Subgroups — C₂×D₄×C₁₃×C₄⋊C₄ #15720449

Order 3328.

4718 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₁₃	C₂	1	2	yes	maximal
2	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₁₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
4	D₄×C₁₃×C₄⋊C₄	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#389	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#385	C₂	1	4	yes	maximal, complemented
7	C₂×C₁₃×#384	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#380	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₃	C₂²	1	4	yes	—
12	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
13	C₂×C₄×D₄×C₁₃	—	2	16	no	—
14	C₂×C₄×D₄×C₁₃	C₄	1	16	yes	complemented
15	C₂×C₄×D₄×C₁₃	C₂²	1	16	yes	—
16	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
17	C₂²×C₁₃×C₄⋊C₄	—	2	16	no	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	16	yes	complemented
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
29	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#389	C₂²	1	16	yes	complemented
31	C₁₃×#385	C₂²	1	32	yes	complemented
32	C₁₃×#384	C₂²	1	8	yes	complemented
33	C₁₃×#380	C₂²	1	16	yes	complemented
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
35	C₂×C₁₃×#95	C₂²	1	2	yes	—
36	C₂×C₁₃×#95	C₂²	1	4	yes	—
37	C₂⁵×C₁₃	C₂³	1	2	yes	—
38	C₂²×D₄×C₁₃	C₂×C₄	1	8	yes	—
39	C₂²×D₄×C₁₃	D₄	1	8	yes	—
40	C₂²×D₄×C₁₃	Q₈	1	8	yes	—
41	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
42	C₂³×C₄×C₁₃	—	2	8	no	—
43	C₂³×C₄×C₁₃	—	2	8	no	—
44	C₂³×C₄×C₁₃	—	2	16	no	—
45	C₂³×C₄×C₁₃	—	2	16	no	—
46	C₂³×C₄×C₁₃	—	4	8	no	—
47	C₂³×C₄×C₁₃	C₂×C₄	1	16	yes	complemented
48	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	16	yes	—
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₄×D₄×C₁₃	—	2	64	no	—
58	C₄×D₄×C₁₃	C₂×C₄	1	64	yes	complemented
59	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	64	no	—
64	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
65	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
66	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	direct product factor
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
75	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
76	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
77	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
78	C₂×C₄²×C₁₃	—	2	8	no	—
79	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	complemented
80	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
81	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
82	C₁₃×#95	C₂³	1	8	yes	—
83	C₁₃×#95	C₂³	1	16	yes	—
84	C₂×D₄×C₄⋊C₄	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂⁴×C₁₃	—	2	4	no	—
86	C₂⁴×C₁₃	—	2	4	no	—
87	C₂⁴×C₁₃	—	2	4	no	—
88	C₂⁴×C₁₃	—	2	4	no	—
89	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
90	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
91	C₂⁴×C₁₃	C₂×Q₈	1	8	yes	—
92	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
93	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
94	C₂×D₄×C₁₃	C₄⋊C₄	1	64	yes	direct product factor
95	C₂×D₄×C₁₃	C₂²×C₄	1	16	yes	—
96	C₂×D₄×C₁₃	C₂×D₄	1	16	yes	—
97	C₂×D₄×C₁₃	C₂×Q₈	1	16	yes	—
98	C₂²×C₄×C₁₃	—	2	4	no	—
99	C₂²×C₄×C₁₃	—	2	4	no	—
100	C₂²×C₄×C₁₃	—	2	4	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	4	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	64	no	—
105	C₂²×C₄×C₁₃	—	2	16	no	—
