Subgroups — C₂×D₄×C₁₃×Q₁₆ #15747385

Order 3328.

2742 conjugacy classes of subgroups.

The subgroup lattice has 402 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	2	yes	maximal, complemented
2	C₂×D₄×Q₈×C₁₃	C₂	1	2	yes	maximal
3	D₄×C₁₃×Q₁₆	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₃×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#467	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#462	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#451	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₁₃	C₂²	1	4	yes	—
11	C₂²×C₁₃×Q₁₆	—	2	16	no	—
12	C₂²×C₁₃×Q₁₆	C₂²	1	4	yes	—
13	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
15	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×Q₁₆	C₂²	1	16	yes	complemented
17	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
18	D₄×Q₈×C₁₃	—	2	8	no	—
19	D₄×Q₈×C₁₃	C₂²	1	16	yes	—
20	C₂×C₁₃×C₄⋊Q₈	—	2	2	no	—
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₃×C₂²⋊Q₈	—	2	4	no	—
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
24	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃	—	2	2	no	—
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#494	C₂²	1	8	yes	complemented
28	C₁₃×#467	C₂²	1	16	yes	complemented
29	C₁₃×#462	C₂²	1	16	yes	complemented
30	C₁₃×#451	C₂²	1	32	yes	complemented
31	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	complemented
32	C₈×D₄×C₁₃	C₂²	1	8	yes	—
33	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#103	C₂²	1	4	yes	—
36	C₂×C₁₃×#103	C₂²	1	2	yes	—
37	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
39	C₂²×Q₈×C₁₃	—	2	4	no	—
40	C₂²×Q₈×C₁₃	—	2	8	no	—
41	C₂²×Q₈×C₁₃	—	2	16	no	—
42	C₂²×Q₈×C₁₃	—	4	8	no	—
43	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
44	C₂²×Q₈×C₁₃	C₂³	1	16	yes	—
45	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
46	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	—	2	4	no	—
48	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
49	C₂×C₁₃×Q₁₆	—	2	16	no	—
50	C₂×C₁₃×Q₁₆	—	2	64	no	—
51	C₂×C₁₃×Q₁₆	—	2	8	no	—
52	C₂×C₁₃×Q₁₆	—	4	4	no	—
53	C₂×C₁₃×Q₁₆	D₄	1	8	yes	direct product factor
54	C₂×C₁₃×Q₁₆	C₂³	1	16	yes	—
55	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
56	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
57	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
58	C₂²×C₈×C₁₃	—	2	8	no	—
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
61	C₂²×C₈×C₁₃	C₂³	1	8	yes	—
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×C₄⋊Q₈	—	2	16	no	—
64	C₁₃×C₄⋊Q₈	—	2	4	no	—
65	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
66	C₁₃×C₂²⋊Q₈	—	2	8	no	—
67	C₁₃×C₂²⋊Q₈	—	2	32	no	—
68	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
69	C₄×Q₈×C₁₃	—	2	4	no	—
70	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
71	C₄×D₄×C₁₃	—	2	16	no	—
72	C₄×D₄×C₁₃	D₄	1	4	yes	—
73	C₄×D₄×C₁₃	C₂³	1	4	yes	—
74	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
78	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
81	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
82	C₂×C₄²×C₁₃	—	2	2	no	—
83	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
84	C₁₃×#107	C₂³	1	4	yes	—
85	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
86	C₁₃×#103	C₂³	1	8	yes	—
87	C₁₃×#103	C₂³	1	16	yes	—
88	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
89	C₄×C₈×C₁₃	C₂³	1	4	yes	—
90	C₂×D₄×Q₁₆	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
92	C₂×Q₈×C₁₃	—	2	2	no	—
93	C₂×Q₈×C₁₃	—	2	16	no	—
94	C₂×Q₈×C₁₃	—	2	4	no	—
95	C₂×Q₈×C₁₃	—	2	4	no	—
96	C₂×Q₈×C₁₃	—	2	32	no	—
97	C₂×Q₈×C₁₃	—	2	8	no	—
98	C₂×Q₈×C₁₃	—	2	8	no	—
99	C₂×Q₈×C₁₃	—	4	16	no	—
100	C₂×Q₈×C₁₃	—	4	16	no	—
101	C₂×Q₈×C₁₃	—	4	32	no	—
102	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	—
103	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
104	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
105	C₂×D₄×C₁₃	Q₁₆	1	8	yes	direct product factor
