Subgroups — C₂×#13129169 #16770512

Order 3328.

8814 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129169	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719425	C₂	1	4	yes	maximal, complemented
3	C₂×#11719418	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11719423	C₂	1	2	yes	maximal, complemented
5	C₂×#11719511	C₂	1	4	yes	maximal, complemented
6	C₂×#11719422	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×D₄×C₂²⋊D₁₃	C₂	1	4	yes	maximal, complemented
8	C₂×#11719424	C₂	1	4	yes	maximal, complemented
9	C₂×#11719420	C₂	1	4	yes	maximal, complemented
10	C₂×#11719509	C₂	1	4	yes	maximal, complemented
11	C₂×#11719184	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₁₃	C₂²	1	4	yes	complemented
14	C₂³×D₄×C₁₃	C₂²	1	2	yes	complemented
15	C₂³×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
16	C₂²×#6129	C₂²	1	4	yes	complemented
17	C₂²×D₄×D₁₃	C₂²	1	4	yes	complemented
18	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#127	C₂²	1	4	yes	complemented
20	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₃×#127	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#127	C₂²	1	16	yes	complemented
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×#88207	C₂²	1	8	yes	complemented
25	C₂²×C₂²⋊Dic₁₃	C₂²	1	4	yes	complemented
26	#11719511	C₂²	1	64	yes	complemented
27	#11719509	C₂²	1	64	yes	complemented
28	C₂×#88194	C₂²	1	4	yes	complemented
29	C₂×#88193	C₂²	1	8	yes	complemented
30	C₂×#88193	C₂²	1	8	yes	complemented
31	C₂×#88193	C₂²	1	8	yes	complemented
32	C₂×#88193	C₂²	1	8	yes	complemented
33	D₄×C₂²⋊D₁₃	C₂²	1	64	yes	complemented
34	C₂×#88192	C₂²	1	4	yes	complemented
35	C₂×#88192	C₂²	1	4	yes	complemented
36	C₂×#88191	C₂²	1	8	yes	complemented
37	C₂×#88191	C₂²	1	4	yes	complemented
38	C₂×#88191	C₂²	1	4	yes	complemented
39	C₂×#88190	C₂²	1	4	yes	complemented
40	C₂×#88189	C₂²	1	4	yes	complemented
41	C₂×#88189	C₂²	1	8	yes	complemented
42	C₂×#88189	C₂²	1	4	yes	complemented
43	C₂×D₄×Dic₁₃	C₂²	1	4	yes	complemented
44	C₂×D₄×Dic₁₃	C₂²	1	4	yes	complemented
45	C₂×#88184	C₂²	1	2	yes	—
46	C₂×#88183	C₂²	1	4	yes	complemented
47	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
48	C₂×#88178	C₂²	1	2	yes	complemented
49	#11719425	C₂²	1	64	yes	complemented
50	#11719424	C₂²	1	64	yes	complemented
51	#11719423	C₂²	1	32	yes	complemented
52	#11719422	C₂²	1	16	yes	complemented
53	#11719420	C₂²	1	64	yes	complemented
54	#11719418	C₂²	1	16	yes	complemented
55	#11719184	C₂²	1	32	yes	complemented
56	C₂×#88130	C₂²	1	4	yes	complemented
57	C₂×#88129	C₂²	1	2	yes	complemented
58	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
59	C₂×#88126	C₂²	1	4	yes	complemented
60	C₂×#88124	C₂²	1	2	yes	complemented
61	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
62	C₂⁵×C₁₃	C₂³	1	4	yes	—
63	C₂⁴×D₁₃	C₂³	1	4	yes	—
64	C₂²×D₄×C₁₃	—	4	16	no	—
65	C₂²×D₄×C₁₃	—	4	8	no	—
66	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
