Subgroups — C₂×#13114889 #15862580

Order 3328.

1330 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88161	C₂	1	1	yes	maximal, characteristic
2	C₂²×#88062	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11718659	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11718666	C₂	1	1	yes	maximal, characteristic
5	C₂×#11718800	C₂	1	1	yes	maximal, characteristic
6	#13114889	C₂	1	8	yes	maximal, direct product factor
7	C₂×#11718151	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#344	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#6127	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
13	C₂×#88180	C₂²	1	1	yes	characteristic
14	C₂²×#6099	C₂²	1	1	yes	characteristic
15	C₂³×#1055	C₂²	1	1	yes	characteristic
16	C₂×#88161	—	2	2	no	—
17	C₂×#88161	—	2	1	no	—
18	C₂×#88161	—	2	1	no	—
19	C₂×#88161	—	2	2	no	—
20	C₂×#88161	C₄	1	4	yes	complemented
21	C₂×#88161	C₄	1	2	yes	complemented
22	C₂×#88161	C₄	1	2	yes	complemented
23	C₂×#88161	C₂²	1	4	yes	—
24	C₂²×#6094	—	2	1	no	—
25	C₂²×C₈×D₁₃	—	2	1	no	—
26	#11718800	—	2	2	no	—
27	#11718800	C₂²	1	4	yes	—
28	C₂×#88065	—	2	2	no	—
29	C₂×#88062	—	2	1	no	—
30	C₂×#88062	—	2	1	no	—
31	C₂×#88062	—	2	2	no	—
32	C₂×#88062	C₂²	1	4	yes	complemented
33	#11718666	—	2	2	no	—
34	#11718666	C₂²	1	4	yes	—
35	#11718659	—	2	2	no	—
36	#11718659	C₂²	1	4	yes	complemented
37	C₂×#88048	—	2	1	no	—
38	C₂×#88047	—	2	1	no	—
39	C₂×#88045	—	2	2	no	—
40	C₁₃×#344	C₂²	1	4	yes	complemented
41	#11718151	C₂²	1	4	yes	complemented
42	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂²×C₂²⋊D₁₃	—	2	1	no	—
44	C₂×#6127	—	2	1	no	—
45	C₂×#6127	—	2	1	no	—
46	C₂×#6127	—	2	1	no	—
47	C₂×#6127	—	2	1	no	—
48	C₂×#6127	—	2	1	no	—
49	C₂×#6127	—	2	1	no	—
50	C₂×#6127	C₂×C₄	1	2	yes	—
51	C₂×#6127	C₂×C₄	1	2	yes	—
52	C₂×#6127	D₄	1	2	yes	—
53	C₂×#6127	D₄	1	2	yes	—
54	C₂×#6127	Q₈	1	2	yes	—
55	C₂×#6127	C₂³	1	2	yes	—
56	C₂²×D₅₂	Q₈	1	1	yes	characteristic
57	C₂²×C₄×D₁₃	—	2	1	no	—
58	C₂²×Dic₂₆	Q₈	1	1	yes	characteristic
59	C₂×C₁₃×M₁₆	—	2	1	no	—
60	C₂×C₁₃×M₁₆	—	2	1	no	—
61	C₂×C₁₃×M₁₆	—	2	1	no	—
62	C₂×C₁₃×M₁₆	—	2	1	no	—
63	C₂×C₁₃×M₁₆	—	2	1	no	—
64	C₂×C₁₃×M₁₆	—	2	1	no	—
65	C₂×C₁₃×M₁₆	—	2	1	no	—
66	C₂×C₁₃×M₁₆	—	2	1	no	—
67	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
68	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
69	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
70	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₃	—	2	1	no	—
72	C₂²×C₈×C₁₃	—	2	1	no	—
73	C₁₃×#117	—	2	1	no	—
74	C₁₃×#117	—	2	1	no	—
75	C₁₃×#117	—	2	1	no	—
76	C₁₃×#117	C₂³	1	2	yes	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₄²×C₁₃	—	2	1	no	—
