Subgroups — C₂×D₁₃×#444 #16727212

Order 3328.

2710 conjugacy classes of subgroups.

The subgroup lattice has 718 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₃×#131	C₂	1	2	yes	maximal, complemented
3	C₂×#11718378	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11718858	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11718555	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11718806	C₂	1	2	yes	maximal, complemented
7	C₂×#11718484	C₂	1	2	yes	maximal, complemented
8	D₁₃×#444	C₂	1	16	yes	maximal, direct product factor
9	C₂×D₁₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×D₁₃×#104	C₂	1	2	yes	maximal, complemented
11	C₂×D₁₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#444	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#41×D₁₃	C₂²	1	2	yes	—
14	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#131	C₂²	1	2	yes	complemented
16	C₂×#88204	C₂²	1	2	yes	—
17	C₂×#88202	C₂²	1	2	yes	complemented
18	D₁₃×#135	C₄	1	8	yes	complemented
19	D₁₃×#135	C₂²	1	8	yes	—
20	C₂×#88173	C₄	1	1	yes	characteristic, complemented
21	C₂×Q₁₆×D₁₃	C₄	1	1	yes	characteristic, complemented
22	C₂×#88170	C₄	1	2	yes	complemented
23	C₂×SD₁₆×D₁₃	C₄	1	2	yes	complemented
24	C₂×#88166	C₄	1	1	yes	characteristic, complemented
25	C₂×D₈×D₁₃	C₄	1	1	yes	characteristic, complemented
26	D₁₃×#131	—	2	8	no	—
27	D₁₃×#131	C₂²	1	16	yes	complemented
28	C₂×#88161	—	2	2	no	—
29	C₂×#88161	C₂²	1	2	yes	complemented
30	C₂×M₁₆×D₁₃	—	2	2	no	—
31	C₂×M₁₆×D₁₃	C₂²	1	2	yes	—
32	C₂×#88158	C₂²	1	1	yes	characteristic
33	C₂×#88155	—	2	2	no	—
34	C₂×#88155	C₂²	1	2	yes	complemented
35	C₂²×C₈×D₁₃	—	2	2	no	—
36	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
37	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
38	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
39	C₁₃×#444	C₂²	1	8	yes	complemented
40	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₁₃×#104	C₂²	1	2	yes	complemented
42	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic, complemented
43	C₂×#88077	C₂²	1	2	yes	complemented
44	#11718858	C₂²	1	8	yes	complemented
45	#11718806	C₂²	1	16	yes	complemented
46	C₂×#88065	C₂²	1	2	yes	complemented
47	C₂×#88062	C₂²	1	2	yes	complemented
48	C₂×#88059	C₂²	1	1	yes	characteristic, complemented
49	C₂×#88055	C₂²	1	1	yes	characteristic, complemented
50	C₂×#88055	C₂²	1	1	yes	characteristic, complemented
51	C₂×#88045	C₂²	1	2	yes	complemented
52	C₂×#88043	C₂²	1	1	yes	characteristic, complemented
53	#11718555	C₂²	1	8	yes	complemented
54	D₁₃×#108	C₂²	1	8	yes	complemented
55	#11718484	C₂²	1	16	yes	complemented
56	D₁₃×#104	C₂²	1	16	yes	complemented
57	#11718378	C₂²	1	8	yes	complemented
58	D₁₃×#97	C₂²	1	8	yes	complemented
59	C₂×C₁₃×#41	C₂³	1	2	yes	—
60	#41×D₁₃	—	2	4	no	—
61	#41×D₁₃	—	2	4	no	—
62	#41×D₁₃	C₂×C₄	1	8	yes	—
63	#41×D₁₃	C₂³	1	8	yes	—
64	C₂×#6131	C₂×C₄	1	2	yes	—
65	C₂×Q₈×D₁₃	C₂×C₄	1	2	yes	—
66	C₂×#6129	—	2	2	no	—
67	C₂×#6129	C₂×C₄	1	2	yes	—
68	C₂×D₄×D₁₃	—	2	2	no	—
69	C₂×D₄×D₁₃	C₂×C₄	1	2	yes	—
70	C₂×#6127	—	2	2	no	—
71	C₂×#6127	C₂³	1	2	yes	—
72	C₂²×C₄×D₁₃	—	2	2	no	—
73	C₂²×C₄×D₁₃	—	2	1	no	—
74	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
75	C₁₃×#135	C₂×C₄	1	4	yes	complemented