67	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
68	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	32	yes	complemented
73	C₂²×D₄×C₁₃	C₂³	1	16	yes	complemented
74	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×C₂²⋊D₁₃	—	4	16	no	—
77	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
78	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
79	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
80	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
81	C₂²×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
82	C₂³×Dic₁₃	C₂³	1	4	yes	—
83	C₂³×Dic₁₃	C₂³	1	8	yes	—
84	C₂×#6129	—	4	16	no	—
85	C₂×#6129	C₂³	1	32	yes	complemented
86	C₂×D₄×D₁₃	—	4	16	no	—
87	C₂×D₄×D₁₃	C₂³	1	32	yes	complemented
88	C₂²×D₅₂	C₂³	1	2	yes	—
89	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
90	C₂²×Dic₂₆	C₂³	1	2	yes	—
91	C₁₃×#127	C₂³	1	8	yes	—
92	C₁₃×#127	C₂³	1	32	yes	complemented
93	C₁₃×#127	C₂³	1	16	yes	complemented
94	C₁₃×#127	C₂³	1	8	yes	complemented
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
99	#88207	C₂³	1	64	yes	complemented
100	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
101	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	—
102	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	—
103	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
104	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
105	C₂×C₂²⋊Dic₁₃	C₂³	1	32	yes	complemented
106	#88194	C₂³	1	32	yes	complemented
107	#88193	C₂³	1	64	yes	complemented
108	#88193	C₂³	1	64	yes	complemented
109	#88193	C₂³	1	64	yes	complemented
110	#88193	C₂³	1	64	yes	complemented
111	#88192	C₂³	1	32	yes	complemented
112	#88192	C₂³	1	32	yes	complemented
113	#88191	C₂³	1	64	yes	complemented
114	#88191	C₂³	1	32	yes	complemented
115	#88191	C₂³	1	32	yes	complemented
116	#88190	C₂³	1	32	yes	complemented
117	#88189	C₂³	1	32	yes	complemented
118	#88189	C₂³	1	64	yes	complemented
119	#88189	C₂³	1	32	yes	complemented
120	D₄×Dic₁₃	C₂³	1	32	yes	complemented
121	D₄×Dic₁₃	C₂³	1	32	yes	complemented
122	#88184	C₂³	1	16	yes	—
123	#88183	C₂³	1	32	yes	complemented
124	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
125	C₂×#6103	C₂³	1	4	yes	—
126	C₂×#6103	C₂³	1	4	yes	—
127	C₂×#6103	C₂³	1	4	yes	—
128	C₂×#6103	C₂³	1	4	yes	—
129	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
130	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
131	#88178	C₂³	1	16	yes	complemented
132	C₂×#6101	C₂³	1	4	yes	—
133	C₂×#6101	C₂³	1	4	yes	—
134	C₂×#6101	C₂³	1	4	yes	—
135	C₂×#6101	C₂³	1	4	yes	—
136	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
137	#88130	C₂³	1	32	yes	complemented
138	#88129	C₂³	1	16	yes	complemented
139	C₄×D₅₂	C₂³	1	16	yes	complemented
140	#88126	C₂³	1	32	yes	complemented
141	#88124	C₂³	1	16	yes	complemented
142	C₄×Dic₂₆	C₂³	1	16	yes	complemented
143	C₂×#3543	—	13	1	no	maximal, Sylow
144	C₂⁴×C₁₃	—	2	16	no	—
