Subgroups — #15768771

Order 3328.

978 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#6099	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718124	C₂	1	4	yes	maximal
4	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#117	C₂²	1	2	yes	—
6	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊Dic₁₃	—	2	1	no	—
8	C₂²×C₄×Dic₁₃	C₂²	1	2	yes	—
9	C₂²×#6099	C₂²	1	2	yes	—
10	C₁₃×#384	C₄	1	2	yes	complemented
11	C₁₃×#382	C₄	1	2	yes	complemented
12	C₁₃×#380	—	2	1	no	—
13	C₁₃×#380	—	2	1	no	—
14	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
15	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
16	C₂×#88071	—	2	1	no	—
17	C₄×C₄⋊Dic₁₃	—	2	2	no	—
18	C₄×C₄⋊Dic₁₃	C₄	1	4	yes	complemented
19	C₄×#6099	—	2	2	no	—
20	C₄×#6099	C₄	1	4	yes	complemented
21	C₂×#88043	—	2	1	no	—
22	C₂×C₄×#1055	—	2	1	no	—
23	#11718124	—	2	8	no	—
24	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
27	C₂³×Dic₁₃	—	2	2	no	—
28	C₁₃×#117	—	2	4	no	—
29	C₁₃×#117	—	2	4	no	—
30	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
31	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
32	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
33	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
34	C₂×C₄²×C₁₃	—	2	2	no	—
35	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
36	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
37	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₃	D₄	1	2	yes	—
40	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
43	C₂×C₄⋊Dic₁₃	—	2	8	no	—
44	C₂×C₄⋊Dic₁₃	—	2	4	no	—
45	C₂×C₄×Dic₁₃	—	2	4	no	—
46	C₂×C₄×Dic₁₃	—	2	4	no	—
47	C₂×C₄×Dic₁₃	—	2	2	no	—
48	C₂×C₄×Dic₁₃	C₂×C₄	1	4	yes	—
49	C₂×#6099	—	2	2	no	—
50	C₂×#6099	—	2	2	no	—
51	C₂×#6099	—	2	2	no	—
52	C₂×#6099	C₂×C₄	1	4	yes	—
53	C₂×#6099	D₄	1	4	yes	—
54	C₂×#6099	Q₈	1	4	yes	—
55	C₂²×#1055	—	2	2	no	—
56	C₁₃×#95	—	2	2	no	—
57	C₁₃×#95	—	2	2	no	—
58	#88071	—	2	4	no	—
59	#88043	—	2	4	no	—
60	C₄×#1055	—	2	4	no	—
61	#10851	—	13	1	no	maximal, Sylow
62	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₃	—	2	4	no	—
64	C₂²×C₄×C₁₃	—	2	4	no	—
65	C₂²×C₄×C₁₃	—	4	2	no	—
66	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
67	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
68	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
73	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
74	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
82	C₂²×C₄×C₁₃	#41	1	2	yes	—
83	C₂²×C₄×C₁₃	#41	1	2	yes	—
84	C₂²×Dic₁₃	—	2	8	no	—
85	C₂²×Dic₁₃	—	2	4	no	—
86	C₂²×Dic₁₃	—	4	4	no	—
87	C₂²×Dic₁₃	—	4	2	no	—
88	C₂²×Dic₁₃	—	4	2	no	—
89	C₁₃×C₄⋊C₄	—	2	8	no	—
90	C₁₃×C₄⋊C₄	—	4	4	no	—
91	C₁₃×C₄⋊C₄	—	4	4	no	—
92	C₁₃×C₂²⋊C₄	—	4	2	no	—
93	C₁₃×C₂²⋊C₄	—	4	2	no	—
94	C₄²×C₁₃	—	4	4	no	—
95	C₄²×C₁₃	C₄²	1	2	yes	—
96	C₄²×C₁₃	C₄²	1	2	yes	—
97	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
98	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
99	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
100	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
