Subgroups — C₂×D₁₃×#550 #16769866

Order 3328.

12918 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#41×D₁₃	C₂	1	2	yes	maximal, complemented
2	C₂×#11719282	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11719258	C₂	1	3	yes	maximal, complemented
4	C₂×#11719423	C₂	1	3	yes	maximal, complemented
5	C₂×#11719539	C₂	1	2	yes	maximal, complemented
6	C₂×#11719304	C₂	1	6	yes	maximal, complemented
7	D₁₃×#550	C₂	1	32	yes	maximal, direct product factor
8	C₂×D₁₃×#127	C₂	1	3	yes	maximal, complemented
9	C₂×D₁₃×#121	C₂	1	6	yes	maximal, complemented
10	C₂×C₄×Q₈×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×D₄×D₁₃	C₂	1	3	yes	maximal, complemented
12	C₂×C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
14	C₂×#41×D₁₃	—	2	32	no	—
15	C₂×#41×D₁₃	C₂²	1	32	yes	complemented
16	C₂²×#6131	C₂²	1	2	yes	complemented
17	C₂²×Q₈×D₁₃	C₂²	1	1	yes	characteristic
18	C₂²×#6129	C₂²	1	6	yes	complemented
19	C₂²×D₄×D₁₃	C₂²	1	3	yes	—
20	C₂²×D₄×D₁₃	C₂²	1	6	yes	—
21	C₂²×D₄×D₁₃	C₂²	1	6	yes	—
22	C₂²×#6127	C₂²	1	6	yes	complemented
23	C₂³×C₄×D₁₃	C₂²	1	6	yes	—
24	C₁₃×#550	C₂²	1	16	yes	complemented
25	C₂×C₁₃×#127	C₂²	1	3	yes	complemented
26	C₂×C₁₃×#121	C₂²	1	6	yes	complemented
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄×D₄×C₁₃	C₂²	1	3	yes	complemented
29	#11719539	C₂²	1	32	yes	complemented
30	C₂×Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
31	C₂×#88194	C₂²	1	6	yes	complemented
32	C₂×#88194	C₂²	1	6	yes	complemented
33	C₂×#88194	C₂²	1	6	yes	complemented
34	C₂×#88193	C₂²	1	12	yes	complemented
35	C₂×#88192	C₂²	1	6	yes	complemented
36	C₂×D₄×Dic₁₃	C₂²	1	3	yes	complemented
37	C₂×#88184	C₂²	1	6	yes	complemented
38	C₂×C₄×C₂²⋊D₁₃	C₂²	1	6	yes	complemented
39	#11719423	C₂²	1	48	yes	complemented
40	D₁₃×#127	C₂²	1	48	yes	complemented
41	D₁₃×#121	C₂²	1	96	yes	complemented
42	#11719304	C₂²	1	96	yes	complemented
43	#11719282	C₂²	1	16	yes	complemented
44	C₄×Q₈×D₁₃	C₂²	1	16	yes	complemented
45	#11719258	C₂²	1	48	yes	complemented
46	C₄×D₄×D₁₃	C₂²	1	48	yes	complemented
47	C₂×#88149	C₂²	1	6	yes	complemented
48	C₂×#88147	C₂²	1	3	yes	complemented
49	C₂×C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊C₄×D₁₃	C₂²	1	3	yes	—
51	C₂×#88141	C₂²	1	3	yes	complemented
52	C₂×#88138	C₂²	1	12	yes	complemented
53	C₂×#88135	C₂²	1	6	yes	complemented
54	C₂×C₂²⋊C₄×D₁₃	C₂²	1	6	yes	—
55	C₂×#88128	C₂²	1	3	yes	complemented
56	C₂×C₄×D₅₂	C₂²	1	3	yes	complemented
57	C₂×C₄²×D₁₃	C₂²	1	3	yes	—
58	C₂×C₄×Dic₂₆	C₂²	1	3	yes	complemented
59	C₂⁴×D₁₃	C₂³	1	6	yes	—
60	C₂×C₁₃×#41	—	2	16	no	—
61	C₂×C₁₃×#41	C₂³	1	16	yes	complemented
62	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
64	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
65	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
66	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