145	C₂⁴×C₁₃	—	4	16	no	—
146	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
147	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
148	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₂⁴×C₁₃	C₂⁴	1	16	yes	—
150	C₂³×D₁₃	—	4	16	no	—
151	C₂³×D₁₃	—	4	8	no	—
152	C₂³×D₁₃	C₂⁴	1	4	yes	—
153	C₂³×D₁₃	C₂⁴	1	16	yes	—
154	C₂×D₄×C₁₃	—	2	16	no	—
155	C₂×D₄×C₁₃	—	2	16	no	—
156	C₂×D₄×C₁₃	—	4	64	no	—
157	C₂×D₄×C₁₃	—	4	16	no	—
158	C₂×D₄×C₁₃	—	4	4	no	—
159	C₂×D₄×C₁₃	—	4	8	no	—
160	C₂×D₄×C₁₃	—	4	4	no	—
161	C₂×D₄×C₁₃	—	4	32	no	—
162	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
163	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
164	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
165	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
166	C₂×D₄×C₁₃	C₂⁴	1	32	yes	—
167	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
168	C₂²×C₄×C₁₃	—	2	4	no	—
169	C₂²×C₄×C₁₃	—	2	8	no	—
170	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
176	C₂×C₂²⋊D₁₃	—	2	16	no	—
177	C₂×C₂²⋊D₁₃	—	4	16	no	—
178	C₂×C₂²⋊D₁₃	—	4	16	no	—
179	C₂×C₂²⋊D₁₃	—	4	16	no	—
180	C₂×C₂²⋊D₁₃	—	4	64	no	—
181	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
182	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
183	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
184	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
185	C₂²×Dic₁₃	—	4	16	no	—
186	C₂²×Dic₁₃	—	4	8	no	—
187	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
188	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
189	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
190	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
191	C₂²×Dic₁₃	C₂⁴	1	32	yes	—
192	#6129	—	4	64	no	—
193	D₄×D₁₃	—	4	64	no	—
194	C₂×D₅₂	—	2	8	no	—
195	C₂×D₅₂	C₂⁴	1	8	yes	—
196	C₂×C₄×D₁₃	—	2	16	no	—
197	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
198	C₂×Dic₂₆	—	2	8	no	—
199	C₂×Dic₂₆	C₂⁴	1	8	yes	—
200	C₄²×C₁₃	C₂⁴	1	4	yes	—
201	C₄²×C₁₃	C₂⁴	1	8	yes	—
202	C₄²×C₁₃	C₂⁴	1	4	yes	—
203	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
204	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
205	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
206	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
207	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
208	#6103	C₂⁴	1	16	yes	—
209	#6103	C₂⁴	1	16	yes	—
210	#6103	C₂⁴	1	16	yes	—
211	#6103	C₂⁴	1	16	yes	—
212	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
213	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
214	#6101	C₂⁴	1	16	yes	—
215	#6101	C₂⁴	1	16	yes	—
216	#6101	C₂⁴	1	16	yes	—
217	#6101	C₂⁴	1	16	yes	—
218	C₄×Dic₁₃	C₂⁴	1	16	yes	—
219	#3543	—	13	32	no	—
220	C₂×#560	—	13	4	no	—
221	C₂×#559	—	13	1	no	—
222	C₂×#550	—	13	2	no	—
223	C₂×#546	—	13	4	no	—
224	C₂×D₄²	—	13	4	no	—
225	C₂×D₄²	—	13	1	no	—
226	C₂×#540	—	13	4	no	—
227	C₂×#535	—	13	4	no	—
228	C₂×#534	—	13	4	no	—
