Subgroups — #15876844

Order 3328.

820 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125317	C₂	1	1	yes	maximal, characteristic
2	#13123754	C₂	1	1	yes	maximal, characteristic, complemented
3	#13115747	C₂	1	1	yes	maximal, characteristic, complemented
4	#13115732	C₂	1	1	yes	maximal, characteristic, complemented
5	#13115368	C₂	1	2	yes	maximal, complemented
6	#13115360	C₂	1	2	yes	maximal, complemented
7	#13115323	C₂	1	2	yes	maximal, complemented
8	#13115313	C₂	1	2	yes	maximal, complemented
9	#13114959	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114591	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₁₃×#518	C₂²	1	2	yes	—
14	#11719510	C₂²	1	2	yes	—
15	C₂×#88186	C₂²	1	2	yes	—
16	#11719450	C₂²	1	2	yes	—
17	C₂×#88158	C₂²	1	1	yes	characteristic
18	C₁₃×#442	—	2	2	no	—
19	C₄×C₁₃×D₈	—	2	2	no	—
20	C₁₃×#427	C₂²	1	1	yes	characteristic
21	C₁₃×#418	C₂²	1	2	yes	—
22	C₁₃×#405	C₂²	1	1	yes	characteristic
23	C₂×#88073	C₂²	1	2	yes	—
24	#11718876	C₂²	1	2	yes	—
25	#11718816	C₄	1	2	yes	complemented
26	#11718815	C₄	1	4	yes	complemented
27	#11718812	C₄	1	2	yes	complemented
28	C₂×#88059	C₂²	1	1	yes	characteristic
29	#11718762	C₂²	1	1	yes	characteristic
30	#11718762	C₂²	1	1	yes	characteristic
31	#11718667	C₂²	1	2	yes	—
32	#11718666	C₂²	1	2	yes	—
33	#11718666	C₂²	1	2	yes	—
34	#11718378	—	2	2	no	—
35	#11718361	—	2	2	no	—
36	#11718152	C₂²	1	1	yes	characteristic
37	#11718149	C₂²	1	1	yes	characteristic
38	#11718125	C₂²	1	2	yes	—
39	#11718123	C₂²	1	2	yes	—
40	#11718123	C₂²	1	1	yes	characteristic
41	#11718123	C₂²	1	1	yes	characteristic
42	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
43	C₂×#6127	C₂³	1	2	yes	—
44	C₂×C₁₃×D₈	—	2	1	no	—
45	C₂×C₁₃×D₈	—	2	1	no	—
46	C₂×C₁₃×D₈	—	2	1	no	—
47	C₂×C₁₃×D₈	—	2	1	no	—
48	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
49	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
50	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₄×D₄×C₁₃	—	2	4	no	—
53	C₄×D₄×C₁₃	—	4	2	no	—
54	C₁₃×#117	C₂³	1	2	yes	—
55	C₁₃×#117	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×C₂²⋊C₄	—	4	2	no	—
57	#88207	—	4	2	no	—
58	#88194	C₂×C₄	1	4	yes	complemented
59	#88192	—	4	2	no	—
60	#88190	C₂×C₄	1	4	yes	complemented
61	C₂×#6105	C₂×C₄	1	4	yes	complemented
62	#88186	—	4	2	no	—
63	#88186	—	4	2	no	—
64	C₂×#6104	C₂×C₄	1	4	yes	complemented
65	#88180	C₂³	1	1	yes	characteristic
66	#88180	C₂³	1	1	yes	characteristic
67	C₂×#6099	C₂³	1	1	yes	characteristic
68	C₂×#6099	C₂³	1	2	yes	—
69	C₂×#6099	C₂³	1	1	yes	characteristic
70	#88161	—	4	2	no	—
71	M₁₆×D₁₃	—	4	2	no	—
72	C₂×Dic₅₂	C₂×C₄	1	1	yes	characteristic, complemented
73	#88158	—	2	1	no	—
74	#88158	—	2	1	no	—
75	#88158	—	2	1	no	—
76	#88158	—	2	1	no	—
77	C₂×D₁₀₄	C₂×C₄	1	1	yes	characteristic, complemented
