Subgroups — SD₁₆×C₄⋊Dic₁₃ #15881322

Order 3328.

1030 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×Dic₁₃	C₂	1	2	yes	maximal
2	Q₈×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	#13115565	C₂	1	2	yes	maximal, complemented
5	#13115106	C₂	1	2	yes	maximal, complemented
6	#13115099	C₂	1	2	yes	maximal
7	#13114993	C₂	1	1	yes	maximal, characteristic, complemented
8	#13114841	C₂	1	1	yes	maximal, characteristic, complemented
9	#13114836	C₂	1	1	yes	maximal, characteristic
10	C₈×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×Q₈×Dic₁₃	C₂²	1	2	yes	—
16	C₂×D₄×Dic₁₃	C₂²	1	2	yes	—
17	C₂²×C₄⋊Dic₁₃	—	2	1	no	—
18	C₄×C₁₃×SD₁₆	C₄	1	8	yes	complemented
19	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×#88075	C₂²	1	2	yes	—
24	C₂×#88072	C₂²	1	2	yes	—
25	#11718873	—	2	1	no	—
26	SD₁₆×Dic₁₃	—	2	8	no	—
27	C₂×#88057	C₂²	1	2	yes	—
28	C₂×#88057	C₂²	1	2	yes	—
29	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
30	#11718646	—	2	2	no	—
31	#11718646	C₂²	1	2	yes	—
32	#11718646	C₂²	1	2	yes	—
33	#11718611	—	2	2	no	—
34	#11718596	—	2	1	no	—
35	#11718596	C₂²	1	1	yes	characteristic
36	#11718596	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊Dic₁₃	—	2	1	no	—
38	C₄×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊#1055	C₂²	1	1	yes	characteristic
40	#11718142	C₂²	1	2	yes	—
41	#11718121	C₂²	1	2	yes	—
42	#11718121	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	—	2	1	no	—
46	C₂³×Dic₁₃	—	2	2	no	—
47	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	—
48	C₂×C₁₃×SD₁₆	D₄	1	4	yes	—
49	C₂×C₁₃×SD₁₆	Q₈	1	4	yes	—
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₄×Q₈×C₁₃	—	2	2	no	—
53	C₄×Q₈×C₁₃	C₂×C₄	1	4	yes	complemented
54	C₄×D₄×C₁₃	—	2	2	no	—
55	C₄×D₄×C₁₃	C₂×C₄	1	4	yes	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
58	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
59	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
60	C₂×C₄²×C₁₃	—	2	1	no	—
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
63	Q₈×Dic₁₃	—	2	4	no	—
64	Q₈×Dic₁₃	—	4	2	no	—
65	D₄×Dic₁₃	—	2	4	no	—
66	D₄×Dic₁₃	—	4	2	no	—
67	C₂×C₄⋊Dic₁₃	—	2	1	no	—
68	C₂×C₄⋊Dic₁₃	—	2	1	no	—
69	C₂×C₄⋊Dic₁₃	—	2	2	no	—
70	C₂×C₄⋊Dic₁₃	—	2	2	no	—
71	C₂×C₄⋊Dic₁₃	—	2	1	no	—
72	C₂×C₄⋊Dic₁₃	—	2	1	no	—
73	C₂×C₄⋊Dic₁₃	—	2	2	no	—
74	C₂×C₄⋊Dic₁₃	—	4	4	no	—
75	C₂×C₄⋊Dic₁₃	D₄	1	1	yes	characteristic
76	C₂×C₄⋊Dic₁₃	D₄	1	1	yes	characteristic
77	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
78	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
79	C₂×C₄×Dic₁₃	—	2	2	no	—
80	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
81	C₂²×#1055	C₂³	1	2	yes	—
82	C₁₃×#106	C₂×C₄	1	4	yes	complemented
83	C₁₃×#103	C₂×C₄	1	4	yes	complemented
84	C₁₃×#102	C₂×C₄	1	4	yes	—
85	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
86	#88075	—	2	4	no	—
87	#88072	—	2	4	no	—
88	#88071	—	2	2	no	—
89	#88071	—	2	2	no	—
90	#88071	D₄	1	2	yes	—
91	#88057	—	2	4	no	—
92	#88057	—	4	2	no	—
93	C₈×Dic₁₃	—	2	4	no	—
94	C₄⋊#1055	—	2	2	no	—
95	C₄⋊C₄×SD₁₆	—	13	1	no	maximal, Sylow
96	C₂⁴×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×Q₈×C₁₃	—	2	1	no	—
