Subgroups — C₂×#13123753 #16727240

Order 3328.

2642 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719524	C₂	1	2	yes	maximal, complemented
2	#13123753	C₂	1	16	yes	maximal, direct product factor
3	C₂×#11718858	C₂	1	4	yes	maximal, complemented
4	C₂×#11718857	C₂	1	4	yes	maximal, complemented
5	C₂²×#88059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11718897	C₂	1	2	yes	maximal, complemented
7	C₂×#11718762	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₃×#135	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₁₃×#41	C₂²	1	2	yes	—
10	C₂×C₁₃×#135	C₄	1	2	yes	complemented
11	C₂×C₁₃×#135	C₄	1	2	yes	complemented
12	C₂×C₁₃×#135	C₄	1	8	yes	complemented
13	C₂×C₁₃×#135	C₂²	1	2	yes	—
14	C₂×C₁₃×#135	C₂²	1	2	yes	—
15	C₂×C₁₃×#135	C₂²	1	8	yes	—
16	C₂²×C₁₃×Q₁₆	C₄	1	1	yes	characteristic, complemented
17	C₂²×C₁₃×SD₁₆	C₄	1	2	yes	complemented
18	C₂²×C₁₃×D₈	C₄	1	1	yes	characteristic, complemented
19	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
20	#11719524	—	2	8	no	—
21	#11719524	C₂²	1	16	yes	complemented
22	C₂×#88202	—	2	4	no	—
23	C₂×#88202	C₂²	1	8	yes	complemented
24	C₂×#88180	C₂²	1	1	yes	characteristic
25	C₂²×#6099	—	2	4	no	—
26	C₂²×#6099	C₂²	1	2	yes	—
27	C₂²×#6099	C₂²	1	1	yes	characteristic
28	#11718897	C₂²	1	16	yes	complemented
29	C₂×#88077	C₂²	1	8	yes	complemented
30	#11718858	C₂²	1	32	yes	complemented
31	#11718857	C₂²	1	32	yes	complemented
32	C₂×#88059	C₂²	1	2	yes	complemented
33	C₂×#88059	C₂²	1	2	yes	complemented
34	C₂×#88059	C₂²	1	8	yes	complemented
35	#11718762	C₂²	1	8	yes	complemented
36	C₂×#88055	C₂²	1	2	yes	complemented
37	C₂×C₈×Dic₁₃	C₂²	1	2	yes	complemented
38	C₂×C₁₃×#41	—	2	2	no	—
39	C₂×C₁₃×#41	—	2	4	no	—
40	C₂×C₁₃×#41	—	2	2	no	—
41	C₂×C₁₃×#41	—	2	4	no	—
42	C₂×C₁₃×#41	C₂×C₄	1	4	yes	—
43	C₂×C₁₃×#41	C₂×C₄	1	8	yes	—
44	C₂×C₁₃×#41	C₂³	1	4	yes	—
45	C₂×C₁₃×#41	C₂³	1	8	yes	—
46	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
47	C₂²×D₄×C₁₃	—	2	2	no	—
48	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
49	C₂³×C₄×C₁₃	—	2	2	no	—
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₁₃×#135	C₂×C₄	1	8	yes	—
52	C₁₃×#135	C₂×C₄	1	8	yes	—
53	C₁₃×#135	C₂×C₄	1	16	yes	complemented
54	C₁₃×#135	C₂×C₄	1	16	yes	complemented
55	C₁₃×#135	C₂³	1	8	yes	—
56	C₁₃×#135	C₂³	1	8	yes	—
57	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
58	C₂×C₁₃×Q₁₆	C₂×C₄	1	2	yes	—
59	C₂×C₁₃×Q₁₆	C₂×C₄	1	8	yes	complemented
60	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	—
61	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	—
62	C₂×C₁₃×SD₁₆	C₂×C₄	1	16	yes	complemented
63	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
64	C₂×C₁₃×D₈	C₂×C₄	1	2	yes	—
65	C₂×C₁₃×D₈	C₂×C₄	1	8	yes	complemented
66	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
74	C₂×C₂²⋊Dic₁₃	—	2	1	no	—
75	#88202	—	2	32	no	—
76	#88202	—	2	16	no	—
77	#88202	C₂³	1	32	yes	complemented
78	#88180	—	2	2	no	—
79	#88180	C₂³	1	4	yes	—
80	C₂×C₄⋊Dic₁₃	—	2	1	no	—
81	C₂×C₄×Dic₁₃	C₂³	1	2	yes	—
82	C₂×#6099	—	2	2	no	—
83	C₂×#6099	—	2	4	no	—
