Subgroups — C₂×#13129892 #16789089

Order 3328.

606 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₁₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#11719089	C₂	1	1	yes	maximal, characteristic
3	#13129892	C₂	1	4	yes	maximal, direct product factor
4	C₂×D₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
5	C₂×#88237	C₄	1	1	yes	characteristic
6	C₂×D₁₃⋊M₁₆	C₄	1	1	yes	characteristic
7	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
8	C₂²×#6092	C₄	1	2	yes	complemented
9	#11719089	—	2	1	no	—
10	#11719089	—	2	1	no	—
11	#11719089	C₄	1	2	yes	—
12	#11719089	C₂²	1	2	yes	—
13	C₂×#88100	—	2	1	no	—
14	C₂×C₈×#261	—	2	1	no	—
15	C₂×D₁₃⋊C₁₆	—	2	1	no	—
16	C₂×D₁₃⋊C₁₆	—	2	1	no	—
17	C₂×D₁₃⋊C₁₆	—	2	1	no	—
18	C₂×D₁₃⋊C₁₆	—	2	1	no	—
19	C₂×D₁₃⋊C₁₆	C₄	1	2	yes	complemented
20	C₂×D₁₃⋊C₁₆	C₂²	1	2	yes	—
21	C₂×C₁₃×M₃₂	C₄	1	1	yes	characteristic, complemented
22	C₂×#88052	C₄	1	1	yes	characteristic, complemented
23	D₁₃×M₃₂	—	2	1	no	—
24	D₁₃×M₃₂	—	2	1	no	—
25	D₁₃×M₃₂	C₄	1	2	yes	complemented
26	D₁₃×M₃₂	C₂²	1	2	yes	—
27	C₂×#88038	—	2	1	no	—
28	C₂×C₁₆×D₁₃	—	2	1	no	—
29	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂×C₂²⋊#261	—	2	1	no	—
31	C₂×#6122	—	2	1	no	—
32	#88237	—	2	1	no	—
33	#88237	—	2	1	no	—
34	#88237	C₈	1	2	yes	—
35	#88237	C₂×C₄	1	2	yes	—
36	C₂×C₄⋊#261	C₈	1	2	yes	—
37	C₂×C₄×#261	—	2	1	no	—
38	D₁₃⋊M₁₆	—	2	1	no	—
39	D₁₃⋊M₁₆	—	2	1	no	—
40	D₁₃⋊M₁₆	C₈	1	2	yes	—
41	D₁₃⋊M₁₆	C₂×C₄	1	2	yes	—
42	C₂×#6118	C₈	1	2	yes	—
43	C₂×D₁₃⋊C₈	—	2	1	no	—
44	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₁₃	C₂×C₄	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	D₄	1	1	yes	characteristic
52	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
53	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
54	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
55	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
56	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
57	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
58	C₂×#6092	—	2	2	no	—
59	C₂×#6092	—	2	2	no	—
60	C₂×#6092	C₂×C₄	1	4	yes	complemented
61	#88100	—	2	2	no	—
62	#88100	—	2	2	no	—
63	C₈×#261	—	2	2	no	—
64	C₈×#261	—	2	2	no	—
65	D₁₃⋊C₁₆	—	2	2	no	—
66	D₁₃⋊C₁₆	—	2	2	no	—
67	D₁₃⋊C₁₆	—	2	2	no	—
68	D₁₃⋊C₁₆	—	2	2	no	—
69	C₁₃×M₃₂	—	2	1	no	—
70	C₁₃×M₃₂	C₂×C₄	1	2	yes	complemented
71	C₂×C₁₃×C₁₆	—	2	1	no	—
72	#88052	—	2	1	no	—
73	#88052	C₂×C₄	1	2	yes	complemented
74	C₂×#6090	—	2	1	no	—
75	#88038	—	2	2	no	—
76	#88038	—	2	2	no	—
77	C₁₆×D₁₃	—	2	2	no	—
78	C₁₆×D₁₃	—	2	2	no	—
79	C₂×#1379	—	13	1	no	maximal, Sylow
80	C₂³×D₁₃	M₁₆	1	1	yes	characteristic
81	C₂²×#261	—	2	2	no	—
82	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
83	C₂²×Dic₁₃	M₁₆	1	1	yes	characteristic
84	C₂×C₄×D₁₃	C₄²	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	C₂×C₈	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
91	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
92	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
93	C₂×C₄×D₁₃	M₁₆	1	1	yes	characteristic
