Subgroups — C₂×#13128713 #16771280

Order 3328.

8622 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128713	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719290	C₂	1	4	yes	maximal, complemented
3	C₂×#11719282	C₂	1	4	yes	maximal, complemented
4	C₂×#11719335	C₂	1	8	yes	maximal, complemented
5	C₂×#11719403	C₂	1	4	yes	maximal, complemented
6	C₂×#11719230	C₂	1	2	yes	maximal, complemented
7	C₂×#11719430	C₂	1	4	yes	maximal, complemented
8	C₂²×#88128	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#11719226	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×#6127	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#6131	C₂²	1	8	yes	complemented
13	C₂²×#6127	C₂²	1	1	yes	characteristic
14	C₂³×D₅₂	C₂²	1	2	yes	—
15	C₂³×D₅₂	C₂²	1	4	yes	—
16	C₁₃×#533	C₂²	1	16	yes	complemented
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
18	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	—
20	C₂×C₄×Q₈×C₁₃	C₂²	1	4	yes	complemented
21	C₂×C₁₃×#117	C₂²	1	2	yes	—
22	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×#88201	C₂²	1	8	yes	complemented
24	C₂×C₄×C₂²⋊D₁₃	C₂²	1	4	yes	—
25	C₂×#88180	C₂²	1	1	yes	characteristic
26	#11719430	C₂²	1	64	yes	complemented
27	#11719403	C₂²	1	64	yes	complemented
28	#11719335	C₂²	1	128	yes	complemented
29	#11719290	C₂²	1	64	yes	complemented
30	#11719282	C₂²	1	64	yes	complemented
31	#11719230	C₂²	1	32	yes	complemented
32	#11719226	C₂²	1	32	yes	complemented
33	C₂×#88149	C₂²	1	16	yes	complemented
34	C₂×#88149	C₂²	1	8	yes	complemented
35	C₂×#88149	C₂²	1	8	yes	complemented
36	C₂×#88148	C₂²	1	16	yes	complemented
37	C₂×#88147	C₂²	1	8	yes	complemented
38	C₂×#88147	C₂²	1	8	yes	complemented
39	C₂×#88136	C₂²	1	8	yes	—
40	C₂×C₂²⋊C₄×D₁₃	C₂²	1	8	yes	—
41	C₂×#88129	C₂²	1	4	yes	complemented
42	C₂×#88128	C₂²	1	2	yes	—
43	C₂×#88128	C₂²	1	4	yes	—
44	C₂×#88128	C₂²	1	2	yes	—
45	C₂×#88128	C₂²	1	16	yes	complemented
46	C₂×#88128	C₂²	1	4	yes	complemented
47	C₄×#6127	C₂²	1	16	yes	complemented
48	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
49	C₂×C₄×D₅₂	C₂²	1	8	yes	complemented
50	C₂×#88126	C₂²	1	2	yes	complemented
51	C₂×C₄²×D₁₃	C₂²	1	2	yes	complemented
52	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
53	C₂⁴×D₁₃	C₂³	1	4	yes	—
54	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₂²⋊D₁₃	C₂³	1	2	yes	—
58	C₂×#6131	—	4	32	no	—
59	C₂×#6131	C₂³	1	64	yes	complemented
60	C₂×#6127	—	2	8	no	—
61	C₂×#6127	C₂³	1	8	yes	—
62	C₂²×D₅₂	—	2	16	no	—
63	C₂²×D₅₂	—	4	16	no	—
64	C₂²×D₅₂	C₂³	1	4	yes	—
65	C₂²×D₅₂	C₂³	1	1	yes	characteristic
66	C₂²×D₅₂	C₂³	1	4	yes	—
67	C₂²×D₅₂	C₂³	1	8	yes	—