67	C₂²×C₂²⋊D₁₃	C₂³	1	6	yes	—
68	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
69	C₂²×C₂²⋊D₁₃	C₂³	1	12	yes	—
70	C₂³×Dic₁₃	C₂³	1	6	yes	—
71	#41×D₁₃	—	2	256	no	—
72	C₂×#6131	—	2	16	no	—
73	C₂×#6131	C₂³	1	16	yes	complemented
74	C₂×Q₈×D₁₃	D₄	1	16	yes	complemented
75	C₂×Q₈×D₁₃	C₂³	1	8	yes	—
76	C₂×#6129	—	2	48	no	—
77	C₂×#6129	C₂³	1	48	yes	complemented
78	C₂×D₄×D₁₃	—	2	48	no	—
79	C₂×D₄×D₁₃	—	2	24	no	—
80	C₂×D₄×D₁₃	—	4	24	no	—
81	C₂×D₄×D₁₃	C₂³	1	24	yes	—
82	C₂×D₄×D₁₃	C₂³	1	48	yes	—
83	C₂×D₄×D₁₃	C₂³	1	48	yes	—
84	C₂×#6127	—	2	48	no	—
85	C₂×#6127	C₂³	1	48	yes	complemented
86	C₂²×D₅₂	C₂³	1	3	yes	—
87	C₂²×D₅₂	C₂³	1	6	yes	—
88	C₂²×D₅₂	C₂³	1	6	yes	—
89	C₂²×C₄×D₁₃	—	2	48	no	—
90	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
91	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
92	C₂²×C₄×D₁₃	C₂³	1	2	yes	—
93	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
94	C₂²×C₄×D₁₃	C₂³	1	48	yes	—
95	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
96	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
97	C₂²×Dic₂₆	C₂³	1	3	yes	—
98	C₁₃×#127	C₂³	1	24	yes	complemented
99	C₁₃×#121	C₂³	1	48	yes	complemented
100	C₄×Q₈×C₁₃	C₂³	1	8	yes	complemented
101	C₄×D₄×C₁₃	C₂³	1	24	yes	complemented
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	3	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
105	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
106	C₂×C₂²⋊Dic₁₃	C₂³	1	6	yes	—
107	Q₈×Dic₁₃	C₂³	1	8	yes	complemented
108	#88194	C₂³	1	48	yes	complemented
109	#88194	C₂³	1	48	yes	complemented
110	#88194	C₂³	1	48	yes	complemented
111	#88193	C₂³	1	96	yes	complemented
112	#88192	C₂³	1	48	yes	complemented
113	D₄×Dic₁₃	C₂³	1	24	yes	complemented
114	#88184	C₂³	1	48	yes	complemented
115	C₄×C₂²⋊D₁₃	C₂³	1	48	yes	complemented
116	C₂×#6103	C₂³	1	6	yes	—
117	C₂×#6103	C₂³	1	6	yes	—
118	C₂×C₄⋊Dic₁₃	C₂³	1	3	yes	—
119	C₂×C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
120	C₂×#6101	C₂³	1	6	yes	—
121	C₂×#6101	C₂³	1	2	yes	—
122	C₂×C₄×Dic₁₃	C₂³	1	3	yes	—
123	C₂×C₄×Dic₁₃	C₂³	1	3	yes	—
124	C₂×C₄×Dic₁₃	C₂³	1	3	yes	—
125	#88149	C₂³	1	48	yes	complemented
126	#88147	C₂³	1	24	yes	complemented
127	C₄⋊C₄×D₁₃	C₂³	1	8	yes	—
128	C₄⋊C₄×D₁₃	C₂³	1	24	yes	—
129	#88141	C₂³	1	24	yes	complemented
130	#88138	C₂³	1	96	yes	complemented
131	#88135	C₂³	1	48	yes	complemented
132	C₂²⋊C₄×D₁₃	C₂³	1	48	yes	—
133	#88128	C₂³	1	24	yes	complemented
134	C₄×D₅₂	C₂³	1	24	yes	complemented
135	C₄²×D₁₃	C₂³	1	24	yes	—
136	C₄×Dic₂₆	C₂³	1	24	yes	complemented
137	C₂²×#550	—	13	1	no	maximal, Sylow
138	C₂⁴×C₁₃	C₂⁴	1	6	yes	—
139	C₂³×D₁₃	—	2	24	no	—
140	C₂³×D₁₃	—	2	24	no	—
141	C₂³×D₁₃	—	2	24	no	—
142	C₂³×D₁₃	C₂⁴	1	24	yes	—
143	C₂³×D₁₃	C₂⁴	1	6	yes	—
144	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
145	C₁₃×#41	—	2	64	no	—
