Subgroups — C₂×#13128534 #16770973

Order 3328.

7390 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128534	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719236	C₂	1	8	yes	maximal, complemented
3	C₂×#11719232	C₂	1	8	yes	maximal, complemented
4	C₂×#11719188	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11719220	C₂	1	4	yes	maximal, complemented
6	C₂×#11719198	C₂	1	1	yes	maximal, characteristic
7	C₂×#11719184	C₂	1	4	yes	maximal, complemented
8	C₂²×#88183	C₂	1	2	yes	maximal, complemented
9	C₂×#11719191	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂³×C₂²⋊D₁₃	C₂²	1	2	yes	—
13	C₂×C₁₃×#117	C₂²	1	8	yes	complemented
14	C₂×C₁₃×#117	C₂²	1	16	yes	complemented
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
16	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₃	C₂²	1	2	yes	complemented
19	C₂²×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
20	C₂×#88184	C₂²	1	4	yes	—
21	C₂×#88183	C₂²	1	8	yes	—
22	C₂×#88183	C₂²	1	4	yes	complemented
23	C₂×#88183	C₂²	1	4	yes	complemented
24	C₂×#88183	C₂²	1	32	yes	complemented
25	C₂×C₄×C₂²⋊D₁₃	C₂²	1	8	yes	complemented
26	C₂²×#6103	C₂²	1	4	yes	complemented
27	C₂×#88178	C₂²	1	4	yes	complemented
28	C₂²×#6101	C₂²	1	4	yes	complemented
29	#11719236	C₂²	1	128	yes	complemented
30	#11719232	C₂²	1	128	yes	complemented
31	#11719220	C₂²	1	64	yes	complemented
32	C₂×#88152	C₂²	1	8	yes	complemented
33	C₂×#88150	C₂²	1	8	yes	complemented
34	C₂×#88148	C₂²	1	8	yes	complemented
35	C₂×#88143	C₂²	1	8	yes	complemented
36	#11719198	C₂²	1	16	yes	—
37	C₂×#88140	C₂²	1	4	yes	—
38	C₂×#88136	C₂²	1	4	yes	—
39	#11719191	C₂²	1	32	yes	complemented
40	C₂×#88135	C₂²	1	8	yes	—
41	C₂×C₂²⋊C₄×D₁₃	C₂²	1	4	yes	complemented
42	#11719188	C₂²	1	16	yes	complemented
43	C₂×#88132	C₂²	1	8	yes	complemented
44	C₂×#88131	C₂²	1	4	yes	complemented
45	#11719184	C₂²	1	64	yes	complemented
46	C₂×#88130	C₂²	1	8	yes	complemented
47	C₂×#88129	C₂²	1	4	yes	complemented
48	C₂×C₄×D₅₂	C₂²	1	4	yes	complemented
49	C₂×#88126	C₂²	1	8	yes	complemented
50	C₂×#88124	C₂²	1	4	yes	complemented
51	C₂×C₄×Dic₂₆	C₂²	1	4	yes	complemented
52	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
53	C₂⁴×D₁₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₃	—	2	8	no	—
55	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
59	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
61	C₂²×C₂²⋊D₁₃	—	2	16	no	—
62	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
63	C₂²×C₂²⋊D₁₃	C₂³	1	16	yes	—
64	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
65	C₂³×Dic₁₃	C₂³	1	2	yes	—
66	C₂³×Dic₁₃	C₂³	1	4	yes	—
67	C₂²×D₅₂	C₂³	1	4	yes	—
68	C₂²×C₄×D₁₃	C₂³	1	8	yes	—
