Subgroups — D₁₃×#2222 #16017478

Order 3328.

638 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₃×#504	C₂	1	1	yes	maximal, characteristic
3	D₁₃×#473	C₂	1	2	yes	maximal
4	#13116962	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116961	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116960	C₂	1	2	yes	maximal, complemented
7	#13116959	C₂	1	2	yes	maximal, complemented
8	#13116958	C₂	1	1	yes	maximal, characteristic, complemented
9	D₁₃×#368	C₂	1	1	yes	maximal, characteristic, complemented
10	D₁₃×#362	C₂	1	2	yes	maximal, complemented
11	C₁₃×#2222	C₂	1	1	yes	maximal, characteristic, complemented
12	D₁₃×#137	—	2	2	no	—
13	C₂×Q₁₆×D₁₃	C₂²	1	2	yes	—
14	D₁₃×#131	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×Q₃₂	C₂²	1	1	yes	characteristic, complemented
16	C₁₃×#504	C₂²	1	1	yes	characteristic
17	C₁₃×#473	C₂²	1	2	yes	—
18	#11718865	—	2	2	no	—
19	#11718853	C₂²	1	2	yes	—
20	C₂×#88069	C₂²	1	2	yes	complemented
21	#11718804	C₂²	1	2	yes	—
22	#11718801	C₂²	1	1	yes	characteristic
23	D₁₃×Q₃₂	—	2	1	no	—
24	D₁₃×Q₃₂	—	2	1	no	—
25	D₁₃×Q₃₂	—	2	1	no	—
26	D₁₃×Q₃₂	—	2	1	no	—
27	#11718568	—	2	1	no	—
28	#11718568	C₂²	1	1	yes	characteristic
29	D₁₃×M₃₂	—	2	1	no	—
30	D₁₃×M₃₂	C₂²	1	1	yes	characteristic
31	C₂×Dic₁₀₄	C₂²	1	1	yes	characteristic, complemented
32	#11718562	—	2	1	no	—
33	#11718562	C₂²	1	1	yes	characteristic
34	C₂×C₁₆×D₁₃	—	2	1	no	—
35	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
36	#11718557	C₂²	1	2	yes	—
37	D₁₃×#108	C₂²	1	2	yes	—
38	#11718416	—	2	2	no	—
39	D₁₃×#101	—	2	2	no	—
40	C₁₃×#368	C₂²	1	1	yes	characteristic, complemented
41	C₁₃×#362	C₂²	1	2	yes	complemented
42	#11718157	C₂²	1	2	yes	complemented
43	#11718109	C₂²	1	2	yes	complemented
44	#11718098	C₂²	1	1	yes	characteristic, complemented
45	#11718088	C₂²	1	2	yes	complemented
46	#11718085	C₂²	1	2	yes	complemented
47	#41×D₁₃	D₄	1	1	yes	characteristic
48	C₂×Q₈×D₁₃	—	2	2	no	—
49	C₁₃×#137	—	2	2	no	—
50	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
51	C₁₃×#131	C₂³	1	1	yes	characteristic
52	#88205	—	2	2	no	—
53	#88202	D₄	1	1	yes	characteristic
54	C₂×#6107	—	2	2	no	—
55	#88196	—	2	2	no	—
56	#88172	—	4	2	no	—
57	Q₁₆×D₁₃	—	2	2	no	—
58	Q₁₆×D₁₃	—	2	2	no	—
59	Q₁₆×D₁₃	—	2	2	no	—
60	Q₁₆×D₁₃	—	2	2	no	—
61	Q₁₆×D₁₃	—	4	2	no	—
62	#88169	—	4	2	no	—
63	SD₁₆×D₁₃	—	4	2	no	—
64	#88163	—	2	2	no	—
