Subgroups — C₂×#13128226 #16769773

Order 3328.

7302 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128226	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719239	C₂	1	4	yes	maximal, complemented
3	C₂×#11719223	C₂	1	2	yes	maximal, complemented
4	C₂×#11719240	C₂	1	2	yes	maximal, complemented
5	C₂×#11719220	C₂	1	4	yes	maximal, complemented
6	C₂×#11719199	C₂	1	4	yes	maximal, complemented
7	C₂×#11719175	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11719182	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#11719233	C₂	1	8	yes	maximal, complemented
10	C₂×#11719496	C₂	1	2	yes	maximal, complemented
11	C₂×C₄×#6127	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂²×#6127	C₂²	1	2	yes	—
15	C₂×C₁₃×#117	C₂²	1	2	yes	—
16	C₂×C₁₃×#117	C₂²	1	2	yes	—
17	C₂×C₁₃×#117	C₂²	1	4	yes	—
18	C₂×C₁₃×#117	C₂²	1	16	yes	complemented
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×#88207	C₂²	1	4	yes	—
24	#11719496	C₂²	1	32	yes	complemented
25	C₂×#88184	C₂²	1	4	yes	—
26	C₂×#88184	C₂²	1	4	yes	—
27	C₂×#88183	C₂²	1	4	yes	—
28	C₂×C₄×C₂²⋊D₁₃	C₂²	1	8	yes	—
29	C₂×C₄×C₂²⋊D₁₃	C₂²	1	8	yes	—
30	C₂×#88180	C₂²	1	2	yes	—
31	C₂×#88178	C₂²	1	4	yes	—
32	C₂×#88178	C₂²	1	4	yes	—
33	#11719240	C₂²	1	32	yes	complemented
34	#11719239	C₂²	1	64	yes	complemented
35	#11719233	C₂²	1	128	yes	complemented
36	#11719223	C₂²	1	32	yes	complemented
37	#11719220	C₂²	1	64	yes	complemented
38	C₂×#88152	C₂²	1	8	yes	complemented
39	C₂×#88150	C₂²	1	8	yes	complemented
40	C₂×#88148	C₂²	1	8	yes	complemented
41	C₂×#88143	C₂²	1	8	yes	complemented
42	#11719199	C₂²	1	64	yes	complemented
43	C₂×#88139	C₂²	1	8	yes	—
44	C₂×#88138	C₂²	1	8	yes	—
45	C₂×#88137	C₂²	1	8	yes	—
46	C₂×#88133	C₂²	1	8	yes	—
47	#11719182	C₂²	1	16	yes	complemented
48	C₂×#88129	C₂²	1	2	yes	complemented
49	C₂×#88128	C₂²	1	1	yes	characteristic, complemented
50	C₄×#6127	C₂²	1	32	yes	complemented
51	C₂×C₄×D₅₂	C₂²	1	4	yes	complemented
52	C₂×C₄×D₅₂	C₂²	1	4	yes	complemented
53	C₂×#88126	C₂²	1	4	yes	complemented
54	C₂×C₄²×D₁₃	C₂²	1	4	yes	complemented
55	#11719175	C₂²	1	16	yes	complemented
56	C₂×#88124	C₂²	1	2	yes	complemented
57	C₂×#88123	C₂²	1	1	yes	characteristic, complemented
58	C₂×#88123	C₂²	1	2	yes	complemented
59	C₂×C₄×Dic₂₆	C₂²	1	4	yes	complemented
60	C₂×C₄×Dic₂₆	C₂²	1	4	yes	complemented
61	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	—	2	8	no	—
63	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
67	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
68	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₂²⋊D₁₃	C₂³	1	4	yes	—
71	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
72	C₂×#6127	—	2	16	no	—
73	C₂×#6127	C₂³	1	16	yes	—
74	C₂²×D₅₂	C₂³	1	2	yes	—
75	C₂²×D₅₂	C₂³	1	4	yes	—
76	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
77	C₂²×C₄×D₁₃	C₂³	1	8	yes	—
