Subgroups — C₂×C₄×#88251 #16769520

Order 3328.

12378 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88251	C₂	1	1	yes	maximal, characteristic
2	C₄×#88251	C₂	1	32	yes	maximal, direct product factor
3	C₂×#11719209	C₂	1	2	yes	maximal, complemented
4	C₂×#11719251	C₂	1	4	yes	maximal, complemented
5	C₂×#11719503	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11719191	C₂	1	4	yes	maximal, complemented
7	C₂×#11719250	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×#6127	C₂	1	2	yes	maximal, complemented
9	C₂×C₄×#6129	C₂	1	4	yes	maximal, complemented
10	C₂²×C₄×C₂²⋊D₁₃	C₂	1	4	yes	maximal, complemented
11	C₂×C₄×D₄×D₁₃	C₂	1	4	yes	maximal, complemented
12	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	complemented
15	C₂³×C₂²⋊D₁₃	C₂²	1	4	yes	—
16	C₂×#88251	C₄	1	32	yes	direct product factor
17	C₂×#88251	C₂²	1	16	yes	—
18	C₂²×#6129	C₂²	1	4	yes	—
19	C₂²×D₄×D₁₃	C₂²	1	4	yes	—
20	C₂²×#6127	C₂²	1	2	yes	—
21	C₂³×C₄×D₁₃	C₂²	1	4	yes	complemented
22	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
23	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
24	C₂×C₄×D₄×C₁₃	C₂²	1	16	yes	complemented
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
27	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₂²⋊Dic₁₃	C₂²	1	4	yes	complemented
29	#11719503	C₂²	1	16	yes	complemented
30	C₂×D₄×Dic₁₃	C₂²	1	4	yes	complemented
31	C₂×D₄×Dic₁₃	C₂²	1	4	yes	complemented
32	C₂×C₄×C₂²⋊D₁₃	C₂²	1	8	yes	complemented
33	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
34	C₂×C₄×C₂²⋊D₁₃	C₂²	1	8	yes	complemented
35	C₂×C₄×C₂²⋊D₁₃	C₂²	1	8	yes	complemented
36	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
37	C₂×C₄×C₂²⋊D₁₃	C₂²	1	64	yes	complemented
38	C₂²×#6103	C₂²	1	4	yes	complemented
39	C₂×#88180	C₂²	1	2	yes	complemented
40	C₂²×#6101	C₂²	1	4	yes	complemented
41	C₂²×C₄×Dic₁₃	C₂²	1	4	yes	complemented
42	#11719251	C₂²	1	64	yes	complemented
43	#11719250	C₂²	1	64	yes	complemented
44	C₄×D₄×D₁₃	C₂²	1	64	yes	complemented
45	C₄×#6129	C₂²	1	64	yes	complemented
46	#11719209	C₂²	1	32	yes	complemented
47	C₂×#88147	C₂²	1	4	yes	complemented
48	C₂×#88146	C₂²	1	4	yes	complemented
49	C₂×C₄⋊C₄×D₁₃	C₂²	1	4	yes	complemented
50	C₂×#88141	C₂²	1	4	yes	complemented
51	#11719191	C₂²	1	64	yes	complemented
52	C₂×#88135	C₂²	1	8	yes	complemented
53	C₂×#88135	C₂²	1	8	yes	complemented
54	C₂×C₂²⋊C₄×D₁₃	C₂²	1	8	yes	complemented
55	C₂×#88131	C₂²	1	8	yes	complemented
56	C₄×#6127	C₂²	1	32	yes	complemented
57	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
58	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
59	C₂×#88126	C₂²	1	4	yes	complemented
60	C₂×C₄²×D₁₃	C₂²	1	4	yes	complemented
61	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
62	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
63	C₂⁵×C₁₃	C₂³	1	2	yes	—
64	C₂⁴×D₁₃	C₂³	1	4	yes	—
65	C₂²×D₄×C₁₃	C₂×C₄	1	16	yes	complemented
66	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
67	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
68	C₂³×C₄×C₁₃	—	4	8	no	—
69	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
74	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₁₃	C₂³	1	16	yes	complemented
76	C₂²×C₂²⋊D₁₃	C₂×C₄	1	64	yes	complemented
77	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
78	C₂²×C₂²⋊D₁₃	C₂³	1	32	yes	—
79	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
80	C₂³×Dic₁₃	C₂³	1	4	yes	—
81	C₂³×Dic₁₃	C₂³	1	4	yes	—