68	C₂²×D₅₂	C₂³	1	16	yes	—
69	C₂²×D₅₂	C₂³	1	8	yes	—
70	C₂²×D₅₂	C₂³	1	32	yes	—
71	C₂²×D₅₂	C₂³	1	16	yes	—
72	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
73	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
74	C₂²×C₄×D₁₃	C₂³	1	16	yes	—
75	C₂²×Dic₂₆	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
77	C₁₃×#125	C₂³	1	16	yes	complemented
78	C₁₃×C₂²⋊Q₈	C₂³	1	32	yes	—
79	C₄×Q₈×C₁₃	C₂³	1	32	yes	complemented
80	C₁₃×#117	C₂³	1	16	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
84	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
85	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
89	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
90	C₂×C₂²⋊Dic₁₃	C₂³	1	2	yes	—
91	#88201	C₂³	1	64	yes	complemented
92	C₄×C₂²⋊D₁₃	C₂³	1	32	yes	—
93	C₂×#6103	C₂³	1	4	yes	—
94	C₂×#6103	C₂³	1	16	yes	—
95	C₂×#6103	C₂³	1	16	yes	—
96	#88180	C₂³	1	8	yes	—
97	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
98	C₂×#6101	C₂³	1	4	yes	—
99	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
100	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
101	#88149	C₂³	1	64	yes	complemented
102	#88149	C₂³	1	64	yes	complemented
103	#88149	C₂³	1	128	yes	complemented
104	#88148	C₂³	1	128	yes	complemented
105	#88147	C₂³	1	64	yes	complemented
106	#88147	C₂³	1	64	yes	complemented
107	#88136	C₂³	1	64	yes	—
108	C₂²⋊C₄×D₁₃	C₂³	1	64	yes	—
109	#88129	C₂³	1	32	yes	complemented
110	#88128	C₂³	1	16	yes	—
111	#88128	C₂³	1	32	yes	—
112	#88128	C₂³	1	16	yes	—
113	#88128	C₂³	1	32	yes	complemented
114	C₄×D₅₂	C₂³	1	16	yes	complemented
115	C₄×D₅₂	C₂³	1	64	yes	complemented
116	#88126	C₂³	1	16	yes	complemented
117	C₄²×D₁₃	C₂³	1	16	yes	complemented
118	C₄×Dic₂₆	C₂³	1	16	yes	complemented
119	C₂×#3508	—	13	1	no	maximal, Sylow
120	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₂³×D₁₃	—	2	16	no	—
122	C₂³×D₁₃	—	4	16	no	—
123	C₂³×D₁₃	C₂⁴	1	8	yes	—
124	C₂³×D₁₃	C₂⁴	1	2	yes	—
125	C₂³×D₁₃	C₂⁴	1	16	yes	—
126	C₂×Q₈×C₁₃	—	2	16	no	—
127	C₂×Q₈×C₁₃	C₂⁴	1	16	yes	—
128	C₂²×C₄×C₁₃	—	2	8	no	—
129	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
130	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
137	C₂×C₂²⋊D₁₃	—	2	8	no	—
138	C₂×C₂²⋊D₁₃	C₂⁴	1	8	yes	—
139	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
140	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
141	#6131	—	4	128	no	—
142	#6127	—	2	32	no	—
143	C₂×D₅₂	—	2	16	no	—
144	C₂×D₅₂	—	2	16	no	—
145	C₂×D₅₂	—	2	4	no	—
146	C₂×D₅₂	—	2	64	no	—
147	C₂×D₅₂	—	2	32	no	—
148	C₂×D₅₂	—	4	64	no	—
149	C₂×D₅₂	—	4	16	no	—
150	C₂×D₅₂	—	4	32	no	—
151	C₂×D₅₂	C₂⁴	1	16	yes	—
