Subgroups — C₂×#13117219 #16021190

Order 3328.

7630 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88180	C₂	1	2	yes	maximal, complemented
2	#13117219	C₂	1	16	yes	maximal, direct product factor
3	C₂×#11718872	C₂	1	2	yes	maximal, complemented
4	C₂×#11718873	C₂	1	4	yes	maximal, complemented
5	C₂×#11718908	C₂	1	2	yes	maximal
6	C₂×C₄×C₂²⋊Dic₁₃	C₂	1	4	yes	maximal, complemented
7	C₂⁵×C₄×C₁₃	C₂	1	1	yes	maximal, characteristic
8	C₂⁶×C₁₃	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₃	—	2	16	no	—
10	C₂⁴×C₄×C₁₃	C₄	1	16	yes	complemented
11	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₁₃	C₂²	1	8	yes	—
15	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊Dic₁₃	C₂²	1	8	yes	—
17	C₂²×C₂²⋊Dic₁₃	C₂²	1	4	yes	—
18	C₂×#88180	—	2	16	no	—
19	C₂×#88180	C₂²	1	16	yes	complemented
20	C₂²×C₄⋊Dic₁₃	C₂²	1	4	yes	complemented
21	C₂²×C₄×Dic₁₃	C₂²	1	4	yes	complemented
22	#11718908	C₂²	1	16	yes	—
23	#11718873	C₂²	1	32	yes	complemented
24	#11718872	C₂²	1	16	yes	complemented
25	C₄×C₂²⋊Dic₁₃	C₂²	1	32	yes	complemented
26	C₂×#88071	C₂²	1	8	yes	complemented
27	C₂⁵×C₁₃	—	2	8	no	—
28	C₂⁵×C₁₃	—	2	16	no	—
29	C₂⁵×C₁₃	C₂×C₄	1	8	yes	—
30	C₂⁵×C₁₃	C₂³	1	4	yes	—
31	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
32	C₂⁵×C₁₃	C₂³	1	2	yes	—
33	C₂³×C₄×C₁₃	—	2	8	no	—
34	C₂³×C₄×C₁₃	—	2	128	no	—
35	C₂³×C₄×C₁₃	—	2	16	no	—
36	C₂³×C₄×C₁₃	—	2	16	no	—
37	C₂³×C₄×C₁₃	—	2	64	no	—
38	C₂³×C₄×C₁₃	C₂×C₄	1	8	yes	—
39	C₂³×C₄×C₁₃	C₂×C₄	1	16	yes	—
40	C₂³×C₄×C₁₃	C₂×C₄	1	16	yes	—
41	C₂³×C₄×C₁₃	C₂×C₄	1	8	yes	—
42	C₂³×C₄×C₁₃	C₂×C₄	1	64	yes	complemented
43	C₂³×C₄×C₁₃	D₄	1	16	yes	—
44	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
46	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
47	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×Dic₁₃	C₂³	1	8	yes	—
52	C₂×C₂²⋊Dic₁₃	—	2	16	no	—
53	C₂×C₂²⋊Dic₁₃	—	2	32	no	—
54	C₂×C₂²⋊Dic₁₃	C₂³	1	16	yes	—
55	C₂×C₂²⋊Dic₁₃	C₂³	1	32	yes	—
56	#88180	—	2	64	no	—
57	C₂×C₄⋊Dic₁₃	—	2	16	no	—
58	C₂×C₄⋊Dic₁₃	C₂³	1	16	yes	complemented
59	C₂×C₄×Dic₁₃	—	2	16	no	—
60	C₂×C₄×Dic₁₃	C₂³	1	16	yes	complemented
61	#88071	C₂³	1	32	yes	complemented
62	C₂×#2280	—	13	1	no	maximal, Sylow
63	C₂⁴×C₁₃	—	2	128	no	—
64	C₂⁴×C₁₃	—	2	32	no	—
65	C₂⁴×C₁₃	—	2	64	no	—
66	C₂⁴×C₁₃	—	2	16	no	—
67	C₂⁴×C₁₃	—	2	8	no	—
68	C₂⁴×C₁₃	—	2	32	no	—
69	C₂⁴×C₁₃	—	2	8	no	—
70	C₂⁴×C₁₃	—	2	8	no	—
71	C₂⁴×C₁₃	C₂²×C₄	1	16	yes	—
72	C₂⁴×C₁₃	C₂²×C₄	1	4	yes	—
73	C₂⁴×C₁₃	C₂²×C₄	1	8	yes	—
74	C₂⁴×C₁₃	C₂×D₄	1	8	yes	—
75	C₂⁴×C₁₃	#41	1	16	yes	—
76	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
