Subgroups — C₂×#11719314 #13128274

Order 1664.

2536 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×D₁₃	C₂	1	2	yes	maximal, complemented
3	C₂³×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#88194	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#88191	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719314	C₂	1	16	yes	maximal, direct product factor
9	C₂×#88149	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#88147	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#88138	C₂	1	2	yes	maximal, complemented
12	C₂×#88136	C₂	1	2	yes	maximal, complemented
13	C₂⁴×D₁₃	C₂²	1	2	yes	complemented
14	C₂⁴×D₁₃	C₂²	1	2	yes	complemented
15	C₂²×D₄×C₁₃	C₂²	1	2	yes	complemented
16	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
17	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
20	C₂²×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
21	C₂²×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
22	C₂×D₄×D₁₃	—	2	16	no	—
23	C₂×D₄×D₁₃	—	2	8	no	—
24	C₂×D₄×D₁₃	C₂²	1	8	yes	complemented
25	C₂×D₄×D₁₃	C₂²	1	16	yes	complemented
26	C₂²×D₅₂	—	2	8	no	—
27	C₂²×D₅₂	C₂²	1	1	yes	characteristic
28	C₂²×D₅₂	C₂²	1	8	yes	complemented
29	C₂²×D₅₂	C₂²	1	2	yes	complemented
30	C₂²×D₅₂	C₂²	1	2	yes	complemented
31	C₂²×D₅₂	C₂²	1	1	yes	characteristic, complemented
32	C₂²×C₄×D₁₃	C₂²	1	2	yes	complemented
33	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#121	C₂²	1	8	yes	complemented
35	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
37	C₂×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
38	#88194	C₂²	1	8	yes	complemented
39	#88191	C₂²	1	16	yes	complemented
40	C₄×C₂²⋊D₁₃	C₂²	1	8	yes	complemented
41	C₂×#6103	C₂²	1	1	yes	characteristic, complemented
42	C₂×#6103	C₂²	1	2	yes	complemented
43	C₂×#6103	C₂²	1	2	yes	complemented
44	C₂×#6101	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
46	#88149	C₂²	1	8	yes	complemented
47	#88147	C₂²	1	8	yes	complemented
48	#88138	C₂²	1	16	yes	complemented
49	#88136	C₂²	1	16	yes	complemented
50	C₂⁴×C₁₃	C₂³	1	2	yes	—
51	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
52	C₂³×D₁₃	—	2	8	no	—
53	C₂³×D₁₃	—	2	8	no	—
54	C₂³×D₁₃	—	2	8	no	—
55	C₂³×D₁₃	—	2	8	no	—