78	C₂²×Dic₂₆	C₂³	1	2	yes	—
79	C₂²×Dic₂₆	C₂³	1	4	yes	—
80	C₁₃×#117	C₂³	1	16	yes	—
81	C₁₃×#117	C₂³	1	32	yes	—
82	C₁₃×#117	C₂³	1	16	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
88	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
89	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
90	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
91	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
94	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
95	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
96	#88207	C₂³	1	32	yes	—
97	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	—
98	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
99	#88184	C₂³	1	32	yes	—
100	#88184	C₂³	1	32	yes	—
101	#88183	C₂³	1	32	yes	—
102	C₄×C₂²⋊D₁₃	C₂³	1	64	yes	—
103	C₄×C₂²⋊D₁₃	C₂³	1	64	yes	—
104	C₂×#6103	C₂³	1	8	yes	—
105	C₂×#6103	C₂³	1	8	yes	—
106	C₂×#6103	C₂³	1	8	yes	—
107	#88180	C₂³	1	16	yes	—
108	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
109	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
110	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
111	#88178	C₂³	1	32	yes	—
112	#88178	C₂³	1	32	yes	—
113	C₂×#6101	C₂³	1	8	yes	—
114	C₂×#6101	C₂³	1	8	yes	—
115	C₂×#6101	C₂³	1	8	yes	—
116	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
117	C₂×C₄×Dic₁₃	C₂³	1	8	yes	—
118	#88152	C₂³	1	64	yes	complemented
119	#88150	C₂³	1	64	yes	complemented
120	#88148	C₂³	1	64	yes	complemented
121	#88143	C₂³	1	64	yes	complemented
122	#88139	C₂³	1	64	yes	—
123	#88138	C₂³	1	64	yes	—
124	#88137	C₂³	1	64	yes	—
125	#88133	C₂³	1	64	yes	—
126	#88129	C₂³	1	16	yes	complemented
127	#88128	C₂³	1	8	yes	complemented
128	C₄×D₅₂	C₂³	1	32	yes	complemented
129	C₄×D₅₂	C₂³	1	32	yes	complemented
130	#88126	C₂³	1	32	yes	complemented
131	C₄²×D₁₃	C₂³	1	32	yes	complemented
132	#88124	C₂³	1	16	yes	complemented
133	#88123	C₂³	1	16	yes	complemented
134	#88123	C₂³	1	8	yes	complemented
135	C₄×Dic₂₆	C₂³	1	32	yes	complemented
136	C₄×Dic₂₆	C₂³	1	32	yes	complemented
137	C₂×#3455	—	13	1	no	maximal, Sylow
138	C₂⁴×C₁₃	—	2	4	no	—
139	C₂⁴×C₁₃	—	4	4	no	—
140	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
141	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
143	C₂³×D₁₃	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₁₃	—	2	4	no	—
145	C₂²×C₄×C₁₃	—	2	8	no	—
146	C₂²×C₄×C₁₃	—	2	8	no	—
147	C₂²×C₄×C₁₃	—	2	32	no	—
148	C₂²×C₄×C₁₃	—	4	4	no	—
149	C₂²×C₄×C₁₃	—	4	4	no	—
150	C₂²×C₄×C₁₃	#41	1	8	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
155	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
160	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₂×C₂²⋊D₁₃	—	2	16	no	—
164	C₂×C₂²⋊D₁₃	—	4	16	no	—
165	C₂×C₂²⋊D₁₃	C₂⁴	1	16	yes	—
166	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
167	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