84	C₂×#6099	—	2	32	no	—
85	C₂×#6099	—	2	8	no	—
86	C₂×#6099	D₄	1	2	yes	—
87	C₂×#6099	D₄	1	2	yes	—
88	C₂×#6099	D₄	1	4	yes	—
89	C₂×#6099	C₂³	1	4	yes	—
90	C₂×#6099	C₂³	1	8	yes	—
91	C₂×#6099	C₂³	1	4	yes	—
92	C₂²×#1055	—	2	2	no	—
93	C₂²×#1055	—	2	8	no	—
94	C₂²×#1055	C₂³	1	2	yes	—
95	#88077	C₂³	1	32	yes	complemented
96	#88059	C₂³	1	8	yes	complemented
97	#88059	C₂³	1	8	yes	complemented
98	#88055	C₂³	1	8	yes	complemented
99	C₈×Dic₁₃	C₂³	1	8	yes	complemented
100	C₂×#2957	—	13	1	no	maximal, Sylow
101	C₂⁴×C₁₃	—	2	2	no	—
102	C₂⁴×C₁₃	#41	1	1	yes	characteristic
103	C₁₃×#41	—	2	8	no	—
104	C₁₃×#41	—	2	8	no	—
105	C₁₃×#41	—	2	8	no	—
106	C₁₃×#41	—	2	8	no	—
107	C₁₃×#41	—	2	4	no	—
108	C₁₃×#41	—	2	4	no	—
109	C₁₃×#41	—	2	8	no	—
110	C₁₃×#41	C₂²×C₄	1	8	yes	—
111	C₁₃×#41	C₂²×C₄	1	16	yes	—
112	C₁₃×#41	C₂⁴	1	8	yes	—
113	C₂×Q₈×C₁₃	—	2	2	no	—
114	C₂×Q₈×C₁₃	—	2	4	no	—
115	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
116	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
117	C₂×D₄×C₁₃	—	2	4	no	—
118	C₂×D₄×C₁₃	—	2	8	no	—
119	C₂×D₄×C₁₃	—	2	4	no	—
120	C₂×D₄×C₁₃	—	2	8	no	—
121	C₂×D₄×C₁₃	—	2	2	no	—
122	C₂×D₄×C₁₃	—	2	4	no	—
123	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
124	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	4	no	—
127	C₂²×C₄×C₁₃	—	2	8	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	8	no	—
130	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	#41	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
140	C₂²×Dic₁₃	—	2	2	no	—
141	C₁₃×Q₁₆	C₂²×C₄	1	8	yes	—
142	C₁₃×Q₁₆	C₂²×C₄	1	8	yes	—
143	C₁₃×SD₁₆	C₂²×C₄	1	16	yes	—
144	C₁₃×SD₁₆	C₂²×C₄	1	16	yes	—
145	C₁₃×D₈	C₂²×C₄	1	8	yes	—
146	C₁₃×D₈	C₂²×C₄	1	8	yes	—
147	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
150	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
153	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
155	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
156	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
157	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
158	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
159	C₂²⋊Dic₁₃	—	2	4	no	—
160	C₄⋊Dic₁₃	—	2	4	no	—
161	C₄×Dic₁₃	—	2	2	no	—
162	C₄×Dic₁₃	C₂⁴	1	4	yes	—
163	#6099	—	2	8	no	—
164	#6099	—	2	4	no	—
165	#6099	—	2	32	no	—
166	#6099	C₂×D₄	1	8	yes	—
167	#6099	C₂×D₄	1	8	yes	—
168	#6099	C₂⁴	1	8	yes	—
169	C₂×#1055	—	2	4	no	—
170	C₂×#1055	—	2	8	no	—
171	C₂×#1055	—	2	32	no	—
172	C₂×#1055	C₂×D₄	1	4	yes	—
173	C₂×#1055	C₂×D₄	1	4	yes	—
174	C₂×#1055	C₂⁴	1	4	yes	—
175	C₂²×#135	D₁₃	1	1	yes	characteristic
176	C₂×#568	—	13	2	no	—
177	#2957	—	13	16	no	—
178	C₂×#444	—	13	4	no	—
179	C₂×#443	—	13	4	no	—
180	C₂²×#108	—	13	1	no	—
181	C₂×#421	—	13	2	no	—
182	C₂×#405	—	13	1	no	—
183	C₂³×C₁₃	—	2	4	no	—
184	C₂³×C₁₃	—	2	8	no	—
185	C₂³×C₁₃	—	4	2	no	—
186	C₂³×C₁₃	—	8	4	no	—
187	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
188	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
189	C₂³×C₁₃	C₄×D₄	1	2	yes	—
190	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
