Subgroups — #15832208

Order 3328.

616 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123961	C₂	1	1	yes	maximal, characteristic
2	#41×#1055	C₂	1	1	yes	maximal, characteristic
3	#13113627	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113624	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113622	C₂	1	2	yes	maximal, complemented
6	#13113619	C₂	1	2	yes	maximal, complemented
7	#13113597	C₂	1	2	yes	maximal, complemented
8	#13113591	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113582	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11718072	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2990	C₂	1	1	yes	maximal, characteristic
12	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₁₃×#446	—	2	1	no	—
14	C₁₃×#435	—	2	2	no	—
15	C₈×D₄×C₁₃	—	2	1	no	—
16	C₁₃×#432	C₂²	1	2	yes	—
17	C₁₃×#431	C₂²	1	1	yes	characteristic
18	C₁₃×#423	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
20	#11718685	—	2	1	no	—
21	Q₈×#1055	C₄	1	1	yes	characteristic
22	Q₈×#1055	C₄	1	1	yes	characteristic
23	#11718672	—	2	2	no	—
24	D₄×#1055	—	2	1	no	—
25	D₄×#1055	C₄	1	1	yes	characteristic
26	D₄×#1055	C₄	1	2	yes	—
27	D₄×#1055	C₄	1	1	yes	characteristic
28	D₄×#1055	C₄	1	2	yes	—
29	#11718587	C₂²	1	2	yes	—
30	#11718586	C₂²	1	1	yes	characteristic
31	#11718586	C₂²	1	2	yes	—
32	#11718586	C₂²	1	1	yes	characteristic
33	#11718585	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊#1055	C₂²	1	2	yes	—
35	C₂×C₄×#1055	C₂²	1	2	yes	—
36	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
37	#11718072	C₂²	1	2	yes	—
38	#11718072	C₂²	1	2	yes	—
39	#11718072	C₂²	1	2	yes	—
40	#11718072	C₂²	1	1	yes	characteristic
41	#11718072	C₂²	1	2	yes	—
42	#11718072	C₂²	1	1	yes	characteristic
43	#11718071	C₂²	1	1	yes	characteristic
44	#11718071	C₂²	1	2	yes	—
45	#11718071	C₂²	1	1	yes	characteristic
46	#11718071	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	Q₈	1	1	yes	characteristic
48	C₂×C₁₃×M₁₆	—	2	1	no	—
49	C₂²×C₈×C₁₃	—	2	2	no	—
50	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₄×Q₈×C₁₃	D₄	1	1	yes	characteristic
52	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
53	C₄×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₄×D₄×C₁₃	D₄	1	1	yes	characteristic
55	C₄×D₄×C₁₃	D₄	1	2	yes	—
56	C₁₃×#117	Q₈	1	1	yes	characteristic
57	C₁₃×#117	Q₈	1	2	yes	—
58	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
59	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
60	C₂×#6099	—	2	1	no	—
61	C₂²×#1055	—	2	2	no	—
62	C₂²×#1055	C₂×C₄	1	2	yes	—
63	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
64	C₂²×#1055	C₂×C₄	1	2	yes	—
65	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
66	C₁₃×C₄⋊C₈	—	2	2	no	—
67	C₁₃×C₄⋊C₈	—	2	1	no	—
68	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
69	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
70	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
71	C₁₃×C₂²⋊C₈	—	2	1	no	—
72	C₁₃×C₂²⋊C₈	—	2	2	no	—
73	C₁₃×#97	—	2	2	no	—
74	C₄×C₈×C₁₃	—	2	1	no	—
75	C₂²⋊#1055	—	2	2	no	—
76	C₂²⋊#1055	—	2	1	no	—
77	C₂²⋊#1055	C₂×C₄	1	2	yes	—
78	C₂²⋊#1055	C₂×C₄	1	2	yes	—
79	C₂²⋊#1055	C₂×C₄	1	2	yes	—
80	C₄⋊#1055	—	2	1	no	—
81	C₄⋊#1055	—	2	2	no	—
82	C₄⋊#1055	C₂×C₄	1	2	yes	—
83	C₄⋊#1055	C₂×C₄	1	2	yes	—
84	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
