Subgroups — #15832174

Order 3328.

634 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123803	C₂	1	1	yes	maximal, characteristic
2	#13123404	C₂	1	1	yes	maximal, characteristic
3	#13113624	C₂	1	2	yes	maximal, complemented
4	#13113622	C₂	1	2	yes	maximal, complemented
5	#13113612	C₂	1	1	yes	maximal, characteristic, complemented
6	#13113606	C₂	1	1	yes	maximal, characteristic, complemented
7	#13113604	C₂	1	2	yes	maximal, complemented
8	#13113594	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113589	C₂	1	2	yes	maximal, complemented
10	C₂×#11718072	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2925	C₂	1	1	yes	maximal, characteristic
12	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂×#88202	—	2	1	no	—
14	C₁₃×#433	—	2	2	no	—
15	C₁₃×#432	C₂²	1	2	yes	—
16	C₁₃×#431	C₂²	1	2	yes	—
17	C₁₃×#423	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₁₃×#408	—	2	1	no	—
20	C₁₃×#405	—	2	1	no	—
21	#11718685	C₄	1	1	yes	characteristic
22	#11718685	C₄	1	1	yes	characteristic
23	#11718673	C₄	1	1	yes	characteristic
24	#11718673	C₄	1	1	yes	characteristic
25	#11718672	C₄	1	2	yes	—
26	#11718672	C₄	1	2	yes	—
27	#11718660	—	2	1	no	—
28	#11718660	—	2	2	no	—
29	#11718586	C₂²	1	1	yes	characteristic
30	#11718586	C₂²	1	2	yes	—
31	#11718585	C₂²	1	2	yes	—
32	#11718585	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊#1055	C₂²	1	2	yes	—
35	C₄×#6099	C₂²	1	2	yes	—
36	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
37	#11718072	C₂²	1	1	yes	characteristic
38	#11718072	C₂²	1	2	yes	—
39	#11718072	C₂²	1	2	yes	—
40	#11718072	C₂²	1	1	yes	characteristic
41	#11718072	C₂²	1	1	yes	characteristic
42	#11718072	C₂²	1	1	yes	characteristic
43	#11718071	C₂²	1	2	yes	—
44	#11718071	C₂²	1	2	yes	—
45	#11718071	C₂²	1	2	yes	—
46	#11718071	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
48	C₂×C₁₃×M₁₆	—	2	1	no	—
49	C₂²×C₈×C₁₃	—	2	1	no	—
50	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₄×Q₈×C₁₃	Q₈	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	Q₈	1	2	yes	—
55	C₄×D₄×C₁₃	Q₈	1	1	yes	characteristic
56	C₁₃×#117	D₄	1	1	yes	characteristic
57	C₁₃×#117	D₄	1	2	yes	—
58	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
60	#88202	—	4	4	no	—
61	C₂×#6099	—	2	2	no	—
62	C₂×#6099	—	2	1	no	—
63	C₂×#6099	C₂×C₄	1	2	yes	—
64	C₂×#6099	C₂×C₄	1	2	yes	—
65	C₂²×#1055	—	2	2	no	—
66	C₂²×#1055	—	2	1	no	—
67	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
68	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
69	C₁₃×C₄⋊C₈	—	2	1	no	—
70	C₁₃×C₄⋊C₈	—	2	1	no	—
71	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
72	C₁₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
73	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
74	C₁₃×C₂²⋊C₈	—	2	2	no	—
75	C₁₃×C₂²⋊C₈	—	2	2	no	—
76	C₁₃×#97	—	2	2	no	—
77	C₄×C₈×C₁₃	—	2	2	no	—
78	C₂²⋊#1055	C₂×C₄	1	2	yes	—
79	C₂²⋊#1055	C₂×C₄	1	2	yes	—
80	C₂²⋊#1055	C₂×C₄	1	2	yes	—
81	C₄⋊#1055	—	2	2	no	—
82	C₄⋊#1055	—	2	1	no	—
83	C₄⋊#1055	—	2	2	no	—
84	C₄⋊#1055	—	2	1	no	—
85	C₄⋊#1055	C₂×C₄	1	2	yes	—
86	C₄⋊#1055	C₂×C₄	1	2	yes	—
87	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
88	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
89	C₄⋊#1055	C₂³	1	1	yes	characteristic
90	C₄⋊#1055	C₂³	1	1	yes	characteristic
