Subgroups — C₂×#13123744 #16727230

Order 3328.

2674 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719473	C₂	1	1	yes	maximal, characteristic
2	C₂×#11719455	C₂	1	2	yes	maximal, complemented
3	#13123744	C₂	1	16	yes	maximal, direct product factor
4	C₂×#11718378	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11718484	C₂	1	2	yes	maximal, complemented
6	C₂×#11718857	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11718556	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11718805	C₂	1	2	yes	maximal, complemented
9	C₂×#11718554	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×D₁₃×#104	C₂	1	2	yes	maximal, complemented
11	C₂×#11718368	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#444	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#41×D₁₃	C₂²	1	2	yes	—
14	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#131	C₂²	1	2	yes	complemented
16	C₂×#88204	C₂²	1	2	yes	—
17	C₂×#88202	C₂²	1	2	yes	complemented
18	#11719473	C₄	1	8	yes	complemented
19	#11719473	C₂²	1	8	yes	—
20	C₂×#88172	C₄	1	2	yes	complemented
21	C₂×#88169	C₄	1	2	yes	complemented
22	C₂×#88168	C₄	1	2	yes	complemented
23	C₂×#88165	C₄	1	2	yes	complemented
24	#11719455	—	2	8	no	—
25	#11719455	C₂²	1	16	yes	complemented
26	C₂×#88161	—	2	2	no	—
27	C₂×#88161	C₂²	1	2	yes	complemented
28	C₂×M₁₆×D₁₃	—	2	2	no	—
29	C₂×M₁₆×D₁₃	C₂²	1	2	yes	—
30	C₂×#88158	C₂²	1	1	yes	characteristic
31	C₂×#88155	—	2	2	no	—
32	C₂×#88155	C₂²	1	2	yes	complemented
33	C₂²×#6094	—	2	2	no	—
34	C₂²×#6094	C₂²	1	1	yes	characteristic
35	C₂²×#6094	C₂²	1	1	yes	characteristic
36	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#444	C₂²	1	8	yes	complemented
38	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₁₃×#104	C₂²	1	2	yes	complemented
40	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
41	C₂×#88077	C₂²	1	2	yes	complemented
42	#11718857	C₂²	1	8	yes	complemented
43	#11718805	C₂²	1	16	yes	complemented
44	C₂×#88065	C₂²	1	2	yes	complemented
45	C₂×#88062	C₂²	1	2	yes	complemented
46	C₂×#88059	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
49	C₂×#88045	C₂²	1	2	yes	complemented
50	C₂×#88043	C₂²	1	1	yes	characteristic, complemented
51	#11718556	C₂²	1	8	yes	complemented
52	#11718554	C₂²	1	8	yes	complemented
53	#11718484	C₂²	1	16	yes	complemented
54	D₁₃×#104	C₂²	1	16	yes	complemented
55	#11718378	C₂²	1	8	yes	complemented
56	#11718368	C₂²	1	8	yes	complemented
57	C₂×C₁₃×#41	C₂³	1	2	yes	—
58	#41×D₁₃	—	2	4	no	—
59	#41×D₁₃	—	2	4	no	—
60	#41×D₁₃	C₂×C₄	1	8	yes	—
61	#41×D₁₃	C₂³	1	8	yes	—
62	C₂×#6131	C₂×C₄	1	2	yes	—
63	C₂×Q₈×D₁₃	C₂×C₄	1	2	yes	—
64	C₂×#6129	—	2	2	no	—
65	C₂×#6129	C₂×C₄	1	2	yes	—
66	C₂×D₄×D₁₃	—	2	2	no	—
67	C₂×D₄×D₁₃	C₂×C₄	1	2	yes	—
68	C₂×#6127	—	2	2	no	—
69	C₂×#6127	C₂³	1	2	yes	—
70	C₂²×C₄×D₁₃	—	2	2	no	—
71	C₂²×C₄×D₁₃	—	2	1	no	—
72	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×#135	C₂×C₄	1	4	yes	complemented
74	C₁₃×#135	C₂³	1	4	yes	—
75	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
