Subgroups — #15866167

Order 3328.

780 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123487	C₂	1	1	yes	maximal, characteristic, complemented
2	#13123264	C₂	1	1	yes	maximal, characteristic, complemented
3	#13115486	C₂	1	2	yes	maximal, complemented
4	#13115437	C₂	1	2	yes	maximal, complemented
5	#13115165	C₂	1	2	yes	maximal
6	#13115113	C₂	1	2	yes	maximal, complemented
7	#13114742	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#88077	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#88077	C₂	1	1	yes	maximal, characteristic, complemented
10	#13114584	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2943	C₂	1	1	yes	maximal, characteristic
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
14	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
15	C₂×#88202	C₂²	1	2	yes	—
16	C₁₃×#442	C₄	1	2	yes	complemented
17	C₁₃×#441	C₄	1	2	yes	complemented
18	C₁₃×#440	C₄	1	2	yes	complemented
19	C₁₃×#440	C₄	1	2	yes	complemented
20	C₁₃×#427	C₂²	1	1	yes	characteristic
21	C₁₃×#416	C₂²	1	1	yes	characteristic
22	C₁₃×#416	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
24	C₂×#88077	C₂²	1	2	yes	—
25	C₂×#88077	C₂²	1	2	yes	—
26	#11718895	C₂²	1	2	yes	—
27	C₂×#88059	C₂²	1	2	yes	—
28	#11718661	—	2	1	no	—
29	#11718661	—	2	1	no	—
30	#11718660	C₂²	1	2	yes	—
31	#11718658	—	2	2	no	—
32	#11718658	C₂²	1	2	yes	—
33	C₄²×Dic₁₃	C₂²	1	1	yes	characteristic
34	#11718587	—	2	2	no	—
35	C₄×#6099	—	2	1	no	—
36	C₄×#6099	C₂²	1	1	yes	characteristic
37	C₄×#6099	C₂²	1	1	yes	characteristic
38	C₂×#88043	—	2	1	no	—
39	C₂×#88043	C₂²	1	1	yes	characteristic
40	#11718144	C₂²	1	2	yes	—
41	#11718142	C₂²	1	2	yes	—
42	#11718142	C₂²	1	2	yes	—
43	#11718124	C₂²	1	2	yes	—
44	#11718124	C₂²	1	2	yes	—
45	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
46	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
47	C₁₃×#135	—	2	4	no	—
48	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×SD₁₆	C₂×C₄	1	1	yes	characteristic
51	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
55	C₄×Q₈×C₁₃	C₂×C₄	1	2	yes	—
56	C₄×D₄×C₁₃	—	2	2	no	—
57	C₄×D₄×C₁₃	—	2	2	no	—
58	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
59	C₄×D₄×C₁₃	C₂×C₄	1	2	yes	—
60	C₁₃×#117	—	2	1	no	—
61	C₁₃×#117	—	2	1	no	—
62	C₁₃×#117	C₂³	1	1	yes	characteristic
63	C₁₃×#117	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	—	2	1	no	—
65	C₂×C₄²×C₁₃	—	2	1	no	—
66	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
67	#88202	—	2	4	no	—
68	#88202	—	2	4	no	—
69	C₂×C₄×Dic₁₃	—	2	2	no	—
70	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
71	C₂×#6099	—	2	2	no	—
72	C₂×#6099	C₂³	1	2	yes	—
73	C₂×#6099	C₂³	1	2	yes	—
74	C₂²×#1055	—	2	2	no	—
75	C₂²×#1055	C₂³	1	2	yes	—
76	C₁₃×#107	C₂×C₄	1	2	yes	—
77	C₁₃×#106	C₂×C₄	1	2	yes	—
78	C₁₃×#103	C₂×C₄	1	2	yes	—
79	C₁₃×#103	C₂×C₄	1	2	yes	—
80	C₁₃×#102	C₂×C₄	1	2	yes	—
81	C₁₃×#102	C₂×C₄	1	2	yes	—
82	C₁₃×#97	C₂×C₄	1	2	yes	—
83	C₁₃×#97	C₂×C₄	1	2	yes	—
84	#88077	—	2	4	no	—
85	#88077	—	2	4	no	—
86	C₂²⋊#1055	—	2	2	no	—
87	C₂²⋊#1055	—	2	2	no	—
88	#88059	—	2	4	no	—
89	C₄⋊#1055	—	2	2	no	—
90	C₄⋊#1055	—	2	2	no	—
91	#88043	—	2	1	no	—
92	#88043	—	2	1	no	—
93	#88043	—	2	2	no	—
94	#88043	D₄	1	2	yes	—
95	#88043	D₄	1	1	yes	characteristic