106	C₂²×C₄×C₁₃	—	2	16	no	—
107	C₂²×C₄×C₁₃	—	2	4	no	—
108	C₂²×C₄×C₁₃	—	2	8	no	—
109	C₂²×C₄×C₁₃	—	2	8	no	—
110	C₂²×C₄×C₁₃	—	2	32	no	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	2	8	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	2	32	no	—
115	C₂²×C₄×C₁₃	—	4	16	no	—
116	C₂²×C₄×C₁₃	—	4	64	no	—
117	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
119	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
120	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₁₃	C₂²×C₄	1	32	yes	complemented
122	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
123	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
125	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
126	C₂²×C₄×C₁₃	#41	1	4	yes	—
127	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
129	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
134	C₁₃×C₄⋊C₄	—	2	32	no	—
135	C₁₃×C₄⋊C₄	—	2	16	no	—
136	C₁₃×C₄⋊C₄	—	2	16	no	—
137	C₁₃×C₄⋊C₄	—	2	8	no	—
138	C₁₃×C₄⋊C₄	—	4	8	no	—
139	C₁₃×C₄⋊C₄	C₂²×C₄	1	16	yes	complemented
140	C₁₃×C₄⋊C₄	C₂×D₄	1	16	yes	direct product factor
141	C₁₃×C₂²⋊C₄	—	2	32	no	—
142	C₁₃×C₂²⋊C₄	C₂²×C₄	1	32	yes	complemented
143	C₄²×C₁₃	—	2	16	no	—
144	C₄²×C₁₃	C₂²×C₄	1	16	yes	complemented
145	C₂²×C₄×D₄	C₂×C₁₃	1	2	yes	—
146	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic
147	C₂³×C₄⋊C₄	C₂×C₁₃	1	2	yes	complemented
148	D₄×C₄⋊C₄	C₂×C₁₃	1	16	yes	direct product factor
149	C₂×#389	C₂×C₁₃	1	2	yes	complemented
150	C₂×#385	C₂×C₁₃	1	4	yes	complemented
151	C₂×#384	C₂×C₁₃	1	1	yes	characteristic, complemented
152	C₂×#380	C₂×C₁₃	1	2	yes	complemented
153	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
154	C₂³×C₁₃	—	2	16	no	—
155	C₂³×C₁₃	—	2	16	no	—
156	C₂³×C₁₃	—	2	16	no	—
157	C₂³×C₁₃	—	2	16	no	—
158	C₂³×C₁₃	—	2	16	no	—
159	C₂³×C₁₃	—	2	16	no	—
160	C₂³×C₁₃	—	2	4	no	—
161	C₂³×C₁₃	—	2	4	no	—
162	C₂³×C₁₃	—	2	4	no	—
163	C₂³×C₁₃	—	2	4	no	—
164	C₂³×C₁₃	C₂×C₄⋊C₄	1	32	yes	complemented
165	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
166	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
167	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
168	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
169	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
170	C₂³×C₁₃	C₂²×Q₈	1	8	yes	—
171	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
172	C₂³×C₁₃	C₂×#41	1	2	yes	—
173	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
174	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
175	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
176	D₄×C₁₃	C₂×C₄⋊C₄	1	64	yes	direct product factor
177	C₂×C₄×C₁₃	—	2	16	no	—
178	C₂×C₄×C₁₃	—	2	8	no	—
179	C₂×C₄×C₁₃	—	2	16	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	4	no	—
182	C₂×C₄×C₁₃	—	2	4	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	4	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	64	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	8	no	—
189	C₂×C₄×C₁₃	—	2	8	no	—
190	C₂×C₄×C₁₃	—	2	4	no	—
191	C₂×C₄×C₁₃	—	2	8	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	4	64	no	—
194	C₂×C₄×C₁₃	—	4	16	no	—
195	C₂×C₄×C₁₃	—	4	8	no	—
196	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	16	yes	complemented
197	C₂×C₄×C₁₃	C₄×D₄	1	16	yes	complemented
198	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
199	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