76	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	complemented
77	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic, complemented
78	C₁₃×#131	—	2	4	no	—
79	C₁₃×#131	C₂³	1	8	yes	complemented
80	C₂×C₁₃×M₁₆	—	2	2	no	—
81	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
82	C₂²×C₈×C₁₃	—	2	2	no	—
83	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	#88204	C₂×C₄	1	8	yes	complemented
87	#88204	C₂³	1	8	yes	—
88	#88202	—	2	4	no	—
89	#88202	C₂³	1	8	yes	complemented
90	C₂×#6107	C₂×C₄	1	2	yes	complemented
91	C₂×#6106	C₂×C₄	1	2	yes	complemented
92	C₂×#6105	C₂×C₄	1	2	yes	complemented
93	C₂×#6104	C₂×C₄	1	2	yes	complemented
94	C₂×C₄×Dic₁₃	—	2	1	no	—
95	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
96	C₂×#6099	—	2	2	no	—
97	C₂×#6099	C₂³	1	2	yes	—
98	C₂²×#1055	—	2	2	no	—
99	C₂²×#1055	C₂³	1	1	yes	characteristic
100	C₂²×#1055	C₂³	1	1	yes	characteristic
101	#88172	C₂×C₄	1	16	yes	complemented
102	#88169	C₂×C₄	1	16	yes	complemented
103	#88168	C₂×C₄	1	16	yes	complemented
104	#88165	C₂×C₄	1	16	yes	complemented
105	#88161	—	2	4	no	—
106	#88161	—	2	16	no	—
107	#88161	C₂³	1	8	yes	complemented
108	M₁₆×D₁₃	—	2	4	no	—
109	M₁₆×D₁₃	—	2	16	no	—
110	M₁₆×D₁₃	C₂³	1	8	yes	—
111	C₂×Dic₅₂	C₂×C₄	1	1	yes	characteristic, complemented
112	#88158	C₂×C₄	1	4	yes	complemented
113	#88158	C₂³	1	4	yes	—
114	C₂×D₁₀₄	C₂×C₄	1	1	yes	characteristic, complemented
115	C₂×#6095	C₂×C₄	1	2	yes	complemented
116	#88155	—	2	4	no	—
117	#88155	—	2	16	no	—
118	#88155	C₂³	1	8	yes	complemented
119	C₂×#6094	—	2	2	no	—
120	C₂×#6094	—	2	2	no	—
121	C₂×#6094	—	2	2	no	—
122	C₂×#6094	—	2	16	no	—
123	C₂×#6094	C₂×C₄	1	2	yes	—
124	C₂×#6094	C₂×C₄	1	2	yes	—
125	C₂×#6094	C₂×C₄	1	4	yes	—
126	C₂×#6094	D₄	1	2	yes	—
127	C₂×#6094	D₄	1	2	yes	—
128	C₂×#6094	D₄	1	4	yes	—
129	C₂×#6094	C₂³	1	4	yes	—
130	C₂×#6094	C₂³	1	4	yes	—
131	C₂×C₈×D₁₃	—	2	2	no	—
132	C₂×C₈×D₁₃	—	2	2	no	—
133	C₂×C₈×D₁₃	—	2	2	no	—
134	C₄²×D₁₃	—	2	2	no	—
135	C₄²×D₁₃	C₂³	1	4	yes	—
136	C₁₃×#108	C₂³	1	4	yes	complemented
137	C₁₃×#104	C₂³	1	8	yes	complemented
138	C₁₃×#97	C₂³	1	4	yes	complemented
139	#88077	C₂³	1	8	yes	complemented
140	#88065	C₂³	1	8	yes	complemented
141	#88062	C₂³	1	8	yes	complemented
142	#88059	C₂³	1	4	yes	complemented
143	C₈×Dic₁₃	C₂³	1	4	yes	complemented
144	C₈×Dic₁₃	C₂³	1	4	yes	complemented
145	#88045	C₂³	1	8	yes	complemented
146	#88043	C₂³	1	4	yes	complemented
147	C₂×#2956	—	13	1	no	maximal, Sylow
148	C₂³×D₁₃	—	2	2	no	—
149	C₂³×D₁₃	#41	1	1	yes	characteristic
150	C₁₃×#41	—	2	2	no	—
151	C₁₃×#41	—	2	2	no	—
152	C₁₃×#41	C₂²×C₄	1	4	yes	—
153	C₁₃×#41	C₂⁴	1	4	yes	—
154	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
155	C₂×D₄×C₁₃	—	2	2	no	—
156	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₂×C₂²⋊D₁₃	—	2	2	no	—
161	C₂×C₂²⋊D₁₃	—	2	2	no	—
162	C₂×C₂²⋊D₁₃	—	2	2	no	—
163	C₂²×Dic₁₃	—	2	1	no	—
164	C₂²×Dic₁₃	—	2	2	no	—
165	C₂²×Dic₁₃	#41	1	1	yes	characteristic
166	#6131	—	2	4	no	—
167	#6131	C₂²×C₄	1	8	yes	—
168	Q₈×D₁₃	—	2	4	no	—
