Subgroups — #16799520

Order 3328.

780 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131515	C₂	1	1	yes	maximal, characteristic
2	C₄×D₁₃⋊M₁₆	C₂	1	1	yes	maximal, characteristic
3	#13130952	C₂	1	4	yes	maximal, complemented
4	#13130790	C₂	1	4	yes	maximal
5	C₄×#88104	C₂	1	2	yes	maximal, complemented
6	C₄×#88103	C₂	1	2	yes	maximal, complemented
7	D₁₃×#431	C₂	1	1	yes	maximal, characteristic
8	C₂×D₁₃⋊M₁₆	C₂²	1	2	yes	—
9	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
10	#11719128	—	2	1	no	—
11	#11719127	C₂²	1	2	yes	—
12	#11719125	—	2	1	no	—
13	C₄×#6122	—	2	1	no	—
14	C₄×#6122	—	2	1	no	—
15	C₂×#88104	C₂²	1	4	yes	—
16	C₂×#88103	C₂²	1	4	yes	—
17	#11719055	—	2	1	no	—
18	#11719053	C₂²	1	2	yes	—
19	#11719049	—	2	1	no	—
20	C₄×#6118	C₂²	1	2	yes	—
21	C₄×#6118	C₂²	1	2	yes	—
22	C₄×#6118	C₂²	1	2	yes	—
23	#11719047	—	2	1	no	—
24	C₄×D₁₃⋊C₈	—	2	1	no	—
25	C₁₃×#431	C₄	1	1	yes	characteristic
26	#11718586	C₄	1	1	yes	characteristic
27	#11718494	C₄	1	2	yes	—
28	D₁₃×C₄⋊C₈	C₂²	1	2	yes	—
29	D₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
30	#11718379	C₄	1	2	yes	—
31	#11718346	C₄	1	1	yes	characteristic
32	#11718346	C₄	1	1	yes	characteristic
33	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
35	#11718268	C₂²	1	4	yes	—
36	#11718268	C₂²	1	4	yes	—
37	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
38	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
39	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
40	C₂×#6122	—	2	2	no	—
41	D₁₃⋊M₁₆	—	2	8	no	—
42	C₂×#6118	C₂³	1	4	yes	—
43	C₂×#6118	C₂³	1	4	yes	—
44	C₂×D₁₃⋊C₈	—	2	2	no	—
45	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
48	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
49	C₂×C₈×D₁₃	C₂³	1	2	yes	—
50	C₂×C₈×D₁₃	C₂³	1	2	yes	—
51	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₁₃	D₄	1	1	yes	characteristic
54	C₄²×D₁₃	D₄	1	1	yes	characteristic
55	C₄²×D₁₃	Q₈	1	1	yes	characteristic
56	C₄²×D₁₃	Q₈	1	1	yes	characteristic
57	C₄²×D₁₃	C₂³	1	1	yes	characteristic
58	C₄²×D₁₃	C₂³	1	1	yes	characteristic
59	C₂²⋊#1057	—	2	2	no	—
60	#88112	—	2	2	no	—
61	#88112	—	2	2	no	—
62	#88111	—	2	2	no	—
63	#88110	—	2	2	no	—
64	#88110	—	2	2	no	—
65	#88110	—	2	2	no	—
66	C₄×#1057	—	2	2	no	—
67	C₄×#1057	—	2	2	no	—
68	C₄×#1057	—	2	2	no	—
69	#88104	—	2	8	no	—
70	#88103	—	2	8	no	—
71	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
72	C₁₃×C₂²⋊C₈	C₂×C₄	1	2	yes	—
73	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
74	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
75	C₂²⋊#1055	C₂×C₄	1	2	yes	—
76	#88060	C₂×C₄	1	2	yes	—
77	#88060	C₂×C₄	1	2	yes	—
78	#88054	C₂×C₄	1	2	yes	—
79	#88054	C₂×C₄	1	2	yes	—
80	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
81	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
82	C₄⋊#1055	C₂×C₄	1	2	yes	—
83	C₄×#1055	C₂×C₄	1	1	yes	characteristic
84	C₄×#1055	C₂×C₄	1	1	yes	characteristic
85	#21370	—	13	1	no	maximal, Sylow
