Subgroups — C₂×#13116463 #16015620

Order 3328.

1154 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88155	C₂	1	1	yes	maximal, characteristic
2	C₂²×#88052	C₂	1	1	yes	maximal, characteristic, complemented
3	#13116463	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718100	C₂	1	4	yes	maximal, complemented
5	C₂²×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#6127	C₄	1	1	yes	characteristic
7	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂²×#6099	C₄	1	1	yes	characteristic
9	C₂×#88155	—	2	1	no	—
10	C₂×#88155	—	2	2	no	—
11	C₂×#88155	—	2	1	no	—
12	C₂×#88155	—	2	2	no	—
13	C₂×#88155	C₄	1	4	yes	—
14	C₂×#88155	C₄	1	2	yes	—
15	C₂×#88155	C₂²	1	2	yes	—
16	C₂×#88155	C₂²	1	4	yes	—
17	C₂²×#6094	—	2	1	no	—
18	C₂²×C₈×D₁₃	—	2	1	no	—
19	C₂×C₁₃×M₃₂	—	2	1	no	—
20	C₂×C₁₃×M₃₂	—	2	1	no	—
21	C₂×C₁₃×M₃₂	—	2	2	no	—
22	C₂×C₁₃×M₃₂	C₂²	1	4	yes	complemented
23	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	complemented
24	C₂×#88052	—	2	1	no	—
25	C₂×#88052	—	2	2	no	—
26	C₂×#88052	C₂²	1	2	yes	complemented
27	C₂×#88052	C₂²	1	4	yes	complemented
28	C₂²×#6090	—	2	1	no	—
29	#11718100	C₂²	1	16	yes	complemented
30	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₂²⋊D₁₃	—	2	1	no	—
32	C₂×#6127	—	2	1	no	—
33	C₂×#6127	—	2	2	no	—
34	C₂×#6127	—	2	1	no	—
35	C₂×#6127	—	2	2	no	—
36	C₂×#6127	C₈	1	2	yes	—
37	C₂×#6127	C₈	1	4	yes	—
38	C₂×#6127	C₂×C₄	1	2	yes	—
39	C₂×#6127	C₂×C₄	1	4	yes	—
40	C₂²×D₅₂	C₈	1	1	yes	characteristic
41	C₂²×C₄×D₁₃	—	2	1	no	—
42	C₂²×Dic₂₆	C₈	1	1	yes	characteristic
43	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
45	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	D₄	1	2	yes	—
48	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	D₄	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂×#6099	—	2	1	no	—
54	C₂×#6099	—	2	2	no	—
55	C₂×#6099	C₂×C₄	1	2	yes	—
56	C₂×#6099	C₂×C₄	1	4	yes	—
57	C₂²×#1055	—	2	1	no	—
58	#88155	—	2	4	no	—
59	#88155	—	2	4	no	—
60	#88155	—	2	4	no	—
61	#88155	—	2	4	no	—
62	#88155	—	2	2	no	—
63	#88155	—	2	2	no	—
64	#88155	—	2	4	no	—
65	#88155	C₂×C₄	1	4	yes	—
66	#88155	C₂×C₄	1	8	yes	—
67	#88155	C₂³	1	4	yes	—
68	C₂×#6094	—	2	2	no	—
69	C₂×#6094	—	2	4	no	—
70	C₂×#6094	—	2	2	no	—
71	C₂×#6094	—	2	4	no	—
72	C₂×C₈×D₁₃	—	2	4	no	—
73	C₂×C₈×D₁₃	—	2	2	no	—
74	C₂×C₈×D₁₃	—	2	4	no	—
75	C₂×C₈×D₁₃	—	2	2	no	—
76	C₁₃×M₃₂	—	2	4	no	—
77	C₁₃×M₃₂	—	2	4	no	—
78	C₂×C₁₃×C₁₆	—	2	2	no	—
79	C₂×C₁₃×C₁₆	—	2	2	no	—
80	C₂×C₁₃×C₁₆	C₂³	1	4	yes	complemented
81	#88052	—	2	4	no	—
82	#88052	—	2	2	no	—
83	#88052	C₂³	1	4	yes	complemented
84	C₂×#6090	—	2	4	no	—
85	C₂×#6090	—	2	2	no	—
86	C₂×#2117	—	13	1	no	maximal, Sylow
87	C₂⁴×C₁₃	M₁₆	1	1	yes	characteristic
88	C₂³×D₁₃	—	2	1	no	—
89	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
92	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
95	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
99	C₂×C₂²⋊D₁₃	—	2	2	no	—
100	C₂×C₂²⋊D₁₃	—	2	4	no	—
101	C₂×C₂²⋊D₁₃	—	2	2	no	—
102	C₂×C₂²⋊D₁₃	—	2	4	no	—