78	C₂×#6095	C₂×C₄	1	2	yes	complemented
79	#88155	—	2	4	no	—
80	C₁₃×#107	—	2	1	no	—
81	C₁₃×#106	—	2	1	no	—
82	C₁₃×#102	—	2	4	no	—
83	C₁₃×#97	D₄	1	2	yes	complemented
84	C₄×C₈×C₁₃	D₄	1	2	yes	complemented
85	#88073	—	4	2	no	—
86	#88072	—	4	2	no	—
87	#88059	—	2	1	no	—
88	#88059	—	2	1	no	—
89	#88055	—	2	1	no	—
90	#88055	C₂×C₄	1	2	yes	complemented
91	C₈×Dic₁₃	—	2	1	no	—
92	C₈×Dic₁₃	C₂×C₄	1	2	yes	complemented
93	#88046	—	4	2	no	—
94	#88045	—	2	4	no	—
95	#88045	—	4	2	no	—
96	#22286	—	13	1	no	maximal, Sylow
97	C₂⁴×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	—	2	2	no	—
100	C₂×D₄×C₁₃	—	2	2	no	—
101	C₂×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
104	C₂²×C₄×C₁₃	—	4	4	no	—
105	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
106	C₂×C₂²⋊D₁₃	—	2	2	no	—
107	C₂×C₂²⋊D₁₃	—	4	4	no	—
108	#6127	—	2	2	no	—
109	#6127	—	2	2	no	—
110	#6127	—	2	2	no	—
111	#6127	—	2	2	no	—
112	C₂×D₅₂	C₂²×C₄	1	2	yes	—
113	C₂×C₄×D₁₃	—	2	2	no	—
114	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
115	C₁₃×D₈	—	2	2	no	—
116	C₁₃×D₈	—	2	2	no	—
117	C₁₃×D₈	—	2	2	no	—
118	C₁₃×D₈	—	2	2	no	—
119	C₁₃×M₁₆	—	2	1	no	—
120	C₁₃×M₁₆	—	2	1	no	—
121	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
127	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₂²⋊C₄	—	2	1	no	—
131	C₁₃×C₂²⋊C₄	—	2	2	no	—
132	C₁₃×C₂²⋊C₄	—	4	4	no	—
133	C₄²×C₁₃	—	2	2	no	—
134	C₄²×C₁₃	C₂×D₄	1	2	yes	—
135	C₂²⋊Dic₁₃	—	2	1	no	—
136	C₂²⋊Dic₁₃	—	2	1	no	—
137	C₂²⋊Dic₁₃	—	4	4	no	—
138	#6105	—	4	4	no	—
139	#6104	—	4	4	no	—
140	C₄⋊Dic₁₃	—	2	1	no	—
141	C₄⋊Dic₁₃	—	2	1	no	—
142	C₄×Dic₁₃	—	2	1	no	—
143	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
144	#6099	—	2	1	no	—
145	#6099	—	2	1	no	—
146	#6099	—	2	2	no	—
147	#6099	—	2	1	no	—
148	#6099	—	2	2	no	—
149	#6099	—	2	1	no	—
150	C₂×#1055	—	2	1	no	—
151	C₂×#1055	—	2	2	no	—
152	C₂×#1055	C₂²×C₄	1	2	yes	—
153	Dic₅₂	—	2	1	no	—
154	Dic₅₂	—	2	1	no	—
155	D₁₀₄	—	2	1	no	—
156	D₁₀₄	—	2	1	no	—
157	#6095	—	2	2	no	—
158	#6095	—	2	2	no	—
159	#6094	—	4	4	no	—
160	C₈×D₁₃	—	4	4	no	—
161	#3155	—	13	1	no	—
162	#2957	—	13	1	no	—
163	#2948	D₁₃	1	1	yes	characteristic, complemented
164	#1978	—	13	1	no	—
165	#1976	—	13	1	no	—
166	#1911	—	13	2	no	—
167	#1910	—	13	2	no	—
168	#1904	—	13	2	no	—
169	#1903	—	13	2	no	—
170	#1833	—	13	1	no	—
171	#1747	—	13	1	no	—
172	C₂³×C₁₃	—	2	4	no	—
173	C₂³×C₁₃	—	4	2	no	—
174	C₂³×C₁₃	—	4	2	no	—
175	C₂³×C₁₃	—	16	2	no	—
176	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂²×D₁₃	—	2	2	no	—
178	D₄×C₁₃	—	2	4	no	—
179	D₄×C₁₃	—	2	4	no	—
180	D₄×C₁₃	—	4	2	no	—
181	D₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	16	4	no	—
185	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
189	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