85	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
86	C₄⋊#1055	C₂³	1	1	yes	characteristic
87	C₄⋊#1055	C₂³	1	1	yes	characteristic
88	C₄⋊#1055	C₂³	1	2	yes	—
89	#88043	—	2	2	no	—
90	C₄×#1055	—	2	1	no	—
91	C₄×#1055	C₂×C₄	1	2	yes	—
92	C₄×#1055	C₂×C₄	1	1	yes	characteristic
93	C₄×#1055	C₂×C₄	1	2	yes	—
94	C₄×#1055	C₂×C₄	1	1	yes	characteristic
95	C₄×#1055	C₂³	1	1	yes	characteristic
96	C₄×#1055	C₂³	1	2	yes	—
97	C₄×#1055	C₂³	1	1	yes	characteristic
98	#17834	—	13	1	no	maximal, Sylow
99	C₁₃×#41	—	2	4	no	—
100	C₂×Q₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
101	C₂×D₄×C₁₃	C₄⋊C₄	1	2	yes	—
102	C₂×D₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
109	C₁₃×M₁₆	—	8	1	no	—
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
112	C₂×C₈×C₁₃	—	2	2	no	—
113	C₂×C₈×C₁₃	—	8	2	no	—
114	C₁₃×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
115	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
116	C₁₃×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
117	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
118	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
119	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
120	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
121	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
122	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₁₃	C₂×D₄	1	2	yes	—
125	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
126	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
127	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
128	#6099	—	8	1	no	—
129	C₂×#1055	—	2	4	no	—
130	C₂×#1055	—	2	2	no	—
131	C₂×#1055	—	2	1	no	—
132	C₂×#1055	—	2	1	no	—
133	C₂×#1055	—	2	2	no	—
134	C₂×#1055	—	4	2	no	—
135	C₂×#1055	—	4	1	no	—
136	C₂×#1055	—	8	2	no	—
137	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
138	C₂×#1055	C₂²×C₄	1	2	yes	—
139	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
140	C₂×#1055	C₂²×C₄	1	2	yes	—
141	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
142	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
143	#2990	—	13	1	no	—
144	#2990	D₁₃	1	1	yes	characteristic
145	C₈×#41	—	13	1	no	—
146	#1574	—	13	1	no	—
147	#1574	—	13	1	no	—
148	#1573	—	13	2	no	—
149	#1573	—	13	2	no	—
150	#1568	—	13	2	no	—
151	#1566	—	13	1	no	—
152	#1564	—	13	1	no	—
153	C₂×#334	—	13	2	no	—
154	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
156	Q₈×C₁₃	—	2	2	no	—
157	D₄×C₁₃	—	2	4	no	—
158	D₄×C₁₃	#108	1	4	yes	—
159	C₂×C₄×C₁₃	—	2	4	no	—
160	C₂×C₄×C₁₃	—	2	2	no	—
161	C₂×C₄×C₁₃	—	2	1	no	—
162	C₂×C₄×C₁₃	—	2	2	no	—
163	C₂×C₄×C₁₃	—	2	1	no	—
164	C₂×C₄×C₁₃	—	2	2	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
170	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
171	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
174	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
178	C₈×C₁₃	—	4	1	no	—
179	C₈×C₁₃	—	4	1	no	—
180	C₈×C₁₃	—	4	2	no	—
181	#1055	—	2	2	no	—
182	#1055	—	2	1	no	—
183	#1055	—	2	1	no	—
184	#1055	—	2	2	no	—
185	#1055	—	2	1	no	—
186	#1055	—	4	1	no	—
187	#1055	—	4	1	no	—
188	#1055	—	4	2	no	—
189	#1055	#131	1	2	yes	—
190	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
191	#446	—	2	1	no	—
192	#446	—	26	1	no	—
193	C₈×Q₈	—	13	1	no	—
194	C₈×Q₈	—	13	1	no	—
195	#435	—	2	2	no	—
196	#435	—	26	2	no	—