200	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
201	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
202	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
203	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
204	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
205	C₂×C₄×C₁₃	C₂²×Q₈	1	4	yes	—
206	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
207	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
208	C₂⁴×C₄	C₂²×C₁₃	1	4	yes	—
209	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
210	C₂×C₄×D₄	—	2	16	no	—
211	C₂×C₄×D₄	C₄×C₁₃	1	16	yes	complemented
212	C₂×C₄×D₄	C₂²×C₁₃	1	16	yes	—
213	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
214	C₂²×C₄⋊C₄	—	2	16	no	—
215	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
216	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
217	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
218	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
219	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
220	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
221	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
222	C₂²×C₄⋊C₄	C₂²×C₁₃	1	16	yes	complemented
223	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
224	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
225	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
226	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
227	#389	C₂²×C₁₃	1	16	yes	complemented
228	#385	C₂²×C₁₃	1	32	yes	complemented
229	#384	C₂²×C₁₃	1	8	yes	complemented
230	#380	C₂²×C₁₃	1	16	yes	complemented
231	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
232	C₂×#95	C₂²×C₁₃	1	2	yes	—
233	C₂×#95	C₂²×C₁₃	1	4	yes	—
234	C₂²×C₁₃	—	2	64	no	—
235	C₂²×C₁₃	—	2	8	no	—
236	C₂²×C₁₃	—	2	8	no	—
237	C₂²×C₁₃	—	2	8	no	—
238	C₂²×C₁₃	—	2	8	no	—
239	C₂²×C₁₃	—	2	8	no	—
240	C₂²×C₁₃	—	2	8	no	—
241	C₂²×C₁₃	C₂²×C₄⋊C₄	1	4	yes	—
242	C₂²×C₁₃	C₂²×C₄⋊C₄	1	16	yes	complemented
243	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
244	C₂²×C₁₃	#520	1	4	yes	—
245	C₂²×C₁₃	D₄²	1	4	yes	—
246	C₂²×C₁₃	#547	1	4	yes	—
247	C₂²×C₁₃	D₄×Q₈	1	4	yes	—
248	C₂²×C₁₃	#554	1	4	yes	—
249	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
250	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
251	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
252	C₂²×C₁₃	C₂³×Q₈	1	1	yes	characteristic
253	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
254	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
255	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
256	C₄×C₁₃	—	2	8	no	—
257	C₄×C₁₃	—	2	4	no	—
258	C₄×C₁₃	—	2	8	no	—
259	C₄×C₁₃	—	4	8	no	—
260	C₄×C₁₃	—	4	4	no	—
261	C₄×C₁₃	C₂²×C₄⋊C₄	1	8	yes	complemented
262	C₄×C₁₃	C₂×C₄×D₄	1	8	yes	complemented
263	C₂⁵	C₂³×C₁₃	1	2	yes	—
264	C₂²×D₄	C₂×C₄×C₁₃	1	8	yes	—
265	C₂²×D₄	D₄×C₁₃	1	8	yes	—
266	C₂²×D₄	Q₈×C₁₃	1	8	yes	—
267	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
268	C₂³×C₄	—	2	8	no	—
269	C₂³×C₄	—	2	8	no	—
270	C₂³×C₄	—	2	16	no	—
271	C₂³×C₄	—	2	16	no	—
272	C₂³×C₄	—	4	8	no	—
273	C₂³×C₄	C₂×C₄×C₁₃	1	16	yes	complemented
274	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
275	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
276	C₂³×C₄	C₂³×C₁₃	1	16	yes	—
277	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
