Subgroups — #15845622

Order 3328.

704 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13124285	C₂	1	2	yes	maximal, complemented
2	#13123802	C₂	1	1	yes	maximal, characteristic, complemented
3	#13114401	C₂	1	2	yes	maximal, complemented
4	#13114394	C₂	1	2	yes	maximal, complemented
5	#13114351	C₂	1	1	yes	maximal, characteristic, complemented
6	#13114346	C₂	1	1	yes	maximal, characteristic, complemented
7	#13114317	C₂	1	1	yes	maximal, characteristic, complemented
8	#13114312	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#11718049	C₂	1	1	yes	maximal, characteristic, complemented
10	#13113485	C₂	1	2	yes	maximal, complemented
11	C₁₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#532	C₂²	1	2	yes	—
13	C₂×#88204	—	2	2	no	—
14	C₄×#6127	C₂²	1	1	yes	characteristic
15	C₁₃×#500	C₂²	1	1	yes	characteristic
16	C₁₃×#493	C₂²	1	1	yes	characteristic
17	C₁₃×#486	C₂²	1	2	yes	—
18	C₁₃×#466	—	2	1	no	—
19	C₁₃×#466	—	2	1	no	—
20	C₄×C₁₃×D₈	—	2	1	no	—
21	C₄×C₁₃×D₈	—	2	1	no	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	#11718894	—	2	2	no	—
24	#11718772	—	2	1	no	—
25	#11718772	—	2	1	no	—
26	#11718751	C₂²	1	2	yes	—
27	#11718744	C₂²	1	2	yes	—
28	#11718736	C₂²	1	2	yes	—
29	#11718733	C₂²	1	2	yes	—
30	#11718718	—	2	2	no	—
31	#11718715	—	2	2	no	—
32	#11718586	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊#1055	C₂²	1	2	yes	—
34	#11718349	C₂²	1	1	yes	characteristic
35	#11718349	C₂²	1	1	yes	characteristic
36	C₄×#6094	—	2	1	no	—
37	#11718346	—	2	1	no	—
38	#11718340	C₂²	1	1	yes	characteristic
39	#11718340	C₂²	1	1	yes	characteristic
40	#11718139	C₂²	1	2	yes	—
41	#11718139	C₂²	1	2	yes	—
42	#11718136	C₂²	1	2	yes	—
43	#11718136	C₂²	1	2	yes	—
44	#11718049	C₂²	1	2	yes	—
45	#11718049	C₂²	1	1	yes	characteristic
46	#11718049	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#41	—	2	2	no	—
48	C₂×#6127	D₄	1	1	yes	characteristic
49	C₂×C₁₃×D₈	—	2	1	no	—
50	C₂×C₁₃×D₈	—	2	1	no	—
51	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
53	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
54	C₁₃×#127	C₂³	1	2	yes	—
55	C₁₃×#124	—	2	2	no	—
56	C₁₃×#121	—	2	2	no	—
57	C₁₃×#121	—	2	2	no	—
58	C₄×D₄×C₁₃	—	2	2	no	—
59	C₄×D₄×C₁₃	—	2	2	no	—
60	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	#88204	—	4	8	no	—
62	C₂×#6107	—	2	2	no	—
63	C₂×#6106	—	2	2	no	—
64	C₂×#6105	—	2	2	no	—
65	C₂×#6104	—	2	2	no	—
66	C₄×C₂²⋊D₁₃	—	2	1	no	—
67	C₄×C₂²⋊D₁₃	—	2	1	no	—
68	#88180	D₄	1	1	yes	characteristic
69	C₂²×#1055	—	2	2	no	—
70	C₂×#6094	—	2	1	no	—
71	C₂×#6094	—	2	1	no	—
72	C₄×D₅₂	D₄	1	1	yes	characteristic
73	C₄×D₅₂	C₂³	1	1	yes	characteristic
74	#88126	—	2	1	no	—
75	C₄²×D₁₃	—	2	1	no	—
76	C₄×Dic₂₆	D₄	1	1	yes	characteristic