229	C₂²×#127	D₁₃	1	1	yes	characteristic, complemented
230	C₂×#529	—	13	2	no	—
231	C₂³×C₁₃	—	2	4	no	—
232	C₂³×C₁₃	—	2	16	no	—
233	C₂³×C₁₃	—	2	8	no	—
234	C₂³×C₁₃	—	2	8	no	—
235	C₂³×C₁₃	—	2	16	no	—
236	C₂³×C₁₃	—	2	32	no	—
237	C₂³×C₁₃	—	4	32	no	—
238	C₂³×C₁₃	—	8	32	no	—
239	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
240	C₂³×C₁₃	C₂⁵	1	8	yes	—
241	C₂³×C₁₃	C₂⁵	1	8	yes	—
242	C₂³×C₁₃	C₂⁵	1	2	yes	—
243	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
244	C₂²×D₁₃	—	2	8	no	—
245	C₂²×D₁₃	—	2	8	no	—
246	C₂²×D₁₃	—	2	8	no	—
247	C₂²×D₁₃	—	4	32	no	—
248	C₂²×D₁₃	—	4	16	no	—
249	C₂²×D₁₃	—	8	32	no	—
250	C₂²×D₁₃	C₂⁵	1	8	yes	—
251	D₄×C₁₃	—	2	32	no	—
252	D₄×C₁₃	—	2	32	no	—
253	D₄×C₁₃	—	4	32	no	—
254	D₄×C₁₃	—	4	8	no	—
255	D₄×C₁₃	—	4	16	no	—
256	D₄×C₁₃	—	4	8	no	—
257	C₂×C₄×C₁₃	—	2	8	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	4	no	—
261	C₂×C₄×C₁₃	—	2	16	no	—
262	C₂×C₄×C₁₃	H(5,𝔽₂)	1	8	yes	—
263	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
264	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
265	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
266	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
267	C₂²⋊D₁₃	—	2	32	no	—
268	C₂²⋊D₁₃	—	4	32	no	—
269	C₂²⋊D₁₃	—	4	32	no	—
270	C₂²⋊D₁₃	—	4	32	no	—
271	C₂×Dic₁₃	—	2	8	no	—
272	C₂×Dic₁₃	—	2	8	no	—
273	C₂×Dic₁₃	—	2	8	no	—
274	C₂×Dic₁₃	—	4	32	no	—
275	C₂×Dic₁₃	—	4	16	no	—
276	C₂×Dic₁₃	C₂⁵	1	8	yes	—
277	C₂×Dic₁₃	C₂⁵	1	8	yes	—
278	C₂×Dic₁₃	C₂⁵	1	8	yes	—
279	D₅₂	—	2	16	no	—
280	C₄×D₁₃	—	2	32	no	—
281	Dic₂₆	—	2	16	no	—
282	C₂²×#41	—	13	4	no	—
283	C₂³×D₄	—	13	4	no	—
284	C₂³×D₄	—	13	4	no	—
285	C₂³×D₄	C₂×D₁₃	1	2	yes	complemented
286	C₂³×D₄	C₂×D₁₃	1	4	yes	complemented
287	#560	—	13	64	no	—
288	#559	—	13	16	no	—
289	#550	—	13	32	no	—
290	#546	—	13	64	no	—
291	D₄²	—	13	64	no	—
292	D₄²	—	13	16	no	—
293	#540	—	13	64	no	—
294	#535	—	13	64	no	—
295	#534	—	13	64	no	—
296	C₂×#127	—	13	4	no	—
297	C₂×#127	C₂×D₁₃	1	1	yes	characteristic
298	C₂×#127	C₂×D₁₃	1	4	yes	complemented
299	C₂×#127	C₂×D₁₃	1	1	yes	characteristic, complemented
300	C₂×#127	C₂×D₁₃	1	2	yes	complemented
301	C₂×#127	C₂×D₁₃	1	16	yes	complemented
302	#529	—	13	32	no	—
303	C₂×#126	—	13	4	no	—
304	C₂×#125	—	13	2	no	—
305	C₂×#124	—	13	4	no	—
306	C₂×#124	—	13	2	no	—
307	C₂×#123	—	13	4	no	—
308	C₂×#123	—	13	4	no	—
309	C₂×#123	—	13	8	no	—
310	C₂×#123	—	13	4	no	—
311	C₂×C₂²⋊Q₈	—	13	2	no	—
312	C₂×#121	—	13	4	no	—
313	C₂×#121	—	13	4	no	—
314	C₂×#121	—	13	8	no	—
315	C₂×#121	—	13	8	no	—
316	C₂×#121	—	13	8	no	—
317	C₂×#121	—	13	8	no	—
318	C₂×#121	—	13	2	no	—
319	C₂×#120	—	13	8	no	—
320	C₂×#120	—	13	4	no	—
321	C₂×#120	—	13	4	no	—
322	C₂×#120	—	13	8	no	—
323	C₂×C₄×Q₈	—	13	2	no	—
324	C₂×C₄×D₄	—	13	4	no	—
325	C₂×C₄×D₄	—	13	4	no	—
326	C₂×C₄×D₄	—	13	4	no	—
327	C₂×C₄×D₄	—	13	2	no	—
328	C₂×#117	—	13	4	no	—
329	C₂²×C₂²⋊C₄	—	13	4	no	—
330	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
331	C₂²×C₁₃	—	2	4	no	—