56	C₂³×D₁₃	—	4	4	no	—
57	C₂³×D₁₃	—	4	4	no	—
58	C₂³×D₁₃	C₂³	1	2	yes	—
59	C₂³×D₁₃	C₂³	1	2	yes	—
60	C₂³×D₁₃	C₂³	1	1	yes	characteristic
61	C₂³×D₁₃	C₂³	1	8	yes	complemented
62	C₂³×D₁₃	C₂³	1	8	yes	complemented
63	C₂×D₄×C₁₃	—	2	8	no	—
64	C₂×D₄×C₁₃	—	2	4	no	—
65	C₂×D₄×C₁₃	C₂³	1	8	yes	complemented
66	C₂×D₄×C₁₃	C₂³	1	4	yes	complemented
67	C₂²×C₄×C₁₃	—	2	4	no	—
68	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
70	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₁₃	C₂³	1	4	yes	complemented
72	C₂×C₂²⋊D₁₃	—	2	8	no	—
73	C₂×C₂²⋊D₁₃	—	2	8	no	—
74	C₂×C₂²⋊D₁₃	—	4	4	no	—
75	C₂×C₂²⋊D₁₃	D₄	1	8	yes	complemented
76	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
77	C₂×C₂²⋊D₁₃	C₂³	1	8	yes	complemented
78	C₂×C₂²⋊D₁₃	C₂³	1	8	yes	complemented
79	C₂×C₂²⋊D₁₃	C₂³	1	8	yes	complemented
80	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
81	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
82	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
83	D₄×D₁₃	—	2	64	no	—
84	D₄×D₁₃	—	2	32	no	—
85	C₂×D₅₂	—	2	8	no	—
86	C₂×D₅₂	—	2	8	no	—
87	C₂×D₅₂	—	2	4	no	—
88	C₂×D₅₂	—	2	32	no	—
89	C₂×D₅₂	D₄	1	8	yes	complemented
90	C₂×D₅₂	C₂³	1	4	yes	—
91	C₂×D₅₂	C₂³	1	8	yes	complemented
92	C₂×D₅₂	C₂³	1	8	yes	complemented
93	C₂×D₅₂	C₂³	1	4	yes	complemented
94	C₂×C₄×D₁₃	—	2	4	no	—
95	C₂×C₄×D₁₃	—	2	8	no	—
96	C₂×C₄×D₁₃	C₂³	1	8	yes	complemented
97	C₂×C₄×D₁₃	C₂³	1	4	yes	complemented
98	C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
99	C₁₃×C₂²⋊C₄	C₂³	1	8	yes	complemented
100	C₂²⋊Dic₁₃	C₂³	1	4	yes	complemented
101	#6103	C₂³	1	4	yes	complemented
102	#6103	C₂³	1	8	yes	complemented
103	#6103	C₂³	1	8	yes	complemented
104	#6101	C₂³	1	4	yes	complemented
105	C₄×Dic₁₃	C₂³	1	4	yes	complemented
106	C₂×D₄²	—	13	1	no	maximal, Sylow
107	C₂³×C₁₃	—	2	2	no	—
108	C₂³×C₁₃	—	2	2	no	—
109	C₂³×C₁₃	—	2	4	no	—
110	C₂³×C₁₃	—	2	4	no	—
111	C₂³×C₁₃	—	2	4	no	—
112	C₂³×C₁₃	C₂×D₄	1	4	yes	complemented
113	C₂³×C₁₃	C₂⁴	1	4	yes	—
114	C₂³×C₁₃	C₂⁴	1	2	yes	—
115	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
116	C₂²×D₁₃	—	2	2	no	—
117	C₂²×D₁₃	—	2	4	no	—
118	C₂²×D₁₃	—	2	4	no	—
119	C₂²×D₁₃	—	2	2	no	—
120	C₂²×D₁₃	—	2	4	no	—
121	C₂²×D₁₃	—	2	4	no	—
122	C₂²×D₁₃	—	2	16	no	—