91	C₄⋊#1055	C₂³	1	2	yes	—
92	#88043	C₂×C₄	1	2	yes	—
93	#88043	C₂×C₄	1	2	yes	—
94	C₄×#1055	C₂×C₄	1	1	yes	characteristic
95	C₄×#1055	C₂×C₄	1	1	yes	characteristic
96	C₄×#1055	C₂³	1	1	yes	characteristic
97	C₄×#1055	C₂³	1	1	yes	characteristic
98	C₄×#1055	C₂³	1	2	yes	—
99	#17830	—	13	1	no	maximal, Sylow
100	C₁₃×#41	—	2	2	no	—
101	C₁₃×#41	—	2	2	no	—
102	C₂×Q₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂×D₄×C₁₃	C₄⋊C₄	1	2	yes	—
104	C₂×D₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
110	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
111	C₁₃×M₁₆	—	4	2	no	—
112	C₂×C₈×C₁₃	—	2	1	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	4	2	no	—
116	C₁₃×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
117	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
118	C₁₃×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
119	C₁₃×C₄⋊C₄	C₄⋊C₄	1	1	yes	characteristic
120	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
121	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
122	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	2	yes	—
123	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
125	C₄²×C₁₃	C₂×D₄	1	2	yes	—
126	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
128	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
129	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
130	#6099	—	2	4	no	—
131	#6099	—	4	2	no	—
132	#6099	—	4	4	no	—
133	#6099	—	4	2	no	—
134	C₂×#1055	—	2	2	no	—
135	C₂×#1055	—	2	1	no	—
136	C₂×#1055	—	2	2	no	—
137	C₂×#1055	—	2	1	no	—
138	C₂×#1055	—	4	1	no	—
139	C₂×#1055	—	4	4	no	—
140	C₂×#1055	—	4	2	no	—
141	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
142	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
143	C₂×#1055	C₂²×C₄	1	2	yes	—
144	C₂×#1055	C₂²×C₄	1	2	yes	—
145	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
146	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
147	#2965	—	13	1	no	—
148	#2925	D₁₃	1	1	yes	characteristic
149	#2906	—	13	1	no	—
150	#1574	—	13	2	no	—
151	#1573	—	13	2	no	—
152	#1571	—	13	1	no	—
153	#1570	—	13	1	no	—
154	#1569	—	13	2	no	—
155	#1567	—	13	1	no	—
156	#1565	—	13	2	no	—
157	C₂×#334	—	13	1	no	—
158	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
159	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
160	Q₈×C₁₃	—	2	2	no	—
161	D₄×C₁₃	—	2	4	no	—
162	D₄×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	2	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	4	1	no	—
170	C₂×C₄×C₁₃	—	4	2	no	—
171	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
173	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
174	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
175	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
178	C₂×C₄×C₁₃	#137	1	2	yes	—
179	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
182	C₈×C₁₃	—	4	2	no	—
183	C₈×C₁₃	—	4	1	no	—
184	C₈×C₁₃	—	4	1	no	—
185	#1055	—	2	1	no	—
186	#1055	—	2	2	no	—
187	#1055	—	2	1	no	—
188	#1055	—	2	1	no	—
189	#1055	—	2	2	no	—
190	#1055	—	4	1	no	—
191	#1055	—	4	2	no	—
192	#1055	—	4	1	no	—
193	#1055	#131	1	2	yes	complemented
194	C₂×#131	—	26	1	no	—
195	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
196	#446	—	13	1	no	—
197	#446	—	13	1	no	—
198	#436	—	13	1	no	—
