Subgroups — C₂×D₄²×D₁₃ #16769825

Order 3328.

20038 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₄×D₁₃	C₂	1	4	yes	maximal, complemented
2	C₂×D₄×D₅₂	C₂	1	2	yes	maximal, complemented
3	C₂×#11719422	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11719314	C₂	1	4	yes	maximal, complemented
5	C₂×D₄×C₂²⋊D₁₃	C₂	1	4	yes	maximal, complemented
6	C₂×#11719295	C₂	1	4	yes	maximal, complemented
7	D₄²×D₁₃	C₂	1	32	yes	maximal, direct product factor
8	C₂×D₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×D₁₃×#121	C₂	1	4	yes	maximal, complemented
10	C₂×D₁₃×#120	C₂	1	4	yes	maximal, complemented
11	C₂×C₄×D₄×D₁₃	C₂	1	2	yes	maximal, complemented
12	C₂×D₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁵×D₁₃	C₂²	1	4	yes	complemented
14	C₂³×D₄×C₁₃	C₂²	1	4	yes	complemented
15	C₂³×C₂²⋊D₁₃	C₂²	1	8	yes	complemented
16	C₂²×D₄×D₁₃	—	2	64	no	—
17	C₂²×D₄×D₁₃	C₂²	1	2	yes	—
18	C₂²×D₄×D₁₃	C₂²	1	8	yes	complemented
19	C₂²×D₄×D₁₃	C₂²	1	4	yes	complemented
20	C₂²×D₄×D₁₃	C₂²	1	2	yes	complemented
21	C₂²×D₄×D₁₃	C₂²	1	4	yes	complemented
22	C₂²×D₄×D₁₃	C₂²	1	64	yes	complemented
23	C₂²×D₄×D₁₃	C₂²	1	8	yes	complemented
24	C₂²×D₄×D₁₃	C₂²	1	4	yes	complemented
25	C₂³×D₅₂	C₂²	1	4	yes	complemented
26	C₂³×C₄×D₁₃	C₂²	1	4	yes	complemented
27	D₄²×C₁₃	C₂²	1	16	yes	complemented
28	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
30	C₂×C₁₃×#120	C₂²	1	4	yes	complemented
31	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
32	C₂×#88207	C₂²	1	4	yes	complemented
33	C₂×#88194	C₂²	1	2	yes	complemented
34	C₂×#88194	C₂²	1	4	yes	complemented
35	C₂×#88193	C₂²	1	8	yes	complemented
36	D₄×C₂²⋊D₁₃	C₂²	1	64	yes	complemented
37	C₂×#88192	C₂²	1	4	yes	complemented
38	C₂×#88191	C₂²	1	4	yes	complemented
39	C₂×#88191	C₂²	1	8	yes	complemented
40	C₂×D₄×Dic₁₃	C₂²	1	2	yes	complemented
41	C₂×#88184	C₂²	1	4	yes	complemented
42	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
43	#11719422	C₂²	1	16	yes	complemented
44	D₁₃×#127	C₂²	1	16	yes	complemented
45	#11719314	C₂²	1	64	yes	complemented
46	D₁₃×#121	C₂²	1	64	yes	complemented
47	#11719295	C₂²	1	64	yes	complemented
48	D₁₃×#120	C₂²	1	64	yes	complemented
49	D₄×D₅₂	C₂²	1	32	yes	complemented
50	C₄×D₄×D₁₃	C₂²	1	32	yes	complemented
51	C₂×#88149	C₂²	1	4	yes	complemented
52	C₂×#88147	C₂²	1	2	yes	complemented
53	C₂×C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
54	C₂×#88138	C₂²	1	8	yes	complemented
55	C₂×#88136	C₂²	1	8	yes	complemented
56	C₂×#88136	C₂²	1	4	yes	complemented
57	C₂×#88135	C₂²	1	4	yes	complemented
58	C₂×C₂²⋊C₄×D₁₃	C₂²	1	4	yes	complemented
59	C₂×C₂²⋊C₄×D₁₃	C₂²	1	4	yes	complemented
60	C₂×#88128	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
62	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
63	C₂⁵×C₁₃	C₂³	1	4	yes	complemented
64	C₂⁴×D₁₃	—	2	64	no	—
65	C₂⁴×D₁₃	—	4	16	no	—
66	C₂⁴×D₁₃	C₂³	1	4	yes	—
67	C₂⁴×D₁₃	C₂³	1	4	yes	—
68	C₂⁴×D₁₃	C₂³	1	32	yes	complemented
69	C₂⁴×D₁₃	C₂³	1	8	yes	complemented
70	C₂⁴×D₁₃	C₂³	1	4	yes	complemented
71	C₂²×D₄×C₁₃	—	2	32	no	—
72	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
73	C₂²×D₄×C₁₃	C₂³	1	8	yes	complemented
74	C₂²×D₄×C₁₃	C₂³	1	4	yes	complemented
75	C₂²×D₄×C₁₃	C₂³	1	2	yes	complemented
76	C₂²×D₄×C₁₃	C₂³	1	32	yes	complemented
77	C₂³×C₄×C₁₃	C₂³	1	4	yes	complemented
78	C₂²×C₂²⋊D₁₃	—	2	64	no	—
79	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
80	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	complemented
81	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	complemented
82	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	complemented
83	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	complemented
84	C₂²×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
85	C₂³×Dic₁₃	C₂³	1	4	yes	complemented
86	C₂×D₄×D₁₃	—	2	64	no	—
87	C₂×D₄×D₁₃	—	2	32	no	—
88	C₂×D₄×D₁₃	—	2	64	no	—
89	C₂×D₄×D₁₃	—	2	512	no	—
