Subgroups — #15867635

Order 3328.

666 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13117314	C₂	1	1	yes	maximal, characteristic
2	#13115773	C₂	1	1	yes	maximal, characteristic
3	#13115554	C₂	1	1	yes	maximal, characteristic
4	#13115552	C₂	1	1	yes	maximal, characteristic
5	#13115401	C₂	1	2	yes	maximal
6	#13115399	C₂	1	2	yes	maximal
7	#13114692	C₂	1	2	yes	maximal
8	C₄⋊C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
9	#13114586	C₂	1	2	yes	maximal
10	C₄×#88055	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	#11718891	C₄	1	1	yes	characteristic
16	#11718891	C₄	1	1	yes	characteristic
17	C₂×#88055	C₂²	1	1	yes	characteristic
18	C₂×#88055	C₂²	1	1	yes	characteristic
19	C₂×#88055	C₂²	1	1	yes	characteristic
20	C₂×#88055	C₂²	1	1	yes	characteristic
21	C₂×#88054	C₂²	1	2	yes	—
22	C₂×#88054	C₂²	1	2	yes	—
23	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
24	#11718646	C₄	1	1	yes	characteristic
25	#11718646	C₄	1	1	yes	characteristic
26	#11718642	C₄	1	2	yes	—
27	#11718642	C₄	1	2	yes	—
28	C₄×C₄⋊Dic₁₃	C₂²	1	2	yes	—
29	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
30	#11718593	C₂²	1	2	yes	—
31	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
33	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
34	C₁₃×#336	C₂²	1	2	yes	—
35	C₁₃×#336	C₂²	1	2	yes	—
36	#11718142	C₂²	1	2	yes	—
37	#11718142	C₂²	1	2	yes	—
38	#11718142	C₂²	1	2	yes	—
39	#11718116	C₂²	1	2	yes	—
40	#11718116	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₄×Q₈×C₁₃	—	2	2	no	—
46	C₄×Q₈×C₁₃	—	2	2	no	—
47	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
48	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
51	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊Dic₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
54	C₂×C₄⋊Dic₁₃	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
60	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
61	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
62	C₂²×#1055	C₂³	1	2	yes	—
63	C₂²×#1055	C₂³	1	1	yes	characteristic
64	C₂²×#1055	C₂³	1	1	yes	characteristic
65	C₁₃×C₄⋊C₈	—	2	2	no	—
66	C₄×C₈×C₁₃	—	2	2	no	—
67	#88071	C₂×C₄	1	2	yes	—
68	#88071	C₂×C₄	1	2	yes	—
69	#88071	C₂×C₄	1	2	yes	—
70	#88071	C₂×C₄	1	2	yes	—
71	#88071	C₂×C₄	1	2	yes	—
72	#88071	C₂×C₄	1	2	yes	—
73	#88071	C₂×C₄	1	2	yes	—
74	#88055	—	2	2	no	—
75	#88055	—	2	2	no	—
76	#88055	—	2	2	no	—
77	#88055	Q₈	1	4	yes	complemented
78	#88054	—	2	4	no	—
79	#88054	—	2	4	no	—
80	C₈×Dic₁₃	—	2	4	no	—
81	C₄⋊#1055	—	2	2	no	—
82	C₄×#1055	—	2	2	no	—
83	#21343	—	13	1	no	maximal, Sylow
84	C₂×Q₈×C₁₃	—	2	2	no	—
85	C₂×Q₈×C₁₃	—	2	2	no	—
86	C₂×Q₈×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
92	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
93	C₂²×Dic₁₃	C₂²×C₄	1	2	yes	—
94	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₈×C₁₃	—	2	1	no	—
99	C₂×C₈×C₁₃	—	2	1	no	—
100	C₂×C₈×C₁₃	—	2	1	no	—
101	C₂×C₈×C₁₃	—	2	1	no	—
102	C₂×C₈×C₁₃	—	2	2	no	—