65	#88161	—	2	1	no	—
66	#88161	D₄	1	1	yes	characteristic
67	M₁₆×D₁₃	—	2	1	no	—
68	M₁₆×D₁₃	—	2	2	no	—
69	M₁₆×D₁₃	D₄	1	1	yes	characteristic
70	C₂×Dic₅₂	C₂³	1	2	yes	—
71	#88155	—	2	1	no	—
72	#88155	C₂³	1	1	yes	characteristic
73	C₂×C₈×D₁₃	—	2	1	no	—
74	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×Q₃₂	—	2	1	no	—
76	C₁₃×Q₃₂	—	2	1	no	—
77	C₁₃×M₃₂	—	2	1	no	—
78	C₁₃×M₃₂	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₁₆	—	2	1	no	—
80	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
81	C₁₃×#108	C₂³	1	2	yes	—
82	C₁₃×#101	—	2	2	no	—
83	#88076	—	2	2	no	—
84	#88069	—	2	2	no	—
85	#88069	—	2	2	no	—
86	#88064	—	2	2	no	—
87	#88064	—	2	2	no	—
88	#88062	—	2	2	no	—
89	#88059	C₂³	1	2	yes	—
90	#88052	—	2	1	no	—
91	#88052	C₂³	1	1	yes	characteristic
92	C₂×#6090	—	2	1	no	—
93	C₂×#6090	C₂³	1	1	yes	characteristic
94	Dic₁₀₄	—	2	1	no	—
95	Dic₁₀₄	—	2	1	no	—
96	#88038	—	2	1	no	—
97	#88038	—	2	1	no	—
98	#88038	—	2	1	no	—
99	C₁₆×D₁₃	—	2	1	no	—
100	C₁₆×D₁₃	—	2	1	no	—
101	C₁₆×D₁₃	—	2	1	no	—
102	C₁₆×D₁₃	D₄	1	1	yes	characteristic
103	C₁₆×D₁₃	D₄	1	1	yes	characteristic
104	C₁₆×D₁₃	D₄	1	1	yes	characteristic
105	C₁₆×D₁₃	D₄	1	1	yes	characteristic
106	C₂×#2222	—	13	1	no	maximal, Sylow
107	C₁₃×#41	C₂×D₄	1	1	yes	characteristic
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	#6131	D₈	1	1	yes	characteristic
110	Q₈×D₁₃	—	4	2	no	—
111	Q₈×D₁₃	—	4	2	no	—
112	Q₈×D₁₃	—	4	2	no	—
113	Q₈×D₁₃	—	4	2	no	—
114	Q₈×D₁₃	D₈	1	1	yes	characteristic
115	#6129	—	2	1	no	—
116	#6129	D₈	1	1	yes	characteristic
117	D₄×D₁₃	—	2	1	no	—
118	D₄×D₁₃	D₈	1	1	yes	characteristic
119	#6127	—	2	1	no	—
120	#6127	C₂×D₄	1	1	yes	characteristic
121	C₂×C₄×D₁₃	—	2	1	no	—
122	C₂×C₄×D₁₃	—	4	2	no	—
123	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×Dic₂₆	—	2	2	no	—
125	C₂×Dic₂₆	—	4	2	no	—
126	C₁₃×Q₁₆	—	2	2	no	—
127	C₁₃×Q₁₆	—	2	2	no	—
128	C₁₃×Q₁₆	—	4	2	no	—
129	C₁₃×SD₁₆	—	4	2	no	—
130	C₁₃×M₁₆	—	2	1	no	—
131	C₁₃×M₁₆	—	2	2	no	—
132	C₁₃×M₁₆	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
135	#6107	—	4	2	no	—
136	#6107	—	4	2	no	—
137	#6107	—	4	2	no	—
138	#6107	—	4	2	no	—
139	#6106	—	4	2	no	—
140	#6105	—	4	2	no	—
141	#6099	—	2	1	no	—
142	#6099	—	2	2	no	—
143	#6099	C₂×D₄	1	1	yes	characteristic
144	C₂×#1055	—	2	1	no	—
145	C₂×#1055	C₂×D₄	1	1	yes	characteristic
146	Dic₅₂	—	2	2	no	—
147	Dic₅₂	—	2	2	no	—
148	Dic₅₂	—	4	2	no	—
