Subgroups — C₂×#13128690 #16770875

Order 3328.

7994 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128690	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719290	C₂	1	4	yes	maximal, complemented
3	C₂×#11719289	C₂	1	2	yes	maximal, complemented
4	C₂×#11719439	C₂	1	2	yes	maximal, complemented
5	C₂×#11719400	C₂	1	4	yes	maximal, complemented
6	C₂×#11719282	C₂	1	2	yes	maximal, complemented
7	C₂×#11719431	C₂	1	2	yes	maximal, complemented
8	C₂×#11719349	C₂	1	4	yes	maximal, complemented
9	C₂×#11719230	C₂	1	2	yes	maximal, complemented
10	C₂×#11719182	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#11719332	C₂	1	4	yes	maximal, complemented
12	C₂×#11719228	C₂	1	2	yes	maximal, complemented
13	C₂²×C₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#6131	C₂²	1	4	yes	complemented
16	C₂²×#6127	C₂²	1	2	yes	—
17	C₂³×D₅₂	C₂²	1	1	yes	characteristic
18	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
19	C₁₃×#533	C₂²	1	16	yes	complemented
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₃×#125	C₂²	1	2	yes	complemented
23	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
26	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#117	C₂²	1	2	yes	—
28	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×#88201	C₂²	1	8	yes	complemented
30	C₂×#88200	C₂²	1	4	yes	complemented
31	C₂×#88184	C₂²	1	2	yes	—
32	C₂×#88184	C₂²	1	2	yes	—
33	C₂²×#6103	C₂²	1	2	yes	—
34	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
35	#11719439	C₂²	1	32	yes	complemented
36	#11719431	C₂²	1	32	yes	complemented
37	#11719400	C₂²	1	64	yes	complemented
38	#11719349	C₂²	1	64	yes	complemented
39	#11719332	C₂²	1	64	yes	complemented
40	#11719290	C₂²	1	64	yes	complemented
41	#11719289	C₂²	1	32	yes	complemented
42	#11719282	C₂²	1	32	yes	complemented
43	#11719230	C₂²	1	32	yes	complemented
44	#11719228	C₂²	1	32	yes	complemented
45	C₂×#88152	C₂²	1	8	yes	complemented
46	C₂×#88149	C₂²	1	4	yes	—
47	C₂×#88149	C₂²	1	4	yes	—
48	C₂×#88149	C₂²	1	4	yes	complemented
49	C₂×#88149	C₂²	1	8	yes	complemented
50	C₂×#88148	C₂²	1	8	yes	complemented
51	C₂×#88148	C₂²	1	8	yes	complemented
52	C₂×#88147	C₂²	1	8	yes	complemented
53	C₂×#88146	C₂²	1	4	yes	complemented
54	C₂×#88146	C₂²	1	4	yes	complemented
55	C₂×C₄⋊C₄×D₁₃	C₂²	1	4	yes	complemented
56	C₂×#88136	C₂²	1	8	yes	—
57	C₂×#88135	C₂²	1	8	yes	—
58	#11719182	C₂²	1	16	yes	complemented
59	C₂×#88129	C₂²	1	4	yes	—
60	C₂×#88129	C₂²	1	2	yes	complemented
61	C₂×#88128	C₂²	1	4	yes	—
62	C₂×#88128	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₄×D₅₂	C₂²	1	2	yes	—
64	C₂×C₄×D₅₂	C₂²	1	2	yes	—
65	C₂×C₄×D₅₂	C₂²	1	2	yes	—
66	C₂×C₄×D₅₂	C₂²	1	2	yes	—
67	C₂×C₄×D₅₂	C₂²	1	16	yes	complemented
68	C₂×C₄×D₅₂	C₂²	1	4	yes	complemented
69	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
70	C₂×C₄×D₅₂	C₂²	1	2	yes	complemented
71	C₂×#88123	C₂²	1	1	yes	characteristic, complemented
72	C₂×C₄×Dic₂₆	C₂²	1	4	yes	complemented
73	C₂⁴×D₁₃	C₂³	1	2	yes	—
74	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
75	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
80	C₂³×Dic₁₃	C₂³	1	2	yes	—
81	C₂×#6131	—	4	16	no	—
82	C₂×#6131	C₂³	1	32	yes	complemented