69	C₂²×Dic₂₆	C₂³	1	4	yes	—
70	C₁₃×#117	C₂³	1	64	yes	complemented
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	complemented
73	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
74	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
75	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
76	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
77	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
78	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
79	C₂×C₄²×C₁₃	C₂³	1	16	yes	complemented
80	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
81	C₂×C₂²⋊Dic₁₃	C₂³	1	16	yes	—
82	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
83	#88184	C₂³	1	32	yes	—
84	#88183	C₂³	1	64	yes	—
85	#88183	C₂³	1	32	yes	complemented
86	#88183	C₂³	1	32	yes	complemented
87	C₄×C₂²⋊D₁₃	C₂³	1	64	yes	complemented
88	C₂×#6103	C₂³	1	8	yes	—
89	C₂×#6103	C₂³	1	8	yes	—
90	C₂×#6103	C₂³	1	8	yes	—
91	C₂×#6103	C₂³	1	8	yes	—
92	C₂×#6103	C₂³	1	32	yes	complemented
93	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
94	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
95	#88178	C₂³	1	32	yes	complemented
96	C₂×#6101	C₂³	1	8	yes	—
97	C₂×#6101	C₂³	1	8	yes	—
98	C₂×#6101	C₂³	1	8	yes	—
99	C₂×#6101	C₂³	1	8	yes	—
100	C₂×#6101	C₂³	1	32	yes	complemented
101	C₂×C₄×Dic₁₃	C₂³	1	8	yes	—
102	#88152	C₂³	1	64	yes	complemented
103	#88150	C₂³	1	64	yes	complemented
104	#88148	C₂³	1	64	yes	complemented
105	#88143	C₂³	1	64	yes	complemented
106	#88140	C₂³	1	32	yes	—
107	#88136	C₂³	1	32	yes	—
108	#88135	C₂³	1	64	yes	—
109	C₂²⋊C₄×D₁₃	C₂³	1	32	yes	complemented
110	#88132	C₂³	1	64	yes	complemented
111	#88131	C₂³	1	32	yes	complemented
112	#88130	C₂³	1	64	yes	complemented
113	#88129	C₂³	1	32	yes	complemented
114	C₄×D₅₂	C₂³	1	32	yes	complemented
115	#88126	C₂³	1	64	yes	complemented
116	#88124	C₂³	1	32	yes	complemented
117	C₄×Dic₂₆	C₂³	1	32	yes	complemented
118	C₂×#3491	—	13	1	no	maximal, Sylow
119	C₂⁴×C₁₃	—	4	4	no	—
120	C₂⁴×C₁₃	#41	1	8	yes	—
121	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
122	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
123	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
124	C₂³×D₁₃	—	2	8	no	—
125	C₂³×D₁₃	—	4	8	no	—
126	C₂³×D₁₃	C₂⁴	1	4	yes	—
127	C₂³×D₁₃	C₂⁴	1	8	yes	—
128	C₂²×C₄×C₁₃	—	2	16	no	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	2	32	no	—
132	C₂²×C₄×C₁₃	—	4	4	no	—
133	C₂²×C₄×C₁₃	—	4	4	no	—
134	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
139	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
143	C₂×C₂²⋊D₁₃	—	2	16	no	—
144	C₂×C₂²⋊D₁₃	—	2	16	no	—
145	C₂×C₂²⋊D₁₃	—	2	64	no	—
146	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