149	#6095	—	4	2	no	—
150	#6094	—	2	1	no	—
151	#6094	—	2	1	no	—
152	#6094	—	2	1	no	—
153	#6094	—	4	2	no	—
154	C₈×D₁₃	—	2	1	no	—
155	C₈×D₁₃	—	2	1	no	—
156	C₈×D₁₃	—	2	1	no	—
157	C₈×D₁₃	—	4	2	no	—
158	C₈×D₁₃	C₂×D₄	1	1	yes	characteristic
159	C₈×D₁₃	C₂×D₄	1	1	yes	characteristic
160	C₈×D₁₃	#41	1	1	yes	characteristic
161	C₈×D₁₃	#41	1	1	yes	characteristic
162	C₁₃×C₁₆	—	2	1	no	—
163	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
164	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
165	#6090	—	2	1	no	—
166	#6090	C₂×D₄	1	1	yes	characteristic
167	#6090	C₂×D₄	1	1	yes	characteristic
168	C₂²×Q₃₂	—	13	1	no	—
169	C₂×#504	—	13	1	no	—
170	C₂×#473	—	13	2	no	—
171	#2222	—	13	1	no	—
172	#2222	—	13	1	no	—
173	#2222	—	13	2	no	—
174	#2222	—	13	1	no	—
175	#2222	—	13	2	no	—
176	#2222	D₁₃	1	1	yes	characteristic, direct product factor
177	C₂×#368	—	13	1	no	—
178	C₂×#362	—	13	2	no	—
179	C₂²×D₁₃	—	2	1	no	—
180	C₂²×D₁₃	#135	1	1	yes	characteristic
181	Q₈×C₁₃	—	4	2	no	—
182	Q₈×C₁₃	—	4	2	no	—
183	Q₈×C₁₃	C₂×D₈	1	1	yes	characteristic
184	D₄×C₁₃	—	2	1	no	—
185	D₄×C₁₃	C₂×D₈	1	1	yes	characteristic
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
189	C₂²⋊D₁₃	—	2	1	no	—
190	C₂²⋊D₁₃	—	2	1	no	—
191	C₂²⋊D₁₃	—	2	1	no	—
192	C₂×Dic₁₃	—	2	1	no	—
193	C₂×Dic₁₃	—	4	2	no	—
194	C₂×Dic₁₃	#135	1	1	yes	characteristic
195	D₅₂	—	2	1	no	—
196	D₅₂	C₂×D₈	1	1	yes	characteristic
197	C₄×D₁₃	—	2	1	no	—
198	C₄×D₁₃	—	2	1	no	—
199	C₄×D₁₃	—	2	1	no	—
200	C₄×D₁₃	—	8	2	no	—
201	C₄×D₁₃	—	8	2	no	—
202	C₄×D₁₃	#121	1	1	yes	characteristic
203	C₄×D₁₃	#121	1	1	yes	characteristic
204	C₄×D₁₃	C₂×D₈	1	1	yes	characteristic
205	C₄×D₁₃	C₂×D₈	1	1	yes	characteristic
206	Dic₂₆	—	2	1	no	—
207	Dic₂₆	—	4	2	no	—
208	Dic₂₆	—	4	2	no	—
209	Dic₂₆	—	8	2	no	—
210	Dic₂₆	—	8	2	no	—
211	Dic₂₆	C₂×D₈	1	1	yes	characteristic
212	C₈×C₁₃	—	2	1	no	—
213	C₈×C₁₃	—	4	2	no	—
214	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
215	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
216	#1055	—	2	1	no	—
217	#1055	—	4	2	no	—
218	#1055	#121	1	1	yes	characteristic
219	#1055	#121	1	1	yes	characteristic
220	C₂×#137	—	26	2	no	—
221	C₂²×Q₁₆	—	13	2	no	—
222	C₂×#131	—	13	1	no	—
223	C₂×Q₃₂	—	13	2	no	—
224	C₂×Q₃₂	—	13	1	no	—
225	C₂×Q₃₂	—	26	1	no	—
226	C₂×Q₃₂	—	26	1	no	—
227	C₂×Q₃₂	—	26	1	no	—
228	C₂×Q₃₂	—	26	1	no	—
