Subgroups — C₂×D₄×C₁₃×SD₁₆ #15747380

Order 3328.

3226 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
2	C₂×D₄×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic
4	D₄×C₁₃×SD₁₆	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#465	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#448	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#450	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×Q₈×C₁₃	C₂²	1	2	yes	complemented
14	C₂³×D₄×C₁₃	—	2	1	no	—
15	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
16	C₂²×C₁₃×SD₁₆	—	2	16	no	—
17	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
20	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
21	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	complemented
22	C₂²×C₁₃×SD₁₆	C₂²	1	16	yes	complemented
23	C₂³×C₈×C₁₃	C₂²	1	2	yes	complemented
24	D₄×Q₈×C₁₃	—	2	4	no	—
25	D₄×Q₈×C₁₃	C₂²	1	8	yes	complemented
26	D₄²×C₁₃	—	2	4	no	—
27	D₄²×C₁₃	C₂²	1	8	yes	—
28	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
29	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
32	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
33	C₂×C₁₃×#121	—	2	1	no	—
34	C₂×C₁₃×#121	C₂²	1	2	yes	—
35	C₂×C₁₃×#120	—	2	2	no	—
36	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₄×D₄×C₁₃	—	2	1	no	—
38	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#492	C₂²	1	8	yes	complemented
41	C₁₃×#465	C₂²	1	16	yes	complemented
42	C₁₃×#461	C₂²	1	8	yes	complemented
43	C₁₃×#460	C₂²	1	8	yes	complemented
44	C₁₃×#450	C₂²	1	16	yes	complemented
45	C₁₃×#448	C₂²	1	16	yes	complemented
46	C₄×C₁₃×SD₁₆	C₂²	1	8	yes	complemented
47	C₈×D₄×C₁₃	C₂²	1	8	yes	complemented
48	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
51	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
54	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	complemented
55	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
56	C₂⁵×C₁₃	—	2	2	no	—
57	C₂²×Q₈×C₁₃	—	2	2	no	—
58	C₂²×Q₈×C₁₃	—	2	4	no	—
59	C₂²×Q₈×C₁₃	—	2	8	no	—
60	C₂²×Q₈×C₁₃	—	4	4	no	—
61	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
62	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	C₂³	1	8	yes	complemented
64	C₂²×D₄×C₁₃	—	2	8	no	—
65	C₂²×D₄×C₁₃	—	2	2	no	—
66	C₂²×D₄×C₁₃	—	2	8	no	—
67	C₂²×D₄×C₁₃	—	2	2	no	—
68	C₂²×D₄×C₁₃	—	2	1	no	—
69	C₂²×D₄×C₁₃	—	2	4	no	—
70	C₂²×D₄×C₁₃	—	2	1	no	—
71	C₂²×D₄×C₁₃	—	4	4	no	—
72	C₂²×D₄×C₁₃	—	4	8	no	—
73	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
74	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
75	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
76	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	—	2	2	no	—
78	C₂³×C₄×C₁₃	—	2	1	no	—
79	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
80	C₂×C₁₃×SD₁₆	—	2	8	no	—
81	C₂×C₁₃×SD₁₆	—	2	8	no	—
82	C₂×C₁₃×SD₁₆	—	2	64	no	—
83	C₂×C₁₃×SD₁₆	—	2	8	no	—
84	C₂×C₁₃×SD₁₆	—	4	4	no	—
85	C₂×C₁₃×SD₁₆	D₄	1	8	yes	direct product factor
86	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
87	C₂×C₁₃×SD₁₆	C₂³	1	4	yes	—
88	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	complemented
89	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	complemented
90	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	complemented
