Subgroups — C₂×#13123754 #16727241

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	C₂²×#88158	C₂	1	1	yes	maximal, characteristic
2	C₂×#11719450	C₂	1	2	yes	maximal, complemented
3	#13123754	C₂	1	16	yes	maximal, direct product factor
4	C₂×#11718378	C₂	1	4	yes	maximal, complemented
5	C₂×#11718361	C₂	1	4	yes	maximal, complemented
6	C₂²×#88059	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#11718666	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#6127	C₂²	1	2	yes	—
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
13	C₂²×#6099	C₂²	1	2	yes	—
14	#11719450	—	2	8	no	—
15	#11719450	C₂²	1	16	yes	complemented
16	C₂×#88161	—	2	4	no	—
17	C₂×M₁₆×D₁₃	—	2	4	no	—
18	C₂²×Dic₅₂	C₄	1	1	yes	characteristic, complemented
19	C₂×#88158	C₄	1	2	yes	complemented
20	C₂×#88158	C₄	1	2	yes	complemented
21	C₂×#88158	C₄	1	8	yes	complemented
22	C₂×#88158	C₂²	1	2	yes	—
23	C₂×#88158	C₂²	1	2	yes	—
24	C₂×#88158	C₂²	1	8	yes	—
25	C₂²×D₁₀₄	C₄	1	1	yes	characteristic, complemented
26	C₂²×#6095	C₄	1	2	yes	complemented
27	C₂×#88155	C₂²	1	8	yes	complemented
28	C₁₃×#405	C₂²	1	8	yes	complemented
29	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
30	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
31	C₂×#88059	C₂²	1	2	yes	complemented
32	C₂×#88059	C₂²	1	2	yes	complemented
33	C₂×#88059	C₂²	1	8	yes	complemented
34	#11718666	C₂²	1	16	yes	complemented
35	C₂×#88045	C₂²	1	8	yes	complemented
36	#11718378	C₂²	1	32	yes	complemented
37	#11718361	C₂²	1	32	yes	complemented
38	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
39	C₂²×C₂²⋊D₁₃	—	2	2	no	—
40	C₂×#6127	—	2	2	no	—
41	C₂×#6127	—	2	4	no	—
42	C₂×#6127	—	2	2	no	—
43	C₂×#6127	—	2	4	no	—
44	C₂×#6127	C₂×C₄	1	4	yes	—
45	C₂×#6127	C₂×C₄	1	8	yes	—
46	C₂×#6127	C₂³	1	8	yes	—
47	C₂×#6127	C₂³	1	4	yes	—
48	C₂²×D₅₂	C₂×C₄	1	2	yes	—
49	C₂²×C₄×D₁₃	—	2	2	no	—
50	C₂²×Dic₂₆	C₂×C₄	1	2	yes	—
51	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
52	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
53	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
54	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
55	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
63	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
64	C₁₃×#117	—	2	2	no	—
65	C₁₃×#117	C₂³	1	4	yes	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
69	C₂×#6099	—	2	2	no	—
70	C₂×#6099	—	2	4	no	—
71	C₂×#6099	C₂³	1	8	yes	—
72	C₂×#6099	C₂³	1	4	yes	—
73	C₂²×#1055	—	2	2	no	—
74	#88161	—	2	32	no	—
75	M₁₆×D₁₃	—	2	32	no	—
76	C₂×Dic₅₂	C₂×C₄	1	2	yes	—
77	C₂×Dic₅₂	C₂×C₄	1	2	yes	—
78	C₂×Dic₅₂	C₂×C₄	1	8	yes	complemented
79	#88158	C₂×C₄	1	8	yes	—
80	#88158	C₂×C₄	1	8	yes	—
81	#88158	C₂×C₄	1	16	yes	complemented
82	#88158	C₂×C₄	1	16	yes	complemented
83	#88158	C₂³	1	8	yes	—
84	#88158	C₂³	1	8	yes	—
85	C₂×D₁₀₄	C₂×C₄	1	2	yes	—
86	C₂×D₁₀₄	C₂×C₄	1	2	yes	—
87	C₂×D₁₀₄	C₂×C₄	1	8	yes	complemented
88	C₂×#6095	C₂×C₄	1	4	yes	—
89	C₂×#6095	C₂×C₄	1	4	yes	—
90	C₂×#6095	C₂×C₄	1	16	yes	complemented
91	#88155	—	2	16	no	—
92	#88155	C₂³	1	32	yes	complemented
93	C₂×#6094	—	2	8	no	—
94	C₂×C₈×D₁₃	—	2	8	no	—
95	C₁₃×#97	C₂³	1	8	yes	complemented
96	C₄×C₈×C₁₃	C₂³	1	8	yes	complemented
97	#88059	C₂³	1	8	yes	complemented
98	#88059	C₂³	1	8	yes	complemented
99	#88045	C₂³	1	32	yes	complemented
100	C₂×#2957	—	13	1	no	maximal, Sylow
101	C₂⁴×C₁₃	#41	1	1	yes	characteristic
