Subgroups — #15834940

Order 3328.

604 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13123938	C₂	1	1	yes	maximal, characteristic, complemented
2	#13123903	C₂	1	1	yes	maximal, characteristic
3	#13113739	C₂	1	2	yes	maximal, complemented
4	#13113680	C₂	1	2	yes	maximal, complemented
5	#13113673	C₂	1	2	yes	maximal, complemented
6	SD₁₆⋊#1055	C₂	1	2	yes	maximal, complemented
7	#13113584	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113257	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113253	C₂	1	1	yes	maximal, characteristic
10	#13113125	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3167	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#533	C₂²	1	1	yes	characteristic
13	C₁₃×#532	C₂²	1	1	yes	characteristic
14	C₁₃×#498	C₄	1	1	yes	characteristic
15	C₁₃×#492	C₄	1	1	yes	characteristic
16	C₁₃×#487	C₄	1	1	yes	characteristic
17	C₁₃×#486	C₄	1	1	yes	characteristic
18	C₁₃×#465	C₄	1	2	yes	—
19	C₁₃×#465	C₄	1	2	yes	—
20	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
21	C₄×C₁₃×SD₁₆	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	#11718895	—	2	2	no	—
24	#11718685	—	2	1	no	—
25	#11718685	C₂²	1	2	yes	—
26	Q₈×#1055	—	2	1	no	—
27	Q₈×#1055	C₂²	1	2	yes	—
28	#11718673	—	2	1	no	—
29	#11718673	C₂²	1	2	yes	—
30	D₄×#1055	—	2	1	no	—
31	D₄×#1055	C₂²	1	2	yes	—
32	#11718661	—	2	2	no	—
33	#11718586	C₂²	1	1	yes	characteristic
34	#11718586	C₂²	1	1	yes	characteristic
35	#11718586	C₂²	1	1	yes	characteristic
36	C₄×#6099	C₂²	1	1	yes	characteristic
37	Q₈⋊#1055	C₂²	1	2	yes	—
38	Q₈⋊#1055	C₂²	1	2	yes	—
39	D₄⋊#1055	C₂²	1	2	yes	—
40	D₄⋊#1055	C₂²	1	2	yes	—
41	#11718050	C₂²	1	1	yes	characteristic
42	#11718050	C₂²	1	1	yes	characteristic
43	#11718049	C₂²	1	1	yes	characteristic
44	#11718049	C₂²	1	1	yes	characteristic
45	#11718047	C₂²	1	2	yes	—
46	#11718046	C₂²	1	2	yes	—
47	C₂×C₁₃×#41	—	2	1	no	—
48	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
49	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	—
50	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
52	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
53	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
55	C₁₃×#127	C₂×C₄	1	1	yes	characteristic
56	C₁₃×#125	—	2	1	no	—
57	C₁₃×#124	—	2	1	no	—
58	C₁₃×C₂²⋊Q₈	—	2	1	no	—
59	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
60	C₁₃×#121	—	2	1	no	—
61	C₁₃×#121	C₂×C₄	1	2	yes	—
62	C₄×Q₈×C₁₃	—	2	1	no	—
63	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
64	C₄×D₄×C₁₃	—	2	1	no	—
65	C₄×D₄×C₁₃	C₂³	1	2	yes	—
66	C₁₃×#117	—	2	1	no	—
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	C₂×#6099	—	2	1	no	—
69	C₂×#6099	—	2	2	no	—
70	C₂²×#1055	—	2	2	no	—
71	C₁₃×#106	C₂×C₄	1	2	yes	—
72	C₁₃×#106	C₂×C₄	1	2	yes	—
73	C₁₃×#103	C₂×C₄	1	2	yes	—
74	C₁₃×#103	C₂×C₄	1	2	yes	—
75	C₁₃×#102	C₂×C₄	1	2	yes	—
76	C₁₃×#102	C₂×C₄	1	2	yes	—
77	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
78	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
79	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²⋊#1055	—	2	1	no	—