123	C₂²×D₁₃	—	2	4	no	—
124	C₂²×D₁₃	—	2	16	no	—
125	C₂²×D₁₃	—	2	16	no	—
126	C₂²×D₁₃	—	2	16	no	—
127	C₂²×D₁₃	—	4	8	no	—
128	C₂²×D₁₃	—	4	8	no	—
129	C₂²×D₁₃	—	4	32	no	—
130	C₂²×D₁₃	—	4	32	no	—
131	C₂²×D₁₃	C₂×D₄	1	4	yes	complemented
132	C₂²×D₁₃	C₂×D₄	1	8	yes	complemented
133	C₂²×D₁₃	C₂⁴	1	4	yes	—
134	C₂²×D₁₃	C₂⁴	1	4	yes	—
135	C₂²×D₁₃	C₂⁴	1	2	yes	—
136	D₄×C₁₃	—	2	16	no	—
137	D₄×C₁₃	—	2	8	no	—
138	C₂×C₄×C₁₃	—	2	4	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	8	no	—
141	C₂×C₄×C₁₃	C₂×D₄	1	4	yes	complemented
142	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
143	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
144	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
145	C₂²⋊D₁₃	—	2	16	no	—
146	C₂²⋊D₁₃	—	2	16	no	—
147	C₂²⋊D₁₃	—	4	8	no	—
148	C₂²⋊D₁₃	C₂×D₄	1	16	yes	complemented
149	C₂×Dic₁₃	—	2	2	no	—
150	C₂×Dic₁₃	—	2	2	no	—
151	C₂×Dic₁₃	C₂×D₄	1	4	yes	complemented
152	C₂×Dic₁₃	C₂⁴	1	2	yes	—
153	C₂×Dic₁₃	C₂⁴	1	2	yes	—
154	C₂×Dic₁₃	C₂⁴	1	2	yes	—
155	D₅₂	—	2	16	no	—
156	D₅₂	—	2	16	no	—
157	D₅₂	—	2	8	no	—
158	D₅₂	C₂×D₄	1	16	yes	complemented
159	C₄×D₁₃	—	2	8	no	—
160	C₄×D₁₃	—	2	16	no	—
161	C₂³×D₄	—	13	2	no	—
162	C₂³×D₄	—	13	1	no	—
163	C₂³×D₄	—	13	1	no	—
164	D₄²	—	13	16	no	—
165	C₂×#127	—	13	1	no	—
166	C₂×#121	—	13	1	no	—
167	C₂×#121	—	13	2	no	—
168	C₂×#121	D₁₃	1	1	yes	characteristic, complemented
169	C₂×#120	—	13	2	no	—
170	C₂×#120	—	13	2	no	—
171	C₂×C₄×D₄	—	13	1	no	—
172	C₂×C₄×D₄	—	13	1	no	—
173	C₂²×C₁₃	—	2	8	no	—
174	C₂²×C₁₃	—	2	2	no	—
175	C₂²×C₁₃	—	2	2	no	—
176	C₂²×C₁₃	—	2	4	no	—
177	C₂²×C₁₃	—	2	4	no	—
178	C₂²×C₁₃	—	2	4	no	—
179	C₂²×C₁₃	—	4	8	no	—
180	C₂²×C₁₃	C₂²×D₄	1	2	yes	—
181	C₂²×C₁₃	C₂²×D₄	1	2	yes	—
182	C₂²×C₁₃	C₂²×D₄	1	4	yes	complemented
183	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
184	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
185	C₂×D₁₃	—	2	8	no	—
186	C₂×D₁₃	—	2	16	no	—
187	C₂×D₁₃	—	2	2	no	—
188	C₂×D₁₃	—	2	4	no	—
189	C₂×D₁₃	—	2	4	no	—
190	C₂×D₁₃	—	2	2	no	—
191	C₂×D₁₃	—	2	4	no	—
192	C₂×D₁₃	—	2	4	no	—
193	C₂×D₁₃	—	2	4	no	—
194	C₂×D₁₃	—	4	32	no	—
195	C₂×D₁₃	—	4	32	no	—
196	C₂×D₁₃	—	4	8	no	—
197	C₂×D₁₃	C₂²×D₄	1	4	yes	complemented
198	C₂×D₁₃	C₂²×D₄	1	8	yes	complemented
