Subgroups — C₂×#13129240 #16770720

Order 3328.

8802 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129240	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719388	C₂	1	3	yes	maximal, complemented
3	C₂×#11719375	C₂	1	6	yes	maximal, complemented
4	C₂×#11719295	C₂	1	6	yes	maximal, complemented
5	C₂×#11719379	C₂	1	6	yes	maximal, complemented
6	C₂×#11719297	C₂	1	6	yes	maximal, complemented
7	C₂×#11719373	C₂	1	3	yes	maximal, complemented
8	C₂×C₁₃×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₂²⋊D₁₃	C₂²	1	6	yes	complemented
10	C₂²×#6131	C₂²	1	3	yes	complemented
11	C₂²×#6129	C₂²	1	3	yes	complemented
12	C₂²×D₄×D₁₃	C₂²	1	6	yes	complemented
13	C₁₃×H(3,𝔽₄)	C₂²	1	16	yes	complemented
14	C₂×C₁₃×#124	C₂²	1	6	yes	complemented
15	C₂×C₁₃×#124	C₂²	1	3	yes	complemented
16	C₂×C₁₃×#120	C₂²	1	6	yes	complemented
17	C₂×#88207	C₂²	1	2	yes	complemented
18	C₂×#88201	C₂²	1	6	yes	complemented
19	C₂×#88198	C₂²	1	3	yes	complemented
20	C₂×#88194	C₂²	1	3	yes	—
21	C₂×#88194	C₂²	1	6	yes	complemented
22	C₂×#88193	C₂²	1	12	yes	complemented
23	C₂×#88191	C₂²	1	6	yes	complemented
24	#11719388	C₂²	1	48	yes	complemented
25	#11719379	C₂²	1	96	yes	complemented
26	#11719375	C₂²	1	96	yes	complemented
27	#11719373	C₂²	1	48	yes	complemented
28	#11719297	C₂²	1	96	yes	complemented
29	#11719295	C₂²	1	96	yes	complemented
30	C₂×#88139	C₂²	1	12	yes	complemented
31	C₂×#88138	C₂²	1	12	yes	complemented
32	C₂×#88138	C₂²	1	12	yes	complemented
33	C₂×#88136	C₂²	1	12	yes	complemented
34	C₂×#88136	C₂²	1	6	yes	complemented
35	C₂×#88135	C₂²	1	12	yes	complemented
36	C₂×#88131	C₂²	1	6	yes	complemented
37	C₂×#88129	C₂²	1	3	yes	complemented
38	C₂×#88128	C₂²	1	2	yes	complemented
39	C₂×#88126	C₂²	1	6	yes	complemented
40	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
41	C₂⁵×C₁₃	C₂³	1	2	yes	—
42	C₂⁴×D₁₃	C₂³	1	6	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	3	yes	—
44	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
45	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
46	C₂²×C₂²⋊D₁₃	—	4	24	no	—
47	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
48	C₂²×C₂²⋊D₁₃	C₂³	1	6	yes	—
49	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
50	C₂²×C₂²⋊D₁₃	C₂³	1	48	yes	complemented
51	C₂³×Dic₁₃	C₂³	1	6	yes	—
52	C₂×#6131	—	4	12	no	—
53	C₂×#6131	C₂³	1	24	yes	complemented
54	C₂×#6129	—	4	12	no	—
55	C₂×#6129	C₂³	1	24	yes	complemented
56	C₂×D₄×D₁₃	—	4	24	no	—
57	C₂×D₄×D₁₃	C₂³	1	48	yes	complemented
58	C₂²×D₅₂	C₂³	1	6	yes	—
59	C₂²×D₅₂	C₂³	1	6	yes	—
60	C₂²×D₅₂	C₂³	1	3	yes	—