169	Q₈×D₁₃	C₂²×C₄	1	8	yes	—
170	#6129	—	2	8	no	—
171	#6129	—	2	8	no	—
172	#6129	—	2	4	no	—
173	#6129	C₂²×C₄	1	8	yes	—
174	D₄×D₁₃	—	2	8	no	—
175	D₄×D₁₃	—	2	8	no	—
176	D₄×D₁₃	—	2	4	no	—
177	D₄×D₁₃	C₂²×C₄	1	8	yes	—
178	#6127	—	2	2	no	—
179	#6127	—	2	2	no	—
180	#6127	—	2	8	no	—
181	#6127	—	2	8	no	—
182	#6127	C₂²×C₄	1	4	yes	—
183	#6127	C₂⁴	1	4	yes	—
184	C₂×D₅₂	—	2	2	no	—
185	C₂×D₅₂	C₂²×C₄	1	2	yes	—
186	C₂×C₄×D₁₃	—	2	2	no	—
187	C₂×C₄×D₁₃	—	2	2	no	—
188	C₂×C₄×D₁₃	—	2	2	no	—
189	C₂×C₄×D₁₃	—	2	8	no	—
190	C₂×C₄×D₁₃	—	2	8	no	—
191	C₂×C₄×D₁₃	—	2	4	no	—
192	C₂×C₄×D₁₃	—	4	4	no	—
193	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
194	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
195	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
196	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
197	C₂×C₄×D₁₃	#41	1	2	yes	—
198	C₂×C₄×D₁₃	C₂⁴	1	2	yes	—
199	C₂×Dic₂₆	—	2	2	no	—
200	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
201	C₁₃×Q₁₆	C₂²×C₄	1	4	yes	complemented
202	C₁₃×SD₁₆	C₂²×C₄	1	8	yes	complemented
203	C₁₃×D₈	C₂²×C₄	1	4	yes	complemented
204	C₁₃×M₁₆	—	2	2	no	—
205	C₁₃×M₁₆	—	2	8	no	—
206	C₁₃×M₁₆	C₂⁴	1	4	yes	—
207	C₂×C₈×C₁₃	—	2	2	no	—
208	C₂×C₈×C₁₃	—	2	8	no	—
209	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
210	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
211	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
212	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
213	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
214	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
215	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
216	C₄²×C₁₃	—	2	1	no	—
217	C₄²×C₁₃	C₂⁴	1	2	yes	—
218	#6107	C₂²×C₄	1	8	yes	complemented
219	#6106	C₂²×C₄	1	8	yes	complemented
220	#6105	C₂²×C₄	1	8	yes	complemented
221	#6104	C₂²×C₄	1	8	yes	complemented
222	C₄×Dic₁₃	—	2	1	no	—
223	C₄×Dic₁₃	—	2	4	no	—
224	C₄×Dic₁₃	C₂⁴	1	2	yes	—
225	#6099	—	2	2	no	—
226	#6099	—	2	8	no	—
227	#6099	C₂⁴	1	4	yes	—
228	C₂×#1055	—	2	2	no	—
229	C₂×#1055	—	2	8	no	—
230	C₂×#1055	C₂²×C₄	1	2	yes	—
231	C₂×#1055	C₂²×C₄	1	2	yes	—
232	C₂×#1055	C₂×D₄	1	1	yes	characteristic
233	C₂×#1055	C₂×D₄	1	1	yes	characteristic
234	C₂×#1055	C₂×D₄	1	2	yes	—
235	C₂×#1055	C₂⁴	1	2	yes	—
236	C₂×#1055	C₂⁴	1	2	yes	—
237	Dic₅₂	C₂²×C₄	1	4	yes	complemented
238	D₁₀₄	C₂²×C₄	1	4	yes	complemented
239	#6095	C₂²×C₄	1	8	yes	complemented
240	#6094	—	2	8	no	—
241	#6094	—	2	8	no	—
242	#6094	—	2	8	no	—
243	#6094	C₂²×C₄	1	8	yes	—
244	#6094	C₂²×C₄	1	8	yes	—
245	#6094	C₂×D₄	1	8	yes	—
246	#6094	C₂×D₄	1	8	yes	—
247	C₈×D₁₃	—	2	8	no	—
248	C₈×D₁₃	—	2	8	no	—
249	C₈×D₁₃	—	2	8	no	—
250	C₂×#575	—	13	1	no	—
251	C₂×#568	—	13	2	no	—
252	#2956	—	13	16	no	—
253	C₂×#444	—	13	2	no	—
254	C₂×#444	—	13	1	no	—
255	C₂×#444	D₁₃	1	1	yes	characteristic, complemented
256	C₂×#443	—	13	1	no	—
257	C₂×#443	—	13	1	no	—
258	C₂×#443	—	13	2	no	—
259	C₂×#430	—	13	1	no	—
260	C₂²×#104	—	13	2	no	—
261	C₂×C₄×M₁₆	—	13	1	no	—
262	C₂³×C₁₃	—	2	2	no	—