91	C₂²×C₈×C₁₃	—	2	8	no	—
92	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
93	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
94	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₁₃	C₂³	1	8	yes	complemented
96	C₁₃×C₄⋊Q₈	—	2	8	no	—
97	C₁₃×C₄⋊Q₈	—	2	2	no	—
98	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	complemented
99	C₁₃×#127	—	2	2	no	—
100	C₁₃×#127	C₂³	1	4	yes	—
101	C₁₃×C₂²⋊Q₈	—	2	4	no	—
102	C₁₃×C₂²⋊Q₈	—	2	16	no	—
103	C₁₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
104	C₁₃×#121	—	2	4	no	—
105	C₁₃×#121	—	2	8	no	—
106	C₁₃×#121	C₂³	1	8	yes	—
107	C₁₃×#120	—	2	16	no	—
108	C₄×Q₈×C₁₃	—	2	2	no	—
109	C₄×Q₈×C₁₃	C₂³	1	4	yes	complemented
110	C₄×D₄×C₁₃	—	2	8	no	—
111	C₄×D₄×C₁₃	—	2	2	no	—
112	C₄×D₄×C₁₃	D₄	1	4	yes	—
113	C₄×D₄×C₁₃	C₂³	1	4	yes	—
114	C₄×D₄×C₁₃	C₂³	1	4	yes	—
115	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
119	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
120	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
123	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
124	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
125	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
126	C₂×C₄²×C₁₃	—	2	1	no	—
127	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
128	C₁₃×#106	C₂³	1	4	yes	complemented
129	C₁₃×C₄⋊C₈	C₂³	1	4	yes	complemented
130	C₁₃×#103	C₂³	1	4	yes	complemented
131	C₁₃×#103	C₂³	1	8	yes	complemented
132	C₁₃×#102	C₂³	1	4	yes	—
133	C₁₃×#102	C₂³	1	8	yes	complemented
134	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	complemented
135	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
136	C₂×D₄×SD₁₆	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
137	C₂⁴×C₁₃	—	2	1	no	—
138	C₂⁴×C₁₃	—	2	2	no	—
139	C₂⁴×C₁₃	—	2	8	no	—
140	C₂⁴×C₁₃	—	4	8	no	—
141	C₂⁴×C₁₃	—	4	8	no	—
142	C₂⁴×C₁₃	—	8	4	no	—
143	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	—	2	8	no	—
147	C₂×Q₈×C₁₃	—	2	2	no	—
148	C₂×Q₈×C₁₃	—	2	16	no	—
149	C₂×Q₈×C₁₃	—	2	4	no	—
150	C₂×Q₈×C₁₃	—	2	4	no	—
151	C₂×Q₈×C₁₃	—	4	8	no	—
152	C₂×Q₈×C₁₃	—	4	8	no	—
153	C₂×Q₈×C₁₃	—	4	16	no	—
154	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	complemented
155	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
156	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
157	C₂×D₄×C₁₃	—	2	16	no	—
158	C₂×D₄×C₁₃	—	2	8	no	—
159	C₂×D₄×C₁₃	—	2	1	no	—
160	C₂×D₄×C₁₃	—	2	4	no	—
161	C₂×D₄×C₁₃	—	2	8	no	—
162	C₂×D₄×C₁₃	—	2	2	no	—
163	C₂×D₄×C₁₃	—	2	4	no	—
164	C₂×D₄×C₁₃	—	2	4	no	—
165	C₂×D₄×C₁₃	—	2	2	no	—
166	C₂×D₄×C₁₃	—	2	4	no	—
167	C₂×D₄×C₁₃	—	4	8	no	—
168	C₂×D₄×C₁₃	—	4	16	no	—
169	C₂×D₄×C₁₃	—	4	8	no	—
170	C₂×D₄×C₁₃	—	4	8	no	—
171	C₂×D₄×C₁₃	—	4	32	no	—
172	C₂×D₄×C₁₃	—	4	4	no	—
173	C₂×D₄×C₁₃	—	8	2	no	—
174	C₂×D₄×C₁₃	SD₁₆	1	8	yes	direct product factor
175	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
176	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
177	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
178	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₃	—	2	1	no	—
180	C₂²×C₄×C₁₃	—	2	4	no	—
181	C₂²×C₄×C₁₃	—	2	4	no	—
182	C₂²×C₄×C₁₃	—	2	8	no	—
183	C₂²×C₄×C₁₃	—	2	1	no	—
184	C₂²×C₄×C₁₃	—	2	1	no	—
185	C₂²×C₄×C₁₃	—	2	2	no	—
186	C₂²×C₄×C₁₃	—	2	4	no	—
187	C₂²×C₄×C₁₃	—	4	8	no	—