103	C₂×C₈×C₁₃	—	2	2	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
106	C₂×C₈×C₁₃	#41	1	2	yes	—
107	C₁₃×C₄⋊C₄	—	2	2	no	—
108	C₁₃×C₄⋊C₄	—	2	4	no	—
109	C₄²×C₁₃	—	2	2	no	—
110	C₄²×C₁₃	—	2	2	no	—
111	C₄²×C₁₃	#41	1	2	yes	—
112	C₄²×C₁₃	#41	1	2	yes	—
113	C₄⋊Dic₁₃	—	2	2	no	—
114	C₄⋊Dic₁₃	—	2	2	no	—
115	C₄⋊Dic₁₃	—	4	2	no	—
116	C₄⋊Dic₁₃	—	4	2	no	—
117	C₄×Dic₁₃	—	2	2	no	—
118	C₄×Dic₁₃	—	2	2	no	—
119	C₄×Dic₁₃	—	2	2	no	—
120	C₄×Dic₁₃	—	2	2	no	—
121	C₄×Dic₁₃	—	2	1	no	—
122	C₄×Dic₁₃	—	2	1	no	—
123	C₄×Dic₁₃	—	4	1	no	—
124	C₄×Dic₁₃	—	4	1	no	—
125	C₄×Dic₁₃	C₂×Q₈	1	2	yes	—
126	C₄×Dic₁₃	#41	1	2	yes	—
127	C₂×#1055	—	2	1	no	—
128	C₂×#1055	—	2	1	no	—
129	C₂×#1055	—	2	1	no	—
130	C₂×#1055	—	2	1	no	—
131	C₂×#1055	—	2	2	no	—
132	C₂×#1055	—	2	2	no	—
133	C₂×#1055	—	2	2	no	—
134	C₂×#1055	C₂×Q₈	1	2	yes	—
135	C₂×#1055	#41	1	2	yes	—
136	#2295	—	13	1	no	—
137	#1984	—	13	1	no	—
138	#1984	D₁₃	1	1	yes	characteristic
139	#1939	—	13	1	no	—
140	#1939	—	13	1	no	—
141	#1917	—	13	2	no	—
142	#1917	—	13	2	no	—
143	#1768	—	13	2	no	—
144	C₄×C₄⋊C₈	—	13	1	no	—
145	#1746	—	13	2	no	—
146	C₄×#97	—	13	1	no	—
147	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
148	Q₈×C₁₃	—	4	4	no	—
149	C₂×C₄×C₁₃	—	2	1	no	—
150	C₂×C₄×C₁₃	—	2	1	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	#117	1	2	yes	—
158	C₂×C₄×C₁₃	#117	1	2	yes	—
159	C₂×C₄×C₁₃	#131	1	2	yes	—
160	C₂×C₄×C₁₃	#131	1	2	yes	—
161	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
167	C₂×Dic₁₃	—	2	1	no	—
168	C₂×Dic₁₃	—	2	1	no	—
169	C₂×Dic₁₃	—	2	1	no	—
170	C₂×Dic₁₃	—	2	1	no	—
171	C₂×Dic₁₃	—	2	2	no	—
172	C₂×Dic₁₃	—	2	2	no	—
173	C₂×Dic₁₃	—	2	1	no	—
174	C₂×Dic₁₃	—	2	1	no	—
175	C₂×Dic₁₃	—	2	1	no	—
176	C₂×Dic₁₃	—	2	1	no	—
177	C₂×Dic₁₃	—	2	2	no	—
178	C₂×Dic₁₃	—	2	2	no	—
179	C₂×Dic₁₃	—	2	1	no	—
180	C₂×Dic₁₃	—	2	1	no	—
181	C₂×Dic₁₃	—	2	2	no	—
182	C₂×Dic₁₃	—	2	2	no	—
183	C₂×Dic₁₃	C₄×Q₈	1	2	yes	—
184	C₂×Dic₁₃	C₄×Q₈	1	2	yes	—
185	C₈×C₁₃	—	2	2	no	—
186	C₈×C₁₃	—	2	2	no	—
187	C₈×C₁₃	—	4	2	no	—
188	#1055	—	2	2	no	—
189	#1055	—	2	2	no	—
190	#1055	—	4	2	no	—
191	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
192	C₂×C₄⋊C₈	—	13	2	no	—
193	C₂×C₄⋊C₈	—	13	2	no	—
194	C₂×C₄⋊C₈	—	13	1	no	—
195	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
196	C₂×#97	—	13	1	no	—
197	C₂×#97	—	13	1	no	—
198	C₂×#97	—	13	1	no	—
199	C₂×#97	—	13	1	no	—
200	C₂×C₄×C₈	—	13	2	no	—
201	C₂×C₄×C₈	—	13	1	no	—
202	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
203	#391	—	13	1	no	—
204	#391	—	13	1	no	—
205	#389	—	13	1	no	—
206	#389	—	13	1	no	—
207	#387	—	13	2	no	—
208	#387	—	13	2	no	—
209	C₄×C₄⋊C₄	—	13	2	no	—
210	C₄×C₄⋊C₄	—	13	1	no	—
211	#376	—	13	2	no	—
212	C₄³	—	13	1	no	—
213	#336	—	13	2	no	—
214	#336	—	13	2	no	—
215	#336	—	13	2	no	—
216	#336	—	13	2	no	—
217	#336	—	13	2	no	—
218	#336	C₂×D₁₃	1	2	yes	—
219	#336	C₂×D₁₃	1	2	yes	—
220	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
221	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