80	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
81	#88180	—	2	1	no	—
82	#88180	—	2	1	no	—
83	#88180	—	2	1	no	—
84	#88180	C₂³	1	2	yes	—
85	C₂×C₄⋊Dic₁₃	—	2	1	no	—
86	C₂×C₄×Dic₁₃	—	2	1	no	—
87	C₂×#6099	—	2	1	no	—
88	C₂×#6099	—	2	1	no	—
89	C₂×#6099	—	2	1	no	—
90	C₂×#6099	—	2	1	no	—
91	C₂×#6099	—	2	1	no	—
92	C₂×#6099	C₂³	1	2	yes	—
93	C₂²×#1055	—	2	1	no	—
94	C₂²×#1055	C₂×C₄	1	2	yes	—
95	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
96	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
97	C₂²×#1055	D₄	1	2	yes	—
98	C₂²×#1055	D₄	1	1	yes	characteristic
99	C₂²×#1055	D₄	1	1	yes	characteristic
100	C₂²×#1055	D₄	1	2	yes	—
101	C₂²×#1055	D₄	1	1	yes	characteristic
102	C₂²×#1055	D₄	1	1	yes	characteristic
103	C₂²×#1055	C₂³	1	2	yes	—
104	#88161	—	2	4	no	—
105	#88161	—	2	4	no	—
106	#88161	—	2	4	no	—
107	#88161	—	2	4	no	—
108	#88161	—	2	4	no	—
109	#88161	—	2	4	no	—
110	#88161	C₂×C₄	1	8	yes	complemented
111	#88161	C₂×C₄	1	8	yes	complemented
112	C₂×#6094	—	2	4	no	—
113	C₂×#6094	—	2	2	no	—
114	C₂×#6094	—	2	2	no	—
115	C₂×#6094	—	2	4	no	—
116	C₂×C₈×D₁₃	—	2	4	no	—
117	C₂×C₈×D₁₃	—	2	2	no	—
118	C₂×C₈×D₁₃	—	2	2	no	—
119	C₂×C₈×D₁₃	—	2	4	no	—
120	#88065	—	2	8	no	—
121	#88062	—	2	4	no	—
122	#88062	—	2	4	no	—
123	#88048	—	2	4	no	—
124	#88047	—	2	4	no	—
125	#88045	—	2	8	no	—
126	C₂×#1814	—	13	1	no	maximal, Sylow
127	C₂⁴×C₁₃	#41	1	1	yes	characteristic
128	C₂³×D₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	4	1	no	—
130	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
141	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
144	C₂×C₂²⋊D₁₃	—	2	2	no	—
145	C₂×C₂²⋊D₁₃	—	2	2	no	—
146	C₂×C₂²⋊D₁₃	—	2	2	no	—
147	C₂×C₂²⋊D₁₃	—	2	2	no	—
148	C₂×C₂²⋊D₁₃	—	2	2	no	—
149	C₂×C₂²⋊D₁₃	—	2	2	no	—
150	C₂²×Dic₁₃	—	2	1	no	—
151	C₂²×Dic₁₃	—	4	1	no	—
152	#6127	—	2	2	no	—
153	#6127	—	2	2	no	—
154	#6127	—	2	2	no	—
155	#6127	—	2	2	no	—
156	#6127	—	2	2	no	—
157	#6127	—	2	2	no	—
158	#6127	—	2	2	no	—
159	#6127	—	2	2	no	—
160	#6127	—	2	2	no	—
161	#6127	—	2	2	no	—
162	#6127	—	2	2	no	—
163	#6127	—	2	2	no	—
164	#6127	C₄⋊C₄	1	4	yes	—
165	#6127	C₄⋊C₄	1	4	yes	—
166	#6127	C₂²×C₄	1	4	yes	—
167	#6127	C₂×D₄	1	4	yes	—
168	C₂×D₅₂	—	2	1	no	—
169	C₂×D₅₂	—	2	1	no	—
170	C₂×D₅₂	—	2	1	no	—
171	C₂×D₅₂	C₄⋊C₄	1	2	yes	—
172	C₂×D₅₂	C₄⋊C₄	1	2	yes	—
173	C₂×D₅₂	C₂×Q₈	1	2	yes	—
174	C₂×C₄×D₁₃	—	2	2	no	—
175	C₂×C₄×D₁₃	—	2	2	no	—
176	C₂×C₄×D₁₃	—	2	2	no	—
177	C₂×C₄×D₁₃	—	2	2	no	—
178	C₂×C₄×D₁₃	—	2	2	no	—
179	C₂×C₄×D₁₃	—	2	2	no	—
180	C₂×Dic₂₆	—	2	1	no	—
181	C₂×Dic₂₆	—	2	1	no	—
182	C₂×Dic₂₆	—	2	1	no	—
183	C₂×Dic₂₆	C₄⋊C₄	1	2	yes	—
184	C₂×Dic₂₆	C₄⋊C₄	1	2	yes	—
185	C₂×Dic₂₆	C₂×Q₈	1	2	yes	—
186	C₁₃×M₁₆	—	2	2	no	—