99	C₂×Q₈×C₁₃	—	2	1	no	—
100	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
101	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
102	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
103	C₂×D₄×C₁₃	—	2	1	no	—
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	—	2	1	no	—
106	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
107	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
108	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₃	—	4	2	no	—
114	C₂²×C₄×C₁₃	—	4	2	no	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₂²×Dic₁₃	—	2	2	no	—
119	C₂²×Dic₁₃	—	2	2	no	—
120	C₂²×Dic₁₃	—	4	4	no	—
121	C₂²×Dic₁₃	—	4	4	no	—
122	C₂²×Dic₁₃	—	8	2	no	—
123	C₂²×Dic₁₃	C₂×D₄	1	2	yes	—
124	C₂²×Dic₁₃	C₂×D₄	1	2	yes	—
125	C₁₃×SD₁₆	C₄⋊C₄	1	16	yes	complemented
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
132	C₁₃×C₄⋊C₄	—	2	4	no	—
133	C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
136	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
137	C₁₃×C₂²⋊C₄	—	2	4	no	—
138	C₄²×C₁₃	—	2	4	no	—
139	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
140	C₄²×C₁₃	#41	1	2	yes	—
141	C₂²⋊Dic₁₃	—	4	4	no	—
142	C₄⋊Dic₁₃	—	2	2	no	—
143	C₄⋊Dic₁₃	—	2	2	no	—
144	C₄⋊Dic₁₃	—	2	2	no	—
145	C₄⋊Dic₁₃	—	2	2	no	—
146	C₄⋊Dic₁₃	—	2	2	no	—
147	C₄⋊Dic₁₃	—	4	4	no	—
148	C₄⋊Dic₁₃	—	4	2	no	—
149	C₄⋊Dic₁₃	—	4	2	no	—
150	C₄⋊Dic₁₃	—	4	4	no	—
151	C₄⋊Dic₁₃	—	8	2	no	—
152	C₄⋊Dic₁₃	—	8	1	no	—
153	C₄⋊Dic₁₃	—	8	1	no	—
154	C₄⋊Dic₁₃	SD₁₆	1	4	yes	direct product factor
155	C₄×Dic₁₃	—	2	2	no	—
156	C₄×Dic₁₃	—	2	2	no	—
157	C₄×Dic₁₃	—	4	4	no	—
158	C₂×#1055	—	2	2	no	—
159	C₂×#1055	—	2	2	no	—
160	C₂×#1055	—	2	2	no	—
161	C₂×C₄×SD₁₆	—	13	2	no	—
162	C₂×C₄×SD₁₆	D₁₃	1	1	yes	characteristic
163	Q₈×C₄⋊C₄	—	13	1	no	—
164	D₄×C₄⋊C₄	—	13	1	no	—
165	#1941	—	13	2	no	—
166	#1865	—	13	2	no	—
167	#1864	—	13	2	no	—
168	#1844	—	13	1	no	—
169	#1803	—	13	1	no	—
170	#1802	—	13	1	no	—
171	C₈×C₄⋊C₄	—	13	1	no	—
172	C₂³×C₁₃	—	2	2	no	—
173	C₂³×C₁₃	—	2	2	no	—
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	—	4	1	no	—
176	C₂³×C₁₃	—	4	1	no	—
177	C₂³×C₁₃	—	4	1	no	—
178	C₂³×C₁₃	—	4	1	no	—
179	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₁₃	—	2	2	no	—
181	Q₈×C₁₃	—	2	2	no	—
182	Q₈×C₁₃	—	2	2	no	—
183	Q₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	complemented
184	D₄×C₁₃	—	2	2	no	—
185	D₄×C₁₃	—	2	2	no	—
186	D₄×C₁₃	—	2	2	no	—
187	D₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	—	4	1	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	8	no	—
200	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
201	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
202	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
203	C₂×C₄×C₁₃	#135	1	2	yes	—
204	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
209	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
210	C₂×Dic₁₃	—	2	2	no	—
211	C₂×Dic₁₃	—	2	2	no	—
212	C₂×Dic₁₃	—	2	2	no	—
213	C₂×Dic₁₃	—	2	2	no	—
214	C₂×Dic₁₃	—	2	2	no	—
215	C₂×Dic₁₃	—	4	2	no	—
216	C₂×Dic₁₃	—	4	2	no	—
217	C₂×Dic₁₃	—	4	2	no	—
218	C₂×Dic₁₃	—	4	2	no	—