101	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
102	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
103	C₄⋊Dic₁₃	—	2	16	no	—
104	C₄×Dic₁₃	—	2	8	no	—
105	C₄×Dic₁₃	—	4	4	no	—
106	#6099	—	2	4	no	—
107	#6099	—	2	4	no	—
108	#6099	—	2	4	no	—
109	#6099	C₄⋊C₄	1	8	yes	complemented
110	C₂×#1055	—	2	4	no	—
111	C₂×#1055	—	2	4	no	—
112	C₂×#1055	—	2	4	no	—
113	C₂×C₄×M₁₆	—	13	1	no	—
114	#2285	D₁₃	1	1	yes	characteristic
115	C₂×C₄×C₄⋊C₄	—	13	1	no	—
116	C₂×#339	—	13	4	no	—
117	C₂³×C₁₃	—	2	2	no	—
118	C₂³×C₁₃	—	2	2	no	—
119	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂³×C₁₃	#124	1	1	yes	characteristic
123	C₂³×C₁₃	#124	1	1	yes	characteristic
124	C₂³×C₁₃	#127	1	1	yes	characteristic
125	C₂³×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
126	C₂×C₄×C₁₃	—	2	2	no	—
127	C₂×C₄×C₁₃	—	2	2	no	—
128	C₂×C₄×C₁₃	—	2	2	no	—
129	C₂×C₄×C₁₃	—	2	4	no	—
130	C₂×C₄×C₁₃	—	2	4	no	—
131	C₂×C₄×C₁₃	—	4	2	no	—
132	C₂×C₄×C₁₃	—	4	2	no	—
133	C₂×C₄×C₁₃	—	4	4	no	—
134	C₂×C₄×C₁₃	—	4	4	no	—
135	C₂×C₄×C₁₃	—	4	4	no	—
136	C₂×C₄×C₁₃	#95	1	2	yes	—
137	C₂×C₄×C₁₃	#95	1	2	yes	—
138	C₂×C₄×C₁₃	#95	1	2	yes	—
139	C₂×C₄×C₁₃	#95	1	2	yes	—
140	C₂×C₄×C₁₃	#104	1	4	yes	—
141	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
142	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
144	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₃	#117	1	2	yes	—
147	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
148	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
149	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
150	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
151	C₂×C₄×C₁₃	#121	1	2	yes	—
152	C₂×C₄×C₁₃	#121	1	2	yes	—
153	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
154	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
155	C₂×C₄×C₁₃	#125	1	2	yes	—
156	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
157	C₂×Dic₁₃	—	2	8	no	—
158	C₂×Dic₁₃	—	4	8	no	—
159	C₂×Dic₁₃	—	4	8	no	—
160	C₂×Dic₁₃	—	4	4	no	—
161	C₂×Dic₁₃	—	4	4	no	—
162	#1055	—	2	8	no	—
163	C₂²×M₁₆	—	13	2	no	—
164	C₂×#117	C₂×D₁₃	1	2	yes	—
165	C₂²×C₄⋊C₄	—	26	1	no	—
166	C₂²×C₄²	—	13	2	no	—
167	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
168	C₄×M₁₆	—	13	4	no	—
169	C₄×M₁₆	—	26	2	no	—
170	C₂×#97	—	26	1	no	—
171	C₂×C₄×C₈	—	26	1	no	—
172	#384	Dic₁₃	1	2	yes	complemented
173	#382	Dic₁₃	1	2	yes	complemented
174	#380	—	2	1	no	—
175	#380	—	2	1	no	—
176	C₄×C₄⋊C₄	—	2	1	no	—
177	C₄×C₄⋊C₄	—	2	1	no	—
178	C₄×C₄⋊C₄	—	13	4	no	—
179	C₄×C₄⋊C₄	—	26	2	no	—
180	C₂×#95	—	26	1	no	—
181	#339	—	26	8	no	—
182	C₂²×C₁₃	—	2	2	no	—
183	C₂²×C₁₃	—	2	2	no	—
184	C₂²×C₁₃	—	2	2	no	—
185	C₂²×C₁₃	—	2	2	no	—
186	C₂²×C₁₃	—	2	1	no	—
187	C₂²×C₁₃	—	2	1	no	—
188	C₂²×C₁₃	—	2	1	no	—
189	C₂²×C₁₃	—	2	1	no	—
190	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
191	C₂²×C₁₃	#382	1	1	yes	characteristic
192	C₂²×C₁₃	#384	1	1	yes	characteristic
193	C₂²×C₁₃	#390	1	1	yes	characteristic
194	C₂²×C₁₃	#390	1	1	yes	characteristic
195	C₂²×C₁₃	#391	1	1	yes	characteristic