86	C₂³×D₁₃	C₂×Q₈	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
91	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
93	C₂×C₄×D₁₃	—	2	4	no	—
94	C₂×C₄×D₁₃	—	2	4	no	—
95	C₂×C₄×D₁₃	—	4	2	no	—
96	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
108	#6122	—	2	8	no	—
109	C₂×#1057	—	2	4	no	—
110	C₂×#1057	—	2	4	no	—
111	#6118	—	2	4	no	—
112	#6118	—	2	4	no	—
113	#6118	—	2	4	no	—
114	#6118	#41	1	8	yes	—
115	D₁₃⋊C₈	—	2	8	no	—
116	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
118	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
119	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
120	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
123	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
124	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
125	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
126	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
127	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
128	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
131	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
132	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
133	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂×#1055	C₂²×C₄	1	2	yes	—
135	C₂×#1055	C₂²×C₄	1	2	yes	—
136	C₈×D₁₃	—	2	4	no	—
137	C₈×D₁₃	—	2	4	no	—
138	#2920	—	13	1	no	—
139	C₂×#431	—	13	1	no	—
140	C₂×C₄×M₁₆	—	13	1	no	—
141	#1950	—	13	4	no	—
142	#1855	—	13	4	no	—
143	C₄×#108	—	13	2	no	—
144	C₄×#108	—	13	2	no	—
145	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂²×D₁₃	—	2	2	no	—
147	C₂²×D₁₃	—	2	2	no	—
148	C₂²×D₁₃	—	4	1	no	—
149	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂²×D₁₃	C₂²×Q₈	1	1	yes	characteristic
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	4	1	no	—
154	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×Dic₁₃	—	2	2	no	—
161	C₂×Dic₁₃	—	2	2	no	—
162	C₂×Dic₁₃	—	2	2	no	—
163	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
168	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
169	C₄×D₁₃	—	2	2	no	—
170	C₄×D₁₃	—	2	2	no	—
171	C₄×D₁₃	—	2	2	no	—
172	C₄×D₁₃	—	2	2	no	—
173	C₄×D₁₃	—	2	2	no	—
174	C₄×D₁₃	—	2	2	no	—
175	C₄×D₁₃	—	2	2	no	—
176	C₄×D₁₃	—	2	2	no	—
177	C₄×D₁₃	—	4	1	no	—
178	C₄×D₁₃	—	4	1	no	—
179	C₄×D₁₃	#108	1	4	yes	complemented
180	C₄×D₁₃	C₂×#41	1	4	yes	—
181	#1057	—	2	8	no	—
182	#1057	—	4	4	no	—
183	C₈×C₁₃	—	2	2	no	—
184	C₈×C₁₃	—	2	2	no	—
185	#1055	—	2	2	no	—
186	#1055	—	2	2	no	—
187	C₂²×M₁₆	—	13	2	no	—
188	C₂²×C₄²	—	13	1	no	—
189	#432	—	26	1	no	—
190	#432	—	26	1	no	—
191	#431	—	13	1	no	—
192	#431	—	13	2	no	—
193	#431	—	13	2	no	—
194	#431	—	13	1	no	—
195	#431	—	13	1	no	—
196	#431	—	26	1	no	—
197	#431	—	26	1	no	—
198	#431	#261	1	1	yes	characteristic
199	C₂×#108	—	13	4	no	—
200	C₂×#108	—	13	4	no	—
201	#423	—	13	2	no	—
202	C₂×C₄⋊C₈	—	13	2	no	—
203	#407	—	13	2	no	—
204	C₂×C₂²⋊C₈	—	13	2	no	—
205	C₄×M₁₆	—	13	2	no	—
206	C₄×M₁₆	—	13	2	no	—
207	C₄×M₁₆	—	13	2	no	—