219	C₂×Dic₁₃	—	4	2	no	—
220	C₂×Dic₁₃	—	4	2	no	—
221	C₂×Dic₁₃	—	8	8	no	—
222	C₂×Dic₁₃	C₂×SD₁₆	1	4	yes	—
223	C₈×C₁₃	—	2	2	no	—
224	C₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	complemented
225	#1055	—	4	2	no	—
226	C₂²×SD₁₆	C₂×D₁₃	1	1	yes	characteristic
227	C₂×C₄×Q₈	—	13	2	no	—
228	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
229	C₂×C₄×D₄	—	13	2	no	—
230	C₂×C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
231	C₂²×C₄⋊C₄	—	26	1	no	—
232	C₄×SD₁₆	—	26	8	no	—
233	C₄×SD₁₆	Dic₁₃	1	8	yes	complemented
234	C₂×#106	—	13	2	no	—
235	C₂×#106	—	13	2	no	—
236	C₂×#106	C₂×D₁₃	1	1	yes	characteristic
237	C₂×C₄⋊C₈	—	13	1	no	—
238	C₂×#103	—	13	2	no	—
239	C₂×#103	C₂×D₁₃	1	1	yes	characteristic
240	C₂×#102	—	13	2	no	—
241	C₂×#102	C₂×D₁₃	1	1	yes	characteristic
242	C₂×C₄×C₈	—	13	2	no	—
243	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
244	#389	—	13	2	no	—
245	#389	—	13	2	no	—
246	#389	—	26	2	no	—
247	#385	—	26	2	no	—
248	#384	—	13	1	no	—
249	#384	—	13	1	no	—
250	#384	—	26	1	no	—
251	#380	—	26	1	no	—
252	C₄×C₄⋊C₄	—	13	1	no	—
253	C₄×C₄⋊C₄	—	26	1	no	—
254	#340	—	13	2	no	—
255	#340	—	13	2	no	—
256	#336	—	13	2	no	—
257	C₂²×C₁₃	—	2	4	no	—
258	C₂²×C₁₃	—	4	2	no	—
259	C₂²×C₁₃	—	4	2	no	—
260	C₂²×C₁₃	—	4	2	no	—
261	C₂²×C₁₃	—	4	2	no	—
262	C₂²×C₁₃	—	4	2	no	—
263	C₂²×C₁₃	—	4	2	no	—
264	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
265	C₂²×C₁₃	D₄²	1	1	yes	characteristic
266	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
267	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
268	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
269	C₂²×C₁₃	#577	1	1	yes	characteristic
270	C₂²×C₁₃	#577	1	1	yes	characteristic
271	C₄×C₁₃	—	2	4	no	—
272	C₄×C₁₃	—	2	2	no	—
273	C₄×C₁₃	—	4	2	no	—
274	C₄×C₁₃	—	4	2	no	—
275	C₄×C₁₃	C₄×SD₁₆	1	4	yes	complemented
276	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
277	C₄×C₁₃	#520	1	1	yes	characteristic
278	C₄×C₁₃	#547	1	1	yes	characteristic
279	C₄×C₁₃	#554	1	1	yes	characteristic
280	Dic₁₃	—	2	4	no	—
281	Dic₁₃	—	4	2	no	—
282	Dic₁₃	—	8	2	no	—
283	Dic₁₃	—	8	2	no	—
284	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
285	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
286	C₂³×C₄	—	2	1	no	—
287	C₂³×C₄	—	26	2	no	—
288	C₂×SD₁₆	Dic₂₆	1	4	yes	—
289	C₂×SD₁₆	D₅₂	1	4	yes	—
290	C₂×SD₁₆	C₂×Dic₁₃	1	4	yes	—
291	C₂²×C₈	—	13	2	no	—
292	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
293	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
294	C₄×Q₈	—	2	2	no	—
295	C₄×Q₈	—	26	4	no	—
296	C₄×Q₈	—	52	2	no	—
297	C₄×Q₈	C₂×Dic₁₃	1	4	yes	complemented
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	—	26	4	no	—
300	C₄×D₄	—	52	2	no	—
301	C₄×D₄	C₂×Dic₁₃	1	4	yes	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	13	1	no	—
304	C₂×C₄⋊C₄	—	13	1	no	—
305	C₂×C₄⋊C₄	—	13	2	no	—
306	C₂×C₄⋊C₄	—	13	2	no	—
307	C₂×C₄⋊C₄	—	26	2	no	—
308	C₂×C₄⋊C₄	—	26	2	no	—
309	C₂×C₄⋊C₄	—	26	1	no	—
310	C₂×C₄⋊C₄	—	26	1	no	—
311	C₂×C₄⋊C₄	—	26	2	no	—
312	C₂×C₄⋊C₄	—	26	1	no	—
313	C₂×C₄⋊C₄	—	26	1	no	—
314	C₂×C₄⋊C₄	—	52	4	no	—