90	C₂×D₄×D₁₃	—	2	32	no	—
91	C₂×D₄×D₁₃	—	2	32	no	—
92	C₂×D₄×D₁₃	—	4	8	no	—
93	C₂×D₄×D₁₃	D₄	1	32	yes	direct product factor
94	C₂×D₄×D₁₃	C₂³	1	16	yes	—
95	C₂×D₄×D₁₃	C₂³	1	64	yes	complemented
96	C₂×D₄×D₁₃	C₂³	1	32	yes	complemented
97	C₂×D₄×D₁₃	C₂³	1	16	yes	complemented
98	C₂×D₄×D₁₃	C₂³	1	32	yes	complemented
99	C₂×D₄×D₁₃	C₂³	1	64	yes	complemented
100	C₂×D₄×D₁₃	C₂³	1	32	yes	complemented
101	C₂²×D₅₂	—	2	32	no	—
102	C₂²×D₅₂	C₂³	1	2	yes	—
103	C₂²×D₅₂	C₂³	1	32	yes	complemented
104	C₂²×D₅₂	C₂³	1	4	yes	complemented
105	C₂²×D₅₂	C₂³	1	8	yes	complemented
106	C₂²×D₅₂	C₂³	1	2	yes	complemented
107	C₂²×C₄×D₁₃	—	2	32	no	—
108	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
109	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
110	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
111	C₂²×C₄×D₁₃	C₂³	1	32	yes	complemented
112	C₂²×C₄×D₁₃	C₂³	1	4	yes	complemented
113	C₂²×C₄×D₁₃	C₂³	1	4	yes	complemented
114	C₁₃×#127	C₂³	1	8	yes	complemented
115	C₁₃×#121	C₂³	1	32	yes	complemented
116	C₁₃×#120	C₂³	1	32	yes	complemented
117	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
118	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	complemented
119	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
120	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	complemented
121	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic, complemented
122	#88207	C₂³	1	32	yes	complemented
123	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	complemented
124	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	complemented
125	#88194	C₂³	1	32	yes	complemented
126	#88194	C₂³	1	16	yes	complemented
127	#88193	C₂³	1	64	yes	complemented
128	#88192	C₂³	1	32	yes	complemented
129	#88191	C₂³	1	64	yes	complemented
130	#88191	C₂³	1	32	yes	complemented
131	D₄×Dic₁₃	C₂³	1	16	yes	complemented
132	#88184	C₂³	1	32	yes	complemented
133	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
134	C₂×#6103	C₂³	1	4	yes	complemented
135	C₂×#6103	C₂³	1	4	yes	complemented
136	C₂×#6103	C₂³	1	8	yes	complemented
137	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	complemented
138	C₂×#6101	C₂³	1	4	yes	complemented
139	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic, complemented
140	C₂×C₄×Dic₁₃	C₂³	1	2	yes	complemented
141	#88149	C₂³	1	32	yes	complemented
142	#88147	C₂³	1	16	yes	complemented
143	C₄⋊C₄×D₁₃	C₂³	1	16	yes	complemented
144	#88138	C₂³	1	64	yes	complemented
145	#88136	C₂³	1	64	yes	complemented
146	#88136	C₂³	1	32	yes	complemented
147	#88135	C₂³	1	32	yes	complemented
148	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	complemented
149	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	complemented
150	#88128	C₂³	1	8	yes	complemented
151	C₄×D₅₂	C₂³	1	16	yes	complemented
152	C₄²×D₁₃	C₂³	1	8	yes	complemented
153	C₂²×D₄²	—	13	1	no	maximal, Sylow
154	C₂⁴×C₁₃	—	2	32	no	—
155	C₂⁴×C₁₃	—	4	8	no	—
156	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
157	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
158	C₂⁴×C₁₃	C₂⁴	1	16	yes	complemented
159	C₂³×D₁₃	—	2	16	no	—
160	C₂³×D₁₃	—	2	16	no	—
161	C₂³×D₁₃	—	2	32	no	—
162	C₂³×D₁₃	—	2	32	no	—
163	C₂³×D₁₃	—	2	32	no	—
164	C₂³×D₁₃	—	2	32	no	—
165	C₂³×D₁₃	—	2	256	no	—
166	C₂³×D₁₃	—	2	16	no	—
167	C₂³×D₁₃	—	4	64	no	—
168	C₂³×D₁₃	—	4	8	no	—
169	C₂³×D₁₃	—	4	16	no	—
170	C₂³×D₁₃	—	4	256	no	—
171	C₂³×D₁₃	C₂×D₄	1	32	yes	complemented
172	C₂³×D₁₃	C₂⁴	1	16	yes	—
173	C₂³×D₁₃	C₂⁴	1	4	yes	—
174	C₂³×D₁₃	C₂⁴	1	16	yes	—
175	C₂³×D₁₃	C₂⁴	1	4	yes	—
176	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
177	C₂³×D₁₃	C₂⁴	1	32	yes	complemented
178	C₂³×D₁₃	C₂⁴	1	16	yes	complemented
179	C₂×D₄×C₁₃	—	2	32	no	—
180	C₂×D₄×C₁₃	—	2	128	no	—
181	C₂×D₄×C₁₃	—	2	16	no	—
182	C₂×D₄×C₁₃	—	4	4	no	—
183	C₂×D₄×C₁₃	C₂×D₄	1	16	yes	complemented
184	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