96	#88043	D₄	1	1	yes	characteristic
97	C₄×#1055	—	2	1	no	—
98	C₄×#1055	—	2	1	no	—
99	C₄×#1055	—	2	2	no	—
100	#21139	—	13	1	no	maximal, Sylow
101	C₁₃×#41	—	2	2	no	—
102	C₁₃×#41	—	2	2	no	—
103	C₁₃×#41	—	2	2	no	—
104	C₁₃×#41	#41	1	4	yes	—
105	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×D₄×C₁₃	—	2	1	no	—
108	C₂×D₄×C₁₃	—	2	1	no	—
109	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×D₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	#41	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
117	C₂²×Dic₁₃	—	2	2	no	—
118	C₁₃×Q₁₆	—	2	2	no	—
119	C₁₃×SD₁₆	—	2	2	no	—
120	C₁₃×SD₁₆	—	2	2	no	—
121	C₁₃×D₈	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
130	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
131	C₁₃×C₂²⋊C₄	—	2	1	no	—
132	C₁₃×C₂²⋊C₄	—	2	1	no	—
133	C₁₃×C₂²⋊C₄	—	2	2	no	—
134	C₁₃×C₂²⋊C₄	—	2	2	no	—
135	C₄²×C₁₃	—	2	2	no	—
136	C₄²×C₁₃	—	2	2	no	—
137	C₄²×C₁₃	—	2	1	no	—
138	C₄²×C₁₃	—	2	1	no	—
139	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
140	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₄×Dic₁₃	—	2	2	no	—
143	C₄×Dic₁₃	—	2	2	no	—
144	C₄×Dic₁₃	—	4	4	no	—
145	#6099	—	2	8	no	—
146	#6099	—	2	2	no	—
147	#6099	—	2	2	no	—
148	#6099	—	2	2	no	—
149	#6099	#41	1	4	yes	—
150	C₂×#1055	—	2	8	no	—
151	C₂×#1055	—	2	2	no	—
152	C₂×#1055	—	2	2	no	—
153	C₂×#1055	—	2	2	no	—
154	C₂×#1055	—	2	2	no	—
155	C₂×#1055	C₂×D₄	1	2	yes	—
156	C₂×#1055	C₂×D₄	1	2	yes	—
157	#2943	D₁₃	1	1	yes	characteristic
158	#2923	—	13	1	no	—
159	#2875	—	13	1	no	—
160	#1929	—	13	2	no	—
161	#1922	—	13	2	no	—
162	#1876	—	13	2	no	—
163	#1866	—	13	2	no	—
164	#1778	—	13	1	no	—
165	C₄×#104	—	13	1	no	—
166	C₄×#104	—	13	1	no	—
167	#1745	—	13	1	no	—
168	C₂³×C₁₃	—	2	1	no	—
169	C₂³×C₁₃	—	2	1	no	—
170	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
171	Q₈×C₁₃	—	2	1	no	—
172	Q₈×C₁₃	—	2	1	no	—
173	Q₈×C₁₃	—	2	1	no	—
174	Q₈×C₁₃	#117	1	2	yes	—
175	D₄×C₁₃	—	2	4	no	—
176	D₄×C₁₃	—	2	1	no	—
177	D₄×C₁₃	—	2	1	no	—
178	D₄×C₁₃	—	2	1	no	—
179	D₄×C₁₃	—	4	2	no	—
180	D₄×C₁₃	#117	1	2	yes	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	8	2	no	—
189	C₂×C₄×C₁₃	—	8	2	no	—
190	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
191	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
192	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
195	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
196	C₂×Dic₁₃	—	2	4	no	—
197	C₂×Dic₁₃	—	4	2	no	—
198	C₂×Dic₁₃	—	4	2	no	—
199	C₈×C₁₃	—	2	1	no	—
200	C₈×C₁₃	—	2	1	no	—
201	C₈×C₁₃	—	2	2	no	—
202	#1055	—	2	2	no	—
203	#1055	—	2	4	no	—
204	#1055	—	2	2	no	—
205	#1055	—	4	2	no	—
206	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
207	C₂×#131	—	13	2	no	—
208	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
209	C₄×#41	C₂×D₁₃	1	1	yes	characteristic
210	#442	Dic₁₃	1	2	yes	complemented
211	#441	Dic₁₃	1	2	yes	complemented
212	#440	Dic₁₃	1	2	yes	complemented
213	#440	Dic₁₃	1	2	yes	complemented
214	#433	—	26	1	no	—
215	#433	—	26	1	no	—
216	#432	—	26	2	no	—
217	C₂×#108	—	13	2	no	—
218	#427	C₂×D₁₃	1	1	yes	characteristic
219	#424	—	13	2	no	—
220	C₂×#104	—	13	2	no	—
221	C₂×#104	—	13	2	no	—
222	#416	C₂×D₁₃	1	1	yes	characteristic
223	#416	C₂×D₁₃	1	1	yes	characteristic