106	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	4	no	—
110	C₂²×C₄×C₁₃	—	2	16	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₃	—	4	16	no	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₁₃×Q₁₆	—	2	32	no	—
121	C₁₃×Q₁₆	—	2	16	no	—
122	C₁₃×Q₁₆	—	4	8	no	—
123	C₁₃×Q₁₆	C₂×D₄	1	16	yes	direct product factor
124	C₂×C₈×C₁₃	—	2	4	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	16	no	—
127	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
128	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
129	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
130	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
131	C₁₃×C₄⋊C₄	—	2	8	no	—
132	C₁₃×C₄⋊C₄	—	2	8	no	—
133	C₁₃×C₄⋊C₄	—	2	8	no	—
134	C₁₃×C₄⋊C₄	—	2	16	no	—
135	C₁₃×C₄⋊C₄	—	2	2	no	—
136	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
137	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
138	C₁₃×C₂²⋊C₄	—	2	16	no	—
139	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
140	C₄²×C₁₃	—	2	8	no	—
141	C₄²×C₁₃	C₂×D₄	1	2	yes	—
142	C₄²×C₁₃	C₂⁴	1	2	yes	—
143	C₂³×Q₁₆	C₂×C₁₃	1	2	yes	complemented
144	C₂×D₄×Q₈	C₂×C₁₃	1	2	yes	—
145	D₄×Q₁₆	C₂×C₁₃	1	16	yes	direct product factor
146	C₂×#494	C₂×C₁₃	1	1	yes	characteristic, complemented
147	C₂×#467	C₂×C₁₃	1	2	yes	complemented
148	C₂×#462	C₂×C₁₃	1	2	yes	complemented
149	C₂×#451	C₂×C₁₃	1	4	yes	complemented
150	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
151	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic
152	C₂³×C₁₃	—	2	4	no	—
153	C₂³×C₁₃	—	2	4	no	—
154	C₂³×C₁₃	C₂×Q₁₆	1	8	yes	complemented
155	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
156	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
157	Q₈×C₁₃	—	2	8	no	—
158	Q₈×C₁₃	—	2	4	no	—
159	Q₈×C₁₃	—	2	8	no	—
160	Q₈×C₁₃	—	2	8	no	—
161	Q₈×C₁₃	—	4	32	no	—
162	Q₈×C₁₃	—	4	8	no	—
163	Q₈×C₁₃	C₂²×D₄	1	8	yes	—
164	D₄×C₁₃	C₂×Q₁₆	1	16	yes	direct product factor
165	C₂×C₄×C₁₃	—	2	4	no	—
166	C₂×C₄×C₁₃	—	2	8	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	2	8	no	—
170	C₂×C₄×C₁₃	—	2	4	no	—
171	C₂×C₄×C₁₃	—	2	4	no	—
172	C₂×C₄×C₁₃	—	2	4	no	—
173	C₂×C₄×C₁₃	—	2	8	no	—
174	C₂×C₄×C₁₃	—	4	32	no	—
175	C₂×C₄×C₁₃	—	4	8	no	—
176	C₂×C₄×C₁₃	—	4	4	no	—
177	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	complemented
178	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
179	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
180	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
182	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
183	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
184	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
185	C₈×C₁₃	—	2	4	no	—
186	C₈×C₁₃	—	2	2	no	—
187	C₈×C₁₃	C₂²×D₄	1	4	yes	—
188	C₂³×Q₈	C₂²×C₁₃	1	4	yes	—
189	C₂²×Q₁₆	—	2	16	no	—
190	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
191	C₂²×Q₁₆	C₂²×C₁₃	1	4	yes	—
192	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
193	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
194	C₂²×Q₁₆	C₂²×C₁₃	1	16	yes	complemented
195	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
196	D₄×Q₈	—	2	8	no	—
197	D₄×Q₈	C₂²×C₁₃	1	16	yes	—
198	C₂×C₄⋊Q₈	—	2	2	no	—
199	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
200	C₂×C₂²⋊Q₈	—	2	4	no	—
201	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	—
202	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
203	C₂×C₄×D₄	—	2	2	no	—
204	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
205	#494	C₂²×C₁₃	1	8	yes	complemented
206	#467	C₂²×C₁₃	1	16	yes	complemented
207	#462	C₂²×C₁₃	1	16	yes	complemented
208	#451	C₂²×C₁₃	1	32	yes	complemented
209	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	complemented
210	C₈×D₄	C₂²×C₁₃	1	8	yes	—
211	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
212	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×#103	C₂²×C₁₃	1	2	yes	—
214	C₂×#103	C₂²×C₁₃	1	4	yes	—
215	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