82	C₂²⋊#1055	—	2	1	no	—
83	C₂²⋊#1055	—	2	2	no	—
84	C₂²⋊#1055	—	2	2	no	—
85	C₂²⋊#1055	D₄	1	2	yes	—
86	C₄⋊#1055	—	2	2	no	—
87	C₄⋊#1055	—	2	2	no	—
88	C₄⋊#1055	D₄	1	1	yes	characteristic
89	C₄⋊#1055	D₄	1	1	yes	characteristic
90	C₄⋊#1055	C₂³	1	1	yes	characteristic
91	C₄⋊#1055	C₂³	1	1	yes	characteristic
92	C₄⋊#1055	C₂³	1	1	yes	characteristic
93	C₄⋊#1055	C₂³	1	1	yes	characteristic
94	#88043	—	2	1	no	—
95	#88043	—	2	2	no	—
96	C₄×#1055	—	2	1	no	—
97	C₄×#1055	—	2	1	no	—
98	C₄×#1055	—	2	2	no	—
99	C₄×#1055	C₂³	1	2	yes	—
100	C₄×#1055	C₂³	1	2	yes	—
101	#18089	—	13	1	no	maximal, Sylow
102	C₁₃×#41	—	8	1	no	—
103	C₁₃×#41	—	8	1	no	—
104	C₂×Q₈×C₁₃	—	2	1	no	—
105	C₂×Q₈×C₁₃	—	2	1	no	—
106	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	1	no	—
109	C₂×D₄×C₁₃	—	2	1	no	—
110	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
115	C₁₃×SD₁₆	—	2	4	no	—
116	C₁₃×SD₁₆	—	4	2	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	—	4	1	no	—
119	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₁₃×C₄⋊C₄	—	2	1	no	—
124	C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₁₃×C₄⋊C₄	—	2	1	no	—
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	2	no	—
132	C₁₃×C₂²⋊C₄	—	2	2	no	—
133	C₁₃×C₂²⋊C₄	—	2	2	no	—
134	C₄²×C₁₃	—	2	2	no	—
135	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₁₃	#41	1	1	yes	characteristic
138	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
139	#6099	—	4	2	no	—
140	#6099	—	8	2	no	—
141	C₂×#1055	—	2	1	no	—
142	C₂×#1055	—	2	1	no	—
143	C₂×#1055	—	2	1	no	—
144	C₂×#1055	—	2	1	no	—
145	C₂×#1055	—	2	2	no	—
146	C₂×#1055	—	8	2	no	—
147	C₂×#1055	C₂×D₄	1	2	yes	—
148	C₂×#1055	C₂×D₄	1	2	yes	—
149	#3167	D₁₃	1	1	yes	characteristic
150	#2986	—	13	1	no	—
151	#2979	—	13	1	no	—
152	#1592	—	13	2	no	—
153	#1583	—	13	2	no	—
154	#1582	—	13	2	no	—
155	SD₁₆⋊C₈	—	13	2	no	—
156	#1564	—	13	1	no	—
157	#1485	—	13	1	no	—
158	#1484	—	13	1	no	—
159	#1451	—	13	1	no	—
160	C₂³×C₁₃	—	2	2	no	—
161	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
162	Q₈×C₁₃	—	2	2	no	—
163	Q₈×C₁₃	—	2	2	no	—
164	Q₈×C₁₃	—	4	2	no	—
165	Q₈×C₁₃	—	8	1	no	—
166	D₄×C₁₃	—	2	2	no	—
167	D₄×C₁₃	—	2	2	no	—
168	D₄×C₁₃	—	4	2	no	—
169	D₄×C₁₃	—	8	1	no	—
170	D₄×C₁₃	—	8	2	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	1	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
187	C₈×C₁₃	—	2	1	no	—
188	C₈×C₁₃	—	2	1	no	—
189	C₈×C₁₃	—	2	1	no	—
190	C₈×C₁₃	#131	1	2	yes	—
191	#1055	—	2	2	no	—
192	#1055	—	2	2	no	—
193	#1055	—	4	2	no	—
194	#1055	—	4	1	no	—
195	#1055	—	4	1	no	—
196	#1055	—	4	1	no	—
197	#1055	—	4	1	no	—
198	#533	C₂×D₁₃	1	1	yes	characteristic
199	#532	C₂×D₁₃	1	1	yes	characteristic
200	#498	Dic₁₃	1	1	yes	characteristic
201	#492	Dic₁₃	1	1	yes	characteristic
202	#487	Dic₁₃	1	1	yes	characteristic
203	#486	Dic₁₃	1	1	yes	characteristic
204	#465	Dic₁₃	1	2	yes	—
205	#465	Dic₁₃	1	2	yes	—
206	#446	—	13	2	no	—
207	#446	—	26	1	no	—
208	C₈×Q₈	—	13	2	no	—
209	C₈×Q₈	—	26	1	no	—
210	C₄×SD₁₆	C₂×D₁₃	1	2	yes	—
211	C₄×SD₁₆	C₂×D₁₃	1	2	yes	—
212	#436	—	13	2	no	—