187	C₁₃×M₁₆	—	2	2	no	—
188	C₁₃×M₁₆	—	2	2	no	—
189	C₁₃×M₁₆	—	2	2	no	—
190	C₁₃×M₁₆	—	2	2	no	—
191	C₁₃×M₁₆	—	4	1	no	—
192	C₁₃×M₁₆	—	4	1	no	—
193	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
194	C₂×C₈×C₁₃	—	2	2	no	—
195	C₂×C₈×C₁₃	—	2	2	no	—
196	C₂×C₈×C₁₃	—	2	2	no	—
197	C₂×C₈×C₁₃	—	2	2	no	—
198	C₂×C₈×C₁₃	—	4	1	no	—
199	C₂×C₈×C₁₃	—	4	1	no	—
200	C₁₃×C₄⋊C₄	—	2	2	no	—
201	C₁₃×C₄⋊C₄	—	4	1	no	—
202	C₁₃×C₂²⋊C₄	—	2	2	no	—
203	C₁₃×C₂²⋊C₄	—	4	1	no	—
204	C₄²×C₁₃	—	2	2	no	—
205	C₄²×C₁₃	—	4	1	no	—
206	C₂²⋊Dic₁₃	—	2	2	no	—
207	C₂²⋊Dic₁₃	—	4	1	no	—
208	C₄⋊Dic₁₃	—	2	2	no	—
209	C₄⋊Dic₁₃	—	4	1	no	—
210	C₄×Dic₁₃	—	2	2	no	—
211	C₄×Dic₁₃	—	4	1	no	—
212	#6099	—	2	2	no	—
213	#6099	—	2	2	no	—
214	#6099	—	4	1	no	—
215	#6099	—	4	1	no	—
216	C₂×#1055	—	2	2	no	—
217	C₂×#1055	—	4	1	no	—
218	C₂×#1055	—	4	1	no	—
219	C₂×#1055	C₂²⋊C₄	1	2	yes	—
220	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
221	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
222	C₂×#1055	C₂²⋊C₄	1	2	yes	—
223	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
224	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
225	C₂×#1055	C₂²⋊C₄	1	2	yes	—
226	C₂×#1055	C₂²⋊C₄	1	2	yes	—
227	C₂×#1055	C₂²⋊C₄	1	2	yes	—
228	C₂×#1055	C₂²⋊C₄	1	2	yes	—
229	C₂×#1055	C₂²×C₄	1	2	yes	—
230	C₂×#1055	C₂²×C₄	1	2	yes	—
231	C₂×#1055	C₂×D₄	1	2	yes	—
232	C₂×#1055	C₂×D₄	1	2	yes	—
233	C₂×#1055	C₂×D₄	1	2	yes	—
234	C₂×#1055	C₂×D₄	1	2	yes	—
235	#6094	—	2	8	no	—
236	#6094	—	2	8	no	—
237	C₈×D₁₃	—	2	8	no	—
238	C₈×D₁₃	—	2	8	no	—
239	C₂²×#131	—	13	1	no	—
240	C₂²×#108	—	13	1	no	—
241	C₂×#427	—	13	1	no	—
242	C₂×#421	—	13	1	no	—
243	C₂×#421	—	13	1	no	—
244	#1814	—	13	8	no	—
245	C₂×#344	—	13	1	no	—
246	C₂×#344	D₁₃	1	1	yes	characteristic, complemented
247	C₂³×C₁₃	—	4	2	no	—
248	C₂³×C₁₃	#117	1	1	yes	characteristic
249	C₂³×C₁₃	#117	1	1	yes	characteristic
250	C₂³×C₁₃	#121	1	1	yes	characteristic
251	C₂³×C₁₃	#121	1	1	yes	characteristic
252	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
253	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
254	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
255	C₂²×D₁₃	—	2	2	no	—
256	C₂²×D₁₃	—	2	2	no	—
257	C₂²×D₁₃	—	2	2	no	—
258	C₂²×D₁₃	—	4	4	no	—
259	C₂×C₄×C₁₃	—	4	2	no	—
260	C₂×C₄×C₁₃	—	8	2	no	—
261	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
270	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
271	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
272	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
273	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
274	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
