Subgroups — C₂×#13129900 #16789115

Order 3328.

614 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃⋊M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₃⋊#108	C₂	1	1	yes	maximal, characteristic
3	#13129900	C₂	1	4	yes	maximal, direct product factor
4	C₂×D₁₃×#106	C₂	1	1	yes	maximal, characteristic
5	C₂×D₁₃⋊M₁₆	—	2	1	no	—
6	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×D₁₃	—	2	1	no	—
8	C₂×#88106	—	2	1	no	—
9	D₁₃⋊#108	—	2	1	no	—
10	D₁₃⋊#108	—	2	1	no	—
11	D₁₃⋊#108	C₄	1	2	yes	complemented
12	D₁₃⋊#108	C₂²	1	2	yes	—
13	C₂×#88104	—	2	1	no	—
14	C₂×#88103	C₄	1	2	yes	complemented
15	D₁₃⋊M₃₂	—	2	1	no	—
16	D₁₃⋊M₃₂	—	2	1	no	—
17	D₁₃⋊M₃₂	C₄	1	2	yes	complemented
18	D₁₃⋊M₃₂	C₂²	1	2	yes	—
19	C₂×#88098	—	2	1	no	—
20	C₂×D₁₃⋊C₁₆	C₄	1	2	yes	complemented
21	C₂×C₁₃×#106	C₄	1	1	yes	characteristic
22	C₂×#88057	C₄	1	1	yes	characteristic
23	C₂×#88048	—	2	1	no	—
24	D₁₃×#106	—	2	1	no	—
25	D₁₃×#106	—	2	1	no	—
26	D₁₃×#106	C₄	1	2	yes	—
27	D₁₃×#106	C₂²	1	2	yes	—
28	C₂²×C₄×D₁₃	—	4	1	no	—
29	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
30	C₂×#6122	—	4	1	no	—
31	D₁₃⋊M₁₆	—	2	2	no	—
32	D₁₃⋊M₁₆	—	2	2	no	—
33	D₁₃⋊M₁₆	—	4	1	no	—
34	D₁₃⋊M₁₆	—	4	1	no	—
35	C₂×#6118	—	2	2	no	—
36	C₂×D₁₃⋊C₈	—	4	1	no	—
37	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
39	C₂×C₄⋊Dic₁₃	—	2	1	no	—
40	C₂×#6101	—	4	1	no	—
41	C₂²×#1055	D₄	1	1	yes	characteristic
42	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
48	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
49	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
50	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
51	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
52	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
53	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
54	C₄⋊C₄×D₁₃	—	2	2	no	—
55	C₄⋊C₄×D₁₃	—	2	2	no	—
56	C₄⋊C₄×D₁₃	—	4	1	no	—
57	C₄⋊C₄×D₁₃	—	4	1	no	—
58	#88106	—	2	2	no	—
59	#88106	—	2	2	no	—
60	C₂×#6092	—	2	2	no	—
61	#88104	—	2	2	no	—
62	#88104	—	2	2	no	—
63	#88103	—	2	2	no	—
64	#88103	C₂×C₄	1	4	yes	complemented
65	#88098	—	2	2	no	—
66	#88098	—	2	2	no	—
67	D₁₃⋊C₁₆	—	2	2	no	—
68	D₁₃⋊C₁₆	C₂×C₄	1	4	yes	complemented
69	C₁₃×#106	—	2	1	no	—
70	C₁₃×#106	C₂×C₄	1	2	yes	—
71	#88057	—	2	1	no	—
72	#88057	C₂×C₄	1	2	yes	—
73	#88048	—	2	2	no	—
74	#88048	—	2	2	no	—
75	C₂×#1383	—	13	1	no	maximal, Sylow
76	C₂³×D₁₃	SD₁₆	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	—	4	1	no	—
78	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×Dic₁₃	—	4	1	no	—
80	C₂²×Dic₁₃	D₈	1	1	yes	characteristic
81	C₂×C₄×D₁₃	—	4	2	no	—
82	C₂×C₄×D₁₃	—	4	2	no	—
83	C₂×C₄×D₁₃	—	8	4	no	—
84	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
88	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
89	C₂×C₄×D₁₃	D₈	1	1	yes	characteristic
90	C₂×C₄×D₁₃	SD₁₆	1	1	yes	characteristic
91	C₂×C₄×D₁₃	SD₁₆	1	1	yes	characteristic