208	C₄×M₁₆	—	26	1	no	—
209	C₄×M₁₆	—	26	1	no	—
210	C₂×#97	—	26	1	no	—
211	C₂×C₄×C₈	—	13	1	no	—
212	C₂×C₄×C₈	—	13	1	no	—
213	C₂×C₄×C₈	—	26	1	no	—
214	#341	—	13	4	no	—
215	#341	—	13	4	no	—
216	C₂²×C₁₃	—	2	1	no	—
217	C₂²×C₁₃	—	2	1	no	—
218	C₂²×C₁₃	—	2	1	no	—
219	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
220	C₂×D₁₃	—	2	1	no	—
221	C₂×D₁₃	—	2	1	no	—
222	C₂×D₁₃	—	2	1	no	—
223	C₂×D₁₃	—	2	1	no	—
224	C₂×D₁₃	—	4	4	no	—
225	C₂×D₁₃	C₂×#108	1	2	yes	—
226	C₂×D₁₃	#533	1	2	yes	—
227	C₄×C₁₃	—	2	1	no	—
228	C₄×C₁₃	—	2	1	no	—
229	C₄×C₁₃	—	2	1	no	—
230	C₄×C₁₃	—	2	1	no	—
231	C₄×C₁₃	C₂×#108	1	2	yes	—
232	C₄×C₁₃	C₄×#41	1	2	yes	—
233	Dic₁₃	—	2	1	no	—
234	Dic₁₃	—	2	1	no	—
235	Dic₁₃	—	2	1	no	—
236	Dic₁₃	C₂×#108	1	2	yes	—
237	Dic₁₃	#430	1	2	yes	—
238	Dic₁₃	#525	1	2	yes	—
239	C₂³×C₄	—	13	1	no	—
240	C₂³×C₄	—	13	1	no	—
241	C₂³×C₄	—	13	1	no	—
242	C₂×M₁₆	—	13	4	no	—
243	C₂×M₁₆	—	13	4	no	—
244	C₂×M₁₆	—	26	8	no	—
245	C₂×M₁₆	—	26	2	no	—
246	C₂²×C₈	—	13	2	no	—
247	C₂²×C₈	—	13	2	no	—
248	C₂²×C₈	—	26	2	no	—
249	C₂×C₄²	—	13	1	no	—
250	C₂×C₄²	—	13	1	no	—
251	C₂×C₄²	—	13	1	no	—
252	C₂×C₄²	—	13	1	no	—
253	C₂×C₄²	—	13	1	no	—
254	C₂×C₄²	—	13	1	no	—
255	C₂×C₄²	—	13	1	no	—
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	C₂×#261	1	1	yes	characteristic
261	#108	—	26	8	no	—
262	#108	—	26	8	no	—
263	C₄⋊C₈	—	13	2	no	—
264	C₄⋊C₈	—	13	2	no	—
265	C₄⋊C₈	—	13	2	no	—
266	C₄⋊C₈	—	26	2	no	—
267	C₄⋊C₈	—	26	2	no	—
268	C₄⋊C₈	C₂×#261	1	2	yes	—
269	C₂²⋊C₈	—	13	2	no	—
270	C₂²⋊C₈	—	13	2	no	—
271	C₂²⋊C₈	—	13	2	no	—
272	C₂²⋊C₈	—	26	2	no	—
273	C₂²⋊C₈	—	26	2	no	—
274	C₂²⋊C₈	C₂×#261	1	2	yes	—
275	#97	—	26	2	no	—
276	#97	—	26	2	no	—
277	#97	—	26	2	no	—
278	C₄×C₈	—	13	2	no	—
279	C₄×C₈	—	13	2	no	—
280	C₄×C₈	—	13	1	no	—
281	C₄×C₈	—	13	1	no	—
282	C₄×C₈	—	26	2	no	—
283	C₄×C₈	—	26	2	no	—
284	C₄×C₈	—	26	2	no	—
285	C₄×C₈	C₂×#261	1	1	yes	characteristic
286	C₄×C₈	C₂×#261	1	1	yes	characteristic
287	C₂×C₁₃	—	4	1	no	—
288	C₂×C₁₃	#2296	1	1	yes	characteristic
289	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
290	C₂×C₁₃	C₂×#430	1	1	yes	characteristic
291	D₁₃	—	2	2	no	—
292	D₁₃	—	2	2	no	—
293	C₂⁴	—	13	1	no	—
294	C₂²×C₄	—	13	1	no	—
295	C₂²×C₄	—	13	1	no	—
296	C₂²×C₄	—	13	1	no	—
297	C₂²×C₄	—	13	1	no	—
298	C₂²×C₄	—	13	1	no	—
299	C₂²×C₄	—	13	1	no	—
300	C₂²×C₄	—	13	1	no	—
301	C₂²×C₄	—	13	1	no	—
302	C₂²×C₄	—	13	1	no	—
303	C₂²×C₄	—	13	1	no	—
304	C₂²×C₄	—	13	1	no	—
305	C₂²×C₄	—	13	1	no	—
306	C₂²×C₄	—	13	1	no	—
307	C₂²×C₄	—	13	1	no	—
308	C₂²×C₄	—	13	1	no	—
309	C₂²×C₄	—	26	4	no	—
310	C₂²×C₄	—	26	4	no	—
311	C₂²×C₄	—	52	2	no	—
312	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
313	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
314	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
315	M₁₆	—	13	8	no	—
316	M₁₆	—	26	4	no	—
317	M₁₆	—	26	8	no	—
318	M₁₆	—	26	4	no	—
319	M₁₆	—	26	4	no	—
320	C₂×C₈	—	13	2	no	—
321	C₂×C₈	—	13	2	no	—
322	C₂×C₈	—	26	4	no	—
323	C₂×C₈	—	26	4	no	—
