Subgroups — C₁₃×C₂²⋊C₄×Q₁₆ #15708789

Order 3328.

1398 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×Q₁₆	C₂	1	2	yes	maximal, complemented
3	Q₈×C₁₃×C₂²⋊C₄	C₂	1	2	yes	maximal
4	C₁₃×#1969	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1878	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1808	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1787	C₂	1	2	yes	maximal
8	C₈×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₁₃	C₂²	1	2	yes	—
10	C₂²×C₁₃×Q₁₆	—	2	8	no	—
11	C₂²×C₁₃×Q₁₆	C₄	1	8	yes	complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
13	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	—
17	C₄×C₁₃×Q₁₆	—	2	8	no	—
18	C₂×C₁₃×#107	C₂²	1	2	yes	—
19	C₂×C₁₃×#103	C₂²	1	4	yes	—
20	C₂×C₁₃×#103	C₂²	1	4	yes	—
21	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
23	C₁₃×#391	—	2	4	no	—
24	C₁₃×#391	C₂²	1	4	yes	—
25	C₁₃×#380	—	2	2	no	—
26	C₁₃×#380	C₂²	1	2	yes	—
27	C₄×C₁₃×C₂²⋊C₄	—	2	2	no	—
28	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₁₃×#340	C₂²	1	2	yes	—
30	C₁₃×#336	C₂²	1	2	yes	—
31	C₂²×Q₈×C₁₃	—	2	2	no	—
32	C₂²×Q₈×C₁₃	—	2	4	no	—
33	C₂²×Q₈×C₁₃	—	2	8	no	—
34	C₂²×Q₈×C₁₃	—	4	4	no	—
35	C₂²×Q₈×C₁₃	C₂×C₄	1	8	yes	—
36	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
37	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₃	—	2	2	no	—
39	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
40	C₂×C₁₃×Q₁₆	—	2	8	no	—
41	C₂×C₁₃×Q₁₆	—	2	32	no	—
42	C₂×C₁₃×Q₁₆	—	2	4	no	—
43	C₂×C₁₃×Q₁₆	C₂×C₄	1	8	yes	—
44	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	—
45	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	—
46	C₂×C₁₃×Q₁₆	D₄	1	8	yes	—
47	C₂²×C₈×C₁₃	—	2	4	no	—
48	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
49	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₄×Q₈×C₁₃	—	2	8	no	—
53	C₄×Q₈×C₁₃	—	4	4	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
55	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
56	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
58	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	—	2	4	no	—
60	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
61	C₁₃×#107	—	2	4	no	—
62	C₁₃×#103	—	2	8	no	—
63	C₁₃×#103	—	4	4	no	—
64	C₁₃×C₂²⋊C₈	—	2	2	no	—
65	C₄×C₈×C₁₃	—	2	4	no	—
66	C₁₃×#95	—	2	4	no	—
67	C₁₃×#95	—	2	4	no	—
68	C₁₃×#95	—	2	2	no	—
69	C₁₃×#95	D₄	1	2	yes	—
70	C₂²⋊C₄×Q₁₆	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
71	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
72	C₂×Q₈×C₁₃	—	2	8	no	—
73	C₂×Q₈×C₁₃	—	2	2	no	—
74	C₂×Q₈×C₁₃	—	2	2	no	—
75	C₂×Q₈×C₁₃	—	2	4	no	—
76	C₂×Q₈×C₁₃	—	2	16	no	—
77	C₂×Q₈×C₁₃	—	2	4	no	—
78	C₂×Q₈×C₁₃	—	2	4	no	—
79	C₂×Q₈×C₁₃	—	4	8	no	—
80	C₂×Q₈×C₁₃	—	4	8	no	—
81	C₂×Q₈×C₁₃	—	4	16	no	—
82	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
83	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
84	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	2	no	—
88	C₂²×C₄×C₁₃	—	2	8	no	—
89	C₂²×C₄×C₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₃	—	2	4	no	—
91	C₂²×C₄×C₁₃	—	4	8	no	—