199	C₄×C₁₃	—	2	4	no	—
200	C₄×C₁₃	—	2	2	no	—
201	C₄×C₁₃	C₂²×D₄	1	4	yes	complemented
202	Dic₁₃	—	2	2	no	—
203	Dic₁₃	—	2	2	no	—
204	Dic₁₃	C₂²×D₄	1	4	yes	complemented
205	C₂⁵	—	13	2	no	—
206	C₂⁵	—	13	2	no	—
207	C₂²×D₄	—	13	1	no	—
208	C₂²×D₄	—	13	2	no	—
209	C₂²×D₄	—	13	2	no	—
210	C₂²×D₄	—	13	2	no	—
211	C₂²×D₄	—	13	16	no	—
212	C₂²×D₄	—	13	8	no	—
213	C₂²×D₄	—	13	1	no	—
214	C₂²×D₄	—	13	2	no	—
215	C₂²×D₄	—	13	2	no	—
216	C₂²×D₄	—	13	1	no	—
217	C₂²×D₄	—	13	8	no	—
218	C₂²×D₄	—	26	8	no	—
219	C₂²×D₄	—	26	16	no	—
220	C₂²×D₄	—	26	8	no	—
221	C₂²×D₄	C₂×D₁₃	1	2	yes	complemented
222	C₂²×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
223	C₂³×C₄	—	13	2	no	—
224	C₂³×C₄	—	13	1	no	—
225	C₂³×C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
226	#127	—	13	8	no	—
227	#121	—	13	8	no	—
228	#121	—	13	16	no	—
229	#121	C₂×D₁₃	1	8	yes	complemented
230	#120	—	13	16	no	—
231	#120	—	13	16	no	—
232	C₄×D₄	—	13	8	no	—
233	C₄×D₄	—	13	8	no	—
234	C₂×C₄⋊C₄	—	13	1	no	—
235	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
236	C₂×C₂²⋊C₄	—	13	1	no	—
237	C₂×C₂²⋊C₄	—	13	2	no	—
238	C₂×C₂²⋊C₄	—	13	1	no	—
239	C₂×C₂²⋊C₄	—	13	2	no	—
240	C₂×C₂²⋊C₄	C₂×D₁₃	1	2	yes	complemented
241	C₂×C₄²	—	13	1	no	—
242	C₂×C₁₃	—	2	4	no	—
243	C₂×C₁₃	—	4	4	no	—
244	C₂×C₁₃	D₄²	1	4	yes	complemented
245	C₂×C₁₃	C₂³×D₄	1	1	yes	characteristic
246	C₂×C₁₃	C₂³×D₄	1	1	yes	characteristic
247	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
248	D₁₃	—	2	4	no	—
249	D₁₃	—	2	8	no	—
250	D₁₃	—	4	4	no	—
251	C₂⁴	—	13	1	no	—
252	C₂⁴	—	13	2	no	—
253	C₂⁴	—	13	2	no	—
254	C₂⁴	—	13	8	no	—
255	C₂⁴	—	13	8	no	—
256	C₂⁴	—	26	8	no	—
257	C₂⁴	—	26	8	no	—
258	C₂⁴	—	26	8	no	—
259	C₂⁴	—	26	8	no	—
260	C₂⁴	—	52	4	no	—
261	C₂⁴	—	52	4	no	—
262	C₂⁴	C₂²×D₁₃	1	2	yes	—
263	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
264	C₂×D₄	—	2	8	no	—
265	C₂×D₄	—	2	4	no	—
266	C₂×D₄	—	13	8	no	—
267	C₂×D₄	—	13	4	no	—
268	C₂×D₄	—	13	8	no	—
269	C₂×D₄	—	13	8	no	—
270	C₂×D₄	—	13	8	no	—
271	C₂×D₄	—	13	8	no	—
272	C₂×D₄	—	13	4	no	—
273	C₂×D₄	—	13	8	no	—
274	C₂×D₄	—	13	8	no	—
275	C₂×D₄	—	13	4	no	—
276	C₂×D₄	—	26	32	no	—
277	C₂×D₄	—	26	8	no	—
278	C₂×D₄	—	26	8	no	—
279	C₂×D₄	—	26	8	no	—
280	C₂×D₄	—	26	64	no	—
281	C₂×D₄	—	26	32	no	—
