Subgroups — C₂×#13114890 #15862581

Order 3328.

1330 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88059	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11718767	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11718897	C₂	1	2	yes	maximal
4	#13114890	C₂	1	8	yes	maximal, direct product factor
5	C₂×#11718151	C₂	1	2	yes	maximal, complemented
6	C₂²×C₁₃×#131	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×#131	—	2	1	no	—
9	C₂×C₁₃×#131	—	2	1	no	—
10	C₂×C₁₃×#131	—	2	2	no	—
11	C₂×C₁₃×#131	—	2	2	no	—
12	C₂×C₁₃×#131	C₄	1	2	yes	complemented
13	C₂×C₁₃×#131	C₄	1	2	yes	complemented
14	C₂×C₁₃×#131	C₄	1	4	yes	complemented
15	C₂×C₁₃×#131	C₂²	1	4	yes	—
16	C₂²×C₁₃×M₁₆	—	2	1	no	—
17	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₁₃	—	2	1	no	—
19	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×#88180	C₂²	1	2	yes	—
21	C₂²×#6099	C₂²	1	2	yes	—
22	#11718897	—	2	4	no	—
23	#11718897	C₂²	1	8	yes	—
24	C₂×#88077	—	2	4	no	—
25	C₂×#88059	—	2	1	no	—
26	C₂×#88059	—	2	1	no	—
27	C₂×#88059	—	2	2	no	—
28	C₂×#88059	C₂²	1	4	yes	complemented
29	#11718767	—	2	2	no	—
30	#11718767	C₂²	1	4	yes	complemented
31	C₂×#88058	—	2	1	no	—
32	C₂×#88057	—	2	1	no	—
33	#11718151	C₂²	1	8	yes	complemented
34	C₂×C₁₃×#41	—	2	1	no	—
35	C₂×C₁₃×#41	—	2	1	no	—
36	C₂×C₁₃×#41	—	2	1	no	—
37	C₂×C₁₃×#41	—	2	1	no	—
38	C₂×C₁₃×#41	—	2	1	no	—
39	C₂×C₁₃×#41	—	2	1	no	—
40	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
41	C₂×C₁₃×#41	C₂×C₄	1	2	yes	—
42	C₂×C₁₃×#41	D₄	1	2	yes	—
43	C₂×C₁₃×#41	D₄	1	2	yes	—
44	C₂×C₁₃×#41	Q₈	1	2	yes	—
45	C₂×C₁₃×#41	C₂³	1	2	yes	—
46	C₂²×Q₈×C₁₃	Q₈	1	1	yes	characteristic
47	C₂²×D₄×C₁₃	—	2	1	no	—
48	C₂²×D₄×C₁₃	Q₈	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	—	2	1	no	—
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₁₃×#131	—	2	4	no	—
52	C₁₃×#131	—	2	4	no	—
53	C₁₃×#131	—	2	4	no	—
54	C₁₃×#131	—	2	4	no	—
55	C₁₃×#131	—	2	4	no	—
56	C₁₃×#131	—	2	4	no	—
57	C₁₃×#131	C₂×C₄	1	8	yes	complemented
58	C₁₃×#131	C₂×C₄	1	8	yes	complemented
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	2	no	—
63	C₂×C₁₃×M₁₆	—	2	2	no	—
64	C₂×C₁₃×M₁₆	—	2	4	no	—
65	C₂×C₁₃×M₁₆	—	2	4	no	—
66	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
67	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
68	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
69	C₂²×C₈×C₁₃	—	2	1	no	—
70	C₂²×C₈×C₁₃	—	2	2	no	—
71	C₂²×C₈×C₁₃	—	2	2	no	—
72	C₂²×C₈×C₁₃	—	2	4	no	—
73	C₂²×C₈×C₁₃	—	2	4	no	—
74	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
77	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	D₄	1	2	yes	—
80	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
81	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
82	C₂²×C₈×C₁₃	D₄	1	2	yes	—
83	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
84	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
85	#88180	—	2	2	no	—
86	#88180	—	2	2	no	—
87	#88180	—	2	2	no	—
88	#88180	C₂³	1	4	yes	—
89	C₂×C₄⋊Dic₁₃	—	2	2	no	—
90	C₂×C₄×Dic₁₃	—	2	2	no	—
91	C₂×#6099	—	2	2	no	—
92	C₂×#6099	—	2	2	no	—
93	C₂×#6099	—	2	2	no	—
94	C₂×#6099	—	2	2	no	—
95	C₂×#6099	—	2	2	no	—
96	C₂×#6099	C₂³	1	4	yes	—
97	C₂²×#1055	—	2	2	no	—
98	#88077	—	2	16	no	—
99	#88059	—	2	4	no	—
100	#88059	—	2	4	no	—