324	C₂×C₈	—	26	4	no	—
325	C₂×C₈	—	26	8	no	—
326	C₂×C₈	—	26	4	no	—
327	C₂×C₈	C₂²×#261	1	2	yes	—
328	C₂×C₈	C₂²×#261	1	2	yes	—
329	C₄²	—	13	1	no	—
330	C₄²	—	13	1	no	—
331	C₄²	—	13	1	no	—
332	C₄²	—	13	1	no	—
333	C₄²	—	13	1	no	—
334	C₄²	—	13	1	no	—
335	C₄²	—	13	1	no	—
336	C₄²	—	13	1	no	—
337	C₄²	—	13	1	no	—
338	C₄²	—	13	1	no	—
339	C₄²	—	13	1	no	—
340	C₄²	—	13	1	no	—
341	C₄²	C₄⋊#261	1	1	yes	characteristic
342	C₄²	C₄⋊#261	1	1	yes	characteristic
343	C₄²	C₂²×#261	1	1	yes	characteristic
344	C₄²	C₂²×#261	1	1	yes	characteristic
345	C₁₃	#21370	1	1	yes	characteristic, complemented, Sylow
346	C₂³	—	13	1	no	—
347	C₂³	—	13	1	no	—
348	C₂³	—	26	2	no	—
349	C₂³	—	26	2	no	—
350	C₂³	—	52	1	no	—
351	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	13	1	no	—
356	C₂×C₄	—	13	1	no	—
357	C₂×C₄	—	13	1	no	—
358	C₂×C₄	—	13	4	no	—
359	C₂×C₄	—	13	4	no	—
360	C₂×C₄	—	13	1	no	—
361	C₂×C₄	—	13	1	no	—
362	C₂×C₄	—	13	1	no	—
363	C₂×C₄	—	26	2	no	—
364	C₂×C₄	—	26	2	no	—
365	C₂×C₄	—	26	2	no	—
366	C₂×C₄	—	26	2	no	—
367	C₂×C₄	—	26	2	no	—
368	C₂×C₄	—	26	2	no	—
369	C₂×C₄	—	26	2	no	—
370	C₂×C₄	—	26	2	no	—
371	C₂×C₄	—	26	2	no	—
372	C₂×C₄	—	26	2	no	—
373	C₂×C₄	—	26	2	no	—
374	C₂×C₄	—	52	1	no	—
375	C₂×C₄	—	52	1	no	—
376	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
377	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
378	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
379	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
380	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
381	C₂×C₄	C₂³×#261	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	2	2	no	—
384	C₈	—	26	8	no	—
385	C₈	—	26	2	no	—
386	C₈	—	26	2	no	—
387	C₈	—	52	4	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	13	2	no	—
392	C₂²	—	13	2	no	—
393	C₂²	—	26	1	no	—
394	C₂²	—	26	1	no	—
395	C₂²	—	26	1	no	—
396	C₂²	—	26	1	no	—
397	C₂²	—	52	4	no	—
398	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	13	2	no	—
404	C₄	—	13	2	no	—
405	C₄	—	13	2	no	—
406	C₄	—	26	1	no	—
407	C₄	—	26	1	no	—
408	C₄	—	26	1	no	—
409	C₄	D₁₃⋊#108	1	2	yes	—
410	C₄	#41×#261	1	2	yes	—
411	C₂	—	4	1	no	—
412	C₂	—	26	2	no	—
413	C₂	—	26	2	no	—
414	C₂	#13131296	1	1	yes	characteristic
415	C₂	C₂×D₁₃⋊#108	1	1	yes	characteristic
416	C₂	D₁₃⋊#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#261
Fitting	C₁₃×#431	C₄
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₂×Q₈
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#431	#261
hypocenter	C₁₃	#21370
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #431

Complements

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

N	H ≅ G/N	type
3. #13130952	C₂	semidirect
5. C₄×#88104	C₂	semidirect
6. C₄×#88103	C₂	semidirect
179. C₄×D₁₃	#108	semidirect
345. C₁₃	#21370	semidirect

Maximal subgroups

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

subgroup	index
#13131515	2
C₄×D₁₃⋊M₁₆	2
#13130952	2
#13130790	2
C₄×#88104	2
C₄×#88103	2
D₁₃×#431	2
#21370	13