94	C₂×C₄×D₁₃	M₁₆	1	1	yes	characteristic
95	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²⋊#261	—	2	2	no	—
97	C₂²⋊#261	—	2	2	no	—
98	#6122	—	2	2	no	—
99	#6122	—	2	2	no	—
100	C₂×#1057	—	2	2	no	—
101	C₄⋊#261	—	2	2	no	—
102	C₄⋊#261	C₂×C₈	1	4	yes	—
103	C₄×#261	—	2	2	no	—
104	C₄×#261	—	2	2	no	—
105	#6118	—	2	2	no	—
106	#6118	C₂×C₈	1	4	yes	—
107	D₁₃⋊C₈	—	2	2	no	—
108	D₁₃⋊C₈	—	2	2	no	—
109	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
110	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×#1055	C₄²	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	C₂²×C₄	1	1	yes	characteristic
121	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₈×D₁₃	C₂²⋊C₄	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	C₂×D₄	1	1	yes	characteristic
134	C₈×D₁₃	C₂×D₄	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	C₁₃×C₁₆	—	2	2	no	—
139	#6090	—	2	2	no	—
140	C₂²×M₃₂	—	13	1	no	—
141	C₂³×C₁₆	—	13	1	no	—
142	C₂×#405	—	13	1	no	—
143	#1379	—	13	4	no	—
144	C₂³×C₁₃	#97	1	1	yes	characteristic
145	C₂²×D₁₃	—	2	4	no	—
146	C₂²×D₁₃	#97	1	1	yes	characteristic
147	C₂²×D₁₃	C₂²⋊C₈	1	1	yes	characteristic
148	C₂²×D₁₃	C₂²⋊C₈	1	1	yes	characteristic
149	C₂²×D₁₃	C₄⋊C₈	1	1	yes	characteristic
150	C₂²×D₁₃	C₄⋊C₈	1	1	yes	characteristic
151	C₂²×D₁₃	C₂×M₁₆	1	1	yes	characteristic
152	C₂×#261	—	2	4	no	—
153	C₂×#261	—	4	4	no	—
154	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
155	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
157	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
158	C₂×C₄×C₁₃	#97	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
160	C₂×Dic₁₃	#97	1	1	yes	characteristic
161	C₂×Dic₁₃	C₂²⋊C₈	1	1	yes	characteristic
162	C₂×Dic₁₃	C₂²⋊C₈	1	1	yes	characteristic
163	C₂×Dic₁₃	C₄⋊C₈	1	1	yes	characteristic
164	C₂×Dic₁₃	C₄⋊C₈	1	1	yes	characteristic
165	C₂×Dic₁₃	C₂×M₁₆	1	1	yes	characteristic
166	C₄×D₁₃	#95	1	1	yes	characteristic
167	C₄×D₁₃	#95	1	1	yes	characteristic
168	C₄×D₁₃	C₄×C₈	1	1	yes	characteristic
169	C₄×D₁₃	C₄×C₈	1	1	yes	characteristic
170	C₄×D₁₃	C₂²⋊C₈	1	1	yes	characteristic
171	C₄×D₁₃	C₂²⋊C₈	1	1	yes	characteristic
172	C₄×D₁₃	C₂²⋊C₈	1	1	yes	characteristic
173	C₄×D₁₃	C₂²⋊C₈	1	1	yes	characteristic
174	C₄×D₁₃	C₄⋊C₈	1	1	yes	characteristic
175	C₄×D₁₃	C₄⋊C₈	1	1	yes	characteristic
176	C₄×D₁₃	C₄⋊C₈	1	1	yes	characteristic
177	C₄×D₁₃	C₄⋊C₈	1	1	yes	characteristic
178	C₄×D₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₄×D₁₃	C₂²×C₈	1	1	yes	characteristic
181	C₄×D₁₃	C₂²×C₈	1	1	yes	characteristic
182	#1057	—	2	4	no	—
183	C₈×C₁₃	#95	1	1	yes	characteristic
184	C₈×C₁₃	#95	1	1	yes	characteristic
185	C₈×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
187	#1055	#95	1	1	yes	characteristic
188	#1055	#95	1	1	yes	characteristic
189	#1055	C₂×C₂²⋊C₄	1	1	yes	characteristic
190	#1055	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂²×M₁₆	—	13	1	no	—
192	C₂³×C₈	—	13	1	no	—
193	C₂×#117	—	13	1	no	—
194	C₂×M₃₂	—	13	1	no	—
195	C₂×M₃₂	—	13	2	no	—
196	C₂×M₃₂	—	13	2	no	—
197	C₂×M₃₂	—	26	1	no	—
198	C₂×M₃₂	—	26	1	no	—