229	C₂×Q₃₂	C₂×D₁₃	1	1	yes	characteristic, complemented
230	#504	—	13	1	no	—
231	#504	—	13	1	no	—
232	#504	—	13	1	no	—
233	#504	—	26	1	no	—
234	#504	—	26	1	no	—
235	#504	C₂×D₁₃	1	1	yes	characteristic
236	C₂×M₃₂	—	13	1	no	—
237	C₂×M₃₂	—	26	1	no	—
238	C₂²×C₁₆	—	13	1	no	—
239	C₂²×C₁₆	—	26	1	no	—
240	#473	—	13	2	no	—
241	#473	—	13	2	no	—
242	#473	—	13	2	no	—
243	#473	—	26	2	no	—
244	#473	—	26	2	no	—
245	#473	C₂×D₁₃	1	2	yes	—
246	C₂×#108	—	13	2	no	—
247	C₂×#101	—	26	2	no	—
248	#368	—	13	1	no	—
249	#368	—	13	2	no	—
250	#368	C₂×D₁₃	1	1	yes	characteristic, complemented
251	#362	—	13	2	no	—
252	#362	—	13	2	no	—
253	#362	—	13	2	no	—
254	#362	C₂×D₁₃	1	2	yes	complemented
255	C₂²×C₁₃	—	2	1	no	—
256	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
257	C₂×D₁₃	—	2	2	no	—
258	C₂×D₁₃	—	2	1	no	—
259	C₂×D₁₃	—	4	2	no	—
260	C₂×D₁₃	#466	1	1	yes	characteristic
261	C₂×D₁₃	#466	1	1	yes	characteristic
262	C₄×C₁₃	—	2	1	no	—
263	C₄×C₁₃	—	8	2	no	—
264	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
265	C₄×C₁₃	C₂²×D₈	1	1	yes	characteristic
266	Dic₁₃	—	2	1	no	—
267	Dic₁₃	—	8	2	no	—
268	Dic₁₃	#466	1	1	yes	characteristic
269	Dic₁₃	#466	1	1	yes	characteristic
270	C₂×#41	—	13	1	no	—
271	C₂²×Q₈	—	26	2	no	—
272	#137	—	2	2	no	—
273	#137	—	26	2	no	—
274	#137	—	26	2	no	—
275	#137	—	26	2	no	—
276	#137	—	52	2	no	—
277	#137	—	52	2	no	—
278	C₂×Q₁₆	—	13	2	no	—
279	C₂×Q₁₆	—	26	2	no	—
280	C₂×Q₁₆	—	26	2	no	—
281	C₂×Q₁₆	—	26	2	no	—
282	C₂×Q₁₆	—	26	2	no	—
283	C₂×Q₁₆	—	26	2	no	—
284	C₂×Q₁₆	—	52	2	no	—
285	C₂×Q₁₆	C₂²×D₁₃	1	2	yes	—
286	C₂×SD₁₆	—	52	2	no	—
287	#131	—	13	1	no	—
288	#131	—	13	1	no	—
289	#131	—	13	1	no	—
290	#131	—	26	1	no	—
291	#131	—	26	1	no	—
292	#131	C₂²×D₁₃	1	1	yes	characteristic
293	C₂×M₁₆	—	13	1	no	—
294	C₂×M₁₆	—	26	1	no	—
295	C₂×M₁₆	—	26	2	no	—
296	C₂²×C₈	—	13	1	no	—
297	C₂²×C₈	—	26	1	no	—
298	Q₃₂	—	2	1	no	—
299	Q₃₂	—	2	1	no	—
300	Q₃₂	—	26	2	no	—
301	Q₃₂	—	26	2	no	—
302	Q₃₂	—	26	1	no	—
303	Q₃₂	—	26	1	no	—
304	M₃₂	—	2	1	no	—
305	M₃₂	—	13	1	no	—
306	M₃₂	—	26	1	no	—
307	M₃₂	—	26	1	no	—
308	M₃₂	—	26	1	no	—
309	M₃₂	—	26	1	no	—
310	M₃₂	C₂²×D₁₃	1	1	yes	characteristic
311	C₂×C₁₆	—	2	1	no	—
312	C₂×C₁₆	—	13	1	no	—
313	C₂×C₁₆	—	13	1	no	—
314	C₂×C₁₆	—	13	1	no	—
315	C₂×C₁₆	—	13	1	no	—
316	C₂×C₁₆	—	13	1	no	—
317	C₂×C₁₆	—	26	1	no	—
318	C₂×C₁₆	—	26	1	no	—
319	C₂×C₁₆	—	26	1	no	—
320	C₂×C₁₆	—	26	1	no	—