224	#408	—	13	2	no	—
225	#405	—	13	2	no	—
226	#405	—	26	2	no	—
227	C₄×M₁₆	—	13	1	no	—
228	C₄×M₁₆	—	13	1	no	—
229	C₄×M₁₆	—	26	1	no	—
230	C₂×#97	—	13	1	no	—
231	C₂×#97	—	26	1	no	—
232	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
233	C₄³	—	13	1	no	—
234	#341	—	13	2	no	—
235	#339	—	13	2	no	—
236	#339	—	13	2	no	—
237	#336	—	13	2	no	—
238	#336	—	13	2	no	—
239	C₂²×C₁₃	—	2	2	no	—
240	C₂²×C₁₃	—	2	2	no	—
241	C₂²×C₁₃	—	4	2	no	—
242	C₂²×C₁₃	—	4	2	no	—
243	C₂²×C₁₃	—	4	1	no	—
244	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
245	C₂²×C₁₃	#529	1	2	yes	—
246	C₄×C₁₃	—	2	2	no	—
247	C₄×C₁₃	—	2	2	no	—
248	C₄×C₁₃	—	2	2	no	—
249	C₄×C₁₃	—	4	2	no	—
250	C₄×C₁₃	—	4	2	no	—
251	C₄×C₁₃	—	4	1	no	—
252	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
253	C₄×C₁₃	C₄×#41	1	1	yes	characteristic
254	C₄×C₁₃	#525	1	2	yes	—
255	Dic₁₃	—	4	4	no	—
256	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
257	C₂×#41	C₂²×D₁₃	1	1	yes	characteristic
258	#135	—	2	4	no	—
259	C₂×Q₁₆	C₂×Dic₁₃	1	1	yes	characteristic
260	C₂×SD₁₆	C₂×Dic₁₃	1	1	yes	characteristic
261	C₂×SD₁₆	C₂×Dic₁₃	1	1	yes	characteristic
262	C₂×D₈	C₂×Dic₁₃	1	1	yes	characteristic
263	#131	—	26	4	no	—
264	#131	—	26	4	no	—
265	C₂×M₁₆	—	13	2	no	—
266	C₂×M₁₆	—	13	2	no	—
267	C₂×M₁₆	—	26	2	no	—
268	C₂²×C₈	—	13	2	no	—
269	C₂²×C₈	—	26	2	no	—
270	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
271	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
272	C₄×Q₈	C₂×Dic₁₃	1	2	yes	—
273	C₄×Q₈	C₂×Dic₁₃	1	2	yes	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	C₂×Dic₁₃	1	2	yes	—
277	C₄×D₄	C₂×Dic₁₃	1	2	yes	—
278	#117	—	2	1	no	—
279	#117	—	2	1	no	—
280	#117	C₂²×D₁₃	1	1	yes	characteristic
281	#117	C₂²×D₁₃	1	1	yes	characteristic
282	C₂×C₄²	—	2	1	no	—
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	—	13	2	no	—
285	C₂×C₄²	—	26	2	no	—
286	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
287	#108	—	26	4	no	—
288	#107	C₂×Dic₁₃	1	2	yes	—
289	#106	C₂×Dic₁₃	1	2	yes	—
290	C₄⋊C₈	—	26	2	no	—
291	C₄⋊C₈	—	26	2	no	—
292	#104	—	26	4	no	—
293	#104	—	26	4	no	—
294	#103	C₂×Dic₁₃	1	2	yes	—
295	#103	C₂×Dic₁₃	1	2	yes	—
296	#102	C₂×Dic₁₃	1	2	yes	—
297	#102	C₂×Dic₁₃	1	2	yes	—
298	C₂²⋊C₈	—	26	2	no	—
299	C₂²⋊C₈	—	26	2	no	—
300	#97	—	13	1	no	—
301	#97	—	13	1	no	—
302	#97	—	13	2	no	—
303	#97	—	26	2	no	—
304	#97	—	26	1	no	—
305	#97	—	26	1	no	—
306	#97	C₂×Dic₁₃	1	2	yes	—
307	#97	C₂×Dic₁₃	1	2	yes	—
308	C₄×C₈	—	26	2	no	—
309	C₄×C₈	—	26	1	no	—
310	C₄×C₈	—	26	1	no	—
311	C₂×C₁₃	—	2	2	no	—
312	C₂×C₁₃	—	4	2	no	—
313	C₂×C₁₃	—	8	1	no	—
314	C₂×C₁₃	#2290	1	1	yes	characteristic
315	C₂×C₁₃	#2956	1	2	yes	—
316	#41	—	2	2	no	—
317	#41	—	2	2	no	—
318	#41	—	2	2	no	—
319	#41	#6127	1	4	yes	—
320	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
321	C₂×Q₈	C₂²×Dic₁₃	1	1	yes	characteristic
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
325	C₂×D₄	C₂²×Dic₁₃	1	1	yes	characteristic
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	26	2	no	—
331	C₂²×C₄	#6129	1	2	yes	—
332	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
333	Q₁₆	—	2	2	no	—
334	SD₁₆	—	2	2	no	—
335	SD₁₆	—	2	2	no	—
336	D₈	—	2	2	no	—
337	M₁₆	—	13	4	no	—
338	M₁₆	—	26	8	no	—
339	M₁₆	—	26	2	no	—