82	C₂³×Dic₁₃	C₂³	1	4	yes	—
83	#88251	C₂×C₄	1	256	yes	direct product factor
84	C₂×#6129	C₂×C₄	1	64	yes	complemented
85	C₂×#6129	C₂³	1	32	yes	—
86	C₂×D₄×D₁₃	C₂×C₄	1	64	yes	complemented
87	C₂×D₄×D₁₃	C₂³	1	32	yes	—
88	C₂×#6127	C₂×C₄	1	32	yes	complemented
89	C₂×#6127	C₂³	1	16	yes	—
90	C₂²×D₅₂	C₂³	1	2	yes	—
91	C₂²×C₄×D₁₃	—	4	16	no	—
92	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
93	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
94	C₂²×C₄×D₁₃	C₂³	1	8	yes	—
95	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
96	C₂²×C₄×D₁₃	C₂³	1	32	yes	complemented
97	C₂²×Dic₂₆	C₂³	1	2	yes	—
98	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
99	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	complemented
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	complemented
104	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
105	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
106	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
107	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	—
108	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
109	C₂×C₂²⋊Dic₁₃	C₂³	1	32	yes	complemented
110	D₄×Dic₁₃	C₂³	1	32	yes	complemented
111	D₄×Dic₁₃	C₂³	1	32	yes	complemented
112	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
113	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
114	C₄×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
115	C₄×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
116	C₄×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
117	C₂×#6103	C₂³	1	4	yes	—
118	C₂×#6103	C₂³	1	4	yes	—
119	C₂×#6103	C₂³	1	8	yes	—
120	C₂×#6103	C₂³	1	32	yes	complemented
121	#88180	C₂³	1	16	yes	complemented
122	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
123	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
124	C₂×#6101	C₂³	1	4	yes	—
125	C₂×#6101	C₂³	1	4	yes	—
126	C₂×#6101	C₂³	1	8	yes	—
127	C₂×#6101	C₂³	1	32	yes	complemented
128	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
129	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
130	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
131	C₂×C₄×Dic₁₃	C₂³	1	8	yes	—
132	C₂×C₄×Dic₁₃	C₂³	1	32	yes	complemented
133	#88147	C₂³	1	32	yes	complemented
134	#88146	C₂³	1	32	yes	complemented
135	C₄⋊C₄×D₁₃	C₂³	1	32	yes	complemented
136	#88141	C₂³	1	32	yes	complemented
137	#88135	C₂³	1	64	yes	complemented
138	#88135	C₂³	1	64	yes	complemented
139	C₂²⋊C₄×D₁₃	C₂³	1	64	yes	complemented
140	#88131	C₂³	1	64	yes	complemented
141	C₄×D₅₂	C₂³	1	16	yes	complemented
142	C₄×D₅₂	C₂³	1	16	yes	complemented
143	#88126	C₂³	1	32	yes	complemented
144	C₄²×D₁₃	C₂³	1	32	yes	complemented
145	C₄×Dic₂₆	C₂³	1	16	yes	complemented
146	C₄×Dic₂₆	C₂³	1	16	yes	complemented
147	C₂×C₄×H(5,𝔽₂)	—	13	1	no	maximal, Sylow
148	C₂⁴×C₁₃	—	4	4	no	—
149	C₂⁴×C₁₃	—	4	4	no	—
150	C₂⁴×C₁₃	C₂²×C₄	1	16	yes	complemented
151	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
153	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
154	C₂³×D₁₃	—	4	8	no	—
155	C₂³×D₁₃	—	4	8	no	—
156	C₂³×D₁₃	C₂²×C₄	1	32	yes	complemented
157	C₂³×D₁₃	C₂⁴	1	4	yes	—
158	C₂³×D₁₃	C₂⁴	1	16	yes	—
159	C₂×D₄×C₁₃	C₂²×C₄	1	32	yes	complemented
160	C₂×D₄×C₁₃	C₂²×C₄	1	64	yes	complemented
161	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
162	C₂²×C₄×C₁₃	—	2	16	no	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	4	32	no	—
165	C₂²×C₄×C₁₃	—	4	4	no	—