168	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
169	#6127	—	2	64	no	—
170	C₂×D₅₂	—	2	8	no	—
171	C₂×D₅₂	—	4	8	no	—
172	C₂×D₅₂	C₂⁴	1	8	yes	—
173	C₂×D₅₂	C₂⁴	1	16	yes	—
174	C₂×C₄×D₁₃	—	2	16	no	—
175	C₂×C₄×D₁₃	—	4	16	no	—
176	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
177	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
178	C₂×Dic₂₆	—	2	8	no	—
179	C₂×Dic₂₆	—	4	8	no	—
180	C₂×Dic₂₆	C₂⁴	1	8	yes	—
181	C₂×Dic₂₆	C₂⁴	1	16	yes	—
182	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
183	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
184	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
185	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
186	C₄²×C₁₃	C₂⁴	1	8	yes	—
187	C₄²×C₁₃	C₂⁴	1	8	yes	—
188	C₄²×C₁₃	C₂⁴	1	4	yes	—
189	C₄²×C₁₃	C₂⁴	1	4	yes	—
190	C₄²×C₁₃	C₂⁴	1	8	yes	—
191	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
192	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
193	#6103	C₂⁴	1	32	yes	—
194	#6103	C₂⁴	1	32	yes	—
195	#6103	C₂⁴	1	32	yes	—
196	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
197	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
198	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
199	#6101	C₂⁴	1	32	yes	—
200	#6101	C₂⁴	1	32	yes	—
201	#6101	C₂⁴	1	32	yes	—
202	C₄×Dic₁₃	C₂⁴	1	16	yes	—
203	C₄×Dic₁₃	C₂⁴	1	32	yes	—
204	#3455	—	13	32	no	—
205	C₂×#542	—	13	4	no	—
206	C₂×#541	—	13	2	no	—
207	C₂×#540	—	13	2	no	—
208	C₂×#539	—	13	4	no	—
209	C₂×#538	—	13	4	no	—
210	C₂×#533	—	13	1	no	—
211	C₂×#532	—	13	1	no	—
212	C₂×#529	—	13	8	no	—
213	C₂×#525	—	13	2	no	—
214	C₂×C₄×#41	—	13	2	no	—
215	C₂²×#117	D₁₃	1	1	yes	characteristic, complemented
216	C₂³×C₁₃	—	2	4	no	—
217	C₂³×C₁₃	—	2	8	no	—
218	C₂³×C₁₃	—	2	4	no	—
219	C₂³×C₁₃	—	2	8	no	—
220	C₂³×C₁₃	—	4	8	no	—
221	C₂³×C₁₃	—	4	16	no	—
222	C₂³×C₁₃	C₂×#41	1	4	yes	—
223	C₂³×C₁₃	C₂⁵	1	4	yes	—
224	C₂³×C₁₃	C₂⁵	1	2	yes	—
225	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
226	C₂²×D₁₃	—	2	8	no	—
227	C₂²×D₁₃	—	2	16	no	—
228	C₂²×D₁₃	C₂⁵	1	8	yes	—
229	C₂×C₄×C₁₃	—	2	8	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	8	no	—
233	C₂×C₄×C₁₃	—	2	4	no	—
234	C₂×C₄×C₁₃	—	2	16	no	—
235	C₂×C₄×C₁₃	—	2	16	no	—
236	C₂×C₄×C₁₃	—	4	8	no	—
237	C₂×C₄×C₁₃	—	4	8	no	—
238	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
239	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
240	C₂×C₄×C₁₃	C₂×#41	1	16	yes	—
241	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
242	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
243	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
244	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
245	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
246	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
247	C₂²⋊D₁₃	—	2	32	no	—
248	C₂²⋊D₁₃	—	4	32	no	—
249	C₂×Dic₁₃	—	2	8	no	—
250	C₂×Dic₁₃	—	2	16	no	—