340	M₁₆	—	26	2	no	—
341	M₁₆	—	26	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	13	2	no	—
345	C₂×C₈	—	13	2	no	—
346	C₂×C₈	—	26	8	no	—
347	C₂×C₈	—	26	2	no	—
348	C₂×C₈	—	26	2	no	—
349	C₂×C₈	—	26	2	no	—
350	C₂×C₈	—	26	2	no	—
351	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
352	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
353	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
357	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
358	C₂²⋊C₄	—	2	1	no	—
359	C₂²⋊C₄	—	2	1	no	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	26	2	no	—
367	C₄²	—	26	2	no	—
368	C₄²	—	52	4	no	—
369	C₄²	D₄×D₁₃	1	1	yes	characteristic
370	C₄²	D₄×D₁₃	1	1	yes	characteristic
371	C₄²	C₂²×Dic₁₃	1	2	yes	—
372	C₁₃	#21139	1	1	yes	characteristic, complemented, Sylow
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	C₂×#6129	1	1	yes	characteristic
376	Q₈	—	2	1	no	—
377	Q₈	—	2	1	no	—
378	Q₈	—	2	1	no	—
379	Q₈	#88180	1	2	yes	—
380	D₄	—	2	4	no	—
381	D₄	—	2	1	no	—
382	D₄	—	2	1	no	—
383	D₄	—	2	1	no	—
384	D₄	—	4	2	no	—
385	D₄	#88180	1	2	yes	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	8	2	no	—
394	C₂×C₄	—	8	2	no	—
395	C₂×C₄	—	26	4	no	—
396	C₂×C₄	—	52	2	no	—
397	C₂×C₄	—	52	2	no	—
398	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
399	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
400	C₂×C₄	C₂×#6127	1	2	yes	—
401	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
402	C₂×C₄	#41×D₁₃	1	2	yes	—
403	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
404	C₈	—	2	1	no	—
405	C₈	—	2	1	no	—
406	C₈	—	2	2	no	—
407	C₈	—	26	2	no	—
408	C₈	—	26	2	no	—
409	C₈	—	26	4	no	—
410	C₈	—	52	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	2	no	—
416	C₂²	#11719243	1	2	yes	—
417	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	2	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	2	no	—
424	C₄	—	52	4	no	—
425	C₄	#11719252	1	2	yes	—
426	C₄	C₂×#88180	1	1	yes	characteristic
427	C₄	#41×Dic₁₃	1	1	yes	characteristic
428	C₂	—	2	2	no	—
429	C₂	—	4	2	no	—
430	C₂	—	8	1	no	—
431	C₂	#13117281	1	1	yes	characteristic
432	C₂	#13123746	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₁₃×#2943	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×C₁₃×#135	C₂²
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	#2943	D₁₃
hypocenter	C₁₃	#21139
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2943

Complements

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

N	H ≅ G/N	type
1. #13123487	C₂	semidirect
2. #13123264	C₂	semidirect
3. #13115486	C₂	semidirect
4. #13115437	C₂	semidirect
6. #13115113	C₂	semidirect
7. #13114742	C₂	semidirect
8. C₄×#88077	C₂	semidirect
9. C₄×#88077	C₂	semidirect
10. #13114584	C₂	semidirect
16. C₁₃×#442	C₄	semidirect
17. C₁₃×#441	C₄	semidirect
18. C₁₃×#440	C₄	semidirect
19. C₁₃×#440	C₄	semidirect
210. #442	Dic₁₃	semidirect
211. #441	Dic₁₃	semidirect
212. #440	Dic₁₃	semidirect
213. #440	Dic₁₃	semidirect
372. C₁₃	#21139	semidirect

Maximal subgroups

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

subgroup	index
#13123487	2
#13123264	2
#13115486	2
#13115437	2
#13115165	2
#13115113	2
#13114742	2
C₄×#88077	2
#13114584	2
C₁₃×#2943	2
#21139	13