332	C₂²×C₁₃	—	2	8	no	—
333	C₂²×C₁₃	—	2	16	no	—
334	C₂²×C₁₃	—	2	8	no	—
335	C₂²×C₁₃	—	2	8	no	—
336	C₂²×C₁₃	—	2	16	no	—
337	C₂²×C₁₃	—	4	16	no	—
338	C₂²×C₁₃	—	4	16	no	—
339	C₂²×C₁₃	—	8	32	no	—
340	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
341	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
342	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
343	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
344	C₂×D₁₃	—	2	8	no	—
345	C₂×D₁₃	—	2	8	no	—
346	C₂×D₁₃	—	2	8	no	—
347	C₂×D₁₃	—	4	16	no	—
348	C₂×D₁₃	—	8	32	no	—
349	C₄×C₁₃	—	2	2	no	—
350	C₄×C₁₃	—	2	2	no	—
351	C₄×C₁₃	—	2	4	no	—
352	C₄×C₁₃	C₂×H(5,𝔽₂)	1	8	yes	—
353	Dic₁₃	—	2	8	no	—
354	Dic₁₃	—	2	8	no	—
355	Dic₁₃	—	2	8	no	—
356	C₂⁵	—	13	4	no	—
357	C₂⁵	C₂²×D₁₃	1	4	yes	—
358	C₂×#41	—	13	32	no	—
359	C₂×#41	—	52	16	no	—
360	C₂²×Q₈	—	13	2	no	—
361	C₂²×D₄	—	4	16	no	—
362	C₂²×D₄	—	4	8	no	—
363	C₂²×D₄	—	13	4	no	—
364	C₂²×D₄	—	13	8	no	—
365	C₂²×D₄	—	13	8	no	—
366	C₂²×D₄	—	13	8	no	—
367	C₂²×D₄	—	13	32	no	—
368	C₂²×D₄	—	13	32	no	—
369	C₂²×D₄	—	13	2	no	—
370	C₂²×D₄	—	52	16	no	—
371	C₂²×D₄	—	52	16	no	—
372	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
373	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
374	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
375	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
376	C₂²×D₄	C₂²×D₁₃	1	8	yes	—
377	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
378	C₂²×D₄	C₂²×D₁₃	1	16	yes	complemented
379	C₂²×D₄	C₂²×D₁₃	1	32	yes	complemented
380	C₂³×C₄	—	13	8	no	—
381	C₂³×C₄	—	13	4	no	—
382	C₂³×C₄	—	13	4	no	—
383	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
384	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
385	#127	—	13	32	no	—
386	#127	C₂²×D₁₃	1	8	yes	—
387	#127	C₂²×D₁₃	1	32	yes	complemented
388	#127	C₂²×D₁₃	1	8	yes	complemented
389	#127	C₂²×D₁₃	1	16	yes	complemented
390	#126	—	13	32	no	—
391	#125	—	13	16	no	—
392	#124	—	13	32	no	—
393	#124	—	13	16	no	—
394	#123	—	13	32	no	—
395	#123	—	13	32	no	—
396	#123	—	13	64	no	—
397	#123	—	13	32	no	—
398	C₂²⋊Q₈	—	13	16	no	—
399	#121	—	13	64	no	—
400	#121	—	13	64	no	—
401	#121	—	13	64	no	—
402	#121	—	13	32	no	—
403	#121	—	13	32	no	—
404	#121	—	13	64	no	—
405	#121	—	13	16	no	—
406	#120	—	13	64	no	—
407	#120	—	13	32	no	—
408	#120	—	13	32	no	—
409	#120	—	13	64	no	—
410	C₄×Q₈	—	13	16	no	—
411	C₄×D₄	—	13	32	no	—
412	C₄×D₄	—	13	32	no	—
413	C₄×D₄	—	13	32	no	—
414	C₄×D₄	—	13	16	no	—
415	#117	—	13	32	no	—
416	C₂×C₄⋊C₄	—	13	4	no	—
417	C₂×C₄⋊C₄	—	13	4	no	—
418	C₂×C₄⋊C₄	—	13	2	no	—
419	C₂×C₄⋊C₄	—	13	2	no	—
420	C₂×C₄⋊C₄	—	13	4	no	—
421	C₂×C₄⋊C₄	—	13	4	no	—
422	C₂×C₂²⋊C₄	—	13	4	no	—
423	C₂×C₂²⋊C₄	—	13	4	no	—
424	C₂×C₂²⋊C₄	—	13	4	no	—
425	C₂×C₂²⋊C₄	—	13	32	no	—
426	C₂×C₂²⋊C₄	—	13	8	no	—
427	C₂×C₂²⋊C₄	—	13	8	no	—
428	C₂×C₂²⋊C₄	—	13	4	no	—
429	C₂×C₂²⋊C₄	—	13	4	no	—
430	C₂×C₂²⋊C₄	—	13	4	no	—
431	C₂×C₂²⋊C₄	—	13	4	no	—
432	C₂×C₄²	—	13	4	no	—