92	C₂×C₄×D₁₃	SD₁₆	1	1	yes	characteristic
93	C₂×C₄×D₁₃	Q₁₆	1	1	yes	characteristic
94	C₂×C₄×D₁₃	Q₁₆	1	1	yes	characteristic
95	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
96	#6122	—	4	2	no	—
97	#6122	—	4	2	no	—
98	C₂×#1057	—	4	2	no	—
99	#6118	—	2	4	no	—
100	#6118	—	4	2	no	—
101	D₁₃⋊C₈	—	4	2	no	—
102	D₁₃⋊C₈	—	4	2	no	—
103	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
104	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
105	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₁₃×C₄⋊C₄	—	2	2	no	—
110	C₁₃×C₄⋊C₄	—	4	1	no	—
111	C₄⋊Dic₁₃	—	2	2	no	—
112	C₄⋊Dic₁₃	—	4	1	no	—
113	#6101	—	4	2	no	—
114	#6101	—	4	2	no	—
115	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
116	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
117	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
118	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
119	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
120	C₂×#1055	C₂×D₄	1	1	yes	characteristic
121	C₈×D₁₃	C₄²	1	1	yes	characteristic
122	C₈×D₁₃	C₄²	1	1	yes	characteristic
123	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
127	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
128	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
129	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
130	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
131	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
132	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
133	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₈×D₁₃	C₂×D₄	1	1	yes	characteristic
136	C₈×D₁₃	C₂×Q₈	1	1	yes	characteristic
137	#6092	—	2	4	no	—
138	C₂²×M₃₂	—	13	1	no	—
139	C₂²×#108	—	13	1	no	—
140	C₂²×#106	—	13	1	no	—
141	#1383	—	13	4	no	—
142	C₂³×C₁₃	#102	1	1	yes	characteristic
143	C₂²×D₁₃	—	2	4	no	—
144	C₂²×D₁₃	#102	1	1	yes	characteristic
145	C₂²×D₁₃	#103	1	1	yes	characteristic
146	C₂²×D₁₃	#103	1	1	yes	characteristic
147	C₂²×D₁₃	#106	1	1	yes	characteristic
148	C₂²×D₁₃	#106	1	1	yes	characteristic
149	C₂²×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
150	C₂×C₄×C₁₃	—	4	2	no	—
151	C₂×C₄×C₁₃	—	8	2	no	—
152	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
153	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
154	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
155	C₂×C₄×C₁₃	#103	1	1	yes	characteristic
156	C₂×C₄×C₁₃	#103	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
158	C₂×Dic₁₃	—	4	2	no	—
159	C₂×Dic₁₃	—	8	2	no	—
160	C₂×Dic₁₃	#102	1	1	yes	characteristic
161	C₂×Dic₁₃	#102	1	1	yes	characteristic
162	C₂×Dic₁₃	#102	1	1	yes	characteristic
163	C₂×Dic₁₃	#107	1	1	yes	characteristic
164	C₂×Dic₁₃	#107	1	1	yes	characteristic
165	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
166	C₄×D₁₃	—	8	4	no	—
167	C₄×D₁₃	—	8	4	no	—
168	C₄×D₁₃	#95	1	1	yes	characteristic
169	C₄×D₁₃	#95	1	1	yes	characteristic