61	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
62	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
63	C₂²×Dic₂₆	C₂³	1	3	yes	—
64	C₁₃×#124	C₂³	1	24	yes	complemented
65	C₁₃×#124	C₂³	1	48	yes	complemented
66	C₁₃×#120	C₂³	1	48	yes	complemented
67	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
68	C₂×C₁₃×C₂²⋊C₄	C₂³	1	12	yes	—
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
71	#88207	C₂³	1	16	yes	complemented
72	C₂×C₂²⋊Dic₁₃	C₂³	1	6	yes	—
73	#88201	C₂³	1	48	yes	complemented
74	#88198	C₂³	1	24	yes	complemented
75	#88194	C₂³	1	24	yes	—
76	#88194	C₂³	1	48	yes	complemented
77	#88193	C₂³	1	96	yes	complemented
78	#88191	C₂³	1	48	yes	complemented
79	C₂×#6103	C₂³	1	12	yes	—
80	C₂×#6103	C₂³	1	12	yes	—
81	C₂×#6101	C₂³	1	12	yes	—
82	C₂×C₄×Dic₁₃	C₂³	1	3	yes	—
83	C₂×C₄×Dic₁₃	C₂³	1	6	yes	—
84	#88139	C₂³	1	96	yes	complemented
85	#88138	C₂³	1	96	yes	complemented
86	#88138	C₂³	1	96	yes	complemented
87	#88136	C₂³	1	96	yes	complemented
88	#88136	C₂³	1	48	yes	complemented
89	#88135	C₂³	1	96	yes	complemented
90	#88131	C₂³	1	48	yes	complemented
91	#88129	C₂³	1	24	yes	complemented
92	#88128	C₂³	1	16	yes	complemented
93	#88126	C₂³	1	48	yes	complemented
94	C₄²×D₁₃	C₂³	1	8	yes	complemented
95	C₂×#3549	—	13	1	no	maximal, Sylow
96	C₂⁴×C₁₃	—	4	12	no	—
97	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
98	C₂⁴×C₁₃	C₂⁴	1	8	yes	—
99	C₂³×D₁₃	—	4	24	no	—
100	C₂³×D₁₃	—	4	12	no	—
101	C₂³×D₁₃	C₂⁴	1	6	yes	—
102	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
103	C₂³×D₁₃	C₂⁴	1	24	yes	—
104	C₂×Q₈×C₁₃	—	4	6	no	—
105	C₂×Q₈×C₁₃	C₂⁴	1	12	yes	—
106	C₂×D₄×C₁₃	—	4	12	no	—
107	C₂×D₄×C₁₃	—	4	6	no	—
108	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
109	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
110	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
111	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
112	C₂×C₂²⋊D₁₃	—	2	48	no	—
113	C₂×C₂²⋊D₁₃	—	4	96	no	—
114	C₂×C₂²⋊D₁₃	—	4	12	no	—
115	C₂×C₂²⋊D₁₃	—	4	24	no	—
116	C₂×C₂²⋊D₁₃	C₂⁴	1	48	yes	—
117	C₂×C₂²⋊D₁₃	C₂⁴	1	24	yes	—
118	C₂×C₂²⋊D₁₃	C₂⁴	1	48	yes	—
119	C₂²×Dic₁₃	—	2	24	no	—
120	C₂²×Dic₁₃	C₂⁴	1	24	yes	—
121	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
122	C₂²×Dic₁₃	C₂⁴	1	3	yes	—
123	#6131	—	4	48	no	—
124	#6129	—	4	48	no	—
125	D₄×D₁₃	—	4	96	no	—
126	C₂×D₅₂	—	4	12	no	—
127	C₂×D₅₂	—	4	6	no	—
128	C₂×D₅₂	—	4	12	no	—
129	C₂×D₅₂	C₂⁴	1	24	yes	—
130	C₂×D₅₂	C₂⁴	1	24	yes	—
131	C₂×D₅₂	C₂⁴	1	12	yes	—
132	C₂×C₄×D₁₃	—	2	24	no	—
133	C₂×C₄×D₁₃	—	2	12	no	—