147	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
148	C₂²×Dic₁₃	—	2	8	no	—
149	C₂²×Dic₁₃	—	4	8	no	—
150	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
151	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
152	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
153	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
154	C₂×D₅₂	—	4	8	no	—
155	C₂×D₅₂	C₂⁴	1	16	yes	—
156	C₂×C₄×D₁₃	—	4	16	no	—
157	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
158	C₂×Dic₂₆	—	4	8	no	—
159	C₂×Dic₂₆	C₂⁴	1	16	yes	—
160	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
161	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
162	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
163	C₄²×C₁₃	C₂⁴	1	16	yes	—
164	C₄²×C₁₃	C₂⁴	1	16	yes	—
165	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
166	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
167	#6103	C₂⁴	1	32	yes	—
168	#6103	C₂⁴	1	32	yes	—
169	#6103	C₂⁴	1	32	yes	—
170	#6103	C₂⁴	1	32	yes	—
171	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
172	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
173	#6101	C₂⁴	1	32	yes	—
174	#6101	C₂⁴	1	32	yes	—
175	#6101	C₂⁴	1	32	yes	—
176	#6101	C₂⁴	1	32	yes	—
177	C₄×Dic₁₃	C₂⁴	1	32	yes	—
178	#3491	—	13	32	no	—
179	C₂×#552	—	13	8	no	—
180	C₂×#551	—	13	8	no	—
181	C₂×#543	—	13	1	no	—
182	C₂×#539	—	13	4	no	—
183	C₂×#534	—	13	1	no	—
184	C₂×#529	—	13	4	no	—
185	C₂²×#123	—	13	2	no	—
186	C₂×#518	—	13	2	no	—
187	C₂²×#117	D₁₃	1	1	yes	characteristic, complemented
188	C₂³×C₁₃	—	2	8	no	—
189	C₂³×C₁₃	—	2	4	no	—
190	C₂³×C₁₃	—	4	16	no	—
191	C₂³×C₁₃	—	4	8	no	—
192	C₂³×C₁₃	C₂×#41	1	8	yes	—
193	C₂³×C₁₃	C₂×#41	1	4	yes	—
194	C₂³×C₁₃	C₂×#41	1	16	yes	—
195	C₂³×C₁₃	C₂⁵	1	2	yes	—
196	C₂³×C₁₃	C₂⁵	1	4	yes	—
197	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
198	C₂²×D₁₃	—	2	8	no	—
199	C₂²×D₁₃	—	2	16	no	—
200	C₂²×D₁₃	—	2	16	no	—
201	C₂²×D₁₃	—	4	16	no	—
202	C₂²×D₁₃	—	8	16	no	—
203	C₂²×D₁₃	C₂⁵	1	8	yes	—
204	C₂×C₄×C₁₃	—	2	32	no	—
205	C₂×C₄×C₁₃	—	2	8	no	—
206	C₂×C₄×C₁₃	—	2	8	no	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	8	no	—
210	C₂×C₄×C₁₃	—	2	8	no	—
211	C₂×C₄×C₁₃	—	4	8	no	—
212	C₂×C₄×C₁₃	—	4	8	no	—
213	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
214	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
215	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
216	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
217	C₂²⋊D₁₃	—	2	32	no	—
218	C₂²⋊D₁₃	—	2	32	no	—
219	C₂×Dic₁₃	—	2	16	no	—
220	C₂×Dic₁₃	—	2	8	no	—
221	C₂×Dic₁₃	—	2	16	no	—
222	C₂×Dic₁₃	—	4	16	no	—
223	C₂×Dic₁₃	C₂⁵	1	8	yes	—
224	C₂×Dic₁₃	C₂⁵	1	16	yes	—
225	D₅₂	—	4	16	no	—