213	#436	—	26	1	no	—
214	C₈×D₄	—	13	2	no	—
215	C₈×D₄	—	26	1	no	—
216	#433	—	26	2	no	—
217	#431	—	13	1	no	—
218	#431	—	13	1	no	—
219	#431	—	13	1	no	—
220	#408	—	26	2	no	—
221	C₄×M₁₆	—	13	1	no	—
222	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
223	#335	—	13	1	no	—
224	#335	—	13	1	no	—
225	#334	—	13	1	no	—
226	#334	—	13	1	no	—
227	Q₈⋊C₈	—	13	2	no	—
228	Q₈⋊C₈	—	13	2	no	—
229	D₄⋊C₈	—	13	2	no	—
230	D₄⋊C₈	—	13	2	no	—
231	#322	—	13	2	no	—
232	#322	—	13	2	no	—
233	C₂²×C₁₃	—	2	1	no	—
234	C₂²×C₁₃	—	2	1	no	—
235	C₂²×C₁₃	—	2	1	no	—
236	C₂²×C₁₃	—	4	2	no	—
237	C₂²×C₁₃	—	4	2	no	—
238	C₂²×C₁₃	—	4	2	no	—
239	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
240	C₄×C₁₃	—	2	1	no	—
241	C₄×C₁₃	—	2	1	no	—
242	C₄×C₁₃	—	2	1	no	—
243	C₄×C₁₃	—	4	2	no	—
244	C₄×C₁₃	—	4	2	no	—
245	C₄×C₁₃	—	4	2	no	—
246	C₄×C₁₃	#444	1	2	yes	—
247	C₄×C₁₃	C₂×#131	1	1	yes	characteristic
248	C₄×C₁₃	#568	1	1	yes	characteristic
249	C₄×C₁₃	#577	1	1	yes	characteristic
250	C₄×C₁₃	#577	1	1	yes	characteristic
251	C₂×#41	—	2	1	no	—
252	C₂×SD₁₆	C₂×Dic₁₃	1	2	yes	—
253	C₂×SD₁₆	C₂×Dic₁₃	1	2	yes	—
254	C₂×M₁₆	—	26	2	no	—
255	C₂×M₁₆	—	26	1	no	—
256	C₂²×C₈	—	26	2	no	—
257	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
258	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
259	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
260	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
261	C₄⋊Q₈	C₂×Dic₁₃	1	1	yes	characteristic
262	#127	C₂×Dic₁₃	1	1	yes	characteristic
263	#125	—	2	1	no	—
264	#124	—	2	1	no	—
265	C₂²⋊Q₈	—	2	1	no	—
266	C₂²⋊Q₈	C₂×Dic₁₃	1	2	yes	—
267	#121	—	2	1	no	—
268	#121	C₂×Dic₁₃	1	2	yes	—
269	C₄×Q₈	—	2	1	no	—
270	C₄×Q₈	C₂²×D₁₃	1	2	yes	—
271	C₄×D₄	—	2	1	no	—
272	C₄×D₄	C₂²×D₁₃	1	2	yes	—
273	#117	—	2	1	no	—
274	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
275	#106	C₂×Dic₁₃	1	2	yes	—
276	#106	C₂×Dic₁₃	1	2	yes	—
277	C₄⋊C₈	—	13	1	no	—
278	C₄⋊C₈	—	13	1	no	—
279	C₄⋊C₈	—	13	1	no	—
280	C₄⋊C₈	—	13	1	no	—
281	C₄⋊C₈	—	13	1	no	—
282	C₄⋊C₈	—	13	1	no	—
283	C₄⋊C₈	—	26	2	no	—
284	C₄⋊C₈	—	26	2	no	—
285	#103	C₂×Dic₁₃	1	2	yes	—
286	#103	C₂×Dic₁₃	1	2	yes	—
287	#102	C₂×Dic₁₃	1	2	yes	—
288	#102	C₂×Dic₁₃	1	2	yes	—
289	C₂²⋊C₈	—	13	2	no	—
290	C₂²⋊C₈	—	26	2	no	—
291	C₂²⋊C₈	—	26	2	no	—
292	C₂²⋊C₈	—	26	1	no	—
293	C₂²⋊C₈	—	26	1	no	—
294	#97	—	26	2	no	—
295	#97	—	26	1	no	—
296	C₄×C₈	—	13	2	no	—
297	C₄×C₈	—	13	2	no	—
298	C₄×C₈	—	26	2	no	—
299	C₄×C₈	—	26	1	no	—
300	C₄×C₈	—	26	1	no	—
301	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
302	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
303	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
304	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
305	C₂×C₁₃	—	4	1	no	—
306	C₂×C₁₃	—	8	2	no	—
307	C₂×C₁₃	#2935	1	1	yes	characteristic
308	C₂×C₁₃	#2949	1	1	yes	characteristic
309	C₂×C₁₃	C₂×#444	1	1	yes	characteristic
310	#41	—	8	1	no	—
311	#41	—	8	1	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	C₂²×Dic₁₃	1	2	yes	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