134	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
135	C₂×C₄×D₁₃	C₂⁴	1	24	yes	—
136	C₂×Dic₂₆	—	4	6	no	—
137	C₂×Dic₂₆	C₂⁴	1	12	yes	—
138	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
139	C₁₃×C₂²⋊C₄	C₂⁴	1	48	yes	—
140	C₄²×C₁₃	C₂⁴	1	4	yes	—
141	C₄²×C₁₃	C₂⁴	1	8	yes	—
142	C₂²⋊Dic₁₃	C₂⁴	1	24	yes	—
143	#6103	C₂⁴	1	48	yes	—
144	#6103	C₂⁴	1	48	yes	—
145	#6101	C₂⁴	1	48	yes	—
146	C₄×Dic₁₃	C₂⁴	1	12	yes	—
147	C₄×Dic₁₃	C₂⁴	1	24	yes	—
148	#3549	—	13	32	no	—
149	C₂×H(3,𝔽₄)	—	13	3	no	—
150	C₂×H(3,𝔽₄)	D₁₃	1	1	yes	characteristic, complemented
151	C₂×#555	—	13	6	no	—
152	C₂×D₄²	—	13	6	no	—
153	C₂×#535	—	13	6	no	—
154	C₂×#535	—	13	6	no	—
155	C₂×#532	—	13	3	no	—
156	C₂³×C₁₃	—	2	12	no	—
157	C₂³×C₁₃	—	2	24	no	—
158	C₂³×C₁₃	—	4	24	no	—
159	C₂³×C₁₃	—	8	16	no	—
160	C₂³×C₁₃	C₂⁵	1	12	yes	—
161	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
162	C₂²×D₁₃	—	2	6	no	—
163	C₂²×D₁₃	—	2	12	no	—
164	C₂²×D₁₃	—	2	24	no	—
165	C₂²×D₁₃	—	4	48	no	—
166	C₂²×D₁₃	—	4	24	no	—
167	C₂²×D₁₃	—	8	48	no	—
168	C₂²×D₁₃	C₂⁵	1	12	yes	—
169	C₂²×D₁₃	C₂⁵	1	2	yes	—
170	Q₈×C₁₃	—	4	12	no	—
171	D₄×C₁₃	—	4	24	no	—
172	D₄×C₁₃	—	4	12	no	—
173	C₂×C₄×C₁₃	—	2	6	no	—
174	C₂×C₄×C₁₃	—	2	12	no	—
175	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
176	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
177	C₂²⋊D₁₃	—	2	96	no	—
178	C₂²⋊D₁₃	—	4	24	no	—
179	C₂²⋊D₁₃	—	4	48	no	—
180	C₂×Dic₁₃	—	2	12	no	—
181	C₂×Dic₁₃	—	2	48	no	—
182	C₂×Dic₁₃	H(5,𝔽₂)	1	12	yes	—
183	C₂×Dic₁₃	C₂⁵	1	12	yes	—
184	C₂×Dic₁₃	C₂⁵	1	6	yes	—
185	D₅₂	—	4	24	no	—
186	D₅₂	—	4	12	no	—
187	D₅₂	—	4	24	no	—
188	C₄×D₁₃	—	2	48	no	—
189	C₄×D₁₃	—	2	24	no	—
190	Dic₂₆	—	4	12	no	—
191	C₂²×#41	—	13	3	no	—
192	C₂²×#41	—	13	3	no	—
193	C₂³×D₄	—	13	6	no	—
194	C₂³×D₄	—	13	6	no	—
195	H(3,𝔽₄)	—	13	48	no	—
196	H(3,𝔽₄)	C₂×D₁₃	1	16	yes	complemented
197	#555	—	13	96	no	—
198	D₄²	—	13	96	no	—
199	#535	—	13	96	no	—
200	#535	—	13	96	no	—
201	#532	—	13	48	no	—
202	C₂×C₄⋊Q₈	—	13	3	no	—
203	C₂×#127	—	13	3	no	—
204	C₂×#127	—	13	6	no	—
205	C₂×#127	—	13	2	no	—
206	C₂×#124	—	13	6	no	—
207	C₂×#124	—	13	12	no	—
208	C₂×#124	—	13	3	no	—
209	C₂×#124	C₂×D₁₃	1	3	yes	complemented
210	C₂×#124	C₂×D₁₃	1	6	yes	complemented
211	C₂×#121	—	13	12	no	—
212	C₂×#121	—	13	12	no	—
213	C₂×#121	—	13	12	no	—
214	C₂×#120	—	13	2	no	—
215	C₂×#120	—	13	6	no	—
216	C₂×#120	—	13	6	no	—
217	C₂×#120	—	13	12	no	—
218	C₂×#120	C₂×D₁₃	1	6	yes	complemented
219	C₂×C₄×D₄	—	13	12	no	—
220	C₂×#117	—	13	6	no	—
221	C₂×#117	—	13	6	no	—
222	C₂²×C₄²	—	13	1	no	—
223	C₂²×C₁₃	—	2	12	no	—