433	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
434	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
435	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
436	C₂×C₄²	C₂²×D₁₃	1	8	yes	complemented
437	C₂×C₁₃	—	2	4	no	—
438	C₂×C₁₃	—	4	8	no	—
439	C₂×C₁₃	—	4	8	no	—
440	C₂×C₁₃	#3543	1	4	yes	complemented
441	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
442	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
443	D₁₃	—	4	8	no	—
444	C₂⁴	—	2	16	no	—
445	C₂⁴	—	4	16	no	—
446	C₂⁴	—	13	4	no	—
447	C₂⁴	—	13	16	no	—
448	C₂⁴	—	52	8	no	—
449	C₂⁴	—	52	16	no	—
450	C₂⁴	C₂³×D₁₃	1	4	yes	—
451	C₂⁴	C₂³×D₁₃	1	4	yes	—
452	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
453	C₂⁴	C₂³×D₁₃	1	16	yes	—
454	#41	—	52	64	no	—
455	C₂×Q₈	—	13	8	no	—
456	C₂×Q₈	—	26	8	no	—
457	C₂×D₄	—	2	16	no	—
458	C₂×D₄	—	2	16	no	—
459	C₂×D₄	—	4	64	no	—
460	C₂×D₄	—	4	16	no	—
461	C₂×D₄	—	4	4	no	—
462	C₂×D₄	—	4	8	no	—
463	C₂×D₄	—	4	4	no	—
464	C₂×D₄	—	4	32	no	—
465	C₂×D₄	—	13	16	no	—
466	C₂×D₄	—	13	32	no	—
467	C₂×D₄	—	13	32	no	—
468	C₂×D₄	—	13	32	no	—
469	C₂×D₄	—	13	8	no	—
470	C₂×D₄	—	26	16	no	—
471	C₂×D₄	—	26	8	no	—
472	C₂×D₄	—	52	64	no	—
473	C₂×D₄	—	52	16	no	—
474	C₂×D₄	—	52	16	no	—
475	C₂×D₄	—	52	16	no	—
476	C₂×D₄	—	52	64	no	—
477	C₂×D₄	C₂³×D₁₃	1	16	yes	—
478	C₂×D₄	C₂³×D₁₃	1	16	yes	—
479	C₂×D₄	C₂³×D₁₃	1	8	yes	—
480	C₂×D₄	C₂³×D₁₃	1	16	yes	—
481	C₂×D₄	C₂³×D₁₃	1	32	yes	—
482	C₂×D₄	C₂³×D₁₃	1	8	yes	—
483	C₂²×C₄	—	2	4	no	—
484	C₂²×C₄	—	2	8	no	—
485	C₂²×C₄	—	13	4	no	—
486	C₂²×C₄	—	13	4	no	—
487	C₂²×C₄	—	13	4	no	—
488	C₂²×C₄	—	13	32	no	—
489	C₂²×C₄	—	13	16	no	—
490	C₂²×C₄	—	13	16	no	—
491	C₂²×C₄	—	26	16	no	—
492	C₂²×C₄	—	52	8	no	—
493	C₂²×C₄	—	52	16	no	—
494	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
495	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
496	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
497	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
498	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
499	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
500	C₄⋊C₄	—	13	16	no	—
501	C₄⋊C₄	—	13	16	no	—
502	C₄⋊C₄	—	13	8	no	—
503	C₄⋊C₄	—	13	8	no	—
504	C₄⋊C₄	—	13	16	no	—
505	C₄⋊C₄	—	13	16	no	—
506	C₂²⋊C₄	—	13	16	no	—
507	C₂²⋊C₄	—	13	16	no	—
508	C₂²⋊C₄	—	13	16	no	—
509	C₂²⋊C₄	—	13	32	no	—
510	C₂²⋊C₄	—	13	32	no	—
511	C₂²⋊C₄	—	13	16	no	—
512	C₂²⋊C₄	—	13	16	no	—
513	C₂²⋊C₄	—	13	16	no	—
514	C₂²⋊C₄	—	13	16	no	—
515	C₄²	—	13	16	no	—
516	C₄²	C₂³×D₁₃	1	8	yes	—
517	C₄²	C₂³×D₁₃	1	4	yes	—
518	C₄²	C₂³×D₁₃	1	4	yes	—
519	C₁₃	C₂×#3543	1	1	yes	characteristic, complemented, Sylow
520	C₂³	—	2	4	no	—
521	C₂³	—	2	16	no	—
522	C₂³	—	2	8	no	—
523	C₂³	—	2	16	no	—
524	C₂³	—	2	8	no	—
525	C₂³	—	2	32	no	—
526	C₂³	—	4	32	no	—
527	C₂³	—	8	32	no	—
528	C₂³	—	13	8	no	—
529	C₂³	—	26	8	no	—
530	C₂³	—	26	8	no	—
531	C₂³	—	26	8	no	—
532	C₂³	—	52	16	no	—
533	C₂³	—	52	32	no	—
534	C₂³	—	104	32	no	—
535	C₂³	#88251	1	4	yes	—