275	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
276	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
277	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
278	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
279	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
280	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
281	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
282	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
284	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
288	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
289	C₂²⋊D₁₃	—	2	4	no	—
290	C₂²⋊D₁₃	—	2	4	no	—
291	C₂²⋊D₁₃	—	2	4	no	—
292	C₂²⋊D₁₃	—	2	4	no	—
293	C₂×Dic₁₃	—	2	2	no	—
294	C₂×Dic₁₃	—	2	2	no	—
295	C₂×Dic₁₃	—	2	2	no	—
296	C₂×Dic₁₃	—	4	2	no	—
297	C₂×Dic₁₃	—	8	2	no	—
298	D₅₂	—	2	2	no	—
299	D₅₂	—	2	2	no	—
300	D₅₂	—	2	2	no	—
301	D₅₂	C₂×C₄⋊C₄	1	4	yes	—
302	C₄×D₁₃	—	2	4	no	—
303	C₄×D₁₃	—	2	4	no	—
304	C₄×D₁₃	—	2	4	no	—
305	C₄×D₁₃	—	2	4	no	—
306	Dic₂₆	—	2	2	no	—
307	Dic₂₆	—	2	2	no	—
308	Dic₂₆	—	2	2	no	—
309	Dic₂₆	C₂×C₄⋊C₄	1	4	yes	—
310	C₈×C₁₃	—	2	4	no	—
311	C₈×C₁₃	—	4	2	no	—
312	#1055	—	4	2	no	—
313	#1055	C₂×C₂²⋊C₄	1	2	yes	—
314	#1055	C₂×C₂²⋊C₄	1	2	yes	—
315	#1055	C₂×C₂²⋊C₄	1	2	yes	—
316	#1055	C₂×C₂²⋊C₄	1	2	yes	—
317	C₂²×#41	—	13	1	no	—
318	C₂×#131	—	13	2	no	—
319	C₂×#131	—	13	2	no	—
320	C₂×#131	—	13	4	no	—
321	C₂×#131	—	13	4	no	—
322	C₂×#131	—	26	1	no	—
323	C₂×#131	—	26	1	no	—
324	C₂×#131	—	26	2	no	—
325	C₂×#131	—	26	2	no	—
326	C₂²×M₁₆	—	13	1	no	—
327	C₂²×M₁₆	—	26	1	no	—
328	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
329	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
330	C₂³×C₈	—	13	1	no	—
331	C₂³×C₈	—	26	1	no	—
332	C₂×#117	—	13	1	no	—
333	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
334	C₂×#108	—	13	4	no	—
335	C₂×#108	—	26	1	no	—
336	C₂×#108	—	26	1	no	—
337	C₂×#108	—	26	2	no	—
338	#427	—	13	4	no	—
339	#427	—	26	2	no	—
340	C₂×#107	—	26	1	no	—
341	C₂×#106	—	26	1	no	—
342	#421	—	13	4	no	—
343	#421	—	13	4	no	—
344	#421	—	26	2	no	—
345	#421	—	26	2	no	—
346	C₂×#104	—	26	2	no	—
347	C₂×#104	—	26	2	no	—
348	#344	—	13	4	no	—
349	#344	C₂×D₁₃	1	4	yes	complemented
350	C₂²×C₁₃	—	2	2	no	—
351	C₂²×C₁₃	—	2	2	no	—
352	C₂²×C₁₃	—	2	2	no	—
353	C₂²×C₁₃	—	4	1	no	—
354	C₂²×C₁₃	—	4	1	no	—
355	C₂²×C₁₃	—	4	1	no	—
356	C₂²×C₁₃	—	4	1	no	—
357	C₂²×C₁₃	#380	1	1	yes	characteristic
358	C₂²×C₁₃	#380	1	1	yes	characteristic
359	C₂²×C₁₃	#380	1	1	yes	characteristic
360	C₂²×C₁₃	#380	1	1	yes	characteristic
361	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
362	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
363	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