278	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
279	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
280	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
281	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
282	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
283	C₄×D₄	—	2	64	no	—
284	C₄×D₄	C₂×C₄×C₁₃	1	64	yes	complemented
285	C₂×C₄⋊C₄	—	2	16	no	—
286	C₂×C₄⋊C₄	—	2	8	no	—
287	C₂×C₄⋊C₄	—	2	8	no	—
288	C₂×C₄⋊C₄	—	2	4	no	—
289	C₂×C₄⋊C₄	—	2	64	no	—
290	C₂×C₄⋊C₄	—	4	4	no	—
291	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	complemented
292	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	direct product factor
293	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
294	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
295	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
296	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
297	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
298	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
299	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
300	C₂×C₂²⋊C₄	—	2	16	no	—
301	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	16	yes	complemented
302	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
303	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
304	C₂×C₄²	—	2	8	no	—
305	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	complemented
306	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
307	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
308	#95	C₂³×C₁₃	1	8	yes	—
309	#95	C₂³×C₁₃	1	16	yes	—
310	C₂×C₁₃	—	2	16	no	—
311	C₂×C₁₃	D₄×C₄⋊C₄	1	8	yes	direct product factor
312	C₂×C₁₃	C₂³×C₄⋊C₄	1	1	yes	characteristic
313	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
314	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
315	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
316	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
317	C₂×C₁₃	C₂×D₄×Q₈	1	1	yes	characteristic
318	C₂×C₁₃	C₂×#554	1	1	yes	characteristic
319	C₂⁴	—	2	4	no	—
320	C₂⁴	—	2	4	no	—
321	C₂⁴	—	2	4	no	—
322	C₂⁴	—	2	4	no	—
323	C₂⁴	C₂²×C₄×C₁₃	1	8	yes	—
324	C₂⁴	C₂×D₄×C₁₃	1	8	yes	—
325	C₂⁴	C₂×Q₈×C₁₃	1	8	yes	—
326	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
327	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
328	C₂×D₄	C₁₃×C₄⋊C₄	1	64	yes	direct product factor
329	C₂×D₄	C₂²×C₄×C₁₃	1	16	yes	—
330	C₂×D₄	C₂×D₄×C₁₃	1	16	yes	—
331	C₂×D₄	C₂×Q₈×C₁₃	1	16	yes	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	64	no	—
339	C₂²×C₄	—	2	16	no	—
340	C₂²×C₄	—	2	16	no	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	8	no	—
343	C₂²×C₄	—	2	8	no	—
344	C₂²×C₄	—	2	32	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	8	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	32	no	—
349	C₂²×C₄	—	4	16	no	—
350	C₂²×C₄	—	4	64	no	—
351	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
352	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
353	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
354	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
355	C₂²×C₄	C₂²×C₄×C₁₃	1	32	yes	complemented
356	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
357	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
358	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
359	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