166	C₂²×C₄×C₁₃	—	4	8	no	—
167	C₂²×C₄×C₁₃	—	4	2	no	—
168	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	complemented
169	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
172	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₂×C₂²⋊D₁₃	C₂²×C₄	1	32	yes	complemented
181	C₂×C₂²⋊D₁₃	C₂²×C₄	1	64	yes	complemented
182	C₂×C₂²⋊D₁₃	C₂²×C₄	1	256	yes	complemented
183	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
184	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
185	C₂²×Dic₁₃	—	4	8	no	—
186	C₂²×Dic₁₃	—	4	8	no	—
187	C₂²×Dic₁₃	C₂²×C₄	1	32	yes	complemented
188	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
189	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
190	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
191	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
192	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
193	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
194	#6129	C₂²×C₄	1	256	yes	complemented
195	D₄×D₁₃	C₂²×C₄	1	256	yes	complemented
196	#6127	C₂²×C₄	1	128	yes	complemented
197	C₂×D₅₂	C₂²×C₄	1	16	yes	complemented
198	C₂×D₅₂	C₂⁴	1	8	yes	—
199	C₂×C₄×D₁₃	—	2	16	no	—
200	C₂×C₄×D₁₃	—	4	64	no	—
201	C₂×C₄×D₁₃	—	4	16	no	—
202	C₂×C₄×D₁₃	—	4	8	no	—
203	C₂×C₄×D₁₃	C₂²×C₄	1	32	yes	complemented
204	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
205	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
206	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
207	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
208	C₂×Dic₂₆	C₂²×C₄	1	16	yes	complemented
209	C₂×Dic₂₆	C₂⁴	1	8	yes	—
210	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
211	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
212	C₄²×C₁₃	C₂⁴	1	8	yes	—
213	C₄²×C₁₃	C₂⁴	1	8	yes	—
214	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
215	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
216	#6103	C₂⁴	1	16	yes	—
217	#6103	C₂⁴	1	16	yes	—
218	#6103	C₂⁴	1	32	yes	—
219	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
220	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
221	#6101	C₂⁴	1	16	yes	—
222	#6101	C₂⁴	1	16	yes	—
223	#6101	C₂⁴	1	32	yes	—
224	C₄×Dic₁₃	C₂⁴	1	16	yes	—
225	C₄×Dic₁₃	C₂⁴	1	16	yes	—
226	C₄×Dic₁₃	C₂⁴	1	16	yes	—
227	C₄×Dic₁₃	C₂⁴	1	32	yes	—
228	C₂²×H(5,𝔽₂)	—	13	1	no	—
229	C₄×H(5,𝔽₂)	—	13	32	no	—
230	C₂×#520	—	13	4	no	—
231	C₂×#520	—	13	2	no	—
232	C₂×#518	—	13	1	no	—
233	C₂×#518	—	13	4	no	—
234	C₂×#518	—	13	4	no	—
235	C₂×C₄×#41	—	13	2	no	—
236	C₂×C₄×#41	—	13	4	no	—
237	C₂²×C₄×D₄	—	13	4	no	—
238	C₂²×C₄×D₄	—	13	4	no	—
239	C₂²×C₄×D₄	D₁₃	1	1	yes	characteristic, complemented
240	C₂³×C₁₃	—	2	8	no	—
241	C₂³×C₁₃	—	2	2	no	—
242	C₂³×C₁₃	—	2	8	no	—
243	C₂³×C₁₃	—	2	2	no	—
244	C₂³×C₁₃	—	4	8	no	—
245	C₂³×C₁₃	—	4	32	no	—
246	C₂³×C₁₃	—	4	8	no	—
247	C₂³×C₁₃	C₂³×C₄	1	16	yes	—
248	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
249	C₂³×C₁₃	C₂³×C₄	1	32	yes	complemented
250	C₂³×C₁₃	C₂⁵	1	2	yes	—
251	C₂³×C₁₃	C₂⁵	1	8	yes	—
252	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
253	C₂²×D₁₃	—	2	8	no	—
254	C₂²×D₁₃	—	2	8	no	—
255	C₂²×D₁₃	—	4	16	no	—
256	C₂²×D₁₃	—	4	64	no	—
257	C₂²×D₁₃	—	4	16	no	—
258	C₂²×D₁₃	C₂³×C₄	1	16	yes	—
259	C₂²×D₁₃	C₂³×C₄	1	64	yes	complemented
260	C₂²×D₁₃	C₂⁵	1	8	yes	—
261	D₄×C₁₃	C₂³×C₄	1	64	yes	complemented
262	C₂×C₄×C₁₃	—	2	8	no	—
263	C₂×C₄×C₁₃	—	2	2	no	—
264	C₂×C₄×C₁₃	—	2	4	no	—
265	C₂×C₄×C₁₃	—	2	32	no	—