101	#88058	—	2	4	no	—
102	#88057	—	2	4	no	—
103	C₂×#1814	—	13	1	no	maximal, Sylow
104	C₂⁴×C₁₃	—	2	1	no	—
105	C₂⁴×C₁₃	#41	1	1	yes	characteristic
106	C₁₃×#41	—	2	2	no	—
107	C₁₃×#41	—	2	2	no	—
108	C₁₃×#41	—	2	2	no	—
109	C₁₃×#41	—	2	2	no	—
110	C₁₃×#41	—	2	2	no	—
111	C₁₃×#41	—	2	2	no	—
112	C₁₃×#41	—	2	2	no	—
113	C₁₃×#41	—	2	2	no	—
114	C₁₃×#41	—	2	2	no	—
115	C₁₃×#41	—	2	2	no	—
116	C₁₃×#41	—	2	2	no	—
117	C₁₃×#41	—	2	2	no	—
118	C₁₃×#41	C₄⋊C₄	1	4	yes	—
119	C₁₃×#41	C₄⋊C₄	1	4	yes	—
120	C₁₃×#41	C₂²×C₄	1	4	yes	—
121	C₁₃×#41	C₂×D₄	1	4	yes	—
122	C₂×Q₈×C₁₃	—	2	1	no	—
123	C₂×Q₈×C₁₃	—	2	1	no	—
124	C₂×Q₈×C₁₃	—	2	1	no	—
125	C₂×Q₈×C₁₃	C₄⋊C₄	1	2	yes	—
126	C₂×Q₈×C₁₃	C₄⋊C₄	1	2	yes	—
127	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
128	C₂×D₄×C₁₃	—	2	2	no	—
129	C₂×D₄×C₁₃	—	2	2	no	—
130	C₂×D₄×C₁₃	—	2	2	no	—
131	C₂×D₄×C₁₃	—	2	2	no	—
132	C₂×D₄×C₁₃	—	2	2	no	—
133	C₂×D₄×C₁₃	—	2	2	no	—
134	C₂×D₄×C₁₃	—	2	1	no	—
135	C₂×D₄×C₁₃	—	2	1	no	—
136	C₂×D₄×C₁₃	—	2	1	no	—
137	C₂×D₄×C₁₃	C₄⋊C₄	1	2	yes	—
138	C₂×D₄×C₁₃	C₄⋊C₄	1	2	yes	—
139	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	2	no	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	2	2	no	—
145	C₂²×C₄×C₁₃	—	2	2	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₂²×Dic₁₃	—	4	2	no	—
162	C₁₃×M₁₆	—	2	2	no	—
163	C₁₃×M₁₆	—	2	2	no	—
164	C₁₃×M₁₆	—	2	2	no	—
165	C₁₃×M₁₆	—	2	8	no	—
166	C₁₃×M₁₆	—	2	8	no	—
167	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
168	C₂×C₈×C₁₃	—	2	2	no	—
169	C₂×C₈×C₁₃	—	2	2	no	—
170	C₂×C₈×C₁₃	—	2	2	no	—
171	C₂×C₈×C₁₃	—	2	8	no	—
172	C₂×C₈×C₁₃	—	2	8	no	—
173	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
176	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
177	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
179	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
180	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
181	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
182	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
183	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
184	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
185	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
186	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
187	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
188	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
189	C₂²⋊Dic₁₃	—	2	4	no	—
190	C₂²⋊Dic₁₃	—	4	2	no	—
191	C₄⋊Dic₁₃	—	2	4	no	—
192	C₄⋊Dic₁₃	—	4	2	no	—
193	C₄×Dic₁₃	—	2	4	no	—
194	C₄×Dic₁₃	—	4	2	no	—
195	#6099	—	2	4	no	—
196	#6099	—	2	4	no	—
197	#6099	—	4	2	no	—
198	#6099	—	4	2	no	—
199	C₂×#1055	—	2	4	no	—
200	C₂×#1055	—	4	2	no	—
201	C₂×#1055	—	4	2	no	—
202	C₂²×#131	D₁₃	1	1	yes	characteristic
203	C₂²×#108	—	13	1	no	—
204	C₂×#427	—	13	1	no	—
205	C₂×#421	—	13	2	no	—
206	#1814	—	13	8	no	—
207	C₂×#344	—	13	2	no	—
208	C₂³×C₁₃	—	2	2	no	—
209	C₂³×C₁₃	—	2	2	no	—
210	C₂³×C₁₃	—	2	2	no	—
211	C₂³×C₁₃	—	4	2	no	—
212	C₂³×C₁₃	—	4	4	no	—
213	C₂³×C₁₃	#117	1	1	yes	characteristic
214	C₂³×C₁₃	#117	1	1	yes	characteristic
215	C₂³×C₁₃	#121	1	1	yes	characteristic
216	C₂³×C₁₃	#121	1	1	yes	characteristic
217	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
218	C₂³×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
