Subgroups — D₄×C₁₃×C₄⋊C₈ #15708985

Order 3328.

1200 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₄×C₁₃	C₂	1	2	yes	maximal
2	C₂²×C₁₃×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₄²×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1939	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1850	C₂	1	4	yes	maximal, complemented
6	C₁₃×#1842	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1797	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₈×C₁₃	C₂²	1	4	yes	—
10	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
11	C₂×C₄×D₄×C₁₃	C₄	1	1	yes	characteristic
12	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
14	C₈×D₄×C₁₃	—	2	8	no	—
15	C₂×C₁₃×C₄⋊C₈	—	2	8	no	—
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	—
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
23	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
24	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
25	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
26	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₄×C₁₃×C₂²⋊C₄	C₄	1	2	yes	—
28	C₄×C₁₃×C₂²⋊C₄	C₄	1	2	yes	—
29	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₄³×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#336	C₂²	1	2	yes	—
32	C₁₃×#336	C₂²	1	4	yes	—
33	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
36	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
37	C₂²×C₈×C₁₃	—	2	8	no	—
38	C₂²×C₈×C₁₃	—	2	8	no	—
39	C₂²×C₈×C₁₃	—	4	4	no	—
40	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
41	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
42	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
43	C₄×D₄×C₁₃	—	2	4	no	—
44	C₄×D₄×C₁₃	C₈	1	8	yes	complemented
45	C₄×D₄×C₁₃	D₄	1	4	yes	—
46	C₄×D₄×C₁₃	Q₈	1	4	yes	—
47	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
48	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
50	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₁₃	—	2	4	no	—
54	C₂×C₄²×C₁₃	—	2	4	no	—
55	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
63	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×C₄⋊C₈	—	2	8	no	—
66	C₁₃×C₄⋊C₈	—	2	4	no	—
67	C₁₃×C₄⋊C₈	—	2	4	no	—
68	C₁₃×C₄⋊C₈	—	2	2	no	—
69	C₁₃×C₄⋊C₈	—	4	2	no	—
70	C₁₃×C₄⋊C₈	D₄	1	4	yes	direct product factor
71	C₁₃×C₂²⋊C₈	—	2	8	no	—
72	C₄×C₈×C₁₃	—	2	4	no	—
73	C₁₃×#95	C₂×C₄	1	2	yes	—
74	C₁₃×#95	C₂×C₄	1	2	yes	—
75	C₁₃×#95	C₂×C₄	1	2	yes	—
76	D₄×C₄⋊C₈	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
78	C₂×D₄×C₁₃	C₄⋊C₄	1	4	yes	—
79	C₂×D₄×C₁₃	C₂×C₈	1	4	yes	—
80	C₂×D₄×C₁₃	M₁₆	1	4	yes	—
81	C₂²×C₄×C₁₃	—	2	4	no	—
82	C₂²×C₄×C₁₃	—	2	4	no	—
83	C₂²×C₄×C₁₃	—	2	2	no	—
84	C₂²×C₄×C₁₃	—	2	2	no	—
85	C₂²×C₄×C₁₃	—	2	2	no	—
86	C₂²×C₄×C₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	4	no	—
88	C₂²×C₄×C₁₃	—	2	4	no	—
89	C₂²×C₄×C₁₃	—	4	2	no	—
90	C₂²×C₄×C₁₃	C₂×C₈	1	8	yes	complemented
91	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
102	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	—	2	4	no	—
107	C₂×C₈×C₁₃	—	2	4	no	—
108	C₂×C₈×C₁₃	—	2	2	no	—
109	C₂×C₈×C₁₃	—	2	4	no	—
110	C₂×C₈×C₁₃	—	2	2	no	—
111	C₂×C₈×C₁₃	—	4	16	no	—
112	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
113	C₁₃×C₄⋊C₄	—	2	2	no	—
114	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
115	C₁₃×C₄⋊C₄	C₂×C₈	1	4	yes	complemented
116	C₁₃×C₂²⋊C₄	—	2	4	no	—
117	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
118	C₁₃×C₂²⋊C₄	C₂×C₈	1	8	yes	complemented
119	C₄²×C₁₃	—	2	4	no	—
120	C₄²×C₁₃	—	2	4	no	—
121	C₄²×C₁₃	—	2	2	no	—
122	C₄²×C₁₃	—	2	2	no	—
123	C₄²×C₁₃	—	2	2	no	—
124	C₄²×C₁₃	—	2	2	no	—
125	C₄²×C₁₃	—	2	1	no	—
126	C₄²×C₁₃	—	2	1	no	—
127	C₄²×C₁₃	—	4	1	no	—
128	C₄²×C₁₃	C₂×C₈	1	4	yes	complemented
129	C₄²×C₁₃	C₂×D₄	1	2	yes	—
130	C₄²×C₁₃	C₂×D₄	1	2	yes	—
131	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
132	C₄²×C₁₃	#41	1	2	yes	—