321	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
322	#108	—	13	2	no	—
323	#108	—	26	2	no	—
324	#108	C₂²×D₁₃	1	2	yes	—
325	#101	—	2	2	no	—
326	#101	—	26	2	no	—
327	#101	—	26	2	no	—
328	#101	—	26	2	no	—
329	C₂×C₁₃	—	2	1	no	—
330	C₂×C₁₃	—	4	1	no	—
331	C₂×C₁₃	C₂×#466	1	1	yes	characteristic
332	D₁₃	—	2	1	no	—
333	D₁₃	—	4	1	no	—
334	D₁₃	#2222	1	2	yes	direct product factor
335	#41	—	13	1	no	—
336	#41	—	13	1	no	—
337	#41	—	13	1	no	—
338	#41	—	26	1	no	—
339	#41	—	26	1	no	—
340	#41	D₄×D₁₃	1	1	yes	characteristic
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	13	1	no	—
343	C₂×Q₈	—	26	2	no	—
344	C₂×Q₈	—	52	2	no	—
345	C₂×Q₈	—	52	2	no	—
346	C₂×Q₈	—	52	2	no	—
347	C₂×Q₈	—	52	2	no	—
348	C₂×Q₈	—	52	2	no	—
349	C₂×D₄	—	13	1	no	—
350	C₂×D₄	—	26	1	no	—
351	C₂²×C₄	—	13	1	no	—
352	C₂²×C₄	—	26	1	no	—
353	C₂²×C₄	—	52	2	no	—
354	Q₁₆	—	2	2	no	—
355	Q₁₆	—	2	2	no	—
356	Q₁₆	—	4	2	no	—
357	Q₁₆	—	26	2	no	—
358	Q₁₆	—	26	2	no	—
359	Q₁₆	—	52	2	no	—
360	Q₁₆	—	52	2	no	—
361	Q₁₆	—	52	2	no	—
362	Q₁₆	—	52	2	no	—
363	Q₁₆	—	52	2	no	—
364	SD₁₆	—	4	2	no	—
365	SD₁₆	—	52	2	no	—
366	SD₁₆	—	52	2	no	—
367	SD₁₆	—	52	2	no	—
368	M₁₆	—	2	1	no	—
369	M₁₆	—	2	2	no	—
370	M₁₆	—	13	1	no	—
371	M₁₆	—	26	1	no	—
372	M₁₆	—	26	1	no	—
373	M₁₆	—	26	1	no	—
374	M₁₆	—	26	1	no	—
375	M₁₆	—	26	2	no	—
376	M₁₆	—	52	2	no	—
377	M₁₆	D₄×D₁₃	1	1	yes	characteristic
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	13	1	no	—
380	C₂×C₈	—	13	1	no	—
381	C₂×C₈	—	13	1	no	—
382	C₂×C₈	—	13	1	no	—
383	C₂×C₈	—	13	1	no	—
384	C₂×C₈	—	26	1	no	—
385	C₂×C₈	—	26	1	no	—
386	C₂×C₈	—	26	1	no	—
387	C₂×C₈	—	26	1	no	—
388	C₂×C₈	—	52	2	no	—
389	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
390	C₁₆	—	2	1	no	—
391	C₁₆	—	13	1	no	—
392	C₁₆	—	13	1	no	—
393	C₁₆	—	26	1	no	—
394	C₁₆	D₄×D₁₃	1	1	yes	characteristic
395	C₁₆	D₄×D₁₃	1	1	yes	characteristic
396	C₁₃	C₂×#2222	1	1	yes	characteristic, complemented, Sylow
397	C₂³	—	13	1	no	—
398	C₂³	—	26	1	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	13	1	no	—
402	Q₈	—	26	1	no	—
403	Q₈	—	52	2	no	—
404	Q₈	—	52	2	no	—
405	Q₈	—	104	2	no	—
406	Q₈	—	104	2	no	—
407	Q₈	D₈×D₁₃	1	1	yes	characteristic
408	D₄	—	2	1	no	—
409	D₄	—	13	1	no	—
410	D₄	—	26	1	no	—
411	D₄	—	26	1	no	—
412	D₄	—	26	1	no	—
413	D₄	—	26	1	no	—
414	D₄	D₈×D₁₃	1	1	yes	characteristic
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	13	1	no	—