185	C₂×D₄×C₁₃	C₂⁴	1	32	yes	complemented
186	C₂×D₄×C₁₃	C₂⁴	1	16	yes	complemented
187	C₂×D₄×C₁₃	C₂⁴	1	8	yes	complemented
188	C₂²×C₄×C₁₃	—	2	16	no	—
189	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	complemented
193	C₂×C₂²⋊D₁₃	—	2	32	no	—
194	C₂×C₂²⋊D₁₃	—	2	32	no	—
195	C₂×C₂²⋊D₁₃	—	2	256	no	—
196	C₂×C₂²⋊D₁₃	—	2	32	no	—
197	C₂×C₂²⋊D₁₃	—	4	8	no	—
198	C₂×C₂²⋊D₁₃	C₂×D₄	1	32	yes	complemented
199	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
200	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	complemented
201	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	complemented
202	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	complemented
203	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	complemented
204	C₂²×Dic₁₃	—	2	16	no	—
205	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
206	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
207	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
208	C₂²×Dic₁₃	C₂⁴	1	16	yes	complemented
209	D₄×D₁₃	—	2	256	no	—
210	D₄×D₁₃	—	2	128	no	—
211	D₄×D₁₃	—	2	256	no	—
212	D₄×D₁₃	—	2	128	no	—
213	D₄×D₁₃	—	2	128	no	—
214	D₄×D₁₃	—	4	32	no	—
215	D₄×D₁₃	C₂×D₄	1	128	yes	direct product factor
216	C₂×D₅₂	—	2	32	no	—
217	C₂×D₅₂	—	2	16	no	—
218	C₂×D₅₂	—	2	128	no	—
219	C₂×D₅₂	—	4	4	no	—
220	C₂×D₅₂	C₂×D₄	1	16	yes	complemented
221	C₂×D₅₂	C₂⁴	1	8	yes	—
222	C₂×D₅₂	C₂⁴	1	16	yes	complemented
223	C₂×D₅₂	C₂⁴	1	32	yes	complemented
224	C₂×D₅₂	C₂⁴	1	8	yes	complemented
225	C₂×C₄×D₁₃	—	2	16	no	—
226	C₂×C₄×D₁₃	—	2	4	no	—
227	C₂×C₄×D₁₃	—	2	16	no	—
228	C₂×C₄×D₁₃	—	2	16	no	—
229	C₂×C₄×D₁₃	—	2	128	no	—
230	C₂×C₄×D₁₃	C₂×D₄	1	16	yes	complemented
231	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
232	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
233	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
234	C₂×C₄×D₁₃	C₂⁴	1	16	yes	complemented
235	C₂×C₄×D₁₃	C₂⁴	1	16	yes	complemented
236	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	complemented
237	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	complemented
238	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	complemented
239	C₄²×C₁₃	C₂⁴	1	4	yes	complemented
240	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	complemented
241	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	complemented
242	#6103	C₂⁴	1	16	yes	complemented
243	#6103	C₂⁴	1	16	yes	complemented
244	#6103	C₂⁴	1	32	yes	complemented
245	C₄⋊Dic₁₃	C₂⁴	1	8	yes	complemented
246	#6101	C₂⁴	1	16	yes	complemented
247	C₄×Dic₁₃	C₂⁴	1	4	yes	complemented
248	C₄×Dic₁₃	C₂⁴	1	8	yes	complemented
249	C₂⁴×D₄	—	13	4	no	—
250	C₂×D₄²	—	13	4	no	—
251	C₂×D₄²	—	13	32	no	—
252	C₂×D₄²	—	13	1	no	—
253	C₂×D₄²	—	13	4	no	—
254	C₂×D₄²	—	13	4	no	—
255	C₂×D₄²	—	13	2	no	—
256	C₂×D₄²	D₁₃	1	1	yes	characteristic, direct product factor
257	C₂²×#127	—	13	1	no	—
258	C₂²×#121	—	13	4	no	—
259	C₂²×#120	—	13	4	no	—
260	C₂²×C₄×D₄	—	13	2	no	—
261	C₂³×C₁₃	—	2	8	no	—
262	C₂³×C₁₃	—	2	8	no	—
263	C₂³×C₁₃	—	2	16	no	—
264	C₂³×C₁₃	—	2	64	no	—
265	C₂³×C₁₃	—	2	8	no	—
266	C₂³×C₁₃	—	4	16	no	—
267	C₂³×C₁₃	—	4	64	no	—
268	C₂³×C₁₃	C₂²×D₄	1	16	yes	complemented
269	C₂³×C₁₃	C₂⁵	1	8	yes	—
270	C₂³×C₁₃	C₂⁵	1	8	yes	—
271	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
272	C₂²×D₁₃	—	2	8	no	—
273	C₂²×D₁₃	—	2	8	no	—
274	C₂²×D₁₃	—	2	128	no	—
275	C₂²×D₁₃	—	2	32	no	—
276	C₂²×D₁₃	—	2	32	no	—
277	C₂²×D₁₃	—	2	16	no	—
278	C₂²×D₁₃	—	2	64	no	—
279	C₂²×D₁₃	—	2	8	no	—
280	C₂²×D₁₃	—	2	64	no	—
281	C₂²×D₁₃	—	2	64	no	—
282	C₂²×D₁₃	—	2	64	no	—
283	C₂²×D₁₃	—	2	32	no	—
284	C₂²×D₁₃	—	4	16	no	—
285	C₂²×D₁₃	—	4	32	no	—
286	C₂²×D₁₃	—	4	64	no	—
287	C₂²×D₁₃	—	4	512	no	—
288	C₂²×D₁₃	—	4	128	no	—
289	C₂²×D₁₃	—	4	64	no	—
290	C₂²×D₁₃	C₂²×D₄	1	8	yes	—
291	C₂²×D₁₃	C₂²×D₄	1	64	yes	complemented
292	C₂²×D₁₃	C₂²×D₄	1	16	yes	complemented
293	C₂²×D₁₃	H(5,𝔽₂)	1	4	yes	—