188	C₂²×C₄×C₁₃	—	4	4	no	—
189	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
190	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
192	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
195	C₁₃×SD₁₆	—	2	16	no	—
196	C₁₃×SD₁₆	—	2	16	no	—
197	C₁₃×SD₁₆	—	2	16	no	—
198	C₁₃×SD₁₆	—	4	8	no	—
199	C₁₃×SD₁₆	C₂×D₄	1	16	yes	direct product factor
200	C₂×C₈×C₁₃	—	2	4	no	—
201	C₂×C₈×C₁₃	—	2	2	no	—
202	C₂×C₈×C₁₃	—	2	16	no	—
203	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	complemented
204	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
205	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
206	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
207	C₁₃×C₄⋊C₄	—	2	4	no	—
208	C₁₃×C₄⋊C₄	—	2	4	no	—
209	C₁₃×C₄⋊C₄	—	2	4	no	—
210	C₁₃×C₄⋊C₄	—	2	8	no	—
211	C₁₃×C₄⋊C₄	—	2	1	no	—
212	C₁₃×C₄⋊C₄	—	2	1	no	—
213	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
214	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
215	C₁₃×C₄⋊C₄	C₂⁴	1	2	yes	—
216	C₁₃×C₂²⋊C₄	—	2	8	no	—
217	C₁₃×C₂²⋊C₄	—	2	4	no	—
218	C₁₃×C₂²⋊C₄	—	2	8	no	—
219	C₁₃×C₂²⋊C₄	C₂×D₄	1	8	yes	—
220	C₄²×C₁₃	—	2	4	no	—
221	C₄²×C₁₃	C₂×D₄	1	2	yes	—
222	C₄²×C₁₃	C₂⁴	1	2	yes	—
223	C₂³×SD₁₆	C₂×C₁₃	1	2	yes	complemented
224	C₂×D₄×Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
225	C₂×D₄²	C₂×C₁₃	1	1	yes	characteristic
226	D₄×SD₁₆	C₂×C₁₃	1	16	yes	direct product factor
227	C₂×#492	C₂×C₁₃	1	1	yes	characteristic, complemented
228	C₂×#465	C₂×C₁₃	1	2	yes	complemented
229	C₂×#460	C₂×C₁₃	1	1	yes	characteristic, complemented
230	C₂×#461	C₂×C₁₃	1	1	yes	characteristic, complemented
231	C₂×#448	C₂×C₁₃	1	2	yes	complemented
232	C₂×#450	C₂×C₁₃	1	2	yes	complemented
233	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
234	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
235	C₂³×C₁₃	—	2	4	no	—
236	C₂³×C₁₃	—	2	4	no	—
237	C₂³×C₁₃	—	2	4	no	—
238	C₂³×C₁₃	—	2	2	no	—
239	C₂³×C₁₃	—	2	4	no	—
240	C₂³×C₁₃	—	4	16	no	—
241	C₂³×C₁₃	—	4	2	no	—
242	C₂³×C₁₃	—	4	2	no	—
243	C₂³×C₁₃	—	4	4	no	—
244	C₂³×C₁₃	—	4	4	no	—
245	C₂³×C₁₃	—	4	16	no	—
246	C₂³×C₁₃	—	4	4	no	—
247	C₂³×C₁₃	—	8	8	no	—
248	C₂³×C₁₃	—	8	32	no	—
249	C₂³×C₁₃	C₂×SD₁₆	1	8	yes	complemented
250	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
251	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
252	Q₈×C₁₃	—	2	4	no	—
253	Q₈×C₁₃	—	2	2	no	—
254	Q₈×C₁₃	—	2	4	no	—
255	Q₈×C₁₃	—	2	4	no	—
256	Q₈×C₁₃	—	4	16	no	—
257	Q₈×C₁₃	—	4	4	no	—
258	Q₈×C₁₃	C₂²×D₄	1	4	yes	complemented
259	D₄×C₁₃	—	2	4	no	—
260	D₄×C₁₃	—	2	4	no	—
261	D₄×C₁₃	—	2	2	no	—
262	D₄×C₁₃	—	2	4	no	—
263	D₄×C₁₃	—	4	16	no	—
264	D₄×C₁₃	—	4	16	no	—
265	D₄×C₁₃	—	4	4	no	—
266	D₄×C₁₃	—	4	8	no	—
267	D₄×C₁₃	—	8	4	no	—
268	D₄×C₁₃	C₂×SD₁₆	1	16	yes	direct product factor
269	D₄×C₁₃	C₂²×D₄	1	4	yes	—
270	C₂×C₄×C₁₃	—	2	4	no	—
271	C₂×C₄×C₁₃	—	2	4	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	2	no	—
274	C₂×C₄×C₁₃	—	2	8	no	—
275	C₂×C₄×C₁₃	—	2	4	no	—
276	C₂×C₄×C₁₃	—	2	4	no	—
277	C₂×C₄×C₁₃	—	2	2	no	—
278	C₂×C₄×C₁₃	—	2	2	no	—
279	C₂×C₄×C₁₃	—	2	4	no	—
280	C₂×C₄×C₁₃	—	4	16	no	—
281	C₂×C₄×C₁₃	—	4	4	no	—
282	C₂×C₄×C₁₃	—	4	2	no	—
283	C₂×C₄×C₁₃	—	4	2	no	—
284	C₂×C₄×C₁₃	—	4	8	no	—
285	C₂×C₄×C₁₃	C₂×SD₁₆	1	4	yes	complemented
286	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