224	C₂²×C₁₃	—	2	24	no	—
225	C₂²×C₁₃	—	4	24	no	—
226	C₂²×C₁₃	—	8	16	no	—
227	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
228	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
229	C₂×D₁₃	—	2	6	no	—
230	C₂×D₁₃	—	2	12	no	—
231	C₂×D₁₃	—	2	24	no	—
232	C₂×D₁₃	—	4	4	no	—
233	C₂×D₁₃	—	4	24	no	—
234	C₂×D₁₃	—	8	48	no	—
235	C₄×C₁₃	—	2	6	no	—
236	C₄×C₁₃	—	2	12	no	—
237	Dic₁₃	—	2	12	no	—
238	Dic₁₃	C₂×H(5,𝔽₂)	1	12	yes	—
239	C₂⁵	—	13	6	no	—
240	C₂⁵	C₂²×D₁₃	1	2	yes	—
241	C₂×#41	—	13	24	no	—
242	C₂×#41	—	13	24	no	—
243	C₂×#41	—	52	12	no	—
244	C₂×#41	—	52	12	no	—
245	C₂²×Q₈	—	13	3	no	—
246	C₂²×Q₈	C₂²×D₁₃	1	3	yes	—
247	C₂²×D₄	—	13	12	no	—
248	C₂²×D₄	—	13	12	no	—
249	C₂²×D₄	—	13	6	no	—
250	C₂²×D₄	—	13	48	no	—
251	C₂²×D₄	—	13	48	no	—
252	C₂²×D₄	—	13	3	no	—
253	C₂²×D₄	—	13	6	no	—
254	C₂²×D₄	—	13	6	no	—
255	C₂²×D₄	—	52	24	no	—
256	C₂²×D₄	—	52	24	no	—
257	C₂²×D₄	C₂²×D₁₃	1	3	yes	—
258	C₂²×D₄	C₂²×D₁₃	1	6	yes	—
259	C₂³×C₄	—	13	6	no	—
260	C₂³×C₄	—	13	6	no	—
261	C₂³×C₄	—	13	3	no	—
262	C₄⋊Q₈	—	13	24	no	—
263	#127	—	13	24	no	—
264	#127	—	13	48	no	—
265	#127	—	13	16	no	—
266	#124	—	13	48	no	—
267	#124	—	13	96	no	—
268	#124	—	13	24	no	—
269	#124	C₂²×D₁₃	1	24	yes	complemented
270	#124	C₂²×D₁₃	1	48	yes	complemented
271	#121	—	13	96	no	—
272	#121	—	13	96	no	—
273	#121	—	13	96	no	—
274	#120	—	13	16	no	—
275	#120	—	13	48	no	—
276	#120	—	13	48	no	—
277	#120	—	13	96	no	—
278	#120	C₂²×D₁₃	1	48	yes	complemented
279	C₄×D₄	—	13	96	no	—
280	#117	—	13	48	no	—
281	#117	—	13	48	no	—
282	C₂×C₄⋊C₄	—	13	12	no	—
283	C₂×C₂²⋊C₄	—	13	6	no	—
284	C₂×C₂²⋊C₄	—	13	12	no	—
285	C₂×C₂²⋊C₄	—	13	12	no	—
286	C₂×C₂²⋊C₄	C₂²×D₁₃	1	6	yes	—
287	C₂×C₂²⋊C₄	C₂²×D₁₃	1	12	yes	—
288	C₂×C₄²	—	13	6	no	—
289	C₂×C₄²	—	13	3	no	—
290	C₂×C₄²	—	13	8	no	—
291	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
292	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
293	C₂×C₁₃	—	4	12	no	—
294	C₂×C₁₃	#3549	1	4	yes	complemented
295	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	3	yes	—
296	D₁₃	—	4	2	no	—
297	D₁₃	—	4	12	no	—
298	C₂⁴	—	4	12	no	—
299	C₂⁴	—	13	6	no	—
300	C₂⁴	—	13	1	no	—
301	C₂⁴	—	13	24	no	—
302	C₂⁴	—	52	12	no	—
303	C₂⁴	—	52	24	no	—
304	C₂⁴	C₂³×D₁₃	1	6	yes	—
305	C₂⁴	C₂³×D₁₃	1	8	yes	—
306	#41	—	52	48	no	—
307	#41	—	52	48	no	—
308	C₂×Q₈	—	4	6	no	—
309	C₂×Q₈	—	13	12	no	—
310	C₂×Q₈	—	52	6	no	—
311	C₂×Q₈	C₂³×D₁₃	1	12	yes	—
312	C₂×D₄	—	4	12	no	—
313	C₂×D₄	—	4	6	no	—
314	C₂×D₄	—	13	48	no	—
315	C₂×D₄	—	13	48	no	—
316	C₂×D₄	—	13	24	no	—
317	C₂×D₄	—	13	12	no	—