226	C₄×D₁₃	—	4	32	no	—
227	Dic₂₆	—	4	16	no	—
228	C₂³×D₄	—	13	2	no	—
229	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
230	#552	—	13	128	no	—
231	#551	—	13	128	no	—
232	#543	—	13	16	no	—
233	#539	—	13	64	no	—
234	#534	—	13	16	no	—
235	#529	—	13	64	no	—
236	C₂×#126	—	13	8	no	—
237	C₂×#126	—	13	8	no	—
238	C₂×#125	—	13	8	no	—
239	C₂×#125	—	13	4	no	—
240	C₂×#124	—	13	4	no	—
241	C₂×#123	—	13	8	no	—
242	C₂×#123	—	13	4	no	—
243	C₂×#123	—	13	4	no	—
244	C₂×#123	—	13	32	no	—
245	C₂×#123	—	13	8	no	—
246	C₂×#123	—	13	4	no	—
247	C₂×C₂²⋊Q₈	—	13	4	no	—
248	C₂×C₂²⋊Q₈	—	13	8	no	—
249	C₂×C₂²⋊Q₈	—	13	8	no	—
250	C₂×#121	—	13	4	no	—
251	C₂×#120	—	13	4	no	—
252	#518	—	13	32	no	—
253	C₂×C₄×Q₈	—	13	4	no	—
254	C₂×C₄×D₄	—	13	8	no	—
255	C₂×C₄×D₄	—	13	8	no	—
256	C₂×C₄×D₄	—	13	4	no	—
257	C₂×#117	—	13	4	no	—
258	C₂×#117	—	13	8	no	—
259	C₂×#117	C₂×D₁₃	1	8	yes	complemented
260	C₂×#117	C₂×D₁₃	1	16	yes	complemented
261	C₂²×C₄⋊C₄	—	13	4	no	—
262	C₂²×C₄⋊C₄	C₂×D₁₃	1	2	yes	complemented
263	C₂²×C₂²⋊C₄	—	13	2	no	—
264	C₂²×C₂²⋊C₄	—	13	4	no	—
265	C₂²×C₂²⋊C₄	—	13	4	no	—
266	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
267	C₂²×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
268	C₂²×C₄²	C₂×D₁₃	1	2	yes	complemented
269	C₂²×C₁₃	—	2	8	no	—
270	C₂²×C₁₃	—	2	4	no	—
271	C₂²×C₁₃	—	2	16	no	—
272	C₂²×C₁₃	—	2	8	no	—
273	C₂²×C₁₃	—	4	16	no	—
274	C₂²×C₁₃	C₂²×#41	1	8	yes	—
275	C₂²×C₁₃	C₂²×#41	1	4	yes	—
276	C₂²×C₁₃	C₂²×#41	1	2	yes	—
277	C₂²×C₁₃	#585	1	4	yes	—
278	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
279	C₂×D₁₃	—	2	8	no	—
280	C₂×D₁₃	—	2	16	no	—
281	C₂×D₁₃	—	4	16	no	—
282	C₂×D₁₃	—	8	16	no	—
283	C₄×C₁₃	—	2	4	no	—
284	C₄×C₁₃	—	2	4	no	—
285	C₄×C₁₃	—	2	8	no	—
286	C₄×C₁₃	—	2	8	no	—
287	Dic₁₃	—	2	8	no	—
288	Dic₁₃	—	2	16	no	—
289	C₂⁵	—	13	2	no	—
290	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
291	C₂²×Q₈	—	13	4	no	—
292	C₂²×D₄	—	13	4	no	—
293	C₂²×D₄	—	13	4	no	—
294	C₂²×D₄	—	13	16	no	—
295	C₂²×D₄	—	13	4	no	—
296	C₂²×D₄	—	26	16	no	—
297	C₂³×C₄	—	2	8	no	—
298	C₂³×C₄	—	13	2	no	—
299	C₂³×C₄	—	13	4	no	—
300	C₂³×C₄	—	13	8	no	—
301	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
302	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
303	C₂³×C₄	C₂²×D₁₃	1	8	yes	—
304	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
305	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
306	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
307	#126	—	13	64	no	—
308	#126	—	13	64	no	—
309	#125	—	13	64	no	—
310	#125	—	13	32	no	—
311	#124	—	13	32	no	—
312	#123	—	13	32	no	—
313	#123	—	13	32	no	—
314	#123	—	13	64	no	—
315	#123	—	13	64	no	—
316	#123	—	13	32	no	—