219	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
220	Q₈×C₁₃	—	2	2	no	—
221	Q₈×C₁₃	—	2	2	no	—
222	Q₈×C₁₃	—	2	2	no	—
223	Q₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
224	D₄×C₁₃	—	2	4	no	—
225	D₄×C₁₃	—	2	4	no	—
226	D₄×C₁₃	—	2	4	no	—
227	D₄×C₁₃	—	2	4	no	—
228	D₄×C₁₃	—	2	2	no	—
229	D₄×C₁₃	—	2	2	no	—
230	D₄×C₁₃	—	2	2	no	—
231	D₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	4	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
247	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
248	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
249	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
250	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
251	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
252	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
253	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
254	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
261	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
262	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
263	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
267	C₂×Dic₁₃	—	4	4	no	—
268	C₂×Dic₁₃	—	8	4	no	—
269	C₈×C₁₃	—	2	4	no	—
270	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
271	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
272	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
273	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
274	#1055	—	4	4	no	—
275	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic
276	C₂×#131	—	2	1	no	—
277	C₂×#131	—	2	1	no	—
278	C₂×#131	—	2	2	no	—
279	C₂×#131	—	2	2	no	—
280	C₂×#131	Dic₁₃	1	2	yes	complemented
281	C₂×#131	Dic₁₃	1	2	yes	complemented
282	C₂×#131	Dic₁₃	1	4	yes	complemented
283	C₂×#131	C₂×D₁₃	1	4	yes	—
284	C₂²×M₁₆	—	2	1	no	—
285	C₂²×M₁₆	—	13	2	no	—
286	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
287	C₂³×C₈	—	2	1	no	—
288	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
289	C₂×#117	—	13	2	no	—
290	C₂×#108	—	13	4	no	—
291	C₂×#108	—	26	1	no	—
292	C₂×#108	—	26	1	no	—
293	C₂×#108	—	26	2	no	—
294	#427	—	13	4	no	—
295	#427	—	26	2	no	—
296	C₂×#107	—	26	1	no	—
297	C₂×#106	—	26	1	no	—
298	#421	—	13	8	no	—
299	#421	—	26	4	no	—
300	C₂×#104	—	26	4	no	—
301	#344	—	13	8	no	—
302	C₂²×C₁₃	—	2	2	no	—
303	C₂²×C₁₃	—	2	2	no	—
304	C₂²×C₁₃	—	2	2	no	—
305	C₂²×C₁₃	—	2	4	no	—
306	C₂²×C₁₃	—	4	1	no	—
307	C₂²×C₁₃	—	4	1	no	—
308	C₂²×C₁₃	—	4	1	no	—
309	C₂²×C₁₃	—	4	1	no	—
310	C₂²×C₁₃	—	4	4	no	—
311	C₂²×C₁₃	—	4	4	no	—
312	C₂²×C₁₃	—	4	4	no	—
313	C₂²×C₁₃	#380	1	1	yes	characteristic
314	C₂²×C₁₃	#380	1	1	yes	characteristic
315	C₂²×C₁₃	#380	1	1	yes	characteristic
316	C₂²×C₁₃	#380	1	1	yes	characteristic
317	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
318	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
319	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
320	C₄×C₁₃	—	2	4	no	—
321	C₄×C₁₃	#380	1	1	yes	characteristic
322	C₄×C₁₃	#380	1	1	yes	characteristic
323	C₄×C₁₃	#380	1	1	yes	characteristic
324	C₄×C₁₃	#380	1	1	yes	characteristic
325	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
326	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
327	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