83	C₂×#6127	—	2	16	no	—
84	C₂×#6127	C₂³	1	16	yes	—
85	C₂²×D₅₂	—	2	8	no	—
86	C₂²×D₅₂	C₂³	1	2	yes	—
87	C₂²×D₅₂	C₂³	1	2	yes	—
88	C₂²×D₅₂	C₂³	1	2	yes	—
89	C₂²×D₅₂	C₂³	1	8	yes	—
90	C₂²×D₅₂	C₂³	1	2	yes	—
91	C₂²×D₅₂	C₂³	1	2	yes	—
92	C₂²×D₅₂	C₂³	1	8	yes	—
93	C₂²×D₅₂	C₂³	1	8	yes	—
94	C₂²×C₄×D₁₃	—	4	8	no	—
95	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
96	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
97	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
98	C₂²×C₄×D₁₃	C₂³	1	16	yes	—
99	C₂²×C₄×D₁₃	C₂³	1	8	yes	—
100	C₂²×Dic₂₆	C₂³	1	2	yes	—
101	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
102	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
103	C₁₃×#125	C₂³	1	16	yes	complemented
104	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
105	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	—
106	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
107	C₄×Q₈×C₁₃	C₂³	1	16	yes	complemented
108	C₁₃×#117	C₂³	1	16	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
115	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
116	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
117	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
122	#88201	C₂³	1	64	yes	complemented
123	#88200	C₂³	1	32	yes	complemented
124	#88184	C₂³	1	16	yes	—
125	#88184	C₂³	1	16	yes	—
126	C₂×#6103	C₂³	1	4	yes	—
127	C₂×#6103	C₂³	1	4	yes	—
128	C₂×#6103	C₂³	1	16	yes	—
129	C₂×#6103	C₂³	1	4	yes	—
130	C₂×#6103	C₂³	1	4	yes	—
131	C₂×#6103	C₂³	1	8	yes	—
132	C₂×#6103	C₂³	1	8	yes	—
133	C₂×#6103	C₂³	1	8	yes	—
134	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
135	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
136	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
137	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
138	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	—
139	C₂×#6101	C₂³	1	8	yes	—
140	C₂×C₄×Dic₁₃	C₂³	1	8	yes	—
141	#88152	C₂³	1	64	yes	complemented
142	#88149	C₂³	1	32	yes	—
143	#88149	C₂³	1	32	yes	—
144	#88149	C₂³	1	32	yes	complemented
145	#88149	C₂³	1	64	yes	complemented
146	#88148	C₂³	1	64	yes	complemented
147	#88148	C₂³	1	64	yes	complemented
148	#88147	C₂³	1	64	yes	complemented
149	#88146	C₂³	1	32	yes	complemented
150	#88146	C₂³	1	32	yes	complemented
151	C₄⋊C₄×D₁₃	C₂³	1	32	yes	complemented
152	#88136	C₂³	1	64	yes	—
153	#88135	C₂³	1	64	yes	—
154	#88129	C₂³	1	32	yes	—
155	#88129	C₂³	1	16	yes	complemented
156	#88128	C₂³	1	32	yes	—
157	#88128	C₂³	1	8	yes	complemented
158	C₄×D₅₂	C₂³	1	16	yes	—
159	C₄×D₅₂	C₂³	1	16	yes	—
160	C₄×D₅₂	C₂³	1	16	yes	—
161	C₄×D₅₂	C₂³	1	16	yes	—
162	C₄×D₅₂	C₂³	1	16	yes	complemented
163	C₄×D₅₂	C₂³	1	16	yes	complemented
164	C₄×D₅₂	C₂³	1	32	yes	complemented
165	#88123	C₂³	1	8	yes	complemented
166	C₄×Dic₂₆	C₂³	1	32	yes	complemented
167	C₂×#3506	—	13	1	no	maximal, Sylow
168	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
169	C₂³×D₁₃	—	2	8	no	—
170	C₂³×D₁₃	—	4	4	no	—
171	C₂³×D₁₃	—	4	4	no	—
172	C₂³×D₁₃	C₂⁴	1	4	yes	—
173	C₂³×D₁₃	C₂⁴	1	4	yes	—
174	C₂³×D₁₃	C₂⁴	1	8	yes	—
175	C₂×Q₈×C₁₃	—	2	8	no	—
176	C₂×Q₈×C₁₃	—	4	4	no	—
177	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