152	C₂×D₅₂	C₂⁴	1	4	yes	—
153	C₂×D₅₂	C₂⁴	1	16	yes	—
154	C₂×D₅₂	C₂⁴	1	32	yes	—
155	C₂×D₅₂	C₂⁴	1	32	yes	—
156	C₂×D₅₂	C₂⁴	1	64	yes	—
157	C₂×C₄×D₁₃	—	2	8	no	—
158	C₂×C₄×D₁₃	—	2	16	no	—
159	C₂×C₄×D₁₃	—	4	32	no	—
160	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
161	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
162	C₂×C₄×D₁₃	C₂⁴	1	64	yes	—
163	C₂×Dic₂₆	—	2	4	no	—
164	C₂×Dic₂₆	C₂⁴	1	4	yes	—
165	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
166	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
167	C₁₃×C₄⋊C₄	C₂⁴	1	32	yes	—
168	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
169	C₄²×C₁₃	C₂⁴	1	8	yes	—
170	C₄²×C₁₃	C₂⁴	1	4	yes	—
171	C₄²×C₁₃	C₂⁴	1	4	yes	—
172	C₄²×C₁₃	C₂⁴	1	16	yes	—
173	C₂²⋊Dic₁₃	C₂⁴	1	8	yes	—
174	#6103	C₂⁴	1	16	yes	—
175	#6103	C₂⁴	1	64	yes	—
176	#6103	C₂⁴	1	64	yes	—
177	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
178	#6101	C₂⁴	1	16	yes	—
179	C₄×Dic₁₃	C₂⁴	1	16	yes	—
180	C₄×Dic₁₃	C₂⁴	1	8	yes	—
181	#3508	—	13	32	no	—
182	C₂×#559	—	13	4	no	—
183	C₂×#550	—	13	4	no	—
184	C₂×#546	—	13	8	no	—
185	C₂×#540	—	13	4	no	—
186	C₂×#535	—	13	2	no	—
187	C₂×#533	D₁₃	1	1	yes	characteristic, complemented
188	C₂×#532	—	13	4	no	—
189	C₂²×#127	—	13	1	no	—
190	C₂×#518	—	13	2	no	—
191	C₂×C₄×#41	—	13	1	no	—
192	C₂³×C₁₃	—	2	4	no	—
193	C₂³×C₁₃	C₂×#41	1	4	yes	—
194	C₂³×C₁₃	C₂⁵	1	2	yes	—
195	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
196	C₂²×D₁₃	—	2	4	no	—
197	C₂²×D₁₃	—	2	16	no	—
198	C₂²×D₁₃	—	2	8	no	—
199	C₂²×D₁₃	—	2	32	no	—
200	C₂²×D₁₃	—	2	32	no	—
201	C₂²×D₁₃	—	4	32	no	—
202	C₂²×D₁₃	—	8	32	no	—
203	C₂²×D₁₃	C₂⁵	1	16	yes	—
204	C₂²×D₁₃	C₂⁵	1	4	yes	—
205	Q₈×C₁₃	—	2	32	no	—
206	C₂×C₄×C₁₃	—	2	16	no	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	2	16	no	—
209	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
210	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
211	C₂×C₄×C₁₃	C₂×#41	1	16	yes	complemented
212	C₂×C₄×C₁₃	H(5,𝔽₂)	1	8	yes	—
213	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
214	C₂×C₄×C₁₃	C₂⁵	1	16	yes	—
215	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
216	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
217	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
218	C₂²⋊D₁₃	—	2	16	no	—
219	C₂×Dic₁₃	—	2	4	no	—
220	C₂×Dic₁₃	—	2	8	no	—
221	C₂×Dic₁₃	C₂⁵	1	4	yes	—
222	C₂×Dic₁₃	C₂⁵	1	8	yes	—
223	D₅₂	—	2	32	no	—
224	D₅₂	—	2	32	no	—
225	D₅₂	—	2	8	no	—
226	D₅₂	—	2	64	no	—
227	D₅₂	—	4	32	no	—
228	D₅₂	—	4	64	no	—
229	C₄×D₁₃	—	2	16	no	—
230	C₄×D₁₃	—	2	32	no	—
231	C₄×D₁₃	—	4	64	no	—
232	Dic₂₆	—	2	8	no	—
233	C₂²×#41	—	13	8	no	—
234	C₂²×#41	—	13	1	no	—