191	C₂³×C₁₃	C₂×#41	1	2	yes	—
192	Q₈×C₁₃	—	2	4	no	—
193	Q₈×C₁₃	—	2	8	no	—
194	Q₈×C₁₃	C₂³×C₄	1	8	yes	—
195	D₄×C₁₃	—	2	8	no	—
196	D₄×C₁₃	—	2	16	no	—
197	D₄×C₁₃	—	2	8	no	—
198	D₄×C₁₃	—	2	4	no	—
199	D₄×C₁₃	—	2	8	no	—
200	D₄×C₁₃	C₂³×C₄	1	8	yes	—
201	C₂×C₄×C₁₃	—	2	8	no	—
202	C₂×C₄×C₁₃	—	2	4	no	—
203	C₂×C₄×C₁₃	—	2	8	no	—
204	C₂×C₄×C₁₃	—	2	16	no	—
205	C₂×C₄×C₁₃	—	2	8	no	—
206	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
207	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
209	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
211	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
212	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
213	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
214	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
217	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
218	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
223	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
224	C₂×Dic₁₃	—	2	4	no	—
225	C₂×Dic₁₃	—	4	4	no	—
226	C₈×C₁₃	C₂³×C₄	1	2	yes	—
227	C₈×C₁₃	C₂³×C₄	1	2	yes	—
228	C₈×C₁₃	C₂³×C₄	1	2	yes	—
229	C₈×C₁₃	C₂³×C₄	1	2	yes	—
230	#1055	—	2	8	no	—
231	#1055	C₂²×D₄	1	8	yes	—
232	C₂²×#41	C₂×D₁₃	1	2	yes	—
233	C₂×#135	Dic₁₃	1	2	yes	complemented
234	C₂×#135	Dic₁₃	1	2	yes	complemented
235	C₂×#135	Dic₁₃	1	8	yes	complemented
236	C₂×#135	C₂×D₁₃	1	2	yes	—
237	C₂×#135	C₂×D₁₃	1	2	yes	—
238	C₂×#135	C₂×D₁₃	1	8	yes	—
239	C₂²×Q₁₆	Dic₁₃	1	1	yes	characteristic, complemented
240	C₂²×SD₁₆	Dic₁₃	1	2	yes	complemented
241	C₂²×D₈	Dic₁₃	1	1	yes	characteristic, complemented
242	#568	—	13	16	no	—
243	#568	—	26	8	no	—
244	C₂×#131	—	13	8	no	—
245	C₂×#131	—	26	4	no	—
246	C₂²×M₁₆	—	13	1	no	—
247	C₂²×M₁₆	—	13	2	no	—
248	C₂²×M₁₆	—	26	4	no	—
249	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
250	C₂×#117	—	13	1	no	—
251	#444	—	13	32	no	—
252	#443	—	13	32	no	—
253	C₂×#108	—	13	2	no	—
254	C₂×#108	—	13	2	no	—
255	C₂×#108	—	13	8	no	—
256	#421	—	13	16	no	—
257	C₂×#104	—	13	8	no	—
258	#405	—	13	8	no	—
259	C₂×#97	—	13	2	no	—
260	C₂×C₄×C₈	—	13	2	no	—
261	C₂²×C₁₃	—	2	2	no	—
262	C₂²×C₁₃	—	2	2	no	—
263	C₂²×C₁₃	—	2	2	no	—
264	C₂²×C₁₃	—	2	8	no	—
265	C₂²×C₁₃	—	4	2	no	—
266	C₂²×C₁₃	—	4	2	no	—
267	C₂²×C₁₃	—	4	8	no	—
268	C₂²×C₁₃	—	8	8	no	—
269	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
270	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
271	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
272	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
273	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
274	C₄×C₁₃	—	2	8	no	—
275	C₄×C₁₃	C₂×C₄×D₄	1	2	yes	—
276	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
277	C₄×C₁₃	C₂×C₄×D₄	1	2	yes	—
278	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
279	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
280	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
281	Dic₁₃	—	4	4	no	—
282	C₂×#41	—	2	2	no	—
283	C₂×#41	—	2	4	no	—
284	C₂×#41	—	2	2	no	—
285	C₂×#41	—	2	4	no	—