287	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
288	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
290	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
291	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
292	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
293	C₈×C₁₃	—	2	4	no	—
294	C₈×C₁₃	—	2	2	no	—
295	C₈×C₁₃	C₂²×D₄	1	4	yes	complemented
296	C₂³×Q₈	C₂²×C₁₃	1	2	yes	complemented
297	C₂³×D₄	—	2	1	no	—
298	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
299	C₂²×SD₁₆	—	2	16	no	—
300	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
301	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
302	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
303	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
304	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	complemented
305	C₂²×SD₁₆	C₂²×C₁₃	1	16	yes	complemented
306	C₂³×C₈	C₂²×C₁₃	1	2	yes	complemented
307	D₄×Q₈	—	2	4	no	—
308	D₄×Q₈	C₂²×C₁₃	1	8	yes	complemented
309	D₄²	—	2	4	no	—
310	D₄²	C₂²×C₁₃	1	8	yes	—
311	C₂×C₄⋊Q₈	—	2	1	no	—
312	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
313	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
314	C₂×C₂²⋊Q₈	—	2	2	no	—
315	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
316	C₂×#121	—	2	1	no	—
317	C₂×#121	C₂²×C₁₃	1	2	yes	—
318	C₂×#120	—	2	2	no	—
319	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
320	C₂×C₄×D₄	—	2	1	no	—
321	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
323	#492	C₂²×C₁₃	1	8	yes	complemented
324	#465	C₂²×C₁₃	1	16	yes	complemented
325	#461	C₂²×C₁₃	1	8	yes	complemented
326	#460	C₂²×C₁₃	1	8	yes	complemented
327	#450	C₂²×C₁₃	1	16	yes	complemented
328	#448	C₂²×C₁₃	1	16	yes	complemented
329	C₄×SD₁₆	C₂²×C₁₃	1	8	yes	complemented
330	C₈×D₄	C₂²×C₁₃	1	8	yes	complemented
331	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic, complemented
332	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
333	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic, complemented
334	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
335	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
337	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	complemented
338	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
339	C₂²×C₁₃	—	2	4	no	—
340	C₂²×C₁₃	—	2	16	no	—
341	C₂²×C₁₃	—	2	4	no	—
342	C₂²×C₁₃	—	2	4	no	—
343	C₂²×C₁₃	—	4	8	no	—
344	C₂²×C₁₃	—	4	2	no	—
345	C₂²×C₁₃	—	4	2	no	—
346	C₂²×C₁₃	—	4	4	no	—
347	C₂²×C₁₃	—	4	4	no	—
348	C₂²×C₁₃	—	4	4	no	—
349	C₂²×C₁₃	—	8	32	no	—
350	C₂²×C₁₃	—	8	8	no	—
351	C₂²×C₁₃	D₄²	1	2	yes	—
352	C₂²×C₁₃	C₂²×SD₁₆	1	2	yes	—
353	C₂²×C₁₃	C₂²×SD₁₆	1	8	yes	complemented
354	C₂²×C₁₃	#577	1	2	yes	—
355	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
356	C₄×C₁₃	—	2	4	no	—
357	C₄×C₁₃	—	2	4	no	—
358	C₄×C₁₃	—	2	2	no	—
359	C₄×C₁₃	—	4	4	no	—
360	C₄×C₁₃	—	4	2	no	—
361	C₄×C₁₃	—	4	2	no	—
362	C₄×C₁₃	D₄²	1	2	yes	—
363	C₄×C₁₃	C₂²×SD₁₆	1	4	yes	complemented
364	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
365	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
366	C₂⁵	—	2	2	no	—
367	C₂²×Q₈	—	2	2	no	—
368	C₂²×Q₈	—	2	4	no	—
369	C₂²×Q₈	—	2	8	no	—
370	C₂²×Q₈	—	4	4	no	—