103	C₂²×Dic₁₃	—	2	1	no	—
104	#6127	—	2	4	no	—
105	#6127	—	2	4	no	—
106	#6127	—	2	4	no	—
107	#6127	—	2	4	no	—
108	#6127	—	2	2	no	—
109	#6127	—	2	2	no	—
110	#6127	—	2	4	no	—
111	#6127	C₂×C₈	1	4	yes	—
112	#6127	C₂×C₈	1	8	yes	—
113	#6127	C₂²×C₄	1	4	yes	—
114	C₂×D₅₂	—	2	2	no	—
115	C₂×D₅₂	—	2	1	no	—
116	C₂×D₅₂	C₂×C₈	1	4	yes	—
117	C₂×D₅₂	C₂×C₈	1	2	yes	—
118	C₂×C₄×D₁₃	—	2	4	no	—
119	C₂×C₄×D₁₃	—	2	2	no	—
120	C₂×C₄×D₁₃	—	2	4	no	—
121	C₂×C₄×D₁₃	—	2	2	no	—
122	C₂×Dic₂₆	—	2	2	no	—
123	C₂×Dic₂₆	—	2	1	no	—
124	C₂×Dic₂₆	C₂×C₈	1	4	yes	—
125	C₂×Dic₂₆	C₂×C₈	1	2	yes	—
126	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
127	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
128	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
130	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
131	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
132	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
133	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
135	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
144	#6099	—	2	4	no	—
145	#6099	—	2	2	no	—
146	#6099	C₂²×C₄	1	4	yes	—
147	C₂×#1055	—	2	4	no	—
148	C₂×#1055	—	2	2	no	—
149	#6094	—	2	8	no	—
150	#6094	—	2	4	no	—
151	#6094	—	2	4	no	—
152	C₈×D₁₃	—	2	8	no	—
153	C₈×D₁₃	—	2	4	no	—
154	C₈×D₁₃	—	2	4	no	—
155	C₁₃×C₁₆	—	2	4	no	—
156	#6090	—	2	4	no	—
157	C₂²×#131	—	13	1	no	—
158	C₂²×M₃₂	—	13	1	no	—
159	C₂²×M₃₂	D₁₃	1	1	yes	characteristic, complemented
160	#2117	—	13	8	no	—
161	C₂×#350	—	13	4	no	—
162	C₂³×C₁₃	—	4	2	no	—
163	C₂³×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
164	C₂³×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
165	C₂³×C₁₃	C₂²⋊C₈	1	2	yes	—
166	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
167	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
168	C₂²×D₁₃	—	2	4	no	—
169	C₂²×D₁₃	—	2	2	no	—
170	C₂²×D₁₃	—	4	4	no	—
171	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
172	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
174	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
176	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
177	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
178	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
181	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
183	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
185	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
187	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
189	C₂²⋊D₁₃	—	2	4	no	—
190	C₂²⋊D₁₃	—	2	8	no	—
191	C₂²⋊D₁₃	—	2	4	no	—
192	C₂×Dic₁₃	—	2	4	no	—
193	C₂×Dic₁₃	—	2	2	no	—
194	D₅₂	—	2	2	no	—
195	D₅₂	—	2	4	no	—
196	D₅₂	C₂²×C₈	1	4	yes	—
197	C₄×D₁₃	—	2	4	no	—
198	C₄×D₁₃	—	2	8	no	—
199	C₄×D₁₃	—	2	4	no	—
200	Dic₂₆	—	2	2	no	—
201	Dic₂₆	—	2	4	no	—
202	Dic₂₆	C₂²×C₈	1	4	yes	—
203	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
204	C₈×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
206	C₈×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