76	C₁₃×#135	C₂³	1	4	yes	—
77	C₂×C₁₃×Q₁₆	C₂×C₄	1	1	yes	characteristic, complemented
78	C₂×C₁₃×SD₁₆	C₂×C₄	1	2	yes	complemented
79	C₂×C₁₃×D₈	C₂×C₄	1	1	yes	characteristic, complemented
80	C₁₃×#131	—	2	4	no	—
81	C₁₃×#131	C₂³	1	8	yes	complemented
82	C₂×C₁₃×M₁₆	—	2	2	no	—
83	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
84	C₂²×C₈×C₁₃	—	2	2	no	—
85	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	#88204	C₂×C₄	1	8	yes	complemented
89	#88204	C₂³	1	8	yes	—
90	#88202	—	2	4	no	—
91	#88202	C₂³	1	8	yes	complemented
92	C₂×#6107	C₂×C₄	1	2	yes	complemented
93	C₂×#6106	C₂×C₄	1	2	yes	complemented
94	C₂×#6105	C₂×C₄	1	2	yes	complemented
95	C₂×#6104	C₂×C₄	1	2	yes	complemented
96	C₂×C₄×Dic₁₃	—	2	1	no	—
97	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
98	C₂×#6099	—	2	2	no	—
99	C₂×#6099	C₂³	1	2	yes	—
100	C₂²×#1055	—	2	2	no	—
101	C₂²×#1055	C₂³	1	1	yes	characteristic
102	C₂²×#1055	C₂³	1	1	yes	characteristic
103	#88173	C₂×C₄	1	8	yes	complemented
104	Q₁₆×D₁₃	C₂×C₄	1	8	yes	complemented
105	#88170	C₂×C₄	1	16	yes	complemented
106	SD₁₆×D₁₃	C₂×C₄	1	16	yes	complemented
107	#88166	C₂×C₄	1	8	yes	complemented
108	D₈×D₁₃	C₂×C₄	1	8	yes	complemented
109	#88161	—	2	4	no	—
110	#88161	—	2	16	no	—
111	#88161	C₂³	1	8	yes	complemented
112	M₁₆×D₁₃	—	2	4	no	—
113	M₁₆×D₁₃	—	2	16	no	—
114	M₁₆×D₁₃	C₂³	1	8	yes	—
115	C₂×Dic₅₂	C₂×C₄	1	1	yes	characteristic, complemented
116	#88158	C₂×C₄	1	4	yes	complemented
117	#88158	C₂³	1	4	yes	—
118	C₂×D₁₀₄	C₂×C₄	1	1	yes	characteristic, complemented
119	C₂×#6095	C₂×C₄	1	2	yes	complemented
120	#88155	—	2	4	no	—
121	#88155	—	2	16	no	—
122	#88155	C₂³	1	8	yes	complemented
123	C₂×#6094	—	2	2	no	—
124	C₂×#6094	—	2	2	no	—
125	C₂×#6094	—	2	2	no	—
126	C₂×C₈×D₁₃	—	2	2	no	—
127	C₂×C₈×D₁₃	—	2	2	no	—
128	C₂×C₈×D₁₃	—	2	2	no	—
129	C₂×C₈×D₁₃	—	2	16	no	—
130	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
131	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
132	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
133	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
134	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
135	C₂×C₈×D₁₃	D₄	1	2	yes	—
136	C₂×C₈×D₁₃	D₄	1	2	yes	—
137	C₂×C₈×D₁₃	D₄	1	4	yes	—
138	C₂×C₈×D₁₃	C₂³	1	4	yes	—
139	C₂×C₈×D₁₃	C₂³	1	4	yes	—
140	C₄²×D₁₃	—	2	2	no	—
141	C₄²×D₁₃	C₂³	1	4	yes	—
142	C₁₃×#108	C₂³	1	4	yes	complemented
143	C₁₃×#104	C₂³	1	8	yes	complemented
144	C₁₃×#97	C₂³	1	4	yes	complemented
145	#88077	C₂³	1	8	yes	complemented
146	#88065	C₂³	1	8	yes	complemented
147	#88062	C₂³	1	8	yes	complemented
148	#88059	C₂³	1	4	yes	complemented
149	#88055	C₂³	1	4	yes	complemented
150	#88055	C₂³	1	4	yes	complemented
151	#88045	C₂³	1	8	yes	complemented
152	#88043	C₂³	1	4	yes	complemented
153	C₂²×#444	—	13	1	no	maximal, Sylow
154	C₂³×D₁₃	—	2	2	no	—
155	C₂³×D₁₃	#41	1	1	yes	characteristic
156	C₁₃×#41	—	2	2	no	—
157	C₁₃×#41	—	2	2	no	—
158	C₁₃×#41	C₂²×C₄	1	4	yes	—
159	C₁₃×#41	C₂⁴	1	4	yes	—
160	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
161	C₂×D₄×C₁₃	—	2	2	no	—
162	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
163	C₂²×C₄×C₁₃	—	2	2	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₂×C₂²⋊D₁₃	—	2	2	no	—
167	C₂×C₂²⋊D₁₃	—	2	2	no	—