536	C₂³	C₂⁴×D₁₃	1	8	yes	—
537	C₂³	C₂⁴×D₁₃	1	8	yes	—
538	C₂³	C₂⁴×D₁₃	1	2	yes	—
539	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
540	Q₈	—	26	16	no	—
541	D₄	—	2	32	no	—
542	D₄	—	2	32	no	—
543	D₄	—	4	32	no	—
544	D₄	—	4	8	no	—
545	D₄	—	4	16	no	—
546	D₄	—	4	8	no	—
547	D₄	—	26	32	no	—
548	D₄	—	26	16	no	—
549	D₄	—	52	32	no	—
550	D₄	—	52	32	no	—
551	D₄	—	52	32	no	—
552	C₂×C₄	—	2	8	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	16	no	—
557	C₂×C₄	—	13	8	no	—
558	C₂×C₄	—	13	8	no	—
559	C₂×C₄	—	13	8	no	—
560	C₂×C₄	—	26	8	no	—
561	C₂×C₄	—	26	8	no	—
562	C₂×C₄	—	26	8	no	—
563	C₂×C₄	—	26	32	no	—
564	C₂×C₄	—	52	16	no	—
565	C₂×C₄	—	52	32	no	—
566	C₂×C₄	#88251	1	8	yes	—
567	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
568	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
569	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
570	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
571	C₂²	—	2	4	no	—
572	C₂²	—	2	8	no	—
573	C₂²	—	2	16	no	—
574	C₂²	—	2	8	no	—
575	C₂²	—	2	16	no	—
576	C₂²	—	2	8	no	—
577	C₂²	—	4	16	no	—
578	C₂²	—	4	16	no	—
579	C₂²	—	8	32	no	—
580	C₂²	—	26	8	no	—
581	C₂²	—	26	8	no	—
582	C₂²	—	26	8	no	—
583	C₂²	—	52	16	no	—
584	C₂²	—	104	32	no	—
585	C₂²	C₂×#88251	1	4	yes	—
586	C₂²	C₂×#88251	1	2	yes	—
587	C₂²	C₂×#88251	1	4	yes	—
588	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
589	C₄	—	2	2	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	4	no	—
592	C₄	—	26	8	no	—
593	C₄	—	26	8	no	—
594	C₄	—	26	8	no	—
595	C₄	C₂×#88251	1	8	yes	—
596	C₂	—	2	4	no	—
597	C₂	—	4	8	no	—
598	C₂	—	4	8	no	—
599	C₂	—	52	8	no	—
600	C₂	#13129169	1	4	yes	direct product factor
601	C₂	C₂²×#88251	1	1	yes	characteristic
602	C₂	C₂²×#88251	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₁₃×#127	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂²×#127	D₁₃
hypocenter	C₁₃	C₂×#3543
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×#127

Complements

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

N	H ≅ G/N	type
1. #13129169	C₂	direct (N × H)
2. C₂×#11719425	C₂	semidirect
3. C₂×#11719418	C₂	semidirect
4. C₂×#11719423	C₂	semidirect
5. C₂×#11719511	C₂	semidirect
6. C₂×#11719422	C₂	semidirect
7. C₂×D₄×C₂²⋊D₁₃	C₂	semidirect
8. C₂×#11719424	C₂	semidirect
9. C₂×#11719420	C₂	semidirect
10. C₂×#11719509	C₂	semidirect
11. C₂×#11719184	C₂	semidirect
12. C₂²×C₁₃×#127	C₂	semidirect
13. C₂³×D₄×C₁₃	C₂²	semidirect
14. C₂³×D₄×C₁₃	C₂²	semidirect
15. C₂³×C₂²⋊D₁₃	C₂²	semidirect
16. C₂²×#6129	C₂²	semidirect
17. C₂²×D₄×D₁₃	C₂²	semidirect
19. C₂×C₁₃×#127	C₂²	semidirect
20. C₂×C₁₃×#127	C₂²	semidirect
21. C₂×C₁₃×#127	C₂²	semidirect
22. C₂×C₁₃×#127	C₂²	semidirect
23. C₂²×C₄²×C₁₃	C₂²	semidirect
24. C₂×#88207	C₂²	semidirect
25. C₂²×C₂²⋊Dic₁₃	C₂²	semidirect
26. #11719511	C₂²	semidirect
27. #11719509	C₂²	semidirect
28. C₂×#88194	C₂²	semidirect
29. C₂×#88193	C₂²	semidirect
30. C₂×#88193	C₂²	semidirect