364	C₂×D₁₃	—	2	4	no	—
365	C₂×D₁₃	—	4	4	no	—
366	C₂×D₁₃	—	4	4	no	—
367	C₂×D₁₃	—	4	4	no	—
368	C₄×C₁₃	—	8	2	no	—
369	C₄×C₁₃	#380	1	1	yes	characteristic
370	C₄×C₁₃	#380	1	1	yes	characteristic
371	C₄×C₁₃	#380	1	1	yes	characteristic
372	C₄×C₁₃	#380	1	1	yes	characteristic
373	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
374	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
375	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
376	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
377	Dic₁₃	—	2	4	no	—
378	Dic₁₃	—	8	2	no	—
379	C₂×#41	—	13	2	no	—
380	C₂×#41	—	13	2	no	—
381	C₂×#41	—	13	2	no	—
382	C₂×#41	—	13	2	no	—
383	C₂×#41	—	13	2	no	—
384	C₂×#41	—	13	2	no	—
385	C₂×#41	—	26	1	no	—
386	C₂×#41	—	26	1	no	—
387	C₂×#41	—	26	1	no	—
388	C₂×#41	—	26	1	no	—
389	C₂×#41	—	26	1	no	—
390	C₂×#41	—	26	1	no	—
391	C₂²×Q₈	—	13	1	no	—
392	C₂²×D₄	—	13	1	no	—
393	C₂²×D₄	—	26	1	no	—
394	C₂³×C₄	—	26	1	no	—
395	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
396	#131	—	13	8	no	—
397	#131	—	13	8	no	—
398	#131	—	26	4	no	—
399	#131	—	26	4	no	—
400	#131	—	26	4	no	—
401	#131	—	26	4	no	—
402	#131	—	26	4	no	—
403	#131	—	26	4	no	—
404	C₂×M₁₆	—	2	1	no	—
405	C₂×M₁₆	—	2	1	no	—
406	C₂×M₁₆	—	2	1	no	—
407	C₂×M₁₆	—	2	1	no	—
408	C₂×M₁₆	—	2	1	no	—
409	C₂×M₁₆	—	2	1	no	—
410	C₂×M₁₆	—	2	1	no	—
411	C₂×M₁₆	—	2	1	no	—
412	C₂×M₁₆	—	13	2	no	—
413	C₂×M₁₆	—	26	2	no	—
414	C₂×M₁₆	—	26	2	no	—
415	C₂×M₁₆	—	26	4	no	—
416	C₂×M₁₆	—	26	4	no	—
417	C₂×M₁₆	—	26	1	no	—
418	C₂×M₁₆	—	26	1	no	—
419	C₂×M₁₆	—	26	1	no	—
420	C₂×M₁₆	—	26	1	no	—
421	C₂×M₁₆	—	26	1	no	—
422	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
423	C₂×M₁₆	C₄×D₁₃	1	2	yes	—
424	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
425	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
426	C₂²×C₈	—	2	1	no	—
427	C₂²×C₈	—	2	1	no	—
428	C₂²×C₈	—	13	1	no	—
429	C₂²×C₈	—	13	1	no	—
430	C₂²×C₈	—	13	2	no	—
431	C₂²×C₈	—	13	1	no	—
432	C₂²×C₈	—	13	1	no	—
433	C₂²×C₈	—	13	1	no	—
434	C₂²×C₈	—	13	1	no	—
435	C₂²×C₈	—	13	2	no	—
436	C₂²×C₈	—	13	2	no	—
437	C₂²×C₈	—	13	2	no	—
438	C₂²×C₈	—	26	2	no	—
439	C₂²×C₈	—	26	2	no	—
440	C₂²×C₈	—	26	4	no	—
441	C₂²×C₈	—	26	4	no	—
442	C₂²×C₈	—	26	1	no	—
443	#117	—	2	1	no	—
444	#117	—	2	1	no	—
445	#117	—	2	1	no	—
446	#117	—	13	2	no	—
447	#117	—	26	1	no	—
448	#117	—	26	1	no	—
449	#117	—	26	1	no	—
450	#117	C₂²×D₁₃	1	2	yes	—
451	C₂×C₄⋊C₄	—	2	1	no	—
452	C₂×C₄⋊C₄	—	26	1	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	26	1	no	—
455	C₂×C₄²	—	2	1	no	—
456	C₂×C₄²	—	26	1	no	—
457	#108	—	26	4	no	—
458	#108	—	26	4	no	—
459	#107	—	26	4	no	—
460	#106	—	26	4	no	—