168	C₂×C₂²⋊D₁₃	—	2	2	no	—
169	C₂²×Dic₁₃	—	2	2	no	—
170	C₂²×Dic₁₃	—	2	1	no	—
171	C₂²×Dic₁₃	#41	1	1	yes	characteristic
172	#6131	—	2	4	no	—
173	#6131	C₂²×C₄	1	8	yes	—
174	Q₈×D₁₃	—	2	4	no	—
175	Q₈×D₁₃	C₂²×C₄	1	8	yes	—
176	#6129	—	2	8	no	—
177	#6129	—	2	8	no	—
178	#6129	—	2	4	no	—
179	#6129	C₂²×C₄	1	8	yes	—
180	D₄×D₁₃	—	2	8	no	—
181	D₄×D₁₃	—	2	8	no	—
182	D₄×D₁₃	—	2	4	no	—
183	D₄×D₁₃	C₂²×C₄	1	8	yes	—
184	#6127	—	2	2	no	—
185	#6127	—	2	2	no	—
186	#6127	—	2	8	no	—
187	#6127	—	2	8	no	—
188	#6127	C₂²×C₄	1	4	yes	—
189	#6127	C₂⁴	1	4	yes	—
190	C₂×D₅₂	—	2	2	no	—
191	C₂×D₅₂	C₂²×C₄	1	2	yes	—
192	C₂×C₄×D₁₃	—	2	2	no	—
193	C₂×C₄×D₁₃	—	2	2	no	—
194	C₂×C₄×D₁₃	—	2	2	no	—
195	C₂×C₄×D₁₃	—	2	8	no	—
196	C₂×C₄×D₁₃	—	2	8	no	—
197	C₂×C₄×D₁₃	—	2	4	no	—
198	C₂×C₄×D₁₃	—	4	4	no	—
199	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
202	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
203	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
204	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
205	C₂×C₄×D₁₃	#41	1	2	yes	—
206	C₂×C₄×D₁₃	C₂⁴	1	2	yes	—
207	C₂×Dic₂₆	—	2	2	no	—
208	C₂×Dic₂₆	C₂²×C₄	1	2	yes	—
209	C₁₃×Q₁₆	C₂²×C₄	1	4	yes	complemented
210	C₁₃×SD₁₆	C₂²×C₄	1	8	yes	complemented
211	C₁₃×D₈	C₂²×C₄	1	4	yes	complemented
212	C₁₃×M₁₆	—	2	2	no	—
213	C₁₃×M₁₆	—	2	8	no	—
214	C₁₃×M₁₆	C₂⁴	1	4	yes	—
215	C₂×C₈×C₁₃	—	2	2	no	—
216	C₂×C₈×C₁₃	—	2	8	no	—
217	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
219	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
220	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
221	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
222	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
223	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
224	C₄²×C₁₃	—	2	1	no	—
225	C₄²×C₁₃	C₂⁴	1	2	yes	—
226	#6107	C₂²×C₄	1	8	yes	complemented
227	#6106	C₂²×C₄	1	8	yes	complemented
228	#6105	C₂²×C₄	1	8	yes	complemented
229	#6104	C₂²×C₄	1	8	yes	complemented
230	C₄×Dic₁₃	—	2	1	no	—
231	C₄×Dic₁₃	—	2	4	no	—
232	C₄×Dic₁₃	C₂⁴	1	2	yes	—
233	#6099	—	2	2	no	—
234	#6099	—	2	8	no	—
235	#6099	C₂⁴	1	4	yes	—
236	C₂×#1055	—	2	2	no	—
237	C₂×#1055	—	2	8	no	—
238	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
239	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
240	C₂×#1055	C₂²×C₄	1	2	yes	—
241	C₂×#1055	C₂×D₄	1	2	yes	—
242	C₂×#1055	C₂×D₄	1	2	yes	—
243	C₂×#1055	C₂⁴	1	2	yes	—
244	C₂×#1055	C₂⁴	1	2	yes	—
245	Dic₅₂	C₂²×C₄	1	4	yes	complemented
246	D₁₀₄	C₂²×C₄	1	4	yes	complemented
247	#6095	C₂²×C₄	1	8	yes	complemented
248	#6094	—	2	8	no	—
249	#6094	—	2	8	no	—
250	#6094	—	2	8	no	—
251	C₈×D₁₃	—	2	8	no	—
252	C₈×D₁₃	—	2	8	no	—
253	C₈×D₁₃	—	2	8	no	—
254	C₈×D₁₃	C₂²×C₄	1	4	yes	—
255	C₈×D₁₃	C₂²×C₄	1	4	yes	—
256	C₈×D₁₃	C₂²×C₄	1	4	yes	—
257	C₈×D₁₃	C₂²×C₄	1	4	yes	—
258	C₈×D₁₃	C₂×D₄	1	8	yes	—
259	C₈×D₁₃	C₂×D₄	1	8	yes	—
260	C₂²×#135	—	13	1	no	—
261	C₂²×#131	—	13	2	no	—
262	C₂×#444	—	13	16	no	—
263	C₂×#444	—	13	1	no	—
264	C₂×#444	—	13	2	no	—
265	C₂×#444	—	13	1	no	—
266	C₂×#444	—	13	1	no	—
267	C₂×#444	—	13	2	no	—
268	C₂×#444	D₁₃	1	1	yes	characteristic, direct product factor
269	C₂²×#108	—	13	1	no	—
270	C₂²×#104	—	13	2	no	—
271	C₂²×#97	—	13	1	no	—
272	C₂³×C₁₃	—	2	2	no	—