77	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
78	C₁₃×#107	—	2	1	no	—
79	C₁₃×#107	—	2	1	no	—
80	C₁₃×#102	—	2	2	no	—
81	C₁₃×#102	—	2	2	no	—
82	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
83	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
84	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	#88075	—	2	2	no	—
87	#88075	—	2	2	no	—
88	#88072	—	2	2	no	—
89	#88072	—	2	2	no	—
90	C₂²⋊#1055	—	2	1	no	—
91	#88060	—	2	1	no	—
92	#88060	—	2	1	no	—
93	#88055	—	2	1	no	—
94	#88055	—	2	1	no	—
95	#88054	—	2	1	no	—
96	#88054	—	2	1	no	—
97	C₄⋊#1055	—	2	2	no	—
98	C₄⋊#1055	C₂³	1	2	yes	—
99	C₄⋊#1055	C₂³	1	2	yes	—
100	C₄⋊#1055	C₂³	1	1	yes	characteristic
101	C₄⋊#1055	C₂³	1	1	yes	characteristic
102	C₄×#1055	—	2	1	no	—
103	#19157	—	13	1	no	maximal, Sylow
104	C₁₃×#41	—	4	4	no	—
105	C₁₃×#41	—	4	4	no	—
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂×D₄×C₁₃	—	4	2	no	—
111	C₂²×C₄×C₁₃	—	4	2	no	—
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
115	C₂×C₂²⋊D₁₃	—	2	1	no	—
116	#6127	—	2	4	no	—
117	C₂×D₅₂	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₁₃	—	2	1	no	—
119	C₂×C₄×D₁₃	—	2	1	no	—
120	C₂×C₄×D₁₃	—	2	1	no	—
121	C₂×Dic₂₆	C₂×D₄	1	1	yes	characteristic
122	C₁₃×D₈	—	4	2	no	—
123	C₁₃×D₈	—	4	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	4	1	no	—
126	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₂²⋊C₄	—	4	2	no	—
133	C₁₃×C₂²⋊C₄	—	4	2	no	—
134	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₃	#41	1	1	yes	characteristic
137	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₂²⋊Dic₁₃	—	2	1	no	—
139	#6107	—	4	4	no	—
140	#6106	—	4	4	no	—
141	#6105	—	4	4	no	—
142	#6104	—	4	4	no	—
143	#6103	—	2	1	no	—
144	#6103	—	2	1	no	—
145	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
146	C₄⋊Dic₁₃	C₂×D₄	1	1	yes	characteristic
147	#6101	—	2	1	no	—
148	#6101	—	2	1	no	—
149	C₄×Dic₁₃	—	2	1	no	—
150	C₄×Dic₁₃	—	2	1	no	—
151	C₄×Dic₁₃	—	2	1	no	—
152	C₂×#1055	—	2	1	no	—
153	C₂×#1055	—	2	1	no	—
154	C₂×#1055	—	2	2	no	—
155	C₂×#1055	—	2	2	no	—
156	C₂×#1055	—	4	4	no	—
157	#6094	—	4	2	no	—
158	#6094	—	4	2	no	—
159	#3169	D₁₃	1	1	yes	characteristic, complemented
160	#3035	—	13	2	no	—
161	#2965	—	13	1	no	—
162	#1702	—	13	2	no	—
163	#1701	—	13	2	no	—
164	#1694	—	13	1	no	—
165	#1693	—	13	1	no	—
166	#1688	—	13	1	no	—
167	#1687	—	13	1	no	—
168	C₂×#334	—	13	1	no	—
169	#1540	—	13	2	no	—
170	C₂³×C₁₃	—	4	2	no	—
171	C₂³×C₁₃	#121	1	1	yes	characteristic
172	C₂²×D₁₃	—	2	1	no	—
173	Q₈×C₁₃	—	4	2	no	—
174	Q₈×C₁₃	—	4	2	no	—
175	D₄×C₁₃	—	4	2	no	—
176	D₄×C₁₃	—	4	2	no	—
177	D₄×C₁₃	—	4	2	no	—
178	D₄×C₁₃	—	4	2	no	—
179	D₄×C₁₃	—	8	2	no	—
180	D₄×C₁₃	—	8	4	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	8	4	no	—