266	C₂×C₄×C₁₃	—	2	8	no	—
267	C₂×C₄×C₁₃	—	4	8	no	—
268	C₂×C₄×C₁₃	—	4	16	no	—
269	C₂×C₄×C₁₃	—	4	4	no	—
270	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
271	C₂×C₄×C₁₃	C₂³×C₄	1	16	yes	complemented
272	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	complemented
273	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
274	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
275	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
276	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
277	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
278	C₂²⋊D₁₃	C₂³×C₄	1	64	yes	complemented
279	C₂²⋊D₁₃	C₂³×C₄	1	128	yes	complemented
280	C₂×Dic₁₃	—	2	8	no	—
281	C₂×Dic₁₃	—	2	8	no	—
282	C₂×Dic₁₃	—	4	16	no	—
283	C₂×Dic₁₃	—	4	16	no	—
284	C₂×Dic₁₃	C₂³×C₄	1	16	yes	—
285	C₂×Dic₁₃	C₂³×C₄	1	64	yes	complemented
286	C₂×Dic₁₃	C₂⁵	1	8	yes	—
287	C₂×Dic₁₃	C₂⁵	1	8	yes	—
288	C₂×Dic₁₃	C₂⁵	1	8	yes	—
289	D₅₂	C₂³×C₄	1	32	yes	complemented
290	C₄×D₁₃	—	2	32	no	—
291	C₄×D₁₃	—	4	32	no	—
292	C₄×D₁₃	—	4	16	no	—
293	C₄×D₁₃	C₂³×C₄	1	64	yes	complemented
294	Dic₂₆	C₂³×C₄	1	32	yes	complemented
295	C₂×H(5,𝔽₂)	—	13	32	no	—
296	C₂×H(5,𝔽₂)	—	13	16	no	—
297	C₂²×#41	—	13	4	no	—
298	C₂²×#41	—	13	2	no	—
299	C₂³×D₄	—	13	4	no	—
300	C₂³×D₄	—	13	4	no	—
301	C₂³×D₄	C₂×D₁₃	1	1	yes	characteristic
302	C₂⁴×C₄	—	13	4	no	—
303	C₂⁴×C₄	C₂×D₁₃	1	2	yes	complemented
304	#520	—	13	64	no	—
305	#520	—	13	32	no	—
306	#518	—	13	16	no	—
307	#518	—	13	64	no	—
308	#518	—	13	64	no	—
309	C₄×#41	—	13	64	no	—
310	C₄×#41	—	13	32	no	—
311	C₂×C₄×Q₈	—	13	4	no	—
312	C₂×C₄×Q₈	—	13	2	no	—
313	C₂×C₄×Q₈	—	13	2	no	—
314	C₂×C₄×D₄	—	13	4	no	—
315	C₂×C₄×D₄	—	13	4	no	—
316	C₂×C₄×D₄	—	13	4	no	—
317	C₂×C₄×D₄	—	13	8	no	—
318	C₂×C₄×D₄	—	13	8	no	—
319	C₂×C₄×D₄	—	13	8	no	—
320	C₂×C₄×D₄	—	13	4	no	—
321	C₂×C₄×D₄	—	13	64	no	—
322	C₂×C₄×D₄	—	13	64	no	—
323	C₂×C₄×D₄	—	13	4	no	—
324	C₂×C₄×D₄	—	13	8	no	—
325	C₂×C₄×D₄	—	13	8	no	—
326	C₂×C₄×D₄	—	13	2	no	—
327	C₂×C₄×D₄	—	13	2	no	—
328	C₂×C₄×D₄	C₂×D₁₃	1	4	yes	complemented
329	C₂×C₄×D₄	C₂×D₁₃	1	4	yes	complemented
330	C₂×C₄×D₄	C₂×D₁₃	1	16	yes	complemented
331	C₂×#117	—	13	2	no	—
332	C₂×#117	—	13	4	no	—
333	C₂×#117	—	13	8	no	—
334	C₂×#117	—	13	4	no	—
335	C₂²×C₄⋊C₄	—	13	4	no	—
336	C₂²×C₄⋊C₄	—	13	4	no	—
337	C₂²×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
338	C₂²×C₂²⋊C₄	—	13	4	no	—
339	C₂²×C₂²⋊C₄	—	13	4	no	—
340	C₂²×C₂²⋊C₄	—	13	8	no	—
341	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	complemented
342	C₂²×C₄²	—	13	4	no	—
343	C₂²×C₄²	—	13	4	no	—
344	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
345	C₂²×C₁₃	—	2	8	no	—
346	C₂²×C₁₃	—	2	2	no	—
347	C₂²×C₁₃	—	2	8	no	—
348	C₂²×C₁₃	—	2	2	no	—
349	C₂²×C₁₃	—	2	32	no	—
350	C₂²×C₁₃	—	2	8	no	—
351	C₂²×C₁₃	—	4	32	no	—
352	C₂²×C₁₃	C₂⁴×C₄	1	16	yes	—
353	C₂²×C₁₃	C₂⁴×C₄	1	4	yes	—
354	C₂²×C₁₃	C₂⁴×C₄	1	2	yes	—
355	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
356	C₂²×C₁₃	#585	1	2	yes	—
357	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
358	C₂×D₁₃	—	2	8	no	—
359	C₂×D₁₃	—	2	8	no	—
360	C₂×D₁₃	—	2	32	no	—
361	C₂×D₁₃	—	4	64	no	—
362	C₂×D₁₃	C₂⁴×C₄	1	16	yes	—
363	C₄×C₁₃	—	2	8	no	—
364	C₄×C₁₃	—	2	2	no	—
365	C₄×C₁₃	—	2	4	no	—
366	C₄×C₁₃	C₂⁴×C₄	1	8	yes	—
367	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	complemented
368	Dic₁₃	—	2	8	no	—
369	Dic₁₃	—	2	8	no	—
370	Dic₁₃	C₂⁴×C₄	1	16	yes	—
371	C₂⁵	—	13	4	no	—
372	C₂⁵	C₂²×D₁₃	1	2	yes	—