216	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
217	C₂²×C₁₃	—	2	4	no	—
218	C₂²×C₁₃	—	2	16	no	—
219	C₂²×C₁₃	—	2	4	no	—
220	C₂²×C₁₃	D₄²	1	2	yes	—
221	C₂²×C₁₃	C₂²×Q₁₆	1	2	yes	—
222	C₂²×C₁₃	C₂²×Q₁₆	1	8	yes	complemented
223	C₂²×C₁₃	#578	1	2	yes	—
224	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
225	C₄×C₁₃	—	2	4	no	—
226	C₄×C₁₃	—	2	8	no	—
227	C₄×C₁₃	—	2	2	no	—
228	C₄×C₁₃	—	4	8	no	—
229	C₄×C₁₃	—	4	4	no	—
230	C₄×C₁₃	D₄²	1	2	yes	—
231	C₄×C₁₃	C₂²×Q₁₆	1	4	yes	complemented
232	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
233	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
234	C₂²×Q₈	—	2	4	no	—
235	C₂²×Q₈	—	2	8	no	—
236	C₂²×Q₈	—	2	16	no	—
237	C₂²×Q₈	—	4	8	no	—
238	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
239	C₂²×Q₈	C₂³×C₁₃	1	16	yes	—
240	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
241	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
242	C₂³×C₄	—	2	4	no	—
243	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
244	C₂×Q₁₆	—	2	16	no	—
245	C₂×Q₁₆	—	2	64	no	—
246	C₂×Q₁₆	—	2	8	no	—
247	C₂×Q₁₆	—	4	4	no	—
248	C₂×Q₁₆	D₄×C₁₃	1	8	yes	direct product factor
249	C₂×Q₁₆	C₂³×C₁₃	1	16	yes	—
250	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
251	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
252	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
253	C₂²×C₈	—	2	8	no	—
254	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
255	C₂²×C₈	C₂³×C₁₃	1	8	yes	—
256	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
258	C₄⋊Q₈	—	2	16	no	—
259	C₄⋊Q₈	—	2	4	no	—
260	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
261	C₂²⋊Q₈	—	2	8	no	—
262	C₂²⋊Q₈	—	2	32	no	—
263	C₂²⋊Q₈	C₂³×C₁₃	1	16	yes	—
264	C₄×Q₈	—	2	4	no	—
265	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
266	C₄×D₄	—	2	16	no	—
267	C₄×D₄	D₄×C₁₃	1	4	yes	—
268	C₄×D₄	C₂³×C₁₃	1	4	yes	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	4	no	—
273	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
275	C₂×C₂²⋊C₄	—	2	4	no	—
276	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
279	#107	C₂³×C₁₃	1	4	yes	—
280	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
281	#103	C₂³×C₁₃	1	8	yes	—
282	#103	C₂³×C₁₃	1	16	yes	—
283	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
284	C₄×C₈	C₂³×C₁₃	1	4	yes	—
285	C₂×C₁₃	—	2	8	no	—
286	C₂×C₁₃	D₄×Q₁₆	1	4	yes	direct product factor
287	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
288	C₂×C₁₃	C₂³×Q₁₆	1	1	yes	characteristic
289	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
290	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	16	no	—
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	2	4	no	—
295	C₂×Q₈	—	2	32	no	—
296	C₂×Q₈	—	2	8	no	—
297	C₂×Q₈	—	2	8	no	—
298	C₂×Q₈	—	4	16	no	—
299	C₂×Q₈	—	4	16	no	—
300	C₂×Q₈	—	4	32	no	—
301	C₂×Q₈	C₂×D₄×C₁₃	1	8	yes	—
302	C₂×Q₈	C₂⁴×C₁₃	1	8	yes	—
303	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
304	C₂×D₄	C₁₃×Q₁₆	1	8	yes	direct product factor
305	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	2	4	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	16	no	—
312	C₂²×C₄	—	4	16	no	—
313	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
316	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
318	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
319	Q₁₆	—	2	32	no	—
320	Q₁₆	—	2	16	no	—
321	Q₁₆	—	4	8	no	—
322	Q₁₆	C₂×D₄×C₁₃	1	16	yes	direct product factor
323	C₂×C₈	—	2	4	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	16	no	—
326	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
327	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
328	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
329	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄⋊C₄	—	2	8	no	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	2	16	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
336	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
337	C₂²⋊C₄	—	2	16	no	—