209	#1055	—	2	4	no	—
210	C₂²×#41	—	13	1	no	—
211	C₂×#131	—	13	2	no	—
212	C₂×#131	—	13	4	no	—
213	C₂×#131	—	13	2	no	—
214	C₂×#131	—	13	4	no	—
215	C₂×#131	—	26	2	no	—
216	C₂×#131	—	26	1	no	—
217	C₂×#131	—	26	1	no	—
218	C₂×#131	—	26	2	no	—
219	C₂²×M₁₆	—	13	1	no	—
220	C₂²×M₁₆	—	26	1	no	—
221	C₂³×C₈	—	26	1	no	—
222	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
223	C₂×M₃₂	—	2	1	no	—
224	C₂×M₃₂	—	2	1	no	—
225	C₂×M₃₂	—	2	2	no	—
226	C₂×M₃₂	—	13	2	no	—
227	C₂×M₃₂	—	13	4	no	—
228	C₂×M₃₂	—	26	2	no	—
229	C₂×M₃₂	—	26	1	no	—
230	C₂×M₃₂	C₂×D₁₃	1	4	yes	complemented
231	C₂²×C₁₆	—	26	1	no	—
232	C₂²×C₁₆	C₂×D₁₃	1	2	yes	complemented
233	#350	—	13	16	no	—
234	C₂²×C₁₃	—	2	2	no	—
235	C₂²×C₁₃	—	2	2	no	—
236	C₂²×C₁₃	—	2	2	no	—
237	C₂²×C₁₃	—	4	2	no	—
238	C₂²×C₁₃	—	4	2	no	—
239	C₂²×C₁₃	C₂×C₂²⋊C₈	1	2	yes	—
240	C₂²×C₁₃	C₂×C₂²⋊C₈	1	2	yes	—
241	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
242	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
243	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
244	C₂×D₁₃	—	2	4	no	—
245	C₂×D₁₃	—	4	8	no	—
246	C₂×D₁₃	—	4	4	no	—
247	C₄×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
248	C₄×C₁₃	C₂×C₂²⋊C₈	1	2	yes	—
249	C₄×C₁₃	C₂×C₂²⋊C₈	1	2	yes	—
250	C₄×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
251	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
252	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
253	Dic₁₃	—	2	4	no	—
254	C₂×#41	—	13	2	no	—
255	C₂×#41	—	13	4	no	—
256	C₂×#41	—	13	2	no	—
257	C₂×#41	—	13	4	no	—
258	C₂×#41	—	26	1	no	—
259	C₂×#41	—	26	2	no	—
260	C₂×#41	—	26	2	no	—
261	C₂×#41	—	26	1	no	—
262	C₂²×Q₈	—	13	1	no	—
263	C₂²×D₄	—	13	1	no	—
264	C₂²×D₄	—	26	1	no	—
265	C₂³×C₄	—	26	1	no	—
266	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
267	#131	—	13	4	no	—
268	#131	—	13	8	no	—
269	#131	—	13	4	no	—
270	#131	—	26	4	no	—
271	#131	—	26	4	no	—
272	#131	—	26	4	no	—
273	#131	—	26	4	no	—
274	#131	—	26	2	no	—
275	#131	—	26	2	no	—
276	#131	—	26	4	no	—
277	C₂×M₁₆	—	13	2	no	—
278	C₂×M₁₆	—	13	4	no	—
279	C₂×M₁₆	—	26	2	no	—
280	C₂×M₁₆	—	26	1	no	—
281	C₂×M₁₆	—	26	4	no	—
282	C₂×M₁₆	—	26	2	no	—
283	C₂×M₁₆	—	26	2	no	—
284	C₂×M₁₆	—	26	4	no	—
285	C₂²×C₈	—	26	1	no	—
286	C₂²×C₈	—	26	4	no	—
287	C₂²×C₈	—	26	2	no	—
288	C₂²×C₈	—	26	4	no	—
289	C₂²×C₈	—	26	2	no	—
290	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
291	C₂²×C₈	C₄×D₁₃	1	2	yes	—
292	C₂²×C₈	D₅₂	1	2	yes	—
293	C₂²×C₈	D₅₂	1	1	yes	characteristic
294	C₂²×C₈	D₅₂	1	1	yes	characteristic
295	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
296	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
297	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
298	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
299	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
300	M₃₂	—	2	4	no	—
301	M₃₂	—	2	4	no	—
302	M₃₂	—	13	4	no	—
303	M₃₂	—	26	4	no	—
304	M₃₂	—	26	2	no	—
305	C₂×C₁₆	—	2	2	no	—
306	C₂×C₁₆	—	2	2	no	—