461	#104	—	26	8	no	—
462	#104	—	26	8	no	—
463	C₂×C₁₃	—	2	1	no	—
464	C₂×C₁₃	—	2	1	no	—
465	C₂×C₁₃	—	2	1	no	—
466	C₂×C₁₃	—	2	1	no	—
467	C₂×C₁₃	—	2	1	no	—
468	C₂×C₁₃	—	2	1	no	—
469	C₂×C₁₃	#1814	1	2	yes	complemented
470	C₂×C₁₃	C₂×#380	1	1	yes	characteristic
471	D₁₃	—	4	4	no	—
472	C₂⁴	—	26	1	no	—
473	C₂⁴	#6127	1	1	yes	characteristic
474	#41	—	13	4	no	—
475	#41	—	13	4	no	—
476	#41	—	13	4	no	—
477	#41	—	13	4	no	—
478	#41	—	26	2	no	—
479	#41	—	26	2	no	—
480	#41	—	26	2	no	—
481	#41	—	26	2	no	—
482	#41	—	26	2	no	—
483	#41	—	26	2	no	—
484	#41	—	26	2	no	—
485	#41	—	26	2	no	—
486	#41	—	26	2	no	—
487	#41	—	26	2	no	—
488	#41	—	26	2	no	—
489	#41	—	26	2	no	—
490	C₂×Q₈	—	13	2	no	—
491	C₂×Q₈	—	13	2	no	—
492	C₂×Q₈	—	13	2	no	—
493	C₂×Q₈	—	26	1	no	—
494	C₂×Q₈	—	26	1	no	—
495	C₂×Q₈	—	26	1	no	—
496	C₂×D₄	—	13	2	no	—
497	C₂×D₄	—	13	2	no	—
498	C₂×D₄	—	13	2	no	—
499	C₂×D₄	—	26	2	no	—
500	C₂×D₄	—	26	2	no	—
501	C₂×D₄	—	26	2	no	—
502	C₂×D₄	—	26	2	no	—
503	C₂×D₄	—	26	2	no	—
504	C₂×D₄	—	26	2	no	—
505	C₂×D₄	—	26	1	no	—
506	C₂×D₄	—	26	1	no	—
507	C₂×D₄	—	26	1	no	—
508	C₂²×C₄	—	4	1	no	—
509	C₂²×C₄	—	26	1	no	—
510	C₂²×C₄	—	26	2	no	—
511	C₂²×C₄	—	26	2	no	—
512	C₂²×C₄	—	26	2	no	—
513	C₂²×C₄	—	26	2	no	—
514	C₂²×C₄	—	26	2	no	—
515	C₂²×C₄	—	26	2	no	—
516	C₂²×C₄	—	52	1	no	—
517	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
518	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
519	C₂²×C₄	#6127	1	1	yes	characteristic
520	C₂²×C₄	#6127	1	1	yes	characteristic
521	C₂²×C₄	#6127	1	1	yes	characteristic
522	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
523	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
524	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
525	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
526	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
527	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
528	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
529	C₂²×C₄	Q₈×D₁₃	1	1	yes	characteristic
530	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
531	M₁₆	—	2	2	no	—
532	M₁₆	—	2	2	no	—
533	M₁₆	—	2	2	no	—
534	M₁₆	—	2	2	no	—
535	M₁₆	—	2	2	no	—
536	M₁₆	—	4	1	no	—
537	M₁₆	—	4	1	no	—
538	M₁₆	—	26	8	no	—
539	M₁₆	—	26	8	no	—
540	M₁₆	—	26	2	no	—
541	M₁₆	—	26	2	no	—
542	M₁₆	—	52	1	no	—
543	M₁₆	—	52	1	no	—
544	M₁₆	C₂×C₄×D₁₃	1	4	yes	—
545	C₂×C₈	—	2	2	no	—
546	C₂×C₈	—	2	2	no	—
547	C₂×C₈	—	2	2	no	—
548	C₂×C₈	—	2	2	no	—
549	C₂×C₈	—	4	1	no	—
550	C₂×C₈	—	4	1	no	—
551	C₂×C₈	—	13	1	no	—
552	C₂×C₈	—	13	1	no	—
553	C₂×C₈	—	13	2	no	—
554	C₂×C₈	—	13	1	no	—
555	C₂×C₈	—	13	1	no	—
556	C₂×C₈	—	13	2	no	—
557	C₂×C₈	—	13	2	no	—
558	C₂×C₈	—	13	2	no	—