315	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	26	2	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	—	13	2	no	—
321	C₂×C₄²	—	26	2	no	—
322	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
323	#106	—	26	4	no	—
324	#106	—	52	2	no	—
325	#106	C₂×Dic₁₃	1	4	yes	complemented
326	C₄⋊C₈	—	26	2	no	—
327	#103	—	26	4	no	—
328	#103	C₂×Dic₁₃	1	4	yes	complemented
329	#102	—	26	4	no	—
330	#102	C₂×Dic₁₃	1	4	yes	—
331	C₄×C₈	—	26	4	no	—
332	C₄×C₈	C₂×Dic₁₃	1	4	yes	complemented
333	#95	—	13	2	no	—
334	#95	—	26	2	no	—
335	#95	—	26	2	no	—
336	C₂×C₁₃	—	4	4	no	—
337	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
338	C₂×C₁₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
339	C₂×C₁₃	#2952	1	1	yes	characteristic
340	C₂×C₁₃	D₄×SD₁₆	1	1	yes	characteristic
341	C₂×C₁₃	#3284	1	1	yes	characteristic
342	C₂×C₁₃	Q₈×SD₁₆	1	1	yes	characteristic
343	C₂×C₁₃	#3381	1	1	yes	characteristic
344	C₂⁴	—	2	1	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	C₂×Dic₂₆	1	2	yes	—
349	C₂×Q₈	C₂×D₅₂	1	2	yes	—
350	C₂×Q₈	C₂²×Dic₁₃	1	2	yes	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	C₂×Dic₂₆	1	2	yes	—
355	C₂×D₄	C₂×D₅₂	1	2	yes	—
356	C₂×D₄	C₂²×Dic₁₃	1	2	yes	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	13	2	no	—
364	C₂²×C₄	—	13	2	no	—
365	C₂²×C₄	—	26	2	no	—
366	C₂²×C₄	—	26	2	no	—
367	C₂²×C₄	—	52	4	no	—
368	C₂²×C₄	—	52	4	no	—
369	C₂²×C₄	—	104	2	no	—
370	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
371	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
372	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
373	SD₁₆	C₄⋊Dic₁₃	1	16	yes	direct product factor
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	26	2	no	—
377	C₂×C₈	—	26	2	no	—
378	C₂×C₈	—	26	2	no	—
379	C₂×C₈	C₂×Dic₂₆	1	2	yes	—
380	C₂×C₈	C₂×D₅₂	1	2	yes	—
381	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
382	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	13	4	no	—
387	C₄⋊C₄	—	26	2	no	—
388	C₄⋊C₄	—	26	2	no	—
389	C₄⋊C₄	—	26	2	no	—
390	C₄⋊C₄	—	26	2	no	—
391	C₄⋊C₄	—	26	2	no	—
392	C₄⋊C₄	—	52	4	no	—
393	C₄⋊C₄	—	52	4	no	—
394	C₄⋊C₄	—	52	2	no	—
395	C₄⋊C₄	—	52	2	no	—
396	C₄⋊C₄	—	104	1	no	—
397	C₄⋊C₄	—	104	1	no	—
398	C₄⋊C₄	—	104	2	no	—
399	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
400	C₄⋊C₄	C₂²×Dic₁₃	1	2	yes	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	—	52	4	no	—
403	C₄²	—	2	4	no	—
404	C₄²	—	26	2	no	—
405	C₄²	—	26	2	no	—
406	C₄²	—	52	4	no	—
407	C₄²	#6129	1	2	yes	—
408	C₄²	C₂²×Dic₁₃	1	2	yes	—
409	C₁₃	C₄⋊C₄×SD₁₆	1	1	yes	characteristic, complemented, Sylow
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	1	no	—
417	C₂³	C₂×D₄×D₁₃	1	1	yes	characteristic
418	Q₈	—	2	2	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	2	2	no	—
421	Q₈	C₂×C₄⋊Dic₁₃	1	4	yes	complemented
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	2	2	no	—
425	D₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	8	no	—
438	C₂×C₄	—	13	4	no	—
439	C₂×C₄	—	26	2	no	—
440	C₂×C₄	—	26	2	no	—
441	C₂×C₄	—	26	2	no	—
442	C₂×C₄	—	26	2	no	—
443	C₂×C₄	—	26	2	no	—
444	C₂×C₄	—	52	2	no	—
445	C₂×C₄	—	52	2	no	—
446	C₂×C₄	—	52	2	no	—
447	C₂×C₄	—	52	2	no	—