178	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
179	C₂²×C₄×C₁₃	—	2	4	no	—
180	C₂²×C₄×C₁₃	—	4	2	no	—
181	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
182	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
188	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
192	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
193	C₂×C₂²⋊D₁₃	—	2	16	no	—
194	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
195	C₂²×Dic₁₃	—	4	4	no	—
196	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
197	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
198	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
199	#6131	—	4	64	no	—
200	#6127	—	2	64	no	—
201	C₂×D₅₂	—	2	8	no	—
202	C₂×D₅₂	—	2	8	no	—
203	C₂×D₅₂	—	2	8	no	—
204	C₂×D₅₂	—	2	32	no	—
205	C₂×D₅₂	—	2	8	no	—
206	C₂×D₅₂	—	4	4	no	—
207	C₂×D₅₂	—	4	16	no	—
208	C₂×D₅₂	—	4	16	no	—
209	C₂×D₅₂	C₂⁴	1	8	yes	—
210	C₂×D₅₂	C₂⁴	1	8	yes	—
211	C₂×D₅₂	C₂⁴	1	8	yes	—
212	C₂×D₅₂	C₂⁴	1	8	yes	—
213	C₂×D₅₂	C₂⁴	1	8	yes	—
214	C₂×D₅₂	C₂⁴	1	32	yes	—
215	C₂×D₅₂	C₂⁴	1	32	yes	—
216	C₂×C₄×D₁₃	—	2	16	no	—
217	C₂×C₄×D₁₃	—	2	16	no	—
218	C₂×C₄×D₁₃	—	4	32	no	—
219	C₂×C₄×D₁₃	—	4	8	no	—
220	C₂×C₄×D₁₃	—	4	16	no	—
221	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
222	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
223	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
224	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
225	C₂×Dic₂₆	—	2	8	no	—
226	C₂×Dic₂₆	C₂⁴	1	8	yes	—
227	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
228	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
229	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
230	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
231	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
232	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
233	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
234	C₄²×C₁₃	C₂⁴	1	16	yes	—
235	C₄²×C₁₃	C₂⁴	1	4	yes	—
236	C₄²×C₁₃	C₂⁴	1	4	yes	—
237	C₄²×C₁₃	C₂⁴	1	4	yes	—
238	C₄²×C₁₃	C₂⁴	1	4	yes	—
239	#6103	C₂⁴	1	16	yes	—
240	#6103	C₂⁴	1	16	yes	—
241	#6103	C₂⁴	1	16	yes	—
242	#6103	C₂⁴	1	16	yes	—
243	#6103	C₂⁴	1	32	yes	—
244	#6103	C₂⁴	1	32	yes	—
245	#6103	C₂⁴	1	32	yes	—
246	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
247	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
248	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
249	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
250	#6101	C₂⁴	1	32	yes	—
251	C₄×Dic₁₃	C₂⁴	1	32	yes	—
252	#3506	—	13	32	no	—
253	C₂×#559	—	13	4	no	—
254	C₂×#556	—	13	2	no	—
255	C₂×#555	—	13	2	no	—
256	C₂×#553	—	13	4	no	—
257	C₂×#550	—	13	2	no	—
258	C₂×#547	—	13	2	no	—
259	C₂×#538	—	13	4	no	—
260	C₂×#535	—	13	2	no	—
261	C₂×#533	D₁₃	1	1	yes	characteristic, complemented
262	C₂×#532	—	13	1	no	—
263	C₂×#525	—	13	4	no	—
264	C₂×#520	—	13	2	no	—
265	C₂²×C₄×D₄	—	13	1	no	—
266	C₂³×C₁₃	—	2	2	no	—
267	C₂³×C₁₃	—	2	2	no	—
268	C₂³×C₁₃	C₂×#41	1	4	yes	—
269	C₂³×C₁₃	C₂⁵	1	2	yes	—
270	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
271	C₂²×D₁₃	—	2	8	no	—
272	C₂²×D₁₃	—	2	16	no	—
273	C₂²×D₁₃	—	2	8	no	—
274	C₂²×D₁₃	—	2	8	no	—
275	C₂²×D₁₃	—	2	8	no	—
276	C₂²×D₁₃	—	2	8	no	—