146	C₂×Q₈×C₁₃	C₂×D₄	1	8	yes	complemented
147	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
148	C₂×D₄×C₁₃	—	2	24	no	—
149	C₂×D₄×C₁₃	—	2	12	no	—
150	C₂×D₄×C₁₃	—	4	12	no	—
151	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
152	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
153	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
154	C₂²×C₄×C₁₃	—	2	24	no	—
155	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
157	C₂²×C₄×C₁₃	C₂⁴	1	24	yes	—
158	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
159	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₂×C₂²⋊D₁₃	—	2	48	no	—
161	C₂×C₂²⋊D₁₃	—	2	24	no	—
162	C₂×C₂²⋊D₁₃	—	4	24	no	—
163	C₂×C₂²⋊D₁₃	C₂⁴	1	24	yes	—
164	C₂×C₂²⋊D₁₃	C₂⁴	1	48	yes	—
165	C₂×C₂²⋊D₁₃	C₂⁴	1	48	yes	—
166	C₂²×Dic₁₃	—	2	24	no	—
167	C₂²×Dic₁₃	C₂⁴	1	24	yes	—
168	C₂²×Dic₁₃	C₂⁴	1	3	yes	—
169	C₂²×Dic₁₃	C₂⁴	1	2	yes	—
170	C₂²×Dic₁₃	C₂⁴	1	3	yes	—
171	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
172	#6131	—	2	64	no	—
173	Q₈×D₁₃	C₂×D₄	1	64	yes	complemented
174	#6129	—	2	192	no	—
175	D₄×D₁₃	—	2	192	no	—
176	D₄×D₁₃	—	2	96	no	—
177	D₄×D₁₃	—	4	96	no	—
178	#6127	—	2	192	no	—
179	C₂×D₅₂	—	2	24	no	—
180	C₂×D₅₂	—	2	12	no	—
181	C₂×D₅₂	—	4	12	no	—
182	C₂×D₅₂	C₂⁴	1	12	yes	—
183	C₂×D₅₂	C₂⁴	1	24	yes	—
184	C₂×D₅₂	C₂⁴	1	24	yes	—
185	C₂×C₄×D₁₃	—	2	8	no	—
186	C₂×C₄×D₁₃	—	2	12	no	—
187	C₂×C₄×D₁₃	—	2	24	no	—
188	C₂×C₄×D₁₃	—	2	24	no	—
189	C₂×C₄×D₁₃	—	2	192	no	—
190	C₂×C₄×D₁₃	C₂×D₄	1	24	yes	—
191	C₂×C₄×D₁₃	#41	1	8	yes	complemented
192	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
193	C₂×C₄×D₁₃	C₂⁴	1	24	yes	—
194	C₂×C₄×D₁₃	C₂⁴	1	8	yes	—
195	C₂×C₄×D₁₃	C₂⁴	1	24	yes	—
196	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
197	C₂×C₄×D₁₃	C₂⁴	1	4	yes	—
198	C₂×Dic₂₆	C₂×D₄	1	24	yes	complemented
199	C₂×Dic₂₆	C₂⁴	1	12	yes	—
200	C₁₃×C₄⋊C₄	C₂⁴	1	12	yes	—
201	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
202	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
203	C₄²×C₁₃	C₂⁴	1	12	yes	—
204	C₂²⋊Dic₁₃	C₂⁴	1	24	yes	—
205	#6103	C₂⁴	1	24	yes	—
206	#6103	C₂⁴	1	24	yes	—
207	C₄⋊Dic₁₃	C₂⁴	1	12	yes	—
208	C₄⋊Dic₁₃	C₂⁴	1	4	yes	—
209	#6101	C₂⁴	1	24	yes	—
210	#6101	C₂⁴	1	8	yes	—
211	C₄×Dic₁₃	C₂⁴	1	12	yes	—
212	C₄×Dic₁₃	C₂⁴	1	12	yes	—
213	C₄×Dic₁₃	C₂⁴	1	12	yes	—
214	C₂³×#41	—	13	2	no	—
215	C₂×#550	—	13	2	no	—
216	C₂×#550	—	13	32	no	—
217	C₂×#550	—	13	3	no	—
218	C₂×#550	—	13	6	no	—
219	C₂×#550	—	13	1	no	—
220	C₂×#550	—	13	3	no	—
221	C₂×#550	D₁₃	1	1	yes	characteristic, direct product factor
222	C₂²×#127	—	13	3	no	—
223	C₂²×#121	—	13	6	no	—
224	C₂²×C₄×Q₈	—	13	1	no	—
225	C₂²×C₄×D₄	—	13	3	no	—
226	C₂³×C₁₃	—	2	12	no	—
227	C₂³×C₁₃	—	2	12	no	—
228	C₂³×C₁₃	—	2	12	no	—
229	C₂³×C₁₃	C₂⁵	1	12	yes	—
230	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
231	C₂²×D₁₃	—	2	12	no	—
232	C₂²×D₁₃	—	2	12	no	—