92	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₁₃	#41	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
98	C₁₃×Q₁₆	—	2	16	no	—
99	C₁₃×Q₁₆	—	2	8	no	—
100	C₁₃×Q₁₆	C₂²⋊C₄	1	16	yes	direct product factor
101	C₂×C₈×C₁₃	—	2	2	no	—
102	C₂×C₈×C₁₃	—	2	8	no	—
103	C₂×C₈×C₁₃	—	2	2	no	—
104	C₂×C₈×C₁₃	—	2	2	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
107	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
108	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
109	C₁₃×C₄⋊C₄	—	2	4	no	—
110	C₁₃×C₄⋊C₄	—	2	4	no	—
111	C₁₃×C₄⋊C₄	—	4	8	no	—
112	C₁₃×C₂²⋊C₄	—	2	2	no	—
113	C₁₃×C₂²⋊C₄	—	4	4	no	—
114	C₁₃×C₂²⋊C₄	Q₁₆	1	4	yes	direct product factor
115	C₄²×C₁₃	—	2	2	no	—
116	C₄²×C₁₃	—	2	2	no	—
117	C₄²×C₁₃	—	4	8	no	—
118	C₂³×Q₁₆	C₂×C₁₃	1	1	yes	characteristic
119	C₂×C₄×Q₁₆	C₂×C₁₃	1	2	yes	complemented
120	Q₈×C₂²⋊C₄	C₂×C₁₃	1	2	yes	—
121	#1969	C₂×C₁₃	1	2	yes	complemented
122	#1878	C₂×C₁₃	1	4	yes	complemented
123	#1808	C₂×C₁₃	1	1	yes	characteristic
124	#1787	C₂×C₁₃	1	2	yes	—
125	C₈×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
126	C₂³×C₁₃	—	2	2	no	—
127	C₂³×C₁₃	—	2	2	no	—
128	C₂³×C₁₃	C₄×D₄	1	2	yes	—
129	C₂³×C₁₃	C₂×Q₁₆	1	2	yes	—
130	C₂³×C₁₃	#135	1	2	yes	—
131	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
132	Q₈×C₁₃	—	2	4	no	—
133	Q₈×C₁₃	—	2	8	no	—
134	Q₈×C₁₃	—	2	4	no	—
135	Q₈×C₁₃	—	2	4	no	—
136	Q₈×C₁₃	—	4	16	no	—
137	Q₈×C₁₃	—	4	4	no	—
138	Q₈×C₁₃	C₂×C₂²⋊C₄	1	8	yes	—
139	C₂×C₄×C₁₃	—	2	4	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	2	8	no	—
142	C₂×C₄×C₁₃	—	2	2	no	—
143	C₂×C₄×C₁₃	—	2	2	no	—
144	C₂×C₄×C₁₃	—	2	2	no	—
145	C₂×C₄×C₁₃	—	2	2	no	—
146	C₂×C₄×C₁₃	—	2	4	no	—
147	C₂×C₄×C₁₃	—	2	4	no	—
148	C₂×C₄×C₁₃	—	2	2	no	—
149	C₂×C₄×C₁₃	—	2	2	no	—
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	4	16	no	—
152	C₂×C₄×C₁₃	—	4	4	no	—
153	C₂×C₄×C₁₃	—	4	4	no	—
154	C₂×C₄×C₁₃	—	4	4	no	—
155	C₂×C₄×C₁₃	—	4	4	no	—
156	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
157	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	complemented
158	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
160	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
162	C₈×C₁₃	—	2	2	no	—
163	C₈×C₁₃	—	4	2	no	—
164	C₈×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
165	C₂³×Q₈	C₂²×C₁₃	1	2	yes	—
166	C₂²×Q₁₆	—	2	8	no	—
167	C₂²×Q₁₆	C₄×C₁₃	1	8	yes	complemented
168	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
169	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
170	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
171	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
172	C₂×C₄×Q₈	C₂²×C₁₃	1	4	yes	—
173	C₄×Q₁₆	—	2	8	no	—
174	C₂×#107	C₂²×C₁₃	1	2	yes	—
175	C₂×#103	C₂²×C₁₃	1	4	yes	—
176	C₂×#103	C₂²×C₁₃	1	4	yes	—
177	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
178	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
179	#391	—	2	4	no	—
180	#391	C₂²×C₁₃	1	4	yes	—
181	#380	—	2	2	no	—
182	#380	C₂²×C₁₃	1	2	yes	—
183	C₄×C₂²⋊C₄	—	2	2	no	—
184	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
185	#340	C₂²×C₁₃	1	2	yes	—
186	#336	C₂²×C₁₃	1	2	yes	—
187	C₂²×C₁₃	—	2	2	no	—
188	C₂²×C₁₃	—	2	2	no	—