307	C₂×C₁₆	—	26	4	no	—
308	C₂×C₁₆	—	26	2	no	—
309	C₂×C₁₆	C₂²×D₁₃	1	4	yes	complemented
310	C₂×C₁₃	—	2	2	no	—
311	C₂×C₁₃	—	2	1	no	—
312	C₂×C₁₃	—	2	2	no	—
313	C₂×C₁₃	—	2	1	no	—
314	C₂×C₁₃	#2117	1	2	yes	complemented
315	C₂×C₁₃	C₂²×C₂²⋊C₈	1	1	yes	characteristic
316	D₁₃	—	4	4	no	—
317	C₂⁴	—	26	1	no	—
318	C₂⁴	#6094	1	1	yes	characteristic
319	#41	—	13	4	no	—
320	#41	—	13	8	no	—
321	#41	—	13	4	no	—
322	#41	—	26	2	no	—
323	#41	—	26	4	no	—
324	#41	—	26	4	no	—
325	#41	—	26	2	no	—
326	#41	—	26	4	no	—
327	#41	—	26	4	no	—
328	#41	—	26	4	no	—
329	C₂×Q₈	—	13	4	no	—
330	C₂×Q₈	—	13	2	no	—
331	C₂×Q₈	—	26	2	no	—
332	C₂×Q₈	—	26	1	no	—
333	C₂×D₄	—	13	4	no	—
334	C₂×D₄	—	13	2	no	—
335	C₂×D₄	—	26	2	no	—
336	C₂×D₄	—	26	4	no	—
337	C₂×D₄	—	26	2	no	—
338	C₂×D₄	—	26	4	no	—
339	C₂×D₄	—	26	2	no	—
340	C₂×D₄	—	26	1	no	—
341	C₂²×C₄	—	26	1	no	—
342	C₂²×C₄	—	26	4	no	—
343	C₂²×C₄	—	26	2	no	—
344	C₂²×C₄	—	26	4	no	—
345	C₂²×C₄	—	26	2	no	—
346	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
347	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
348	C₂²×C₄	C₈×D₁₃	1	2	yes	—
349	C₂²×C₄	#6094	1	1	yes	characteristic
350	C₂²×C₄	#6094	1	2	yes	—
351	C₂²×C₄	#6103	1	1	yes	characteristic
352	C₂²×C₄	#6103	1	2	yes	—
353	C₂²×C₄	#6103	1	1	yes	characteristic
354	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
355	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
356	M₁₆	—	13	4	no	—
357	M₁₆	—	26	4	no	—
358	M₁₆	—	26	2	no	—
359	M₁₆	—	26	8	no	—
360	M₁₆	—	26	4	no	—
361	M₁₆	—	26	4	no	—
362	C₂×C₈	—	26	4	no	—
363	C₂×C₈	—	26	2	no	—
364	C₂×C₈	—	26	8	no	—
365	C₂×C₈	—	26	4	no	—
366	C₂×C₈	—	26	4	no	—
367	C₂×C₈	#6103	1	1	yes	characteristic
368	C₂×C₈	#6103	1	2	yes	—
369	C₂×C₈	#6103	1	2	yes	—
370	C₂×C₈	#6103	1	1	yes	characteristic
371	C₂×C₈	#6103	1	2	yes	—
372	C₂×C₈	#6103	1	2	yes	—
373	C₂×C₈	#6103	1	2	yes	—
374	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
375	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
376	C₂×C₈	C₂×D₅₂	1	2	yes	—
377	C₂×C₈	C₂×D₅₂	1	2	yes	—
378	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
379	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
380	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
381	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
382	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
383	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
384	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
385	C₁₆	—	2	4	no	—
386	C₁₆	—	26	4	no	—
387	C₁₃	C₂×#2117	1	1	yes	characteristic, complemented, Sylow
388	C₂³	—	4	2	no	—
389	C₂³	—	26	4	no	—
390	C₂³	—	26	2	no	—
391	C₂³	—	52	4	no	—
392	C₂³	#88060	1	1	yes	characteristic
393	C₂³	#88060	1	1	yes	characteristic
394	C₂³	#88060	1	2	yes	—
395	C₂³	C₂×#6094	1	1	yes	characteristic
396	C₂³	C₂×#6094	1	2	yes	—
397	Q₈	—	13	4	no	—
398	Q₈	—	26	4	no	—
399	Q₈	—	26	2	no	—
400	D₄	—	13	4	no	—
401	D₄	—	26	4	no	—
402	D₄	—	26	4	no	—
403	D₄	—	26	8	no	—
404	D₄	—	26	4	no	—
405	D₄	—	26	2	no	—