317	C₂²⋊Q₈	—	13	32	no	—
318	C₂²⋊Q₈	—	13	64	no	—
319	C₂²⋊Q₈	—	13	64	no	—
320	#121	—	13	32	no	—
321	#120	—	13	32	no	—
322	C₄×Q₈	—	13	32	no	—
323	C₄×D₄	—	13	64	no	—
324	C₄×D₄	—	13	64	no	—
325	C₄×D₄	—	13	32	no	—
326	#117	—	13	32	no	—
327	#117	—	13	64	no	—
328	#117	C₂²×D₁₃	1	64	yes	complemented
329	C₂×C₄⋊C₄	—	13	8	no	—
330	C₂×C₄⋊C₄	—	13	8	no	—
331	C₂×C₄⋊C₄	—	13	32	no	—
332	C₂×C₄⋊C₄	—	13	8	no	—
333	C₂×C₄⋊C₄	—	13	8	no	—
334	C₂×C₄⋊C₄	—	13	4	no	—
335	C₂×C₄⋊C₄	—	13	4	no	—
336	C₂×C₄⋊C₄	C₂²×D₁₃	1	8	yes	—
337	C₂×C₄⋊C₄	C₂²×D₁₃	1	16	yes	complemented
338	C₂×C₂²⋊C₄	—	13	4	no	—
339	C₂×C₂²⋊C₄	—	13	4	no	—
340	C₂×C₂²⋊C₄	—	13	16	no	—
341	C₂×C₂²⋊C₄	—	13	8	no	—
342	C₂×C₂²⋊C₄	—	13	8	no	—
343	C₂×C₂²⋊C₄	—	13	8	no	—
344	C₂×C₂²⋊C₄	—	13	32	no	—
345	C₂×C₂²⋊C₄	—	13	8	no	—
346	C₂×C₂²⋊C₄	—	13	32	no	—
347	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
348	C₂×C₂²⋊C₄	C₂²×D₁₃	1	8	yes	—
349	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
350	C₂×C₂²⋊C₄	C₂²×D₁₃	1	8	yes	—
351	C₂×C₄²	—	13	8	no	—
352	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
353	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
354	C₂×C₄²	C₂²×D₁₃	1	16	yes	complemented
355	C₂×C₁₃	—	2	8	no	—
356	C₂×C₁₃	—	2	4	no	—
357	C₂×C₁₃	#3491	1	4	yes	complemented
358	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
359	C₂×C₁₃	C₂×#585	1	2	yes	—
360	D₁₃	—	4	8	no	—
361	C₂⁴	—	4	4	no	—
362	C₂⁴	—	13	4	no	—
363	C₂⁴	—	13	8	no	—
364	C₂⁴	—	26	8	no	—
365	C₂⁴	—	52	8	no	—
366	C₂⁴	#6127	1	8	yes	—
367	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
368	C₂⁴	C₂³×D₁₃	1	2	yes	—
369	C₂⁴	C₂³×D₁₃	1	4	yes	—
370	C₂×Q₈	—	13	16	no	—
371	C₂×Q₈	—	52	8	no	—
372	C₂×D₄	—	13	16	no	—
373	C₂×D₄	—	13	16	no	—
374	C₂×D₄	—	13	16	no	—
375	C₂×D₄	—	26	16	no	—
376	C₂×D₄	—	26	16	no	—
377	C₂×D₄	—	26	64	no	—
378	C₂×D₄	—	52	8	no	—
379	C₂²×C₄	—	2	16	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	32	no	—
383	C₂²×C₄	—	4	4	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	—	13	8	no	—
386	C₂²×C₄	—	13	4	no	—
387	C₂²×C₄	—	13	8	no	—
388	C₂²×C₄	—	13	16	no	—
389	C₂²×C₄	—	13	32	no	—
390	C₂²×C₄	—	26	8	no	—
391	C₂²×C₄	—	52	16	no	—
392	C₂²×C₄	—	52	8	no	—
393	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
394	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
395	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
396	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
397	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
398	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
399	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
400	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
401	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