233	C₂²×D₁₃	—	2	12	no	—
234	C₂²×D₁₃	—	2	48	no	—
235	C₂²×D₁₃	—	2	48	no	—
236	C₂²×D₁₃	—	2	48	no	—
237	C₂²×D₁₃	—	4	96	no	—
238	C₂²×D₁₃	C₂²×D₄	1	4	yes	—
239	C₂²×D₁₃	C₂×#41	1	4	yes	—
240	C₂²×D₁₃	H(5,𝔽₂)	1	4	yes	—
241	C₂²×D₁₃	C₂⁵	1	12	yes	—
242	C₂²×D₁₃	C₂⁵	1	2	yes	—
243	Q₈×C₁₃	C₂²×D₄	1	16	yes	complemented
244	D₄×C₁₃	—	2	48	no	—
245	D₄×C₁₃	—	2	24	no	—
246	D₄×C₁₃	—	4	24	no	—
247	C₂×C₄×C₁₃	—	2	4	no	—
248	C₂×C₄×C₁₃	—	2	6	no	—
249	C₂×C₄×C₁₃	—	2	48	no	—
250	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
251	C₂×C₄×C₁₃	C₂×#41	1	4	yes	complemented
252	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
253	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
254	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
255	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
256	C₂²⋊D₁₃	—	2	96	no	—
257	C₂²⋊D₁₃	—	2	48	no	—
258	C₂²⋊D₁₃	—	4	48	no	—
259	C₂×Dic₁₃	—	2	4	no	—
260	C₂×Dic₁₃	—	2	6	no	—
261	C₂×Dic₁₃	—	2	48	no	—
262	C₂×Dic₁₃	C₂²×D₄	1	12	yes	—
263	C₂×Dic₁₃	C₂×#41	1	4	yes	complemented
264	C₂×Dic₁₃	C₂⁵	1	6	yes	—
265	C₂×Dic₁₃	C₂⁵	1	4	yes	—
266	C₂×Dic₁₃	C₂⁵	1	6	yes	—
267	C₂×Dic₁₃	C₂⁵	1	2	yes	—
268	D₅₂	—	2	48	no	—
269	D₅₂	—	2	24	no	—
270	D₅₂	—	4	24	no	—
271	C₄×D₁₃	—	2	16	no	—
272	C₄×D₁₃	—	2	24	no	—
273	C₄×D₁₃	—	2	48	no	—
274	C₄×D₁₃	—	2	48	no	—
275	C₄×D₁₃	C₂²×D₄	1	48	yes	—
276	C₄×D₁₃	C₂×#41	1	16	yes	complemented
277	Dic₂₆	C₂²×D₄	1	48	yes	complemented
278	C₂²×#41	—	13	32	no	—
279	C₂²×#41	—	13	2	no	—
280	C₂²×#41	—	13	6	no	—
281	C₂²×#41	—	13	6	no	—
282	C₂²×#41	—	26	32	no	—
283	C₂²×#41	C₂×D₁₃	1	2	yes	complemented
284	C₂³×Q₈	—	13	1	no	—
285	C₂³×D₄	—	13	6	no	—
286	C₂³×D₄	—	13	3	no	—
287	C₂³×D₄	—	13	6	no	—
288	C₂⁴×C₄	—	13	6	no	—
289	#550	—	13	32	no	—
290	#550	—	13	48	no	—
291	#550	—	13	96	no	—
292	#550	—	13	16	no	—
293	#550	—	13	48	no	—
294	#550	C₂×D₁₃	1	16	yes	direct product factor
295	C₂×#127	—	13	6	no	—
296	C₂×#127	—	13	6	no	—
297	C₂×#127	—	13	6	no	—
298	C₂×#127	—	13	48	no	—
299	C₂×#127	—	13	3	no	—
300	C₂×#127	C₂×D₁₃	1	3	yes	complemented
301	C₂×#121	—	13	6	no	—
302	C₂×#121	—	13	12	no	—
303	C₂×#121	—	13	6	no	—
304	C₂×#121	—	13	96	no	—
305	C₂×#121	—	13	6	no	—
306	C₂×#121	—	13	12	no	—
307	C₂×#121	C₂×D₁₃	1	6	yes	complemented
308	C₂×C₄×Q₈	—	13	1	no	—
309	C₂×C₄×Q₈	—	13	16	no	—
310	C₂×C₄×Q₈	—	13	3	no	—
311	C₂×C₄×Q₈	—	13	3	no	—
312	C₂×C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
313	C₂×C₄×D₄	—	13	3	no	—
314	C₂×C₄×D₄	—	13	6	no	—
315	C₂×C₄×D₄	—	13	48	no	—
316	C₂×C₄×D₄	—	13	3	no	—
317	C₂×C₄×D₄	—	13	6	no	—
318	C₂×C₄×D₄	—	13	3	no	—
319	C₂×C₄×D₄	C₂×D₁₃	1	3	yes	complemented
320	C₂²×C₄⋊C₄	—	13	1	no	—
321	C₂²×C₄⋊C₄	—	13	3	no	—
322	C₂²×C₂²⋊C₄	—	13	6	no	—
323	C₂²×C₄²	—	13	3	no	—
324	C₂²×C₁₃	—	2	12	no	—
325	C₂²×C₁₃	—	2	12	no	—
326	C₂²×C₁₃	—	2	12	no	—
327	C₂²×C₁₃	—	4	24	no	—
328	C₂²×C₁₃	C₂³×D₄	1	2	yes	—