294	C₂²×D₁₃	C₂⁵	1	8	yes	—
295	C₂²×D₁₃	C₂⁵	1	8	yes	—
296	C₂²×D₁₃	C₂⁵	1	2	yes	—
297	D₄×C₁₃	—	2	64	no	—
298	D₄×C₁₃	—	2	32	no	—
299	D₄×C₁₃	—	4	8	no	—
300	D₄×C₁₃	C₂²×D₄	1	32	yes	complemented
301	C₂×C₄×C₁₃	—	2	8	no	—
302	C₂×C₄×C₁₃	—	2	2	no	—
303	C₂×C₄×C₁₃	—	2	32	no	—
304	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	complemented
305	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
306	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
307	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
308	C₂²⋊D₁₃	—	2	64	no	—
309	C₂²⋊D₁₃	—	2	64	no	—
310	C₂²⋊D₁₃	—	2	64	no	—
311	C₂²⋊D₁₃	—	4	16	no	—
312	C₂²⋊D₁₃	C₂²×D₄	1	64	yes	complemented
313	C₂×Dic₁₃	—	2	8	no	—
314	C₂×Dic₁₃	—	2	2	no	—
315	C₂×Dic₁₃	—	2	32	no	—
316	C₂×Dic₁₃	C₂²×D₄	1	8	yes	complemented
317	C₂×Dic₁₃	C₂⁵	1	2	yes	—
318	C₂×Dic₁₃	C₂⁵	1	8	yes	—
319	C₂×Dic₁₃	C₂⁵	1	4	yes	—
320	D₅₂	—	2	64	no	—
321	D₅₂	—	2	32	no	—
322	D₅₂	—	4	8	no	—
323	D₅₂	C₂²×D₄	1	32	yes	complemented
324	C₄×D₁₃	—	2	32	no	—
325	C₄×D₁₃	—	2	8	no	—
326	C₄×D₁₃	—	2	32	no	—
327	C₄×D₁₃	—	2	32	no	—
328	C₄×D₁₃	C₂²×D₄	1	32	yes	complemented
329	C₂⁶	—	13	4	no	—
330	C₂³×D₄	—	13	2	no	—
331	C₂³×D₄	—	13	8	no	—
332	C₂³×D₄	—	13	4	no	—
333	C₂³×D₄	—	13	8	no	—
334	C₂³×D₄	—	13	4	no	—
335	C₂³×D₄	—	13	8	no	—
336	C₂³×D₄	—	13	4	no	—
337	C₂³×D₄	—	13	64	no	—
338	C₂³×D₄	—	13	2	no	—
339	C₂³×D₄	—	13	4	no	—
340	C₂³×D₄	—	26	64	no	—
341	C₂³×D₄	C₂×D₁₃	1	4	yes	complemented
342	C₂⁴×C₄	—	13	4	no	—
343	D₄²	—	13	64	no	—
344	D₄²	—	13	16	no	—
345	D₄²	—	13	64	no	—
346	D₄²	—	13	64	no	—
347	D₄²	—	13	32	no	—
348	D₄²	C₂×D₁₃	1	16	yes	direct product factor
349	C₂×#127	—	13	2	no	—
350	C₂×#127	—	13	4	no	—
351	C₂×#127	—	13	16	no	—
352	C₂×#127	—	13	1	no	—
353	C₂×#127	C₂×D₁₃	1	1	yes	characteristic, complemented
354	C₂×#121	—	13	4	no	—
355	C₂×#121	—	13	8	no	—
356	C₂×#121	—	13	4	no	—
357	C₂×#121	—	13	64	no	—
358	C₂×#121	—	13	4	no	—
359	C₂×#121	—	13	8	no	—
360	C₂×#121	C₂×D₁₃	1	4	yes	complemented
361	C₂×#120	—	13	4	no	—
362	C₂×#120	—	13	8	no	—
363	C₂×#120	—	13	4	no	—
364	C₂×#120	—	13	64	no	—
365	C₂×#120	—	13	4	no	—
366	C₂×#120	—	13	8	no	—
367	C₂×#120	C₂×D₁₃	1	4	yes	complemented
368	C₂×C₄×D₄	—	13	2	no	—
369	C₂×C₄×D₄	—	13	4	no	—
370	C₂×C₄×D₄	—	13	32	no	—
371	C₂×C₄×D₄	—	13	2	no	—
372	C₂×C₄×D₄	—	13	4	no	—
373	C₂×C₄×D₄	—	13	2	no	—
374	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	complemented
375	C₂²×C₄⋊C₄	—	13	2	no	—
376	C₂²×C₂²⋊C₄	—	13	4	no	—
377	C₂²×C₂²⋊C₄	—	13	4	no	—
378	C₂²×C₄²	—	13	1	no	—
379	C₂²×C₁₃	—	2	8	no	—
380	C₂²×C₁₃	—	2	8	no	—
381	C₂²×C₁₃	—	2	32	no	—
382	C₂²×C₁₃	—	2	16	no	—
383	C₂²×C₁₃	—	2	8	no	—
384	C₂²×C₁₃	—	4	64	no	—
385	C₂²×C₁₃	—	4	16	no	—
386	C₂²×C₁₃	C₂³×D₄	1	4	yes	—
387	C₂²×C₁₃	C₂³×D₄	1	16	yes	complemented
388	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
389	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
390	C₂×D₁₃	—	2	8	no	—
391	C₂×D₁₃	—	2	8	no	—
392	C₂×D₁₃	—	2	32	no	—
393	C₂×D₁₃	—	2	128	no	—
394	C₂×D₁₃	—	2	16	no	—
395	C₂×D₁₃	—	2	8	no	—
396	C₂×D₁₃	—	4	64	no	—
397	C₂×D₁₃	—	4	128	no	—
398	C₂×D₁₃	—	4	16	no	—
399	C₂×D₁₃	—	4	64	no	—
400	C₂×D₁₃	D₄²	1	16	yes	direct product factor
401	C₂×D₁₃	C₂³×D₄	1	8	yes	—
402	C₂×D₁₃	C₂³×D₄	1	16	yes	complemented
403	C₂×D₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
404	C₄×C₁₃	—	2	8	no	—
405	C₄×C₁₃	—	2	2	no	—
406	C₄×C₁₃	C₂³×D₄	1	8	yes	complemented
407	Dic₁₃	—	2	8	no	—
408	Dic₁₃	—	2	2	no	—
409	Dic₁₃	C₂³×D₄	1	8	yes	complemented
410	C₂⁵	—	13	4	no	—
411	C₂⁵	—	13	4	no	—
412	C₂⁵	—	13	4	no	—
413	C₂⁵	—	13	8	no	—
414	C₂⁵	—	13	32	no	—
415	C₂⁵	—	26	64	no	—
416	C₂⁵	—	52	16	no	—
417	C₂⁵	C₂²×D₁₃	1	4	yes	complemented
418	C₂²×D₄	—	2	32	no	—
419	C₂²×D₄	—	13	4	no	—
420	C₂²×D₄	—	13	32	no	—
421	C₂²×D₄	—	13	16	no	—
422	C₂²×D₄	—	13	8	no	—
423	C₂²×D₄	—	13	8	no	—
424	C₂²×D₄	—	13	8	no	—
425	C₂²×D₄	—	13	64	no	—
426	C₂²×D₄	—	13	4	no	—
427	C₂²×D₄	—	13	32	no	—