197	C₈×D₄	—	2	1	no	—
198	C₈×D₄	—	13	2	no	—
199	C₈×D₄	—	13	1	no	—
200	C₈×D₄	—	13	2	no	—
201	C₈×D₄	—	13	1	no	—
202	C₈×D₄	—	26	1	no	—
203	#432	—	13	2	no	—
204	#432	C₂×D₁₃	1	2	yes	—
205	#431	—	13	2	no	—
206	#431	—	13	1	no	—
207	#431	—	13	1	no	—
208	#431	C₂×D₁₃	1	1	yes	characteristic
209	#423	—	13	1	no	—
210	#423	C₂×D₁₃	1	1	yes	characteristic
211	C₂×C₄⋊C₈	—	13	2	no	—
212	C₂×C₄⋊C₈	C₂×D₁₃	1	2	yes	—
213	C₂×C₄×C₈	—	13	2	no	—
214	C₂×C₄×C₈	—	13	1	no	—
215	#335	—	13	1	no	—
216	#335	—	13	1	no	—
217	#335	—	13	2	no	—
218	#335	—	13	2	no	—
219	#334	—	13	1	no	—
220	#334	—	13	2	no	—
221	#334	—	13	2	no	—
222	#334	—	13	2	no	—
223	#334	—	13	1	no	—
224	#334	—	13	2	no	—
225	C₂²×C₁₃	—	2	2	no	—
226	C₂²×C₁₃	—	2	2	no	—
227	C₂²×C₁₃	—	2	1	no	—
228	C₂²×C₁₃	—	2	1	no	—
229	C₂²×C₁₃	—	2	1	no	—
230	C₂²×C₁₃	C₂×#108	1	4	yes	—
231	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
232	C₄×C₁₃	—	2	2	no	—
233	C₄×C₁₃	—	2	1	no	—
234	C₄×C₁₃	—	2	2	no	—
235	C₄×C₁₃	—	2	1	no	—
236	C₄×C₁₃	—	2	1	no	—
237	C₄×C₁₃	—	2	2	no	—
238	C₄×C₁₃	C₂×#108	1	2	yes	—
239	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
240	C₄×C₁₃	#568	1	1	yes	characteristic
241	C₄×C₁₃	#577	1	1	yes	characteristic
242	C₄×C₁₃	#577	1	1	yes	characteristic
243	C₂×#41	Dic₂₆	1	1	yes	characteristic
244	C₂×M₁₆	—	2	1	no	—
245	C₂×M₁₆	—	26	1	no	—
246	C₂²×C₈	—	2	2	no	—
247	C₂²×C₈	—	13	2	no	—
248	C₂²×C₈	—	13	1	no	—
249	C₂²×C₈	—	13	2	no	—
250	C₂²×C₈	—	13	1	no	—
251	C₂²×C₈	—	26	2	no	—
252	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
253	C₄×Q₈	C₂²⋊D₁₃	1	1	yes	characteristic
254	C₄×D₄	C₄×D₁₃	1	2	yes	—
255	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
256	C₄×D₄	C₂²⋊D₁₃	1	1	yes	characteristic
257	C₄×D₄	C₂²⋊D₁₃	1	2	yes	—
258	#117	Dic₂₆	1	1	yes	characteristic
259	#117	Dic₂₆	1	2	yes	—
260	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
261	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
262	C₄⋊C₈	—	2	2	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	13	2	no	—
265	C₄⋊C₈	—	13	2	no	—
266	C₄⋊C₈	—	13	1	no	—
267	C₄⋊C₈	—	13	1	no	—
268	C₄⋊C₈	—	13	1	no	—
269	C₄⋊C₈	—	13	2	no	—
270	C₄⋊C₈	—	13	1	no	—
271	C₄⋊C₈	—	26	2	no	—
272	C₄⋊C₈	—	26	1	no	—
273	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
274	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
275	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
276	C₂²⋊C₈	—	2	1	no	—
277	C₂²⋊C₈	—	2	2	no	—
278	C₂²⋊C₈	—	13	2	no	—
279	C₂²⋊C₈	—	13	2	no	—
280	C₂²⋊C₈	—	13	2	no	—
281	C₂²⋊C₈	—	26	1	no	—
282	C₂²⋊C₈	—	26	2	no	—
283	#97	—	2	2	no	—
284	#97	—	26	2	no	—
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	—	13	2	no	—
287	C₄×C₈	—	13	1	no	—
288	C₄×C₈	—	13	2	no	—
289	C₄×C₈	—	13	1	no	—
290	C₄×C₈	—	13	1	no	—
291	C₄×C₈	—	13	2	no	—
292	C₄×C₈	—	13	1	no	—
293	C₄×C₈	—	26	1	no	—
294	C₂×C₁₃	—	2	4	no	—
295	C₂×C₁₃	—	4	1	no	—
296	C₂×C₁₃	#2906	1	1	yes	characteristic
297	C₂×C₁₃	#2912	1	1	yes	characteristic
298	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
299	#41	—	2	4	no	—
300	C₂×Q₈	#6101	1	1	yes	characteristic
301	C₂×D₄	#6101	1	2	yes	—
302	C₂×D₄	#6101	1	1	yes	characteristic
303	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
304	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
307	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
308	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
