—	2	2	no	—
222	C₄×D₁₃	—	2	2	no	—
223	Dic₂₆	—	2	2	no	—
224	C₈×C₁₃	—	2	1	no	—
225	C₈×C₁₃	—	2	1	no	—
226	C₈×C₁₃	—	2	1	no	—
227	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
228	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
229	#1055	—	2	1	no	—
230	#1055	—	2	1	no	—
231	#1055	—	2	1	no	—
232	#1055	#131	1	2	yes	—
233	C₄×#41	—	13	1	no	—
234	C₂×M₃₂	—	13	1	no	—
235	C₂×M₃₂	—	13	1	no	—
236	C₂×M₃₂	—	13	1	no	—
237	C₂×M₃₂	C₂×D₁₃	1	1	yes	characteristic
238	C₂²×C₁₆	—	13	1	no	—
239	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
240	C₈×Q₈	—	13	1	no	—
241	C₈×Q₈	—	13	1	no	—
242	C₈×D₄	—	13	1	no	—
243	C₈×D₄	—	13	1	no	—
244	C₈×D₄	—	13	1	no	—
245	C₈×D₄	—	13	1	no	—
246	C₈×D₄	—	13	1	no	—
247	C₈×D₄	C₂×D₁₃	1	1	yes	characteristic
248	#431	—	13	1	no	—
249	#431	—	13	1	no	—
250	#431	—	13	1	no	—
251	C₂×C₄×C₈	—	13	1	no	—
252	C₂×C₄×C₈	—	13	1	no	—
253	C₂×C₄×C₈	—	13	1	no	—
254	C₄⋊C₁₆	—	13	1	no	—
255	C₄⋊C₁₆	—	13	1	no	—
256	C₄⋊C₁₆	—	13	1	no	—
257	C₄⋊C₁₆	—	13	1	no	—
258	C₄⋊C₁₆	—	13	1	no	—
259	C₄⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic
260	C₂²⋊C₁₆	—	13	1	no	—
261	C₂²⋊C₁₆	—	13	1	no	—
262	C₂²⋊C₁₆	—	13	1	no	—
263	C₂²⋊C₁₆	—	13	1	no	—
264	C₂²⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic
265	C₂²⋊C₁₆	C₂×D₁₃	1	1	yes	characteristic
266	#346	—	13	1	no	—
267	#346	—	13	1	no	—
268	#346	—	13	1	no	—
269	#346	C₂×D₁₃	1	1	yes	characteristic
270	C₄×C₁₆	—	13	1	no	—
271	C₄×C₁₆	—	13	1	no	—
272	C₄×C₁₆	—	13	1	no	—
273	C₄×C₁₆	—	13	1	no	—
274	C₄×C₁₆	—	13	1	no	—
275	C₄×C₁₆	—	13	1	no	—
276	C₂²×C₁₃	—	2	1	no	—
277	C₂²×C₁₃	—	2	1	no	—
278	C₂²×C₁₃	—	2	1	no	—
279	C₂²×C₁₃	—	2	1	no	—
280	C₂²×C₁₃	—	2	1	no	—
281	C₂²×C₁₃	C₂×M₃₂	1	2	yes	—
282	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
283	C₂×D₁₃	—	2	1	no	—
284	C₂×D₁₃	—	2	1	no	—
285	C₂×D₁₃	—	2	1	no	—
286	C₄×C₁₃	—	2	1	no	—
287	C₄×C₁₃	—	2	1	no	—
288	C₄×C₁₃	—	2	1	no	—
289	C₄×C₁₃	—	2	1	no	—
290	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
291	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
292	Dic₁₃	—	2	1	no	—
293	Dic₁₃	—	2	1	no	—
294	Dic₁₃	—	2	1	no	—
295	Dic₁₃	—	2	1	no	—
296	Dic₁₃	C₂×M₃₂	1	2	yes	—
297	Dic₁₃	C₂×M₃₂	1	2	yes	—
298	Dic₁₃	#504	1	2	yes	—
299	C₂×#41	—	13	1	no	—
300	C₂²×C₈	—	13	1	no	—
301	C₂²×C₈	—	13	1	no	—
302	C₂²×C₈	—	13	1	no	—
303	C₂²×C₈	—	13	1	no	—
304	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
305	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
306	C₄×Q₈	—	13	1	no	—
307	C₄×Q₈	—	13	1	no	—
308	C₄×D₄	—	13	1	no	—
309	C₄×D₄	—	13	1	no	—
310	C₄×D₄	—	13	1	no	—
311	C₄×D₄	—	13	1	no	—
312	C₄×D₄	—	13	1	no	—
313	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
314	#117	—	13	1	no	—
315	#117	—	13	1	no	—
316	#117	—	13	1	no	—
317	C₂×C₄²	—	13	1	no	—
318	C₂×C₄²	—	13	1	no	—
319	C₂×C₄²	—	13	1	no	—