235	C₂³×D₄	—	13	2	no	—
236	C₂³×D₄	—	13	4	no	—
237	#559	—	13	64	no	—
238	#550	—	13	64	no	—
239	#546	—	13	128	no	—
240	#540	—	13	64	no	—
241	#535	—	13	32	no	—
242	#533	C₂×D₁₃	1	16	yes	complemented
243	#532	—	13	64	no	—
244	C₂×C₄⋊Q₈	C₂×D₁₃	1	2	yes	complemented
245	C₂×#127	—	13	2	no	—
246	C₂×#127	—	13	2	no	—
247	C₂×#127	—	13	4	no	—
248	C₂×#127	—	13	16	no	—
249	C₂×#127	—	13	4	no	—
250	C₂×#125	C₂×D₁₃	1	2	yes	complemented
251	C₂×#124	—	13	8	no	—
252	C₂×#124	—	13	4	no	—
253	C₂×#123	—	13	16	no	—
254	C₂×C₂²⋊Q₈	C₂×D₁₃	1	4	yes	—
255	C₂×#121	—	13	8	no	—
256	C₂×#121	—	13	8	no	—
257	C₂×#121	—	13	16	no	—
258	C₂×#120	—	13	8	no	—
259	#518	—	13	32	no	—
260	C₄×#41	—	13	16	no	—
261	C₂×C₄×Q₈	—	13	2	no	—
262	C₂×C₄×Q₈	C₂×D₁₃	1	4	yes	complemented
263	C₂×C₄×D₄	—	13	4	no	—
264	C₂×C₄×D₄	—	13	8	no	—
265	C₂×C₄×D₄	—	13	8	no	—
266	C₂×C₄×D₄	—	13	2	no	—
267	C₂×C₄×D₄	—	13	8	no	—
268	C₂×#117	—	13	1	no	—
269	C₂×#117	—	13	2	no	—
270	C₂×#117	C₂×D₁₃	1	2	yes	—
271	C₂²×C₂²⋊C₄	—	13	8	no	—
272	C₂²×C₄²	—	13	2	no	—
273	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
274	C₂²×C₁₃	—	2	4	no	—
275	C₂²×C₁₃	—	2	8	no	—
276	C₂²×C₁₃	C₂²×#41	1	4	yes	—
277	C₂²×C₁₃	C₂²×#41	1	2	yes	—
278	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
279	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
280	C₂×D₁₃	—	2	4	no	—
281	C₂×D₁₃	—	2	16	no	—
282	C₂×D₁₃	—	2	8	no	—
283	C₂×D₁₃	—	2	32	no	—
284	C₂×D₁₃	—	4	8	no	—
285	C₂×D₁₃	—	4	32	no	—
286	C₂×D₁₃	—	8	32	no	—
287	C₄×C₁₃	—	2	16	no	—
288	C₄×C₁₃	—	2	4	no	—
289	C₄×C₁₃	C₂²×#41	1	4	yes	—
290	C₄×C₁₃	C₂²×#41	1	4	yes	—
291	C₄×C₁₃	C₂×H(5,𝔽₂)	1	8	yes	—
292	Dic₁₃	—	2	4	no	—
293	Dic₁₃	—	2	8	no	—
294	C₂⁵	—	13	4	no	—
295	C₂×#41	—	13	64	no	—
296	C₂×#41	—	13	8	no	—
297	C₂×#41	—	26	8	no	—
298	C₂×#41	—	52	32	no	—
299	C₂²×Q₈	—	13	1	no	—
300	C₂²×Q₈	C₂²×D₁₃	1	4	yes	—
301	C₂²×D₄	—	13	2	no	—
302	C₂²×D₄	—	13	4	no	—
303	C₂²×D₄	—	13	4	no	—
304	C₂²×D₄	—	13	1	no	—
305	C₂²×D₄	—	13	8	no	—
306	C₂²×D₄	—	13	16	no	—
307	C₂²×D₄	—	13	16	no	—
308	C₂²×D₄	—	13	8	no	—
309	C₂²×D₄	—	13	32	no	—
310	C₂²×D₄	—	26	16	no	—
311	C₂²×D₄	—	52	16	no	—
312	C₂³×C₄	—	13	2	no	—
313	C₂³×C₄	—	13	4	no	—
314	C₂³×C₄	—	13	16	no	—
315	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
316	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
317	C₄⋊Q₈	C₂²×D₁₃	1	16	yes	complemented
318	#127	—	13	16	no	—
319	#127	—	13	16	no	—
320	#127	—	13	32	no	—
321	#127	—	13	32	no	—
322	#125	C₂²×D₁₃	1	16	yes	complemented
323	#124	—	13	64	no	—
324	#124	—	13	32	no	—
325	#123	—	13	128	no	—
326	C₂²⋊Q₈	C₂²×D₁₃	1	32	yes	—
327	#121	—	13	64	no	—
328	#121	—	13	64	no	—
329	#121	—	13	128	no	—