251	C₂×Dic₁₃	C₂⁵	1	8	yes	—
252	C₂×Dic₁₃	C₂⁵	1	16	yes	—
253	D₅₂	—	2	16	no	—
254	D₅₂	—	4	16	no	—
255	C₄×D₁₃	—	2	32	no	—
256	C₄×D₁₃	—	4	32	no	—
257	Dic₂₆	—	2	16	no	—
258	Dic₂₆	—	4	16	no	—
259	C₂²×#41	—	13	2	no	—
260	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic
261	#542	—	13	64	no	—
262	#541	—	13	32	no	—
263	#540	—	13	32	no	—
264	#539	—	13	64	no	—
265	#538	—	13	64	no	—
266	#533	—	13	16	no	—
267	#532	—	13	16	no	—
268	C₂×C₄⋊Q₈	—	13	1	no	—
269	C₂×C₄⋊Q₈	—	13	2	no	—
270	C₂×#127	—	13	1	no	—
271	#529	—	13	128	no	—
272	C₂×#126	—	13	8	no	—
273	C₂×#126	—	13	8	no	—
274	C₂×#125	—	13	8	no	—
275	C₂×#125	—	13	2	no	—
276	C₂×#124	—	13	8	no	—
277	C₂×#124	—	13	2	no	—
278	#525	—	13	32	no	—
279	C₂×#123	—	13	4	no	—
280	C₂×#123	—	13	8	no	—
281	C₂×#123	—	13	8	no	—
282	C₂×C₂²⋊Q₈	—	13	4	no	—
283	C₂×C₂²⋊Q₈	—	13	4	no	—
284	C₂×C₂²⋊Q₈	—	13	8	no	—
285	C₂×#121	—	13	4	no	—
286	C₂×#121	—	13	4	no	—
287	C₂×#121	—	13	8	no	—
288	C₂×#120	—	13	4	no	—
289	C₄×#41	—	13	32	no	—
290	C₂×C₄×Q₈	—	13	4	no	—
291	C₂×C₄×Q₈	—	13	4	no	—
292	C₂×C₄×D₄	—	13	8	no	—
293	C₂×C₄×D₄	—	13	8	no	—
294	C₂×C₄×D₄	—	13	4	no	—
295	C₂×C₄×D₄	—	13	4	no	—
296	C₂×#117	—	13	2	no	—
297	C₂×#117	—	13	4	no	—
298	C₂×#117	C₂×D₁₃	1	4	yes	—
299	C₂×#117	C₂×D₁₃	1	2	yes	—
300	C₂×#117	C₂×D₁₃	1	2	yes	—
301	C₂×#117	C₂×D₁₃	1	16	yes	complemented
302	C₂²×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
303	C₂²×C₂²⋊C₄	C₂×D₁₃	1	2	yes	—
304	C₂²×C₄²	—	13	4	no	—
305	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
306	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
307	C₂²×C₁₃	—	2	4	no	—
308	C₂²×C₁₃	—	2	8	no	—
309	C₂²×C₁₃	—	2	4	no	—
310	C₂²×C₁₃	—	2	8	no	—
311	C₂²×C₁₃	—	4	16	no	—
312	C₂²×C₁₃	—	4	8	no	—
313	C₂²×C₁₃	C₂²×#41	1	4	yes	—
314	C₂²×C₁₃	C₂²×#41	1	2	yes	—
315	C₂²×C₁₃	#585	1	4	yes	—
316	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
317	C₂×D₁₃	—	2	8	no	—
318	C₂×D₁₃	—	2	16	no	—
319	C₂×D₁₃	—	4	16	no	—
320	C₄×C₁₃	—	2	4	no	—
321	C₄×C₁₃	—	2	4	no	—
322	C₄×C₁₃	—	2	8	no	—
323	C₄×C₁₃	—	2	4	no	—
324	C₄×C₁₃	C₂²×#41	1	4	yes	—
325	C₄×C₁₃	C₂²×#41	1	4	yes	—
326	Dic₁₃	—	2	8	no	—
327	Dic₁₃	—	2	16	no	—
328	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
329	C₂×#41	—	13	16	no	—
330	C₂×#41	—	26	16	no	—
331	C₂²×Q₈	—	13	2	no	—
332	C₂²×Q₈	—	13	4	no	—
333	C₂²×D₄	—	13	4	no	—
334	C₂²×D₄	—	13	8	no	—
335	C₂²×D₄	—	13	2	no	—
336	C₂²×D₄	—	13	4	no	—
337	C₂³×C₄	—	2	8	no	—
338	C₂³×C₄	—	13	4	no	—
339	C₂³×C₄	—	13	8	no	—
340	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
341	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
342	C₂³×C₄	C₂²×D₁₃	1	8	yes	—
343	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
344	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
345	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
346	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