277	C₂²×D₁₃	—	2	8	no	—
278	C₂²×D₁₃	—	4	8	no	—
279	C₂²×D₁₃	—	4	8	no	—
280	C₂²×D₁₃	—	4	32	no	—
281	C₂²×D₁₃	C₂⁵	1	8	yes	—
282	C₂²×D₁₃	C₂⁵	1	8	yes	—
283	Q₈×C₁₃	—	2	16	no	—
284	Q₈×C₁₃	—	4	8	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	8	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	2	8	no	—
289	C₂×C₄×C₁₃	—	2	2	no	—
290	C₂×C₄×C₁₃	—	2	8	no	—
291	C₂×C₄×C₁₃	—	4	4	no	—
292	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
293	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
294	C₂×C₄×C₁₃	C₂×#41	1	16	yes	complemented
295	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
296	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
297	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
298	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
299	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
300	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
301	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
302	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
303	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
304	C₂²⋊D₁₃	—	2	32	no	—
305	C₂×Dic₁₃	—	2	8	no	—
306	C₂×Dic₁₃	—	2	8	no	—
307	C₂×Dic₁₃	—	4	8	no	—
308	C₂×Dic₁₃	C₂⁵	1	8	yes	—
309	C₂×Dic₁₃	C₂⁵	1	8	yes	—
310	D₅₂	—	2	16	no	—
311	D₅₂	—	2	16	no	—
312	D₅₂	—	2	16	no	—
313	D₅₂	—	2	16	no	—
314	D₅₂	—	4	8	no	—
315	D₅₂	—	4	32	no	—
316	D₅₂	—	4	32	no	—
317	C₄×D₁₃	—	2	32	no	—
318	C₄×D₁₃	—	2	32	no	—
319	C₄×D₁₃	—	4	16	no	—
320	C₄×D₁₃	—	4	32	no	—
321	Dic₂₆	—	2	16	no	—
322	C₂²×#41	—	13	4	no	—
323	C₂²×#41	—	13	2	no	—
324	C₂³×D₄	—	13	1	no	—
325	C₂⁴×C₄	—	13	2	no	—
326	#559	—	13	64	no	—
327	#556	—	13	32	no	—
328	#555	—	13	32	no	—
329	#553	—	13	64	no	—
330	#550	—	13	32	no	—
331	#547	—	13	32	no	—
332	#538	—	13	64	no	—
333	#535	—	13	32	no	—
334	#533	C₂×D₁₃	1	16	yes	complemented
335	#532	—	13	16	no	—
336	C₂×C₄⋊Q₈	—	13	1	no	—
337	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
338	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
339	C₂×#127	—	13	4	no	—
340	C₂×#127	—	13	1	no	—
341	C₂×#126	—	13	8	no	—
342	C₂×#125	C₂×D₁₃	1	2	yes	complemented
343	C₂×#124	—	13	8	no	—
344	C₂×#124	—	13	4	no	—
345	C₂×#124	—	13	2	no	—
346	#525	—	13	64	no	—
347	C₂×#123	—	13	8	no	—
348	C₂×#123	—	13	8	no	—
349	C₂×C₂²⋊Q₈	—	13	4	no	—
350	C₂×C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
351	C₂×C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
352	C₂×#121	—	13	2	no	—
353	C₂×#121	—	13	2	no	—
354	C₂×#121	—	13	4	no	—
355	C₂×#121	—	13	4	no	—
356	C₂×#121	—	13	4	no	—
357	C₂×#121	—	13	8	no	—
358	C₂×#120	—	13	8	no	—
359	#520	—	13	32	no	—
360	C₂×C₄×Q₈	—	13	4	no	—
361	C₂×C₄×Q₈	C₂×D₁₃	1	2	yes	complemented
362	C₂×C₄×Q₈	C₂×D₁₃	1	2	yes	complemented
363	C₂×C₄×D₄	—	13	8	no	—
364	C₂×C₄×D₄	—	13	8	no	—
365	C₂×C₄×D₄	—	13	2	no	—
366	C₂×C₄×D₄	—	13	2	no	—
367	C₂×C₄×D₄	—	13	2	no	—
368	C₂×C₄×D₄	—	13	2	no	—
369	C₂×C₄×D₄	—	13	16	no	—
370	C₂×C₄×D₄	—	13	4	no	—
371	C₂×C₄×D₄	—	13	2	no	—
372	C₂×C₄×D₄	—	13	2	no	—
373	C₂×#117	—	13	4	no	—
374	C₂×#117	—	13	4	no	—
375	C₂×#117	C₂×D₁₃	1	2	yes	—
376	C₂²×C₄⋊C₄	—	13	1	no	—
377	C₂²×C₄⋊C₄	—	13	4	no	—
378	C₂²×C₂²⋊C₄	—	13	2	no	—
379	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