77	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
78	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	—	2	32	no	—
80	C₂²×C₄×C₁₃	—	2	16	no	—
81	C₂²×C₄×C₁₃	—	2	8	no	—
82	C₂²×C₄×C₁₃	—	2	64	no	—
83	C₂²×C₄×C₁₃	—	2	64	no	—
84	C₂²×C₄×C₁₃	—	2	256	no	—
85	C₂²×C₄×C₁₃	—	2	32	no	—
86	C₂²×C₄×C₁₃	—	2	32	no	—
87	C₂²×C₄×C₁₃	C₂²⋊C₄	1	64	yes	complemented
88	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
89	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
90	C₂²×C₄×C₁₃	C₂²×C₄	1	32	yes	—
91	C₂²×C₄×C₁₃	C₂²×C₄	1	32	yes	—
92	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
94	C₂²×C₄×C₁₃	C₂²×C₄	1	16	yes	—
95	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
96	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
97	C₂²×C₄×C₁₃	C₂×D₄	1	32	yes	—
98	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
99	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
100	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
101	C₂²×Dic₁₃	—	2	16	no	—
102	C₂²×Dic₁₃	—	2	32	no	—
103	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
104	C₂²⋊Dic₁₃	—	2	32	no	—
105	C₂²⋊Dic₁₃	—	2	64	no	—
106	C₄⋊Dic₁₃	—	2	32	no	—
107	C₄×Dic₁₃	—	2	32	no	—
108	C₂⁵×C₄	D₁₃	1	1	yes	characteristic
109	C₂²×#117	—	13	2	no	—
110	#2280	—	13	16	no	—
111	C₂×#381	—	13	2	no	—
112	C₂×#380	—	13	4	no	—
113	C₂×#379	—	13	2	no	—
114	C₂×C₄×C₂²⋊C₄	—	13	4	no	—
115	C₂³×C₁₃	—	2	128	no	—
116	C₂³×C₁₃	—	2	256	no	—
117	C₂³×C₁₃	—	2	32	no	—
118	C₂³×C₁₃	—	2	16	no	—
119	C₂³×C₁₃	—	2	16	no	—
120	C₂³×C₁₃	—	2	16	no	—
121	C₂³×C₁₃	—	2	64	no	—
122	C₂³×C₁₃	—	2	32	no	—
123	C₂³×C₁₃	—	2	64	no	—
124	C₂³×C₁₃	—	2	8	no	—
125	C₂³×C₁₃	—	2	8	no	—
126	C₂³×C₁₃	—	2	8	no	—
127	C₂³×C₁₃	C₂×C₂²⋊C₄	1	16	yes	—
128	C₂³×C₁₃	#117	1	32	yes	complemented
129	C₂³×C₁₃	C₂³×C₄	1	4	yes	—
130	C₂³×C₁₃	C₂³×C₄	1	8	yes	—
131	C₂³×C₁₃	C₂³×C₄	1	2	yes	—
132	C₂³×C₁₃	C₂²×D₄	1	8	yes	—
133	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
134	C₂³×C₁₃	C₂×#41	1	16	yes	—
135	C₂³×C₁₃	C₂×#41	1	8	yes	—
136	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
137	C₂×C₄×C₁₃	—	2	32	no	—
138	C₂×C₄×C₁₃	—	2	16	no	—
139	C₂×C₄×C₁₃	—	2	8	no	—
140	C₂×C₄×C₁₃	—	2	64	no	—
141	C₂×C₄×C₁₃	—	2	64	no	—
142	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	16	yes	—
143	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	16	yes	—
144	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	64	yes	complemented
145	C₂×C₄×C₁₃	C₂³×C₄	1	8	yes	—
146	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
147	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