273	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
274	C₂²×D₁₃	—	2	4	no	—
275	C₂²×D₁₃	—	2	2	no	—
276	C₂²×D₁₃	—	2	8	no	—
277	C₂²×D₁₃	—	4	8	no	—
278	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
279	C₂²×D₁₃	C₄×D₄	1	2	yes	—
280	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
281	C₂²×D₁₃	C₂×#41	1	2	yes	—
282	Q₈×C₁₃	—	2	2	no	—
283	Q₈×C₁₃	C₂³×C₄	1	4	yes	—
284	D₄×C₁₃	—	2	4	no	—
285	D₄×C₁₃	—	2	4	no	—
286	D₄×C₁₃	—	2	2	no	—
287	D₄×C₁₃	C₂³×C₄	1	4	yes	—
288	C₂×C₄×C₁₃	—	2	2	no	—
289	C₂×C₄×C₁₃	—	2	4	no	—
290	C₂×C₄×C₁₃	—	2	4	no	—
291	C₂×C₄×C₁₃	—	2	2	no	—
292	C₂×C₄×C₁₃	—	4	2	no	—
293	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
294	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
295	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
298	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
299	C₂²⋊D₁₃	—	2	4	no	—
300	C₂²⋊D₁₃	—	2	4	no	—
301	C₂²⋊D₁₃	—	2	8	no	—
302	C₂²⋊D₁₃	—	2	8	no	—
303	C₂×Dic₁₃	—	2	2	no	—
304	C₂×Dic₁₃	—	2	8	no	—
305	C₂×Dic₁₃	—	2	2	no	—
306	C₂×Dic₁₃	—	4	2	no	—
307	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
308	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
309	C₂×Dic₁₃	C₄×D₄	1	2	yes	—
310	C₂×Dic₁₃	C₂×#41	1	2	yes	—
311	D₅₂	—	2	8	no	—
312	D₅₂	—	2	2	no	—
313	D₅₂	C₂³×C₄	1	4	yes	—
314	C₄×D₁₃	—	2	8	no	—
315	C₄×D₁₃	—	2	4	no	—
316	C₄×D₁₃	—	2	4	no	—
317	C₄×D₁₃	—	2	8	no	—
318	C₄×D₁₃	—	4	8	no	—
319	C₄×D₁₃	C₄×D₄	1	2	yes	—
320	C₄×D₁₃	C₄×D₄	1	2	yes	—
321	C₄×D₁₃	C₄×D₄	1	2	yes	—
322	C₄×D₁₃	C₄×D₄	1	2	yes	—
323	C₄×D₁₃	C₂³×C₄	1	2	yes	—
324	C₄×D₁₃	C₂³×C₄	1	2	yes	—
325	C₄×D₁₃	C₂²×D₄	1	2	yes	—
326	C₄×D₁₃	C₂²×D₄	1	2	yes	—
327	Dic₂₆	—	2	2	no	—
328	Dic₂₆	—	2	8	no	—
329	Dic₂₆	C₂³×C₄	1	4	yes	—
330	C₈×C₁₃	—	2	4	no	—
331	C₈×C₁₃	C₂³×C₄	1	2	yes	—
332	C₈×C₁₃	C₂³×C₄	1	2	yes	—
333	C₈×C₁₃	C₂²×D₄	1	4	yes	—
334	#1055	—	2	4	no	—
335	#1055	C₂³×C₄	1	2	yes	—
336	#1055	C₂³×C₄	1	2	yes	—
337	#1055	C₂²×D₄	1	4	yes	—
338	C₂²×#41	—	13	2	no	—
339	C₂×#135	—	13	2	no	—
340	C₂×#135	—	13	8	no	—
341	C₂×#135	—	13	8	no	—
342	C₂×#135	—	13	1	no	—
343	C₂×#135	—	13	2	no	—
344	C₂×#135	—	13	1	no	—
345	C₂×#135	—	13	1	no	—
346	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
347	C₂²×Q₁₆	—	13	1	no	—
348	C₂²×SD₁₆	—	13	2	no	—
349	C₂²×D₈	—	13	1	no	—
350	C₂×#131	—	13	2	no	—
351	C₂×#131	—	13	16	no	—
352	C₂×#131	—	13	2	no	—
353	C₂×#131	—	13	2	no	—
354	C₂×#131	—	26	2	no	—
355	C₂×#131	—	26	2	no	—
356	C₂×#131	—	26	8	no	—
357	C₂×#131	C₂×D₁₃	1	2	yes	complemented
358	C₂²×M₁₆	—	13	2	no	—
359	C₂²×M₁₆	—	26	2	no	—
360	C₂³×C₈	—	13	1	no	—
361	C₂³×C₈	—	13	1	no	—
362	C₂³×C₈	—	26	2	no	—
363	C₂²×C₄²	—	13	1	no	—
364	#444	—	13	8	no	—
365	#444	—	13	16	no	—
366	#444	—	13	8	no	—
367	#444	—	13	16	no	—
368	#444	—	13	8	no	—
369	#444	C₂×D₁₃	1	8	yes	direct product factor
370	C₂×#108	—	13	2	no	—
371	C₂×#108	—	13	1	no	—
372	C₂×#108	—	13	8	no	—
373	C₂×#108	C₂×D₁₃	1	1	yes	characteristic, complemented
374	C₂×#104	—	13	2	no	—
375	C₂×#104	—	13	2	no	—
376	C₂×#104	—	13	2	no	—
377	C₂×#104	—	13	16	no	—
378	C₂×#104	C₂×D₁₃	1	2	yes	complemented
379	C₂×#97	—	13	1	no	—
380	C₂×#97	—	13	1	no	—
381	C₂×#97	—	13	1	no	—
382	C₂×#97	—	13	8	no	—
383	C₂×#97	C₂×D₁₃	1	1	yes	characteristic, complemented
384	C₂²×C₁₃	—	2	2	no	—
385	C₂²×C₁₃	—	2	4	no	—