286	C₂×#41	C₂×Dic₁₃	1	4	yes	—
287	C₂×#41	C₂×Dic₁₃	1	8	yes	—
288	C₂×#41	C₂²×D₁₃	1	4	yes	—
289	C₂×#41	C₂²×D₁₃	1	8	yes	—
290	C₂²×Q₈	C₂×Dic₁₃	1	2	yes	—
291	C₂²×D₄	—	2	2	no	—
292	C₂²×D₄	C₂×Dic₁₃	1	2	yes	—
293	C₂³×C₄	—	2	2	no	—
294	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
295	#135	C₂×Dic₁₃	1	8	yes	—
296	#135	C₂×Dic₁₃	1	8	yes	—
297	#135	C₂×Dic₁₃	1	16	yes	complemented
298	#135	C₂×Dic₁₃	1	16	yes	complemented
299	#135	C₂²×D₁₃	1	8	yes	—
300	#135	C₂²×D₁₃	1	8	yes	—
301	C₂×Q₁₆	C₂×Dic₁₃	1	2	yes	—
302	C₂×Q₁₆	C₂×Dic₁₃	1	2	yes	—
303	C₂×Q₁₆	C₂×Dic₁₃	1	8	yes	complemented
304	C₂×SD₁₆	C₂×Dic₁₃	1	4	yes	—
305	C₂×SD₁₆	C₂×Dic₁₃	1	4	yes	—
306	C₂×SD₁₆	C₂×Dic₁₃	1	16	yes	complemented
307	C₂×D₈	C₂×Dic₁₃	1	2	yes	—
308	C₂×D₈	C₂×Dic₁₃	1	2	yes	—
309	C₂×D₈	C₂×Dic₁₃	1	8	yes	complemented
310	#131	—	13	32	no	—
311	#131	—	26	16	no	—
312	#131	—	26	32	no	—
313	C₂×M₁₆	—	13	2	no	—
314	C₂×M₁₆	—	13	2	no	—
315	C₂×M₁₆	—	13	4	no	—
316	C₂×M₁₆	—	13	4	no	—
317	C₂×M₁₆	—	13	4	no	—
318	C₂×M₁₆	—	13	8	no	—
319	C₂×M₁₆	—	26	8	no	—
320	C₂×M₁₆	—	26	32	no	—
321	C₂×M₁₆	—	26	2	no	—
322	C₂×M₁₆	—	26	4	no	—
323	C₂²×C₈	—	13	2	no	—
324	C₂²×C₈	—	26	8	no	—
325	C₂²×C₈	—	26	2	no	—
326	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
327	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
328	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
329	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
330	C₂²×C₈	C₂×Dic₁₃	1	4	yes	—
331	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
332	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
333	C₂²×C₈	C₂²×D₁₃	1	4	yes	—
334	#117	—	13	4	no	—
335	#117	—	26	2	no	—
336	C₂×C₄⋊C₄	—	26	1	no	—
337	C₂×C₂²⋊C₄	—	26	1	no	—
338	C₂×C₄²	—	13	2	no	—
339	#108	—	13	8	no	—
340	#108	—	13	8	no	—
341	#104	—	13	32	no	—
342	#97	—	13	8	no	—
343	C₄×C₈	—	13	8	no	—
344	C₂×C₁₃	—	2	1	no	—
345	C₂×C₁₃	—	2	2	no	—
346	C₂×C₁₃	—	2	1	no	—
347	C₂×C₁₃	—	2	2	no	—
348	C₂×C₁₃	—	4	8	no	—
349	C₂×C₁₃	#2957	1	2	yes	complemented
350	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
351	C₂⁴	—	2	2	no	—
352	C₂⁴	#6129	1	1	yes	characteristic
353	#41	—	2	8	no	—
354	#41	—	2	8	no	—
355	#41	—	2	8	no	—
356	#41	—	2	4	no	—
357	#41	—	2	8	no	—
358	#41	—	2	4	no	—
359	#41	—	2	8	no	—
360	#41	C₂²×Dic₁₃	1	8	yes	—
361	#41	C₂²×Dic₁₃	1	16	yes	—
362	#41	C₂³×D₁₃	1	8	yes	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	4	no	—
365	C₂×Q₈	C₂²×Dic₁₃	1	4	yes	—
366	C₂×Q₈	C₂²×Dic₁₃	1	8	yes	—
367	C₂×D₄	—	2	4	no	—
368	C₂×D₄	—	2	8	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	8	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	C₂²×Dic₁₃	1	4	yes	—
374	C₂×D₄	C₂²×Dic₁₃	1	8	yes	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	2	8	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	—	26	2	no	—
381	C₂²×C₄	D₄×D₁₃	1	2	yes	—
382	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
383	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
384	C₂²×C₄	#6129	1	1	yes	characteristic
385	C₂²×C₄	#6129	1	2	yes	—
386	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