282	C₂×D₄	—	26	8	no	—
283	C₂×D₄	—	26	4	no	—
284	C₂×D₄	—	52	4	no	—
285	C₂×D₄	C₂²×D₁₃	1	8	yes	complemented
286	C₂×D₄	C₂²×D₁₃	1	4	yes	complemented
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	13	1	no	—
289	C₂²×C₄	—	13	1	no	—
290	C₂²×C₄	—	13	1	no	—
291	C₂²×C₄	—	13	8	no	—
292	C₂²×C₄	—	13	4	no	—
293	C₂²×C₄	—	26	8	no	—
294	C₂²×C₄	—	26	4	no	—
295	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
296	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
297	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
298	C₂²×C₄	C₂²×D₁₃	1	4	yes	complemented
299	C₄⋊C₄	—	13	4	no	—
300	C₄⋊C₄	C₂²×D₁₃	1	4	yes	complemented
301	C₂²⋊C₄	—	13	4	no	—
302	C₂²⋊C₄	—	13	8	no	—
303	C₂²⋊C₄	—	13	4	no	—
304	C₂²⋊C₄	—	13	8	no	—
305	C₂²⋊C₄	C₂²×D₁₃	1	8	yes	complemented
306	C₄²	—	13	4	no	—
307	C₁₃	C₂×D₄²	1	1	yes	characteristic, complemented, Sylow
308	C₂³	—	2	2	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	4	no	—
311	C₂³	—	2	4	no	—
312	C₂³	—	2	4	no	—
313	C₂³	—	13	4	no	—
314	C₂³	—	13	8	no	—
315	C₂³	—	13	2	no	—
316	C₂³	—	13	4	no	—
317	C₂³	—	13	4	no	—
318	C₂³	—	26	16	no	—
319	C₂³	—	26	16	no	—
320	C₂³	—	26	16	no	—
321	C₂³	—	26	4	no	—
322	C₂³	—	26	2	no	—
323	C₂³	—	26	4	no	—
324	C₂³	—	26	2	no	—
325	C₂³	—	26	4	no	—
326	C₂³	—	26	4	no	—
327	C₂³	—	26	16	no	—
328	C₂³	—	26	4	no	—
329	C₂³	—	52	8	no	—
330	C₂³	—	52	8	no	—
331	C₂³	—	52	32	no	—
332	C₂³	—	52	32	no	—
333	C₂³	D₄×D₁₃	1	4	yes	complemented
334	C₂³	C₂³×D₁₃	1	4	yes	—
335	C₂³	C₂³×D₁₃	1	2	yes	—
336	C₂³	C₂³×D₁₃	1	1	yes	characteristic
337	D₄	—	2	16	no	—
338	D₄	—	2	8	no	—
339	D₄	—	13	16	no	—
340	D₄	—	13	16	no	—
341	D₄	—	26	16	no	—
342	D₄	—	26	16	no	—
343	D₄	—	26	16	no	—
344	D₄	—	26	16	no	—
345	D₄	—	26	8	no	—
346	D₄	—	52	8	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	13	4	no	—
351	C₂×C₄	—	13	2	no	—
352	C₂×C₄	—	13	2	no	—
353	C₂×C₄	—	13	2	no	—
354	C₂×C₄	—	26	16	no	—
355	C₂×C₄	—	26	2	no	—
356	C₂×C₄	—	26	2	no	—
357	C₂×C₄	—	26	8	no	—
358	C₂×C₄	D₄×D₁₃	1	4	yes	complemented
359	C₂×C₄	C₂³×D₁₃	1	4	yes	—
360	C₂×C₄	C₂³×D₁₃	1	2	yes	—
361	C₂×C₄	C₂³×D₁₃	1	2	yes	—
362	C₂²	—	2	8	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	2	4	no	—
367	C₂²	—	2	4	no	—
368	C₂²	—	4	8	no	—
369	C₂²	—	13	4	no	—