321	C₂²×C₄	#6129	1	1	yes	characteristic
322	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
323	SD₁₆	—	2	4	no	—
324	SD₁₆	—	4	2	no	—
325	M₁₆	—	52	2	no	—
326	M₁₆	—	104	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	13	2	no	—
330	C₂×C₈	—	13	2	no	—
331	C₂×C₈	—	26	1	no	—
332	C₂×C₈	—	26	1	no	—
333	C₂×C₈	—	26	1	no	—
334	C₂×C₈	—	26	1	no	—
335	C₂×C₈	—	26	2	no	—
336	C₂×C₈	—	104	2	no	—
337	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
338	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
339	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
340	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
348	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
349	C₂²⋊C₄	—	2	2	no	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₄²	—	2	2	no	—
353	C₄²	D₄×D₁₃	1	1	yes	characteristic
354	C₄²	#6129	1	1	yes	characteristic
355	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
356	C₄²	C₂³×D₁₃	1	1	yes	characteristic
357	C₁₃	#18089	1	1	yes	characteristic, complemented, Sylow
358	C₂³	—	2	2	no	—
359	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	Q₈	—	2	2	no	—
362	Q₈	—	4	2	no	—
363	Q₈	—	8	1	no	—
364	D₄	—	2	2	no	—
365	D₄	—	2	2	no	—
366	D₄	—	4	2	no	—
367	D₄	—	8	1	no	—
368	D₄	—	8	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
380	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
381	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
382	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
383	C₂×C₄	C₂×#6129	1	1	yes	characteristic
384	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
385	C₈	—	2	1	no	—
386	C₈	—	2	1	no	—
387	C₈	—	2	1	no	—
388	C₈	—	26	2	no	—
389	C₈	—	26	2	no	—
390	C₈	—	52	2	no	—
391	C₈	—	52	1	no	—
392	C₈	—	52	1	no	—
393	C₈	—	52	1	no	—
394	C₈	—	52	1	no	—
395	C₈	#88202	1	2	yes	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	2	no	—
409	C₄	#11718858	1	2	yes	—
410	C₄	#11719467	1	1	yes	characteristic
411	C₄	#11719467	1	1	yes	characteristic
412	C₄	C₂×#88202	1	1	yes	characteristic
413	C₄	#11719524	1	1	yes	characteristic
414	C₂	—	4	1	no	—
415	C₂	—	8	2	no	—
416	C₂	#13123580	1	1	yes	characteristic
417	C₂	#13123696	1	1	yes	characteristic
418	C₂	C₂×#11718858	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#3167	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₁₃×#532	C₂²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#3167	D₁₃
hypocenter	C₁₃	#18089
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3167

Complements

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

N	H ≅ G/N	type
1. #13123938	C₂	semidirect
3. #13113739	C₂	semidirect
4. #13113680	C₂	semidirect
5. #13113673	C₂	semidirect
6. SD₁₆⋊#1055	C₂	semidirect
7. #13113584	C₂	semidirect
8. #13113257	C₂	semidirect
10. #13113125	C₂	semidirect
357. C₁₃	#18089	semidirect

Maximal subgroups

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

subgroup	index
#13123938	2
#13123903	2
#13113739	2
#13113680	2
#13113673	2
SD₁₆⋊#1055	2
#13113584	2
#13113257	2
#13113253	2
#13113125	2
C₁₃×#3167	2
#18089	13