222	C₂²×C₁₃	C₄×#41	1	1	yes	characteristic
223	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
224	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
225	C₂²×C₁₃	#568	1	1	yes	characteristic
226	C₂²×C₁₃	#568	1	1	yes	characteristic
227	C₄×C₁₃	—	2	2	no	—
228	C₄×C₁₃	—	4	2	no	—
229	C₄×C₁₃	—	4	2	no	—
230	C₄×C₁₃	#433	1	4	yes	—
231	C₄×C₁₃	#529	1	1	yes	characteristic
232	C₄×C₁₃	#529	1	1	yes	characteristic
233	C₄×C₁₃	#533	1	1	yes	characteristic
234	C₄×C₁₃	#533	1	1	yes	characteristic
235	Dic₁₃	—	2	2	no	—
236	Dic₁₃	—	2	2	no	—
237	Dic₁₃	—	4	1	no	—
238	Dic₁₃	—	4	2	no	—
239	Dic₁₃	—	4	1	no	—
240	Dic₁₃	—	4	2	no	—
241	C₂²×Q₈	C₄×D₁₃	1	1	yes	characteristic
242	C₂²×C₈	—	13	1	no	—
243	C₂²×C₈	—	13	1	no	—
244	C₂²×C₈	—	13	2	no	—
245	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
246	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
247	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
248	C₄×Q₈	—	2	2	no	—
249	C₄×Q₈	—	2	2	no	—
250	C₂×C₄⋊C₄	—	13	1	no	—
251	C₂×C₄⋊C₄	—	13	1	no	—
252	C₂×C₄⋊C₄	—	13	2	no	—
253	C₂×C₄⋊C₄	—	13	2	no	—
254	C₂×C₄⋊C₄	C₄×D₁₃	1	2	yes	—
255	C₂×C₄⋊C₄	C₄×D₁₃	1	1	yes	characteristic
256	C₂×C₄²	—	13	1	no	—
257	C₂×C₄²	—	13	1	no	—
258	C₂×C₄²	—	13	1	no	—
259	C₂×C₄²	—	13	1	no	—
260	C₂×C₄²	—	13	2	no	—
261	C₂×C₄²	—	13	1	no	—
262	C₂×C₄²	—	13	1	no	—
263	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
264	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
265	C₄⋊C₈	—	2	2	no	—
266	C₄⋊C₈	—	26	4	no	—
267	C₄⋊C₈	—	26	4	no	—
268	C₄⋊C₈	—	26	2	no	—
269	#97	—	13	4	no	—
270	#97	—	26	2	no	—
271	#97	—	26	2	no	—
272	#97	—	26	2	no	—
273	C₄×C₈	—	2	2	no	—
274	C₄×C₈	—	26	4	no	—
275	C₄×C₈	—	26	2	no	—
276	#95	—	13	2	no	—
277	#95	—	13	2	no	—
278	#95	—	13	2	no	—
279	#95	—	13	2	no	—
280	#95	—	13	2	no	—
281	#95	—	13	2	no	—
282	#95	—	13	2	no	—
283	C₂×C₁₃	#2295	1	1	yes	characteristic
284	C₂×C₁₃	C₂×#433	1	1	yes	characteristic
285	C₂×C₁₃	#2923	1	1	yes	characteristic
286	C₂×C₁₃	#2962	1	1	yes	characteristic
287	C₂×C₁₃	#2962	1	1	yes	characteristic
288	C₂×C₁₃	#2969	1	1	yes	characteristic
289	C₂×C₁₃	#2969	1	1	yes	characteristic
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂²×C₄	—	13	1	no	—
294	C₂²×C₄	—	13	1	no	—
295	C₂²×C₄	—	13	2	no	—
296	C₂²×C₄	—	13	2	no	—
297	C₂²×C₄	—	13	1	no	—
298	C₂²×C₄	—	13	1	no	—
299	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
300	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
301	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
303	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	13	2	no	—
312	C₂×C₈	—	13	2	no	—
313	C₂×C₈	—	26	1	no	—
314	C₂×C₈	—	26	1	no	—
315	C₂×C₈	—	26	1	no	—
316	C₂×C₈	—	26	1	no	—
317	C₂×C₈	—	26	2	no	—
318	C₂×C₈	—	26	2	no	—
319	C₂×C₈	—	26	2	no	—
320	C₂×C₈	Q₈×D₁₃	1	2	yes	—
321	C₂×C₈	#6131	1	2	yes	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	26	2	no	—
325	C₄⋊C₄	—	26	2	no	—
326	C₄⋊C₄	—	52	2	no	—
327	C₄⋊C₄	—	52	2	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	13	2	no	—