320	M₃₂	—	2	2	no	—
321	M₃₂	—	26	2	no	—
322	M₃₂	—	26	2	no	—
323	M₃₂	—	26	2	no	—
324	C₂×C₁₆	—	2	2	no	—
325	C₂×C₁₆	—	13	1	no	—
326	C₂×C₁₆	—	13	1	no	—
327	C₂×C₁₆	—	13	1	no	—
328	C₂×C₁₆	—	13	1	no	—
329	C₂×C₁₆	—	26	2	no	—
330	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
331	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
332	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
333	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
334	C₄⋊C₈	—	13	1	no	—
335	C₄⋊C₈	—	13	1	no	—
336	C₄⋊C₈	—	13	1	no	—
337	C₄⋊C₈	—	13	1	no	—
338	C₄⋊C₈	—	13	1	no	—
339	C₄⋊C₈	C₄×D₁₃	1	1	yes	characteristic
340	C₂²⋊C₈	—	13	1	no	—
341	C₂²⋊C₈	—	13	1	no	—
342	C₂²⋊C₈	—	13	1	no	—
343	C₂²⋊C₈	—	13	1	no	—
344	C₂²⋊C₈	C₄×D₁₃	1	1	yes	characteristic
345	C₂²⋊C₈	C₄×D₁₃	1	1	yes	characteristic
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	—	13	1	no	—
351	C₄×C₈	—	13	1	no	—
352	C₄×C₈	—	13	1	no	—
353	C₄×C₈	—	13	1	no	—
354	C₄×C₈	—	13	1	no	—
355	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
356	C₂×C₁₃	—	2	2	no	—
357	C₂×C₁₃	—	4	1	no	—
358	C₂×C₁₃	C₈×#41	1	1	yes	characteristic
359	C₂×C₁₃	C₂²×M₃₂	1	1	yes	characteristic
360	C₂×C₁₃	C₂×#504	1	1	yes	characteristic
361	D₁₃	—	4	1	no	—
362	#41	—	26	4	no	—
363	C₂×Q₈	—	13	1	no	—
364	C₂×D₄	—	13	1	no	—
365	C₂×D₄	—	13	1	no	—
366	C₂×D₄	C₈×D₁₃	1	1	yes	characteristic
367	C₂²×C₄	—	13	1	no	—
368	C₂²×C₄	—	13	1	no	—
369	C₂²×C₄	—	13	1	no	—
370	C₂²×C₄	—	13	1	no	—
371	C₂²×C₄	—	13	1	no	—
372	C₂²×C₄	—	13	1	no	—
373	C₂²×C₄	—	13	1	no	—
374	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
375	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	13	1	no	—
381	C₂×C₈	—	13	1	no	—
382	C₂×C₈	—	13	1	no	—
383	C₂×C₈	—	13	1	no	—
384	C₂×C₈	—	26	2	no	—
385	C₂×C₈	—	26	2	no	—
386	C₂×C₈	—	26	2	no	—
387	C₂×C₈	—	26	1	no	—
388	C₂×C₈	—	26	1	no	—
389	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
390	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
391	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
392	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
393	C₄⋊C₄	—	13	1	no	—
394	C₄⋊C₄	—	13	1	no	—
395	C₄⋊C₄	—	13	1	no	—
396	C₄⋊C₄	—	13	1	no	—
397	C₄⋊C₄	—	13	1	no	—
398	C₄⋊C₄	C₈×D₁₃	1	1	yes	characteristic
399	C₂²⋊C₄	—	13	1	no	—
400	C₂²⋊C₄	—	13	1	no	—
401	C₂²⋊C₄	—	13	1	no	—
402	C₂²⋊C₄	—	13	1	no	—
403	C₂²⋊C₄	C₈×D₁₃	1	1	yes	characteristic
404	C₂²⋊C₄	C₈×D₁₃	1	1	yes	characteristic
405	C₄²	—	13	1	no	—
406	C₄²	—	13	1	no	—
407	C₄²	—	13	1	no	—
408	C₄²	—	13	1	no	—
409	C₄²	—	13	1	no	—
410	C₄²	—	13	1	no	—
411	C₄²	—	13	1	no	—
412	C₄²	—	13	1	no	—
413	C₄²	—	13	1	no	—
414	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
415	C₁₆	—	2	1	no	—
416	C₁₆	—	2	1	no	—
417	C₁₆	—	2	1	no	—
418	C₁₆	—	13	2	no	—
419	C₁₆	—	26	1	no	—
420	C₁₆	—	26	1	no	—
421	C₁₆	—	26	1	no	—