373	H(5,𝔽₂)	—	13	256	no	—
374	C₂×#41	—	13	64	no	—
375	C₂×#41	—	13	32	no	—
376	C₂×#41	—	13	32	no	—
377	C₂×#41	—	13	16	no	—
378	C₂²×Q₈	—	13	2	no	—
379	C₂²×D₄	—	13	64	no	—
380	C₂²×D₄	—	13	4	no	—
381	C₂²×D₄	—	13	8	no	—
382	C₂²×D₄	—	13	32	no	—
383	C₂²×D₄	—	13	64	no	—
384	C₂²×D₄	—	13	32	no	—
385	C₂²×D₄	—	13	2	no	—
386	C₂²×D₄	C₄×D₁₃	1	16	yes	complemented
387	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
388	C₂²×D₄	C₂²×D₁₃	1	8	yes	—
389	C₂³×C₄	—	4	8	no	—
390	C₂³×C₄	—	13	4	no	—
391	C₂³×C₄	—	13	4	no	—
392	C₂³×C₄	—	13	4	no	—
393	C₂³×C₄	—	13	4	no	—
394	C₂³×C₄	—	13	4	no	—
395	C₂³×C₄	—	13	4	no	—
396	C₂³×C₄	—	13	8	no	—
397	C₂³×C₄	—	13	32	no	—
398	C₂³×C₄	—	52	16	no	—
399	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
400	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
401	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
402	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
403	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
404	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
405	C₂³×C₄	C₂²×D₁₃	1	16	yes	complemented
406	C₄×Q₈	—	13	32	no	—
407	C₄×Q₈	—	13	16	no	—
408	C₄×Q₈	—	13	16	no	—
409	C₄×D₄	—	13	32	no	—
410	C₄×D₄	—	13	32	no	—
411	C₄×D₄	—	13	64	no	—
412	C₄×D₄	—	13	32	no	—
413	C₄×D₄	—	13	64	no	—
414	C₄×D₄	—	13	64	no	—
415	C₄×D₄	—	13	32	no	—
416	C₄×D₄	—	13	32	no	—
417	C₄×D₄	—	13	64	no	—
418	C₄×D₄	—	13	64	no	—
419	C₄×D₄	—	13	16	no	—
420	C₄×D₄	—	13	16	no	—
421	C₄×D₄	C₂²×D₁₃	1	32	yes	complemented
422	C₄×D₄	C₂²×D₁₃	1	32	yes	complemented
423	#117	—	13	16	no	—
424	#117	—	13	32	no	—
425	#117	—	13	64	no	—
426	#117	—	13	32	no	—
427	C₂×C₄⋊C₄	—	13	8	no	—
428	C₂×C₄⋊C₄	—	13	4	no	—
429	C₂×C₄⋊C₄	—	13	2	no	—
430	C₂×C₄⋊C₄	—	13	32	no	—
431	C₂×C₄⋊C₄	—	13	4	no	—
432	C₂×C₄⋊C₄	—	13	2	no	—
433	C₂×C₄⋊C₄	—	13	32	no	—
434	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
435	C₂×C₄⋊C₄	C₂²×D₁₃	1	8	yes	complemented
436	C₂×C₂²⋊C₄	—	13	4	no	—
437	C₂×C₂²⋊C₄	—	13	8	no	—
438	C₂×C₂²⋊C₄	—	13	32	no	—
439	C₂×C₂²⋊C₄	—	13	8	no	—
440	C₂×C₂²⋊C₄	—	13	4	no	—
441	C₂×C₂²⋊C₄	—	13	4	no	—
442	C₂×C₂²⋊C₄	—	13	32	no	—
443	C₂×C₂²⋊C₄	—	13	64	no	—
444	C₂×C₂²⋊C₄	C₂²×D₁₃	1	8	yes	—
445	C₂×C₂²⋊C₄	C₂²×D₁₃	1	16	yes	complemented
446	C₂×C₄²	—	13	8	no	—
447	C₂×C₄²	—	13	4	no	—
448	C₂×C₄²	—	13	4	no	—
449	C₂×C₄²	—	13	32	no	—
450	C₂×C₄²	—	13	4	no	—
451	C₂×C₄²	—	13	32	no	—
452	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
453	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
454	C₂×C₄²	C₂²×D₁₃	1	8	yes	complemented
455	C₂×C₁₃	—	2	16	no	—
456	C₂×C₁₃	—	2	4	no	—
457	C₂×C₁₃	C₄×H(5,𝔽₂)	1	4	yes	complemented
458	C₂×C₁₃	C₂⁵×C₄	1	1	yes	characteristic
459	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
460	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
461	D₁₃	—	2	16	no	—
462	C₂⁴	—	4	4	no	—
463	C₂⁴	—	4	4	no	—
464	C₂⁴	—	13	4	no	—
465	C₂⁴	—	13	32	no	—
466	C₂⁴	—	13	16	no	—
467	C₂⁴	—	52	8	no	—
468	C₂⁴	—	52	8	no	—
469	C₂⁴	C₂×C₄×D₁₃	1	16	yes	complemented
470	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
471	C₂⁴	C₂³×D₁₃	1	4	yes	—
472	C₂⁴	C₂³×D₁₃	1	8	yes	—
473	#41	—	13	256	no	—
474	#41	—	13	128	no	—
475	C₂×Q₈	—	13	16	no	—
476	C₂×Q₈	—	13	8	no	—
477	C₂×D₄	—	13	64	no	—
478	C₂×D₄	—	13	32	no	—
479	C₂×D₄	—	13	256	no	—
480	C₂×D₄	—	13	16	no	—
481	C₂×D₄	—	13	32	no	—
482	C₂×D₄	—	13	256	no	—
483	C₂×D₄	—	13	16	no	—
484	C₂×D₄	—	13	8	no	—
485	C₂×D₄	C₂×C₄×D₁₃	1	32	yes	complemented
486	C₂×D₄	C₂×C₄×D₁₃	1	64	yes	complemented