133	C₂×C₈×D₄	C₂×C₁₃	1	2	yes	—
134	C₂²×C₄⋊C₈	C₂×C₁₃	1	2	yes	complemented
135	C₄²×D₄	C₂×C₁₃	1	1	yes	characteristic
136	#1939	C₂×C₁₃	1	2	yes	complemented
137	#1850	C₂×C₁₃	1	4	yes	complemented
138	#1842	C₂×C₁₃	1	1	yes	characteristic, complemented
139	#1797	C₂×C₁₃	1	2	yes	complemented
140	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
141	C₂³×C₁₃	—	2	2	no	—
142	C₂³×C₁₃	—	2	2	no	—
143	C₂³×C₁₃	—	2	2	no	—
144	C₂³×C₁₃	—	2	2	no	—
145	C₂³×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
146	C₂³×C₁₃	C₂²×C₈	1	4	yes	—
147	C₂³×C₁₃	C₂×M₁₆	1	4	yes	—
148	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
149	D₄×C₁₃	C₄⋊C₈	1	16	yes	direct product factor
150	C₂×C₄×C₁₃	—	2	2	no	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	1	no	—
153	C₂×C₄×C₁₃	—	2	2	no	—
154	C₂×C₄×C₁₃	—	2	1	no	—
155	C₂×C₄×C₁₃	—	2	1	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	1	no	—
158	C₂×C₄×C₁₃	—	2	1	no	—
159	C₂×C₄×C₁₃	—	2	1	no	—
160	C₂×C₄×C₁₃	—	2	4	no	—
161	C₂×C₄×C₁₃	—	2	4	no	—
162	C₂×C₄×C₁₃	—	2	4	no	—
163	C₂×C₄×C₁₃	—	2	4	no	—
164	C₂×C₄×C₁₃	—	2	16	no	—
165	C₂×C₄×C₁₃	—	2	2	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	4	8	no	—
172	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
173	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
174	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
175	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
176	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
177	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
178	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
179	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
180	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
181	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
182	C₂×C₄×C₁₃	#131	1	2	yes	—
183	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
188	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
189	C₈×C₁₃	—	2	4	no	—
190	C₈×C₁₃	—	4	4	no	—
191	C₈×C₁₃	—	4	2	no	—
192	C₂³×C₈	C₂²×C₁₃	1	4	yes	—
193	C₂×C₄×D₄	C₄×C₁₃	1	1	yes	characteristic
194	C₂×C₄×D₄	C₄×C₁₃	1	1	yes	characteristic
195	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
196	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
197	C₈×D₄	—	2	8	no	—
198	C₂×C₄⋊C₈	—	2	8	no	—
199	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
200	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
201	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
202	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	—
203	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
204	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
205	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
206	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
207	C₄×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
208	C₄×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
209	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
210	C₄×C₂²⋊C₄	C₄×C₁₃	1	2	yes	—
211	C₄×C₂²⋊C₄	C₄×C₁₃	1	2	yes	—
212	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
213	C₄³	C₂²×C₁₃	1	1	yes	characteristic
214	#336	C₂²×C₁₃	1	4	yes	—
215	#336	C₂²×C₁₃	1	2	yes	—
216	C₂²×C₁₃	—	2	4	no	—
217	C₂²×C₁₃	—	2	4	no	—
218	C₂²×C₁₃	—	2	4	no	—
219	C₂²×C₁₃	—	2	4	no	—
220	C₂²×C₁₃	—	2	4	no	—
221	C₂²×C₁₃	—	2	4	no	—
222	C₂²×C₁₃	C₂×C₄⋊C₈	1	8	yes	complemented
223	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
224	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
225	C₂²×C₁₃	#520	1	1	yes	characteristic
226	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
227	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
228	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
229	C₂²×C₁₃	#568	1	1	yes	characteristic
230	C₄×C₁₃	—	2	4	no	—
231	C₄×C₁₃	—	2	2	no	—
232	C₄×C₁₃	—	2	4	no	—
233	C₄×C₁₃	—	2	2	no	—
234	C₄×C₁₃	—	2	2	no	—