329	C₂²×C₁₃	C₂²×#41	1	2	yes	—
330	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
331	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
332	C₂×D₁₃	—	2	12	no	—
333	C₂×D₁₃	—	2	12	no	—
334	C₂×D₁₃	—	2	12	no	—
335	C₂×D₁₃	—	4	24	no	—
336	C₂×D₁₃	—	4	96	no	—
337	C₂×D₁₃	#550	1	16	yes	direct product factor
338	C₂×D₁₃	C₂³×D₄	1	4	yes	—
339	C₂×D₁₃	C₂²×#41	1	4	yes	—
340	C₂×D₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
341	C₄×C₁₃	—	2	4	no	—
342	C₄×C₁₃	—	2	6	no	—
343	C₄×C₁₃	C₂³×D₄	1	12	yes	—
344	C₄×C₁₃	C₂²×#41	1	4	yes	complemented
345	Dic₁₃	—	2	4	no	—
346	Dic₁₃	—	2	6	no	—
347	Dic₁₃	C₂³×D₄	1	12	yes	—
348	Dic₁₃	C₂²×#41	1	4	yes	complemented
349	C₂⁵	—	13	6	no	—
350	C₂×#41	—	2	16	no	—
351	C₂×#41	—	13	16	no	—
352	C₂×#41	—	13	48	no	—
353	C₂×#41	—	13	48	no	—
354	C₂×#41	—	26	48	no	—
355	C₂×#41	—	26	48	no	—
356	C₂×#41	—	26	256	no	—
357	C₂×#41	—	26	16	no	—
358	C₂×#41	C₂²×D₁₃	1	16	yes	complemented
359	C₂²×Q₈	—	13	16	no	—
360	C₂²×Q₈	—	13	8	no	—
361	C₂²×Q₈	—	13	3	no	—
362	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
363	C₂²×D₄	—	13	6	no	—
364	C₂²×D₄	—	13	12	no	—
365	C₂²×D₄	—	13	12	no	—
366	C₂²×D₄	—	13	24	no	—
367	C₂²×D₄	—	13	48	no	—
368	C₂²×D₄	—	13	48	no	—
369	C₂²×D₄	—	13	3	no	—
370	C₂²×D₄	—	13	6	no	—
371	C₂²×D₄	—	13	6	no	—
372	C₂²×D₄	—	26	48	no	—
373	C₂²×D₄	—	26	24	no	—
374	C₂²×D₄	—	52	24	no	—
375	C₂²×D₄	C₂²×D₁₃	1	3	yes	—
376	C₂²×D₄	C₂²×D₁₃	1	6	yes	—
377	C₂²×D₄	C₂²×D₁₃	1	6	yes	—
378	C₂³×C₄	—	13	3	no	—
379	C₂³×C₄	—	13	1	no	—
380	C₂³×C₄	—	13	6	no	—
381	C₂³×C₄	—	13	2	no	—
382	C₂³×C₄	—	13	3	no	—
383	C₂³×C₄	—	13	6	no	—
384	C₂³×C₄	—	13	48	no	—
385	C₂³×C₄	—	13	6	no	—
386	C₂³×C₄	—	26	48	no	—
387	C₂³×C₄	C₂²×D₁₃	1	6	yes	—
388	#127	—	13	48	no	—
389	#127	—	13	48	no	—
390	#127	—	13	48	no	—
391	#127	—	13	24	no	—
392	#127	C₂²×D₁₃	1	24	yes	complemented
393	#121	—	13	48	no	—
394	#121	—	13	96	no	—
395	#121	—	13	48	no	—
396	#121	—	13	48	no	—
397	#121	—	13	96	no	—
398	#121	C₂²×D₁₃	1	48	yes	complemented
399	C₄×Q₈	—	13	8	no	—
400	C₄×Q₈	—	13	24	no	—
401	C₄×Q₈	—	13	24	no	—
402	C₄×Q₈	C₂²×D₁₃	1	8	yes	complemented
403	C₄×D₄	—	13	24	no	—
404	C₄×D₄	—	13	48	no	—
405	C₄×D₄	—	13	24	no	—
406	C₄×D₄	—	13	48	no	—
407	C₄×D₄	—	13	24	no	—
408	C₄×D₄	C₂²×D₁₃	1	24	yes	complemented
409	C₂×C₄⋊C₄	—	13	2	no	—
410	C₂×C₄⋊C₄	—	13	1	no	—
411	C₂×C₄⋊C₄	—	13	6	no	—
412	C₂×C₄⋊C₄	—	13	3	no	—
413	C₂×C₄⋊C₄	—	13	8	no	—
414	C₂×C₄⋊C₄	—	13	24	no	—
415	C₂×C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂²×D₁₃	1	3	yes	—
417	C₂×C₂²⋊C₄	—	13	6	no	—
418	C₂×C₂²⋊C₄	—	13	6	no	—
419	C₂×C₂²⋊C₄	—	13	6	no	—
420	C₂×C₂²⋊C₄	—	13	48	no	—
421	C₂×C₂²⋊C₄	C₂²×D₁₃	1	6	yes	—
422	C₂×C₄²	—	13	3	no	—
423	C₂×C₄²	—	13	3	no	—
424	C₂×C₄²	—	13	3	no	—
425	C₂×C₄²	—	13	24	no	—
426	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
427	C₂×C₁₃	—	4	12	no	—