102	C₂³×D₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	#41	1	2	yes	—
112	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
114	C₂×C₂²⋊D₁₃	—	2	4	no	—
115	C₂×C₂²⋊D₁₃	—	2	8	no	—
116	C₂×C₂²⋊D₁₃	—	2	4	no	—
117	C₂×C₂²⋊D₁₃	—	2	8	no	—
118	C₂²×Dic₁₃	—	2	2	no	—
119	#6127	—	2	8	no	—
120	#6127	—	2	8	no	—
121	#6127	—	2	8	no	—
122	#6127	—	2	4	no	—
123	#6127	—	2	8	no	—
124	#6127	—	2	4	no	—
125	#6127	—	2	8	no	—
126	#6127	C₂²×C₄	1	8	yes	—
127	#6127	C₂²×C₄	1	16	yes	—
128	#6127	C₂⁴	1	8	yes	—
129	C₂×D₅₂	—	2	2	no	—
130	C₂×D₅₂	—	2	4	no	—
131	C₂×D₅₂	C₂²×C₄	1	4	yes	—
132	C₂×D₅₂	C₂²×C₄	1	8	yes	—
133	C₂×C₄×D₁₃	—	2	4	no	—
134	C₂×C₄×D₁₃	—	2	8	no	—
135	C₂×C₄×D₁₃	—	2	4	no	—
136	C₂×C₄×D₁₃	—	2	8	no	—
137	C₂×Dic₂₆	—	2	2	no	—
138	C₂×Dic₂₆	—	2	4	no	—
139	C₂×Dic₂₆	C₂²×C₄	1	4	yes	—
140	C₂×Dic₂₆	C₂²×C₄	1	8	yes	—
141	C₁₃×M₁₆	C₂×D₄	1	8	yes	—
142	C₁₃×M₁₆	C₂×D₄	1	8	yes	—
143	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
146	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
149	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
150	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
152	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
153	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
154	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
155	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
156	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
157	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
158	C₁₃×C₄⋊C₄	—	2	4	no	—
159	C₁₃×C₂²⋊C₄	—	2	4	no	—
160	C₄²×C₁₃	—	2	2	no	—
161	C₄²×C₁₃	C₂⁴	1	4	yes	—
162	#6099	—	2	4	no	—
163	#6099	—	2	8	no	—
164	#6099	C₂⁴	1	8	yes	—
165	C₂×#1055	—	2	4	no	—
166	C₂×#1055	—	2	8	no	—
167	Dic₅₂	C₂²×C₄	1	8	yes	—
168	Dic₅₂	C₂²×C₄	1	8	yes	—
169	D₁₀₄	C₂²×C₄	1	8	yes	—
170	D₁₀₄	C₂²×C₄	1	8	yes	—
171	#6095	C₂²×C₄	1	16	yes	—
172	#6095	C₂²×C₄	1	16	yes	—
173	#6094	—	2	32	no	—
174	C₈×D₁₃	—	2	32	no	—
175	C₂²×#135	—	13	1	no	—
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	D₁₃	1	1	yes	characteristic, complemented
183	C₂³×C₁₃	—	4	2	no	—
184	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
185	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
186	C₂³×C₁₃	C₄×D₄	1	2	yes	—
187	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
188	C₂³×C₁₃	C₂×#41	1	2	yes	—
189	C₂²×D₁₃	—	2	4	no	—
190	C₂²×D₁₃	—	2	8	no	—
191	C₂²×D₁₃	—	8	4	no	—
192	C₂×C₄×C₁₃	—	2	4	no	—
193	C₂×C₄×C₁₃	—	4	4	no	—
194	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
195	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
197	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
199	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
200	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
201	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
202	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
205	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
206	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
208	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
211	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
212	C₂²⋊D₁₃	—	2	8	no	—
213	C₂²⋊D₁₃	—	2	16	no	—
214	C₂²⋊D₁₃	—	2	8	no	—
215	C₂×Dic₁₃	—	2	8	no	—
216	C₂×Dic₁₃	—	2	4	no	—
217	D₅₂	—	2	4	no	—
218	D₅₂	—	2	8	no	—
219	D₅₂	C₂³×C₄	1	8	yes	—
220	C₄×D₁₃	—	2	8	no	—
221	C₄×D₁₃	—	2	16	no	—
222	C₄×D₁₃	—	2	8	no	—