328	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
329	Dic₁₃	—	8	4	no	—
330	C₂×#41	—	2	1	no	—
331	C₂×#41	—	2	1	no	—
332	C₂×#41	—	2	1	no	—
333	C₂×#41	—	2	1	no	—
334	C₂×#41	—	2	1	no	—
335	C₂×#41	—	2	1	no	—
336	C₂×#41	Dic₂₆	1	2	yes	—
337	C₂×#41	D₅₂	1	2	yes	—
338	C₂×#41	D₅₂	1	2	yes	—
339	C₂×#41	C₂×Dic₁₃	1	2	yes	—
340	C₂×#41	C₂×Dic₁₃	1	2	yes	—
341	C₂×#41	C₂²×D₁₃	1	2	yes	—
342	C₂²×Q₈	Dic₂₆	1	1	yes	characteristic
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	Dic₂₆	1	1	yes	characteristic
345	C₂³×C₄	—	2	1	no	—
346	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
347	#131	—	2	4	no	—
348	#131	—	2	4	no	—
349	#131	—	2	4	no	—
350	#131	—	2	4	no	—
351	#131	—	2	4	no	—
352	#131	—	2	4	no	—
353	#131	C₂×Dic₁₃	1	8	yes	complemented
354	#131	C₂×Dic₁₃	1	8	yes	complemented
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	2	no	—
359	C₂×M₁₆	—	2	2	no	—
360	C₂×M₁₆	—	2	4	no	—
361	C₂×M₁₆	—	2	4	no	—
362	C₂×M₁₆	—	13	4	no	—
363	C₂×M₁₆	—	26	2	no	—
364	C₂×M₁₆	—	26	2	no	—
365	C₂×M₁₆	—	26	2	no	—
366	C₂×M₁₆	—	26	2	no	—
367	C₂×M₁₆	—	26	2	no	—
368	C₂×M₁₆	C₂×Dic₁₃	1	2	yes	—
369	C₂×M₁₆	C₂×Dic₁₃	1	2	yes	—
370	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
371	C₂²×C₈	—	2	1	no	—
372	C₂²×C₈	—	2	2	no	—
373	C₂²×C₈	—	2	2	no	—
374	C₂²×C₈	—	2	4	no	—
375	C₂²×C₈	—	2	4	no	—
376	C₂²×C₈	—	26	2	no	—
377	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
378	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
379	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
380	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
381	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
382	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
383	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
384	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
385	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
386	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
387	#117	—	13	4	no	—
388	#117	—	26	2	no	—
389	#117	—	26	2	no	—
390	#117	—	26	2	no	—
391	C₂×C₄⋊C₄	—	26	2	no	—
392	C₂×C₂²⋊C₄	—	26	2	no	—
393	C₂×C₄²	—	26	2	no	—
394	#108	—	26	4	no	—
395	#108	—	26	4	no	—
396	#107	—	26	4	no	—
397	#106	—	26	4	no	—
398	#104	—	26	16	no	—
399	C₂×C₁₃	—	2	1	no	—
400	C₂×C₁₃	—	2	1	no	—
401	C₂×C₁₃	—	2	1	no	—
402	C₂×C₁₃	—	2	1	no	—
403	C₂×C₁₃	—	2	1	no	—
404	C₂×C₁₃	—	2	1	no	—
405	C₂×C₁₃	—	4	4	no	—
406	C₂×C₁₃	#1814	1	2	yes	complemented
407	C₂×C₁₃	C₂×#380	1	1	yes	characteristic
408	C₂⁴	—	2	1	no	—
409	C₂⁴	#6127	1	1	yes	characteristic
410	#41	—	2	2	no	—
411	#41	—	2	2	no	—
412	#41	—	2	2	no	—
413	#41	—	2	2	no	—
414	#41	—	2	2	no	—
415	#41	—	2	2	no	—
416	#41	—	2	2	no	—
417	#41	—	2	2	no	—
418	#41	—	2	2	no	—
419	#41	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	2	2	no	—
422	#41	C₄⋊Dic₁₃	1	4	yes	—
423	#41	C₄⋊Dic₁₃	1	4	yes	—
424	#41	C₂×D₅₂	1	4	yes	—
425	#41	C₂²×Dic₁₃	1	4	yes	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×Q₈	C₄⋊Dic₁₃	1	2	yes	—
430	C₂×Q₈	C₄⋊Dic₁₃	1	2	yes	—
431	C₂×Q₈	C₂×Dic₂₆	1	2	yes	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	C₄⋊Dic₁₃	1	2	yes	—
442	C₂×D₄	C₄⋊Dic₁₃	1	2	yes	—
443	C₂×D₄	C₂×Dic₂₆	1	2	yes	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	52	2	no	—
452	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