428	C₂²×D₄	—	13	64	no	—
429	C₂²×D₄	—	13	32	no	—
430	C₂²×D₄	—	13	64	no	—
431	C₂²×D₄	—	13	32	no	—
432	C₂²×D₄	—	13	16	no	—
433	C₂²×D₄	—	13	2	no	—
434	C₂²×D₄	—	13	8	no	—
435	C₂²×D₄	—	13	4	no	—
436	C₂²×D₄	—	13	2	no	—
437	C₂²×D₄	—	13	32	no	—
438	C₂²×D₄	—	26	32	no	—
439	C₂²×D₄	—	26	32	no	—
440	C₂²×D₄	—	26	64	no	—
441	C₂²×D₄	—	26	512	no	—
442	C₂²×D₄	—	26	32	no	—
443	C₂²×D₄	—	26	64	no	—
444	C₂²×D₄	—	26	64	no	—
445	C₂²×D₄	—	26	32	no	—
446	C₂²×D₄	—	52	8	no	—
447	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
448	C₂²×D₄	C₂²×D₁₃	1	8	yes	complemented
449	C₂²×D₄	C₂²×D₁₃	1	4	yes	complemented
450	C₂²×D₄	C₂²×D₁₃	1	2	yes	complemented
451	C₂²×D₄	C₂²×D₁₃	1	32	yes	complemented
452	C₂³×C₄	—	13	2	no	—
453	C₂³×C₄	—	13	4	no	—
454	C₂³×C₄	—	13	1	no	—
455	C₂³×C₄	—	13	4	no	—
456	C₂³×C₄	—	13	4	no	—
457	C₂³×C₄	—	13	4	no	—
458	C₂³×C₄	—	13	32	no	—
459	C₂³×C₄	—	26	32	no	—
460	C₂³×C₄	C₂²×D₁₃	1	4	yes	complemented
461	#127	—	13	16	no	—
462	#127	—	13	32	no	—
463	#127	—	13	8	no	—
464	#127	C₂²×D₁₃	1	8	yes	complemented
465	#121	—	13	32	no	—
466	#121	—	13	64	no	—
467	#121	—	13	32	no	—
468	#121	—	13	32	no	—
469	#121	—	13	64	no	—
470	#121	C₂²×D₁₃	1	32	yes	complemented
471	#120	—	13	32	no	—
472	#120	—	13	64	no	—
473	#120	—	13	32	no	—
474	#120	—	13	32	no	—
475	#120	—	13	64	no	—
476	#120	C₂²×D₁₃	1	32	yes	complemented
477	C₄×D₄	—	13	16	no	—
478	C₄×D₄	—	13	32	no	—
479	C₄×D₄	—	13	16	no	—
480	C₄×D₄	—	13	32	no	—
481	C₄×D₄	—	13	16	no	—
482	C₄×D₄	C₂²×D₁₃	1	16	yes	complemented
483	C₂×C₄⋊C₄	—	13	4	no	—
484	C₂×C₄⋊C₄	—	13	2	no	—
485	C₂×C₄⋊C₄	—	13	16	no	—
486	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	complemented
487	C₂×C₂²⋊C₄	—	13	4	no	—
488	C₂×C₂²⋊C₄	—	13	4	no	—
489	C₂×C₂²⋊C₄	—	13	4	no	—
490	C₂×C₂²⋊C₄	—	13	4	no	—
491	C₂×C₂²⋊C₄	—	13	8	no	—
492	C₂×C₂²⋊C₄	—	13	32	no	—
493	C₂×C₂²⋊C₄	—	13	32	no	—
494	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	complemented
495	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	complemented
496	C₂×C₄²	—	13	1	no	—
497	C₂×C₄²	—	13	2	no	—
498	C₂×C₄²	—	13	8	no	—
499	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic, complemented
500	C₂×C₁₃	—	2	16	no	—
501	C₂×C₁₃	—	4	8	no	—
502	C₂×C₁₃	C₂×D₄²	1	4	yes	complemented
503	C₂×C₁₃	C₂⁴×D₄	1	2	yes	—
504	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
505	D₁₃	—	2	16	no	—
506	D₁₃	—	4	8	no	—
507	D₁₃	C₂×D₄²	1	8	yes	direct product factor
508	C₂⁴	—	2	32	no	—
509	C₂⁴	—	4	8	no	—
510	C₂⁴	—	13	1	no	—
511	C₂⁴	—	13	32	no	—
512	C₂⁴	—	13	16	no	—
513	C₂⁴	—	13	4	no	—
514	C₂⁴	—	13	16	no	—
515	C₂⁴	—	13	4	no	—
516	C₂⁴	—	13	16	no	—
517	C₂⁴	—	13	32	no	—
518	C₂⁴	—	26	16	no	—
519	C₂⁴	—	26	16	no	—
520	C₂⁴	—	26	32	no	—
521	C₂⁴	—	26	32	no	—
522	C₂⁴	—	26	32	no	—
523	C₂⁴	—	26	256	no	—
524	C₂⁴	—	26	16	no	—
525	C₂⁴	—	26	32	no	—
526	C₂⁴	—	52	16	no	—
527	C₂⁴	—	52	8	no	—
528	C₂⁴	—	52	64	no	—
529	C₂⁴	—	52	256	no	—
530	C₂⁴	C₂³×D₁₃	1	4	yes	—
531	C₂⁴	C₂³×D₁₃	1	4	yes	—
532	C₂⁴	C₂³×D₁₃	1	16	yes	complemented
533	C₂×D₄	—	2	32	no	—
534	C₂×D₄	—	2	128	no	—
535	C₂×D₄	—	2	16	no	—
536	C₂×D₄	—	4	4	no	—
537	C₂×D₄	—	13	32	no	—
538	C₂×D₄	—	13	16	no	—
539	C₂×D₄	—	13	128	no	—
540	C₂×D₄	—	13	32	no	—
541	C₂×D₄	—	13	32	no	—
542	C₂×D₄	—	13	32	no	—
543	C₂×D₄	—	13	16	no	—
544	C₂×D₄	—	13	16	no	—
545	C₂×D₄	—	13	8	no	—
546	C₂×D₄	—	13	32	no	—
547	C₂×D₄	—	13	16	no	—
548	C₂×D₄	—	13	8	no	—
549	C₂×D₄	—	26	128	no	—
550	C₂×D₄	—	26	32	no	—
551	C₂×D₄	—	26	128	no	—
552	C₂×D₄	—	26	32	no	—
553	C₂×D₄	—	26	256	no	—
554	C₂×D₄	—	26	128	no	—
555	C₂×D₄	—	26	256	no	—
556	C₂×D₄	—	26	256	no	—
557	C₂×D₄	—	26	32	no	—
558	C₂×D₄	—	26	32	no	—
559	C₂×D₄	—	26	128	no	—
560	C₂×D₄	—	26	16	no	—
561	C₂×D₄	—	52	4	no	—
562	C₂×D₄	—	52	32	no	—
563	C₂×D₄	—	52	8	no	—
564	C₂×D₄	D₄×D₁₃	1	16	yes	direct product factor
565	C₂×D₄	C₂³×D₁₃	1	8	yes	—
566	C₂×D₄	C₂³×D₁₃	1	32	yes	complemented
567	C₂×D₄	C₂³×D₁₃	1	16	yes	complemented