380	C₂²×C₁₃	—	2	2	no	—
381	C₂²×C₁₃	—	2	2	no	—
382	C₂²×C₁₃	—	2	8	no	—
383	C₂²×C₁₃	C₂²×#41	1	4	yes	—
384	C₂²×C₁₃	C₂²×#41	1	2	yes	—
385	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
386	C₂²×C₁₃	#585	1	2	yes	—
387	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
388	C₂×D₁₃	—	2	8	no	—
389	C₂×D₁₃	—	2	8	no	—
390	C₂×D₁₃	—	2	8	no	—
391	C₂×D₁₃	—	2	8	no	—
392	C₂×D₁₃	—	2	8	no	—
393	C₂×D₁₃	—	2	8	no	—
394	C₂×D₁₃	—	4	32	no	—
395	C₂×D₁₃	—	4	16	no	—
396	C₂×D₁₃	—	4	16	no	—
397	C₄×C₁₃	—	2	2	no	—
398	C₄×C₁₃	—	2	8	no	—
399	C₄×C₁₃	—	2	2	no	—
400	C₄×C₁₃	—	2	8	no	—
401	C₄×C₁₃	—	2	2	no	—
402	C₄×C₁₃	C₂²×#41	1	4	yes	—
403	C₄×C₁₃	C₂²×#41	1	4	yes	—
404	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
405	Dic₁₃	—	2	8	no	—
406	Dic₁₃	—	2	8	no	—
407	C₂⁵	—	13	2	no	—
408	C₂×#41	—	13	32	no	—
409	C₂×#41	—	13	16	no	—
410	C₂×#41	—	26	16	no	—
411	C₂×#41	—	52	16	no	—
412	C₂²×Q₈	—	13	2	no	—
413	C₂²×Q₈	C₂²×D₁₃	1	2	yes	—
414	C₂²×Q₈	C₂²×D₁₃	1	2	yes	—
415	C₂²×D₄	—	13	4	no	—
416	C₂²×D₄	—	13	2	no	—
417	C₂²×D₄	—	13	2	no	—
418	C₂²×D₄	—	13	2	no	—
419	C₂²×D₄	—	13	8	no	—
420	C₂²×D₄	—	13	2	no	—
421	C₂²×D₄	—	13	8	no	—
422	C₂²×D₄	—	13	2	no	—
423	C₂²×D₄	—	13	8	no	—
424	C₂²×D₄	—	26	8	no	—
425	C₂³×C₄	—	13	2	no	—
426	C₂³×C₄	—	13	4	no	—
427	C₂³×C₄	—	13	4	no	—
428	C₂³×C₄	—	13	8	no	—
429	C₂³×C₄	—	13	4	no	—
430	C₂³×C₄	—	13	16	no	—
431	C₂³×C₄	—	52	8	no	—
432	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
433	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
434	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
435	C₄⋊Q₈	—	13	8	no	—
436	C₄⋊Q₈	C₂²×D₁₃	1	8	yes	complemented
437	C₄⋊Q₈	C₂²×D₁₃	1	8	yes	complemented
438	#127	—	13	8	no	—
439	#127	—	13	32	no	—
440	#126	—	13	64	no	—
441	#125	C₂²×D₁₃	1	16	yes	complemented
442	#124	—	13	64	no	—
443	#124	—	13	16	no	—
444	#124	—	13	32	no	—
445	#123	—	13	64	no	—
446	#123	—	13	64	no	—
447	C₂²⋊Q₈	—	13	32	no	—
448	C₂²⋊Q₈	C₂²×D₁₃	1	16	yes	—
449	C₂²⋊Q₈	C₂²×D₁₃	1	16	yes	—
450	#121	—	13	16	no	—
451	#121	—	13	16	no	—
452	#121	—	13	32	no	—
453	#121	—	13	32	no	—
454	#121	—	13	32	no	—
455	#121	—	13	64	no	—
456	#120	—	13	64	no	—
457	C₄×Q₈	—	13	32	no	—
458	C₄×Q₈	C₂²×D₁₃	1	16	yes	complemented
459	C₄×Q₈	C₂²×D₁₃	1	16	yes	complemented
460	C₄×D₄	—	13	64	no	—
461	C₄×D₄	—	13	64	no	—
462	C₄×D₄	—	13	16	no	—
463	C₄×D₄	—	13	16	no	—
464	C₄×D₄	—	13	16	no	—
465	C₄×D₄	—	13	16	no	—
466	C₄×D₄	—	13	32	no	—
467	C₄×D₄	—	13	16	no	—
468	C₄×D₄	—	13	16	no	—
469	#117	—	13	32	no	—
470	#117	—	13	32	no	—
471	#117	C₂²×D₁₃	1	16	yes	—
472	C₂×C₄⋊C₄	—	13	2	no	—
473	C₂×C₄⋊C₄	—	13	2	no	—
474	C₂×C₄⋊C₄	—	13	8	no	—
475	C₂×C₄⋊C₄	—	13	8	no	—
476	C₂×C₄⋊C₄	—	13	2	no	—
477	C₂×C₄⋊C₄	—	13	2	no	—
478	C₂×C₄⋊C₄	—	13	32	no	—
479	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
480	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
481	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
482	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
483	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
484	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
485	C₂×C₂²⋊C₄	—	13	4	no	—
486	C₂×C₂²⋊C₄	—	13	4	no	—
487	C₂×C₂²⋊C₄	—	13	16	no	—
