Subgroups — #15756275

Order 3328.

592 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13114816	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂²⋊#1055	C₂	1	1	yes	maximal, characteristic
3	#13112677	C₂	1	2	yes	maximal, complemented
4	#13112677	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#117	C₄	1	1	yes	characteristic
7	C₂×C₁₃×#117	C₄	1	1	yes	characteristic
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
10	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
11	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
12	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
14	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
15	C₁₃×#376	—	2	1	no	—
16	C₄³×C₁₃	—	2	1	no	—
17	C₂×C₂²⋊#1055	—	2	1	no	—
18	C₂×C₂²⋊#1055	—	2	1	no	—
19	C₂×C₄⋊#1055	C₂²	1	2	yes	—
20	C₂×C₄×#1055	C₂²	1	2	yes	—
21	#11718116	—	2	1	no	—
22	#11718116	—	2	1	no	—
23	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
26	C₁₃×#117	—	2	2	no	—
27	C₁₃×#117	—	2	2	no	—
28	C₁₃×#117	—	2	2	no	—
29	C₁₃×#117	C₈	1	4	yes	complemented
30	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
31	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
33	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
34	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
35	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
36	C₂×C₄²×C₁₃	—	2	1	no	—
37	C₂×C₄²×C₁₃	—	2	1	no	—
38	C₂×C₄²×C₁₃	—	2	2	no	—
39	C₂×C₄²×C₁₃	—	2	2	no	—
40	C₂×C₄²×C₁₃	—	2	1	no	—
41	C₂×C₄²×C₁₃	—	2	1	no	—
42	C₂×C₄²×C₁₃	—	2	1	no	—
43	C₂×C₄²×C₁₃	—	2	1	no	—
44	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×#1055	—	2	2	no	—
49	C₂²×#1055	—	2	2	no	—
50	C₁₃×#95	—	2	1	no	—
51	C₁₃×#95	—	2	1	no	—
52	C₁₃×#95	—	2	1	no	—
53	C₁₃×#95	—	2	1	no	—
54	C₂²⋊#1055	—	2	4	no	—
55	C₂²⋊#1055	—	4	2	no	—
56	C₄⋊#1055	—	2	2	no	—
57	C₄⋊#1055	—	2	2	no	—
58	C₄×#1055	—	2	2	no	—
59	C₄×#1055	—	2	2	no	—
60	#8708	—	13	1	no	maximal, Sylow
61	C₂⁴×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₃	—	2	1	no	—
63	C₂²×C₄×C₁₃	—	2	1	no	—
64	C₂²×C₄×C₁₃	—	2	1	no	—
65	C₂²×C₄×C₁₃	—	2	1	no	—
66	C₂²×C₄×C₁₃	—	2	1	no	—
67	C₂²×C₄×C₁₃	—	2	1	no	—
68	C₂²×C₄×C₁₃	—	2	1	no	—
69	C₂²×C₄×C₁₃	—	2	1	no	—
70	C₂²×C₄×C₁₃	—	2	2	no	—
71	C₂²×C₄×C₁₃	—	2	2	no	—
72	C₂²×C₄×C₁₃	—	2	2	no	—
73	C₂²×C₄×C₁₃	—	2	2	no	—
74	C₂²×C₄×C₁₃	—	2	1	no	—
75	C₂²×C₄×C₁₃	—	2	1	no	—
76	C₂²×C₄×C₁₃	—	4	1	no	—
77	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
81	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
82	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
85	C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
90	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
91	C₁₃×C₄⋊C₄	M₁₆	1	2	yes	—
92	C₁₃×C₄⋊C₄	M₁₆	1	2	yes	—
93	C₁₃×C₂²⋊C₄	—	2	4	no	—
94	C₁₃×C₂²⋊C₄	—	2	4	no	—
95	C₄²×C₁₃	—	2	4	no	—
96	C₄²×C₁₃	—	2	4	no	—