568	C₂×D₄	C₂³×D₁₃	1	8	yes	complemented
569	C₂²×C₄	—	2	16	no	—
570	C₂²×C₄	—	13	2	no	—
571	C₂²×C₄	—	13	16	no	—
572	C₂²×C₄	—	13	8	no	—
573	C₂²×C₄	—	13	16	no	—
574	C₂²×C₄	—	13	1	no	—
575	C₂²×C₄	—	13	4	no	—
576	C₂²×C₄	—	13	4	no	—
577	C₂²×C₄	—	13	16	no	—
578	C₂²×C₄	—	13	16	no	—
579	C₂²×C₄	—	13	16	no	—
580	C₂²×C₄	—	26	16	no	—
581	C₂²×C₄	—	26	128	no	—
582	C₂²×C₄	—	26	16	no	—
583	C₂²×C₄	—	26	4	no	—
584	C₂²×C₄	—	26	16	no	—
585	C₂²×C₄	—	26	16	no	—
586	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
587	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
588	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
589	C₂²×C₄	C₂³×D₁₃	1	16	yes	complemented
590	C₄⋊C₄	—	13	16	no	—
591	C₄⋊C₄	—	13	8	no	—
592	C₄⋊C₄	C₂³×D₁₃	1	8	yes	complemented
593	C₂²⋊C₄	—	13	16	no	—
594	C₂²⋊C₄	—	13	16	no	—
595	C₂²⋊C₄	—	13	16	no	—
596	C₂²⋊C₄	—	13	16	no	—
597	C₂²⋊C₄	—	13	32	no	—
598	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	complemented
599	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	complemented
600	C₄²	—	13	4	no	—
601	C₄²	—	13	8	no	—
602	C₄²	C₂³×D₁₃	1	4	yes	complemented
603	C₁₃	C₂²×D₄²	1	1	yes	characteristic, complemented, Sylow
604	C₂³	—	2	8	no	—
605	C₂³	—	2	8	no	—
606	C₂³	—	2	16	no	—
607	C₂³	—	2	64	no	—
608	C₂³	—	2	8	no	—
609	C₂³	—	4	16	no	—
610	C₂³	—	4	64	no	—
611	C₂³	—	13	8	no	—
612	C₂³	—	13	4	no	—
613	C₂³	—	13	2	no	—
614	C₂³	—	13	16	no	—
615	C₂³	—	13	64	no	—
616	C₂³	—	13	8	no	—
617	C₂³	—	13	8	no	—
618	C₂³	—	26	32	no	—
619	C₂³	—	26	128	no	—
620	C₂³	—	26	32	no	—
621	C₂³	—	26	64	no	—
622	C₂³	—	26	64	no	—
623	C₂³	—	26	64	no	—
624	C₂³	—	26	32	no	—
625	C₂³	—	26	8	no	—
626	C₂³	—	26	8	no	—
627	C₂³	—	26	16	no	—
628	C₂³	—	26	64	no	—
629	C₂³	—	26	8	no	—
630	C₂³	—	52	32	no	—
631	C₂³	—	52	16	no	—
632	C₂³	—	52	128	no	—
633	C₂³	—	52	64	no	—
634	C₂³	—	52	512	no	—
635	C₂³	—	52	64	no	—
636	C₂³	C₂×D₄×D₁₃	1	16	yes	complemented
637	C₂³	C₂⁴×D₁₃	1	8	yes	—
638	C₂³	C₂⁴×D₁₃	1	8	yes	—
639	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
640	D₄	—	2	64	no	—
641	D₄	—	2	32	no	—
642	D₄	—	4	8	no	—
643	D₄	—	13	64	no	—
644	D₄	—	13	32	no	—
645	D₄	—	26	64	no	—
646	D₄	—	26	64	no	—
647	D₄	—	26	64	no	—
648	D₄	—	26	64	no	—
649	D₄	—	26	32	no	—
650	D₄	—	52	8	no	—
651	D₄	—	52	16	no	—
652	D₄	C₂×D₄×D₁₃	1	32	yes	direct product factor
653	C₂×C₄	—	2	8	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	32	no	—
656	C₂×C₄	—	13	8	no	—
657	C₂×C₄	—	13	4	no	—
658	C₂×C₄	—	13	32	no	—
659	C₂×C₄	—	13	2	no	—
660	C₂×C₄	—	13	8	no	—
661	C₂×C₄	—	26	32	no	—
662	C₂×C₄	—	26	32	no	—
663	C₂×C₄	—	26	8	no	—
664	C₂×C₄	—	26	32	no	—
665	C₂×C₄	—	26	8	no	—
666	C₂×C₄	—	26	2	no	—
667	C₂×C₄	—	26	32	no	—
668	C₂×C₄	C₂×D₄×D₁₃	1	8	yes	complemented
669	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
670	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
671	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
672	C₂²	—	2	32	no	—
673	C₂²	—	2	8	no	—
674	C₂²	—	2	8	no	—
675	C₂²	—	2	16	no	—
676	C₂²	—	2	8	no	—
677	C₂²	—	4	64	no	—
678	C₂²	—	4	16	no	—
679	C₂²	—	13	16	no	—
680	C₂²	—	13	8	no	—
681	C₂²	—	13	4	no	—
682	C₂²	—	13	16	no	—
683	C₂²	—	26	128	no	—
684	C₂²	—	26	32	no	—
685	C₂²	—	26	8	no	—
686	C₂²	—	26	8	no	—
687	C₂²	—	26	16	no	—
688	C₂²	—	26	8	no	—
689	C₂²	—	52	128	no	—
690	C₂²	—	52	64	no	—
691	C₂²	—	52	64	no	—
692	C₂²	—	52	16	no	—
693	C₂²	C₂²×D₄×D₁₃	1	4	yes	—
694	C₂²	C₂²×D₄×D₁₃	1	16	yes	complemented
695	C₂²	D₁₃×H(5,𝔽₂)	1	2	yes	—
696	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
697	C₄	—	2	8	no	—
698	C₄	—	2	2	no	—
699	C₄	—	13	8	no	—
700	C₄	—	26	8	no	—
701	C₄	—	26	2	no	—
702	C₄	C₂²×D₄×D₁₃	1	8	yes	complemented
703	C₂	—	2	16	no	—
704	C₂	—	4	8	no	—
705	C₂	—	13	8	no	—
706	C₂	—	26	16	no	—
707	C₂	—	52	8	no	—
708	C₂	D₄²×D₁₃	1	4	yes	direct product factor
709	C₂	C₂³×D₄×D₁₃	1	2	yes	—
710	C₂	C₂×D₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×D₄²×C₁₃	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×D₄²	D₁₃