370	C₂²	—	13	8	no	—
371	C₂²	—	26	16	no	—
372	C₂²	—	26	8	no	—
373	C₂²	—	26	4	no	—
374	C₂²	—	26	2	no	—
375	C₂²	—	26	4	no	—
376	C₂²	—	26	2	no	—
377	C₂²	—	26	4	no	—
378	C₂²	—	26	4	no	—
379	C₂²	—	26	4	no	—
380	C₂²	—	52	32	no	—
381	C₂²	—	52	32	no	—
382	C₂²	—	52	8	no	—
383	C₂²	C₂×D₄×D₁₃	1	2	yes	—
384	C₂²	C₂×D₄×D₁₃	1	2	yes	—
385	C₂²	C₂×D₄×D₁₃	1	4	yes	complemented
386	C₂²	#88256	1	2	yes	—
387	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
388	C₄	—	2	2	no	—
389	C₄	—	2	4	no	—
390	C₄	—	13	4	no	—
391	C₄	—	26	2	no	—
392	C₄	—	26	2	no	—
393	C₄	C₂×D₄×D₁₃	1	4	yes	complemented
394	C₂	—	2	4	no	—
395	C₂	—	4	4	no	—
396	C₂	—	26	8	no	—
397	C₂	—	26	4	no	—
398	C₂	—	52	4	no	—
399	C₂	#11719314	1	4	yes	direct product factor
400	C₂	C₂²×D₄×D₁₃	1	1	yes	characteristic
401	C₂	C₂²×D₄×D₁₃	1	1	yes	characteristic
402	C₂	C₂×#88256	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₃
Fitting	C₂×C₁₃×#121	C₂
socle	C₂³×C₁₃	C₂⁴
hypercenter	C₂×#121	D₁₃
hypocenter	C₁₃	C₂×D₄²
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#121

Complements

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

N	H ≅ G/N	type
1. C₂²×D₄×D₁₃	C₂	semidirect
2. C₂²×D₄×D₁₃	C₂	semidirect
3. C₂³×D₅₂	C₂	semidirect
4. C₂×C₁₃×#121	C₂	semidirect
5. C₂×#88194	C₂	semidirect
6. C₂×#88191	C₂	semidirect
7. C₂×C₄×C₂²⋊D₁₃	C₂	semidirect
8. #11719314	C₂	direct (N × H)
9. C₂×#88149	C₂	semidirect
10. C₂×#88147	C₂	semidirect
11. C₂×#88138	C₂	semidirect
12. C₂×#88136	C₂	semidirect
13. C₂⁴×D₁₃	C₂²	semidirect
14. C₂⁴×D₁₃	C₂²	semidirect
15. C₂²×D₄×C₁₃	C₂²	semidirect
16. C₂²×D₄×C₁₃	C₂²	semidirect
17. C₂³×C₄×C₁₃	C₂²	semidirect
19. C₂²×C₂²⋊D₁₃	C₂²	semidirect
20. C₂²×C₂²⋊D₁₃	C₂²	semidirect
21. C₂²×C₂²⋊D₁₃	C₂²	semidirect
24. C₂×D₄×D₁₃	C₂²	semidirect
25. C₂×D₄×D₁₃	C₂²	semidirect
28. C₂²×D₅₂	C₂²	semidirect
29. C₂²×D₅₂	C₂²	semidirect
30. C₂²×D₅₂	C₂²	semidirect
31. C₂²×D₅₂	C₂²	semidirect
32. C₂²×C₄×D₁₃	C₂²	semidirect
33. C₂²×C₄×D₁₃	C₂²	semidirect
34. C₁₃×#121	C₂²	semidirect
35. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
36. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
37. C₂×C₂²⋊Dic₁₃	C₂²	semidirect
38. #88194	C₂²	semidirect
39. #88191	C₂²	semidirect
40. C₄×C₂²⋊D₁₃	C₂²	semidirect