263	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
264	C₂²×D₁₃	—	2	2	no	—
265	C₂²×D₁₃	—	2	8	no	—
266	C₂²×D₁₃	—	4	2	no	—
267	C₂²×D₁₃	—	8	4	no	—
268	C₂²×D₁₃	C₄×D₄	1	2	yes	—
269	C₂²×D₁₃	C₄×D₄	1	2	yes	—
270	C₂²×D₁₃	C₂×#41	1	2	yes	—
271	Q₈×C₁₃	—	2	2	no	—
272	Q₈×C₁₃	C₂³×C₄	1	4	yes	—
273	D₄×C₁₃	—	2	4	no	—
274	D₄×C₁₃	—	2	4	no	—
275	D₄×C₁₃	—	2	2	no	—
276	D₄×C₁₃	C₂³×C₄	1	4	yes	—
277	C₂×C₄×C₁₃	—	2	2	no	—
278	C₂×C₄×C₁₃	—	2	4	no	—
279	C₂×C₄×C₁₃	—	2	4	no	—
280	C₂×C₄×C₁₃	—	2	2	no	—
281	C₂×C₄×C₁₃	—	4	2	no	—
282	C₂×C₄×C₁₃	C₂³×C₄	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	C₂×#41	1	1	yes	characteristic
287	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
288	C₂²⋊D₁₃	—	2	4	no	—
289	C₂²⋊D₁₃	—	2	4	no	—
290	C₂²⋊D₁₃	—	2	8	no	—
291	C₂²⋊D₁₃	—	2	8	no	—
292	C₂×Dic₁₃	—	2	4	no	—
293	C₂×Dic₁₃	—	2	2	no	—
294	C₂×Dic₁₃	—	2	2	no	—
295	C₂×Dic₁₃	—	2	8	no	—
296	C₂×Dic₁₃	C₄×D₄	1	2	yes	—
297	C₂×Dic₁₃	C₄×D₄	1	2	yes	—
298	C₂×Dic₁₃	C₂×#41	1	2	yes	—
299	D₅₂	—	2	8	no	—
300	D₅₂	—	2	2	no	—
301	D₅₂	C₂³×C₄	1	4	yes	—
302	C₄×D₁₃	—	2	8	no	—
303	C₄×D₁₃	—	2	4	no	—
304	C₄×D₁₃	—	2	4	no	—
305	C₄×D₁₃	—	2	8	no	—
306	C₄×D₁₃	—	4	8	no	—
307	C₄×D₁₃	C₄×D₄	1	4	yes	—
308	C₄×D₁₃	C₄×D₄	1	4	yes	—
309	C₄×D₁₃	C₂³×C₄	1	4	yes	—
310	C₄×D₁₃	C₂²×D₄	1	4	yes	—
311	Dic₂₆	—	2	2	no	—
312	Dic₂₆	—	2	8	no	—
313	Dic₂₆	C₂³×C₄	1	4	yes	—
314	C₈×C₁₃	—	2	4	no	—
315	C₈×C₁₃	C₂³×C₄	1	2	yes	—
316	C₈×C₁₃	C₂³×C₄	1	2	yes	—
317	C₈×C₁₃	C₂²×D₄	1	4	yes	—
318	#1055	—	2	4	no	—
319	#1055	C₂³×C₄	1	4	yes	—
320	#1055	C₂²×D₄	1	2	yes	—
321	#1055	C₂²×D₄	1	2	yes	—
322	C₂²×#41	—	13	2	no	—
323	#575	—	13	8	no	—
324	#575	—	13	8	no	—
325	C₂×#137	—	13	2	no	—
326	C₂×#137	—	13	2	no	—
327	C₂×AGL(1,ℤ/8)	—	13	2	no	—
328	C₂×AGL(1,ℤ/8)	—	13	2	no	—
329	C₂×#135	—	13	2	no	—
330	C₂×#135	—	13	1	no	—
331	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
332	#568	—	13	16	no	—
333	#568	—	26	8	no	—
334	C₂×#131	—	13	2	no	—
335	C₂×#131	—	13	2	no	—
336	C₂×#131	—	13	2	no	—
337	C₂×#131	—	26	2	no	—
338	C₂×#131	—	26	2	no	—
339	C₂×#131	C₂×D₁₃	1	2	yes	complemented
340	C₂²×M₁₆	—	13	1	no	—
341	C₂²×M₁₆	—	13	1	no	—
342	C₂²×M₁₆	—	13	2	no	—
343	C₂²×M₁₆	—	26	2	no	—
344	C₂²×M₁₆	—	26	2	no	—
345	C₂²×C₄²	—	13	1	no	—
346	#444	—	13	16	no	—
347	#444	—	13	8	no	—
348	#444	C₂×D₁₃	1	8	yes	complemented
349	#443	—	13	8	no	—
350	#443	—	13	16	no	—
351	#443	—	13	8	no	—
352	#430	—	13	8	no	—
353	C₂×#108	—	13	2	no	—
354	C₂×#108	—	13	1	no	—
355	C₂×#108	C₂×D₁₃	1	1	yes	characteristic, complemented
356	C₂×#104	—	13	2	no	—
357	C₂×#104	—	13	2	no	—
358	C₂×#104	—	13	2	no	—
359	C₂×#104	—	13	16	no	—
360	C₂×#104	C₂×D₁₃	1	2	yes	complemented
361	C₄×M₁₆	—	13	8	no	—
362	C₂×#97	—	13	1	no	—
363	C₂×#97	C₂×D₁₃	1	1	yes	characteristic, complemented
364	C₂×C₄×C₈	—	13	1	no	—
365	C₂×C₄×C₈	—	13	1	no	—
366	C₂²×C₁₃	—	2	2	no	—
367	C₂²×C₁₃	—	2	4	no	—
368	C₂²×C₁₃	—	4	4	no	—
369	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
370	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
371	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