406	C₂×C₄	—	26	4	no	—
407	C₂×C₄	—	26	2	no	—
408	C₂×C₄	—	26	4	no	—
409	C₂×C₄	—	26	8	no	—
410	C₂×C₄	—	26	4	no	—
411	C₂×C₄	#88060	1	2	yes	—
412	C₂×C₄	#88060	1	1	yes	characteristic
413	C₂×C₄	#88060	1	2	yes	—
414	C₂×C₄	#88060	1	1	yes	characteristic
415	C₂×C₄	#88060	1	2	yes	—
416	C₂×C₄	#88060	1	2	yes	—
417	C₂×C₄	#88060	1	2	yes	—
418	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
419	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
420	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
421	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
422	C₂×C₄	C₂×#6094	1	2	yes	—
423	C₂×C₄	C₂×#6094	1	1	yes	characteristic
424	C₂×C₄	C₂×#6103	1	2	yes	—
425	C₂×C₄	C₂×#6103	1	1	yes	characteristic
426	C₂×C₄	C₂×#6103	1	2	yes	—
427	C₂×C₄	C₂×#6103	1	1	yes	characteristic
428	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
429	C₈	—	26	4	no	—
430	C₈	C₂×#6103	1	2	yes	—
431	C₈	C₂×#6103	1	1	yes	characteristic
432	C₈	C₂×#6103	1	2	yes	—
433	C₈	C₂×#6103	1	1	yes	characteristic
434	C₈	C₂²×D₅₂	1	1	yes	characteristic
435	C₈	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	26	4	no	—
442	C₂²	—	52	8	no	—
443	C₂²	—	52	4	no	—
444	C₂²	C₂×#88060	1	2	yes	—
445	C₂²	C₂×#88060	1	1	yes	characteristic
446	C₂²	C₂×#88060	1	2	yes	—
447	C₂²	C₂×#88060	1	1	yes	characteristic
448	C₂²	C₂²×#6094	1	1	yes	characteristic
449	C₄	—	26	4	no	—
450	C₄	C₂×#88060	1	2	yes	—
451	C₄	C₂×#88060	1	1	yes	characteristic
452	C₄	C₂×#88060	1	2	yes	—
453	C₄	C₂×#88060	1	1	yes	characteristic
454	C₄	C₂²×C₈×D₁₃	1	1	yes	characteristic
455	C₄	C₂²×#6103	1	1	yes	characteristic
456	C₂	—	2	2	no	—
457	C₂	—	2	1	no	—
458	C₂	—	2	1	no	—
459	C₂	—	2	2	no	—
460	C₂	—	52	4	no	—
461	C₂	#13116463	1	2	yes	direct product factor
462	C₂	C₂²×#88060	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₅₂
commutator	C₄×C₁₃	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂²×C₁₃×M₃₂	C₂
socle	C₂²×C₁₃	C₂×C₂²⋊C₈
prime radical	C₂²×#6127	C₄
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂²×M₃₂	D₁₃
hypocenter	C₁₃	C₂×#2117
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂³×C₈ ◁ C₂²×M₃₂

Complements

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

N	H ≅ G/N	type
2. C₂²×#88052	C₂	semidirect
3. #13116463	C₂	direct (N × H)
4. C₂×#11718100	C₂	semidirect
5. C₂²×C₁₃×M₃₂	C₂	semidirect
22. C₂×C₁₃×M₃₂	C₂²	semidirect
23. C₂²×C₁₃×C₁₆	C₂²	semidirect
26. C₂×#88052	C₂²	semidirect
27. C₂×#88052	C₂²	semidirect
29. #11718100	C₂²	semidirect
80. C₂×C₁₃×C₁₆	C₂³	semidirect
83. #88052	C₂³	semidirect
159. C₂²×M₃₂	D₁₃	semidirect
230. C₂×M₃₂	C₂×D₁₃	semidirect
232. C₂²×C₁₆	C₂×D₁₃	semidirect
309. C₂×C₁₆	C₂²×D₁₃	semidirect
314. C₂×C₁₃	#2117	semidirect
387. C₁₃	C₂×#2117	semidirect
461. C₂	#13116463	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×#88155	2
C₂²×#88052	2
#13116463	2
C₂×#11718100	2
C₂²×C₁₃×M₃₂	2
C₂×#2117	13

Subgroups — C2×#13116463 #16015620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13116463 #16015620