hypocenter	C₁₃	C₂²×D₄²
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×D₄²

Complements

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

N	H ≅ G/N	type
1. C₂³×D₄×D₁₃	C₂	semidirect
2. C₂×D₄×D₅₂	C₂	semidirect
3. C₂×#11719422	C₂	semidirect
4. C₂×#11719314	C₂	semidirect
5. C₂×D₄×C₂²⋊D₁₃	C₂	semidirect
6. C₂×#11719295	C₂	semidirect
7. D₄²×D₁₃	C₂	direct (N × H)
8. C₂×D₁₃×#127	C₂	semidirect
9. C₂×D₁₃×#121	C₂	semidirect
10. C₂×D₁₃×#120	C₂	semidirect
11. C₂×C₄×D₄×D₁₃	C₂	semidirect
12. C₂×D₄²×C₁₃	C₂	semidirect
13. C₂⁵×D₁₃	C₂²	semidirect
14. C₂³×D₄×C₁₃	C₂²	semidirect
15. C₂³×C₂²⋊D₁₃	C₂²	semidirect
18. C₂²×D₄×D₁₃	C₂²	semidirect
19. C₂²×D₄×D₁₃	C₂²	semidirect
20. C₂²×D₄×D₁₃	C₂²	semidirect
21. C₂²×D₄×D₁₃	C₂²	semidirect
22. C₂²×D₄×D₁₃	C₂²	semidirect
23. C₂²×D₄×D₁₃	C₂²	semidirect
24. C₂²×D₄×D₁₃	C₂²	semidirect
25. C₂³×D₅₂	C₂²	semidirect
26. C₂³×C₄×D₁₃	C₂²	semidirect
27. D₄²×C₁₃	C₂²	semidirect
28. C₂×C₁₃×#127	C₂²	semidirect
29. C₂×C₁₃×#121	C₂²	semidirect
30. C₂×C₁₃×#120	C₂²	semidirect
31. C₂×C₄×D₄×C₁₃	C₂²	semidirect
32. C₂×#88207	C₂²	semidirect
33. C₂×#88194	C₂²	semidirect
34. C₂×#88194	C₂²	semidirect
35. C₂×#88193	C₂²	semidirect
36. D₄×C₂²⋊D₁₃	C₂²	semidirect
37. C₂×#88192	C₂²	semidirect
38. C₂×#88191	C₂²	semidirect
39. C₂×#88191	C₂²	semidirect
40. C₂×D₄×Dic₁₃	C₂²	semidirect
41. C₂×#88184	C₂²	semidirect
42. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
43. #11719422	C₂²	semidirect
44. D₁₃×#127	C₂²	semidirect
45. #11719314	C₂²	semidirect
46. D₁₃×#121	C₂²	semidirect
47. #11719295	C₂²	semidirect
48. D₁₃×#120	C₂²	semidirect
49. D₄×D₅₂	C₂²	semidirect
50. C₄×D₄×D₁₃	C₂²	semidirect
51. C₂×#88149	C₂²	semidirect
52. C₂×#88147	C₂²	semidirect
53. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
54. C₂×#88138	C₂²	semidirect
55. C₂×#88136	C₂²	semidirect
56. C₂×#88136	C₂²	semidirect
57. C₂×#88135	C₂²	semidirect
58. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
59. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
60. C₂×#88128	C₂²	semidirect
61. C₂×C₄×D₅₂	C₂²	semidirect
62. C₂×C₄²×D₁₃	C₂²	semidirect
63. C₂⁵×C₁₃	C₂³	semidirect
68. C₂⁴×D₁₃	C₂³	semidirect
69. C₂⁴×D₁₃	C₂³	semidirect
70. C₂⁴×D₁₃	C₂³	semidirect
73. C₂²×D₄×C₁₃	C₂³	semidirect
74. C₂²×D₄×C₁₃	C₂³	semidirect
75. C₂²×D₄×C₁₃	C₂³	semidirect
76. C₂²×D₄×C₁₃	C₂³	semidirect
77. C₂³×C₄×C₁₃	C₂³	semidirect
80. C₂²×C₂²⋊D₁₃	C₂³	semidirect
81. C₂²×C₂²⋊D₁₃	C₂³	semidirect
82. C₂²×C₂²⋊D₁₃	C₂³	semidirect
83. C₂²×C₂²⋊D₁₃	C₂³	semidirect
84. C₂²×C₂²⋊D₁₃	C₂³	semidirect
85. C₂³×Dic₁₃	C₂³	semidirect
93. C₂×D₄×D₁₃	D₄	direct (N × H)
95. C₂×D₄×D₁₃	C₂³	semidirect
96. C₂×D₄×D₁₃	C₂³	semidirect
97. C₂×D₄×D₁₃	C₂³	semidirect
98. C₂×D₄×D₁₃	C₂³	semidirect
99. C₂×D₄×D₁₃	C₂³	semidirect
100. C₂×D₄×D₁₃	C₂³	semidirect
103. C₂²×D₅₂	C₂³	semidirect
104. C₂²×D₅₂	C₂³	semidirect
105. C₂²×D₅₂	C₂³	semidirect
106. C₂²×D₅₂	C₂³	semidirect
111. C₂²×C₄×D₁₃	C₂³	semidirect
112. C₂²×C₄×D₁₃	C₂³	semidirect
113. C₂²×C₄×D₁₃	C₂³	semidirect
114. C₁₃×#127	C₂³	semidirect
115. C₁₃×#121	C₂³	semidirect
116. C₁₃×#120	C₂³	semidirect
117. C₄×D₄×C₁₃	C₂³	semidirect
118. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
119. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
120. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
121. C₂×C₄²×C₁₃	C₂³	semidirect
122. #88207	C₂³	semidirect
123. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
124. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
125. #88194	C₂³	semidirect
126. #88194	C₂³	semidirect
127. #88193	C₂³	semidirect
128. #88192	C₂³	semidirect
129. #88191	C₂³	semidirect
130. #88191	C₂³	semidirect
131. D₄×Dic₁₃	C₂³	semidirect
132. #88184	C₂³	semidirect
133. C₄×C₂²⋊D₁₃	C₂³	semidirect
134. C₂×#6103	C₂³	semidirect
135. C₂×#6103	C₂³	semidirect
136. C₂×#6103	C₂³	semidirect