488	C₂×C₂²⋊C₄	—	13	8	no	—
489	C₂×C₂²⋊C₄	—	13	8	no	—
490	C₂×C₂²⋊C₄	—	13	4	no	—
491	C₂×C₂²⋊C₄	—	13	8	no	—
492	C₂×C₂²⋊C₄	—	13	4	no	—
493	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
494	C₂×C₄²	—	13	8	no	—
495	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
496	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
497	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
498	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
499	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
500	C₂×C₄²	C₂²×D₁₃	1	8	yes	—
501	C₂×C₁₃	—	2	4	no	—
502	C₂×C₁₃	#3506	1	4	yes	complemented
503	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
504	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
505	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
506	D₁₃	—	4	8	no	—
507	D₁₃	—	4	8	no	—
508	C₂⁴	—	13	4	no	—
509	C₂⁴	—	13	4	no	—
510	C₂⁴	—	13	8	no	—
511	C₂⁴	—	26	8	no	—
512	C₂⁴	—	52	4	no	—
513	C₂⁴	—	52	4	no	—
514	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
515	#41	—	26	64	no	—
516	#41	—	52	64	no	—
517	C₂×Q₈	—	2	8	no	—
518	C₂×Q₈	—	4	4	no	—
519	C₂×Q₈	—	13	8	no	—
520	C₂×Q₈	—	26	8	no	—
521	C₂×Q₈	C₂³×D₁₃	1	8	yes	—
522	C₂×Q₈	C₂³×D₁₃	1	8	yes	—
523	C₂×D₄	—	13	16	no	—
524	C₂×D₄	—	13	8	no	—
525	C₂×D₄	—	13	8	no	—
526	C₂×D₄	—	13	8	no	—
527	C₂×D₄	—	13	8	no	—
528	C₂×D₄	—	13	32	no	—
529	C₂×D₄	—	13	8	no	—
530	C₂×D₄	—	13	32	no	—
531	C₂×D₄	—	26	16	no	—
532	C₂×D₄	—	26	8	no	—
533	C₂×D₄	—	26	8	no	—
534	C₂×D₄	—	26	8	no	—
535	C₂×D₄	—	26	32	no	—
536	C₂×D₄	—	26	8	no	—
537	C₂×D₄	—	52	16	no	—
538	C₂×D₄	—	52	4	no	—
539	C₂×D₄	—	52	16	no	—
540	C₂²×C₄	—	2	4	no	—
541	C₂²×C₄	—	4	2	no	—
542	C₂²×C₄	—	13	4	no	—
543	C₂²×C₄	—	13	4	no	—
544	C₂²×C₄	—	13	8	no	—
545	C₂²×C₄	—	13	16	no	—
546	C₂²×C₄	—	13	16	no	—
547	C₂²×C₄	—	13	32	no	—
548	C₂²×C₄	—	13	16	no	—
549	C₂²×C₄	—	26	16	no	—
550	C₂²×C₄	—	26	16	no	—
551	C₂²×C₄	—	52	32	no	—
552	C₂²×C₄	—	52	8	no	—
553	C₂²×C₄	—	52	16	no	—
554	C₂²×C₄	—	52	4	no	—
555	C₂²×C₄	#6131	1	8	yes	complemented
556	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
557	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
558	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
559	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
560	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
561	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
562	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
563	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
564	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
565	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
566	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
567	C₄⋊C₄	—	13	8	no	—
568	C₄⋊C₄	—	13	8	no	—
569	C₄⋊C₄	—	13	32	no	—
570	C₄⋊C₄	—	13	8	no	—
571	C₄⋊C₄	—	13	8	no	—
572	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
573	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
574	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
575	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
576	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
577	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
578	C₂²⋊C₄	—	13	16	no	—
579	C₂²⋊C₄	—	13	16	no	—