428	C₂×C₁₃	C₂×#550	1	4	yes	complemented
429	C₂×C₁₃	C₂⁴×D₄	1	1	yes	characteristic
430	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
431	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
432	D₁₃	—	4	12	no	—
433	D₁₃	C₂×#550	1	8	yes	direct product factor
434	C₂⁴	—	13	1	no	—
435	C₂⁴	—	13	24	no	—
436	C₂⁴	—	13	6	no	—
437	C₂⁴	—	26	24	no	—
438	C₂⁴	—	26	24	no	—
439	C₂⁴	—	26	24	no	—
440	C₂⁴	C₂³×D₁₃	1	6	yes	—
441	#41	—	2	64	no	—
442	#41	—	26	192	no	—
443	#41	—	26	192	no	—
444	#41	—	26	64	no	—
445	C₂×Q₈	—	13	64	no	—
446	C₂×Q₈	—	13	24	no	—
447	C₂×Q₈	—	13	12	no	—
448	C₂×Q₈	D₄×D₁₃	1	8	yes	complemented
449	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
450	C₂×D₄	—	2	24	no	—
451	C₂×D₄	—	2	12	no	—
452	C₂×D₄	—	4	12	no	—
453	C₂×D₄	—	13	24	no	—
454	C₂×D₄	—	13	48	no	—
455	C₂×D₄	—	13	48	no	—
456	C₂×D₄	—	13	12	no	—
457	C₂×D₄	—	13	24	no	—
458	C₂×D₄	—	13	24	no	—
459	C₂×D₄	—	26	192	no	—
460	C₂×D₄	—	26	96	no	—
461	C₂×D₄	—	26	48	no	—
462	C₂×D₄	—	26	24	no	—
463	C₂×D₄	—	26	24	no	—
464	C₂×D₄	—	26	12	no	—
465	C₂×D₄	—	52	12	no	—
466	C₂×D₄	—	52	96	no	—
467	C₂×D₄	—	52	24	no	—
468	C₂×D₄	C₂³×D₁₃	1	12	yes	—
469	C₂×D₄	C₂³×D₁₃	1	24	yes	—
470	C₂×D₄	C₂³×D₁₃	1	24	yes	—
471	C₂²×C₄	—	2	24	no	—
472	C₂²×C₄	—	13	1	no	—
473	C₂²×C₄	—	13	3	no	—
474	C₂²×C₄	—	13	24	no	—
475	C₂²×C₄	—	13	8	no	—
476	C₂²×C₄	—	13	4	no	—
477	C₂²×C₄	—	13	12	no	—
478	C₂²×C₄	—	13	24	no	—
479	C₂²×C₄	—	13	3	no	—
480	C₂²×C₄	—	13	2	no	—
481	C₂²×C₄	—	13	12	no	—
482	C₂²×C₄	—	13	8	no	—
483	C₂²×C₄	—	13	24	no	—
484	C₂²×C₄	—	13	24	no	—
485	C₂²×C₄	—	26	24	no	—
486	C₂²×C₄	—	26	192	no	—
487	C₂²×C₄	—	26	8	no	—
488	C₂²×C₄	—	26	12	no	—
489	C₂²×C₄	—	26	24	no	—
490	C₂²×C₄	—	26	24	no	—
491	C₂²×C₄	C₂³×D₁₃	1	24	yes	—
492	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
493	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
494	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
495	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
496	C₄⋊C₄	—	13	8	no	—
497	C₄⋊C₄	—	13	4	no	—
498	C₄⋊C₄	—	13	24	no	—
499	C₄⋊C₄	—	13	12	no	—
500	C₄⋊C₄	C₂³×D₁₃	1	4	yes	—
501	C₄⋊C₄	C₂³×D₁₃	1	12	yes	—
502	C₂²⋊C₄	—	13	24	no	—
503	C₂²⋊C₄	—	13	24	no	—
504	C₂²⋊C₄	—	13	24	no	—
505	C₂²⋊C₄	C₂³×D₁₃	1	24	yes	—
506	C₄²	—	13	12	no	—
507	C₄²	—	13	12	no	—
508	C₄²	—	13	12	no	—
509	C₄²	C₂³×D₁₃	1	12	yes	—
510	C₁₃	C₂²×#550	1	1	yes	characteristic, complemented, Sylow
511	C₂³	—	2	12	no	—
512	C₂³	—	2	12	no	—
513	C₂³	—	2	12	no	—
514	C₂³	—	13	4	no	—
515	C₂³	—	13	4	no	—
516	C₂³	—	13	4	no	—
517	C₂³	—	13	2	no	—
518	C₂³	—	13	12	no	—
519	C₂³	—	26	48	no	—
520	C₂³	—	26	48	no	—
521	C₂³	—	26	48	no	—
522	C₂³	—	26	12	no	—
523	C₂³	—	26	12	no	—
524	C₂³	—	26	12	no	—
525	C₂³	—	52	96	no	—
526	C₂³	C₂⁴×D₁₃	1	12	yes	—
527	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
528	Q₈	—	13	48	no	—
529	Q₈	C₂×D₄×D₁₃	1	16	yes	complemented