170	C₄×D₁₃	#102	1	1	yes	characteristic
171	C₄×D₁₃	#102	1	1	yes	characteristic
172	C₄×D₁₃	#103	1	1	yes	characteristic
173	C₄×D₁₃	#103	1	1	yes	characteristic
174	C₄×D₁₃	#103	1	1	yes	characteristic
175	C₄×D₁₃	#103	1	1	yes	characteristic
176	C₄×D₁₃	#106	1	1	yes	characteristic
177	C₄×D₁₃	#106	1	1	yes	characteristic
178	C₄×D₁₃	#107	1	1	yes	characteristic
179	C₄×D₁₃	#107	1	1	yes	characteristic
180	C₄×D₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₄×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
183	C₄×D₁₃	C₂×Q₁₆	1	1	yes	characteristic
184	#1057	—	4	4	no	—
185	C₈×C₁₃	#95	1	1	yes	characteristic
186	C₈×C₁₃	#95	1	1	yes	characteristic
187	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
188	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	#1055	#95	1	1	yes	characteristic
190	#1055	#95	1	1	yes	characteristic
191	#1055	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	#1055	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂²×M₁₆	—	26	1	no	—
194	C₂³×C₈	—	13	1	no	—
195	C₂²×C₄⋊C₄	—	26	1	no	—
196	C₂×M₃₂	—	13	2	no	—
197	C₂×M₃₂	—	13	2	no	—
198	C₂×M₃₂	—	26	1	no	—
199	C₂×M₃₂	—	26	1	no	—
200	C₂×M₃₂	—	26	1	no	—
201	C₂×M₃₂	—	26	1	no	—
202	C₂²×C₁₆	—	13	2	no	—
203	C₂×#108	—	13	2	no	—
204	C₂×#108	—	13	2	no	—
205	C₂×#108	—	13	2	no	—
206	C₂×#108	—	26	1	no	—
207	C₂×#108	—	26	1	no	—
208	C₂×#108	—	26	1	no	—
209	C₂×#106	—	13	1	no	—
210	C₂×#106	—	13	2	no	—
211	C₂×#106	—	13	2	no	—
212	C₂×#106	—	26	1	no	—
213	C₂×#106	—	26	1	no	—
214	C₂×#106	—	26	1	no	—
215	C₂×#106	#261	1	1	yes	characteristic
216	C₂²×C₁₃	—	2	2	no	—
217	C₂²×C₁₃	#340	1	1	yes	characteristic
218	C₂²×C₁₃	#340	1	1	yes	characteristic
219	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
220	C₂×D₁₃	—	2	2	no	—
221	C₂×D₁₃	—	2	2	no	—
222	C₂×D₁₃	—	2	2	no	—
223	C₂×D₁₃	—	2	2	no	—
224	C₂×D₁₃	—	2	2	no	—
225	C₂×D₁₃	#340	1	1	yes	characteristic
226	C₂×D₁₃	#340	1	1	yes	characteristic
227	C₂×D₁₃	#365	1	4	yes	—
228	C₂×D₁₃	C₂×#103	1	1	yes	characteristic
229	C₂×D₁₃	C₂×#106	1	1	yes	characteristic
230	C₄×C₁₃	—	8	2	no	—
231	C₄×C₁₃	#340	1	1	yes	characteristic
232	C₄×C₁₃	#340	1	1	yes	characteristic
233	C₄×C₁₃	C₂×#95	1	1	yes	characteristic
234	C₄×C₁₃	C₂×#103	1	1	yes	characteristic
235	Dic₁₃	—	8	2	no	—
236	Dic₁₃	#340	1	1	yes	characteristic
237	Dic₁₃	#340	1	1	yes	characteristic
238	Dic₁₃	C₂×#102	1	1	yes	characteristic
239	Dic₁₃	C₂×#107	1	1	yes	characteristic
240	C₂³×C₄	—	13	1	no	—
241	C₂³×C₄	—	52	1	no	—
242	C₂×M₁₆	—	26	2	no	—
243	C₂×M₁₆	—	26	2	no	—
244	C₂×M₁₆	—	26	2	no	—
245	C₂×M₁₆	—	52	1	no	—
246	C₂×M₁₆	—	52	1	no	—
247	C₂×M₁₆	—	52	1	no	—
248	C₂²×C₈	—	13	1	no	—
249	C₂²×C₈	—	13	1	no	—
250	C₂²×C₈	—	13	1	no	—
251	C₂²×C₈	—	13	1	no	—
252	C₂²×C₈	—	13	1	no	—
253	C₂²×C₈	—	13	1	no	—
254	C₂²×C₈	—	13	1	no	—
255	C₂²×C₈	—	13	1	no	—
256	C₂²×C₈	—	13	1	no	—
257	C₂²×C₈	—	13	1	no	—
258	C₂²×C₈	—	13	1	no	—
259	C₂²×C₈	—	13	1	no	—