448	C₂×C₄	—	52	2	no	—
449	C₂×C₄	—	52	2	no	—
450	C₂×C₄	—	104	8	no	—
451	C₂×C₄	SD₁₆×D₁₃	1	2	yes	—
452	C₂×C₄	#88170	1	2	yes	—
453	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
454	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
455	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
456	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
457	C₂×C₄	C₂×#6129	1	1	yes	characteristic
458	C₂×C₄	#88256	1	1	yes	characteristic
459	C₂×C₄	#88257	1	1	yes	characteristic
460	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
461	C₈	—	2	2	no	—
462	C₈	—	52	2	no	—
463	C₈	C₂×C₄⋊Dic₁₃	1	4	yes	complemented
464	C₂²	—	2	4	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	D₄×Dic₂₆	1	1	yes	characteristic
472	C₂²	D₄×D₅₂	1	1	yes	characteristic
473	C₂²	C₂×SD₁₆×D₁₃	1	1	yes	characteristic
474	C₂²	C₂×#88170	1	1	yes	characteristic
475	C₂²	#11719475	1	1	yes	characteristic
476	C₂²	#11719475	1	1	yes	characteristic
477	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
478	C₄	—	2	4	no	—
479	C₄	—	2	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	—	26	4	no	—
483	C₄	—	52	2	no	—
484	C₄	—	104	2	no	—
485	C₄	—	104	2	no	—
486	C₄	SD₁₆×Dic₁₃	1	4	yes	complemented
487	C₄	#11719248	1	1	yes	characteristic
488	C₄	#11719260	1	1	yes	characteristic
489	C₄	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
490	C₄	#11719532	1	1	yes	characteristic
491	C₂	—	4	4	no	—
492	C₂	D₄×C₄⋊Dic₁₃	1	1	yes	characteristic
493	C₂	C₂×SD₁₆×Dic₁₃	1	1	yes	characteristic
494	C₂	#13123720	1	1	yes	characteristic
495	C₂	SD₁₆×D₅₂	1	1	yes	characteristic
496	C₂	#13126567	1	1	yes	characteristic
497	C₂	SD₁₆×Dic₂₆	1	1	yes	characteristic
498	C₂	#13127709	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₄×C₁₃×SD₁₆	C₂
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂²×D₄×C₁₃	C₂³
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×C₄×SD₁₆	D₁₃
hypocenter	C₁₃	C₄⋊C₄×SD₁₆
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. Q₈×C₄⋊Dic₁₃	C₂	semidirect
4. #13115565	C₂	semidirect
5. #13115106	C₂	semidirect
7. #13114993	C₂	semidirect
8. #13114841	C₂	semidirect
10. C₈×C₄⋊Dic₁₃	C₂	semidirect
18. C₄×C₁₃×SD₁₆	C₄	semidirect
53. C₄×Q₈×C₁₃	C₂×C₄	semidirect
82. C₁₃×#106	C₂×C₄	semidirect
83. C₁₃×#103	C₂×C₄	semidirect
85. C₄×C₈×C₁₃	C₂×C₄	semidirect
125. C₁₃×SD₁₆	C₄⋊C₄	semidirect
154. C₄⋊Dic₁₃	SD₁₆	direct (N × H)
183. Q₈×C₁₃	C₂×C₄⋊C₄	semidirect
224. C₈×C₁₃	C₂×C₄⋊C₄	semidirect
233. C₄×SD₁₆	Dic₁₃	semidirect
275. C₄×C₁₃	C₄×SD₁₆	semidirect
297. C₄×Q₈	C₂×Dic₁₃	semidirect
325. #106	C₂×Dic₁₃	semidirect
328. #103	C₂×Dic₁₃	semidirect
332. C₄×C₈	C₂×Dic₁₃	semidirect
373. SD₁₆	C₄⋊Dic₁₃	direct (N × H)
409. C₁₃	C₄⋊C₄×SD₁₆	semidirect
421. Q₈	C₂×C₄⋊Dic₁₃	semidirect
463. C₈	C₂×C₄⋊Dic₁₃	semidirect
486. C₄	SD₁₆×Dic₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×Dic₁₃	2
Q₈×C₄⋊Dic₁₃	2
D₄×C₄⋊Dic₁₃	2
#13115565	2
#13115106	2
#13115099	2
#13114993	2
#13114841	2
#13114836	2
C₈×C₄⋊Dic₁₃	2
C₂×C₄×C₁₃×SD₁₆	2
C₄⋊C₄×SD₁₆	13

Subgroups — SD16×C4⋊Dic13 #15881322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₁₆×C₄⋊Dic₁₃ #15881322