372	C₂×D₁₃	—	2	4	no	—
373	C₂×D₁₃	—	2	4	no	—
374	C₂×D₁₃	—	4	2	no	—
375	C₂×D₁₃	—	4	2	no	—
376	C₂×D₁₃	—	4	4	no	—
377	C₂×D₁₃	—	8	8	no	—
378	C₂×D₁₃	C₂×C₄×D₄	1	4	yes	—
379	C₄×C₁₃	—	2	4	no	—
380	C₄×C₁₃	—	4	2	no	—
381	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
382	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
383	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
384	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
385	Dic₁₃	—	2	4	no	—
386	Dic₁₃	—	2	4	no	—
387	Dic₁₃	C₂×C₄×D₄	1	4	yes	—
388	C₂×#41	—	13	8	no	—
389	C₂×#41	—	13	8	no	—
390	C₂×#41	—	13	2	no	—
391	C₂×#41	—	13	2	no	—
392	C₂×#41	—	13	2	no	—
393	C₂×#41	—	26	2	no	—
394	C₂×#41	—	26	2	no	—
395	C₂×#41	—	26	4	no	—
396	C₂×#41	—	26	4	no	—
397	C₂×#41	C₂²×D₁₃	1	2	yes	—
398	C₂²×Q₈	—	13	2	no	—
399	C₂²×D₄	—	13	2	no	—
400	C₂²×D₄	—	26	2	no	—
401	C₂³×C₄	—	13	1	no	—
402	C₂³×C₄	—	26	2	no	—
403	C₂³×C₄	—	26	1	no	—
404	#137	—	13	16	no	—
405	#137	—	13	16	no	—
406	AGL(1,ℤ/8)	—	13	16	no	—
407	AGL(1,ℤ/8)	—	13	16	no	—
408	#135	—	13	8	no	—
409	#135	—	13	8	no	—
410	#135	—	13	4	no	—
411	#135	—	13	4	no	—
412	#135	C₄×D₁₃	1	4	yes	complemented
413	#135	C₂²×D₁₃	1	4	yes	—
414	C₂×Q₁₆	—	13	2	no	—
415	C₂×Q₁₆	—	13	1	no	—
416	C₂×Q₁₆	C₄×D₁₃	1	1	yes	characteristic, complemented
417	C₂×SD₁₆	—	13	2	no	—
418	C₂×SD₁₆	—	13	2	no	—
419	C₂×SD₁₆	—	13	2	no	—
420	C₂×SD₁₆	C₄×D₁₃	1	2	yes	complemented
421	C₂×D₈	—	13	2	no	—
422	C₂×D₈	—	13	1	no	—
423	C₂×D₈	C₄×D₁₃	1	1	yes	characteristic, complemented
424	#131	—	2	4	no	—
425	#131	—	13	8	no	—
426	#131	—	13	8	no	—
427	#131	—	13	8	no	—
428	#131	—	26	16	no	—
429	#131	—	26	4	no	—
430	#131	—	26	4	no	—
431	#131	—	26	16	no	—
432	#131	—	26	4	no	—
433	#131	C₂²×D₁₃	1	8	yes	complemented
434	C₂×M₁₆	—	2	2	no	—
435	C₂×M₁₆	—	13	2	no	—
436	C₂×M₁₆	—	13	2	no	—
437	C₂×M₁₆	—	13	4	no	—
438	C₂×M₁₆	—	13	2	no	—
439	C₂×M₁₆	—	13	2	no	—
440	C₂×M₁₆	—	13	4	no	—
441	C₂×M₁₆	—	13	4	no	—
442	C₂×M₁₆	—	13	4	no	—
443	C₂×M₁₆	—	13	2	no	—
444	C₂×M₁₆	—	13	8	no	—
445	C₂×M₁₆	—	26	2	no	—
446	C₂×M₁₆	—	26	16	no	—
447	C₂×M₁₆	—	26	2	no	—
448	C₂×M₁₆	—	26	2	no	—
449	C₂×M₁₆	—	26	16	no	—
450	C₂×M₁₆	—	26	4	no	—
451	C₂×M₁₆	—	26	2	no	—
452	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
453	C₂²×C₈	—	2	2	no	—
454	C₂²×C₈	—	13	1	no	—
455	C₂²×C₈	—	13	1	no	—
456	C₂²×C₈	—	26	2	no	—
457	C₂²×C₈	—	26	2	no	—
458	C₂²×C₈	—	26	2	no	—
459	C₂²×C₈	—	26	2	no	—
460	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
461	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
462	C₂×C₄²	—	13	1	no	—
463	C₂×C₄²	—	13	4	no	—
464	C₂×C₄²	—	26	2	no	—
465	C₂×C₄²	—	26	1	no	—
466	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
467	#108	—	13	8	no	—
468	#108	—	13	4	no	—
469	#108	C₂²×D₁₃	1	4	yes	complemented
470	#104	—	13	8	no	—
471	#104	—	13	8	no	—
472	#104	—	13	8	no	—
473	#104	C₂²×D₁₃	1	8	yes	complemented
474	#97	—	13	4	no	—
475	#97	C₂²×D₁₃	1	4	yes	complemented
476	C₄×C₈	—	13	4	no	—
477	C₄×C₈	—	13	4	no	—
478	C₂×C₁₃	—	2	1	no	—
479	C₂×C₁₃	—	2	1	no	—