199	#436	—	13	1	no	—
200	#435	—	13	2	no	—
201	#435	—	13	2	no	—
202	#433	—	2	2	no	—
203	#432	C₂×D₁₃	1	2	yes	—
204	#431	—	13	1	no	—
205	#431	—	13	2	no	—
206	#431	C₂×D₁₃	1	2	yes	—
207	#424	—	26	1	no	—
208	#424	—	26	2	no	—
209	#423	—	13	1	no	—
210	#423	—	13	2	no	—
211	#423	C₂×D₁₃	1	1	yes	characteristic
212	C₂×C₄⋊C₈	—	13	1	no	—
213	C₂×C₄⋊C₈	—	13	2	no	—
214	C₂×C₄⋊C₈	C₂×D₁₃	1	1	yes	characteristic
215	#408	—	2	1	no	—
216	#405	—	2	1	no	—
217	C₄×M₁₆	—	13	2	no	—
218	C₂×C₄×C₈	—	13	1	no	—
219	#335	—	13	2	no	—
220	#335	—	13	2	no	—
221	#335	—	13	2	no	—
222	#335	—	13	2	no	—
223	#334	—	13	1	no	—
224	#334	—	13	1	no	—
225	#334	—	13	1	no	—
226	#334	—	13	1	no	—
227	#334	—	13	2	no	—
228	#334	—	13	2	no	—
229	C₂²×C₁₃	—	2	1	no	—
230	C₂²×C₁₃	—	2	1	no	—
231	C₂²×C₁₃	—	2	2	no	—
232	C₂²×C₁₃	—	2	2	no	—
233	C₂²×C₁₃	—	2	2	no	—
234	C₂²×C₁₃	#428	1	2	yes	—
235	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
236	C₄×C₁₃	—	2	1	no	—
237	C₄×C₁₃	—	2	2	no	—
238	C₄×C₁₃	—	2	2	no	—
239	C₄×C₁₃	—	2	1	no	—
240	C₄×C₁₃	—	2	1	no	—
241	C₄×C₁₃	—	2	2	no	—
242	C₄×C₁₃	#428	1	2	yes	—
243	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
244	C₄×C₁₃	#568	1	1	yes	characteristic
245	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
246	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
247	C₂×#41	C₂²⋊D₁₃	1	1	yes	characteristic
248	#131	—	52	4	no	—
249	C₂×M₁₆	—	2	1	no	—
250	C₂×M₁₆	—	13	2	no	—
251	C₂×M₁₆	—	13	2	no	—
252	C₂×M₁₆	—	26	2	no	—
253	C₂×M₁₆	—	26	1	no	—
254	C₂²×C₈	—	2	1	no	—
255	C₂²×C₈	—	13	1	no	—
256	C₂²×C₈	—	13	1	no	—
257	C₂²×C₈	—	26	2	no	—
258	C₂²×C₈	—	26	1	no	—
259	C₄×Q₈	Dic₂₆	1	1	yes	characteristic
260	C₄×Q₈	C₄×D₁₃	1	1	yes	characteristic
261	C₄×D₄	Dic₂₆	1	2	yes	—
262	C₄×D₄	Dic₂₆	1	1	yes	characteristic
263	C₄×D₄	C₄×D₁₃	1	2	yes	—
264	C₄×D₄	C₄×D₁₃	1	1	yes	characteristic
265	#117	C₂²⋊D₁₃	1	1	yes	characteristic
266	#117	C₂²⋊D₁₃	1	2	yes	—
267	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
268	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	13	2	no	—
272	C₄⋊C₈	—	13	2	no	—
273	C₄⋊C₈	—	13	1	no	—
274	C₄⋊C₈	—	13	1	no	—
275	C₄⋊C₈	—	13	1	no	—
276	C₄⋊C₈	—	13	1	no	—
277	C₄⋊C₈	—	13	2	no	—
278	C₄⋊C₈	—	26	2	no	—
279	C₄⋊C₈	—	26	1	no	—
280	C₄⋊C₈	—	26	2	no	—
281	C₄⋊C₈	—	26	1	no	—
282	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
283	C₄⋊C₈	C₂²×D₁₃	1	1	yes	characteristic
284	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
285	C₂²⋊C₈	—	2	2	no	—
286	C₂²⋊C₈	—	2	2	no	—
287	C₂²⋊C₈	—	13	2	no	—
288	C₂²⋊C₈	—	13	2	no	—
289	C₂²⋊C₈	—	13	2	no	—
290	#97	—	2	2	no	—
291	#97	—	13	2	no	—
292	#97	—	13	2	no	—
293	C₄×C₈	—	2	2	no	—
294	C₄×C₈	—	13	1	no	—
295	C₄×C₈	—	13	1	no	—
296	C₄×C₈	—	13	1	no	—
297	C₄×C₈	—	13	1	no	—
298	C₄×C₈	—	13	2	no	—
299	C₂×C₁₃	—	2	2	no	—
300	C₂×C₁₃	—	4	2	no	—
301	C₂×C₁₃	#2906	1	1	yes	characteristic
302	C₂×C₁₃	C₂×#428	1	1	yes	characteristic
303	C₂×C₁₃	#2916	1	1	yes	characteristic
304	#41	—	2	2	no	—
305	#41	—	2	2	no	—
306	C₂×Q₈	#6101	1	1	yes	characteristic
307	C₂×D₄	#6101	1	2	yes	—
308	C₂×D₄	#6101	1	1	yes	characteristic
309	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
310	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
313	C₂²×C₄	C₂×C₂²⋊D₁₃	1	2	yes	—
314	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
315	M₁₆	—	4	2	no	—