386	C₂²×C₁₃	—	4	4	no	—
387	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
388	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
389	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
390	C₂×D₁₃	—	2	2	no	—
391	C₂×D₁₃	—	2	4	no	—
392	C₂×D₁₃	—	2	4	no	—
393	C₂×D₁₃	—	2	4	no	—
394	C₂×D₁₃	—	4	4	no	—
395	C₂×D₁₃	—	4	16	no	—
396	C₂×D₁₃	#444	1	4	yes	direct product factor
397	C₂×D₁₃	C₂×C₄×D₄	1	2	yes	—
398	C₂×D₁₃	C₂×C₄×D₄	1	2	yes	—
399	C₄×C₁₃	—	2	4	no	—
400	C₄×C₁₃	—	4	2	no	—
401	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
402	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
403	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
404	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
405	Dic₁₃	—	2	4	no	—
406	Dic₁₃	—	4	2	no	—
407	Dic₁₃	C₂×C₄×D₄	1	2	yes	—
408	Dic₁₃	C₂×C₄×D₄	1	2	yes	—
409	C₂×#41	—	13	8	no	—
410	C₂×#41	—	13	8	no	—
411	C₂×#41	—	13	2	no	—
412	C₂×#41	—	13	2	no	—
413	C₂×#41	—	13	2	no	—
414	C₂×#41	—	26	2	no	—
415	C₂×#41	—	26	2	no	—
416	C₂×#41	—	26	4	no	—
417	C₂×#41	—	26	4	no	—
418	C₂×#41	C₂²×D₁₃	1	2	yes	—
419	C₂²×Q₈	—	13	2	no	—
420	C₂²×D₄	—	13	2	no	—
421	C₂²×D₄	—	26	2	no	—
422	C₂³×C₄	—	13	1	no	—
423	C₂³×C₄	—	26	2	no	—
424	C₂³×C₄	—	26	1	no	—
425	#135	—	13	8	no	—
426	#135	—	13	8	no	—
427	#135	—	13	8	no	—
428	#135	—	13	16	no	—
429	#135	—	13	8	no	—
430	#135	—	13	4	no	—
431	#135	—	13	4	no	—
432	#135	C₄×D₁₃	1	4	yes	complemented
433	#135	C₂²×D₁₃	1	4	yes	—
434	C₂×Q₁₆	—	13	2	no	—
435	C₂×Q₁₆	—	13	8	no	—
436	C₂×Q₁₆	—	13	1	no	—
437	C₂×Q₁₆	C₄×D₁₃	1	1	yes	characteristic, complemented
438	C₂×SD₁₆	—	13	2	no	—
439	C₂×SD₁₆	—	13	2	no	—
440	C₂×SD₁₆	—	13	16	no	—
441	C₂×SD₁₆	—	13	2	no	—
442	C₂×SD₁₆	C₄×D₁₃	1	2	yes	complemented
443	C₂×D₈	—	13	2	no	—
444	C₂×D₈	—	13	8	no	—
445	C₂×D₈	—	13	1	no	—
446	C₂×D₈	C₄×D₁₃	1	1	yes	characteristic, complemented
447	#131	—	2	4	no	—
448	#131	—	13	8	no	—
449	#131	—	13	8	no	—
450	#131	—	13	8	no	—
451	#131	—	26	16	no	—
452	#131	—	26	4	no	—
453	#131	—	26	16	no	—
454	#131	—	26	4	no	—
455	#131	—	26	4	no	—
456	#131	C₂²×D₁₃	1	8	yes	complemented
457	C₂×M₁₆	—	2	2	no	—
458	C₂×M₁₆	—	13	2	no	—
459	C₂×M₁₆	—	13	8	no	—
460	C₂×M₁₆	—	26	2	no	—
461	C₂×M₁₆	—	26	2	no	—
462	C₂×M₁₆	—	26	16	no	—
463	C₂×M₁₆	—	26	2	no	—
464	C₂×M₁₆	—	26	4	no	—
465	C₂×M₁₆	—	26	2	no	—
466	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
467	C₂²×C₈	—	2	2	no	—
468	C₂²×C₈	—	13	1	no	—
469	C₂²×C₈	—	13	1	no	—
470	C₂²×C₈	—	13	1	no	—
471	C₂²×C₈	—	13	1	no	—
472	C₂²×C₈	—	13	1	no	—
473	C₂²×C₈	—	13	1	no	—
474	C₂²×C₈	—	13	4	no	—
475	C₂²×C₈	—	13	2	no	—
476	C₂²×C₈	—	13	4	no	—
477	C₂²×C₈	—	13	2	no	—
478	C₂²×C₈	—	13	4	no	—
479	C₂²×C₈	—	13	4	no	—
480	C₂²×C₈	—	26	2	no	—
481	C₂²×C₈	—	26	16	no	—
482	C₂²×C₈	—	26	2	no	—
483	C₂²×C₈	—	26	2	no	—
484	C₂²×C₈	—	26	2	no	—
485	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
486	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
487	C₂×C₄²	—	13	1	no	—
488	C₂×C₄²	—	13	4	no	—
489	C₂×C₄²	—	26	2	no	—
490	C₂×C₄²	—	26	1	no	—
491	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
492	#108	—	13	8	no	—
493	#108	—	13	4	no	—
494	#108	C₂²×D₁₃	1	4	yes	complemented
495	#104	—	13	8	no	—
496	#104	—	13	8	no	—
497	#104	—	13	8	no	—