309	M₁₆	—	8	1	no	—
310	M₁₆	—	104	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	8	2	no	—
315	C₂×C₈	—	13	1	no	—
316	C₂×C₈	—	13	1	no	—
317	C₂×C₈	—	13	2	no	—
318	C₂×C₈	—	13	1	no	—
319	C₂×C₈	—	13	2	no	—
320	C₂×C₈	—	13	1	no	—
321	C₂×C₈	—	26	4	no	—
322	C₂×C₈	—	26	2	no	—
323	C₂×C₈	—	26	1	no	—
324	C₂×C₈	—	26	1	no	—
325	C₂×C₈	—	26	2	no	—
326	C₂×C₈	—	52	2	no	—
327	C₂×C₈	—	52	1	no	—
328	C₂×C₈	—	104	2	no	—
329	C₄⋊C₄	#6101	1	2	yes	—
330	C₄⋊C₄	#6101	1	1	yes	characteristic
331	C₄⋊C₄	#6101	1	2	yes	—
332	C₄⋊C₄	#6101	1	1	yes	characteristic
333	C₂²⋊C₄	#6101	1	2	yes	—
334	C₂²⋊C₄	#6101	1	2	yes	—
335	C₂²⋊C₄	#6101	1	2	yes	—
336	C₄²	C₂×Dic₂₆	1	2	yes	—
337	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
338	C₄²	C₂×C₄×D₁₃	1	2	yes	—
339	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
340	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
341	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
342	C₄²	C₂³×D₁₃	1	1	yes	characteristic
343	C₁₃	#17834	1	1	yes	characteristic, complemented, Sylow
344	C₂³	C₂×#6101	1	1	yes	characteristic
345	C₂³	C₂×#6101	1	2	yes	—
346	Q₈	—	2	2	no	—
347	D₄	—	2	4	no	—
348	D₄	#88062	1	4	yes	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	C₂×#6101	1	2	yes	—
360	C₂×C₄	C₂×#6101	1	1	yes	characteristic
361	C₂×C₄	C₂×#6101	1	1	yes	characteristic
362	C₂×C₄	C₂×#6101	1	2	yes	—
363	C₂×C₄	C₂×#6101	1	2	yes	—
364	C₂×C₄	C₂×#6101	1	1	yes	characteristic
365	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
366	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
367	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
368	C₈	—	4	1	no	—
369	C₈	—	4	2	no	—
370	C₈	—	4	1	no	—
371	C₈	—	13	2	no	—
372	C₈	—	26	2	no	—
373	C₈	—	26	1	no	—
374	C₈	—	26	2	no	—
375	C₈	—	26	1	no	—
376	C₈	—	26	1	no	—
377	C₈	—	52	1	no	—
378	C₈	—	52	1	no	—
379	C₈	—	52	2	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	1	no	—
385	C₂²	C₂×#88062	1	4	yes	—
386	C₂²	C₂²×#6101	1	1	yes	characteristic
387	C₄	—	2	2	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	2	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	2	no	—
393	C₄	C₂×#88062	1	2	yes	—
394	C₄	D₁₃×#131	1	1	yes	characteristic
395	C₄	#11719455	1	1	yes	characteristic
396	C₄	#11719541	1	1	yes	characteristic
397	C₄	#11719542	1	1	yes	characteristic
398	C₂	—	2	4	no	—
399	C₂	—	4	1	no	—
400	C₂	#13123402	1	1	yes	characteristic
401	C₂	#13123429	1	1	yes	characteristic
402	C₂	C₂²×#88062	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#2990	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂×C₁₃×#41	Q₈
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2990	D₁₃
hypocenter	C₁₃	#17834
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2990

Complements

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

N	H ≅ G/N	type
3. #13113627	C₂	semidirect
4. #13113624	C₂	semidirect
5. #13113622	C₂	semidirect
6. #13113619	C₂	semidirect
7. #13113597	C₂	semidirect
8. #13113591	C₂	semidirect
9. #13113582	C₂	semidirect
10. C₂×#11718072	C₂	semidirect
343. C₁₃	#17834	semidirect

Maximal subgroups

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

subgroup	index
#13123961	2
#41×#1055	2
#13113627	2
#13113624	2
#13113622	2
#13113619	2
#13113597	2
#13113591	2
#13113582	2
C₂×#11718072	2
C₁₃×#2990	2
#17834	13