318	C₂×D₄	—	13	24	no	—
319	C₂×D₄	—	13	24	no	—
320	C₂×D₄	—	26	48	no	—
321	C₂×D₄	—	52	12	no	—
322	C₂×D₄	—	52	12	no	—
323	C₂×D₄	—	52	6	no	—
324	C₂×D₄	—	52	96	no	—
325	C₂×D₄	—	52	96	no	—
326	C₂×D₄	—	52	24	no	—
327	C₂×D₄	—	52	12	no	—
328	C₂×D₄	C₂³×D₁₃	1	12	yes	—
329	C₂×D₄	C₂³×D₁₃	1	24	yes	—
330	C₂²×C₄	—	13	3	no	—
331	C₂²×C₄	—	13	24	no	—
332	C₂²×C₄	—	13	6	no	—
333	C₂²×C₄	—	13	12	no	—
334	C₂²×C₄	—	13	24	no	—
335	C₂²×C₄	—	26	24	no	—
336	C₂²×C₄	—	26	12	no	—
337	C₂²×C₄	—	26	24	no	—
338	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
339	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
340	C₄⋊C₄	—	13	48	no	—
341	C₂²⋊C₄	—	13	24	no	—
342	C₂²⋊C₄	—	13	48	no	—
343	C₂²⋊C₄	—	13	48	no	—
344	C₂²⋊C₄	C₂³×D₁₃	1	24	yes	—
345	C₂²⋊C₄	C₂³×D₁₃	1	48	yes	—
346	C₄²	—	13	12	no	—
347	C₄²	—	13	24	no	—
348	C₄²	C₂³×D₁₃	1	4	yes	—
349	C₄²	C₂³×D₁₃	1	8	yes	—
350	C₁₃	C₂×#3549	1	1	yes	characteristic, complemented, Sylow
351	C₂³	—	2	12	no	—
352	C₂³	—	2	24	no	—
353	C₂³	—	4	24	no	—
354	C₂³	—	8	16	no	—
355	C₂³	—	13	12	no	—
356	C₂³	—	13	2	no	—
357	C₂³	—	26	6	no	—
358	C₂³	—	26	12	no	—
359	C₂³	—	26	24	no	—
360	C₂³	—	52	24	no	—
361	C₂³	—	52	48	no	—
362	C₂³	—	104	48	no	—
363	C₂³	C₂⁴×D₁₃	1	12	yes	—
364	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
365	Q₈	—	4	12	no	—
366	Q₈	—	52	12	no	—
367	D₄	—	4	24	no	—
368	D₄	—	4	12	no	—
369	D₄	—	26	96	no	—
370	D₄	—	52	24	no	—
371	D₄	—	52	24	no	—
372	D₄	—	52	12	no	—
373	D₄	—	52	48	no	—
374	D₄	—	52	24	no	—
375	C₂×C₄	—	2	12	no	—
376	C₂×C₄	—	2	6	no	—
377	C₂×C₄	—	13	12	no	—
378	C₂×C₄	—	13	6	no	—
379	C₂×C₄	—	13	12	no	—
380	C₂×C₄	—	26	48	no	—
381	C₂×C₄	—	26	24	no	—
382	C₂×C₄	—	26	48	no	—
383	C₂×C₄	—	26	12	no	—
384	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
385	C₂×C₄	C₂⁴×D₁₃	1	12	yes	—
386	C₂²	—	2	12	no	—
387	C₂²	—	2	24	no	—
388	C₂²	—	4	24	no	—
389	C₂²	—	8	16	no	—
390	C₂²	—	26	6	no	—
391	C₂²	—	26	12	no	—
392	C₂²	—	26	24	no	—
393	C₂²	—	52	4	no	—
394	C₂²	—	52	24	no	—
395	C₂²	—	104	48	no	—
396	C₂²	D₁₃×H(5,𝔽₂)	1	6	yes	—
397	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
398	C₄	—	2	12	no	—
399	C₄	—	2	6	no	—
400	C₄	—	13	12	no	—
401	C₄	—	26	12	no	—
402	C₂	—	4	12	no	—
403	C₂	—	52	12	no	—
404	C₂	—	52	2	no	—
405	C₂	#13129240	1	4	yes	direct product factor
406	C₂	C₂×D₁₃×H(5,𝔽₂)	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₁₃×H(3,𝔽₄)	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×H(3,𝔽₄)	D₁₃
hypocenter	C₁₃	C₂×#3549
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×H(3,𝔽₄)

Complements