260	C₂²×C₈	—	13	1	no	—
261	C₂²×C₈	—	52	1	no	—
262	C₂²×C₈	C₂×#261	1	1	yes	characteristic
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	26	2	no	—
265	C₂×C₄⋊C₄	—	26	2	no	—
266	C₂×C₄⋊C₄	—	26	1	no	—
267	C₂×C₄⋊C₄	—	52	1	no	—
268	C₂×C₄⋊C₄	—	52	1	no	—
269	C₂×C₄⋊C₄	—	52	1	no	—
270	M₃₂	—	26	2	no	—
271	M₃₂	—	26	2	no	—
272	M₃₂	—	26	2	no	—
273	M₃₂	—	26	2	no	—
274	C₂×C₁₆	—	13	4	no	—
275	C₂×C₁₆	—	26	2	no	—
276	C₂×C₁₆	—	26	2	no	—
277	#108	—	13	4	no	—
278	#108	—	26	2	no	—
279	#108	—	26	2	no	—
280	#108	—	26	2	no	—
281	#106	—	2	1	no	—
282	#106	—	13	2	no	—
283	#106	—	26	2	no	—
284	#106	—	26	2	no	—
285	#106	—	26	1	no	—
286	#106	C₂×#261	1	2	yes	—
287	C₂×C₁₃	—	2	1	no	—
288	C₂×C₁₃	—	2	1	no	—
289	C₂×C₁₃	#1383	1	2	yes	complemented
290	C₂×C₁₃	C₂×#340	1	1	yes	characteristic
291	D₁₃	—	2	1	no	—
292	D₁₃	—	2	1	no	—
293	D₁₃	#1383	1	2	yes	complemented
294	D₁₃	C₂×#365	1	2	yes	—
295	C₂⁴	—	13	1	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	13	1	no	—
298	C₂²×C₄	—	13	1	no	—
299	C₂²×C₄	—	13	1	no	—
300	C₂²×C₄	—	13	1	no	—
301	C₂²×C₄	—	13	1	no	—
302	C₂²×C₄	—	13	1	no	—
303	C₂²×C₄	—	13	1	no	—
304	C₂²×C₄	—	13	1	no	—
305	C₂²×C₄	—	13	1	no	—
306	C₂²×C₄	—	13	1	no	—
307	C₂²×C₄	—	13	1	no	—
308	C₂²×C₄	—	13	1	no	—
309	C₂²×C₄	—	13	1	no	—
310	C₂²×C₄	—	52	2	no	—
311	C₂²×C₄	—	52	2	no	—
312	C₂²×C₄	—	52	1	no	—
313	C₂²×C₄	—	104	4	no	—
314	C₂²×C₄	C₂²⋊#261	1	1	yes	characteristic
315	M₁₆	—	26	4	no	—
316	M₁₆	—	52	2	no	—
317	M₁₆	—	52	2	no	—
318	M₁₆	—	52	2	no	—
319	C₂×C₈	—	13	1	no	—
320	C₂×C₈	—	13	1	no	—
321	C₂×C₈	—	13	1	no	—
322	C₂×C₈	—	13	1	no	—
323	C₂×C₈	—	13	1	no	—
324	C₂×C₈	—	13	1	no	—
325	C₂×C₈	—	13	1	no	—
326	C₂×C₈	—	13	1	no	—
327	C₂×C₈	—	13	1	no	—
328	C₂×C₈	—	13	1	no	—
329	C₂×C₈	—	13	1	no	—
330	C₂×C₈	—	13	1	no	—
331	C₂×C₈	—	13	1	no	—
332	C₂×C₈	—	13	1	no	—
333	C₂×C₈	—	13	1	no	—
334	C₂×C₈	—	13	1	no	—
335	C₂×C₈	—	13	1	no	—
336	C₂×C₈	—	13	1	no	—
337	C₂×C₈	—	13	1	no	—
338	C₂×C₈	—	13	1	no	—
339	C₂×C₈	—	13	1	no	—
340	C₂×C₈	—	13	1	no	—
341	C₂×C₈	—	52	2	no	—
342	C₂×C₈	—	52	2	no	—
343	C₂×C₈	—	52	2	no	—
344	C₂×C₈	C₄×#261	1	1	yes	characteristic
345	C₂×C₈	C₄×#261	1	1	yes	characteristic
346	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
347	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
348	C₂×C₈	C₂²⋊#261	1	1	yes	characteristic
349	C₂×C₈	C₂²×#261	1	1	yes	characteristic
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	4	1	no	—
352	C₄⋊C₄	—	26	2	no	—
353	C₄⋊C₄	—	52	2	no	—
354	C₄⋊C₄	—	52	2	no	—
355	C₄⋊C₄	—	52	1	no	—
356	C₁₆	—	26	4	no	—
357	C₁₃	C₂×#1383	1	1	yes	characteristic, complemented, Sylow
358	C₂³	—	13	1	no	—
359	C₂³	—	13	1	no	—
360	C₂³	—	13	1	no	—
361	C₂³	—	13	1	no	—
362	C₂³	—	13	1	no	—
363	C₂³	—	13	1	no	—
364	C₂³	—	26	4	no	—
365	C₂³	#88115	1	1	yes	characteristic
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	8	2	no	—
368	C₂×C₄	—	13	1	no	—
369	C₂×C₄	—	13	1	no	—