97	C₄²×C₁₃	—	2	1	no	—
98	C₄²×C₁₃	—	2	1	no	—
99	C₄²×C₁₃	—	2	2	no	—
100	C₄²×C₁₃	—	2	2	no	—
101	C₄²×C₁₃	—	4	2	no	—
102	C₄²×C₁₃	—	4	2	no	—
103	C₄²×C₁₃	—	4	2	no	—
104	C₄²×C₁₃	—	4	1	no	—
105	C₄²×C₁₃	—	4	1	no	—
106	C₄²×C₁₃	#41	1	2	yes	—
107	C₄²×C₁₃	#41	1	2	yes	—
108	C₂×#1055	—	2	4	no	—
109	C₂×#1055	—	4	2	no	—
110	C₂×#1055	—	4	2	no	—
111	C₂×#1055	—	4	2	no	—
112	C₂×#1055	—	4	2	no	—
113	C₂×#1055	—	4	2	no	—
114	C₄×#117	D₁₃	1	1	yes	characteristic
115	#1797	—	13	1	no	—
116	C₄×C₂²⋊C₈	—	13	1	no	—
117	#1279	—	13	2	no	—
118	#1279	—	13	2	no	—
119	C₂³×C₁₃	—	2	1	no	—
120	C₂³×C₁₃	—	2	1	no	—
121	C₂³×C₁₃	—	2	1	no	—
122	C₂³×C₁₃	—	2	1	no	—
123	C₂³×C₁₃	—	2	1	no	—
124	C₂³×C₁₃	—	2	1	no	—
125	C₂³×C₁₃	C₂²⋊C₈	1	2	yes	—
126	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₁₃	—	2	1	no	—
128	C₂×C₄×C₁₃	—	2	1	no	—
129	C₂×C₄×C₁₃	—	2	1	no	—
130	C₂×C₄×C₁₃	—	2	1	no	—
131	C₂×C₄×C₁₃	—	2	1	no	—
132	C₂×C₄×C₁₃	—	2	1	no	—
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	2	no	—
135	C₂×C₄×C₁₃	—	2	2	no	—
136	C₂×C₄×C₁₃	—	2	2	no	—
137	C₂×C₄×C₁₃	—	2	1	no	—
138	C₂×C₄×C₁₃	—	2	2	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	2	no	—
142	C₂×C₄×C₁₃	—	2	1	no	—
143	C₂×C₄×C₁₃	—	2	1	no	—
144	C₂×C₄×C₁₃	—	4	4	no	—
145	C₂×C₄×C₁₃	—	4	1	no	—
146	C₂×C₄×C₁₃	—	4	1	no	—
147	C₂×C₄×C₁₃	—	4	1	no	—
148	C₂×C₄×C₁₃	—	4	1	no	—
149	C₂×C₄×C₁₃	—	4	1	no	—
150	C₂×C₄×C₁₃	—	4	1	no	—
151	C₂×C₄×C₁₃	—	4	1	no	—
152	C₂×C₄×C₁₃	—	4	1	no	—
153	C₂×C₄×C₁₃	—	4	2	no	—
154	C₂×C₄×C₁₃	—	4	2	no	—
155	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
156	C₂×C₄×C₁₃	#104	1	2	yes	—
157	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
158	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
159	C₂×C₄×C₁₃	#123	1	2	yes	—
160	C₂×C₄×C₁₃	#123	1	2	yes	—
161	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
165	C₂×C₄×C₁₃	#135	1	2	yes	—
166	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
168	#1055	—	4	4	no	—
169	#1055	—	8	2	no	—
170	C₂×#117	Dic₁₃	1	1	yes	characteristic
171	C₂×#117	Dic₁₃	1	1	yes	characteristic
172	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
173	C₂×C₄⋊C₈	—	13	2	no	—
174	C₂×C₂²⋊C₈	—	26	1	no	—
175	C₂×C₂²⋊C₈	—	26	1	no	—
176	C₂×C₄×C₈	—	13	2	no	—
177	C₄×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
178	C₄×C₄⋊C₄	Dic₁₃	1	1	yes	characteristic
179	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
180	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
181	C₄×C₂²⋊C₄	—	2	1	no	—
182	C₄×C₂²⋊C₄	—	2	1	no	—
183	#376	—	2	1	no	—
184	C₄³	—	2	1	no	—
185	#336	—	26	1	no	—
186	#336	—	26	1	no	—
187	C₂²×C₁₃	—	2	2	no	—
188	C₂²×C₁₃	—	2	2	no	—
189	C₂²×C₁₃	—	2	2	no	—
190	C₂²×C₁₃	—	4	1	no	—
191	C₂²×C₁₃	—	4	1	no	—
192	C₂²×C₁₃	—	4	1	no	—
193	C₂²×C₁₃	—	4	1	no	—
194	C₂²×C₁₃	#381	1	1	yes	characteristic
195	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