196	C₂²×C₁₃	#391	1	1	yes	characteristic
197	C₂²×C₁₃	C₂×#104	1	2	yes	—
198	C₂²×C₁₃	#421	1	2	yes	—
199	C₄×C₁₃	—	2	2	no	—
200	C₄×C₁₃	—	2	2	no	—
201	C₄×C₁₃	—	2	2	no	—
202	C₄×C₁₃	—	8	4	no	—
203	C₄×C₁₃	#339	1	4	yes	complemented
204	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
205	C₄×C₁₃	#380	1	2	yes	—
206	C₄×C₁₃	#389	1	2	yes	—
207	C₄×C₁₃	#389	1	2	yes	—
208	Dic₁₃	—	4	8	no	—
209	C₂³×C₄	—	26	2	no	—
210	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
211	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
212	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
213	C₂×M₁₆	—	13	4	no	—
214	C₂×M₁₆	—	13	4	no	—
215	C₂×M₁₆	—	13	4	no	—
216	C₂×M₁₆	—	26	2	no	—
217	C₂×M₁₆	—	26	2	no	—
218	C₂×M₁₆	—	26	2	no	—
219	C₂²×C₈	—	26	2	no	—
220	#117	—	2	4	no	—
221	#117	—	2	4	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	—	26	8	no	—
225	C₂×C₄⋊C₄	—	26	4	no	—
226	C₂×C₄⋊C₄	C₂×Dic₁₃	1	4	yes	—
227	C₂×C₂²⋊C₄	—	2	2	no	—
228	C₂×C₄²	—	2	2	no	—
229	C₂×C₄²	—	13	4	no	—
230	C₂×C₄²	—	26	4	no	—
231	C₂×C₄²	—	26	4	no	—
232	C₂×C₄²	—	26	2	no	—
233	C₂×C₄²	Dic₂₆	1	2	yes	—
234	C₂×C₄²	C₄×D₁₃	1	2	yes	—
235	C₂×C₄²	C₄×D₁₃	1	2	yes	—
236	C₂×C₄²	D₅₂	1	2	yes	—
237	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
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	#97	—	26	4	no	—
242	C₄×C₈	—	26	4	no	—
243	#95	—	2	2	no	—
244	#95	—	2	2	no	—
245	#95	—	26	4	no	—
246	C₂×C₁₃	—	2	1	no	—
247	C₂×C₁₃	—	2	1	no	—
248	C₂×C₁₃	—	2	1	no	—
249	C₂×C₁₃	—	2	1	no	—
250	C₂×C₁₃	C₄⋊#95	1	1	yes	characteristic
251	C₂×C₁₃	C₂×#339	1	1	yes	characteristic
252	C₂×C₁₃	#1733	1	1	yes	characteristic
253	C₂×C₁₃	#1980	1	2	yes	—
254	C₂×C₁₃	#1986	1	2	yes	—
255	C₂⁴	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	26	8	no	—
260	C₂²×C₄	—	26	4	no	—
261	C₂²×C₄	—	52	4	no	—
262	C₂²×C₄	—	52	2	no	—
263	C₂²×C₄	—	52	2	no	—
264	C₂²×C₄	#6101	1	2	yes	—
265	C₂²×C₄	#6101	1	2	yes	—
266	C₂²×C₄	#6103	1	2	yes	—
267	C₂²×C₄	#6103	1	2	yes	—
268	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
269	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
270	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
271	C₂²×C₄	C₂²⋊Dic₁₃	1	1	yes	characteristic
272	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
276	C₂²×C₄	D₄×D₁₃	1	2	yes	—
277	C₂²×C₄	#6129	1	2	yes	—
278	C₂²×C₄	Q₈×D₁₃	1	2	yes	—
279	C₂²×C₄	#6131	1	2	yes	—
280	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
282	M₁₆	—	13	8	no	—
283	M₁₆	—	26	4	no	—
284	M₁₆	—	26	4	no	—
285	M₁₆	—	26	4	no	—
286	C₂×C₈	—	26	4	no	—
287	C₂×C₈	—	26	4	no	—
288	C₂×C₈	—	26	4	no	—
289	C₄⋊C₄	—	2	8	no	—
290	C₄⋊C₄	—	4	4	no	—
291	C₄⋊C₄	—	4	4	no	—
292	C₄⋊C₄	—	26	16	no	—
293	C₂²⋊C₄	—	4	2	no	—
294	C₂²⋊C₄	—	4	2	no	—
295	C₄²	—	4	4	no	—
296	C₄²	—	26	8	no	—
297	C₄²	—	52	4	no	—
298	C₄²	C₄×Dic₁₃	1	2	yes	—
299	C₄²	C₄×Dic₁₃	1	2	yes	—
300	C₄²	#6101	1	2	yes	—
301	C₄²	#6101	1	2	yes	—
302	C₄²	C₄⋊Dic₁₃	1	2	yes	—
303	C₄²	C₄⋊Dic₁₃	1	2	yes	—
304	C₄²	#6103	1	2	yes	—
305	C₄²	#6103	1	2	yes	—
306	C₁₃	#10851	1	1	yes	characteristic, complemented, Sylow