487	C₂×D₄	C₂³×D₁₃	1	16	yes	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	2	16	no	—
490	C₂²×C₄	—	4	32	no	—
491	C₂²×C₄	—	4	8	no	—
492	C₂²×C₄	—	4	4	no	—
493	C₂²×C₄	—	4	2	no	—
494	C₂²×C₄	—	13	32	no	—
495	C₂²×C₄	—	13	4	no	—
496	C₂²×C₄	—	13	16	no	—
497	C₂²×C₄	—	13	32	no	—
498	C₂²×C₄	—	13	16	no	—
499	C₂²×C₄	—	13	4	no	—
500	C₂²×C₄	—	13	4	no	—
501	C₂²×C₄	—	13	16	no	—
502	C₂²×C₄	—	13	16	no	—
503	C₂²×C₄	—	13	16	no	—
504	C₂²×C₄	—	13	16	no	—
505	C₂²×C₄	—	13	32	no	—
506	C₂²×C₄	—	26	16	no	—
507	C₂²×C₄	—	52	64	no	—
508	C₂²×C₄	—	52	16	no	—
509	C₂²×C₄	—	52	8	no	—
510	C₂²×C₄	—	52	8	no	—
511	C₂²×C₄	—	52	8	no	—
512	C₂²×C₄	C₂×C₄×D₁₃	1	8	yes	complemented
513	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
514	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
515	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
516	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
517	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
518	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
519	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
520	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
521	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
522	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
523	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
524	C₄⋊C₄	—	13	32	no	—
525	C₄⋊C₄	—	13	16	no	—
526	C₄⋊C₄	—	13	8	no	—
527	C₄⋊C₄	—	13	16	no	—
528	C₄⋊C₄	—	13	8	no	—
529	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
530	C₂²⋊C₄	—	13	16	no	—
531	C₂²⋊C₄	—	13	32	no	—
532	C₂²⋊C₄	—	13	32	no	—
533	C₂²⋊C₄	—	13	16	no	—
534	C₂²⋊C₄	—	13	16	no	—
535	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	—
536	C₄²	—	13	16	no	—
537	C₄²	—	13	32	no	—
538	C₄²	—	13	16	no	—
539	C₄²	—	13	16	no	—
540	C₄²	C₂³×D₁₃	1	8	yes	—
541	C₄²	C₂³×D₁₃	1	8	yes	—
542	C₁₃	C₂×C₄×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
543	C₂³	—	2	2	no	—
544	C₂³	—	2	8	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	8	no	—
547	C₂³	—	4	8	no	—
548	C₂³	—	4	32	no	—
549	C₂³	—	4	8	no	—
550	C₂³	—	13	16	no	—
551	C₂³	—	13	8	no	—
552	C₂³	—	13	64	no	—
553	C₂³	—	26	8	no	—
554	C₂³	—	26	8	no	—
555	C₂³	—	52	16	no	—
556	C₂³	—	52	64	no	—
557	C₂³	—	52	16	no	—
558	C₂³	C₂²×C₄×D₁₃	1	16	yes	—
559	C₂³	C₂²×C₄×D₁₃	1	4	yes	—
560	C₂³	C₂²×C₄×D₁₃	1	32	yes	complemented
561	C₂³	C₂⁴×D₁₃	1	2	yes	—
562	C₂³	C₂⁴×D₁₃	1	8	yes	—
563	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
564	Q₈	—	13	32	no	—
565	D₄	—	13	128	no	—
566	D₄	—	13	64	no	—
567	D₄	—	13	32	no	—
568	D₄	C₂²×C₄×D₁₃	1	64	yes	complemented
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	8	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	8	no	—
573	C₂×C₄	—	2	32	no	—
574	C₂×C₄	—	4	16	no	—
575	C₂×C₄	—	4	8	no	—
576	C₂×C₄	—	4	4	no	—
577	C₂×C₄	—	13	16	no	—
578	C₂×C₄	—	13	64	no	—
579	C₂×C₄	—	13	8	no	—
580	C₂×C₄	—	13	64	no	—
581	C₂×C₄	—	13	8	no	—
582	C₂×C₄	—	13	8	no	—
583	C₂×C₄	—	26	8	no	—
584	C₂×C₄	—	26	8	no	—
585	C₂×C₄	—	26	32	no	—
586	C₂×C₄	—	52	16	no	—
587	C₂×C₄	—	52	32	no	—
588	C₂×C₄	—	52	16	no	—
589	C₂×C₄	—	52	16	no	—
590	C₂×C₄	C₂²×C₄×D₁₃	1	8	yes	—
591	C₂×C₄	C₂²×C₄×D₁₃	1	16	yes	complemented
592	C₂×C₄	#88251	1	4	yes	direct product factor
593	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
594	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
595	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