371	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
372	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
373	C₂²×Q₈	C₂³×C₁₃	1	8	yes	complemented
374	C₂²×D₄	—	2	8	no	—
375	C₂²×D₄	—	2	2	no	—
376	C₂²×D₄	—	2	8	no	—
377	C₂²×D₄	—	2	2	no	—
378	C₂²×D₄	—	2	1	no	—
379	C₂²×D₄	—	2	4	no	—
380	C₂²×D₄	—	2	1	no	—
381	C₂²×D₄	—	4	4	no	—
382	C₂²×D₄	—	4	8	no	—
383	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
384	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
385	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
386	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
387	C₂³×C₄	—	2	2	no	—
388	C₂³×C₄	—	2	1	no	—
389	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
390	C₂×SD₁₆	—	2	8	no	—
391	C₂×SD₁₆	—	2	8	no	—
392	C₂×SD₁₆	—	2	64	no	—
393	C₂×SD₁₆	—	2	8	no	—
394	C₂×SD₁₆	—	4	4	no	—
395	C₂×SD₁₆	D₄×C₁₃	1	8	yes	direct product factor
396	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
397	C₂×SD₁₆	C₂³×C₁₃	1	4	yes	—
398	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	complemented
399	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	complemented
400	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	complemented
401	C₂²×C₈	—	2	8	no	—
402	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
403	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
404	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
405	C₂²×C₈	C₂³×C₁₃	1	8	yes	complemented
406	C₄⋊Q₈	—	2	8	no	—
407	C₄⋊Q₈	—	2	2	no	—
408	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	complemented
409	#127	—	2	2	no	—
410	#127	C₂³×C₁₃	1	4	yes	—
411	C₂²⋊Q₈	—	2	4	no	—
412	C₂²⋊Q₈	—	2	16	no	—
413	C₂²⋊Q₈	C₂³×C₁₃	1	8	yes	complemented
414	#121	—	2	4	no	—
415	#121	—	2	8	no	—
416	#121	C₂³×C₁₃	1	8	yes	—
417	#120	—	2	16	no	—
418	C₄×Q₈	—	2	2	no	—
419	C₄×Q₈	C₂³×C₁₃	1	4	yes	complemented
420	C₄×D₄	—	2	8	no	—
421	C₄×D₄	—	2	2	no	—
422	C₄×D₄	D₄×C₁₃	1	4	yes	—
423	C₄×D₄	C₂³×C₁₃	1	4	yes	—
424	C₄×D₄	C₂³×C₁₃	1	4	yes	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	2	no	—
429	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
432	C₂×C₂²⋊C₄	—	2	2	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	2	no	—
435	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
436	C₂×C₄²	—	2	1	no	—
437	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
438	#106	C₂³×C₁₃	1	4	yes	complemented
439	C₄⋊C₈	C₂³×C₁₃	1	4	yes	complemented
440	#103	C₂³×C₁₃	1	4	yes	complemented
441	#103	C₂³×C₁₃	1	8	yes	complemented
442	#102	C₂³×C₁₃	1	4	yes	—
443	#102	C₂³×C₁₃	1	8	yes	complemented
444	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	complemented
445	C₄×C₈	C₂³×C₁₃	1	4	yes	complemented
446	C₂×C₁₃	—	2	8	no	—
447	C₂×C₁₃	—	4	4	no	—
448	C₂×C₁₃	—	8	4	no	—
449	C₂×C₁₃	D₄×SD₁₆	1	4	yes	direct product factor
450	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
451	C₂×C₁₃	C₂³×SD₁₆	1	1	yes	characteristic
452	C₂×C₁₃	C₂×#577	1	1	yes	characteristic
453	C₂⁴	—	2	1	no	—
454	C₂⁴	—	2	2	no	—
455	C₂⁴	—	2	8	no	—
456	C₂⁴	—	4	8	no	—
457	C₂⁴	—	4	8	no	—
458	C₂⁴	—	8	4	no	—
459	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	2	no	—
462	C₂×Q₈	—	2	8	no	—
463	C₂×Q₈	—	2	2	no	—
464	C₂×Q₈	—	2	16	no	—
465	C₂×Q₈	—	2	4	no	—
466	C₂×Q₈	—	2	4	no	—
467	C₂×Q₈	—	4	8	no	—
468	C₂×Q₈	—	4	8	no	—