580	C₂²⋊C₄	—	13	32	no	—
581	C₂²⋊C₄	—	13	32	no	—
582	C₂²⋊C₄	—	13	16	no	—
583	C₂²⋊C₄	—	13	32	no	—
584	C₂²⋊C₄	—	13	16	no	—
585	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
586	C₄²	—	13	32	no	—
587	C₄²	C₂³×D₁₃	1	4	yes	—
588	C₄²	C₂³×D₁₃	1	4	yes	—
589	C₄²	C₂³×D₁₃	1	4	yes	—
590	C₄²	C₂³×D₁₃	1	4	yes	—
591	C₄²	C₂³×D₁₃	1	16	yes	—
592	C₁₃	C₂×#3506	1	1	yes	characteristic, complemented, Sylow
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	13	8	no	—
596	C₂³	—	13	8	no	—
597	C₂³	—	26	8	no	—
598	C₂³	—	26	16	no	—
599	C₂³	—	26	8	no	—
600	C₂³	—	26	8	no	—
601	C₂³	—	26	8	no	—
602	C₂³	—	26	8	no	—
603	C₂³	—	26	8	no	—
604	C₂³	—	52	8	no	—
605	C₂³	—	52	8	no	—
606	C₂³	—	52	32	no	—
607	C₂³	C₂×#6131	1	4	yes	—
608	C₂³	C₂⁴×D₁₃	1	2	yes	—
609	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
610	Q₈	—	2	16	no	—
611	Q₈	—	4	8	no	—
612	Q₈	—	26	16	no	—
613	D₄	—	26	32	no	—
614	D₄	—	26	16	no	—
615	D₄	—	26	16	no	—
616	D₄	—	26	16	no	—
617	D₄	—	26	16	no	—
618	D₄	—	52	8	no	—
619	D₄	—	52	32	no	—
620	D₄	—	52	32	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	8	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	8	no	—
626	C₂×C₄	—	2	8	no	—
627	C₂×C₄	—	4	4	no	—
628	C₂×C₄	—	13	8	no	—
629	C₂×C₄	—	13	8	no	—
630	C₂×C₄	—	26	8	no	—
631	C₂×C₄	—	26	8	no	—
632	C₂×C₄	—	26	32	no	—
633	C₂×C₄	—	26	32	no	—
634	C₂×C₄	—	52	16	no	—
635	C₂×C₄	—	52	32	no	—
636	C₂×C₄	—	52	8	no	—
637	C₂×C₄	C₂×#6131	1	4	yes	—
638	C₂×C₄	C₂×#6131	1	4	yes	—
639	C₂×C₄	C₂×#6131	1	16	yes	complemented
640	C₂×C₄	#88256	1	4	yes	—
641	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
642	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
643	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
644	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
645	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
646	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
647	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
648	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	8	no	—
652	C₂²	—	26	8	no	—
653	C₂²	—	26	8	no	—
654	C₂²	—	26	8	no	—
655	C₂²	—	26	8	no	—
656	C₂²	—	26	8	no	—
657	C₂²	—	26	8	no	—
658	C₂²	—	52	32	no	—
659	C₂²	—	52	16	no	—
660	C₂²	—	52	16	no	—
661	C₂²	C₂²×#6131	1	4	yes	—
662	C₂²	C₂²×#6131	1	2	yes	—
663	C₂²	C₂×#88256	1	2	yes	—
664	C₂²	#11719648	1	2	yes	—
665	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
666	C₄	—	2	2	no	—
667	C₄	—	2	8	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	2	no	—
670	C₄	—	2	8	no	—
671	C₄	—	26	8	no	—
672	C₄	—	26	8	no	—
673	C₄	C₂²×#6131	1	4	yes	—
674	C₄	C₂²×#6131	1	4	yes	—
675	C₄	C₂×#88256	1	4	yes	—
676	C₂	—	2	4	no	—
677	C₂	—	52	8	no	—
678	C₂	—	52	8	no	—
679	C₂	#13128690	1	4	yes	direct product factor
680	C₂	C₂³×#6131	1	1	yes	characteristic
681	C₂	C₂²×#88256	1	1	yes	characteristic
682	C₂	C₂×#11719648	1	1	yes	characteristic

	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×#3506
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. #13128690	C₂	direct (N × H)
2. C₂×#11719290	C₂	semidirect
3. C₂×#11719289	C₂	semidirect
4. C₂×#11719439	C₂	semidirect
5. C₂×#11719400	C₂	semidirect
6. C₂×#11719282	C₂	semidirect
7. C₂×#11719431	C₂	semidirect