223	Dic₂₆	—	2	4	no	—
224	Dic₂₆	—	2	8	no	—
225	Dic₂₆	C₂³×C₄	1	8	yes	—
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	C₈×C₁₃	C₂²×D₄	1	8	yes	—
231	#1055	—	2	8	no	—
232	C₂²×#41	—	13	2	no	—
233	C₂×#135	—	13	2	no	—
234	C₂×#135	—	13	2	no	—
235	C₂×#135	—	13	8	no	—
236	C₂×#135	—	13	2	no	—
237	C₂×#135	—	13	2	no	—
238	C₂×#135	—	13	8	no	—
239	C₂²×Q₁₆	—	13	1	no	—
240	C₂²×SD₁₆	—	13	2	no	—
241	C₂²×D₈	—	13	1	no	—
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	2	no	—
247	C₂²×M₁₆	—	26	4	no	—
248	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
249	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
250	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
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	C₂×D₁₃	1	8	yes	complemented
259	C₂×#97	C₂×D₁₃	1	2	yes	complemented
260	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	complemented
261	C₂²×C₁₃	—	2	2	no	—
262	C₂²×C₁₃	—	2	2	no	—
263	C₂²×C₁₃	—	2	2	no	—
264	C₂²×C₁₃	—	4	2	no	—
265	C₂²×C₁₃	—	4	2	no	—
266	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
267	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
268	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
269	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
270	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
271	C₂×D₁₃	—	2	8	no	—
272	C₂×D₁₃	—	4	8	no	—
273	C₂×D₁₃	—	8	8	no	—
274	C₄×C₁₃	—	4	4	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	—	2	8	no	—
282	C₂×#41	—	13	4	no	—
283	C₂×#41	—	13	8	no	—
284	C₂×#41	—	13	4	no	—
285	C₂×#41	—	13	8	no	—
286	C₂×#41	—	26	2	no	—
287	C₂×#41	—	26	4	no	—
288	C₂×#41	—	26	2	no	—
289	C₂×#41	—	26	4	no	—
290	C₂²×Q₈	—	13	2	no	—
291	C₂²×D₄	—	13	2	no	—
292	C₂²×D₄	—	26	2	no	—
293	C₂³×C₄	—	26	2	no	—
294	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
295	#135	—	13	8	no	—
296	#135	—	13	8	no	—
297	#135	—	13	16	no	—
298	#135	—	13	16	no	—
299	#135	—	13	8	no	—
300	#135	—	13	8	no	—
301	C₂×Q₁₆	—	13	2	no	—
302	C₂×Q₁₆	—	13	2	no	—
303	C₂×Q₁₆	—	13	8	no	—
304	C₂×SD₁₆	—	13	4	no	—
305	C₂×SD₁₆	—	13	4	no	—
306	C₂×SD₁₆	—	13	16	no	—
307	C₂×D₈	—	13	2	no	—
308	C₂×D₈	—	13	2	no	—
309	C₂×D₈	—	13	8	no	—
310	#131	—	13	32	no	—
311	#131	—	26	32	no	—
312	#131	—	26	16	no	—
313	C₂×M₁₆	—	13	4	no	—
314	C₂×M₁₆	—	13	8	no	—
315	C₂×M₁₆	—	26	2	no	—
316	C₂×M₁₆	—	26	4	no	—
317	C₂×M₁₆	—	26	32	no	—
318	C₂×M₁₆	—	26	8	no	—
319	C₂×M₁₆	D₅₂	1	2	yes	—
320	C₂×M₁₆	D₅₂	1	2	yes	—
321	C₂×M₁₆	D₅₂	1	4	yes	—
322	C₂×M₁₆	C₂²×D₁₃	1	4	yes	—
323	C₂²×C₈	—	26	2	no	—
324	C₂²×C₈	—	26	8	no	—
325	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
326	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
327	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
328	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
329	C₂²×C₈	C₄×D₁₃	1	4	yes	—
330	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
331	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
332	C₂²×C₈	C₂²×D₁₃	1	4	yes	—
333	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
334	#117	—	2	2	no	—
335	#117	C₂²×D₁₃	1	4	yes	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₂²⋊C₄	—	2	1	no	—
338	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
339	#108	—	13	8	no	—
340	#108	—	13	8	no	—
341	#104	—	13	32	no	—
342	#97	C₂²×D₁₃	1	8	yes	complemented
343	C₄×C₈	C₂²×D₁₃	1	8	yes	complemented
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	#2957	1	2	yes	complemented