31. C₂×#88193	C₂²	semidirect
32. C₂×#88193	C₂²	semidirect
33. D₄×C₂²⋊D₁₃	C₂²	semidirect
34. C₂×#88192	C₂²	semidirect
35. C₂×#88192	C₂²	semidirect
36. C₂×#88191	C₂²	semidirect
37. C₂×#88191	C₂²	semidirect
38. C₂×#88191	C₂²	semidirect
39. C₂×#88190	C₂²	semidirect
40. C₂×#88189	C₂²	semidirect
41. C₂×#88189	C₂²	semidirect
42. C₂×#88189	C₂²	semidirect
43. C₂×D₄×Dic₁₃	C₂²	semidirect
44. C₂×D₄×Dic₁₃	C₂²	semidirect
46. C₂×#88183	C₂²	semidirect
47. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
48. C₂×#88178	C₂²	semidirect
49. #11719425	C₂²	semidirect
50. #11719424	C₂²	semidirect
51. #11719423	C₂²	semidirect
52. #11719422	C₂²	semidirect
53. #11719420	C₂²	semidirect
54. #11719418	C₂²	semidirect
55. #11719184	C₂²	semidirect
56. C₂×#88130	C₂²	semidirect
57. C₂×#88129	C₂²	semidirect
58. C₂×C₄×D₅₂	C₂²	semidirect
59. C₂×#88126	C₂²	semidirect
60. C₂×#88124	C₂²	semidirect
61. C₂×C₄×Dic₂₆	C₂²	semidirect
72. C₂²×D₄×C₁₃	C₂³	semidirect
73. C₂²×D₄×C₁₃	C₂³	semidirect
81. C₂²×C₂²⋊D₁₃	C₂³	semidirect
85. C₂×#6129	C₂³	semidirect
87. C₂×D₄×D₁₃	C₂³	semidirect
92. C₁₃×#127	C₂³	semidirect
93. C₁₃×#127	C₂³	semidirect
94. C₁₃×#127	C₂³	semidirect
98. C₂×C₄²×C₁₃	C₂³	semidirect
99. #88207	C₂³	semidirect
105. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
106. #88194	C₂³	semidirect
107. #88193	C₂³	semidirect
108. #88193	C₂³	semidirect
109. #88193	C₂³	semidirect
110. #88193	C₂³	semidirect
111. #88192	C₂³	semidirect
112. #88192	C₂³	semidirect
113. #88191	C₂³	semidirect
114. #88191	C₂³	semidirect
115. #88191	C₂³	semidirect
116. #88190	C₂³	semidirect
117. #88189	C₂³	semidirect
118. #88189	C₂³	semidirect
119. #88189	C₂³	semidirect
120. D₄×Dic₁₃	C₂³	semidirect
121. D₄×Dic₁₃	C₂³	semidirect
123. #88183	C₂³	semidirect
124. C₄×C₂²⋊D₁₃	C₂³	semidirect
131. #88178	C₂³	semidirect
137. #88130	C₂³	semidirect
138. #88129	C₂³	semidirect
139. C₄×D₅₂	C₂³	semidirect
140. #88126	C₂³	semidirect
141. #88124	C₂³	semidirect
142. C₄×Dic₂₆	C₂³	semidirect
229. C₂²×#127	D₁₃	semidirect
285. C₂³×D₄	C₂×D₁₃	semidirect
286. C₂³×D₄	C₂×D₁₃	semidirect
298. C₂×#127	C₂×D₁₃	semidirect
299. C₂×#127	C₂×D₁₃	semidirect
300. C₂×#127	C₂×D₁₃	semidirect
301. C₂×#127	C₂×D₁₃	semidirect
330. C₂²×C₄²	C₂×D₁₃	semidirect
378. C₂²×D₄	C₂²×D₁₃	semidirect
379. C₂²×D₄	C₂²×D₁₃	semidirect
387. #127	C₂²×D₁₃	semidirect
388. #127	C₂²×D₁₃	semidirect
389. #127	C₂²×D₁₃	semidirect
436. C₂×C₄²	C₂²×D₁₃	semidirect
440. C₂×C₁₃	#3543	semidirect
519. C₁₃	C₂×#3543	semidirect
600. C₂	#13129169	direct (N × H)

Maximal subgroups

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

subgroup	index
#13129169	2
C₂×#11719425	2
C₂×#11719418	2
C₂×#11719423	2
C₂×#11719511	2
C₂×#11719422	2
C₂×D₄×C₂²⋊D₁₃	2
C₂×#11719424	2
C₂×#11719420	2
C₂×#11719509	2
C₂×#11719184	2
C₂²×C₁₃×#127	2
C₂×#3543	13

Subgroups — C2×#13129169 #16770512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129169 #16770512