8. C₂×#11719349	C₂	semidirect
9. C₂×#11719230	C₂	semidirect
10. C₂×#11719182	C₂	semidirect
11. C₂×#11719332	C₂	semidirect
12. C₂×#11719228	C₂	semidirect
13. C₂²×C₄×D₅₂	C₂	semidirect
14. C₂×C₁₃×#533	C₂	semidirect
15. C₂²×#6131	C₂²	semidirect
19. C₁₃×#533	C₂²	semidirect
20. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
22. C₂×C₁₃×#125	C₂²	semidirect
25. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
26. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
29. C₂×#88201	C₂²	semidirect
30. C₂×#88200	C₂²	semidirect
35. #11719439	C₂²	semidirect
36. #11719431	C₂²	semidirect
37. #11719400	C₂²	semidirect
38. #11719349	C₂²	semidirect
39. #11719332	C₂²	semidirect
40. #11719290	C₂²	semidirect
41. #11719289	C₂²	semidirect
42. #11719282	C₂²	semidirect
43. #11719230	C₂²	semidirect
44. #11719228	C₂²	semidirect
45. C₂×#88152	C₂²	semidirect
48. C₂×#88149	C₂²	semidirect
49. C₂×#88149	C₂²	semidirect
50. C₂×#88148	C₂²	semidirect
51. C₂×#88148	C₂²	semidirect
52. C₂×#88147	C₂²	semidirect
53. C₂×#88146	C₂²	semidirect
54. C₂×#88146	C₂²	semidirect
55. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
58. #11719182	C₂²	semidirect
60. C₂×#88129	C₂²	semidirect
62. C₂×#88128	C₂²	semidirect
67. C₂×C₄×D₅₂	C₂²	semidirect
68. C₂×C₄×D₅₂	C₂²	semidirect
69. C₂×C₄×D₅₂	C₂²	semidirect
70. C₂×C₄×D₅₂	C₂²	semidirect
71. C₂×#88123	C₂²	semidirect
72. C₂×C₄×Dic₂₆	C₂²	semidirect
82. C₂×#6131	C₂³	semidirect
101. C₁₃×C₄⋊Q₈	C₂³	semidirect
102. C₁₃×C₄⋊Q₈	C₂³	semidirect
103. C₁₃×#125	C₂³	semidirect
106. C₄×Q₈×C₁₃	C₂³	semidirect
107. C₄×Q₈×C₁₃	C₂³	semidirect
122. #88201	C₂³	semidirect
123. #88200	C₂³	semidirect
141. #88152	C₂³	semidirect
144. #88149	C₂³	semidirect
145. #88149	C₂³	semidirect
146. #88148	C₂³	semidirect
147. #88148	C₂³	semidirect
148. #88147	C₂³	semidirect
149. #88146	C₂³	semidirect
150. #88146	C₂³	semidirect
151. C₄⋊C₄×D₁₃	C₂³	semidirect
155. #88129	C₂³	semidirect
157. #88128	C₂³	semidirect
162. C₄×D₅₂	C₂³	semidirect
163. C₄×D₅₂	C₂³	semidirect
164. C₄×D₅₂	C₂³	semidirect
165. #88123	C₂³	semidirect
166. C₄×Dic₂₆	C₂³	semidirect
181. C₂²×C₄×C₁₃	#41	semidirect
261. C₂×#533	D₁₃	semidirect
294. C₂×C₄×C₁₃	C₂×#41	semidirect
334. #533	C₂×D₁₃	semidirect
337. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
338. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
342. C₂×#125	C₂×D₁₃	semidirect
361. C₂×C₄×Q₈	C₂×D₁₃	semidirect
362. C₂×C₄×Q₈	C₂×D₁₃	semidirect
436. C₄⋊Q₈	C₂²×D₁₃	semidirect
437. C₄⋊Q₈	C₂²×D₁₃	semidirect
441. #125	C₂²×D₁₃	semidirect
458. C₄×Q₈	C₂²×D₁₃	semidirect
459. C₄×Q₈	C₂²×D₁₃	semidirect
502. C₂×C₁₃	#3506	semidirect
555. C₂²×C₄	#6131	semidirect
592. C₁₃	C₂×#3506	semidirect
639. C₂×C₄	C₂×#6131	semidirect
679. C₂	#13128690	direct (N × H)

Maximal subgroups

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

subgroup	index
#13128690	2
C₂×#11719290	2
C₂×#11719289	2
C₂×#11719439	2
C₂×#11719400	2
C₂×#11719282	2
C₂×#11719431	2
C₂×#11719349	2
C₂×#11719230	2
C₂×#11719182	2
C₂×#11719332	2
C₂×#11719228	2
C₂²×C₄×D₅₂	2
C₂×C₁₃×#533	2
C₂×#3506	13

Subgroups — C2×#13128690 #16770875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128690 #16770875