402	C₄⋊C₄	—	13	32	no	—
403	C₄⋊C₄	—	13	32	no	—
404	C₄⋊C₄	—	13	32	no	—
405	C₄⋊C₄	—	13	32	no	—
406	C₄⋊C₄	—	13	16	no	—
407	C₄⋊C₄	—	13	16	no	—
408	C₄⋊C₄	C₂³×D₁₃	1	32	yes	—
409	C₂²⋊C₄	—	13	16	no	—
410	C₂²⋊C₄	—	13	16	no	—
411	C₂²⋊C₄	—	13	32	no	—
412	C₂²⋊C₄	—	13	32	no	—
413	C₂²⋊C₄	—	13	32	no	—
414	C₂²⋊C₄	—	13	32	no	—
415	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
416	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
417	C₄²	—	13	32	no	—
418	C₄²	C₂³×D₁₃	1	16	yes	—
419	C₄²	C₂³×D₁₃	1	16	yes	—
420	C₁₃	C₂×#3491	1	1	yes	characteristic, complemented, Sylow
421	C₂³	—	2	4	no	—
422	C₂³	—	2	8	no	—
423	C₂³	—	4	16	no	—
424	C₂³	—	4	8	no	—
425	C₂³	—	13	8	no	—
426	C₂³	—	26	8	no	—
427	C₂³	—	26	16	no	—
428	C₂³	—	26	16	no	—
429	C₂³	—	52	16	no	—
430	C₂³	—	104	16	no	—
431	C₂³	C₂×#6127	1	8	yes	—
432	C₂³	C₂×#6127	1	4	yes	—
433	C₂³	C₂×#6127	1	16	yes	—
434	C₂³	C₂⁴×D₁₃	1	2	yes	—
435	C₂³	C₂⁴×D₁₃	1	4	yes	—
436	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
437	Q₈	—	52	16	no	—
438	D₄	—	26	32	no	—
439	D₄	—	26	32	no	—
440	D₄	—	52	16	no	—
441	C₂×C₄	—	2	32	no	—
442	C₂×C₄	—	2	8	no	—
443	C₂×C₄	—	2	8	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	8	no	—
447	C₂×C₄	—	2	8	no	—
448	C₂×C₄	—	4	8	no	—
449	C₂×C₄	—	4	8	no	—
450	C₂×C₄	—	13	8	no	—
451	C₂×C₄	—	13	16	no	—
452	C₂×C₄	—	26	16	no	—
453	C₂×C₄	—	26	8	no	—
454	C₂×C₄	—	26	16	no	—
455	C₂×C₄	—	52	32	no	—
456	C₂×C₄	—	52	16	no	—
457	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
458	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
459	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
460	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
461	C₂²	—	2	16	no	—
462	C₂²	—	2	8	no	—
463	C₂²	—	2	4	no	—
464	C₂²	—	2	8	no	—
465	C₂²	—	4	16	no	—
466	C₂²	—	26	8	no	—
467	C₂²	—	26	16	no	—
468	C₂²	—	52	16	no	—
469	C₂²	—	104	16	no	—
470	C₂²	C₂²×#6127	1	8	yes	—
471	C₂²	C₂²×#6127	1	4	yes	—
472	C₂²	C₂²×#6127	1	2	yes	—
473	C₂²	#11719648	1	4	yes	—
474	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
475	C₄	—	2	4	no	—
476	C₄	—	2	4	no	—
477	C₄	—	2	8	no	—
478	C₄	—	2	8	no	—
479	C₄	—	26	8	no	—
480	C₄	—	26	16	no	—
481	C₂	—	2	8	no	—
482	C₂	—	2	4	no	—
483	C₂	—	52	8	no	—
484	C₂	#13128534	1	4	yes	direct product factor
485	C₂	C₂³×#6127	1	1	yes	characteristic
486	C₂	C₂×#11719648	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₁₃×#117	C₂
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂×#11719198	C₂
hypercenter	C₂²×#117	D₁₃
hypocenter	C₁₃	C₂×#3491
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×#117

Complements

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

N	H ≅ G/N	type