360	C₂²×C₄	C₁₃×#41	1	4	yes	—
361	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
362	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
363	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
364	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
365	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
366	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
367	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
368	C₄⋊C₄	—	2	32	no	—
369	C₄⋊C₄	—	2	16	no	—
370	C₄⋊C₄	—	2	16	no	—
371	C₄⋊C₄	—	2	8	no	—
372	C₄⋊C₄	—	4	8	no	—
373	C₄⋊C₄	C₂²×C₄×C₁₃	1	16	yes	complemented
374	C₄⋊C₄	C₂×D₄×C₁₃	1	16	yes	direct product factor
375	C₂²⋊C₄	—	2	32	no	—
376	C₂²⋊C₄	C₂²×C₄×C₁₃	1	32	yes	complemented
377	C₄²	—	2	16	no	—
378	C₄²	C₂²×C₄×C₁₃	1	16	yes	complemented
379	C₁₃	C₂×D₄×C₄⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
380	C₂³	—	2	16	no	—
381	C₂³	—	2	16	no	—
382	C₂³	—	2	16	no	—
383	C₂³	—	2	16	no	—
384	C₂³	—	2	16	no	—
385	C₂³	—	2	16	no	—
386	C₂³	—	2	4	no	—
387	C₂³	—	2	4	no	—
388	C₂³	—	2	4	no	—
389	C₂³	—	2	4	no	—
390	C₂³	C₂×C₁₃×C₄⋊C₄	1	32	yes	complemented
391	C₂³	C₂³×C₄×C₁₃	1	8	yes	—
392	C₂³	C₂³×C₄×C₁₃	1	2	yes	—
393	C₂³	C₂²×D₄×C₁₃	1	8	yes	—
394	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
395	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
396	C₂³	C₂²×Q₈×C₁₃	1	8	yes	—
397	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
398	C₂³	C₂×C₁₃×#41	1	2	yes	—
399	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
400	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
401	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
402	D₄	C₂×C₁₃×C₄⋊C₄	1	64	yes	direct product factor
403	C₂×C₄	—	2	16	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	16	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	64	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	4	64	no	—
420	C₂×C₄	—	4	16	no	—
421	C₂×C₄	—	4	8	no	—
422	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	16	yes	complemented
423	C₂×C₄	C₄×D₄×C₁₃	1	16	yes	complemented
424	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
425	C₂×C₄	C₂³×C₄×C₁₃	1	8	yes	—
426	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
427	C₂×C₄	C₂³×C₄×C₁₃	1	4	yes	—
428	C₂×C₄	C₂²×D₄×C₁₃	1	8	yes	—
429	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
430	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
431	C₂×C₄	C₂²×Q₈×C₁₃	1	4	yes	—
432	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
433	C₂²	—	2	64	no	—
434	C₂²	—	2	8	no	—
435	C₂²	—	2	8	no	—
436	C₂²	—	2	8	no	—
437	C₂²	—	2	8	no	—
438	C₂²	—	2	8	no	—
439	C₂²	—	2	8	no	—
440	C₂²	C₂²×C₁₃×C₄⋊C₄	1	4	yes	—
441	C₂²	C₂²×C₁₃×C₄⋊C₄	1	16	yes	complemented
442	C₂²	C₂×C₄×D₄×C₁₃	1	4	yes	—
443	C₂²	C₁₃×#520	1	4	yes	—
444	C₂²	D₄²×C₁₃	1	4	yes	—
445	C₂²	C₁₃×#547	1	4	yes	—
446	C₂²	D₄×Q₈×C₁₃	1	4	yes	—
447	C₂²	C₁₃×#554	1	4	yes	—
448	C₂²	C₂⁴×C₄×C₁₃	1	1	yes	characteristic
449	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
450	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
451	C₂²	C₂³×Q₈×C₁₃	1	1	yes	characteristic
452	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
453	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
454	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
455	C₄	—	2	8	no	—
456	C₄	—	2	4	no	—
457	C₄	—	2	8	no	—
458	C₄	—	4	8	no	—
459	C₄	—	4	4	no	—
460	C₄	C₂²×C₁₃×C₄⋊C₄	1	8	yes	complemented