186	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
187	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
188	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
189	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
190	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
193	C₂²⋊D₁₃	—	4	2	no	—
194	C₂×Dic₁₃	—	2	1	no	—
195	C₂×Dic₁₃	—	2	1	no	—
196	C₂×Dic₁₃	—	2	1	no	—
197	D₅₂	—	2	2	no	—
198	C₄×D₁₃	—	4	2	no	—
199	C₄×D₁₃	—	4	1	no	—
200	C₄×D₁₃	—	4	1	no	—
201	C₄×D₁₃	—	4	2	no	—
202	Dic₂₆	—	2	2	no	—
203	C₈×C₁₃	—	2	1	no	—
204	C₈×C₁₃	—	2	1	no	—
205	C₈×C₁₃	—	2	1	no	—
206	C₈×C₁₃	#135	1	2	yes	complemented
207	#1055	—	4	1	no	—
208	#1055	—	4	2	no	—
209	#1055	—	4	2	no	—
210	#1055	—	4	1	no	—
211	C₂×#135	—	26	2	no	—
212	#532	C₂×D₁₃	1	2	yes	—
213	C₄×#41	—	13	1	no	—
214	#500	C₂×D₁₃	1	1	yes	characteristic
215	#493	C₂×D₁₃	1	1	yes	characteristic
216	#486	C₂×D₁₃	1	2	yes	—
217	#466	—	2	1	no	—
218	#466	—	2	1	no	—
219	#464	—	26	2	no	—
220	#463	—	26	2	no	—
221	#462	—	13	2	no	—
222	#461	—	13	2	no	—
223	#460	—	13	2	no	—
224	#459	—	13	2	no	—
225	#446	—	13	1	no	—
226	#446	—	13	1	no	—
227	C₄×D₈	—	2	1	no	—
228	C₄×D₈	—	2	1	no	—
229	#436	—	13	1	no	—
230	#436	—	13	1	no	—
231	#435	—	26	1	no	—
232	#435	—	26	1	no	—
233	#431	—	13	1	no	—
234	#431	—	26	1	no	—
235	C₂×C₄⋊C₈	—	13	2	no	—
236	#416	—	26	2	no	—
237	C₄×M₁₆	—	26	1	no	—
238	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
239	#334	—	13	1	no	—
240	#334	—	13	1	no	—
241	#334	—	13	2	no	—
242	#332	—	13	2	no	—
243	#332	—	13	2	no	—
244	#331	—	13	2	no	—
245	#331	—	13	2	no	—
246	C₂²×C₁₃	—	2	1	no	—
247	C₂²×C₁₃	—	2	1	no	—
248	C₂²×C₁₃	—	8	2	no	—
249	C₂²×C₁₃	—	8	2	no	—
250	C₂²×C₁₃	—	8	2	no	—
251	C₂²×C₁₃	#469	1	2	yes	—
252	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
253	C₂×D₁₃	—	4	1	no	—
254	C₂×D₁₃	—	4	1	no	—
255	C₂×D₁₃	—	4	1	no	—
256	C₄×C₁₃	—	2	1	no	—
257	C₄×C₁₃	—	2	1	no	—
258	C₄×C₁₃	—	2	1	no	—
259	C₄×C₁₃	—	8	2	no	—
260	C₄×C₁₃	#469	1	2	yes	—
261	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
262	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
263	C₄×C₁₃	#575	1	1	yes	characteristic
264	Dic₁₃	—	4	1	no	—
265	Dic₁₃	—	4	1	no	—
266	Dic₁₃	—	4	1	no	—
267	C₂×#41	—	2	2	no	—
268	C₂×#41	—	13	1	no	—
269	#135	—	52	8	no	—
270	C₂×Q₁₆	—	26	2	no	—
271	C₂×SD₁₆	—	26	2	no	—
272	C₂×SD₁₆	—	26	2	no	—
273	C₂×D₈	—	2	1	no	—
274	C₂×D₈	—	2	1	no	—
275	C₂×D₈	—	26	2	no	—
276	C₂×M₁₆	—	26	1	no	—
277	C₂×M₁₆	—	26	1	no	—
278	C₂²×C₈	—	26	2	no	—
279	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
280	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
281	C₄⋊Q₈	C₂²×D₁₃	1	2	yes	—
282	#127	C₂²×D₁₃	1	2	yes	—
283	#124	—	2	2	no	—