190	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂²⋊D₁₃	—	4	2	no	—
192	C₂²⋊D₁₃	—	4	2	no	—
193	C₂²⋊D₁₃	—	16	4	no	—
194	C₂×Dic₁₃	—	2	2	no	—
195	C₂×Dic₁₃	—	2	2	no	—
196	C₂×Dic₁₃	—	4	1	no	—
197	D₅₂	—	2	2	no	—
198	D₅₂	—	2	2	no	—
199	C₄×D₁₃	—	4	2	no	—
200	C₄×D₁₃	—	4	2	no	—
201	Dic₂₆	—	2	2	no	—
202	Dic₂₆	—	2	2	no	—
203	C₈×C₁₃	—	2	2	no	—
204	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
205	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
206	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
207	C₈×C₁₃	C₄×D₄	1	1	yes	characteristic
208	#1055	—	2	2	no	—
209	#1055	—	4	2	no	—
210	#1055	—	4	1	no	—
211	C₂×AGL(1,ℤ/8)	—	13	2	no	—
212	C₂×#135	—	13	1	no	—
213	C₂²×D₈	C₂×D₁₃	1	1	yes	characteristic
214	#568	—	13	2	no	—
215	#535	—	13	2	no	—
216	#518	C₂×D₁₃	1	2	yes	—
217	#496	—	13	4	no	—
218	#495	—	13	2	no	—
219	#493	—	13	2	no	—
220	#444	—	26	2	no	—
221	#443	—	26	2	no	—
222	#442	—	2	2	no	—
223	C₄×D₈	—	2	2	no	—
224	C₂×#108	—	13	1	no	—
225	#427	C₂×D₁₃	1	1	yes	characteristic
226	#421	—	13	2	no	—
227	#421	—	13	2	no	—
228	#418	—	13	2	no	—
229	#418	C₂×D₁₃	1	2	yes	—
230	C₂×#100	—	13	2	no	—
231	#410	—	13	2	no	—
232	#405	—	13	1	no	—
233	#405	—	13	1	no	—
234	#405	C₂×D₁₃	1	1	yes	characteristic
235	#344	—	13	2	no	—
236	#338	—	13	1	no	—
237	H(3,ℤ/4)	—	13	1	no	—
238	H(3,ℤ/4)	—	13	2	no	—
239	H(3,ℤ/4)	—	13	1	no	—
240	H(3,ℤ/4)	—	13	1	no	—
241	C₂²×C₁₃	—	4	1	no	—
242	C₂²×C₁₃	—	4	4	no	—
243	C₂²×C₁₃	—	8	4	no	—
244	C₂²×C₁₃	—	8	4	no	—
245	C₂²×C₁₃	—	16	2	no	—
246	C₂²×C₁₃	#518	1	1	yes	characteristic
247	C₂²×C₁₃	#535	1	1	yes	characteristic
248	C₂²×C₁₃	#540	1	1	yes	characteristic
249	C₂×D₁₃	—	4	2	no	—
250	C₂×D₁₃	—	8	2	no	—
251	C₄×C₁₃	—	4	2	no	—
252	C₄×C₁₃	—	8	2	no	—
253	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
254	C₄×C₁₃	#518	1	1	yes	characteristic
255	C₄×C₁₃	#535	1	1	yes	characteristic
256	C₄×C₁₃	#540	1	1	yes	characteristic
257	Dic₁₃	—	4	2	no	—
258	Dic₁₃	—	4	2	no	—
259	Dic₁₃	—	8	1	no	—
260	C₂×#41	—	13	2	no	—
261	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
262	AGL(1,ℤ/8)	—	52	2	no	—
263	AGL(1,ℤ/8)	—	52	2	no	—
264	#135	—	26	1	no	—
265	#135	—	26	1	no	—
266	#135	—	26	1	no	—
267	#135	—	26	1	no	—
268	C₂×Q₁₆	—	13	1	no	—
269	C₂×SD₁₆	—	13	4	no	—
270	C₂×SD₁₆	—	13	2	no	—
271	C₂×D₈	—	2	1	no	—
272	C₂×D₈	—	2	1	no	—
273	C₂×D₈	—	2	1	no	—
274	C₂×D₈	—	2	1	no	—
275	C₂×D₈	—	13	4	no	—
276	C₂×D₈	—	13	1	no	—
277	C₂×D₈	C₄×D₁₃	1	2	yes	—
278	C₂×D₈	C₄×D₁₃	1	2	yes	—
279	#131	—	26	4	no	—
280	#131	—	52	2	no	—
281	C₂×M₁₆	—	13	1	no	—
282	C₂×M₁₆	—	13	2	no	—
283	C₂×M₁₆	—	13	1	no	—
284	C₂×M₁₆	—	52	2	no	—
285	C₂×M₁₆	C₂²×D₁₃	1	1	yes	characteristic
286	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
287	#127	—	13	4	no	—
288	#124	—	13	4	no	—
289	#121	—	52	2	no	—
290	#120	—	52	2	no	—