330	#120	—	13	64	no	—
331	C₄×Q₈	—	13	16	no	—
332	C₄×Q₈	C₂²×D₁₃	1	32	yes	complemented
333	C₄×D₄	—	13	32	no	—
334	C₄×D₄	—	13	64	no	—
335	C₄×D₄	—	13	64	no	—
336	C₄×D₄	—	13	16	no	—
337	C₄×D₄	—	13	64	no	—
338	#117	—	13	8	no	—
339	#117	—	13	16	no	—
340	#117	C₂²×D₁₃	1	16	yes	—
341	C₂×C₄⋊C₄	—	13	2	no	—
342	C₂×C₄⋊C₄	—	13	4	no	—
343	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
344	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
345	C₂×C₄⋊C₄	C₂²×D₁₃	1	8	yes	—
346	C₂×C₂²⋊C₄	—	13	2	no	—
347	C₂×C₂²⋊C₄	—	13	16	no	—
348	C₂×C₂²⋊C₄	—	13	4	no	—
349	C₂×C₂²⋊C₄	—	13	16	no	—
350	C₂×C₂²⋊C₄	—	13	64	no	—
351	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
352	C₂×C₄²	—	13	2	no	—
353	C₂×C₄²	—	13	4	no	—
354	C₂×C₄²	—	13	16	no	—
355	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
356	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
357	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
358	C₂×C₄²	C₂²×D₁₃	1	8	yes	—
359	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
360	C₂×C₁₃	—	2	4	no	—
361	C₂×C₁₃	#3508	1	4	yes	complemented
362	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
363	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
364	D₁₃	—	4	4	no	—
365	D₁₃	—	4	16	no	—
366	C₂⁴	—	13	8	no	—
367	C₂⁴	—	13	2	no	—
368	C₂⁴	—	13	16	no	—
369	C₂⁴	—	26	16	no	—
370	C₂⁴	—	52	16	no	—
371	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
372	#41	—	26	32	no	—
373	#41	—	52	128	no	—
374	C₂×Q₈	—	2	16	no	—
375	C₂×Q₈	—	13	4	no	—
376	C₂×Q₈	—	26	4	no	—
377	C₂×Q₈	C₂³×D₁₃	1	16	yes	—
378	C₂×D₄	—	13	8	no	—
379	C₂×D₄	—	13	16	no	—
380	C₂×D₄	—	13	16	no	—
381	C₂×D₄	—	13	4	no	—
382	C₂×D₄	—	13	32	no	—
383	C₂×D₄	—	13	64	no	—
384	C₂×D₄	—	13	32	no	—
385	C₂×D₄	—	26	8	no	—
386	C₂×D₄	—	26	16	no	—
387	C₂×D₄	—	26	16	no	—
388	C₂×D₄	—	26	4	no	—
389	C₂×D₄	—	26	64	no	—
390	C₂×D₄	—	26	32	no	—
391	C₂×D₄	—	52	64	no	—
392	C₂×D₄	—	52	16	no	—
393	C₂×D₄	—	52	32	no	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	13	2	no	—
396	C₂²×C₄	—	13	4	no	—
397	C₂²×C₄	—	13	8	no	—
398	C₂²×C₄	—	13	16	no	—
399	C₂²×C₄	—	13	64	no	—
400	C₂²×C₄	—	26	8	no	—
401	C₂²×C₄	—	26	16	no	—
402	C₂²×C₄	—	52	32	no	—
403	C₂²×C₄	#6131	1	8	yes	complemented
404	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
405	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
406	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
407	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
408	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
409	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
410	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