370	C₂×C₄	—	13	1	no	—
371	C₂×C₄	—	13	1	no	—
372	C₂×C₄	—	13	1	no	—
373	C₂×C₄	—	13	1	no	—
374	C₂×C₄	—	13	1	no	—
375	C₂×C₄	—	13	1	no	—
376	C₂×C₄	—	13	1	no	—
377	C₂×C₄	—	13	1	no	—
378	C₂×C₄	—	13	1	no	—
379	C₂×C₄	—	13	1	no	—
380	C₂×C₄	—	13	1	no	—
381	C₂×C₄	—	13	1	no	—
382	C₂×C₄	—	13	1	no	—
383	C₂×C₄	—	13	1	no	—
384	C₂×C₄	—	13	1	no	—
385	C₂×C₄	—	13	1	no	—
386	C₂×C₄	—	13	1	no	—
387	C₂×C₄	—	13	1	no	—
388	C₂×C₄	—	13	1	no	—
389	C₂×C₄	—	13	1	no	—
390	C₂×C₄	—	52	2	no	—
391	C₂×C₄	—	104	4	no	—
392	C₂×C₄	—	104	4	no	—
393	C₂×C₄	—	104	2	no	—
394	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
395	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
396	C₂×C₄	#88115	1	1	yes	characteristic
397	C₂×C₄	#88117	1	1	yes	characteristic
398	C₂×C₄	#88117	1	1	yes	characteristic
399	C₂×C₄	C₂×C₂²⋊#261	1	1	yes	characteristic
400	C₈	—	13	1	no	—
401	C₈	—	13	1	no	—
402	C₈	—	13	1	no	—
403	C₈	—	13	1	no	—
404	C₈	—	52	4	no	—
405	C₈	(C₂×#261)⋊C₄	1	1	yes	characteristic
406	C₈	(C₂×#261)⋊C₄	1	1	yes	characteristic
407	C₈	C₂×C₄×#261	1	1	yes	characteristic
408	C₈	C₂×C₄⋊#261	1	1	yes	characteristic
409	C₂²	—	2	2	no	—
410	C₂²	—	13	1	no	—
411	C₂²	—	13	1	no	—
412	C₂²	—	13	4	no	—
413	C₂²	—	13	1	no	—
414	C₂²	—	13	1	no	—
415	C₂²	—	26	2	no	—
416	C₂²	—	26	2	no	—
417	C₂²	—	26	2	no	—
418	C₂²	—	26	2	no	—
419	C₂²	—	26	2	no	—
420	C₂²	#11718246	1	1	yes	characteristic
421	C₂²	#11718246	1	1	yes	characteristic
422	C₂²	C₂×#88115	1	1	yes	characteristic
423	C₄	—	8	2	no	—
424	C₄	—	13	1	no	—
425	C₄	—	13	1	no	—
426	C₄	—	13	1	no	—
427	C₄	—	13	1	no	—
428	C₄	—	104	2	no	—
429	C₄	#11718246	1	1	yes	characteristic
430	C₄	#11718246	1	1	yes	characteristic
431	C₄	C₂×(C₂×#261)⋊C₄	1	1	yes	characteristic
432	C₄	C₂×#88117	1	1	yes	characteristic
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	13	2	no	—
436	C₂	—	13	2	no	—
437	C₂	—	26	1	no	—
438	C₂	—	26	1	no	—
439	C₂	#13129900	1	2	yes	direct product factor
440	C₂	C₂×#11718246	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11718246
commutator	C₈×C₁₃	C₂×C₄²
Frattini	C₂×C₈	C₂²×#261
Fitting	C₂×C₁₃×#106	C₄
socle	C₂²×C₁₃	#340
prime radical	C₂³×D₁₃	SD₁₆
cosocle	C₂×C₈×D₁₃	C₂³
hypercenter	C₂×#106	#261
hypocenter	C₁₃	C₂×#1383
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#106

Complements

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

N	H ≅ G/N	type
3. #13129900	C₂	direct (N × H)
11. D₁₃⋊#108	C₄	semidirect
14. C₂×#88103	C₄	semidirect
17. D₁₃⋊M₃₂	C₄	semidirect
20. C₂×D₁₃⋊C₁₆	C₄	semidirect
64. #88103	C₂×C₄	semidirect
68. D₁₃⋊C₁₆	C₂×C₄	semidirect
289. C₂×C₁₃	#1383	semidirect
293. D₁₃	#1383	semidirect
357. C₁₃	C₂×#1383	semidirect
439. C₂	#13129900	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₁₃⋊M₃₂	2
C₂×D₁₃⋊#108	2
#13129900	2
C₂×D₁₃×#106	2
C₂×#1383	13

Subgroups — C2×#13129900 #16789115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129900 #16789115