422	C₁₆	#6129	1	2	yes	complemented
423	C₁₃	#33479	1	1	yes	characteristic, complemented, Sylow
424	C₂³	—	13	1	no	—
425	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
426	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
427	Q₈	—	26	2	no	—
428	D₄	—	2	2	no	—
429	D₄	—	26	2	no	—
430	D₄	—	26	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	13	1	no	—
436	C₂×C₄	—	13	1	no	—
437	C₂×C₄	—	13	1	no	—
438	C₂×C₄	—	13	4	no	—
439	C₂×C₄	—	13	1	no	—
440	C₂×C₄	—	13	1	no	—
441	C₂×C₄	—	13	1	no	—
442	C₂×C₄	—	13	1	no	—
443	C₂×C₄	—	26	2	no	—
444	C₂×C₄	—	26	2	no	—
445	C₂×C₄	—	26	2	no	—
446	C₂×C₄	—	26	2	no	—
447	C₂×C₄	—	26	2	no	—
448	C₂×C₄	—	26	1	no	—
449	C₂×C₄	—	26	1	no	—
450	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
451	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
452	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
453	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
454	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	2	1	no	—
458	C₈	—	13	2	no	—
459	C₈	—	26	1	no	—
460	C₈	—	26	1	no	—
461	C₈	—	26	1	no	—
462	C₈	C₂×#6129	1	1	yes	characteristic
463	C₈	#41×D₁₃	1	1	yes	characteristic
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	26	1	no	—
470	C₂²	—	26	1	no	—
471	C₂²	—	26	1	no	—
472	C₂²	D₁₃×M₃₂	1	2	yes	—
473	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	13	2	no	—
479	C₄	—	13	2	no	—
480	C₄	—	13	2	no	—
481	C₄	—	26	1	no	—
482	C₄	—	26	1	no	—
483	C₄	—	26	1	no	—
484	C₄	—	26	1	no	—
485	C₄	C₄×#6129	1	1	yes	characteristic
486	C₄	D₁₃×#131	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	4	1	no	—
489	C₂	—	52	1	no	—
490	C₂	C₈×#6129	1	1	yes	characteristic
491	C₂	C₂×D₁₃×M₃₂	1	1	yes	characteristic
492	C₂	D₁₃×#504	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	C₂×#6129	C₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	#2168	D₁₃
hypocenter	C₁₃	#33479
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. #13116743	C₂	semidirect
3. #13116742	C₂	semidirect
4. #13116666	C₂	semidirect
5. #13116665	C₂	semidirect
6. #13116662	C₂	semidirect
7. #13116661	C₂	semidirect
8. #13116658	C₂	semidirect
9. #13116634	C₂	semidirect
10. #13116632	C₂	semidirect
11. #13116632	C₂	semidirect
12. #13116429	C₂	semidirect
13. M₃₂×Dic₁₃	C₂	semidirect
14. C₂×C₁₆×Dic₁₃	C₂	semidirect
15. C₁₃×#2168	C₂	semidirect
173. C₁₃×C₁₆	#41	semidirect
177. #6090	#41	semidirect
186. #2168	D₁₃	semidirect
211. C₂×Dic₁₃	M₃₂	semidirect
422. C₁₆	#6129	semidirect
423. C₁₃	#33479	semidirect

Maximal subgroups

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

subgroup	index
C₈×#6129	2
#13116743	2
#13116742	2
#13116666	2
#13116665	2
#13116662	2
#13116661	2
#13116658	2
#13116634	2
#13116632	2
#13116429	2
M₃₂×Dic₁₃	2
C₂×C₁₆×Dic₁₃	2
C₁₃×#2168	2
#33479	13