316	M₁₆	—	26	4	no	—
317	M₁₆	—	52	2	no	—
318	M₁₆	—	52	4	no	—
319	M₁₆	—	52	2	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	4	2	no	—
324	C₂×C₈	—	13	1	no	—
325	C₂×C₈	—	13	1	no	—
326	C₂×C₈	—	13	1	no	—
327	C₂×C₈	—	13	1	no	—
328	C₂×C₈	—	13	2	no	—
329	C₂×C₈	—	13	2	no	—
330	C₂×C₈	—	26	2	no	—
331	C₂×C₈	—	26	1	no	—
332	C₂×C₈	—	26	2	no	—
333	C₂×C₈	—	26	1	no	—
334	C₂×C₈	—	52	1	no	—
335	C₂×C₈	—	52	4	no	—
336	C₂×C₈	—	52	2	no	—
337	C₄⋊C₄	#6101	1	2	yes	—
338	C₄⋊C₄	#6101	1	1	yes	characteristic
339	C₄⋊C₄	#6101	1	2	yes	—
340	C₄⋊C₄	#6101	1	1	yes	characteristic
341	C₂²⋊C₄	#6101	1	2	yes	—
342	C₂²⋊C₄	#6101	1	2	yes	—
343	C₂²⋊C₄	#6101	1	2	yes	—
344	C₄²	C₂×Dic₂₆	1	2	yes	—
345	C₄²	C₂×Dic₂₆	1	1	yes	characteristic
346	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
347	C₄²	C₂×C₄×D₁₃	1	2	yes	—
348	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
349	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
350	C₄²	C₂³×D₁₃	1	1	yes	characteristic
351	C₁₃	#17830	1	1	yes	characteristic, complemented, Sylow
352	C₂³	C₂×#6101	1	2	yes	—
353	C₂³	C₂×#6101	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	D₄	—	2	4	no	—
356	D₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	C₂×#6101	1	2	yes	—
366	C₂×C₄	C₂×#6101	1	2	yes	—
367	C₂×C₄	C₂×#6101	1	1	yes	characteristic
368	C₂×C₄	C₂×#6101	1	1	yes	characteristic
369	C₂×C₄	C₂×#6101	1	2	yes	—
370	C₂×C₄	C₂×#6101	1	1	yes	characteristic
371	C₂×C₄	#88203	1	2	yes	—
372	C₂×C₄	#88205	1	2	yes	—
373	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
375	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
376	C₈	—	4	2	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	1	no	—
379	C₈	—	13	2	no	—
380	C₈	—	26	1	no	—
381	C₈	—	26	2	no	—
382	C₈	—	26	1	no	—
383	C₈	—	26	1	no	—
384	C₈	—	26	2	no	—
385	C₈	—	52	1	no	—
386	C₈	—	52	2	no	—
387	C₈	—	52	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	#11718656	1	2	yes	—
394	C₂²	C₂²×#6101	1	1	yes	characteristic
395	C₄	—	2	1	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	2	no	—
401	C₄	#11718656	1	2	yes	—
402	C₄	D₁₃×#131	1	1	yes	characteristic
403	C₄	#11719455	1	1	yes	characteristic
404	C₄	C₂×#88203	1	1	yes	characteristic
405	C₄	C₂×#88205	1	1	yes	characteristic
406	C₂	—	2	2	no	—
407	C₂	—	4	2	no	—
408	C₂	#13123402	1	1	yes	characteristic
409	C₂	C₂×#11718656	1	1	yes	characteristic
410	C₂	#13123445	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×#2925	C₂
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂×C₁₃×#41	D₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2925	D₁₃
hypocenter	C₁₃	#17830
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ #2925

Complements

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

N	H ≅ G/N	type
3. #13113624	C₂	semidirect
4. #13113622	C₂	semidirect
5. #13113612	C₂	semidirect
6. #13113606	C₂	semidirect
7. #13113604	C₂	semidirect
8. #13113594	C₂	semidirect
9. #13113589	C₂	semidirect
10. C₂×#11718072	C₂	semidirect
193. #1055	#131	semidirect
351. C₁₃	#17830	semidirect

Maximal subgroups

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

subgroup	index
#13123803	2
#13123404	2
#13113624	2
#13113622	2
#13113612	2
#13113606	2
#13113604	2
#13113594	2
#13113589	2
C₂×#11718072	2
C₁₃×#2925	2
#17830	13