498	#104	C₂²×D₁₃	1	8	yes	complemented
499	#97	—	13	4	no	—
500	#97	—	13	4	no	—
501	#97	—	13	4	no	—
502	#97	C₂²×D₁₃	1	4	yes	complemented
503	C₂×C₁₃	—	2	1	no	—
504	C₂×C₁₃	—	2	1	no	—
505	C₂×C₁₃	—	4	4	no	—
506	C₂×C₁₃	C₂×#444	1	2	yes	complemented
507	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
508	D₁₃	—	2	2	no	—
509	D₁₃	—	4	4	no	—
510	D₁₃	C₂×#444	1	4	yes	direct product factor
511	C₂⁴	—	13	1	no	—
512	C₂⁴	—	26	2	no	—
513	#41	—	2	2	no	—
514	#41	—	2	2	no	—
515	#41	—	13	8	no	—
516	#41	—	13	8	no	—
517	#41	—	13	4	no	—
518	#41	—	13	4	no	—
519	#41	—	26	8	no	—
520	#41	—	26	8	no	—
521	#41	—	26	8	no	—
522	#41	—	26	8	no	—
523	#41	—	26	4	no	—
524	#41	—	26	4	no	—
525	#41	—	26	2	no	—
526	#41	—	26	2	no	—
527	#41	C₂×C₄×D₁₃	1	4	yes	—
528	#41	C₂³×D₁₃	1	4	yes	—
529	C₂×Q₈	—	13	8	no	—
530	C₂×Q₈	—	13	2	no	—
531	C₂×Q₈	—	26	2	no	—
532	C₂×Q₈	—	26	4	no	—
533	C₂×Q₈	C₂×C₄×D₁₃	1	2	yes	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	13	8	no	—
536	C₂×D₄	—	13	2	no	—
537	C₂×D₄	—	26	2	no	—
538	C₂×D₄	—	26	4	no	—
539	C₂×D₄	—	26	2	no	—
540	C₂×D₄	—	26	8	no	—
541	C₂×D₄	—	26	8	no	—
542	C₂×D₄	—	26	2	no	—
543	C₂×D₄	—	26	2	no	—
544	C₂×D₄	C₂×C₄×D₁₃	1	2	yes	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	13	1	no	—
548	C₂²×C₄	—	13	1	no	—
549	C₂²×C₄	—	13	1	no	—
550	C₂²×C₄	—	13	2	no	—
551	C₂²×C₄	—	13	2	no	—
552	C₂²×C₄	—	13	1	no	—
553	C₂²×C₄	—	13	1	no	—
554	C₂²×C₄	—	13	2	no	—
555	C₂²×C₄	—	13	2	no	—
556	C₂²×C₄	—	26	8	no	—
557	C₂²×C₄	—	26	2	no	—
558	C₂²×C₄	—	26	8	no	—
559	C₂²×C₄	—	26	2	no	—
560	C₂²×C₄	—	26	4	no	—
561	C₂²×C₄	—	26	2	no	—
562	C₂²×C₄	—	26	2	no	—
563	C₂²×C₄	—	26	1	no	—
564	C₂²×C₄	—	52	4	no	—
565	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
566	Q₁₆	—	13	8	no	—
567	Q₁₆	—	13	4	no	—
568	Q₁₆	C₂×C₄×D₁₃	1	4	yes	complemented
569	SD₁₆	—	13	8	no	—
570	SD₁₆	—	13	8	no	—
571	SD₁₆	—	13	8	no	—
572	SD₁₆	C₂×C₄×D₁₃	1	8	yes	complemented
573	D₈	—	13	8	no	—
574	D₈	—	13	4	no	—
575	D₈	C₂×C₄×D₁₃	1	4	yes	complemented
576	M₁₆	—	2	2	no	—
577	M₁₆	—	2	8	no	—
578	M₁₆	—	13	4	no	—
579	M₁₆	—	26	8	no	—
580	M₁₆	—	26	8	no	—
581	M₁₆	—	26	8	no	—
582	M₁₆	—	26	2	no	—
583	M₁₆	—	26	8	no	—
584	M₁₆	C₂³×D₁₃	1	4	yes	—
585	C₂×C₈	—	2	2	no	—
586	C₂×C₈	—	2	8	no	—
587	C₂×C₈	—	13	1	no	—
588	C₂×C₈	—	13	1	no	—
589	C₂×C₈	—	13	2	no	—
590	C₂×C₈	—	13	2	no	—
591	C₂×C₈	—	13	2	no	—
592	C₂×C₈	—	13	2	no	—
593	C₂×C₈	—	13	2	no	—
594	C₂×C₈	—	13	4	no	—
595	C₂×C₈	—	13	4	no	—
596	C₂×C₈	—	13	4	no	—
597	C₂×C₈	—	13	4	no	—
598	C₂×C₈	—	13	8	no	—
599	C₂×C₈	—	13	8	no	—
600	C₂×C₈	—	26	8	no	—
601	C₂×C₈	—	26	8	no	—
602	C₂×C₈	—	26	8	no	—
603	C₂×C₈	—	26	2	no	—
604	C₂×C₈	—	26	8	no	—
605	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
606	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
607	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
608	C₂×C₈	D₄×D₁₃	1	2	yes	—
609	C₂×C₈	D₄×D₁₃	1	2	yes	—
610	C₂×C₈	C₂³×D₁₃	1	2	yes	—
611	C₂×C₈	C₂³×D₁₃	1	2	yes	—
612	C₄²	—	2	1	no	—
613	C₄²	—	13	2	no	—
614	C₄²	—	26	4	no	—
615	C₄²	—	26	1	no	—
616	C₄²	C₂³×D₁₃	1	2	yes	—
617	C₁₃	C₂²×#444	1	1	yes	characteristic, complemented, Sylow
618	C₂³	—	2	2	no	—
619	C₂³	—	13	1	no	—
620	C₂³	—	13	2	no	—
621	C₂³	—	13	1	no	—
622	C₂³	—	13	2	no	—
623	C₂³	—	26	4	no	—
624	C₂³	—	26	8	no	—