235	C₄×C₁₃	—	4	2	no	—
236	C₄×C₁₃	—	4	1	no	—
237	C₄×C₁₃	C₂×C₄⋊C₈	1	4	yes	complemented
238	C₄×C₁₃	C₈×D₄	1	4	yes	complemented
239	C₄×C₁₃	D₄²	1	1	yes	characteristic
240	C₄×C₁₃	#547	1	1	yes	characteristic
241	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
242	C₄×C₁₃	#554	1	1	yes	characteristic
243	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
244	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
245	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
246	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
247	C₂²×C₈	—	2	8	no	—
248	C₂²×C₈	—	2	8	no	—
249	C₂²×C₈	—	4	4	no	—
250	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
251	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
252	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
253	C₄×D₄	—	2	4	no	—
254	C₄×D₄	C₈×C₁₃	1	8	yes	complemented
255	C₄×D₄	D₄×C₁₃	1	4	yes	—
256	C₄×D₄	Q₈×C₁₃	1	4	yes	—
257	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
261	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
263	C₂×C₄²	—	2	4	no	—
264	C₂×C₄²	—	2	4	no	—
265	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
266	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
267	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
268	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
269	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
270	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
273	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
275	C₄⋊C₈	—	2	8	no	—
276	C₄⋊C₈	—	2	4	no	—
277	C₄⋊C₈	—	2	4	no	—
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	—	4	2	no	—
280	C₄⋊C₈	D₄×C₁₃	1	4	yes	direct product factor
281	C₂²⋊C₈	—	2	8	no	—
282	C₄×C₈	—	2	4	no	—
283	#95	C₂×C₄×C₁₃	1	2	yes	—
284	#95	C₂×C₄×C₁₃	1	2	yes	—
285	#95	C₂×C₄×C₁₃	1	2	yes	—
286	C₂×C₁₃	—	2	8	no	—
287	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
288	C₂×C₁₃	C₂²×C₄⋊C₈	1	1	yes	characteristic
289	C₂×C₁₃	#2906	1	1	yes	characteristic
290	C₂×C₁₃	C₂×C₈×D₄	1	1	yes	characteristic
291	C₂×C₁₃	D₄×M₁₆	1	1	yes	characteristic
292	C₂×C₁₃	#2988	1	1	yes	characteristic
293	C₂×C₁₃	#2990	1	1	yes	characteristic
294	C₂⁴	C₂²×C₄×C₁₃	1	2	yes	—
295	C₂×D₄	C₁₃×C₄⋊C₄	1	4	yes	—
296	C₂×D₄	C₂×C₈×C₁₃	1	4	yes	—
297	C₂×D₄	C₁₃×M₁₆	1	4	yes	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	C₂×C₈×C₁₃	1	8	yes	complemented
308	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
309	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
310	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
311	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
312	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
313	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
314	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
315	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
316	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
318	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
319	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	4	no	—
324	C₂×C₈	—	2	4	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	4	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	4	16	no	—
329	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
332	C₄⋊C₄	C₂×C₈×C₁₃	1	4	yes	complemented
333	C₂²⋊C₄	—	2	4	no	—
334	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	8	yes	—
335	C₂²⋊C₄	C₂×C₈×C₁₃	1	8	yes	complemented
336	C₄²	—	2	4	no	—
337	C₄²	—	2	4	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	4	1	no	—
345	C₄²	C₂×C₈×C₁₃	1	4	yes	complemented
346	C₄²	C₂×D₄×C₁₃	1	2	yes	—
347	C₄²	C₂×D₄×C₁₃	1	2	yes	—
348	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
349	C₄²	C₁₃×#41	1	2	yes	—
350	C₁₃	D₄×C₄⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	2	2	no	—
355	C₂³	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