196	C₂²×C₁₃	#407	1	1	yes	characteristic
197	C₂²×C₁₃	#416	1	1	yes	characteristic
198	C₂²×C₁₃	#417	1	1	yes	characteristic
199	C₂²×C₁₃	C₂×#104	1	1	yes	characteristic
200	C₂²×C₁₃	#421	1	1	yes	characteristic
201	C₄×C₁₃	—	2	2	no	—
202	C₄×C₁₃	—	2	2	no	—
203	C₄×C₁₃	—	2	2	no	—
204	C₄×C₁₃	—	4	1	no	—
205	C₄×C₁₃	—	4	2	no	—
206	C₄×C₁₃	—	4	2	no	—
207	C₄×C₁₃	—	4	2	no	—
208	C₄×C₁₃	—	4	2	no	—
209	C₄×C₁₃	#431	1	1	yes	characteristic
210	C₄×C₁₃	#431	1	1	yes	characteristic
211	C₄×C₁₃	#432	1	1	yes	characteristic
212	C₄×C₁₃	#432	1	1	yes	characteristic
213	C₄×C₁₃	#482	1	2	yes	—
214	C₄×C₁₃	#485	1	2	yes	—
215	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
216	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
217	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
218	C₂²×C₈	—	26	2	no	—
219	C₂²×C₈	—	26	2	no	—
220	#117	—	2	2	no	—
221	#117	—	2	2	no	—
222	#117	—	2	2	no	—
223	#117	#1055	1	4	yes	complemented
224	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
226	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂×Dic₁₃	1	1	yes	characteristic
228	C₂×C₂²⋊C₄	—	2	1	no	—
229	C₂×C₂²⋊C₄	—	2	1	no	—
230	C₂×C₄²	—	2	1	no	—
231	C₂×C₄²	—	2	1	no	—
232	C₂×C₄²	—	2	2	no	—
233	C₂×C₄²	—	2	2	no	—
234	C₂×C₄²	—	2	1	no	—
235	C₂×C₄²	—	2	1	no	—
236	C₂×C₄²	—	2	1	no	—
237	C₂×C₄²	—	2	1	no	—
238	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
239	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
240	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
241	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
242	C₄⋊C₈	—	26	2	no	—
243	C₄⋊C₈	—	26	2	no	—
244	C₂²⋊C₈	—	26	4	no	—
245	C₂²⋊C₈	—	52	2	no	—
246	C₄×C₈	—	26	2	no	—
247	C₄×C₈	—	26	2	no	—
248	#95	—	2	1	no	—
249	#95	—	2	1	no	—
250	#95	—	2	1	no	—
251	#95	—	2	1	no	—
252	C₂×C₁₃	—	4	2	no	—
253	C₂×C₁₃	#1476	1	1	yes	characteristic
254	C₂×C₁₃	#1477	1	1	yes	characteristic
255	C₂×C₁₃	#1488	1	1	yes	characteristic
256	C₂×C₁₃	#1489	1	1	yes	characteristic
257	C₂×C₁₃	#1817	1	1	yes	characteristic
258	C₂×C₁₃	#1825	1	1	yes	characteristic
259	C₂×C₁₃	#1826	1	1	yes	characteristic
260	C₂⁴	C₂²⋊Dic₁₃	1	1	yes	characteristic
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	1	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	4	1	no	—
276	C₂²×C₄	C₂×#1055	1	2	yes	—
277	C₂²×C₄	#6099	1	2	yes	—
278	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
279	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
280	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
281	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
283	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
284	C₂×C₈	—	26	4	no	—
285	C₂×C₈	—	52	2	no	—
286	C₂×C₈	—	52	2	no	—
287	C₂×C₈	—	52	2	no	—
288	C₂×C₈	—	52	2	no	—
289	C₂×C₈	—	52	2	no	—
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	2	1	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	2	1	no	—