480	C₂×C₁₃	—	4	4	no	—
481	C₂×C₁₃	#2956	1	2	yes	complemented
482	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
483	D₁₃	—	2	4	no	—
484	D₁₃	—	4	4	no	—
485	C₂⁴	—	13	1	no	—
486	C₂⁴	—	26	2	no	—
487	#41	—	2	2	no	—
488	#41	—	2	2	no	—
489	#41	—	13	8	no	—
490	#41	—	13	8	no	—
491	#41	—	13	4	no	—
492	#41	—	13	4	no	—
493	#41	—	26	8	no	—
494	#41	—	26	8	no	—
495	#41	—	26	8	no	—
496	#41	—	26	8	no	—
497	#41	—	26	4	no	—
498	#41	—	26	4	no	—
499	#41	—	26	2	no	—
500	#41	—	26	2	no	—
501	#41	C₂×C₄×D₁₃	1	4	yes	—
502	#41	C₂³×D₁₃	1	4	yes	—
503	C₂×Q₈	—	13	8	no	—
504	C₂×Q₈	—	13	2	no	—
505	C₂×Q₈	—	26	2	no	—
506	C₂×Q₈	—	26	4	no	—
507	C₂×Q₈	C₂×C₄×D₁₃	1	2	yes	—
508	C₂×D₄	—	2	2	no	—
509	C₂×D₄	—	13	8	no	—
510	C₂×D₄	—	13	2	no	—
511	C₂×D₄	—	26	2	no	—
512	C₂×D₄	—	26	4	no	—
513	C₂×D₄	—	26	2	no	—
514	C₂×D₄	—	26	8	no	—
515	C₂×D₄	—	26	8	no	—
516	C₂×D₄	—	26	2	no	—
517	C₂×D₄	—	26	2	no	—
518	C₂×D₄	C₂×C₄×D₁₃	1	2	yes	—
519	C₂²×C₄	—	2	2	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	13	1	no	—
522	C₂²×C₄	—	13	2	no	—
523	C₂²×C₄	—	13	2	no	—
524	C₂²×C₄	—	13	2	no	—
525	C₂²×C₄	—	13	2	no	—
526	C₂²×C₄	—	13	2	no	—
527	C₂²×C₄	—	13	2	no	—
528	C₂²×C₄	—	26	8	no	—
529	C₂²×C₄	—	26	2	no	—
530	C₂²×C₄	—	26	8	no	—
531	C₂²×C₄	—	26	2	no	—
532	C₂²×C₄	—	26	4	no	—
533	C₂²×C₄	—	26	2	no	—
534	C₂²×C₄	—	26	1	no	—
535	C₂²×C₄	—	26	2	no	—
536	C₂²×C₄	—	52	4	no	—
537	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
538	Q₁₆	—	13	8	no	—
539	Q₁₆	—	13	4	no	—
540	Q₁₆	C₂×C₄×D₁₃	1	4	yes	complemented
541	SD₁₆	—	13	8	no	—
542	SD₁₆	—	13	8	no	—
543	SD₁₆	—	13	8	no	—
544	SD₁₆	C₂×C₄×D₁₃	1	8	yes	complemented
545	D₈	—	13	8	no	—
546	D₈	—	13	4	no	—
547	D₈	C₂×C₄×D₁₃	1	4	yes	complemented
548	M₁₆	—	2	2	no	—
549	M₁₆	—	2	8	no	—
550	M₁₆	—	13	8	no	—
551	M₁₆	—	13	8	no	—
552	M₁₆	—	13	8	no	—
553	M₁₆	—	13	8	no	—
554	M₁₆	—	13	4	no	—
555	M₁₆	—	26	8	no	—
556	M₁₆	—	26	8	no	—
557	M₁₆	—	26	8	no	—
558	M₁₆	—	26	2	no	—
559	M₁₆	—	26	8	no	—
560	M₁₆	C₂³×D₁₃	1	4	yes	—
561	C₂×C₈	—	2	2	no	—
562	C₂×C₈	—	2	8	no	—
563	C₂×C₈	—	13	2	no	—
564	C₂×C₈	—	13	2	no	—
565	C₂×C₈	—	13	2	no	—
566	C₂×C₈	—	13	1	no	—
567	C₂×C₈	—	13	1	no	—
568	C₂×C₈	—	13	2	no	—
569	C₂×C₈	—	13	2	no	—
570	C₂×C₈	—	26	8	no	—
571	C₂×C₈	—	26	8	no	—
572	C₂×C₈	—	26	8	no	—
573	C₂×C₈	—	26	2	no	—
574	C₂×C₈	—	26	8	no	—
575	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
576	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
577	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
578	C₂×C₈	D₄×D₁₃	1	2	yes	—
579	C₂×C₈	D₄×D₁₃	1	2	yes	—
580	C₂×C₈	C₂³×D₁₃	1	2	yes	—
581	C₂×C₈	C₂³×D₁₃	1	2	yes	—
582	C₄²	—	2	1	no	—
583	C₄²	—	13	2	no	—
584	C₄²	—	26	4	no	—
585	C₄²	—	26	1	no	—
586	C₄²	C₂³×D₁₃	1	2	yes	—
587	C₁₃	C₂×#2956	1	1	yes	characteristic, complemented, Sylow
588	C₂³	—	2	2	no	—
589	C₂³	—	13	2	no	—
590	C₂³	—	13	2	no	—
591	C₂³	—	13	2	no	—
592	C₂³	—	26	8	no	—
593	C₂³	—	26	2	no	—
594	C₂³	—	52	2	no	—
595	C₂³	—	104	4	no	—
596	C₂³	#41×D₁₃	1	1	yes	characteristic
597	Q₈	—	2	2	no	—
598	Q₈	—	13	4	no	—
599	Q₈	—	26	8	no	—