356	C₂³	C₂²×C₈×C₁₃	1	4	yes	—
357	C₂³	C₂×C₁₃×M₁₆	1	4	yes	—
358	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
359	D₄	C₁₃×C₄⋊C₈	1	16	yes	direct product factor
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	16	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	8	no	—
382	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
383	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
384	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
385	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
386	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
387	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
388	C₂×C₄	C₂²×C₈×C₁₃	1	4	yes	—
389	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
390	C₂×C₄	C₂²×C₈×C₁₃	1	2	yes	—
391	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
392	C₂×C₄	C₁₃×#131	1	2	yes	—
393	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
395	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
396	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
397	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
398	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
399	C₈	—	2	4	no	—
400	C₈	—	4	4	no	—
401	C₈	—	4	2	no	—
402	C₂²	—	2	4	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	2	4	no	—
408	C₂²	C₂×C₁₃×C₄⋊C₈	1	8	yes	complemented
409	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
410	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
411	C₂²	C₁₃×#520	1	1	yes	characteristic
412	C₂²	C₂³×C₈×C₁₃	1	1	yes	characteristic
413	C₂²	C₂²×C₁₃×M₁₆	1	1	yes	characteristic
414	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
415	C₂²	C₁₃×#568	1	1	yes	characteristic
416	C₄	—	2	4	no	—
417	C₄	—	2	2	no	—
418	C₄	—	2	4	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	4	1	no	—
423	C₄	C₂×C₁₃×C₄⋊C₈	1	4	yes	complemented
424	C₄	C₈×D₄×C₁₃	1	4	yes	complemented
425	C₄	D₄²×C₁₃	1	1	yes	characteristic
426	C₄	C₁₃×#547	1	1	yes	characteristic
427	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
428	C₄	C₁₃×#554	1	1	yes	characteristic
429	C₂	—	2	8	no	—
430	C₂	D₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
431	C₂	C₂²×C₁₃×C₄⋊C₈	1	1	yes	characteristic
432	C₂	C₁₃×#2906	1	1	yes	characteristic
433	C₂	C₂×C₈×D₄×C₁₃	1	1	yes	characteristic
434	C₂	D₄×C₁₃×M₁₆	1	1	yes	characteristic
435	C₂	C₁₃×#2988	1	1	yes	characteristic
436	C₂	C₁₃×#2990	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂²×D₄×C₁₃	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₃×C₄⋊C₈	C₂	semidirect
4. C₁₃×#1939	C₂	semidirect
5. C₁₃×#1850	C₂	semidirect
6. C₁₃×#1842	C₂	semidirect
7. C₁₃×#1797	C₂	semidirect
8. C₄×C₁₃×C₄⋊C₈	C₂	semidirect
44. C₄×D₄×C₁₃	C₈	semidirect
70. C₁₃×C₄⋊C₈	D₄	direct (N × H)
76. D₄×C₄⋊C₈	C₁₃	direct (N × H)
90. C₂²×C₄×C₁₃	C₂×C₈	semidirect
115. C₁₃×C₄⋊C₄	C₂×C₈	semidirect
118. C₁₃×C₂²⋊C₄	C₂×C₈	semidirect
128. C₄²×C₁₃	C₂×C₈	semidirect
134. C₂²×C₄⋊C₈	C₂×C₁₃	semidirect
136. #1939	C₂×C₁₃	semidirect
137. #1850	C₂×C₁₃	semidirect
138. #1842	C₂×C₁₃	semidirect
139. #1797	C₂×C₁₃	semidirect
140. C₄×C₄⋊C₈	C₂×C₁₃	semidirect
149. D₄×C₁₃	C₄⋊C₈	direct (N × H)
222. C₂²×C₁₃	C₂×C₄⋊C₈	semidirect
237. C₄×C₁₃	C₂×C₄⋊C₈	semidirect
238. C₄×C₁₃	C₈×D₄	semidirect
254. C₄×D₄	C₈×C₁₃	semidirect
280. C₄⋊C₈	D₄×C₁₃	direct (N × H)
307. C₂²×C₄	C₂×C₈×C₁₃	semidirect
332. C₄⋊C₄	C₂×C₈×C₁₃	semidirect
335. C₂²⋊C₄	C₂×C₈×C₁₃	semidirect
345. C₄²	C₂×C₈×C₁₃	semidirect
350. C₁₃	D₄×C₄⋊C₈	direct (N × H)
359. D₄	C₁₃×C₄⋊C₈	direct (N × H)
408. C₂²	C₂×C₁₃×C₄⋊C₈	semidirect
423. C₄	C₂×C₁₃×C₄⋊C₈	semidirect
424. C₄	C₈×D₄×C₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×D₄×C₁₃	2
C₂²×C₁₃×C₄⋊C₈	2
C₄²×D₄×C₁₃	2
C₁₃×#1939	2
C₁₃×#1850	2
C₁₃×#1842	2
C₁₃×#1797	2
C₄×C₁₃×C₄⋊C₈	2
D₄×C₄⋊C₈	13

Subgroups — D4×C13×C4⋊C8 #15708985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₁₃×C₄⋊C₈ #15708985