347	C₄⋊Q₈	—	13	8	no	—
348	C₄⋊Q₈	—	13	16	no	—
349	#127	—	13	8	no	—
350	#126	—	13	64	no	—
351	#126	—	13	64	no	—
352	#125	—	13	64	no	—
353	#125	—	13	16	no	—
354	#124	—	13	64	no	—
355	#124	—	13	16	no	—
356	#123	—	13	32	no	—
357	#123	—	13	64	no	—
358	#123	—	13	64	no	—
359	C₂²⋊Q₈	—	13	32	no	—
360	C₂²⋊Q₈	—	13	32	no	—
361	C₂²⋊Q₈	—	13	64	no	—
362	#121	—	13	32	no	—
363	#121	—	13	32	no	—
364	#121	—	13	64	no	—
365	#120	—	13	32	no	—
366	C₄×Q₈	—	13	32	no	—
367	C₄×Q₈	—	13	32	no	—
368	C₄×D₄	—	13	64	no	—
369	C₄×D₄	—	13	64	no	—
370	C₄×D₄	—	13	32	no	—
371	C₄×D₄	—	13	32	no	—
372	#117	—	13	16	no	—
373	#117	—	13	32	no	—
374	#117	C₂²×D₁₃	1	32	yes	—
375	#117	C₂²×D₁₃	1	16	yes	—
376	#117	C₂²×D₁₃	1	16	yes	—
377	C₂×C₄⋊C₄	—	13	4	no	—
378	C₂×C₄⋊C₄	—	13	8	no	—
379	C₂×C₄⋊C₄	—	13	4	no	—
380	C₂×C₄⋊C₄	—	13	8	no	—
381	C₂×C₄⋊C₄	—	13	8	no	—
382	C₂×C₄⋊C₄	—	13	4	no	—
383	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
384	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
385	C₂×C₄⋊C₄	C₂²×D₁₃	1	16	yes	—
386	C₂×C₂²⋊C₄	—	13	4	no	—
387	C₂×C₂²⋊C₄	—	13	8	no	—
388	C₂×C₂²⋊C₄	—	13	8	no	—
389	C₂×C₂²⋊C₄	—	13	8	no	—
390	C₂×C₂²⋊C₄	—	13	8	no	—
391	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
392	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
393	C₂×C₂²⋊C₄	C₂²×D₁₃	1	16	yes	—
394	C₂×C₄²	—	13	8	no	—
395	C₂×C₄²	—	13	4	no	—
396	C₂×C₄²	—	13	32	no	—
397	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
398	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
399	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
400	C₂×C₄²	C₂²×D₁₃	1	8	yes	—
401	C₂×C₄²	C₂²×D₁₃	1	8	yes	—
402	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
403	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
404	C₂×C₁₃	—	2	4	no	—
405	C₂×C₁₃	—	4	4	no	—
406	C₂×C₁₃	#3455	1	4	yes	complemented
407	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
408	C₂×C₁₃	C₂×#585	1	2	yes	—
409	D₁₃	—	4	8	no	—
410	C₂⁴	—	2	4	no	—
411	C₂⁴	—	4	4	no	—
412	C₂⁴	—	13	4	no	—
413	C₂⁴	C₂³×D₁₃	1	2	yes	—
414	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
415	C₂⁴	C₂³×D₁₃	1	4	yes	—
416	#41	—	26	64	no	—
417	C₂×Q₈	—	13	8	no	—
418	C₂×Q₈	—	13	16	no	—
419	C₂×Q₈	—	26	8	no	—
420	C₂×Q₈	—	52	8	no	—
421	C₂×D₄	—	13	16	no	—
422	C₂×D₄	—	13	32	no	—
423	C₂×D₄	—	13	8	no	—
424	C₂×D₄	—	13	16	no	—
425	C₂×D₄	—	26	16	no	—
426	C₂×D₄	—	26	8	no	—
427	C₂×D₄	—	52	8	no	—
428	C₂×D₄	—	52	16	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	8	no	—
431	C₂²×C₄	—	2	8	no	—
432	C₂²×C₄	—	2	32	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	—	13	4	no	—
436	C₂²×C₄	—	13	8	no	—
437	C₂²×C₄	—	13	16	no	—
438	C₂²×C₄	—	13	32	no	—
439	C₂²×C₄	—	26	16	no	—
440	C₂²×C₄	—	52	16	no	—
441	C₂²×C₄	#6127	1	8	yes	—
442	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
443	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