284	#121	—	2	2	no	—
285	#121	—	2	2	no	—
286	C₄×Q₈	—	13	1	no	—
287	C₄×Q₈	—	13	1	no	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	13	1	no	—
291	C₄×D₄	—	13	1	no	—
292	C₄×D₄	—	26	1	no	—
293	C₄×D₄	—	26	1	no	—
294	#117	—	13	1	no	—
295	#117	—	26	1	no	—
296	C₂×C₄²	—	26	1	no	—
297	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
298	#107	—	2	1	no	—
299	#107	—	2	1	no	—
300	C₄⋊C₈	—	13	1	no	—
301	C₄⋊C₈	—	13	1	no	—
302	C₄⋊C₈	—	13	2	no	—
303	C₄⋊C₈	—	13	2	no	—
304	C₄⋊C₈	—	26	1	no	—
305	C₄⋊C₈	—	26	1	no	—
306	C₄⋊C₈	—	26	2	no	—
307	#103	—	26	2	no	—
308	#103	—	26	2	no	—
309	#102	—	2	2	no	—
310	#102	—	2	2	no	—
311	#102	—	26	2	no	—
312	#102	—	26	2	no	—
313	C₂²⋊C₈	—	26	1	no	—
314	C₂²⋊C₈	—	26	1	no	—
315	C₂²⋊C₈	—	26	1	no	—
316	#97	—	26	1	no	—
317	#97	—	26	1	no	—
318	C₄×C₈	—	26	1	no	—
319	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
320	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
321	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
322	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
323	C₂×C₁₃	—	2	2	no	—
324	C₂×C₁₃	—	16	2	no	—
325	C₂×C₁₃	#3035	1	1	yes	characteristic
326	C₂×C₁₃	C₂×#469	1	1	yes	characteristic
327	C₂×C₁₃	#3067	1	1	yes	characteristic
328	D₁₃	—	8	1	no	—
329	#41	—	4	4	no	—
330	#41	—	4	4	no	—
331	#41	—	26	4	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	13	1	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	4	2	no	—
338	C₂×D₄	—	13	1	no	—
339	C₂×D₄	—	26	1	no	—
340	C₂²×C₄	—	4	2	no	—
341	C₂²×C₄	—	26	1	no	—
342	C₂²×C₄	—	26	1	no	—
343	C₂²×C₄	—	26	1	no	—
344	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
345	C₂²×C₄	#6129	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
347	Q₁₆	—	52	4	no	—
348	SD₁₆	—	52	4	no	—
349	SD₁₆	—	52	4	no	—
350	D₈	—	4	2	no	—
351	D₈	—	4	2	no	—
352	D₈	—	52	4	no	—
353	M₁₆	—	52	2	no	—
354	M₁₆	—	52	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	26	2	no	—
358	C₂×C₈	—	26	2	no	—
359	C₂×C₈	—	26	1	no	—
360	C₂×C₈	—	26	1	no	—
361	C₂×C₈	—	52	4	no	—
362	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
363	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
364	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
365	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	13	1	no	—
369	C₄⋊C₄	—	13	1	no	—
370	C₄⋊C₄	—	26	1	no	—
371	C₄⋊C₄	—	26	1	no	—
372	C₂²⋊C₄	—	4	2	no	—
373	C₂²⋊C₄	—	4	2	no	—
374	C₂²⋊C₄	—	26	1	no	—
375	C₂²⋊C₄	—	26	1	no	—
376	C₂²⋊C₄	—	26	1	no	—
377	C₄²	—	26	1	no	—
378	C₄²	—	26	1	no	—
379	C₄²	—	26	1	no	—
380	C₄²	D₄×D₁₃	1	1	yes	characteristic
381	C₄²	#6129	1	1	yes	characteristic
382	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
383	C₄²	C₂³×D₁₃	1	1	yes	characteristic