469	C₂×Q₈	—	4	16	no	—
470	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	complemented
471	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
472	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
473	C₂×D₄	—	2	16	no	—
474	C₂×D₄	—	2	8	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	4	no	—
477	C₂×D₄	—	2	8	no	—
478	C₂×D₄	—	2	2	no	—
479	C₂×D₄	—	2	4	no	—
480	C₂×D₄	—	2	4	no	—
481	C₂×D₄	—	2	2	no	—
482	C₂×D₄	—	2	4	no	—
483	C₂×D₄	—	4	8	no	—
484	C₂×D₄	—	4	16	no	—
485	C₂×D₄	—	4	8	no	—
486	C₂×D₄	—	4	8	no	—
487	C₂×D₄	—	4	32	no	—
488	C₂×D₄	—	4	4	no	—
489	C₂×D₄	—	8	2	no	—
490	C₂×D₄	C₁₃×SD₁₆	1	8	yes	direct product factor
491	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
492	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
493	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
494	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	4	no	—
497	C₂²×C₄	—	2	4	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	8	no	—
502	C₂²×C₄	—	2	4	no	—
503	C₂²×C₄	—	4	8	no	—
504	C₂²×C₄	—	4	4	no	—
505	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
507	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
508	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
509	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
510	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
511	SD₁₆	—	2	16	no	—
512	SD₁₆	—	2	16	no	—
513	SD₁₆	—	2	16	no	—
514	SD₁₆	—	4	8	no	—
515	SD₁₆	C₂×D₄×C₁₃	1	16	yes	direct product factor
516	C₂×C₈	—	2	4	no	—
517	C₂×C₈	—	2	2	no	—
518	C₂×C₈	—	2	16	no	—
519	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	complemented
520	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
521	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
522	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
523	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	—	2	4	no	—
525	C₄⋊C₄	—	2	4	no	—
526	C₄⋊C₄	—	2	8	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
530	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
531	C₄⋊C₄	C₂⁴×C₁₃	1	2	yes	—
532	C₂²⋊C₄	—	2	8	no	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	2	8	no	—
535	C₂²⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
536	C₄²	—	2	4	no	—
537	C₄²	C₂×D₄×C₁₃	1	2	yes	—
538	C₄²	C₂⁴×C₁₃	1	2	yes	—
539	C₁₃	C₂×D₄×SD₁₆	1	1	yes	characteristic, direct product factor, Sylow
540	C₂³	—	2	4	no	—
541	C₂³	—	2	4	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	4	no	—
545	C₂³	—	4	16	no	—
546	C₂³	—	4	2	no	—
547	C₂³	—	4	2	no	—
548	C₂³	—	4	4	no	—
549	C₂³	—	4	4	no	—
550	C₂³	—	4	16	no	—
551	C₂³	—	4	4	no	—
552	C₂³	—	8	8	no	—
553	C₂³	—	8	32	no	—
554	C₂³	C₂×C₁₃×SD₁₆	1	8	yes	complemented
555	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
556	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
557	Q₈	—	2	4	no	—
558	Q₈	—	2	2	no	—
559	Q₈	—	2	4	no	—
560	Q₈	—	2	4	no	—
561	Q₈	—	4	16	no	—
562	Q₈	—	4	4	no	—
563	Q₈	C₂²×D₄×C₁₃	1	4	yes	complemented
564	D₄	—	2	4	no	—
565	D₄	—	2	4	no	—
566	D₄	—	2	2	no	—
567	D₄	—	2	4	no	—
568	D₄	—	4	16	no	—
569	D₄	—	4	16	no	—
570	D₄	—	4	4	no	—
571	D₄	—	4	8	no	—
572	D₄	—	8	4	no	—
573	D₄	C₂×C₁₃×SD₁₆	1	16	yes	direct product factor
574	D₄	C₂²×D₄×C₁₃	1	4	yes	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	8	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	4	16	no	—