444	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
445	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
446	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
447	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
448	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
449	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
450	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
451	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
452	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
453	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
454	C₄⋊C₄	—	13	16	no	—
455	C₄⋊C₄	—	13	32	no	—
456	C₄⋊C₄	—	13	16	no	—
457	C₄⋊C₄	—	13	32	no	—
458	C₄⋊C₄	—	13	32	no	—
459	C₄⋊C₄	—	13	16	no	—
460	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
461	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
462	C₂²⋊C₄	—	13	16	no	—
463	C₂²⋊C₄	—	13	32	no	—
464	C₂²⋊C₄	—	13	32	no	—
465	C₂²⋊C₄	—	13	32	no	—
466	C₂²⋊C₄	—	13	32	no	—
467	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
468	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
469	C₄²	—	13	16	no	—
470	C₄²	—	13	32	no	—
471	C₄²	C₂³×D₁₃	1	8	yes	—
472	C₄²	C₂³×D₁₃	1	8	yes	—
473	C₄²	C₂³×D₁₃	1	8	yes	—
474	C₄²	C₂³×D₁₃	1	4	yes	—
475	C₄²	C₂³×D₁₃	1	4	yes	—
476	C₁₃	C₂×#3455	1	1	yes	characteristic, complemented, Sylow
477	C₂³	—	2	4	no	—
478	C₂³	—	2	8	no	—
479	C₂³	—	2	4	no	—
480	C₂³	—	2	8	no	—
481	C₂³	—	4	8	no	—
482	C₂³	—	4	16	no	—
483	C₂³	—	13	8	no	—
484	C₂³	—	26	8	no	—
485	C₂³	—	26	16	no	—
486	C₂³	C₂×#6127	1	4	yes	—
487	C₂³	C₂⁴×D₁₃	1	4	yes	—
488	C₂³	C₂⁴×D₁₃	1	2	yes	—
489	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
490	Q₈	—	26	16	no	—
491	Q₈	—	52	16	no	—
492	D₄	—	26	32	no	—
493	D₄	—	26	16	no	—
494	D₄	—	52	16	no	—
495	D₄	—	52	32	no	—
496	C₂×C₄	—	2	8	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	8	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	16	no	—
502	C₂×C₄	—	2	16	no	—
503	C₂×C₄	—	4	8	no	—
504	C₂×C₄	—	4	8	no	—
505	C₂×C₄	—	13	8	no	—
506	C₂×C₄	—	13	16	no	—
507	C₂×C₄	—	26	8	no	—
508	C₂×C₄	—	26	16	no	—
509	C₂×C₄	—	26	32	no	—
510	C₂×C₄	—	52	32	no	—
511	C₂×C₄	C₂×#6127	1	4	yes	—
512	C₂×C₄	C₂×#6127	1	4	yes	—
513	C₂×C₄	C₂×#6127	1	16	yes	—
514	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
515	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
516	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
517	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
518	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
519	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
520	C₂²	—	2	8	no	—
521	C₂²	—	2	4	no	—
522	C₂²	—	2	4	no	—
523	C₂²	—	2	8	no	—
524	C₂²	—	4	16	no	—
525	C₂²	—	4	8	no	—
526	C₂²	—	26	8	no	—
527	C₂²	—	26	16	no	—
528	C₂²	—	52	16	no	—
529	C₂²	C₂²×#6127	1	4	yes	—
530	C₂²	C₂²×#6127	1	2	yes	—
531	C₂²	#11719648	1	4	yes	—