384	C₁₃	#19157	1	1	yes	characteristic, complemented, Sylow
385	C₂³	—	4	2	no	—
386	C₂³	—	26	1	no	—
387	C₂³	#88192	1	1	yes	characteristic
388	Q₈	—	4	2	no	—
389	Q₈	—	4	2	no	—
390	Q₈	—	26	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	4	2	no	—
395	D₄	—	8	2	no	—
396	D₄	—	8	4	no	—
397	D₄	—	26	2	no	—
398	D₄	—	52	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	8	4	no	—
404	C₂×C₄	—	26	1	no	—
405	C₂×C₄	—	26	1	no	—
406	C₂×C₄	—	26	1	no	—
407	C₂×C₄	—	52	2	no	—
408	C₂×C₄	—	52	1	no	—
409	C₂×C₄	—	52	1	no	—
410	C₂×C₄	—	52	2	no	—
411	C₂×C₄	#88165	1	4	yes	—
412	C₂×C₄	#88192	1	1	yes	characteristic
413	C₂×C₄	#88192	1	1	yes	characteristic
414	C₂×C₄	#88192	1	1	yes	characteristic
415	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
416	C₂×C₄	C₂×#6129	1	1	yes	characteristic
417	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
418	C₈	—	2	1	no	—
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	52	2	no	—
422	C₈	—	52	2	no	—
423	C₈	—	52	1	no	—
424	C₈	—	52	1	no	—
425	C₈	#88204	1	2	yes	complemented
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	8	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	52	1	no	—
432	C₂²	—	52	1	no	—
433	C₂²	—	52	1	no	—
434	C₂²	#11718820	1	2	yes	—
435	C₂²	C₂×#88192	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	8	2	no	—
440	C₄	—	52	1	no	—
441	C₄	—	52	1	no	—
442	C₄	—	52	1	no	—
443	C₄	#11718820	1	2	yes	—
444	C₄	C₂×#88165	1	2	yes	—
445	C₄	C₂×#88204	1	1	yes	characteristic
446	C₄	#11719527	1	1	yes	characteristic
447	C₂	—	2	2	no	—
448	C₂	—	16	2	no	—
449	C₂	—	104	1	no	—
450	C₂	#13124285	1	1	yes	characteristic
451	C₂	C₂×#11718820	1	1	yes	characteristic
452	C₂	#13124552	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88192
commutator, cosocle	C₄²×C₁₃	C₂⁴
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#3169	C₂
socle	C₂²×C₁₃	C₂×#121
hypercenter	#3169	D₁₃
hypocenter	C₁₃	#19157
LCS	G ▷ C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3169

Complements

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

N	H ≅ G/N	type
1. #13124285	C₂	semidirect
2. #13123802	C₂	semidirect
3. #13114401	C₂	semidirect
4. #13114394	C₂	semidirect
5. #13114351	C₂	semidirect
6. #13114346	C₂	semidirect
7. #13114317	C₂	semidirect
8. #13114312	C₂	semidirect
9. C₂×#11718049	C₂	semidirect
10. #13113485	C₂	semidirect
11. C₁₃×#3169	C₂	semidirect
159. #3169	D₁₃	semidirect
206. C₈×C₁₃	#135	semidirect
384. C₁₃	#19157	semidirect
425. C₈	#88204	semidirect

Maximal subgroups

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

subgroup	index
#13124285	2
#13123802	2
#13114401	2
#13114394	2
#13114351	2
#13114346	2
#13114317	2
#13114312	2
C₂×#11718049	2
#13113485	2
C₁₃×#3169	2
#19157	13