453	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
456	C₂²×C₄	#6127	1	1	yes	characteristic
457	C₂²×C₄	#6127	1	1	yes	characteristic
458	C₂²×C₄	#6127	1	1	yes	characteristic
459	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
460	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
461	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
462	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
463	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
466	M₁₆	—	2	2	no	—
467	M₁₆	—	2	2	no	—
468	M₁₆	—	2	2	no	—
469	M₁₆	—	2	8	no	—
470	M₁₆	—	2	8	no	—
471	M₁₆	—	26	4	no	—
472	M₁₆	—	26	4	no	—
473	M₁₆	—	52	2	no	—
474	M₁₆	—	52	2	no	—
475	M₁₆	C₂²×Dic₁₃	1	4	yes	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	8	no	—
480	C₂×C₈	—	2	8	no	—
481	C₂×C₈	—	26	4	no	—
482	C₂×C₈	—	52	2	no	—
483	C₂×C₈	—	52	2	no	—
484	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
485	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
486	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
487	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
488	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
489	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
490	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
491	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
492	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
493	C₂×C₈	C₂²⋊Dic₁₃	1	2	yes	—
494	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
495	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
496	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
497	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
498	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
499	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
500	C₄⋊C₄	—	26	4	no	—
501	C₄⋊C₄	—	52	2	no	—
502	C₂²⋊C₄	—	26	4	no	—
503	C₂²⋊C₄	—	52	2	no	—
504	C₄²	—	26	4	no	—
505	C₄²	—	52	2	no	—
506	C₁₃	C₂×#1814	1	1	yes	characteristic, complemented, Sylow
507	C₂³	—	2	2	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	4	2	no	—
511	C₂³	—	4	4	no	—
512	C₂³	#88178	1	1	yes	characteristic
513	C₂³	#88178	1	1	yes	characteristic
514	C₂³	#88180	1	1	yes	characteristic
515	C₂³	#88180	1	1	yes	characteristic
516	C₂³	#88184	1	1	yes	characteristic
517	C₂³	#88184	1	1	yes	characteristic
518	C₂³	C₂×#6127	1	1	yes	characteristic
519	Q₈	—	2	2	no	—
520	Q₈	—	2	2	no	—
521	Q₈	—	2	2	no	—
522	Q₈	C₂×C₄⋊Dic₁₃	1	4	yes	—
523	D₄	—	2	4	no	—
524	D₄	—	2	4	no	—
525	D₄	—	2	4	no	—
526	D₄	—	2	4	no	—
527	D₄	—	2	2	no	—
528	D₄	—	2	2	no	—
529	D₄	—	2	2	no	—
530	D₄	C₂×C₄⋊Dic₁₃	1	4	yes	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	52	4	no	—
539	C₂×C₄	—	104	4	no	—
540	C₂×C₄	#88178	1	1	yes	characteristic
541	C₂×C₄	#88178	1	1	yes	characteristic
542	C₂×C₄	#88178	1	1	yes	characteristic
543	C₂×C₄	#88178	1	1	yes	characteristic
544	C₂×C₄	#88178	1	1	yes	characteristic
545	C₂×C₄	#88178	1	1	yes	characteristic
546	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
547	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
548	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
549	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
550	C₂×C₄	#88180	1	1	yes	characteristic
551	C₂×C₄	#88180	1	1	yes	characteristic