291	C₄×D₄	—	2	4	no	—
292	C₄×D₄	—	4	2	no	—
293	#117	—	13	1	no	—
294	#117	—	13	1	no	—
295	#117	C₂²×D₁₃	1	2	yes	—
296	#117	C₂²×D₁₃	1	1	yes	characteristic
297	C₂×C₂²⋊C₄	—	4	2	no	—
298	#108	—	26	1	no	—
299	#108	—	26	1	no	—
300	#107	—	2	1	no	—
301	#106	—	2	1	no	—
302	#104	—	26	4	no	—
303	#104	—	52	2	no	—
304	#102	—	2	4	no	—
305	#102	—	52	2	no	—
306	#100	—	52	2	no	—
307	#99	—	52	2	no	—
308	#97	—	13	2	no	—
309	#97	—	26	1	no	—
310	#97	C₂²⋊D₁₃	1	2	yes	complemented
311	C₄×C₈	—	13	2	no	—
312	C₄×C₈	—	26	1	no	—
313	C₄×C₈	C₂²⋊D₁₃	1	2	yes	complemented
314	C₂×C₁₃	—	2	1	no	—
315	C₂×C₁₃	—	2	1	no	—
316	C₂×C₁₃	—	2	1	no	—
317	C₂×C₁₃	—	8	4	no	—
318	C₂×C₁₃	#2328	1	1	yes	characteristic
319	D₁₃	—	8	2	no	—
320	C₂⁴	—	2	2	no	—
321	#41	—	26	2	no	—
322	#41	—	26	2	no	—
323	#41	—	26	2	no	—
324	#41	—	26	2	no	—
325	C₂×Q₈	—	13	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	13	2	no	—
332	C₂×D₄	—	26	2	no	—
333	C₂×D₄	—	52	4	no	—
334	C₂×D₄	C₂×C₄×D₁₃	1	4	yes	—
335	C₂²×C₄	—	4	4	no	—
336	C₂²×C₄	—	26	2	no	—
337	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
338	Q₁₆	—	26	1	no	—
339	Q₁₆	—	26	1	no	—
340	SD₁₆	—	26	2	no	—
341	SD₁₆	—	26	2	no	—
342	SD₁₆	—	52	4	no	—
343	D₈	—	2	2	no	—
344	D₈	—	2	2	no	—
345	D₈	—	2	2	no	—
346	D₈	—	2	2	no	—
347	D₈	—	26	1	no	—
348	D₈	—	26	1	no	—
349	D₈	—	52	4	no	—
350	M₁₆	—	2	1	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	26	1	no	—
353	M₁₆	—	26	1	no	—
354	M₁₆	—	26	1	no	—
355	M₁₆	—	26	1	no	—
356	M₁₆	—	26	2	no	—
357	M₁₆	—	26	2	no	—
358	M₁₆	—	52	4	no	—
359	C₂×C₈	—	13	2	no	—
360	C₂×C₈	—	26	1	no	—
361	C₂×C₈	—	26	2	no	—
362	C₂×C₈	—	52	4	no	—
363	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
364	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
365	C₂×C₈	#6127	1	1	yes	characteristic
366	C₂×C₈	#6127	1	1	yes	characteristic
367	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
368	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
369	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	26	1	no	—
373	C₄⋊C₄	—	26	1	no	—
374	C₂²⋊C₄	—	2	1	no	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	4	4	no	—
377	C₂²⋊C₄	—	26	1	no	—
378	C₂²⋊C₄	—	26	1	no	—
379	C₂²⋊C₄	—	52	4	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	13	2	no	—
382	C₄²	—	26	1	no	—
383	C₄²	C₂×C₂²⋊D₁₃	1	2	yes	—
384	C₁₃	#22286	1	1	yes	characteristic, complemented, Sylow
385	C₂³	—	2	4	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	16	2	no	—
389	C₂³	—	26	2	no	—
390	C₂³	#88251	1	1	yes	characteristic
391	Q₈	—	26	2	no	—
392	Q₈	—	26	2	no	—
393	D₄	—	2	4	no	—
394	D₄	—	2	4	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	26	2	no	—
398	D₄	—	26	2	no	—
399	D₄	—	52	2	no	—
400	D₄	—	52	2	no	—
401	D₄	—	208	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	16	4	no	—