596	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
597	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
598	C₂²	—	2	8	no	—
599	C₂²	—	2	32	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	2	8	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	2	8	no	—
604	C₂²	—	4	32	no	—
605	C₂²	—	13	16	no	—
606	C₂²	—	26	32	no	—
607	C₂²	—	26	8	no	—
608	C₂²	—	26	8	no	—
609	C₂²	—	52	64	no	—
610	C₂²	C₂³×C₄×D₁₃	1	16	yes	—
611	C₂²	C₂³×C₄×D₁₃	1	4	yes	—
612	C₂²	C₂³×C₄×D₁₃	1	2	yes	—
613	C₂²	C₂×#88251	1	2	yes	—
614	C₂²	#11719648	1	2	yes	—
615	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
616	C₄	—	2	2	no	—
617	C₄	—	2	8	no	—
618	C₄	—	2	4	no	—
619	C₄	—	13	16	no	—
620	C₄	—	26	8	no	—
621	C₄	—	26	8	no	—
622	C₄	C₂³×C₄×D₁₃	1	8	yes	—
623	C₄	C₂×#88251	1	4	yes	direct product factor
624	C₂	—	2	4	no	—
625	C₂	—	2	16	no	—
626	C₂	—	26	16	no	—
627	C₂	C₄×#88251	1	4	yes	direct product factor
628	C₂	C₂⁴×C₄×D₁₃	1	1	yes	characteristic
629	C₂	C₂²×#88251	1	1	yes	characteristic
630	C₂	C₂×#11719648	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₁₃
commutator	C₂×C₁₃	C₂⁵×C₄
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₄×D₄×C₁₃	C₂
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂²×#88251	C₂
cosocle	C₂²×C₁₃	C₂⁶
hypercenter	C₂²×C₄×D₄	D₁₃
hypocenter	C₁₃	C₂×C₄×H(5,𝔽₂)
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₄×#88251	C₂	direct (N × H)
3. C₂×#11719209	C₂	semidirect
4. C₂×#11719251	C₂	semidirect
5. C₂×#11719503	C₂	semidirect
6. C₂×#11719191	C₂	semidirect
7. C₂×#11719250	C₂	semidirect
8. C₂×C₄×#6127	C₂	semidirect
9. C₂×C₄×#6129	C₂	semidirect
10. C₂²×C₄×C₂²⋊D₁₃	C₂	semidirect
11. C₂×C₄×D₄×D₁₃	C₂	semidirect
12. C₂²×C₄×D₄×C₁₃	C₂	semidirect
14. C₂⁴×C₄×C₁₃	C₂²	semidirect
16. C₂×#88251	C₄	direct (N × H)
21. C₂³×C₄×D₁₃	C₂²	semidirect
22. C₂×C₄×D₄×C₁₃	C₂²	semidirect
23. C₂×C₄×D₄×C₁₃	C₂²	semidirect
24. C₂×C₄×D₄×C₁₃	C₂²	semidirect
25. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
26. C₂²×C₁₃×C₂²⋊C₄	C₂²	semidirect
27. C₂²×C₄²×C₁₃	C₂²	semidirect
28. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
29. #11719503	C₂²	semidirect
30. C₂×D₄×Dic₁₃	C₂²	semidirect
31. C₂×D₄×Dic₁₃	C₂²	semidirect
32. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
33. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
34. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
35. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
36. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
37. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
38. C₂²×#6103	C₂²	semidirect
39. C₂×#88180	C₂²	semidirect
40. C₂²×#6101	C₂²	semidirect
41. C₂²×C₄×Dic₁₃	C₂²	semidirect
42. #11719251	C₂²	semidirect
43. #11719250	C₂²	semidirect
44. C₄×D₄×D₁₃	C₂²	semidirect
45. C₄×#6129	C₂²	semidirect
46. #11719209	C₂²	semidirect
47. C₂×#88147	C₂²	semidirect
48. C₂×#88146	C₂²	semidirect
49. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
50. C₂×#88141	C₂²	semidirect
51. #11719191	C₂²	semidirect
52. C₂×#88135	C₂²	semidirect
53. C₂×#88135	C₂²	semidirect
54. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
55. C₂×#88131	C₂²	semidirect
56. C₄×#6127	C₂²	semidirect
57. C₂×C₄×D₅₂	C₂²	semidirect
58. C₂×C₄×D₅₂	C₂²	semidirect
59. C₂×#88126	C₂²	semidirect
60. C₂×C₄²×D₁₃	C₂²	semidirect
61. C₂×C₄×Dic₂₆	C₂²	semidirect
62. C₂×C₄×Dic₂₆	C₂²	semidirect
65. C₂²×D₄×C₁₃	C₂×C₄	semidirect
75. C₂³×C₄×C₁₃	C₂³	semidirect
76. C₂²×C₂²⋊D₁₃	C₂×C₄	semidirect