199	C₂×M₃₂	—	26	1	no	—
200	C₂×M₃₂	#261	1	1	yes	characteristic, complemented
201	C₂²×C₁₆	—	13	2	no	—
202	C₂²×C₁₆	—	13	2	no	—
203	C₂²×C₁₆	—	13	2	no	—
204	C₂²×C₁₆	—	26	1	no	—
205	C₂²×C₁₆	—	26	1	no	—
206	C₂²×C₁₆	—	26	1	no	—
207	C₂²×C₁₆	—	26	1	no	—
208	C₂²×C₁₆	—	26	1	no	—
209	#405	—	13	2	no	—
210	#405	—	13	2	no	—
211	#405	—	26	1	no	—
212	#405	—	26	1	no	—
213	C₂×#97	—	26	1	no	—
214	C₂×C₄×C₈	—	26	1	no	—
215	C₂²×C₁₃	—	2	2	no	—
216	C₂²×C₁₃	#336	1	1	yes	characteristic
217	C₂²×C₁₃	#336	1	1	yes	characteristic
218	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
219	C₂×D₁₃	—	2	2	no	—
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	#336	1	1	yes	characteristic
225	C₂×D₁₃	#336	1	1	yes	characteristic
226	C₂×D₁₃	#350	1	4	yes	—
227	C₂×D₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
228	C₂×D₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
229	#261	—	4	4	no	—
230	C₄×C₁₃	#336	1	1	yes	characteristic
231	C₄×C₁₃	#336	1	1	yes	characteristic
232	C₄×C₁₃	C₂×#95	1	1	yes	characteristic
233	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
234	Dic₁₃	#336	1	1	yes	characteristic
235	Dic₁₃	#336	1	1	yes	characteristic
236	Dic₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
237	Dic₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
238	C₂³×C₄	—	13	1	no	—
239	C₂×M₁₆	—	13	2	no	—
240	C₂×M₁₆	—	13	2	no	—
241	C₂×M₁₆	—	13	2	no	—
242	C₂×M₁₆	—	26	1	no	—
243	C₂×M₁₆	—	26	1	no	—
244	C₂×M₁₆	—	26	1	no	—
245	C₂²×C₈	—	13	1	no	—
246	C₂²×C₈	—	13	1	no	—
247	C₂²×C₈	—	13	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	—	26	1	no	—
259	C₂²×C₈	C₂×#261	1	1	yes	characteristic
260	#117	—	13	2	no	—
261	#117	—	13	2	no	—
262	#117	—	26	1	no	—
263	#117	—	26	1	no	—
264	C₂×C₄⋊C₄	—	13	2	no	—
265	C₂×C₂²⋊C₄	—	26	1	no	—
266	C₂×C₄²	—	26	1	no	—
267	M₃₂	—	2	1	no	—
268	M₃₂	—	13	2	no	—
269	M₃₂	—	26	2	no	—
270	M₃₂	—	26	2	no	—
271	M₃₂	—	26	1	no	—
272	M₃₂	C₂×#261	1	2	yes	complemented
273	C₂×C₁₆	—	2	1	no	—
274	C₂×C₁₆	—	13	4	no	—
275	C₂×C₁₆	—	26	2	no	—
276	C₂×C₁₆	—	26	2	no	—
277	C₂×C₁₆	—	26	2	no	—
278	C₂×C₁₆	—	26	2	no	—
279	C₂×C₁₆	—	26	2	no	—
280	C₂×C₁₆	—	26	2	no	—
281	C₂×C₁₆	—	26	2	no	—
282	C₂×C₁₆	—	26	2	no	—
283	C₂×C₁₆	—	26	1	no	—
284	#97	—	26	2	no	—
285	#97	—	26	2	no	—
286	C₄×C₈	—	26	2	no	—
287	C₄×C₈	—	26	2	no	—
288	C₂×C₁₃	—	2	1	no	—
289	C₂×C₁₃	—	2	1	no	—
290	C₂×C₁₃	#1379	1	2	yes	complemented
291	C₂×C₁₃	C₂×#336	1	1	yes	characteristic
292	D₁₃	—	2	1	no	—
293	D₁₃	—	2	1	no	—
294	D₁₃	#1379	1	2	yes	complemented
295	D₁₃	C₂×#350	1	2	yes	—
296	C₂⁴	—	13	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	—	26	2	no	—
311	C₂²×C₄	C₄×#261	1	1	yes	characteristic
312	M₁₆	—	13	4	no	—
313	M₁₆	—	26	2	no	—
314	M₁₆	—	26	2	no	—
315	M₁₆	—	26	2	no	—
316	C₂×C₈	—	13	1	no	—
317	C₂×C₈	—	13	1	no	—
318	C₂×C₈	—	13	1	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	—	26	2	no	—
339	C₂×C₈	—	26	2	no	—
340	C₂×C₈	—	26	2	no	—
341	C₂×C₈	C₄×#261	1	1	yes	characteristic
342	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
343	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