189	C₂²×C₁₃	—	2	4	no	—
190	C₂²×C₁₃	—	2	4	no	—
191	C₂²×C₁₃	C₄×Q₁₆	1	4	yes	complemented
192	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
193	C₂²×C₁₃	D₄²	1	2	yes	—
194	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
195	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
196	C₂²×C₁₃	#578	1	2	yes	—
197	C₄×C₁₃	—	2	2	no	—
198	C₄×C₁₃	—	2	8	no	—
199	C₄×C₁₃	—	2	4	no	—
200	C₄×C₁₃	—	4	4	no	—
201	C₄×C₁₃	—	4	2	no	—
202	C₄×C₁₃	—	8	4	no	—
203	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
204	C₄×C₁₃	#518	1	1	yes	characteristic
205	C₄×C₁₃	#546	1	2	yes	—
206	C₂²×Q₈	—	2	2	no	—
207	C₂²×Q₈	—	2	4	no	—
208	C₂²×Q₈	—	2	8	no	—
209	C₂²×Q₈	—	4	4	no	—
210	C₂²×Q₈	C₂×C₄×C₁₃	1	8	yes	—
211	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
212	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
213	C₂³×C₄	—	2	2	no	—
214	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
215	C₂×Q₁₆	—	2	8	no	—
216	C₂×Q₁₆	—	2	32	no	—
217	C₂×Q₁₆	—	2	4	no	—
218	C₂×Q₁₆	C₂×C₄×C₁₃	1	8	yes	—
219	C₂×Q₁₆	C₂×C₄×C₁₃	1	4	yes	—
220	C₂×Q₁₆	C₂×C₄×C₁₃	1	4	yes	—
221	C₂×Q₁₆	D₄×C₁₃	1	8	yes	—
222	C₂²×C₈	—	2	4	no	—
223	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
224	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
225	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
226	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
227	C₄×Q₈	—	2	8	no	—
228	C₄×Q₈	—	4	4	no	—
229	C₂×C₄⋊C₄	—	2	4	no	—
230	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
231	C₂×C₂²⋊C₄	—	2	2	no	—
232	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
233	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
234	C₂×C₄²	—	2	4	no	—
235	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
236	#107	—	2	4	no	—
237	#103	—	2	8	no	—
238	#103	—	4	4	no	—
239	C₂²⋊C₈	—	2	2	no	—
240	C₄×C₈	—	2	4	no	—
241	#95	—	2	4	no	—
242	#95	—	2	4	no	—
243	#95	—	2	2	no	—
244	#95	D₄×C₁₃	1	2	yes	—
245	C₂×C₁₃	—	2	4	no	—
246	C₂×C₁₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
247	C₂×C₁₃	C₂×C₄×Q₁₆	1	1	yes	characteristic
248	C₂×C₁₃	#2950	1	1	yes	characteristic
249	C₂×C₁₃	#3285	1	2	yes	—
250	C₂×C₁₃	D₄×Q₁₆	1	2	yes	—
251	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
252	C₂×Q₈	—	2	8	no	—
253	C₂×Q₈	—	2	2	no	—
254	C₂×Q₈	—	2	2	no	—
255	C₂×Q₈	—	2	4	no	—
256	C₂×Q₈	—	2	16	no	—
257	C₂×Q₈	—	2	4	no	—
258	C₂×Q₈	—	2	4	no	—
259	C₂×Q₈	—	4	8	no	—
260	C₂×Q₈	—	4	8	no	—
261	C₂×Q₈	—	4	16	no	—
262	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
263	C₂×Q₈	C₂²×C₄×C₁₃	1	4	yes	—
264	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	—
265	C₂²×C₄	—	2	2	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	8	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	4	8	no	—
272	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
273	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
274	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
276	C₂²×C₄	C₁₃×#41	1	2	yes	—
277	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
278	Q₁₆	—	2	16	no	—
279	Q₁₆	—	2	8	no	—
280	Q₁₆	C₁₃×C₂²⋊C₄	1	16	yes	direct product factor