1. #13128534	C₂	direct (N × H)
2. C₂×#11719236	C₂	semidirect
3. C₂×#11719232	C₂	semidirect
4. C₂×#11719188	C₂	semidirect
5. C₂×#11719220	C₂	semidirect
7. C₂×#11719184	C₂	semidirect
8. C₂²×#88183	C₂	semidirect
9. C₂×#11719191	C₂	semidirect
10. C₂²×C₁₃×#117	C₂	semidirect
13. C₂×C₁₃×#117	C₂²	semidirect
14. C₂×C₁₃×#117	C₂²	semidirect
15. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
18. C₂²×C₄²×C₁₃	C₂²	semidirect
22. C₂×#88183	C₂²	semidirect
23. C₂×#88183	C₂²	semidirect
24. C₂×#88183	C₂²	semidirect
25. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
26. C₂²×#6103	C₂²	semidirect
27. C₂×#88178	C₂²	semidirect
28. C₂²×#6101	C₂²	semidirect
29. #11719236	C₂²	semidirect
30. #11719232	C₂²	semidirect
31. #11719220	C₂²	semidirect
32. C₂×#88152	C₂²	semidirect
33. C₂×#88150	C₂²	semidirect
34. C₂×#88148	C₂²	semidirect
35. C₂×#88143	C₂²	semidirect
39. #11719191	C₂²	semidirect
41. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
42. #11719188	C₂²	semidirect
43. C₂×#88132	C₂²	semidirect
44. C₂×#88131	C₂²	semidirect
45. #11719184	C₂²	semidirect
46. C₂×#88130	C₂²	semidirect
47. C₂×#88129	C₂²	semidirect
48. C₂×C₄×D₅₂	C₂²	semidirect
49. C₂×#88126	C₂²	semidirect
50. C₂×#88124	C₂²	semidirect
51. C₂×C₄×Dic₂₆	C₂²	semidirect
70. C₁₃×#117	C₂³	semidirect
72. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
79. C₂×C₄²×C₁₃	C₂³	semidirect
85. #88183	C₂³	semidirect
86. #88183	C₂³	semidirect
87. C₄×C₂²⋊D₁₃	C₂³	semidirect
92. C₂×#6103	C₂³	semidirect
95. #88178	C₂³	semidirect
100. C₂×#6101	C₂³	semidirect
102. #88152	C₂³	semidirect
103. #88150	C₂³	semidirect
104. #88148	C₂³	semidirect
105. #88143	C₂³	semidirect
109. C₂²⋊C₄×D₁₃	C₂³	semidirect
110. #88132	C₂³	semidirect
111. #88131	C₂³	semidirect
112. #88130	C₂³	semidirect
113. #88129	C₂³	semidirect
114. C₄×D₅₂	C₂³	semidirect
115. #88126	C₂³	semidirect
116. #88124	C₂³	semidirect
117. C₄×Dic₂₆	C₂³	semidirect
187. C₂²×#117	D₁₃	semidirect
259. C₂×#117	C₂×D₁₃	semidirect
260. C₂×#117	C₂×D₁₃	semidirect
262. C₂²×C₄⋊C₄	C₂×D₁₃	semidirect
268. C₂²×C₄²	C₂×D₁₃	semidirect
328. #117	C₂²×D₁₃	semidirect
337. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
354. C₂×C₄²	C₂²×D₁₃	semidirect
357. C₂×C₁₃	#3491	semidirect
420. C₁₃	C₂×#3491	semidirect
484. C₂	#13128534	direct (N × H)

Maximal subgroups

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

subgroup	index
#13128534	2
C₂×#11719236	2
C₂×#11719232	2
C₂×#11719188	2
C₂×#11719220	2
C₂×#11719198	2
C₂×#11719184	2
C₂²×#88183	2
C₂×#11719191	2
C₂²×C₁₃×#117	2
C₂×#3491	13

Subgroups — C2×#13128534 #16770973

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128534 #16770973