411	C₄⋊C₄	—	13	8	no	—
412	C₄⋊C₄	—	13	16	no	—
413	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
414	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
415	C₄⋊C₄	C₂³×D₁₃	1	32	yes	—
416	C₂²⋊C₄	—	13	8	no	—
417	C₂²⋊C₄	—	13	64	no	—
418	C₂²⋊C₄	—	13	16	no	—
419	C₂²⋊C₄	—	13	64	no	—
420	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
421	C₄²	—	13	8	no	—
422	C₄²	—	13	16	no	—
423	C₄²	C₂³×D₁₃	1	4	yes	—
424	C₄²	C₂³×D₁₃	1	4	yes	—
425	C₄²	C₂³×D₁₃	1	8	yes	—
426	C₄²	C₂³×D₁₃	1	16	yes	—
427	C₁₃	C₂×#3508	1	1	yes	characteristic, complemented, Sylow
428	C₂³	—	2	4	no	—
429	C₂³	—	13	16	no	—
430	C₂³	—	13	4	no	—
431	C₂³	—	26	4	no	—
432	C₂³	—	26	16	no	—
433	C₂³	—	26	8	no	—
434	C₂³	—	26	32	no	—
435	C₂³	—	26	32	no	—
436	C₂³	—	52	32	no	—
437	C₂³	—	104	32	no	—
438	C₂³	C₂×#6131	1	4	yes	—
439	C₂³	C₂⁴×D₁₃	1	2	yes	—
440	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
441	Q₈	—	2	32	no	—
442	Q₈	—	26	8	no	—
443	D₄	—	26	16	no	—
444	D₄	—	26	32	no	—
445	D₄	—	26	32	no	—
446	D₄	—	26	8	no	—
447	D₄	—	26	64	no	—
448	D₄	—	52	32	no	—
449	D₄	—	52	64	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	16	no	—
452	C₂×C₄	—	2	16	no	—
453	C₂×C₄	—	13	4	no	—
454	C₂×C₄	—	13	8	no	—
455	C₂×C₄	—	26	4	no	—
456	C₂×C₄	—	26	8	no	—
457	C₂×C₄	—	26	16	no	—
458	C₂×C₄	—	26	32	no	—
459	C₂×C₄	—	52	64	no	—
460	C₂×C₄	C₂×#6131	1	4	yes	—
461	C₂×C₄	C₂×#6131	1	4	yes	—
462	C₂×C₄	C₂×#6131	1	16	yes	complemented
463	C₂×C₄	#88256	1	8	yes	—
464	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
465	C₂×C₄	C₂⁴×D₁₃	1	16	yes	—
466	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
467	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
468	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
469	C₂²	—	2	8	no	—
470	C₂²	—	2	4	no	—
471	C₂²	—	26	4	no	—
472	C₂²	—	26	16	no	—
473	C₂²	—	26	8	no	—
474	C₂²	—	26	32	no	—
475	C₂²	—	52	8	no	—
476	C₂²	—	52	32	no	—
477	C₂²	—	104	32	no	—
478	C₂²	C₂²×#6131	1	4	yes	—
479	C₂²	C₂²×#6131	1	2	yes	—
480	C₂²	C₂×#88256	1	4	yes	—
481	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
482	C₄	—	2	4	no	—
483	C₄	—	2	16	no	—
484	C₄	—	26	4	no	—
485	C₄	—	26	8	no	—
486	C₄	C₂²×#6131	1	4	yes	—
487	C₄	C₂²×#6131	1	4	yes	—
488	C₄	C₂×#88256	1	8	yes	—
489	C₂	—	2	4	no	—
490	C₂	—	52	16	no	—
491	C₂	—	52	4	no	—
492	C₂	#13128713	1	4	yes	direct product factor
493	C₂	C₂³×#6131	1	1	yes	characteristic
494	C₂	C₂²×#88256	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₁₃×#533	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×#533	D₁₃
hypocenter	C₁₃	C₂×#3508
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