349	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
350	D₁₃	—	4	8	no	—
351	C₂⁴	—	26	2	no	—
352	C₂⁴	#6127	1	1	yes	characteristic
353	#41	—	13	8	no	—
354	#41	—	13	16	no	—
355	#41	—	13	8	no	—
356	#41	—	26	8	no	—
357	#41	—	26	8	no	—
358	#41	—	26	8	no	—
359	#41	—	26	8	no	—
360	#41	—	26	4	no	—
361	#41	—	26	4	no	—
362	#41	—	26	8	no	—
363	C₂×Q₈	—	13	4	no	—
364	C₂×Q₈	—	13	8	no	—
365	C₂×Q₈	—	26	2	no	—
366	C₂×Q₈	—	26	4	no	—
367	C₂×D₄	—	13	4	no	—
368	C₂×D₄	—	13	8	no	—
369	C₂×D₄	—	26	4	no	—
370	C₂×D₄	—	26	8	no	—
371	C₂×D₄	—	26	4	no	—
372	C₂×D₄	—	26	8	no	—
373	C₂×D₄	—	26	2	no	—
374	C₂×D₄	—	26	4	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	26	2	no	—
377	C₂²×C₄	—	26	4	no	—
378	C₂²×C₄	—	26	8	no	—
379	C₂²×C₄	—	26	8	no	—
380	C₂²×C₄	—	26	4	no	—
381	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
382	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
384	C₂²×C₄	C₂×D₅₂	1	2	yes	—
385	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
387	C₂²×C₄	#6127	1	1	yes	characteristic
388	C₂²×C₄	#6127	1	2	yes	—
389	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
390	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
391	Q₁₆	—	13	8	no	—
392	Q₁₆	—	13	8	no	—
393	SD₁₆	—	13	16	no	—
394	SD₁₆	—	13	16	no	—
395	D₈	—	13	8	no	—
396	D₈	—	13	8	no	—
397	M₁₆	—	13	8	no	—
398	M₁₆	—	26	8	no	—
399	M₁₆	—	26	4	no	—
400	M₁₆	—	26	32	no	—
401	M₁₆	C₂×D₅₂	1	8	yes	—
402	M₁₆	C₂×D₅₂	1	8	yes	—
403	C₂×C₈	—	26	8	no	—
404	C₂×C₈	—	26	4	no	—
405	C₂×C₈	—	26	32	no	—
406	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
407	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
408	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
409	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
410	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
411	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
412	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
413	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
414	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
415	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
416	C₂×C₈	C₂×D₅₂	1	4	yes	—
417	C₂×C₈	C₂×D₅₂	1	4	yes	—
418	C₂×C₈	C₂³×D₁₃	1	2	yes	—
419	C₂×C₈	C₂³×D₁₃	1	2	yes	—
420	C₂×C₈	C₂³×D₁₃	1	4	yes	—
421	C₄⋊C₄	—	2	4	no	—
422	C₂²⋊C₄	—	2	4	no	—
423	C₄²	—	2	2	no	—
424	C₄²	C₂³×D₁₃	1	4	yes	—
425	C₁₃	C₂×#2957	1	1	yes	characteristic, complemented, Sylow
426	C₂³	—	4	2	no	—
427	C₂³	—	26	4	no	—
428	C₂³	—	26	8	no	—
429	C₂³	—	104	4	no	—
430	C₂³	C₄×D₅₂	1	1	yes	characteristic
431	C₂³	C₄×D₅₂	1	1	yes	characteristic
432	C₂³	C₄×D₅₂	1	2	yes	—
433	C₂³	C₂×#6127	1	1	yes	characteristic
434	C₂³	C₂×#6127	1	2	yes	—
435	Q₈	—	13	8	no	—
436	Q₈	—	26	8	no	—
437	Q₈	—	26	4	no	—
438	D₄	—	13	8	no	—
439	D₄	—	26	16	no	—
440	D₄	—	26	8	no	—
441	D₄	—	26	8	no	—
442	D₄	—	26	8	no	—
443	D₄	—	26	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	26	8	no	—
447	C₂×C₄	—	26	4	no	—
448	C₂×C₄	—	26	16	no	—
449	C₂×C₄	—	26	8	no	—
450	C₂×C₄	—	26	8	no	—
451	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
452	C₂×C₄	C₄×D₅₂	1	2	yes	—
453	C₂×C₄	C₄×D₅₂	1	2	yes	—
454	C₂×C₄	C₄×D₅₂	1	1	yes	characteristic
455	C₂×C₄	C₄×D₅₂	1	2	yes	—
456	C₂×C₄	C₄×D₅₂	1	2	yes	—
457	C₂×C₄	C₄×D₅₂	1	2	yes	—
458	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
459	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