625	C₂³	—	26	2	no	—
626	C₂³	—	52	8	no	—
627	C₂³	#41×D₁₃	1	1	yes	characteristic
628	Q₈	—	2	2	no	—
629	Q₈	—	13	4	no	—
630	Q₈	—	26	8	no	—
631	Q₈	—	26	2	no	—
632	Q₈	C₂²×C₄×D₁₃	1	4	yes	—
633	D₄	—	2	4	no	—
634	D₄	—	2	4	no	—
635	D₄	—	2	2	no	—
636	D₄	—	13	4	no	—
637	D₄	—	26	8	no	—
638	D₄	—	26	8	no	—
639	D₄	—	26	8	no	—
640	D₄	—	26	4	no	—
641	D₄	—	26	4	no	—
642	D₄	—	26	2	no	—
643	D₄	C₂²×C₄×D₁₃	1	4	yes	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	4	2	no	—
649	C₂×C₄	—	13	1	no	—
650	C₂×C₄	—	13	1	no	—
651	C₂×C₄	—	13	2	no	—
652	C₂×C₄	—	13	2	no	—
653	C₂×C₄	—	13	2	no	—
654	C₂×C₄	—	13	2	no	—
655	C₂×C₄	—	13	2	no	—
656	C₂×C₄	—	13	2	no	—
657	C₂×C₄	—	13	2	no	—
658	C₂×C₄	—	13	2	no	—
659	C₂×C₄	—	13	2	no	—
660	C₂×C₄	—	13	2	no	—
661	C₂×C₄	—	26	8	no	—
662	C₂×C₄	—	26	8	no	—
663	C₂×C₄	—	26	8	no	—
664	C₂×C₄	—	26	2	no	—
665	C₂×C₄	—	26	4	no	—
666	C₂×C₄	—	26	4	no	—
667	C₂×C₄	—	26	2	no	—
668	C₂×C₄	—	52	8	no	—
669	C₂×C₄	—	52	2	no	—
670	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
671	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
672	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
673	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
674	C₂×C₄	#41×D₁₃	1	1	yes	characteristic
675	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
676	C₈	—	2	4	no	—
677	C₈	—	13	2	no	—
678	C₈	—	13	2	no	—
679	C₈	—	13	4	no	—
680	C₈	—	26	4	no	—
681	C₈	C₂²×C₄×D₁₃	1	2	yes	—
682	C₈	C₂²×C₄×D₁₃	1	2	yes	—
683	C₈	C₂×D₄×D₁₃	1	4	yes	—
684	C₂²	—	2	2	no	—
685	C₂²	—	2	4	no	—
686	C₂²	—	4	4	no	—
687	C₂²	—	13	2	no	—
688	C₂²	—	13	4	no	—
689	C₂²	—	13	2	no	—
690	C₂²	—	26	4	no	—
691	C₂²	—	26	4	no	—
692	C₂²	—	26	2	no	—
693	C₂²	—	26	4	no	—
694	C₂²	—	52	16	no	—
695	C₂²	—	52	4	no	—
696	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
697	C₂²	C₄×D₄×D₁₃	1	1	yes	characteristic
698	C₂²	C₂×#41×D₁₃	1	1	yes	characteristic
699	C₄	—	2	4	no	—
700	C₄	—	4	2	no	—
701	C₄	—	13	2	no	—
702	C₄	—	13	2	no	—
703	C₄	—	26	4	no	—
704	C₄	—	52	2	no	—
705	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
706	C₄	C₄×D₄×D₁₃	1	1	yes	characteristic
707	C₄	C₂³×C₄×D₁₃	1	1	yes	characteristic
708	C₄	C₂²×D₄×D₁₃	1	1	yes	characteristic
709	C₂	—	2	1	no	—
710	C₂	—	2	1	no	—
711	C₂	—	4	4	no	—
712	C₂	—	13	4	no	—
713	C₂	—	26	2	no	—
714	C₂	—	52	4	no	—
715	C₂	D₁₃×#444	1	2	yes	direct product factor
716	C₂	C₂×C₄×D₄×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₄×C₁₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₂×C₁₃×#444	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×D₁₃×#135	C₂
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₂×#444	D₁₃
hypocenter	C₁₃	C₂²×#444
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#444

Complements

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

N	H ≅ G/N	type
2. C₂×D₁₃×#131	C₂	semidirect
3. C₂×#11718378	C₂	semidirect
4. C₂×#11718858	C₂	semidirect
5. C₂×#11718555	C₂	semidirect
6. C₂×#11718806	C₂	semidirect
7. C₂×#11718484	C₂	semidirect
8. D₁₃×#444	C₂	direct (N × H)
9. C₂×D₁₃×#108	C₂	semidirect
10. C₂×D₁₃×#104	C₂	semidirect
11. C₂×D₁₃×#97	C₂	semidirect
12. C₂×C₁₃×#444	C₂	semidirect
15. C₂×C₁₃×#131	C₂²	semidirect
17. C₂×#88202	C₂²	semidirect
18. D₁₃×#135	C₄	semidirect