600	Q₈	—	26	2	no	—
601	Q₈	C₂²×C₄×D₁₃	1	4	yes	—
602	D₄	—	2	4	no	—
603	D₄	—	2	4	no	—
604	D₄	—	2	2	no	—
605	D₄	—	13	4	no	—
606	D₄	—	26	8	no	—
607	D₄	—	26	8	no	—
608	D₄	—	26	8	no	—
609	D₄	—	26	4	no	—
610	D₄	—	26	4	no	—
611	D₄	—	26	2	no	—
612	D₄	C₂²×C₄×D₁₃	1	4	yes	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	4	2	no	—
618	C₂×C₄	—	13	2	no	—
619	C₂×C₄	—	13	2	no	—
620	C₂×C₄	—	13	2	no	—
621	C₂×C₄	—	13	4	no	—
622	C₂×C₄	—	13	4	no	—
623	C₂×C₄	—	13	4	no	—
624	C₂×C₄	—	13	4	no	—
625	C₂×C₄	—	26	8	no	—
626	C₂×C₄	—	26	8	no	—
627	C₂×C₄	—	26	8	no	—
628	C₂×C₄	—	26	4	no	—
629	C₂×C₄	—	26	2	no	—
630	C₂×C₄	—	26	2	no	—
631	C₂×C₄	—	26	4	no	—
632	C₂×C₄	—	26	4	no	—
633	C₂×C₄	—	52	8	no	—
634	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
635	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
636	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
637	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
638	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
639	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
640	C₈	—	2	4	no	—
641	C₈	—	13	4	no	—
642	C₈	—	13	2	no	—
643	C₈	—	13	2	no	—
644	C₈	—	26	4	no	—
645	C₈	C₂²×C₄×D₁₃	1	2	yes	—
646	C₈	C₂²×C₄×D₁₃	1	2	yes	—
647	C₈	C₂×D₄×D₁₃	1	4	yes	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	4	no	—
650	C₂²	—	4	4	no	—
651	C₂²	—	13	4	no	—
652	C₂²	—	26	4	no	—
653	C₂²	—	26	4	no	—
654	C₂²	—	52	2	no	—
655	C₂²	—	52	2	no	—
656	C₂²	—	52	4	no	—
657	C₂²	—	104	8	no	—
658	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
659	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
660	C₂²	C₂×#41×D₁₃	1	1	yes	characteristic
661	C₄	—	2	4	no	—
662	C₄	—	4	2	no	—
663	C₄	—	13	4	no	—
664	C₄	—	26	4	no	—
665	C₄	—	26	4	no	—
666	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
667	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
668	C₄	C₂³×C₄×D₁₃	1	1	yes	characteristic
669	C₄	C₂²×D₄×D₁₃	1	1	yes	characteristic
670	C₂	—	2	1	no	—
671	C₂	—	2	1	no	—
672	C₂	—	4	4	no	—
673	C₂	—	26	4	no	—
674	C₂	—	52	4	no	—
675	C₂	#13123744	1	2	yes	direct product factor
676	C₂	C₂×C₄×D₄×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₄×C₁₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₂×C₁₃×#444	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×#11719473	C₂
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₂×#444	D₁₃
hypocenter	C₁₃	C₂×#2956
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#444

Complements

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

N	H ≅ G/N	type
2. C₂×#11719455	C₂	semidirect
3. #13123744	C₂	direct (N × H)
4. C₂×#11718378	C₂	semidirect
5. C₂×#11718484	C₂	semidirect
6. C₂×#11718857	C₂	semidirect
7. C₂×#11718556	C₂	semidirect
8. C₂×#11718805	C₂	semidirect
9. C₂×#11718554	C₂	semidirect
10. C₂×D₁₃×#104	C₂	semidirect
11. C₂×#11718368	C₂	semidirect
12. C₂×C₁₃×#444	C₂	semidirect
15. C₂×C₁₃×#131	C₂²	semidirect
17. C₂×#88202	C₂²	semidirect
18. #11719473	C₄	semidirect
20. C₂×#88172	C₄	semidirect
21. C₂×#88169	C₄	semidirect