586	C₂×C₄	—	4	4	no	—
587	C₂×C₄	—	4	2	no	—
588	C₂×C₄	—	4	2	no	—
589	C₂×C₄	—	4	8	no	—
590	C₂×C₄	C₂×C₁₃×SD₁₆	1	4	yes	complemented
591	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
592	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
593	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
594	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
595	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
596	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
597	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
598	C₈	—	2	4	no	—
599	C₈	—	2	2	no	—
600	C₈	C₂²×D₄×C₁₃	1	4	yes	complemented
601	C₂²	—	2	16	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	2	4	no	—
604	C₂²	—	2	4	no	—
605	C₂²	—	4	8	no	—
606	C₂²	—	4	2	no	—
607	C₂²	—	4	2	no	—
608	C₂²	—	4	4	no	—
609	C₂²	—	4	4	no	—
610	C₂²	—	4	4	no	—
611	C₂²	—	8	32	no	—
612	C₂²	—	8	8	no	—
613	C₂²	D₄²×C₁₃	1	2	yes	—
614	C₂²	C₂²×C₁₃×SD₁₆	1	2	yes	—
615	C₂²	C₂²×C₁₃×SD₁₆	1	8	yes	complemented
616	C₂²	C₁₃×#577	1	2	yes	—
617	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
618	C₄	—	2	2	no	—
619	C₄	—	2	4	no	—
620	C₄	—	2	4	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	4	no	—
624	C₄	D₄²×C₁₃	1	2	yes	—
625	C₄	C₂²×C₁₃×SD₁₆	1	4	yes	complemented
626	C₄	C₂³×D₄×C₁₃	1	1	yes	characteristic
627	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
628	C₂	—	2	8	no	—
629	C₂	—	4	4	no	—
630	C₂	—	8	4	no	—
631	C₂	D₄×C₁₃×SD₁₆	1	4	yes	direct product factor
632	C₂	C₂×D₄²×C₁₃	1	1	yes	characteristic
633	C₂	C₂³×C₁₃×SD₁₆	1	1	yes	characteristic
634	C₂	C₂×C₁₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂×D₄²×C₁₃	C₂
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×SD₁₆	C₂	semidirect
2. C₂×D₄×Q₈×C₁₃	C₂	semidirect
4. D₄×C₁₃×SD₁₆	C₂	direct (N × H)
5. C₂×C₁₃×#492	C₂	semidirect
6. C₂×C₁₃×#465	C₂	semidirect
7. C₂×C₁₃×#460	C₂	semidirect
8. C₂×C₁₃×#461	C₂	semidirect
9. C₂×C₁₃×#448	C₂	semidirect
10. C₂×C₁₃×#450	C₂	semidirect
11. C₂×C₄×C₁₃×SD₁₆	C₂	semidirect
12. C₂×C₈×D₄×C₁₃	C₂	semidirect
13. C₂³×Q₈×C₁₃	C₂²	semidirect
19. C₂²×C₁₃×SD₁₆	C₂²	semidirect
20. C₂²×C₁₃×SD₁₆	C₂²	semidirect
21. C₂²×C₁₃×SD₁₆	C₂²	semidirect
22. C₂²×C₁₃×SD₁₆	C₂²	semidirect
23. C₂³×C₈×C₁₃	C₂²	semidirect
25. D₄×Q₈×C₁₃	C₂²	semidirect
29. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
32. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
36. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
40. C₁₃×#492	C₂²	semidirect
41. C₁₃×#465	C₂²	semidirect
42. C₁₃×#461	C₂²	semidirect
43. C₁₃×#460	C₂²	semidirect
44. C₁₃×#450	C₂²	semidirect
45. C₁₃×#448	C₂²	semidirect
46. C₄×C₁₃×SD₁₆	C₂²	semidirect
47. C₈×D₄×C₁₃	C₂²	semidirect
48. C₂×C₁₃×#106	C₂²	semidirect
49. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
50. C₂×C₁₃×#103	C₂²	semidirect
51. C₂×C₁₃×#103	C₂²	semidirect
53. C₂×C₁₃×#102	C₂²	semidirect
54. C₂×C₁₃×C₂²⋊C₈	C₂²	semidirect
55. C₂×C₄×C₈×C₁₃	C₂²	semidirect
63. C₂²×Q₈×C₁₃	C₂³	semidirect
85. C₂×C₁₃×SD₁₆	D₄	direct (N × H)
88. C₂×C₁₃×SD₁₆	C₂³	semidirect
89. C₂×C₁₃×SD₁₆	C₂³	semidirect
90. C₂×C₁₃×SD₁₆	C₂³	semidirect
95. C₂²×C₈×C₁₃	C₂³	semidirect
98. C₁₃×C₄⋊Q₈	C₂³	semidirect
103. C₁₃×C₂²⋊Q₈	C₂³	semidirect