1. #13128713	C₂	direct (N × H)
2. C₂×#11719290	C₂	semidirect
3. C₂×#11719282	C₂	semidirect
4. C₂×#11719335	C₂	semidirect
5. C₂×#11719403	C₂	semidirect
6. C₂×#11719230	C₂	semidirect
7. C₂×#11719430	C₂	semidirect
8. C₂²×#88128	C₂	semidirect
9. C₂×#11719226	C₂	semidirect
10. C₂×C₄×#6127	C₂	semidirect
11. C₂×C₁₃×#533	C₂	semidirect
12. C₂²×#6131	C₂²	semidirect
16. C₁₃×#533	C₂²	semidirect
17. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
18. C₂×C₁₃×#125	C₂²	semidirect
20. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
23. C₂×#88201	C₂²	semidirect
26. #11719430	C₂²	semidirect
27. #11719403	C₂²	semidirect
28. #11719335	C₂²	semidirect
29. #11719290	C₂²	semidirect
30. #11719282	C₂²	semidirect
31. #11719230	C₂²	semidirect
32. #11719226	C₂²	semidirect
33. C₂×#88149	C₂²	semidirect
34. C₂×#88149	C₂²	semidirect
35. C₂×#88149	C₂²	semidirect
36. C₂×#88148	C₂²	semidirect
37. C₂×#88147	C₂²	semidirect
38. C₂×#88147	C₂²	semidirect
41. C₂×#88129	C₂²	semidirect
45. C₂×#88128	C₂²	semidirect
46. C₂×#88128	C₂²	semidirect
47. C₄×#6127	C₂²	semidirect
48. C₂×C₄×D₅₂	C₂²	semidirect
49. C₂×C₄×D₅₂	C₂²	semidirect
50. C₂×#88126	C₂²	semidirect
51. C₂×C₄²×D₁₃	C₂²	semidirect
52. C₂×C₄×Dic₂₆	C₂²	semidirect
59. C₂×#6131	C₂³	semidirect
76. C₁₃×C₄⋊Q₈	C₂³	semidirect
77. C₁₃×#125	C₂³	semidirect
79. C₄×Q₈×C₁₃	C₂³	semidirect
91. #88201	C₂³	semidirect
101. #88149	C₂³	semidirect
102. #88149	C₂³	semidirect
103. #88149	C₂³	semidirect
104. #88148	C₂³	semidirect
105. #88147	C₂³	semidirect
106. #88147	C₂³	semidirect
109. #88129	C₂³	semidirect
113. #88128	C₂³	semidirect
114. C₄×D₅₂	C₂³	semidirect
115. C₄×D₅₂	C₂³	semidirect
116. #88126	C₂³	semidirect
117. C₄²×D₁₃	C₂³	semidirect
118. C₄×Dic₂₆	C₂³	semidirect
129. C₂²×C₄×C₁₃	#41	semidirect
187. C₂×#533	D₁₃	semidirect
211. C₂×C₄×C₁₃	C₂×#41	semidirect
242. #533	C₂×D₁₃	semidirect
244. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
250. C₂×#125	C₂×D₁₃	semidirect
262. C₂×C₄×Q₈	C₂×D₁₃	semidirect
317. C₄⋊Q₈	C₂²×D₁₃	semidirect
322. #125	C₂²×D₁₃	semidirect
332. C₄×Q₈	C₂²×D₁₃	semidirect
361. C₂×C₁₃	#3508	semidirect
403. C₂²×C₄	#6131	semidirect
427. C₁₃	C₂×#3508	semidirect
462. C₂×C₄	C₂×#6131	semidirect
492. C₂	#13128713	direct (N × H)

Maximal subgroups

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

subgroup	index
#13128713	2
C₂×#11719290	2
C₂×#11719282	2
C₂×#11719335	2
C₂×#11719403	2
C₂×#11719230	2
C₂×#11719430	2
C₂²×#88128	2
C₂×#11719226	2
C₂×C₄×#6127	2
C₂×C₁₃×#533	2
C₂×#3508	13

Subgroups — C2×#13128713 #16771280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128713 #16771280