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

N	H ≅ G/N	type
1. #13129240	C₂	direct (N × H)
2. C₂×#11719388	C₂	semidirect
3. C₂×#11719375	C₂	semidirect
4. C₂×#11719295	C₂	semidirect
5. C₂×#11719379	C₂	semidirect
6. C₂×#11719297	C₂	semidirect
7. C₂×#11719373	C₂	semidirect
8. C₂×C₁₃×H(3,𝔽₄)	C₂	semidirect
9. C₂³×C₂²⋊D₁₃	C₂²	semidirect
10. C₂²×#6131	C₂²	semidirect
11. C₂²×#6129	C₂²	semidirect
12. C₂²×D₄×D₁₃	C₂²	semidirect
13. C₁₃×H(3,𝔽₄)	C₂²	semidirect
14. C₂×C₁₃×#124	C₂²	semidirect
15. C₂×C₁₃×#124	C₂²	semidirect
16. C₂×C₁₃×#120	C₂²	semidirect
17. C₂×#88207	C₂²	semidirect
18. C₂×#88201	C₂²	semidirect
19. C₂×#88198	C₂²	semidirect
21. C₂×#88194	C₂²	semidirect
22. C₂×#88193	C₂²	semidirect
23. C₂×#88191	C₂²	semidirect
24. #11719388	C₂²	semidirect
25. #11719379	C₂²	semidirect
26. #11719375	C₂²	semidirect
27. #11719373	C₂²	semidirect
28. #11719297	C₂²	semidirect
29. #11719295	C₂²	semidirect
30. C₂×#88139	C₂²	semidirect
31. C₂×#88138	C₂²	semidirect
32. C₂×#88138	C₂²	semidirect
33. C₂×#88136	C₂²	semidirect
34. C₂×#88136	C₂²	semidirect
35. C₂×#88135	C₂²	semidirect
36. C₂×#88131	C₂²	semidirect
37. C₂×#88129	C₂²	semidirect
38. C₂×#88128	C₂²	semidirect
39. C₂×#88126	C₂²	semidirect
40. C₂×C₄²×D₁₃	C₂²	semidirect
50. C₂²×C₂²⋊D₁₃	C₂³	semidirect
53. C₂×#6131	C₂³	semidirect
55. C₂×#6129	C₂³	semidirect
57. C₂×D₄×D₁₃	C₂³	semidirect
64. C₁₃×#124	C₂³	semidirect
65. C₁₃×#124	C₂³	semidirect
66. C₁₃×#120	C₂³	semidirect
71. #88207	C₂³	semidirect
73. #88201	C₂³	semidirect
74. #88198	C₂³	semidirect
76. #88194	C₂³	semidirect
77. #88193	C₂³	semidirect
78. #88191	C₂³	semidirect
84. #88139	C₂³	semidirect
85. #88138	C₂³	semidirect
86. #88138	C₂³	semidirect
87. #88136	C₂³	semidirect
88. #88136	C₂³	semidirect
89. #88135	C₂³	semidirect
90. #88131	C₂³	semidirect
91. #88129	C₂³	semidirect
92. #88128	C₂³	semidirect
93. #88126	C₂³	semidirect
94. C₄²×D₁₃	C₂³	semidirect
150. C₂×H(3,𝔽₄)	D₁₃	semidirect
196. H(3,𝔽₄)	C₂×D₁₃	semidirect
209. C₂×#124	C₂×D₁₃	semidirect
210. C₂×#124	C₂×D₁₃	semidirect
218. C₂×#120	C₂×D₁₃	semidirect
269. #124	C₂²×D₁₃	semidirect
270. #124	C₂²×D₁₃	semidirect
278. #120	C₂²×D₁₃	semidirect
294. C₂×C₁₃	#3549	semidirect
350. C₁₃	C₂×#3549	semidirect
405. C₂	#13129240	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#13129240	2
C₂×#11719388	2
C₂×#11719375	2
C₂×#11719295	2
C₂×#11719379	2
C₂×#11719297	2
C₂×#11719373	2
C₂×C₁₃×H(3,𝔽₄)	2
C₂×#3549	13

Subgroups — C2×#13129240 #16770720

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129240 #16770720