148	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
149	C₂×C₄×C₁₃	C₂²×D₄	1	8	yes	—
150	C₂×Dic₁₃	—	2	16	no	—
151	C₂×Dic₁₃	—	2	32	no	—
152	C₂×Dic₁₃	—	4	32	no	—
153	C₂⁶	C₂×D₁₃	1	1	yes	characteristic
154	C₂⁴×C₄	—	2	16	no	—
155	C₂⁴×C₄	Dic₁₃	1	16	yes	complemented
156	C₂⁴×C₄	C₂×D₁₃	1	2	yes	—
157	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
158	C₂⁴×C₄	C₂×D₁₃	1	2	yes	—
159	C₂⁴×C₄	C₂×D₁₃	1	8	yes	—
160	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
161	C₂×#117	—	13	16	no	—
162	C₂×#117	—	26	16	no	—
163	C₂²×C₄⋊C₄	—	13	4	no	—
164	C₂²×C₂²⋊C₄	—	13	4	no	—
165	C₂²×C₂²⋊C₄	—	13	8	no	—
166	C₂²×C₄²	—	13	4	no	—
167	#381	—	13	16	no	—
168	#380	—	13	32	no	—
169	#379	—	13	16	no	—
170	C₄×C₂²⋊C₄	—	13	32	no	—
171	C₂×#95	—	13	8	no	—
172	C₂²×C₁₃	—	2	128	no	—
173	C₂²×C₁₃	—	2	8	no	—
174	C₂²×C₁₃	—	2	8	no	—
175	C₂²×C₁₃	—	2	8	no	—
176	C₂²×C₁₃	—	2	16	no	—
177	C₂²×C₁₃	—	2	32	no	—
178	C₂²×C₁₃	—	2	32	no	—
179	C₂²×C₁₃	—	2	64	no	—
180	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	8	yes	—
181	C₂²×C₁₃	C₂²×C₂²⋊C₄	1	4	yes	—
182	C₂²×C₁₃	C₂×#117	1	8	yes	—
183	C₂²×C₁₃	C₂×#117	1	16	yes	complemented
184	C₂²×C₁₃	#525	1	16	yes	—
185	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
186	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
187	C₂²×C₁₃	C₂²×#41	1	4	yes	—
188	C₄×C₁₃	—	2	8	no	—
189	C₄×C₁₃	C₂²×C₂²⋊C₄	1	8	yes	—
190	C₄×C₁₃	C₂²×C₂²⋊C₄	1	8	yes	—
191	Dic₁₃	—	4	16	no	—
192	C₂⁵	—	2	16	no	—
193	C₂⁵	—	2	8	no	—
194	C₂⁵	C₂×Dic₁₃	1	8	yes	—
195	C₂⁵	C₂²×D₁₃	1	4	yes	—
196	C₂⁵	C₂²×D₁₃	1	2	yes	—
197	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
198	C₂³×C₄	—	2	8	no	—
199	C₂³×C₄	—	2	128	no	—
200	C₂³×C₄	—	2	16	no	—
201	C₂³×C₄	—	2	16	no	—
202	C₂³×C₄	—	2	64	no	—
203	C₂³×C₄	—	13	8	no	—
204	C₂³×C₄	C₂×Dic₁₃	1	8	yes	—
205	C₂³×C₄	C₂×Dic₁₃	1	16	yes	—
206	C₂³×C₄	C₂×Dic₁₃	1	16	yes	—
207	C₂³×C₄	C₂×Dic₁₃	1	8	yes	—
208	C₂³×C₄	C₂×Dic₁₃	1	64	yes	complemented
209	C₂³×C₄	C₂²⋊D₁₃	1	16	yes	—
210	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
211	C₂³×C₄	C₂²×D₁₃	1	8	yes	—
212	C₂³×C₄	C₂²×D₁₃	1	8	yes	—
213	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
214	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
215	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
216	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
217	#117	—	26	64	no	—
218	C₂×C₄⋊C₄	—	13	16	no	—
219	C₂×C₄⋊C₄	—	26	16	no	—
220	C₂×C₂²⋊C₄	—	13	16	no	—
221	C₂×C₂²⋊C₄	—	13	32	no	—
222	C₂×C₂²⋊C₄	—	26	32	no	—
223	C₂×C₂²⋊C₄	—	26	16	no	—
224	C₂×C₄²	—	13	16	no	—
225	C₂×C₄²	—	26	16	no	—
226	#95	—	13	32	no	—