344	C₂×C₈	C₂²⋊#261	1	1	yes	characteristic
345	C₂×C₈	C₂²⋊#261	1	1	yes	characteristic
346	C₂×C₈	C₂²×#261	1	1	yes	characteristic
347	C₄⋊C₄	—	13	4	no	—
348	C₄⋊C₄	—	26	2	no	—
349	C₂²⋊C₄	—	26	2	no	—
350	C₂²⋊C₄	—	26	2	no	—
351	C₄²	—	26	2	no	—
352	C₄²	—	26	2	no	—
353	C₁₆	—	2	2	no	—
354	C₁₆	—	26	4	no	—
355	C₁₆	—	26	2	no	—
356	C₁₃	C₂×#1379	1	1	yes	characteristic, complemented, Sylow
357	C₂³	—	13	1	no	—
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	—	26	4	no	—
364	C₂³	#88100	1	1	yes	characteristic
365	C₂×C₄	—	13	1	no	—
366	C₂×C₄	—	13	1	no	—
367	C₂×C₄	—	13	1	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	—	26	4	no	—
388	C₂×C₄	—	52	4	no	—
389	C₂×C₄	C₈×#261	1	1	yes	characteristic
390	C₂×C₄	C₈×#261	1	1	yes	characteristic
391	C₂×C₄	#88100	1	1	yes	characteristic
392	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
393	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
394	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
395	C₈	—	13	1	no	—
396	C₈	—	13	1	no	—
397	C₈	—	13	1	no	—
398	C₈	—	13	1	no	—
399	C₈	—	26	4	no	—
400	C₈	(C₂×#261)⋊C₄	1	1	yes	characteristic
401	C₈	(C₂×#261)⋊C₄	1	1	yes	characteristic
402	C₈	C₂×C₄⋊#261	1	1	yes	characteristic
403	C₈	C₂×C₂²⋊#261	1	1	yes	characteristic
404	C₂²	—	2	2	no	—
405	C₂²	—	13	4	no	—
406	C₂²	—	13	1	no	—
407	C₂²	—	13	1	no	—
408	C₂²	—	13	1	no	—
409	C₂²	—	13	1	no	—
410	C₂²	—	26	2	no	—
411	C₂²	—	26	2	no	—
412	C₂²	—	26	2	no	—
413	C₂²	—	26	2	no	—
414	C₂²	—	26	2	no	—
415	C₂²	(C₂×#261)⋊C₈	1	1	yes	characteristic
416	C₂²	(C₂×#261)⋊C₈	1	1	yes	characteristic
417	C₂²	C₂×#88100	1	1	yes	characteristic
418	C₄	—	13	1	no	—
419	C₄	—	13	1	no	—
420	C₄	—	13	1	no	—
421	C₄	—	13	1	no	—
422	C₄	—	52	4	no	—
423	C₄	(C₂×#261)⋊C₈	1	1	yes	characteristic
424	C₄	(C₂×#261)⋊C₈	1	1	yes	characteristic
425	C₄	C₂×C₈×#261	1	1	yes	characteristic
426	C₄	C₂×(C₂×#261)⋊C₄	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	13	2	no	—
430	C₂	—	13	2	no	—
431	C₂	—	26	1	no	—
432	C₂	—	26	1	no	—
433	C₂	#13129892	1	2	yes	direct product factor
434	C₂	C₂×(C₂×#261)⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂²⋊#261
commutator	C₄×C₁₃	C₂×C₄×C₈
Frattini	C₂×C₈	C₂²×#261
Fitting	C₂×C₁₃×M₃₂	C₄
socle	C₂²×C₁₃	#336
prime radical	C₂³×D₁₃	M₁₆
cosocle	C₂×C₈×D₁₃	C₂³
hypercenter	C₂×M₃₂	#261
hypocenter	C₁₃	C₂×#1379
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
3. #13129892	C₂	direct (N × H)
8. C₂²×#6092	C₄	semidirect
19. C₂×D₁₃⋊C₁₆	C₄	semidirect
21. C₂×C₁₃×M₃₂	C₄	semidirect
22. C₂×#88052	C₄	semidirect
25. D₁₃×M₃₂	C₄	semidirect
60. C₂×#6092	C₂×C₄	semidirect
70. C₁₃×M₃₂	C₂×C₄	semidirect
73. #88052	C₂×C₄	semidirect
200. C₂×M₃₂	#261	semidirect
272. M₃₂	C₂×#261	semidirect
290. C₂×C₁₃	#1379	semidirect
294. D₁₃	#1379	semidirect
356. C₁₃	C₂×#1379	semidirect
433. C₂	#13129892	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×D₁₃⋊C₁₆	2
C₂×#11719089	2
#13129892	2
C₂×D₁₃×M₃₂	2
C₂×#1379	13

Subgroups — C2×#13129892 #16789089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129892 #16789089