532	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
533	C₄	—	2	4	no	—
534	C₄	—	2	8	no	—
535	C₄	—	2	4	no	—
536	C₄	—	2	4	no	—
537	C₄	—	26	8	no	—
538	C₄	—	26	16	no	—
539	C₄	C₂²×#6127	1	4	yes	—
540	C₄	C₂²×#6127	1	4	yes	—
541	C₂	—	2	4	no	—
542	C₂	—	4	4	no	—
543	C₂	—	52	8	no	—
544	C₂	#13128226	1	4	yes	direct product factor
545	C₂	C₂³×#6127	1	1	yes	characteristic
546	C₂	C₂×#11719648	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂²×C₁₃×#117	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂²×#117	D₁₃
hypocenter	C₁₃	C₂×#3455
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×#117

Complements

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

N	H ≅ G/N	type
1. #13128226	C₂	direct (N × H)
2. C₂×#11719239	C₂	semidirect
3. C₂×#11719223	C₂	semidirect
4. C₂×#11719240	C₂	semidirect
5. C₂×#11719220	C₂	semidirect
6. C₂×#11719199	C₂	semidirect
7. C₂×#11719175	C₂	semidirect
8. C₂×#11719182	C₂	semidirect
9. C₂×#11719233	C₂	semidirect
10. C₂×#11719496	C₂	semidirect
11. C₂×C₄×#6127	C₂	semidirect
12. C₂²×C₁₃×#117	C₂	semidirect
18. C₂×C₁₃×#117	C₂²	semidirect
24. #11719496	C₂²	semidirect
33. #11719240	C₂²	semidirect
34. #11719239	C₂²	semidirect
35. #11719233	C₂²	semidirect
36. #11719223	C₂²	semidirect
37. #11719220	C₂²	semidirect
38. C₂×#88152	C₂²	semidirect
39. C₂×#88150	C₂²	semidirect
40. C₂×#88148	C₂²	semidirect
41. C₂×#88143	C₂²	semidirect
42. #11719199	C₂²	semidirect
47. #11719182	C₂²	semidirect
48. C₂×#88129	C₂²	semidirect
49. C₂×#88128	C₂²	semidirect
50. C₄×#6127	C₂²	semidirect
51. C₂×C₄×D₅₂	C₂²	semidirect
52. C₂×C₄×D₅₂	C₂²	semidirect
53. C₂×#88126	C₂²	semidirect
54. C₂×C₄²×D₁₃	C₂²	semidirect
55. #11719175	C₂²	semidirect
56. C₂×#88124	C₂²	semidirect
57. C₂×#88123	C₂²	semidirect
58. C₂×#88123	C₂²	semidirect
59. C₂×C₄×Dic₂₆	C₂²	semidirect
60. C₂×C₄×Dic₂₆	C₂²	semidirect
118. #88152	C₂³	semidirect
119. #88150	C₂³	semidirect
120. #88148	C₂³	semidirect
121. #88143	C₂³	semidirect
126. #88129	C₂³	semidirect
127. #88128	C₂³	semidirect
128. C₄×D₅₂	C₂³	semidirect
129. C₄×D₅₂	C₂³	semidirect
130. #88126	C₂³	semidirect
131. C₄²×D₁₃	C₂³	semidirect
132. #88124	C₂³	semidirect
133. #88123	C₂³	semidirect
134. #88123	C₂³	semidirect
135. C₄×Dic₂₆	C₂³	semidirect
136. C₄×Dic₂₆	C₂³	semidirect
215. C₂²×#117	D₁₃	semidirect
301. C₂×#117	C₂×D₁₃	semidirect
406. C₂×C₁₃	#3455	semidirect
476. C₁₃	C₂×#3455	semidirect
544. C₂	#13128226	direct (N × H)

Maximal subgroups

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

subgroup	index
#13128226	2
C₂×#11719239	2
C₂×#11719223	2
C₂×#11719240	2
C₂×#11719220	2
C₂×#11719199	2
C₂×#11719175	2
C₂×#11719182	2
C₂×#11719233	2
C₂×#11719496	2
C₂×C₄×#6127	2
C₂²×C₁₃×#117	2
C₂×#3455	13

Subgroups — C2×#13128226 #16769773

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128226 #16769773