418	C₂×C₄	—	13	1	no	—
419	C₂×C₄	—	13	1	no	—
420	C₂×C₄	—	13	1	no	—
421	C₂×C₄	—	13	1	no	—
422	C₂×C₄	—	26	1	no	—
423	C₂×C₄	—	26	1	no	—
424	C₂×C₄	—	26	1	no	—
425	C₂×C₄	—	26	1	no	—
426	C₂×C₄	—	52	2	no	—
427	C₂×C₄	—	104	2	no	—
428	C₂×C₄	—	104	2	no	—
429	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
430	C₈	—	2	1	no	—
431	C₈	—	4	2	no	—
432	C₈	—	13	1	no	—
433	C₈	—	13	1	no	—
434	C₈	—	26	1	no	—
435	C₈	—	52	2	no	—
436	C₈	C₂×D₄×D₁₃	1	1	yes	characteristic
437	C₈	#41×D₁₃	1	1	yes	characteristic
438	C₂²	—	2	1	no	—
439	C₂²	—	13	1	no	—
440	C₂²	—	13	1	no	—
441	C₂²	—	26	2	no	—
442	C₂²	—	26	1	no	—
443	C₂²	—	52	2	no	—
444	C₂²	D₁₃×#135	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	8	2	no	—
447	C₄	—	13	1	no	—
448	C₄	—	13	1	no	—
449	C₄	—	26	1	no	—
450	C₄	—	104	2	no	—
451	C₄	D₁₃×#121	1	1	yes	characteristic
452	C₄	C₂×D₈×D₁₃	1	1	yes	characteristic
453	C₂	—	2	1	no	—
454	C₂	—	4	1	no	—
455	C₂	—	13	2	no	—
456	C₂	—	26	1	no	—
457	C₂	—	52	1	no	—
458	C₂	D₁₃×#466	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₃×#466
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₁₃×#2222	C₂
socle	C₂×C₁₃	C₂×#466
prime radical	#41×D₁₃	D₄
hypercenter	#2222	D₁₃
hypocenter	C₁₃	C₂×#2222
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #2222

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₃×Q₃₂	C₂	semidirect
4. #13116962	C₂	semidirect
5. #13116961	C₂	semidirect
6. #13116960	C₂	semidirect
7. #13116959	C₂	semidirect
8. #13116958	C₂	semidirect
9. D₁₃×#368	C₂	semidirect
10. D₁₃×#362	C₂	semidirect
11. C₁₃×#2222	C₂	semidirect
15. C₂×C₁₃×Q₃₂	C₂²	semidirect
20. C₂×#88069	C₂²	semidirect
31. C₂×Dic₁₀₄	C₂²	semidirect
40. C₁₃×#368	C₂²	semidirect
41. C₁₃×#362	C₂²	semidirect
42. #11718157	C₂²	semidirect
43. #11718109	C₂²	semidirect
44. #11718098	C₂²	semidirect
45. #11718088	C₂²	semidirect
46. #11718085	C₂²	semidirect
176. #2222	D₁₃	direct (N × H)
229. C₂×Q₃₂	C₂×D₁₃	semidirect
250. #368	C₂×D₁₃	semidirect
254. #362	C₂×D₁₃	semidirect
334. D₁₃	#2222	direct (N × H)
396. C₁₃	C₂×#2222	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃×Q₃₂	2
D₁₃×#504	2
D₁₃×#473	2
#13116962	2
#13116961	2
#13116960	2
#13116959	2
#13116958	2
D₁₃×#368	2
D₁₃×#362	2
C₁₃×#2222	2
C₂×#2222	13

Subgroups — D13×#2222 #16017478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#2222 #16017478