22. C₂×#88168	C₄	semidirect
23. C₂×#88165	C₄	semidirect
25. #11719455	C₂²	semidirect
27. C₂×#88161	C₂²	semidirect
32. C₂×#88155	C₂²	semidirect
37. C₁₃×#444	C₂²	semidirect
38. C₂×C₁₃×#108	C₂²	semidirect
39. C₂×C₁₃×#104	C₂²	semidirect
40. C₂×C₁₃×#97	C₂²	semidirect
41. C₂×#88077	C₂²	semidirect
42. #11718857	C₂²	semidirect
43. #11718805	C₂²	semidirect
44. C₂×#88065	C₂²	semidirect
45. C₂×#88062	C₂²	semidirect
46. C₂×#88059	C₂²	semidirect
47. C₂×C₈×Dic₁₃	C₂²	semidirect
48. C₂×C₈×Dic₁₃	C₂²	semidirect
49. C₂×#88045	C₂²	semidirect
50. C₂×#88043	C₂²	semidirect
51. #11718556	C₂²	semidirect
52. #11718554	C₂²	semidirect
53. #11718484	C₂²	semidirect
54. D₁₃×#104	C₂²	semidirect
55. #11718378	C₂²	semidirect
56. #11718368	C₂²	semidirect
73. C₁₃×#135	C₂×C₄	semidirect
75. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
76. C₂×C₁₃×SD₁₆	C₂×C₄	semidirect
77. C₂×C₁₃×D₈	C₂×C₄	semidirect
79. C₁₃×#131	C₂³	semidirect
86. #88204	C₂×C₄	semidirect
89. #88202	C₂³	semidirect
90. C₂×#6107	C₂×C₄	semidirect
91. C₂×#6106	C₂×C₄	semidirect
92. C₂×#6105	C₂×C₄	semidirect
93. C₂×#6104	C₂×C₄	semidirect
101. #88172	C₂×C₄	semidirect
102. #88169	C₂×C₄	semidirect
103. #88168	C₂×C₄	semidirect
104. #88165	C₂×C₄	semidirect
107. #88161	C₂³	semidirect
111. C₂×Dic₅₂	C₂×C₄	semidirect
112. #88158	C₂×C₄	semidirect
114. C₂×D₁₀₄	C₂×C₄	semidirect
115. C₂×#6095	C₂×C₄	semidirect
118. #88155	C₂³	semidirect
136. C₁₃×#108	C₂³	semidirect
137. C₁₃×#104	C₂³	semidirect
138. C₁₃×#97	C₂³	semidirect
139. #88077	C₂³	semidirect
140. #88065	C₂³	semidirect
141. #88062	C₂³	semidirect
142. #88059	C₂³	semidirect
143. C₈×Dic₁₃	C₂³	semidirect
144. C₈×Dic₁₃	C₂³	semidirect
145. #88045	C₂³	semidirect
146. #88043	C₂³	semidirect
201. C₁₃×Q₁₆	C₂²×C₄	semidirect
202. C₁₃×SD₁₆	C₂²×C₄	semidirect
203. C₁₃×D₈	C₂²×C₄	semidirect
218. #6107	C₂²×C₄	semidirect
219. #6106	C₂²×C₄	semidirect
220. #6105	C₂²×C₄	semidirect
221. #6104	C₂²×C₄	semidirect
237. Dic₅₂	C₂²×C₄	semidirect
238. D₁₀₄	C₂²×C₄	semidirect
239. #6095	C₂²×C₄	semidirect
255. C₂×#444	D₁₃	semidirect
339. C₂×#131	C₂×D₁₃	semidirect
348. #444	C₂×D₁₃	semidirect
355. C₂×#108	C₂×D₁₃	semidirect
360. C₂×#104	C₂×D₁₃	semidirect
363. C₂×#97	C₂×D₁₃	semidirect
412. #135	C₄×D₁₃	semidirect
416. C₂×Q₁₆	C₄×D₁₃	semidirect
420. C₂×SD₁₆	C₄×D₁₃	semidirect
423. C₂×D₈	C₄×D₁₃	semidirect
433. #131	C₂²×D₁₃	semidirect
469. #108	C₂²×D₁₃	semidirect
473. #104	C₂²×D₁₃	semidirect
475. #97	C₂²×D₁₃	semidirect
481. C₂×C₁₃	#2956	semidirect
540. Q₁₆	C₂×C₄×D₁₃	semidirect
544. SD₁₆	C₂×C₄×D₁₃	semidirect
547. D₈	C₂×C₄×D₁₃	semidirect
587. C₁₃	C₂×#2956	semidirect
675. C₂	#13123744	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×#11719473	2
C₂×#11719455	2
#13123744	2
C₂×#11718378	2
C₂×#11718484	2
C₂×#11718857	2
C₂×#11718556	2
C₂×#11718805	2
C₂×#11718554	2
C₂×D₁₃×#104	2
C₂×#11718368	2
C₂×C₁₃×#444	2
C₂×#2956	13

Subgroups — C2×#13123744 #16727230

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13123744 #16727230