530	D₄	—	2	48	no	—
531	D₄	—	2	24	no	—
532	D₄	—	4	24	no	—
533	D₄	—	26	48	no	—
534	D₄	—	26	96	no	—
535	D₄	—	26	48	no	—
536	D₄	—	26	24	no	—
537	D₄	—	52	24	no	—
538	D₄	—	52	48	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	6	no	—
541	C₂×C₄	—	2	48	no	—
542	C₂×C₄	—	13	12	no	—
543	C₂×C₄	—	13	4	no	—
544	C₂×C₄	—	13	2	no	—
545	C₂×C₄	—	13	6	no	—
546	C₂×C₄	—	13	48	no	—
547	C₂×C₄	—	13	16	no	—
548	C₂×C₄	—	13	6	no	—
549	C₂×C₄	—	13	4	no	—
550	C₂×C₄	—	26	48	no	—
551	C₂×C₄	—	26	16	no	—
552	C₂×C₄	—	26	24	no	—
553	C₂×C₄	—	26	48	no	—
554	C₂×C₄	—	26	4	no	—
555	C₂×C₄	—	26	6	no	—
556	C₂×C₄	—	26	48	no	—
557	C₂×C₄	C₂×D₄×D₁₃	1	12	yes	—
558	C₂×C₄	#41×D₁₃	1	4	yes	complemented
559	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
560	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
561	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
562	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
563	C₂²	—	2	12	no	—
564	C₂²	—	2	12	no	—
565	C₂²	—	2	12	no	—
566	C₂²	—	4	24	no	—
567	C₂²	—	13	16	no	—
568	C₂²	—	13	4	no	—
569	C₂²	—	13	4	no	—
570	C₂²	—	13	4	no	—
571	C₂²	—	26	12	no	—
572	C₂²	—	26	12	no	—
573	C₂²	—	26	12	no	—
574	C₂²	—	52	96	no	—
575	C₂²	—	52	24	no	—
576	C₂²	C₂²×D₄×D₁₃	1	2	yes	—
577	C₂²	C₂×#41×D₁₃	1	2	yes	—
578	C₂²	D₁₃×H(5,𝔽₂)	1	2	yes	—
579	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
580	C₄	—	2	4	no	—
581	C₄	—	2	6	no	—
582	C₄	—	13	12	no	—
583	C₄	—	13	4	no	—
584	C₄	—	26	4	no	—
585	C₄	—	26	6	no	—
586	C₄	C₂²×D₄×D₁₃	1	12	yes	—
587	C₄	C₂×#41×D₁₃	1	4	yes	complemented
588	C₂	—	4	12	no	—
589	C₂	—	13	8	no	—
590	C₂	—	52	12	no	—
591	C₂	D₁₃×#550	1	4	yes	direct product factor
592	C₂	C₂³×D₄×D₁₃	1	1	yes	characteristic
593	C₂	C₂²×#41×D₁₃	1	1	yes	characteristic
594	C₂	C₂×D₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₁₃×#550	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×#550	D₁₃
hypocenter	C₁₃	C₂²×#550
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#550

Complements

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

N	H ≅ G/N	type
1. C₂²×#41×D₁₃	C₂	semidirect
2. C₂×#11719282	C₂	semidirect
3. C₂×#11719258	C₂	semidirect
4. C₂×#11719423	C₂	semidirect
5. C₂×#11719539	C₂	semidirect
6. C₂×#11719304	C₂	semidirect
7. D₁₃×#550	C₂	direct (N × H)
8. C₂×D₁₃×#127	C₂	semidirect
9. C₂×D₁₃×#121	C₂	semidirect
10. C₂×C₄×Q₈×D₁₃	C₂	semidirect
11. C₂×C₄×D₄×D₁₃	C₂	semidirect
12. C₂×C₁₃×#550	C₂	semidirect
13. C₂²×C₁₃×#41	C₂²	semidirect
15. C₂×#41×D₁₃	C₂²	semidirect
16. C₂²×#6131	C₂²	semidirect
18. C₂²×#6129	C₂²	semidirect
22. C₂²×#6127	C₂²	semidirect
24. C₁₃×#550	C₂²	semidirect
25. C₂×C₁₃×#127	C₂²	semidirect
26. C₂×C₁₃×#121	C₂²	semidirect
27. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
28. C₂×C₄×D₄×C₁₃	C₂²	semidirect
29. #11719539	C₂²	semidirect
30. C₂×Q₈×Dic₁₃	C₂²	semidirect