387	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
389	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
390	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
391	Q₁₆	C₂²×Dic₁₃	1	8	yes	—
392	Q₁₆	C₂²×Dic₁₃	1	8	yes	—
393	SD₁₆	C₂²×Dic₁₃	1	16	yes	—
394	SD₁₆	C₂²×Dic₁₃	1	16	yes	—
395	D₈	C₂²×Dic₁₃	1	8	yes	—
396	D₈	C₂²×Dic₁₃	1	8	yes	—
397	M₁₆	—	13	8	no	—
398	M₁₆	—	13	8	no	—
399	M₁₆	—	13	8	no	—
400	M₁₆	—	26	32	no	—
401	M₁₆	—	26	8	no	—
402	M₁₆	—	26	4	no	—
403	C₂×C₈	—	13	4	no	—
404	C₂×C₈	—	13	4	no	—
405	C₂×C₈	—	13	4	no	—
406	C₂×C₈	—	26	32	no	—
407	C₂×C₈	—	26	8	no	—
408	C₂×C₈	—	26	4	no	—
409	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
410	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
411	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
412	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
413	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
414	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
415	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
416	C₂×C₈	C₂²×Dic₁₃	1	2	yes	—
417	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
418	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
419	C₂×C₈	C₂³×D₁₃	1	2	yes	—
420	C₂×C₈	C₂³×D₁₃	1	2	yes	—
421	C₄⋊C₄	—	26	4	no	—
422	C₂²⋊C₄	—	26	4	no	—
423	C₄²	—	13	4	no	—
424	C₄²	—	26	2	no	—
425	C₁₃	C₂×#2957	1	1	yes	characteristic, complemented, Sylow
426	C₂³	—	2	4	no	—
427	C₂³	—	2	8	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	8	4	no	—
430	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
431	C₂³	D₄×Dic₁₃	1	1	yes	characteristic
432	C₂³	D₄×Dic₁₃	1	2	yes	—
433	C₂³	C₂×#6129	1	1	yes	characteristic
434	C₂³	C₂×#6129	1	2	yes	—
435	Q₈	—	2	4	no	—
436	Q₈	—	2	8	no	—
437	Q₈	C₂³×Dic₁₃	1	8	yes	—
438	D₄	—	2	8	no	—
439	D₄	—	2	16	no	—
440	D₄	—	2	8	no	—
441	D₄	—	2	4	no	—
442	D₄	—	2	8	no	—
443	D₄	C₂³×Dic₁₃	1	8	yes	—
444	C₂×C₄	—	2	8	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	16	no	—
447	C₂×C₄	—	2	8	no	—
448	C₂×C₄	—	2	8	no	—
449	C₂×C₄	—	26	4	no	—
450	C₂×C₄	—	52	4	no	—
451	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
452	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
453	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
454	C₂×C₄	D₄×Dic₁₃	1	1	yes	characteristic
455	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
456	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
457	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
458	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
459	C₂×C₄	C₂×D₄×D₁₃	1	2	yes	—
460	C₂×C₄	C₂×D₄×D₁₃	1	2	yes	—
461	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
462	C₂×C₄	C₂×#6129	1	1	yes	characteristic
463	C₂×C₄	C₂×#6129	1	2	yes	—
464	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
465	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
466	C₂×C₄	C₂³×Dic₁₃	1	2	yes	—
467	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
468	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
469	C₈	—	13	8	no	—
470	C₈	—	26	8	no	—