109. C₄×Q₈×C₁₃	C₂³	semidirect
128. C₁₃×#106	C₂³	semidirect
129. C₁₃×C₄⋊C₈	C₂³	semidirect
130. C₁₃×#103	C₂³	semidirect
131. C₁₃×#103	C₂³	semidirect
133. C₁₃×#102	C₂³	semidirect
134. C₁₃×C₂²⋊C₈	C₂³	semidirect
135. C₄×C₈×C₁₃	C₂³	semidirect
136. C₂×D₄×SD₁₆	C₁₃	direct (N × H)
154. C₂×Q₈×C₁₃	C₂×D₄	semidirect
174. C₂×D₄×C₁₃	SD₁₆	direct (N × H)
199. C₁₃×SD₁₆	C₂×D₄	direct (N × H)
203. C₂×C₈×C₁₃	C₂×D₄	semidirect
223. C₂³×SD₁₆	C₂×C₁₃	semidirect
224. C₂×D₄×Q₈	C₂×C₁₃	semidirect
226. D₄×SD₁₆	C₂×C₁₃	direct (N × H)
227. C₂×#492	C₂×C₁₃	semidirect
228. C₂×#465	C₂×C₁₃	semidirect
229. C₂×#460	C₂×C₁₃	semidirect
230. C₂×#461	C₂×C₁₃	semidirect
231. C₂×#448	C₂×C₁₃	semidirect
232. C₂×#450	C₂×C₁₃	semidirect
233. C₂×C₄×SD₁₆	C₂×C₁₃	semidirect
234. C₂×C₈×D₄	C₂×C₁₃	semidirect
249. C₂³×C₁₃	C₂×SD₁₆	semidirect
258. Q₈×C₁₃	C₂²×D₄	semidirect
268. D₄×C₁₃	C₂×SD₁₆	direct (N × H)
285. C₂×C₄×C₁₃	C₂×SD₁₆	semidirect
295. C₈×C₁₃	C₂²×D₄	semidirect
296. C₂³×Q₈	C₂²×C₁₃	semidirect
302. C₂²×SD₁₆	C₂²×C₁₃	semidirect
303. C₂²×SD₁₆	C₂²×C₁₃	semidirect
304. C₂²×SD₁₆	C₂²×C₁₃	semidirect
305. C₂²×SD₁₆	C₂²×C₁₃	semidirect
306. C₂³×C₈	C₂²×C₁₃	semidirect
308. D₄×Q₈	C₂²×C₁₃	semidirect
312. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
315. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
319. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
323. #492	C₂²×C₁₃	semidirect
324. #465	C₂²×C₁₃	semidirect
325. #461	C₂²×C₁₃	semidirect
326. #460	C₂²×C₁₃	semidirect
327. #450	C₂²×C₁₃	semidirect
328. #448	C₂²×C₁₃	semidirect
329. C₄×SD₁₆	C₂²×C₁₃	semidirect
330. C₈×D₄	C₂²×C₁₃	semidirect
331. C₂×#106	C₂²×C₁₃	semidirect
332. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
333. C₂×#103	C₂²×C₁₃	semidirect
334. C₂×#103	C₂²×C₁₃	semidirect
336. C₂×#102	C₂²×C₁₃	semidirect
337. C₂×C₂²⋊C₈	C₂²×C₁₃	semidirect
338. C₂×C₄×C₈	C₂²×C₁₃	semidirect
353. C₂²×C₁₃	C₂²×SD₁₆	semidirect
363. C₄×C₁₃	C₂²×SD₁₆	semidirect
373. C₂²×Q₈	C₂³×C₁₃	semidirect
395. C₂×SD₁₆	D₄×C₁₃	direct (N × H)
398. C₂×SD₁₆	C₂³×C₁₃	semidirect
399. C₂×SD₁₆	C₂³×C₁₃	semidirect
400. C₂×SD₁₆	C₂³×C₁₃	semidirect
405. C₂²×C₈	C₂³×C₁₃	semidirect
408. C₄⋊Q₈	C₂³×C₁₃	semidirect
413. C₂²⋊Q₈	C₂³×C₁₃	semidirect
419. C₄×Q₈	C₂³×C₁₃	semidirect
438. #106	C₂³×C₁₃	semidirect
439. C₄⋊C₈	C₂³×C₁₃	semidirect
440. #103	C₂³×C₁₃	semidirect
441. #103	C₂³×C₁₃	semidirect
443. #102	C₂³×C₁₃	semidirect
444. C₂²⋊C₈	C₂³×C₁₃	semidirect
445. C₄×C₈	C₂³×C₁₃	semidirect
449. C₂×C₁₃	D₄×SD₁₆	direct (N × H)
470. C₂×Q₈	C₂×D₄×C₁₃	semidirect
490. C₂×D₄	C₁₃×SD₁₆	direct (N × H)
515. SD₁₆	C₂×D₄×C₁₃	direct (N × H)
519. C₂×C₈	C₂×D₄×C₁₃	semidirect
539. C₁₃	C₂×D₄×SD₁₆	direct (N × H)
554. C₂³	C₂×C₁₃×SD₁₆	semidirect
563. Q₈	C₂²×D₄×C₁₃	semidirect
573. D₄	C₂×C₁₃×SD₁₆	direct (N × H)
590. C₂×C₄	C₂×C₁₃×SD₁₆	semidirect
600. C₈	C₂²×D₄×C₁₃	semidirect
615. C₂²	C₂²×C₁₃×SD₁₆	semidirect
625. C₄	C₂²×C₁₃×SD₁₆	semidirect
631. C₂	D₄×C₁₃×SD₁₆	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×SD₁₆	2
C₂×D₄×Q₈×C₁₃	2
C₂×D₄²×C₁₃	2
D₄×C₁₃×SD₁₆	2
C₂×C₁₃×#492	2
C₂×C₁₃×#465	2
C₂×C₁₃×#460	2
C₂×C₁₃×#461	2
C₂×C₁₃×#448	2
C₂×C₁₃×#450	2
C₂×C₄×C₁₃×SD₁₆	2
C₂×C₈×D₄×C₁₃	2
C₂×D₄×SD₁₆	13

Subgroups — C2×D4×C13×SD16 #15747380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄×C₁₃×SD₁₆ #15747380