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	C₂×#6101	1	1	yes	characteristic
310	C₂³	C₂×#6103	1	1	yes	characteristic
311	C₂³	#88190	1	1	yes	characteristic
312	C₂³	#88194	1	1	yes	characteristic
313	C₂³	#88198	1	1	yes	characteristic
314	C₂³	#88201	1	1	yes	characteristic
315	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	26	8	no	—
327	C₂×C₄	—	52	8	no	—
328	C₂×C₄	—	52	8	no	—
329	C₂×C₄	—	52	4	no	—
330	C₂×C₄	—	52	4	no	—
331	C₂×C₄	#88071	1	2	yes	—
332	C₂×C₄	#88071	1	2	yes	—
333	C₂×C₄	#88071	1	2	yes	—
334	C₂×C₄	#88071	1	2	yes	—
335	C₂×C₄	#88077	1	4	yes	—
336	C₂×C₄	#88141	1	2	yes	—
337	C₂×C₄	#88142	1	2	yes	—
338	C₂×C₄	#88144	1	2	yes	—
339	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
340	C₂×C₄	#88146	1	2	yes	—
341	C₂×C₄	#88147	1	2	yes	—
342	C₂×C₄	#88149	1	2	yes	—
343	C₂×C₄	#88151	1	2	yes	—
344	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
345	C₂×C₄	C₂×#6101	1	1	yes	characteristic
346	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
347	C₂×C₄	C₂×#6103	1	1	yes	characteristic
348	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
349	C₂×C₄	#88192	1	2	yes	—
350	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
351	C₂×C₄	#88200	1	2	yes	—
352	C₈	—	26	8	no	—
353	C₂²	—	2	2	no	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	1	no	—
358	C₂²	—	2	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	#11718635	1	1	yes	characteristic
362	C₂²	#11718637	1	1	yes	characteristic
363	C₂²	#11718638	1	1	yes	characteristic
364	C₂²	#11718649	1	1	yes	characteristic
365	C₂²	C₂×#88071	1	1	yes	characteristic
366	C₂²	#11718882	1	1	yes	characteristic
367	C₂²	#11718891	1	1	yes	characteristic
368	C₂²	C₂×#88077	1	2	yes	—
369	C₂²	#11718897	1	2	yes	—
370	C₄	—	2	2	no	—
371	C₄	—	2	2	no	—
372	C₄	—	2	2	no	—
373	C₄	—	8	4	no	—
374	C₄	—	52	8	no	—
375	C₄	#11718124	1	4	yes	complemented
376	C₄	#11718634	1	2	yes	—
377	C₄	C₄⋊C₄×Dic₁₃	1	2	yes	—
378	C₄	#11718646	1	2	yes	—
379	C₄	#11718648	1	2	yes	—
380	C₂	—	2	1	no	—
381	C₂	—	2	1	no	—
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	#13113065	1	1	yes	characteristic
385	C₂	C₂×#11718124	1	1	yes	characteristic
386	C₂	#13114545	1	1	yes	characteristic
387	C₂	#13115756	1	2	yes	—
388	C₂	#13115781	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₁₃×#2285	C₂
socle	C₂³×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₃	C₂×D₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	#2285	D₁₃
hypocenter	C₁₃	#10851
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ #2285

Complements

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

N	H ≅ G/N	type
10. C₁₃×#384	C₄	semidirect
11. C₁₃×#382	C₄	semidirect
18. C₄×C₄⋊Dic₁₃	C₄	semidirect
20. C₄×#6099	C₄	semidirect
109. #6099	C₄⋊C₄	semidirect
172. #384	Dic₁₃	semidirect
173. #382	Dic₁₃	semidirect
203. C₄×C₁₃	#339	semidirect
306. C₁₃	#10851	semidirect
375. C₄	#11718124	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#6099	2
C₂×C₄×C₄⋊Dic₁₃	2
C₂×#11718124	2
C₁₃×#2285	2
#10851	13