405	C₂×C₄	—	26	2	no	—
406	C₂×C₄	—	26	2	no	—
407	C₂×C₄	—	52	2	no	—
408	C₂×C₄	—	52	2	no	—
409	C₂×C₄	—	52	1	no	—
410	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
411	C₂×C₄	C₂×#6127	1	1	yes	characteristic
412	C₂×C₄	#88251	1	1	yes	characteristic
413	C₂×C₄	#88256	1	1	yes	characteristic
414	C₂×C₄	#88256	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	26	2	no	—
418	C₈	—	52	1	no	—
419	C₈	—	52	2	no	—
420	C₈	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
421	C₈	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
422	C₈	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
423	C₈	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
424	C₂²	—	4	1	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	8	4	no	—
427	C₂²	—	8	4	no	—
428	C₂²	—	16	2	no	—
429	C₂²	—	52	2	no	—
430	C₂²	—	104	2	no	—
431	C₂²	#11719250	1	1	yes	characteristic
432	C₂²	#11719267	1	1	yes	characteristic
433	C₂²	#11719510	1	1	yes	characteristic
434	C₄	—	4	2	no	—
435	C₄	—	8	2	no	—
436	C₄	—	52	2	no	—
437	C₄	—	52	2	no	—
438	C₄	—	104	1	no	—
439	C₄	#11719250	1	1	yes	characteristic
440	C₄	#11719267	1	1	yes	characteristic
441	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
442	C₄	#11719535	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	8	4	no	—
447	C₂	—	104	2	no	—
448	C₂	#13117558	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13117558
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#2948	C₂
socle	C₂×C₁₃	#2328
prime radical	#13125317	C₂
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2948	D₁₃
hypocenter	C₁₃	#22286
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #2948

Complements

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

N	H ≅ G/N	type
2. #13123754	C₂	semidirect
3. #13115747	C₂	semidirect
4. #13115732	C₂	semidirect
5. #13115368	C₂	semidirect
6. #13115360	C₂	semidirect
7. #13115323	C₂	semidirect
8. #13115313	C₂	semidirect
9. #13114959	C₂	semidirect
10. #13114591	C₂	semidirect
11. C₁₃×#2948	C₂	semidirect
25. #11718816	C₄	semidirect
26. #11718815	C₄	semidirect
27. #11718812	C₄	semidirect
58. #88194	C₂×C₄	semidirect
60. #88190	C₂×C₄	semidirect
61. C₂×#6105	C₂×C₄	semidirect
64. C₂×#6104	C₂×C₄	semidirect
72. C₂×Dic₅₂	C₂×C₄	semidirect
77. C₂×D₁₀₄	C₂×C₄	semidirect
78. C₂×#6095	C₂×C₄	semidirect
83. C₁₃×#97	D₄	semidirect
84. C₄×C₈×C₁₃	D₄	semidirect
90. #88055	C₂×C₄	semidirect
92. C₈×Dic₁₃	C₂×C₄	semidirect
163. #2948	D₁₃	semidirect
310. #97	C₂²⋊D₁₃	semidirect
313. C₄×C₈	C₂²⋊D₁₃	semidirect
384. C₁₃	#22286	semidirect

Maximal subgroups

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

subgroup	index
#13125317	2
#13123754	2
#13115747	2
#13115732	2
#13115368	2
#13115360	2
#13115323	2
#13115313	2
#13114959	2
#13114591	2
C₁₃×#2948	2
#22286	13