83. #88251	C₂×C₄	direct (N × H)
84. C₂×#6129	C₂×C₄	semidirect
86. C₂×D₄×D₁₃	C₂×C₄	semidirect
88. C₂×#6127	C₂×C₄	semidirect
96. C₂²×C₄×D₁₃	C₂³	semidirect
98. C₄×D₄×C₁₃	C₂³	semidirect
99. C₄×D₄×C₁₃	C₂³	semidirect
101. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
103. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
106. C₂×C₄²×C₁₃	C₂³	semidirect
109. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
110. D₄×Dic₁₃	C₂³	semidirect
111. D₄×Dic₁₃	C₂³	semidirect
112. C₄×C₂²⋊D₁₃	C₂³	semidirect
113. C₄×C₂²⋊D₁₃	C₂³	semidirect
114. C₄×C₂²⋊D₁₃	C₂³	semidirect
115. C₄×C₂²⋊D₁₃	C₂³	semidirect
116. C₄×C₂²⋊D₁₃	C₂³	semidirect
120. C₂×#6103	C₂³	semidirect
121. #88180	C₂³	semidirect
127. C₂×#6101	C₂³	semidirect
132. C₂×C₄×Dic₁₃	C₂³	semidirect
133. #88147	C₂³	semidirect
134. #88146	C₂³	semidirect
135. C₄⋊C₄×D₁₃	C₂³	semidirect
136. #88141	C₂³	semidirect
137. #88135	C₂³	semidirect
138. #88135	C₂³	semidirect
139. C₂²⋊C₄×D₁₃	C₂³	semidirect
140. #88131	C₂³	semidirect
141. C₄×D₅₂	C₂³	semidirect
142. C₄×D₅₂	C₂³	semidirect
143. #88126	C₂³	semidirect
144. C₄²×D₁₃	C₂³	semidirect
145. C₄×Dic₂₆	C₂³	semidirect
146. C₄×Dic₂₆	C₂³	semidirect
150. C₂⁴×C₁₃	C₂²×C₄	semidirect
156. C₂³×D₁₃	C₂²×C₄	semidirect
159. C₂×D₄×C₁₃	C₂²×C₄	semidirect
160. C₂×D₄×C₁₃	C₂²×C₄	semidirect
168. C₂²×C₄×C₁₃	C₂²×C₄	semidirect
180. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
181. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
182. C₂×C₂²⋊D₁₃	C₂²×C₄	semidirect
187. C₂²×Dic₁₃	C₂²×C₄	semidirect
194. #6129	C₂²×C₄	semidirect
195. D₄×D₁₃	C₂²×C₄	semidirect
196. #6127	C₂²×C₄	semidirect
197. C₂×D₅₂	C₂²×C₄	semidirect
203. C₂×C₄×D₁₃	C₂²×C₄	semidirect
208. C₂×Dic₂₆	C₂²×C₄	semidirect
239. C₂²×C₄×D₄	D₁₃	semidirect
249. C₂³×C₁₃	C₂³×C₄	semidirect
259. C₂²×D₁₃	C₂³×C₄	semidirect
261. D₄×C₁₃	C₂³×C₄	semidirect
271. C₂×C₄×C₁₃	C₂³×C₄	semidirect
272. C₂×C₄×C₁₃	H(5,𝔽₂)	semidirect
278. C₂²⋊D₁₃	C₂³×C₄	semidirect
279. C₂²⋊D₁₃	C₂³×C₄	semidirect
285. C₂×Dic₁₃	C₂³×C₄	semidirect
289. D₅₂	C₂³×C₄	semidirect
293. C₄×D₁₃	C₂³×C₄	semidirect
294. Dic₂₆	C₂³×C₄	semidirect
303. C₂⁴×C₄	C₂×D₁₃	semidirect
328. C₂×C₄×D₄	C₂×D₁₃	semidirect
329. C₂×C₄×D₄	C₂×D₁₃	semidirect
330. C₂×C₄×D₄	C₂×D₁₃	semidirect
337. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
341. C₂²×C₂²⋊C₄	C₂×D₁₃	semidirect
344. C₂²×C₄²	C₂×D₁₃	semidirect
367. C₄×C₁₃	C₂×H(5,𝔽₂)	semidirect
386. C₂²×D₄	C₄×D₁₃	semidirect
405. C₂³×C₄	C₂²×D₁₃	semidirect
421. C₄×D₄	C₂²×D₁₃	semidirect
422. C₄×D₄	C₂²×D₁₃	semidirect
435. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
445. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
454. C₂×C₄²	C₂²×D₁₃	semidirect
457. C₂×C₁₃	C₄×H(5,𝔽₂)	semidirect
469. C₂⁴	C₂×C₄×D₁₃	semidirect
485. C₂×D₄	C₂×C₄×D₁₃	semidirect
486. C₂×D₄	C₂×C₄×D₁₃	semidirect
512. C₂²×C₄	C₂×C₄×D₁₃	semidirect
542. C₁₃	C₂×C₄×H(5,𝔽₂)	semidirect
560. C₂³	C₂²×C₄×D₁₃	semidirect
568. D₄	C₂²×C₄×D₁₃	semidirect
591. C₂×C₄	C₂²×C₄×D₁₃	semidirect
592. C₂×C₄	#88251	direct (N × H)
623. C₄	C₂×#88251	direct (N × H)
627. C₂	C₄×#88251	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×#88251	2
C₄×#88251	2
C₂×#11719209	2
C₂×#11719251	2
C₂×#11719503	2
C₂×#11719191	2
C₂×#11719250	2
C₂×C₄×#6127	2
C₂×C₄×#6129	2
C₂²×C₄×C₂²⋊D₁₃	2
C₂×C₄×D₄×D₁₃	2
C₂²×C₄×D₄×C₁₃	2
C₂×C₄×H(5,𝔽₂)	13

Subgroups — C2×C4×#88251 #16769520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#88251 #16769520