331	C₄²	—	13	2	no	—
332	C₄²	—	26	2	no	—
333	C₄²	—	26	2	no	—
334	C₄²	—	26	1	no	—
335	C₄²	—	26	2	no	—
336	C₄²	—	26	1	no	—
337	C₄²	—	26	2	no	—
338	C₄²	—	52	1	no	—
339	C₄²	—	52	1	no	—
340	C₄²	#6129	1	2	yes	—
341	C₄²	#6129	1	2	yes	—
342	C₁₃	#21343	1	1	yes	characteristic, complemented, Sylow
343	C₂³	C₂²×C₄×D₁₃	1	1	yes	characteristic
344	Q₈	—	4	4	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	13	2	no	—
354	C₂×C₄	—	13	2	no	—
355	C₂×C₄	—	26	1	no	—
356	C₂×C₄	—	26	1	no	—
357	C₂×C₄	—	26	1	no	—
358	C₂×C₄	—	26	1	no	—
359	C₂×C₄	—	26	1	no	—
360	C₂×C₄	—	26	2	no	—
361	C₂×C₄	—	26	1	no	—
362	C₂×C₄	—	26	2	no	—
363	C₂×C₄	—	26	1	no	—
364	C₂×C₄	—	26	1	no	—
365	C₂×C₄	—	26	2	no	—
366	C₂×C₄	—	26	2	no	—
367	C₂×C₄	—	26	1	no	—
368	C₂×C₄	—	26	2	no	—
369	C₂×C₄	—	26	1	no	—
370	C₂×C₄	—	26	2	no	—
371	C₂×C₄	#88131	1	2	yes	—
372	C₂×C₄	#88131	1	2	yes	—
373	C₂×C₄	#88155	1	2	yes	—
374	C₂×C₄	#88161	1	2	yes	—
375	C₂×C₄	C₂×#6129	1	1	yes	characteristic
376	C₂×C₄	C₂×#6129	1	1	yes	characteristic
377	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
378	C₂×C₄	C₂×#6131	1	1	yes	characteristic
379	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
380	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
381	C₈	—	2	2	no	—
382	C₈	—	2	2	no	—
383	C₈	—	4	2	no	—
384	C₈	—	26	2	no	—
385	C₈	—	26	2	no	—
386	C₈	—	52	2	no	—
387	C₂²	C₂×#88131	1	1	yes	characteristic
388	C₂²	C₄×Q₈×D₁₃	1	1	yes	characteristic
389	C₂²	C₄×#6131	1	1	yes	characteristic
390	C₂²	C₂×#88155	1	1	yes	characteristic
391	C₂²	C₂×#88161	1	1	yes	characteristic
392	C₂²	#11719455	1	1	yes	characteristic
393	C₂²	#11719455	1	1	yes	characteristic
394	C₄	—	2	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	26	2	no	—
398	C₄	—	26	2	no	—
399	C₄	—	52	1	no	—
400	C₄	—	52	2	no	—
401	C₄	—	52	1	no	—
402	C₄	—	52	2	no	—
403	C₄	#11718381	1	4	yes	—
404	C₄	#11719327	1	1	yes	characteristic
405	C₄	#11719329	1	1	yes	characteristic
406	C₄	#11719385	1	1	yes	characteristic
407	C₄	#11719433	1	1	yes	characteristic
408	C₂	#13117311	1	1	yes	characteristic
409	C₂	C₂×#11718381	1	1	yes	characteristic
410	C₂	#13123483	1	1	yes	characteristic
411	C₂	#13123778	1	1	yes	characteristic
412	C₂	#13123784	1	1	yes	characteristic
413	C₂	#13123839	1	1	yes	characteristic
414	C₂	#13123842	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator, socle, prime radical	C₂³×C₁₃	C₂³×C₄
Fitting	C₁₃×#1984	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#1984	D₁₃
hypocenter	C₁₃	#21343
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1984

Complements

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

N	H ≅ G/N	type
77. #88055	Q₈	semidirect
342. C₁₃	#21343	semidirect

Maximal subgroups

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

subgroup	index
#13117314	2
#13115773	2
#13115554	2
#13115552	2
#13115401	2
#13115399	2
#13114692	2
C₄⋊C₈×Dic₁₃	2
#13114586	2
C₄×#88055	2
C₁₃×#1984	2
#21343	13