20. C₂×#88173	C₄	semidirect
21. C₂×Q₁₆×D₁₃	C₄	semidirect
22. C₂×#88170	C₄	semidirect
23. C₂×SD₁₆×D₁₃	C₄	semidirect
24. C₂×#88166	C₄	semidirect
25. C₂×D₈×D₁₃	C₄	semidirect
27. D₁₃×#131	C₂²	semidirect
29. C₂×#88161	C₂²	semidirect
34. C₂×#88155	C₂²	semidirect
39. C₁₃×#444	C₂²	semidirect
40. C₂×C₁₃×#108	C₂²	semidirect
41. C₂×C₁₃×#104	C₂²	semidirect
42. C₂×C₁₃×#97	C₂²	semidirect
43. C₂×#88077	C₂²	semidirect
44. #11718858	C₂²	semidirect
45. #11718806	C₂²	semidirect
46. C₂×#88065	C₂²	semidirect
47. C₂×#88062	C₂²	semidirect
48. C₂×#88059	C₂²	semidirect
49. C₂×#88055	C₂²	semidirect
50. C₂×#88055	C₂²	semidirect
51. C₂×#88045	C₂²	semidirect
52. C₂×#88043	C₂²	semidirect
53. #11718555	C₂²	semidirect
54. D₁₃×#108	C₂²	semidirect
55. #11718484	C₂²	semidirect
56. D₁₃×#104	C₂²	semidirect
57. #11718378	C₂²	semidirect
58. D₁₃×#97	C₂²	semidirect
75. C₁₃×#135	C₂×C₄	semidirect
77. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
78. C₂×C₁₃×SD₁₆	C₂×C₄	semidirect
79. C₂×C₁₃×D₈	C₂×C₄	semidirect
81. C₁₃×#131	C₂³	semidirect
88. #88204	C₂×C₄	semidirect
91. #88202	C₂³	semidirect
92. C₂×#6107	C₂×C₄	semidirect
93. C₂×#6106	C₂×C₄	semidirect
94. C₂×#6105	C₂×C₄	semidirect
95. C₂×#6104	C₂×C₄	semidirect
103. #88173	C₂×C₄	semidirect
104. Q₁₆×D₁₃	C₂×C₄	semidirect
105. #88170	C₂×C₄	semidirect
106. SD₁₆×D₁₃	C₂×C₄	semidirect
107. #88166	C₂×C₄	semidirect
108. D₈×D₁₃	C₂×C₄	semidirect
111. #88161	C₂³	semidirect
115. C₂×Dic₅₂	C₂×C₄	semidirect
116. #88158	C₂×C₄	semidirect
118. C₂×D₁₀₄	C₂×C₄	semidirect
119. C₂×#6095	C₂×C₄	semidirect
122. #88155	C₂³	semidirect
142. C₁₃×#108	C₂³	semidirect
143. C₁₃×#104	C₂³	semidirect
144. C₁₃×#97	C₂³	semidirect
145. #88077	C₂³	semidirect
146. #88065	C₂³	semidirect
147. #88062	C₂³	semidirect
148. #88059	C₂³	semidirect
149. #88055	C₂³	semidirect
150. #88055	C₂³	semidirect
151. #88045	C₂³	semidirect
152. #88043	C₂³	semidirect
209. C₁₃×Q₁₆	C₂²×C₄	semidirect
210. C₁₃×SD₁₆	C₂²×C₄	semidirect
211. C₁₃×D₈	C₂²×C₄	semidirect
226. #6107	C₂²×C₄	semidirect
227. #6106	C₂²×C₄	semidirect
228. #6105	C₂²×C₄	semidirect
229. #6104	C₂²×C₄	semidirect
245. Dic₅₂	C₂²×C₄	semidirect
246. D₁₀₄	C₂²×C₄	semidirect
247. #6095	C₂²×C₄	semidirect
268. C₂×#444	D₁₃	direct (N × H)
357. C₂×#131	C₂×D₁₃	semidirect
369. #444	C₂×D₁₃	direct (N × H)
373. C₂×#108	C₂×D₁₃	semidirect
378. C₂×#104	C₂×D₁₃	semidirect
383. C₂×#97	C₂×D₁₃	semidirect
396. C₂×D₁₃	#444	direct (N × H)
432. #135	C₄×D₁₃	semidirect
437. C₂×Q₁₆	C₄×D₁₃	semidirect
442. C₂×SD₁₆	C₄×D₁₃	semidirect
446. C₂×D₈	C₄×D₁₃	semidirect
456. #131	C₂²×D₁₃	semidirect
494. #108	C₂²×D₁₃	semidirect
498. #104	C₂²×D₁₃	semidirect
502. #97	C₂²×D₁₃	semidirect
506. C₂×C₁₃	C₂×#444	semidirect
510. D₁₃	C₂×#444	direct (N × H)
568. Q₁₆	C₂×C₄×D₁₃	semidirect
572. SD₁₆	C₂×C₄×D₁₃	semidirect
575. D₈	C₂×C₄×D₁₃	semidirect
617. C₁₃	C₂²×#444	semidirect
715. C₂	D₁₃×#444	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₁₃×#135	2
C₂×D₁₃×#131	2
C₂×#11718378	2
C₂×#11718858	2
C₂×#11718555	2
C₂×#11718806	2
C₂×#11718484	2
D₁₃×#444	2
C₂×D₁₃×#108	2
C₂×D₁₃×#104	2
C₂×D₁₃×#97	2
C₂×C₁₃×#444	2
C₂²×#444	13

Subgroups — C2×D13×#444 #16727212

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃×#444 #16727212