461	C₄	C₂×C₄×D₄×C₁₃	1	8	yes	complemented
462	C₂	—	2	16	no	—
463	C₂	D₄×C₁₃×C₄⋊C₄	1	8	yes	direct product factor
464	C₂	C₂³×C₁₃×C₄⋊C₄	1	1	yes	characteristic
465	C₂	C₂²×C₄×D₄×C₁₃	1	1	yes	characteristic
466	C₂	C₂×C₁₃×#520	1	1	yes	characteristic
467	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
468	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
469	C₂	C₂×D₄×Q₈×C₁₃	1	1	yes	characteristic
470	C₂	C₂×C₁₃×#554	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂³×C₁₃×C₄⋊C₄	C₂	semidirect
4. D₄×C₁₃×C₄⋊C₄	C₂	direct (N × H)
5. C₂×C₁₃×#389	C₂	semidirect
6. C₂×C₁₃×#385	C₂	semidirect
7. C₂×C₁₃×#384	C₂	semidirect
8. C₂×C₁₃×#380	C₂	semidirect
9. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
14. C₂×C₄×D₄×C₁₃	C₄	semidirect
25. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
30. C₁₃×#389	C₂²	semidirect
31. C₁₃×#385	C₂²	semidirect
32. C₁₃×#384	C₂²	semidirect
33. C₁₃×#380	C₂²	semidirect
34. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
47. C₂³×C₄×C₁₃	C₂×C₄	semidirect
58. C₄×D₄×C₁₃	C₂×C₄	semidirect
65. C₂×C₁₃×C₄⋊C₄	C₂×C₄	semidirect
66. C₂×C₁₃×C₄⋊C₄	D₄	direct (N × H)
75. C₂×C₁₃×C₂²⋊C₄	C₂×C₄	semidirect
79. C₂×C₄²×C₁₃	C₂×C₄	semidirect
84. C₂×D₄×C₄⋊C₄	C₁₃	direct (N × H)
94. C₂×D₄×C₁₃	C₄⋊C₄	direct (N × H)
121. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
139. C₁₃×C₄⋊C₄	C₂²×C₄	semidirect
140. C₁₃×C₄⋊C₄	C₂×D₄	direct (N × H)
142. C₁₃×C₂²⋊C₄	C₂²×C₄	semidirect
144. C₄²×C₁₃	C₂²×C₄	semidirect
147. C₂³×C₄⋊C₄	C₂×C₁₃	semidirect
148. D₄×C₄⋊C₄	C₂×C₁₃	direct (N × H)
149. C₂×#389	C₂×C₁₃	semidirect
150. C₂×#385	C₂×C₁₃	semidirect
151. C₂×#384	C₂×C₁₃	semidirect
152. C₂×#380	C₂×C₁₃	semidirect
153. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
164. C₂³×C₁₃	C₂×C₄⋊C₄	semidirect
176. D₄×C₁₃	C₂×C₄⋊C₄	direct (N × H)
196. C₂×C₄×C₁₃	C₂×C₄⋊C₄	semidirect
197. C₂×C₄×C₁₃	C₄×D₄	semidirect
211. C₂×C₄×D₄	C₄×C₁₃	semidirect
222. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
227. #389	C₂²×C₁₃	semidirect
228. #385	C₂²×C₁₃	semidirect
229. #384	C₂²×C₁₃	semidirect
230. #380	C₂²×C₁₃	semidirect
231. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
242. C₂²×C₁₃	C₂²×C₄⋊C₄	semidirect
261. C₄×C₁₃	C₂²×C₄⋊C₄	semidirect
262. C₄×C₁₃	C₂×C₄×D₄	semidirect
273. C₂³×C₄	C₂×C₄×C₁₃	semidirect
284. C₄×D₄	C₂×C₄×C₁₃	semidirect
291. C₂×C₄⋊C₄	C₂×C₄×C₁₃	semidirect
292. C₂×C₄⋊C₄	D₄×C₁₃	direct (N × H)
301. C₂×C₂²⋊C₄	C₂×C₄×C₁₃	semidirect
305. C₂×C₄²	C₂×C₄×C₁₃	semidirect
311. C₂×C₁₃	D₄×C₄⋊C₄	direct (N × H)
328. C₂×D₄	C₁₃×C₄⋊C₄	direct (N × H)
355. C₂²×C₄	C₂²×C₄×C₁₃	semidirect
373. C₄⋊C₄	C₂²×C₄×C₁₃	semidirect
374. C₄⋊C₄	C₂×D₄×C₁₃	direct (N × H)
376. C₂²⋊C₄	C₂²×C₄×C₁₃	semidirect
378. C₄²	C₂²×C₄×C₁₃	semidirect
379. C₁₃	C₂×D₄×C₄⋊C₄	direct (N × H)
390. C₂³	C₂×C₁₃×C₄⋊C₄	semidirect
402. D₄	C₂×C₁₃×C₄⋊C₄	direct (N × H)
422. C₂×C₄	C₂×C₁₃×C₄⋊C₄	semidirect
423. C₂×C₄	C₄×D₄×C₁₃	semidirect
441. C₂²	C₂²×C₁₃×C₄⋊C₄	semidirect
460. C₄	C₂²×C₁₃×C₄⋊C₄	semidirect
461. C₄	C₂×C₄×D₄×C₁₃	semidirect
463. C₂	D₄×C₁₃×C₄⋊C₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₁₃	2
C₂³×C₁₃×C₄⋊C₄	2
D₄×C₁₃×C₄⋊C₄	2
C₂×C₁₃×#389	2
C₂×C₁₃×#385	2
C₂×C₁₃×#384	2
C₂×C₁₃×#380	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×D₄×C₄⋊C₄	13

Subgroups — C2×D4×C13×C4⋊C4 #15720449

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×C₁₃×C₄⋊C₄ #15720449