460	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
461	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₅₂	1	2	yes	—
463	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₅₂	1	2	yes	—
465	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
466	C₂×C₄	C₂×#6127	1	1	yes	characteristic
467	C₂×C₄	C₂×#6127	1	2	yes	—
468	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
469	C₈	—	26	8	no	—
470	C₈	C₂²×C₄×D₁₃	1	2	yes	—
471	C₈	C₂²×C₄×D₁₃	1	2	yes	—
472	C₈	C₂²×C₄×D₁₃	1	2	yes	—
473	C₈	C₂²×C₄×D₁₃	1	2	yes	—
474	C₈	C₂²×D₅₂	1	8	yes	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	4	2	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	26	8	no	—
481	C₂²	—	52	8	no	—
482	C₂²	—	104	8	no	—
483	C₂²	C₂×C₄×D₅₂	1	2	yes	—
484	C₂²	C₂×C₄×D₅₂	1	2	yes	—
485	C₂²	C₂×C₄×D₅₂	1	1	yes	characteristic
486	C₂²	C₂×C₄×D₅₂	1	1	yes	characteristic
487	C₂²	C₂²×#6127	1	1	yes	characteristic
488	C₄	—	4	4	no	—
489	C₄	—	26	8	no	—
490	C₄	C₂×C₄×D₅₂	1	2	yes	—
491	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
492	C₄	C₂×C₄×D₅₂	1	2	yes	—
493	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
494	C₄	C₂³×C₄×D₁₃	1	1	yes	characteristic
495	C₄	C₂³×D₅₂	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	—	52	8	no	—
501	C₂	#13123754	1	2	yes	direct product factor
502	C₂	C₂²×C₄×D₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₅₂
commutator	C₄×C₁₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₂×C₁₃×#405	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂²×#88158	C₂
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₂×#405	D₁₃
hypocenter	C₁₃	C₂×#2957
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×M₁₆ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
2. C₂×#11719450	C₂	semidirect
3. #13123754	C₂	direct (N × H)
4. C₂×#11718378	C₂	semidirect
5. C₂×#11718361	C₂	semidirect
6. C₂²×#88059	C₂	semidirect
7. C₂×#11718666	C₂	semidirect
8. C₂×C₁₃×#405	C₂	semidirect
15. #11719450	C₂²	semidirect
18. C₂²×Dic₅₂	C₄	semidirect
19. C₂×#88158	C₄	semidirect
20. C₂×#88158	C₄	semidirect
21. C₂×#88158	C₄	semidirect
25. C₂²×D₁₀₄	C₄	semidirect
26. C₂²×#6095	C₄	semidirect
27. C₂×#88155	C₂²	semidirect
28. C₁₃×#405	C₂²	semidirect
29. C₂×C₁₃×#97	C₂²	semidirect
30. C₂×C₄×C₈×C₁₃	C₂²	semidirect
31. C₂×#88059	C₂²	semidirect
32. C₂×#88059	C₂²	semidirect
33. C₂×#88059	C₂²	semidirect
34. #11718666	C₂²	semidirect
35. C₂×#88045	C₂²	semidirect
36. #11718378	C₂²	semidirect
37. #11718361	C₂²	semidirect
78. C₂×Dic₅₂	C₂×C₄	semidirect
81. #88158	C₂×C₄	semidirect
82. #88158	C₂×C₄	semidirect
87. C₂×D₁₀₄	C₂×C₄	semidirect
90. C₂×#6095	C₂×C₄	semidirect
92. #88155	C₂³	semidirect
95. C₁₃×#97	C₂³	semidirect
96. C₄×C₈×C₁₃	C₂³	semidirect
97. #88059	C₂³	semidirect
98. #88059	C₂³	semidirect
99. #88045	C₂³	semidirect
182. C₂×#405	D₁₃	semidirect
258. #405	C₂×D₁₃	semidirect
259. C₂×#97	C₂×D₁₃	semidirect
260. C₂×C₄×C₈	C₂×D₁₃	semidirect
342. #97	C₂²×D₁₃	semidirect
343. C₄×C₈	C₂²×D₁₃	semidirect
348. C₂×C₁₃	#2957	semidirect
425. C₁₃	C₂×#2957	semidirect
501. C₂	#13123754	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×#88158	2
C₂×#11719450	2
#13123754	2
C₂×#11718378	2
C₂×#11718361	2
C₂²×#88059	2
C₂×#11718666	2
C₂×C₁₃×#405	2
C₂×#2957	13

Subgroups — C2×#13123754 #16727241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13123754 #16727241