559	C₂×C₈	—	13	2	no	—
560	C₂×C₈	—	13	2	no	—
561	C₂×C₈	—	13	2	no	—
562	C₂×C₈	—	13	2	no	—
563	C₂×C₈	—	13	2	no	—
564	C₂×C₈	—	13	2	no	—
565	C₂×C₈	—	13	2	no	—
566	C₂×C₈	—	13	2	no	—
567	C₂×C₈	—	26	8	no	—
568	C₂×C₈	—	26	8	no	—
569	C₂×C₈	—	26	2	no	—
570	C₂×C₈	—	52	1	no	—
571	C₂×C₈	—	52	1	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	4	1	no	—
574	C₄⋊C₄	—	26	2	no	—
575	C₄⋊C₄	—	52	1	no	—
576	C₂²⋊C₄	—	2	2	no	—
577	C₂²⋊C₄	—	4	1	no	—
578	C₂²⋊C₄	—	26	2	no	—
579	C₂²⋊C₄	—	52	1	no	—
580	C₄²	—	2	2	no	—
581	C₄²	—	4	1	no	—
582	C₄²	—	26	2	no	—
583	C₄²	—	52	1	no	—
584	C₁₃	C₂×#1814	1	1	yes	characteristic, complemented, Sylow
585	C₂³	—	4	2	no	—
586	C₂³	—	26	2	no	—
587	C₂³	—	26	2	no	—
588	C₂³	—	26	2	no	—
589	C₂³	—	52	4	no	—
590	C₂³	#88126	1	1	yes	characteristic
591	C₂³	#88126	1	1	yes	characteristic
592	C₂³	#88138	1	1	yes	characteristic
593	C₂³	#88138	1	1	yes	characteristic
594	C₂³	#88150	1	1	yes	characteristic
595	C₂³	#88150	1	1	yes	characteristic
596	C₂³	C₂×#6127	1	1	yes	characteristic
597	Q₈	—	13	4	no	—
598	Q₈	—	26	2	no	—
599	Q₈	—	26	2	no	—
600	Q₈	—	26	2	no	—
601	D₄	—	13	4	no	—
602	D₄	—	26	4	no	—
603	D₄	—	26	4	no	—
604	D₄	—	26	4	no	—
605	D₄	—	26	4	no	—
606	D₄	—	26	2	no	—
607	D₄	—	26	2	no	—
608	D₄	—	26	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	8	2	no	—
611	C₂×C₄	—	26	2	no	—
612	C₂×C₄	—	26	2	no	—
613	C₂×C₄	—	26	2	no	—
614	C₂×C₄	—	26	4	no	—
615	C₂×C₄	—	26	4	no	—
616	C₂×C₄	—	26	4	no	—
617	C₂×C₄	—	26	4	no	—
618	C₂×C₄	—	52	2	no	—
619	C₂×C₄	—	104	2	no	—
620	C₂×C₄	#88126	1	1	yes	characteristic
621	C₂×C₄	#88126	1	1	yes	characteristic
622	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
623	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
624	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
625	C₂×C₄	C₂²⋊C₄×D₁₃	1	1	yes	characteristic
626	C₂×C₄	#88138	1	1	yes	characteristic
627	C₂×C₄	#88138	1	1	yes	characteristic
628	C₂×C₄	#88138	1	1	yes	characteristic
629	C₂×C₄	#88138	1	1	yes	characteristic
630	C₂×C₄	#88138	1	1	yes	characteristic
631	C₂×C₄	#88138	1	1	yes	characteristic
632	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
633	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
634	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
635	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
636	C₂×C₄	#88150	1	1	yes	characteristic
637	C₂×C₄	#88150	1	1	yes	characteristic
638	C₂×C₄	#88150	1	1	yes	characteristic
639	C₂×C₄	#88150	1	1	yes	characteristic
640	C₂×C₄	#88150	1	1	yes	characteristic
641	C₂×C₄	#88150	1	1	yes	characteristic
642	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
643	C₂×C₄	C₂×#6127	1	1	yes	characteristic