294	C₄⋊C₄	C₂×#1055	1	2	yes	—
295	C₄⋊C₄	C₂×#1055	1	2	yes	—
296	C₄⋊C₄	#6099	1	2	yes	—
297	C₄⋊C₄	#6099	1	2	yes	—
298	C₂²⋊C₄	—	2	4	no	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₄²	—	2	4	no	—
301	C₄²	—	2	4	no	—
302	C₄²	—	2	1	no	—
303	C₄²	—	2	1	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	4	2	no	—
307	C₄²	—	4	2	no	—
308	C₄²	—	4	1	no	—
309	C₄²	—	4	2	no	—
310	C₄²	—	4	1	no	—
311	C₄²	#6127	1	2	yes	—
312	C₄²	#6127	1	2	yes	—
313	C₁₃	#8708	1	1	yes	characteristic, complemented, Sylow
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	C₂²⋊#1055	1	2	yes	—
321	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	C₂²⋊#1055	1	2	yes	—
351	C₂×C₄	#88077	1	2	yes	—
352	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
353	C₂×C₄	C₂×#6099	1	1	yes	characteristic
354	C₂×C₄	C₂×#6099	1	1	yes	characteristic
355	C₂×C₄	C₂×#6099	1	1	yes	characteristic
356	C₂×C₄	#88180	1	1	yes	characteristic
357	C₂×C₄	#88180	1	1	yes	characteristic
358	C₂×C₄	#88183	1	2	yes	—
359	C₂×C₄	#88183	1	2	yes	—
360	C₂×C₄	#88203	1	1	yes	characteristic
361	C₂×C₄	#88204	1	2	yes	—
362	C₂×C₄	#88205	1	1	yes	characteristic
363	C₈	—	52	4	no	—
364	C₈	—	104	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	4	1	no	—
372	C₂²	C₂×C₂²⋊#1055	1	1	yes	characteristic
373	C₂²	#11718868	1	1	yes	characteristic
374	C₂²	#11718872	1	1	yes	characteristic
375	C₂²	#11718893	1	1	yes	characteristic
376	C₂²	#11718894	1	1	yes	characteristic
377	C₂²	C₂×#88077	1	1	yes	characteristic
378	C₂²	#11718897	1	1	yes	characteristic
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	4	1	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	4	2	no	—
386	C₄	—	4	2	no	—
387	C₄	#11718586	1	1	yes	characteristic
388	C₄	#11718586	1	1	yes	characteristic
389	C₄	#11718587	1	1	yes	characteristic
390	C₄	#11718587	1	1	yes	characteristic
391	C₄	#11718657	1	2	yes	—
392	C₄	#11718664	1	2	yes	—
393	C₂	—	4	2	no	—
394	C₂	#13113218	1	1	yes	characteristic
395	C₂	#13113223	1	1	yes	characteristic
396	C₂	#13113270	1	1	yes	characteristic
397	C₂	#13113275	1	1	yes	characteristic
398	C₂	#13114904	1	1	yes	characteristic
399	C₂	#13114931	1	1	yes	characteristic
400	C₂	#13114935	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₄×C₁₃×#117	C₂
socle	C₂³×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₄×#117	D₁₃
hypocenter	C₁₃	#8708
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₄×#117

Complements

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

N	H ≅ G/N	type
3. #13112677	C₂	semidirect
4. #13112677	C₂	semidirect
29. C₁₃×#117	C₈	semidirect
223. #117	#1055	semidirect
313. C₁₃	#8708	semidirect

Maximal subgroups

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

subgroup	index
#13114816	2
C₄×C₂²⋊#1055	2
#13112677	2
C₄×C₁₃×#117	2
#8708	13