281	C₂×C₈	—	2	2	no	—
282	C₂×C₈	—	2	8	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
287	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
288	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	4	8	no	—
292	C₂²⋊C₄	—	2	2	no	—
293	C₂²⋊C₄	—	4	4	no	—
294	C₂²⋊C₄	C₁₃×Q₁₆	1	4	yes	direct product factor
295	C₄²	—	2	2	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	4	8	no	—
298	C₁₃	C₂²⋊C₄×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
299	C₂³	—	2	2	no	—
300	C₂³	—	2	2	no	—
301	C₂³	C₄×D₄×C₁₃	1	2	yes	—
302	C₂³	C₂×C₁₃×Q₁₆	1	2	yes	—
303	C₂³	C₁₃×#135	1	2	yes	—
304	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
305	Q₈	—	2	4	no	—
306	Q₈	—	2	8	no	—
307	Q₈	—	2	4	no	—
308	Q₈	—	2	4	no	—
309	Q₈	—	4	16	no	—
310	Q₈	—	4	4	no	—
311	Q₈	C₂×C₁₃×C₂²⋊C₄	1	8	yes	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	8	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	4	16	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
330	C₂×C₄	C₂×C₁₃×Q₁₆	1	4	yes	complemented
331	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
332	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
333	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
334	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
335	C₈	—	2	2	no	—
336	C₈	—	4	2	no	—
337	C₈	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
338	C₂²	—	2	4	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	2	no	—
342	C₂²	C₄×C₁₃×Q₁₆	1	4	yes	complemented
343	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
344	C₂²	D₄²×C₁₃	1	2	yes	—
345	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
346	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
347	C₂²	C₁₃×#578	1	2	yes	—
348	C₄	—	2	4	no	—
349	C₄	—	2	2	no	—
350	C₄	—	2	8	no	—
351	C₄	—	4	2	no	—
352	C₄	—	4	4	no	—
353	C₄	—	8	4	no	—
354	C₄	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
355	C₄	C₁₃×#518	1	1	yes	characteristic
356	C₄	C₁₃×#546	1	2	yes	—
357	C₂	—	2	4	no	—
358	C₂	D₄×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
359	C₂	C₂×C₄×C₁₃×Q₁₆	1	1	yes	characteristic
360	C₂	C₁₃×#2950	1	1	yes	characteristic
361	C₂	C₁₃×#3285	1	2	yes	—
362	C₂	D₄×C₁₃×Q₁₆	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
4. C₁₃×#1969	C₂	semidirect
5. C₁₃×#1878	C₂	semidirect
11. C₂²×C₁₃×Q₁₆	C₄	semidirect
70. C₂²⋊C₄×Q₁₆	C₁₃	direct (N × H)
100. C₁₃×Q₁₆	C₂²⋊C₄	direct (N × H)
114. C₁₃×C₂²⋊C₄	Q₁₆	direct (N × H)
119. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
121. #1969	C₂×C₁₃	semidirect
122. #1878	C₂×C₁₃	semidirect
157. C₂×C₄×C₁₃	C₂×Q₁₆	semidirect
167. C₂²×Q₁₆	C₄×C₁₃	semidirect
191. C₂²×C₁₃	C₄×Q₁₆	semidirect
280. Q₁₆	C₁₃×C₂²⋊C₄	direct (N × H)
294. C₂²⋊C₄	C₁₃×Q₁₆	direct (N × H)
298. C₁₃	C₂²⋊C₄×Q₁₆	direct (N × H)
330. C₂×C₄	C₂×C₁₃×Q₁₆	semidirect
342. C₂²	C₄×C₁₃×Q₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₁₃×Q₁₆	2
C₂×C₄×C₁₃×Q₁₆	2
Q₈×C₁₃×C₂²⋊C₄	2
C₁₃×#1969	2
C₁₃×#1878	2
C₁₃×#1808	2
C₁₃×#1787	2
C₈×C₁₃×C₂²⋊C₄	2
C₂²⋊C₄×Q₁₆	13

Subgroups — C13×C22⋊C4×Q16 #15708789

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₂²⋊C₄×Q₁₆ #15708789