644	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
645	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
646	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
647	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
648	C₈	—	2	4	no	—
649	C₈	—	4	2	no	—
650	C₈	—	13	2	no	—
651	C₈	—	13	2	no	—
652	C₈	—	13	2	no	—
653	C₈	—	13	2	no	—
654	C₈	—	52	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	2	2	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	1	no	—
662	C₂²	—	26	4	no	—
663	C₂²	—	52	4	no	—
664	C₂²	—	52	4	no	—
665	C₂²	—	52	4	no	—
666	C₂²	#11718328	1	1	yes	characteristic
667	C₂²	#11718328	1	1	yes	characteristic
668	C₂²	#11718328	1	1	yes	characteristic
669	C₂²	#11718328	1	1	yes	characteristic
670	C₂²	C₂×#88126	1	1	yes	characteristic
671	C₂²	C₂×#88138	1	1	yes	characteristic
672	C₂²	C₂×#88150	1	1	yes	characteristic
673	C₄	—	8	2	no	—
674	C₄	—	26	4	no	—
675	C₄	—	104	2	no	—
676	C₄	#11718328	1	1	yes	characteristic
677	C₄	#11718328	1	1	yes	characteristic
678	C₄	#11718328	1	1	yes	characteristic
679	C₄	#11718328	1	1	yes	characteristic
680	C₄	C₂×C₂²⋊C₄×D₁₃	1	1	yes	characteristic
681	C₄	C₂×#88138	1	1	yes	characteristic
682	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
683	C₄	C₂×#88150	1	1	yes	characteristic
684	C₂	—	2	1	no	—
685	C₂	—	2	1	no	—
686	C₂	—	2	1	no	—
687	C₂	—	2	1	no	—
688	C₂	—	2	1	no	—
689	C₂	—	2	1	no	—
690	C₂	—	52	4	no	—
691	C₂	#13114889	1	2	yes	direct product factor
692	C₂	C₂×#11718328	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88138
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#344	C₂
socle	C₂²×C₁₃	#380
prime radical	C₂²×#6127	C₂²
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×#344	D₁₃
hypocenter	C₁₃	C₂×#1814
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
2. C₂²×#88062	C₂	semidirect
3. C₂×#11718659	C₂	semidirect
6. #13114889	C₂	direct (N × H)
7. C₂×#11718151	C₂	semidirect
8. C₂×C₁₃×#344	C₂	semidirect
20. C₂×#88161	C₄	semidirect
21. C₂×#88161	C₄	semidirect
22. C₂×#88161	C₄	semidirect
32. C₂×#88062	C₂²	semidirect
36. #11718659	C₂²	semidirect
40. C₁₃×#344	C₂²	semidirect
41. #11718151	C₂²	semidirect
110. #88161	C₂×C₄	semidirect
111. #88161	C₂×C₄	semidirect
246. C₂×#344	D₁₃	semidirect
349. #344	C₂×D₁₃	semidirect
469. C₂×C₁₃	#1814	semidirect
584. C₁₃	C₂×#1814	semidirect
691. C₂	#13114889	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×#88161	2
C₂²×#88062	2
C₂×#11718659	2
C₂×#11718666	2
C₂×#11718800	2
#13114889	2
C₂×#11718151	2
C₂×C₁₃×#344	2
C₂×#1814	13

Subgroups — C2×#13114889 #15862580

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13114889 #15862580