137. C₂×C₄⋊Dic₁₃	C₂³	semidirect
138. C₂×#6101	C₂³	semidirect
139. C₂×C₄×Dic₁₃	C₂³	semidirect
140. C₂×C₄×Dic₁₃	C₂³	semidirect
141. #88149	C₂³	semidirect
142. #88147	C₂³	semidirect
143. C₄⋊C₄×D₁₃	C₂³	semidirect
144. #88138	C₂³	semidirect
145. #88136	C₂³	semidirect
146. #88136	C₂³	semidirect
147. #88135	C₂³	semidirect
148. C₂²⋊C₄×D₁₃	C₂³	semidirect
149. C₂²⋊C₄×D₁₃	C₂³	semidirect
150. #88128	C₂³	semidirect
151. C₄×D₅₂	C₂³	semidirect
152. C₄²×D₁₃	C₂³	semidirect
158. C₂⁴×C₁₃	C₂⁴	semidirect
171. C₂³×D₁₃	C₂×D₄	semidirect
177. C₂³×D₁₃	C₂⁴	semidirect
178. C₂³×D₁₃	C₂⁴	semidirect
183. C₂×D₄×C₁₃	C₂×D₄	semidirect
185. C₂×D₄×C₁₃	C₂⁴	semidirect
186. C₂×D₄×C₁₃	C₂⁴	semidirect
187. C₂×D₄×C₁₃	C₂⁴	semidirect
192. C₂²×C₄×C₁₃	C₂⁴	semidirect
198. C₂×C₂²⋊D₁₃	C₂×D₄	semidirect
200. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
201. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
202. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
203. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
208. C₂²×Dic₁₃	C₂⁴	semidirect
215. D₄×D₁₃	C₂×D₄	direct (N × H)
220. C₂×D₅₂	C₂×D₄	semidirect
222. C₂×D₅₂	C₂⁴	semidirect
223. C₂×D₅₂	C₂⁴	semidirect
224. C₂×D₅₂	C₂⁴	semidirect
230. C₂×C₄×D₁₃	C₂×D₄	semidirect
234. C₂×C₄×D₁₃	C₂⁴	semidirect
235. C₂×C₄×D₁₃	C₂⁴	semidirect
236. C₁₃×C₄⋊C₄	C₂⁴	semidirect
237. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
238. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
239. C₄²×C₁₃	C₂⁴	semidirect
240. C₂²⋊Dic₁₃	C₂⁴	semidirect
241. C₂²⋊Dic₁₃	C₂⁴	semidirect
242. #6103	C₂⁴	semidirect
243. #6103	C₂⁴	semidirect
244. #6103	C₂⁴	semidirect
245. C₄⋊Dic₁₃	C₂⁴	semidirect
246. #6101	C₂⁴	semidirect
247. C₄×Dic₁₃	C₂⁴	semidirect
248. C₄×Dic₁₃	C₂⁴	semidirect
256. C₂×D₄²	D₁₃	direct (N × H)
268. C₂³×C₁₃	C₂²×D₄	semidirect
291. C₂²×D₁₃	C₂²×D₄	semidirect
292. C₂²×D₁₃	C₂²×D₄	semidirect
300. D₄×C₁₃	C₂²×D₄	semidirect
304. C₂×C₄×C₁₃	C₂²×D₄	semidirect
312. C₂²⋊D₁₃	C₂²×D₄	semidirect
316. C₂×Dic₁₃	C₂²×D₄	semidirect
323. D₅₂	C₂²×D₄	semidirect
328. C₄×D₁₃	C₂²×D₄	semidirect
341. C₂³×D₄	C₂×D₁₃	semidirect
348. D₄²	C₂×D₁₃	direct (N × H)
353. C₂×#127	C₂×D₁₃	semidirect
360. C₂×#121	C₂×D₁₃	semidirect
367. C₂×#120	C₂×D₁₃	semidirect
374. C₂×C₄×D₄	C₂×D₁₃	semidirect
387. C₂²×C₁₃	C₂³×D₄	semidirect
400. C₂×D₁₃	D₄²	direct (N × H)
402. C₂×D₁₃	C₂³×D₄	semidirect
406. C₄×C₁₃	C₂³×D₄	semidirect
409. Dic₁₃	C₂³×D₄	semidirect
417. C₂⁵	C₂²×D₁₃	semidirect
448. C₂²×D₄	C₂²×D₁₃	semidirect
449. C₂²×D₄	C₂²×D₁₃	semidirect
450. C₂²×D₄	C₂²×D₁₃	semidirect
451. C₂²×D₄	C₂²×D₁₃	semidirect
460. C₂³×C₄	C₂²×D₁₃	semidirect
464. #127	C₂²×D₁₃	semidirect
470. #121	C₂²×D₁₃	semidirect
476. #120	C₂²×D₁₃	semidirect
482. C₄×D₄	C₂²×D₁₃	semidirect
486. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
494. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
495. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
499. C₂×C₄²	C₂²×D₁₃	semidirect
502. C₂×C₁₃	C₂×D₄²	semidirect
507. D₁₃	C₂×D₄²	direct (N × H)
532. C₂⁴	C₂³×D₁₃	semidirect
564. C₂×D₄	D₄×D₁₃	direct (N × H)
566. C₂×D₄	C₂³×D₁₃	semidirect
567. C₂×D₄	C₂³×D₁₃	semidirect
568. C₂×D₄	C₂³×D₁₃	semidirect
589. C₂²×C₄	C₂³×D₁₃	semidirect
592. C₄⋊C₄	C₂³×D₁₃	semidirect
598. C₂²⋊C₄	C₂³×D₁₃	semidirect
599. C₂²⋊C₄	C₂³×D₁₃	semidirect
602. C₄²	C₂³×D₁₃	semidirect
603. C₁₃	C₂²×D₄²	semidirect
636. C₂³	C₂×D₄×D₁₃	semidirect
652. D₄	C₂×D₄×D₁₃	direct (N × H)
668. C₂×C₄	C₂×D₄×D₁₃	semidirect
694. C₂²	C₂²×D₄×D₁₃	semidirect
702. C₄	C₂²×D₄×D₁₃	semidirect
708. C₂	D₄²×D₁₃	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×D₄×D₁₃	2
C₂×D₄×D₅₂	2
C₂×#11719422	2
C₂×#11719314	2
C₂×D₄×C₂²⋊D₁₃	2
C₂×#11719295	2
D₄²×D₁₃	2
C₂×D₁₃×#127	2
C₂×D₁₃×#121	2
C₂×D₁₃×#120	2
C₂×C₄×D₄×D₁₃	2
C₂×D₄²×C₁₃	2
C₂²×D₄²	13

Subgroups — C2×D42×D13 #16769825

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₄²×D₁₃ #16769825