471	C₈	C₂³×Dic₁₃	1	2	yes	—
472	C₈	C₂³×Dic₁₃	1	2	yes	—
473	C₈	C₂³×Dic₁₃	1	2	yes	—
474	C₈	C₂³×Dic₁₃	1	2	yes	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	8	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	8	no	—
482	C₂²	—	8	8	no	—
483	C₂²	C₂×D₄×Dic₁₃	1	2	yes	—
484	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
485	C₂²	C₂×D₄×Dic₁₃	1	2	yes	—
486	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
487	C₂²	C₂²×#6129	1	1	yes	characteristic
488	C₄	—	2	8	no	—
489	C₄	—	52	4	no	—
490	C₄	C₂×D₄×Dic₁₃	1	2	yes	—
491	C₄	C₂×D₄×Dic₁₃	1	1	yes	characteristic
492	C₄	C₂×D₄×Dic₁₃	1	1	yes	characteristic
493	C₄	C₂×D₄×Dic₁₃	1	2	yes	—
494	C₄	C₂²×D₄×D₁₃	1	1	yes	characteristic
495	C₄	C₂⁴×Dic₁₃	1	1	yes	characteristic
496	C₂	—	2	1	no	—
497	C₂	—	2	2	no	—
498	C₂	—	2	1	no	—
499	C₂	—	2	2	no	—
500	C₂	—	4	8	no	—
501	C₂	#13123753	1	2	yes	direct product factor
502	C₂	C₂²×D₄×Dic₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₃
commutator	C₄×C₁₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting, prime radical	C₂²×C₁₃×#135	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₂²×#135	D₁₃
hypocenter	C₁₃	C₂×#2957
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#11719524	C₂	semidirect
2. #13123753	C₂	direct (N × H)
3. C₂×#11718858	C₂	semidirect
4. C₂×#11718857	C₂	semidirect
5. C₂²×#88059	C₂	semidirect
6. C₂×#11718897	C₂	semidirect
7. C₂×#11718762	C₂	semidirect
10. C₂×C₁₃×#135	C₄	semidirect
11. C₂×C₁₃×#135	C₄	semidirect
12. C₂×C₁₃×#135	C₄	semidirect
16. C₂²×C₁₃×Q₁₆	C₄	semidirect
17. C₂²×C₁₃×SD₁₆	C₄	semidirect
18. C₂²×C₁₃×D₈	C₄	semidirect
21. #11719524	C₂²	semidirect
23. C₂×#88202	C₂²	semidirect
28. #11718897	C₂²	semidirect
29. C₂×#88077	C₂²	semidirect
30. #11718858	C₂²	semidirect
31. #11718857	C₂²	semidirect
32. C₂×#88059	C₂²	semidirect
33. C₂×#88059	C₂²	semidirect
34. C₂×#88059	C₂²	semidirect
35. #11718762	C₂²	semidirect
36. C₂×#88055	C₂²	semidirect
37. C₂×C₈×Dic₁₃	C₂²	semidirect
53. C₁₃×#135	C₂×C₄	semidirect
54. C₁₃×#135	C₂×C₄	semidirect
59. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
62. C₂×C₁₃×SD₁₆	C₂×C₄	semidirect
65. C₂×C₁₃×D₈	C₂×C₄	semidirect
77. #88202	C₂³	semidirect
95. #88077	C₂³	semidirect
96. #88059	C₂³	semidirect
97. #88059	C₂³	semidirect
98. #88055	C₂³	semidirect
99. C₈×Dic₁₃	C₂³	semidirect
233. C₂×#135	Dic₁₃	semidirect
234. C₂×#135	Dic₁₃	semidirect
235. C₂×#135	Dic₁₃	semidirect
239. C₂²×Q₁₆	Dic₁₃	semidirect
240. C₂²×SD₁₆	Dic₁₃	semidirect
241. C₂²×D₈	Dic₁₃	semidirect
297. #135	C₂×Dic₁₃	semidirect
298. #135	C₂×Dic₁₃	semidirect
303. C₂×Q₁₆	C₂×Dic₁₃	semidirect
306. C₂×SD₁₆	C₂×Dic₁₃	semidirect
309. C₂×D₈	C₂×Dic₁₃	semidirect
349. C₂×C₁₃	#2957	semidirect
425. C₁₃	C₂×#2957	semidirect
501. C₂	#13123753	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×#11719524	2
#13123753	2
C₂×#11718858	2
C₂×#11718857	2
C₂²×#88059	2
C₂×#11718897	2
C₂×#11718762	2
C₂²×C₁₃×#135	2
C₂×#2957	13

Subgroups — C2×#13123753 #16727240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13123753 #16727240