338	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
339	C₄²	—	2	8	no	—
340	C₄²	C₂×D₄×C₁₃	1	2	yes	—
341	C₄²	C₂⁴×C₁₃	1	2	yes	—
342	C₁₃	C₂×D₄×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
343	C₂³	—	2	4	no	—
344	C₂³	—	2	4	no	—
345	C₂³	C₂×C₁₃×Q₁₆	1	8	yes	complemented
346	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
347	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
348	Q₈	—	2	8	no	—
349	Q₈	—	2	4	no	—
350	Q₈	—	2	8	no	—
351	Q₈	—	2	8	no	—
352	Q₈	—	4	32	no	—
353	Q₈	—	4	8	no	—
354	Q₈	C₂²×D₄×C₁₃	1	8	yes	—
355	D₄	C₂×C₁₃×Q₁₆	1	16	yes	direct product factor
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	8	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	8	no	—
365	C₂×C₄	—	4	32	no	—
366	C₂×C₄	—	4	8	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	C₂×C₁₃×Q₁₆	1	4	yes	complemented
369	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
370	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
371	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
372	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
373	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
374	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
375	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
376	C₈	—	2	4	no	—
377	C₈	—	2	2	no	—
378	C₈	C₂²×D₄×C₁₃	1	4	yes	—
379	C₂²	—	2	16	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	4	no	—
382	C₂²	D₄²×C₁₃	1	2	yes	—
383	C₂²	C₂²×C₁₃×Q₁₆	1	2	yes	—
384	C₂²	C₂²×C₁₃×Q₁₆	1	8	yes	complemented
385	C₂²	C₁₃×#578	1	2	yes	—
386	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
387	C₄	—	2	2	no	—
388	C₄	—	2	4	no	—
389	C₄	—	2	8	no	—
390	C₄	—	4	4	no	—
391	C₄	—	4	8	no	—
392	C₄	D₄²×C₁₃	1	2	yes	—
393	C₄	C₂²×C₁₃×Q₁₆	1	4	yes	complemented
394	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
395	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
396	C₂	—	2	8	no	—
397	C₂	D₄×C₁₃×Q₁₆	1	4	yes	direct product factor
398	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
399	C₂	C₂³×C₁₃×Q₁₆	1	1	yes	characteristic
400	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₁₃×Q₁₆	C₂	semidirect
3. D₄×C₁₃×Q₁₆	C₂	direct (N × H)
4. C₂×C₁₃×#494	C₂	semidirect
5. C₂×C₁₃×#467	C₂	semidirect
6. C₂×C₁₃×#462	C₂	semidirect
7. C₂×C₁₃×#451	C₂	semidirect
8. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
16. C₂²×C₁₃×Q₁₆	C₂²	semidirect
27. C₁₃×#494	C₂²	semidirect
28. C₁₃×#467	C₂²	semidirect
29. C₁₃×#462	C₂²	semidirect
30. C₁₃×#451	C₂²	semidirect
31. C₄×C₁₃×Q₁₆	C₂²	semidirect
53. C₂×C₁₃×Q₁₆	D₄	direct (N × H)
90. C₂×D₄×Q₁₆	C₁₃	direct (N × H)
105. C₂×D₄×C₁₃	Q₁₆	direct (N × H)
123. C₁₃×Q₁₆	C₂×D₄	direct (N × H)
143. C₂³×Q₁₆	C₂×C₁₃	semidirect
145. D₄×Q₁₆	C₂×C₁₃	direct (N × H)
146. C₂×#494	C₂×C₁₃	semidirect
147. C₂×#467	C₂×C₁₃	semidirect
148. C₂×#462	C₂×C₁₃	semidirect
149. C₂×#451	C₂×C₁₃	semidirect
150. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
154. C₂³×C₁₃	C₂×Q₁₆	semidirect
164. D₄×C₁₃	C₂×Q₁₆	direct (N × H)
177. C₂×C₄×C₁₃	C₂×Q₁₆	semidirect
194. C₂²×Q₁₆	C₂²×C₁₃	semidirect
205. #494	C₂²×C₁₃	semidirect
206. #467	C₂²×C₁₃	semidirect
207. #462	C₂²×C₁₃	semidirect
208. #451	C₂²×C₁₃	semidirect
209. C₄×Q₁₆	C₂²×C₁₃	semidirect
222. C₂²×C₁₃	C₂²×Q₁₆	semidirect
231. C₄×C₁₃	C₂²×Q₁₆	semidirect
248. C₂×Q₁₆	D₄×C₁₃	direct (N × H)
286. C₂×C₁₃	D₄×Q₁₆	direct (N × H)
304. C₂×D₄	C₁₃×Q₁₆	direct (N × H)
322. Q₁₆	C₂×D₄×C₁₃	direct (N × H)
342. C₁₃	C₂×D₄×Q₁₆	direct (N × H)
345. C₂³	C₂×C₁₃×Q₁₆	semidirect
355. D₄	C₂×C₁₃×Q₁₆	direct (N × H)
368. C₂×C₄	C₂×C₁₃×Q₁₆	semidirect
384. C₂²	C₂²×C₁₃×Q₁₆	semidirect
393. C₄	C₂²×C₁₃×Q₁₆	semidirect
397. C₂	D₄×C₁₃×Q₁₆	direct (N × H)

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×D₄×Q₈×C₁₃	2
D₄×C₁₃×Q₁₆	2
C₂×C₁₃×#494	2
C₂×C₁₃×#467	2
C₂×C₁₃×#462	2
C₂×C₁₃×#451	2
C₂×C₄×C₁₃×Q₁₆	2
C₂×C₈×D₄×C₁₃	2
C₂×D₄×Q₁₆	13

Subgroups — C2×D4×C13×Q16 #15747385

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×C₁₃×Q₁₆ #15747385