31. C₂×#88194	C₂²	semidirect
32. C₂×#88194	C₂²	semidirect
33. C₂×#88194	C₂²	semidirect
34. C₂×#88193	C₂²	semidirect
35. C₂×#88192	C₂²	semidirect
36. C₂×D₄×Dic₁₃	C₂²	semidirect
37. C₂×#88184	C₂²	semidirect
38. C₂×C₄×C₂²⋊D₁₃	C₂²	semidirect
39. #11719423	C₂²	semidirect
40. D₁₃×#127	C₂²	semidirect
41. D₁₃×#121	C₂²	semidirect
42. #11719304	C₂²	semidirect
43. #11719282	C₂²	semidirect
44. C₄×Q₈×D₁₃	C₂²	semidirect
45. #11719258	C₂²	semidirect
46. C₄×D₄×D₁₃	C₂²	semidirect
47. C₂×#88149	C₂²	semidirect
48. C₂×#88147	C₂²	semidirect
51. C₂×#88141	C₂²	semidirect
52. C₂×#88138	C₂²	semidirect
53. C₂×#88135	C₂²	semidirect
55. C₂×#88128	C₂²	semidirect
56. C₂×C₄×D₅₂	C₂²	semidirect
58. C₂×C₄×Dic₂₆	C₂²	semidirect
61. C₂×C₁₃×#41	C₂³	semidirect
73. C₂×#6131	C₂³	semidirect
74. C₂×Q₈×D₁₃	D₄	semidirect
77. C₂×#6129	C₂³	semidirect
85. C₂×#6127	C₂³	semidirect
98. C₁₃×#127	C₂³	semidirect
99. C₁₃×#121	C₂³	semidirect
100. C₄×Q₈×C₁₃	C₂³	semidirect
101. C₄×D₄×C₁₃	C₂³	semidirect
107. Q₈×Dic₁₃	C₂³	semidirect
108. #88194	C₂³	semidirect
109. #88194	C₂³	semidirect
110. #88194	C₂³	semidirect
111. #88193	C₂³	semidirect
112. #88192	C₂³	semidirect
113. D₄×Dic₁₃	C₂³	semidirect
114. #88184	C₂³	semidirect
115. C₄×C₂²⋊D₁₃	C₂³	semidirect
125. #88149	C₂³	semidirect
126. #88147	C₂³	semidirect
129. #88141	C₂³	semidirect
130. #88138	C₂³	semidirect
131. #88135	C₂³	semidirect
133. #88128	C₂³	semidirect
134. C₄×D₅₂	C₂³	semidirect
136. C₄×Dic₂₆	C₂³	semidirect
146. C₂×Q₈×C₁₃	C₂×D₄	semidirect
173. Q₈×D₁₃	C₂×D₄	semidirect
191. C₂×C₄×D₁₃	#41	semidirect
198. C₂×Dic₂₆	C₂×D₄	semidirect
221. C₂×#550	D₁₃	direct (N × H)
243. Q₈×C₁₃	C₂²×D₄	semidirect
251. C₂×C₄×C₁₃	C₂×#41	semidirect
263. C₂×Dic₁₃	C₂×#41	semidirect
276. C₄×D₁₃	C₂×#41	semidirect
277. Dic₂₆	C₂²×D₄	semidirect
283. C₂²×#41	C₂×D₁₃	semidirect
294. #550	C₂×D₁₃	direct (N × H)
300. C₂×#127	C₂×D₁₃	semidirect
307. C₂×#121	C₂×D₁₃	semidirect
312. C₂×C₄×Q₈	C₂×D₁₃	semidirect
319. C₂×C₄×D₄	C₂×D₁₃	semidirect
337. C₂×D₁₃	#550	direct (N × H)
344. C₄×C₁₃	C₂²×#41	semidirect
348. Dic₁₃	C₂²×#41	semidirect
358. C₂×#41	C₂²×D₁₃	semidirect
392. #127	C₂²×D₁₃	semidirect
398. #121	C₂²×D₁₃	semidirect
402. C₄×Q₈	C₂²×D₁₃	semidirect
408. C₄×D₄	C₂²×D₁₃	semidirect
428. C₂×C₁₃	C₂×#550	semidirect
433. D₁₃	C₂×#550	direct (N × H)
448. C₂×Q₈	D₄×D₁₃	semidirect
510. C₁₃	C₂²×#550	semidirect
529. Q₈	C₂×D₄×D₁₃	semidirect
558. C₂×C₄	#41×D₁₃	semidirect
587. C₄	C₂×#41×D₁₃	semidirect
591. C₂	D₁₃×#550	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#41×D₁₃	2
C₂×#11719282	2
C₂×#11719258	2
C₂×#11719423	2
C₂×#11719539	2
C₂×#11719304	2
D₁₃×#550	2
C₂×D₁₃×#127	2
C₂×D₁₃×#121	2
C₂×C₄×Q₈×D₁₃	2
C₂×C₄×D₄×D₁₃	2
C₂×C₁₃×#550	2
C₂²×#550	13

Subgroups — C2×D13×#550 #16769866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃×#550 #16769866