227	C₂×C₁₃	—	2	8	no	—
228	C₂×C₁₃	—	2	16	no	—
229	C₂×C₁₃	#2280	1	8	yes	complemented
230	C₂×C₁₃	C₂³×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₁₃	C₂²×#117	1	2	yes	—
232	C₂×C₁₃	C₂×#525	1	4	yes	—
233	C₂⁴	—	2	128	no	—
234	C₂⁴	—	2	64	no	—
235	C₂⁴	—	2	32	no	—
236	C₂⁴	—	2	32	no	—
237	C₂⁴	—	2	8	no	—
238	C₂⁴	—	2	8	no	—
239	C₂⁴	—	2	16	no	—
240	C₂⁴	—	2	8	no	—
241	C₂⁴	#6127	1	16	yes	—
242	C₂⁴	C₂²×Dic₁₃	1	16	yes	—
243	C₂⁴	C₂²×Dic₁₃	1	8	yes	—
244	C₂⁴	C₂²×Dic₁₃	1	4	yes	—
245	C₂⁴	C₂×C₂²⋊D₁₃	1	8	yes	—
246	C₂⁴	C₂³×D₁₃	1	4	yes	—
247	C₂⁴	C₂³×D₁₃	1	2	yes	—
248	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
249	C₂²×C₄	—	2	32	no	—
250	C₂²×C₄	—	2	16	no	—
251	C₂²×C₄	—	2	8	no	—
252	C₂²×C₄	—	2	64	no	—
253	C₂²×C₄	—	2	64	no	—
254	C₂²×C₄	—	2	256	no	—
255	C₂²×C₄	—	2	32	no	—
256	C₂²×C₄	—	2	32	no	—
257	C₂²×C₄	—	13	16	no	—
258	C₂²×C₄	—	26	32	no	—
259	C₂²×C₄	—	26	16	no	—
260	C₂²×C₄	C₂²⋊Dic₁₃	1	64	yes	complemented
261	C₂²×C₄	C₂²×Dic₁₃	1	8	yes	—
262	C₂²×C₄	C₂²×Dic₁₃	1	16	yes	—
263	C₂²×C₄	C₂²×Dic₁₃	1	32	yes	—
264	C₂²×C₄	C₂²×Dic₁₃	1	32	yes	—
265	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
266	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
267	C₂²×C₄	C₂²×Dic₁₃	1	16	yes	—
268	C₂²×C₄	C₂×C₂²⋊D₁₃	1	8	yes	—
269	C₂²×C₄	C₂×C₂²⋊D₁₃	1	8	yes	—
270	C₂²×C₄	C₂×C₂²⋊D₁₃	1	32	yes	—
271	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
272	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
273	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
274	C₄⋊C₄	—	26	32	no	—
275	C₂²⋊C₄	—	26	64	no	—
276	C₂²⋊C₄	—	26	32	no	—
277	C₄²	—	26	32	no	—
278	C₁₃	C₂×#2280	1	1	yes	characteristic, complemented, Sylow
279	C₂³	—	2	256	no	—
280	C₂³	—	2	128	no	—
281	C₂³	—	2	16	no	—
282	C₂³	—	2	16	no	—
283	C₂³	—	2	64	no	—
284	C₂³	—	2	64	no	—
285	C₂³	—	2	32	no	—
286	C₂³	—	2	32	no	—
287	C₂³	—	2	16	no	—
288	C₂³	—	2	8	no	—
289	C₂³	—	2	8	no	—
290	C₂³	—	2	8	no	—
291	C₂³	#88180	1	32	yes	complemented
292	C₂³	C₂×C₂²⋊Dic₁₃	1	16	yes	—
293	C₂³	C₂×#6127	1	16	yes	—
294	C₂³	C₂×#6127	1	8	yes	—
295	C₂³	C₂³×Dic₁₃	1	8	yes	—
296	C₂³	C₂³×Dic₁₃	1	4	yes	—
297	C₂³	C₂³×Dic₁₃	1	2	yes	—
298	C₂³	C₂²×C₂²⋊D₁₃	1	8	yes	—
299	C₂³	C₂²×C₂²⋊D₁₃	1	4	yes	—
300	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
301	C₂×C₄	—	2	32	no	—
302	C₂×C₄	—	2	16	no	—
303	C₂×C₄	—	2	8	no	—
304	C₂×C₄	—	2	64	no	—
305	C₂×C₄	—	2	64	no	—
306	C₂×C₄	—	26	32	no	—
307	C₂×C₄	—	26	16	no	—
308	C₂×C₄	—	52	32	no	—
309	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	16	yes	—
310	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	16	yes	—