41. C₂×#6103	C₂²	semidirect
42. C₂×#6103	C₂²	semidirect
43. C₂×#6103	C₂²	semidirect
44. C₂×#6101	C₂²	semidirect
45. C₂×C₄×Dic₁₃	C₂²	semidirect
46. #88149	C₂²	semidirect
47. #88147	C₂²	semidirect
48. #88138	C₂²	semidirect
49. #88136	C₂²	semidirect
61. C₂³×D₁₃	C₂³	semidirect
62. C₂³×D₁₃	C₂³	semidirect
65. C₂×D₄×C₁₃	C₂³	semidirect
66. C₂×D₄×C₁₃	C₂³	semidirect
71. C₂²×C₄×C₁₃	C₂³	semidirect
75. C₂×C₂²⋊D₁₃	D₄	semidirect
77. C₂×C₂²⋊D₁₃	C₂³	semidirect
78. C₂×C₂²⋊D₁₃	C₂³	semidirect
79. C₂×C₂²⋊D₁₃	C₂³	semidirect
89. C₂×D₅₂	D₄	semidirect
91. C₂×D₅₂	C₂³	semidirect
92. C₂×D₅₂	C₂³	semidirect
93. C₂×D₅₂	C₂³	semidirect
96. C₂×C₄×D₁₃	C₂³	semidirect
97. C₂×C₄×D₁₃	C₂³	semidirect
98. C₁₃×C₄⋊C₄	C₂³	semidirect
99. C₁₃×C₂²⋊C₄	C₂³	semidirect
100. C₂²⋊Dic₁₃	C₂³	semidirect
101. #6103	C₂³	semidirect
102. #6103	C₂³	semidirect
103. #6103	C₂³	semidirect
104. #6101	C₂³	semidirect
105. C₄×Dic₁₃	C₂³	semidirect
112. C₂³×C₁₃	C₂×D₄	semidirect
131. C₂²×D₁₃	C₂×D₄	semidirect
132. C₂²×D₁₃	C₂×D₄	semidirect
141. C₂×C₄×C₁₃	C₂×D₄	semidirect
148. C₂²⋊D₁₃	C₂×D₄	semidirect
151. C₂×Dic₁₃	C₂×D₄	semidirect
158. D₅₂	C₂×D₄	semidirect
168. C₂×#121	D₁₃	semidirect
182. C₂²×C₁₃	C₂²×D₄	semidirect
197. C₂×D₁₃	C₂²×D₄	semidirect
198. C₂×D₁₃	C₂²×D₄	semidirect
201. C₄×C₁₃	C₂²×D₄	semidirect
204. Dic₁₃	C₂²×D₄	semidirect
221. C₂²×D₄	C₂×D₁₃	semidirect
222. C₂²×D₄	C₂×D₁₃	semidirect
225. C₂³×C₄	C₂×D₁₃	semidirect
229. #121	C₂×D₁₃	semidirect
235. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
240. C₂×C₂²⋊C₄	C₂×D₁₃	semidirect
244. C₂×C₁₃	D₄²	semidirect
285. C₂×D₄	C₂²×D₁₃	semidirect
286. C₂×D₄	C₂²×D₁₃	semidirect
298. C₂²×C₄	C₂²×D₁₃	semidirect
300. C₄⋊C₄	C₂²×D₁₃	semidirect
305. C₂²⋊C₄	C₂²×D₁₃	semidirect
307. C₁₃	C₂×D₄²	semidirect
333. C₂³	D₄×D₁₃	semidirect
358. C₂×C₄	D₄×D₁₃	semidirect
385. C₂²	C₂×D₄×D₁₃	semidirect
393. C₄	C₂×D₄×D₁₃	semidirect
399. C₂	#11719314	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×D₄×D₁₃	2
C₂³×D₅₂	2
C₂×C₁₃×#121	2
C₂×#88194	2
C₂×#88191	2
C₂×C₄×C₂²⋊D₁₃	2
#11719314	2
C₂×#88149	2
C₂×#88147	2
C₂×#88138	2
C₂×#88136	2
C₂×D₄²	13

Subgroups — C2×#11719314 #13128274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11719314 #13128274