552	C₂×C₄	#88184	1	1	yes	characteristic
553	C₂×C₄	#88184	1	1	yes	characteristic
554	C₂×C₄	#88184	1	1	yes	characteristic
555	C₂×C₄	#88184	1	1	yes	characteristic
556	C₂×C₄	#88184	1	1	yes	characteristic
557	C₂×C₄	#88184	1	1	yes	characteristic
558	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
559	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
560	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
561	C₂×C₄	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
562	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
563	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
564	C₂×C₄	C₂×#6127	1	1	yes	characteristic
565	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
566	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
567	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
568	C₈	—	2	4	no	—
569	C₈	—	52	4	no	—
570	C₈	C₂×C₂²⋊Dic₁₃	1	2	yes	—
571	C₈	C₂×C₂²⋊Dic₁₃	1	2	yes	—
572	C₈	C₂×C₂²⋊Dic₁₃	1	2	yes	—
573	C₈	C₂×C₂²⋊Dic₁₃	1	2	yes	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	4	4	no	—
585	C₂²	#11718873	1	1	yes	characteristic
586	C₂²	#11718873	1	1	yes	characteristic
587	C₂²	#11718873	1	1	yes	characteristic
588	C₂²	#11718873	1	1	yes	characteristic
589	C₂²	C₂×#88178	1	1	yes	characteristic
590	C₂²	C₂×#88180	1	1	yes	characteristic
591	C₂²	C₂×#88184	1	1	yes	characteristic
592	C₄	—	2	4	no	—
593	C₄	—	104	4	no	—
594	C₄	#11718873	1	1	yes	characteristic
595	C₄	#11718873	1	1	yes	characteristic
596	C₄	#11718873	1	1	yes	characteristic
597	C₄	#11718873	1	1	yes	characteristic
598	C₄	C₂×#88178	1	1	yes	characteristic
599	C₄	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
600	C₄	C₂×#88184	1	1	yes	characteristic
601	C₄	C₂²×C₂²⋊Dic₁₃	1	1	yes	characteristic
602	C₂	—	2	1	no	—
603	C₂	—	2	1	no	—
604	C₂	—	2	1	no	—
605	C₂	—	2	1	no	—
606	C₂	—	2	1	no	—
607	C₂	—	2	1	no	—
608	C₂	—	4	4	no	—
609	C₂	#13114890	1	2	yes	direct product factor
610	C₂	C₂×#11718873	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88184
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂²×C₁₃×#131	C₂
socle	C₂²×C₁₃	#380
prime radical	C₂²×C₁₃×#41	C₂²
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂²×#131	D₁₃
hypocenter	C₁₃	C₂×#1814
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#131

Complements

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

N	H ≅ G/N	type
1. C₂²×#88059	C₂	semidirect
2. C₂×#11718767	C₂	semidirect
4. #13114890	C₂	direct (N × H)
5. C₂×#11718151	C₂	semidirect
12. C₂×C₁₃×#131	C₄	semidirect
13. C₂×C₁₃×#131	C₄	semidirect
14. C₂×C₁₃×#131	C₄	semidirect
28. C₂×#88059	C₂²	semidirect
30. #11718767	C₂²	semidirect
33. #11718151	C₂²	semidirect
57. C₁₃×#131	C₂×C₄	semidirect
58. C₁₃×#131	C₂×C₄	semidirect
280. C₂×#131	Dic₁₃	semidirect
281. C₂×#131	Dic₁₃	semidirect
282. C₂×#131	Dic₁₃	semidirect
353. #131	C₂×Dic₁₃	semidirect
354. #131	C₂×Dic₁₃	semidirect
406. C₂×C₁₃	#1814	semidirect
506. C₁₃	C₂×#1814	semidirect
609. C₂	#13114890	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×#88059	2
C₂×#11718767	2
C₂×#11718897	2
#13114890	2
C₂×#11718151	2
C₂²×C₁₃×#131	2
C₂×#1814	13

Subgroups — C2×#13114890 #15862581

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13114890 #15862581