311	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	64	yes	complemented
312	C₂×C₄	C₂³×Dic₁₃	1	8	yes	—
313	C₂×C₄	C₂³×Dic₁₃	1	4	yes	—
314	C₂×C₄	C₂³×Dic₁₃	1	4	yes	—
315	C₂×C₄	C₂²×C₂²⋊D₁₃	1	8	yes	—
316	C₂×C₄	C₂²×C₂²⋊D₁₃	1	8	yes	—
317	C₂²	—	2	128	no	—
318	C₂²	—	2	64	no	—
319	C₂²	—	2	32	no	—
320	C₂²	—	2	8	no	—
321	C₂²	—	2	8	no	—
322	C₂²	—	2	8	no	—
323	C₂²	—	2	32	no	—
324	C₂²	—	2	16	no	—
325	C₂²	C₂×#88180	1	8	yes	—
326	C₂²	C₂×#88180	1	16	yes	complemented
327	C₂²	#11719496	1	16	yes	—
328	C₂²	C₂²×C₂²⋊Dic₁₃	1	8	yes	—
329	C₂²	C₂²×C₂²⋊Dic₁₃	1	4	yes	—
330	C₂²	C₂²×#6127	1	4	yes	—
331	C₂²	C₂⁴×Dic₁₃	1	1	yes	characteristic
332	C₂²	C₂³×C₂²⋊D₁₃	1	2	yes	—
333	C₄	—	2	8	no	—
334	C₄	—	52	16	no	—
335	C₄	C₂²×C₂²⋊Dic₁₃	1	8	yes	—
336	C₄	C₂²×C₂²⋊Dic₁₃	1	8	yes	—
337	C₂	—	2	16	no	—
338	C₂	—	2	8	no	—
339	C₂	#13117219	1	8	yes	direct product factor
340	C₂	C₂³×C₂²⋊Dic₁₃	1	1	yes	characteristic
341	C₂	C₂²×#88180	1	2	yes	—
342	C₂	C₂×#11719496	1	4	yes	—

	subgroup	G/H
center	C₂³×C₄	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₁₃
Fitting	C₂⁵×C₄×C₁₃	C₂
socle	C₂⁴×C₁₃	C₂⁴
prime radical	C₂⁶×C₁₃	C₂²
cosocle	C₂³×C₁₃	C₂⁵
hypercenter	C₂⁵×C₄	D₁₃
hypocenter	C₁₃	C₂×#2280
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂⁵×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#88180	C₂	semidirect
2. #13117219	C₂	direct (N × H)
3. C₂×#11718872	C₂	semidirect
4. C₂×#11718873	C₂	semidirect
6. C₂×C₄×C₂²⋊Dic₁₃	C₂	semidirect
10. C₂⁴×C₄×C₁₃	C₄	semidirect
19. C₂×#88180	C₂²	semidirect
20. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
21. C₂²×C₄×Dic₁₃	C₂²	semidirect
23. #11718873	C₂²	semidirect
24. #11718872	C₂²	semidirect
25. C₄×C₂²⋊Dic₁₃	C₂²	semidirect
26. C₂×#88071	C₂²	semidirect
42. C₂³×C₄×C₁₃	C₂×C₄	semidirect
58. C₂×C₄⋊Dic₁₃	C₂³	semidirect
60. C₂×C₄×Dic₁₃	C₂³	semidirect
61. #88071	C₂³	semidirect
87. C₂²×C₄×C₁₃	C₂²⋊C₄	semidirect
128. C₂³×C₁₃	#117	semidirect
144. C₂×C₄×C₁₃	C₂×C₂²⋊C₄	semidirect
155. C₂⁴×C₄	Dic₁₃	semidirect
183. C₂²×C₁₃	C₂×#117	semidirect
208. C₂³×C₄	C₂×Dic₁₃	semidirect
229. C₂×C₁₃	#2280	semidirect
260. C₂²×C₄	C₂²⋊Dic₁₃	semidirect
278. C₁₃	C₂×#2280	semidirect
291. C₂³	#88180	semidirect
311. C₂×C₄	C₂×C₂²⋊Dic₁₃	semidirect
326. C₂²	C₂×#88180	semidirect
339. C₂	#13117219	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×#88180	2
#13117219	2
C₂×#11718872	2
C₂×#11718873	2
C₂×#11718908	2
C₂×C₄×C₂²⋊Dic₁₃	2
C₂⁵×C₄×C₁₃	2
C₂×#2280	13

Subgroups — C2×#13117219 #16021190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13117219 #16021190