Subgroups — C₂×#13123740 #16727225

Order 3328.

2666 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719453	C₂	1	1	yes	maximal, characteristic
2	C₂²×#88155	C₂	1	2	yes	maximal, complemented
3	#13123740	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	C₂×#11718786	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	#11719453	C₄	1	8	yes	complemented
15	#11719453	C₂²	1	8	yes	—
16	C₂×#88163	C₄	1	4	yes	complemented
17	C₂×#88162	C₄	1	4	yes	complemented
18	C₂×#88158	C₂²	1	4	yes	—
19	C₂×#88155	—	2	2	no	—
20	C₂×#88155	—	2	2	no	—
21	C₂×#88155	—	2	8	no	—
22	C₂×#88155	C₂²	1	4	yes	complemented
23	C₂×#88155	C₂²	1	4	yes	complemented
24	C₂×#88155	C₂²	1	16	yes	complemented
25	C₂²×#6094	—	2	2	no	—
26	C₂²×C₈×D₁₃	—	2	2	no	—
27	C₁₃×#405	C₂²	1	8	yes	complemented
28	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
29	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
30	#11718786	C₂²	1	8	yes	complemented
31	C₂×#88059	C₂²	1	4	yes	complemented
32	#11718666	C₂²	1	16	yes	complemented
33	C₂×#88045	C₂²	1	8	yes	complemented
34	#11718378	C₂²	1	32	yes	complemented
35	#11718361	C₂²	1	32	yes	complemented
36	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
37	C₂²×C₂²⋊D₁₃	—	2	2	no	—
38	C₂×#6127	—	2	2	no	—
39	C₂×#6127	—	2	4	no	—
40	C₂×#6127	—	2	2	no	—
41	C₂×#6127	—	2	4	no	—
42	C₂×#6127	C₂×C₄	1	4	yes	—
43	C₂×#6127	C₂×C₄	1	8	yes	—
44	C₂×#6127	C₂³	1	8	yes	—
45	C₂×#6127	C₂³	1	4	yes	—
46	C₂²×D₅₂	C₂×C₄	1	2	yes	—
47	C₂²×C₄×D₁₃	—	2	2	no	—
48	C₂²×Dic₂₆	C₂×C₄	1	2	yes	—
49	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
50	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
51	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
52	C₂²×C₈×C₁₃	D₄	1	2	yes	—
53	C₂²×C₈×C₁₃	D₄	1	2	yes	—
54	C₂²×C₈×C₁₃	D₄	1	4	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
59	C₁₃×#117	—	2	2	no	—
60	C₁₃×#117	C₂³	1	4	yes	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
63	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
64	C₂×#6099	—	2	2	no	—
65	C₂×#6099	—	2	4	no	—
66	C₂×#6099	C₂³	1	8	yes	—
67	C₂×#6099	C₂³	1	4	yes	—
68	C₂²×#1055	—	2	2	no	—
69	#88163	C₂×C₄	1	32	yes	complemented
70	#88162	C₂×C₄	1	32	yes	complemented
71	C₂×Dic₅₂	C₂×C₄	1	4	yes	—
72	#88158	C₂×C₄	1	16	yes	—
73	#88158	C₂³	1	16	yes	—
74	C₂×D₁₀₄	C₂×C₄	1	4	yes	—
75	C₂×#6095	C₂×C₄	1	8	yes	—
76	#88155	—	2	16	no	—
77	#88155	—	2	16	no	—
78	#88155	—	2	8	no	—
79	#88155	—	2	8	no	—
80	#88155	C₂³	1	16	yes	complemented
81	#88155	C₂³	1	16	yes	complemented
82	C₂×#6094	—	2	4	no	—
83	C₂×#6094	—	2	4	no	—
84	C₂×#6094	—	2	16	no	—
85	C₂×C₈×D₁₃	—	2	4	no	—
86	C₂×C₈×D₁₃	—	2	16	no	—
87	C₂×C₈×D₁₃	—	2	4	no	—
88	C₁₃×#97	C₂³	1	8	yes	complemented
89	C₄×C₈×C₁₃	C₂³	1	8	yes	complemented
90	#88059	C₂³	1	16	yes	complemented
91	#88045	C₂³	1	32	yes	complemented
92	C₂×#2955	—	13	1	no	maximal, Sylow
93	C₂⁴×C₁₃	#41	1	1	yes	characteristic
94	C₂³×D₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
101	C₂²×C₄×C₁₃	#41	1	2	yes	—
102	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
104	C₂×C₂²⋊D₁₃	—	2	4	no	—
105	C₂×C₂²⋊D₁₃	—	2	8	no	—
106	C₂×C₂²⋊D₁₃	—	2	4	no	—
107	C₂×C₂²⋊D₁₃	—	2	8	no	—
108	C₂²×Dic₁₃	—	2	2	no	—
109	#6127	—	2	8	no	—
110	#6127	—	2	8	no	—
111	#6127	—	2	8	no	—
112	#6127	—	2	8	no	—
113	#6127	—	2	4	no	—
114	#6127	—	2	4	no	—
115	#6127	—	2	8	no	—
116	#6127	C₂²×C₄	1	8	yes	—
117	#6127	C₂²×C₄	1	16	yes	—
118	#6127	C₂⁴	1	8	yes	—
119	C₂×D₅₂	—	2	2	no	—
120	C₂×D₅₂	—	2	4	no	—
121	C₂×D₅₂	C₂²×C₄	1	4	yes	—
122	C₂×D₅₂	C₂²×C₄	1	8	yes	—
123	C₂×C₄×D₁₃	—	2	4	no	—
124	C₂×C₄×D₁₃	—	2	8	no	—
125	C₂×C₄×D₁₃	—	2	4	no	—
126	C₂×C₄×D₁₃	—	2	8	no	—
127	C₂×Dic₂₆	—	2	2	no	—
128	C₂×Dic₂₆	—	2	4	no	—
129	C₂×Dic₂₆	C₂²×C₄	1	4	yes	—
130	C₂×Dic₂₆	C₂²×C₄	1	8	yes	—
131	C₁₃×M₁₆	C₂²×C₄	1	16	yes	—
132	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
133	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
134	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₁₃	C₂×D₄	1	8	yes	—
136	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₁₃	C₂×D₄	1	8	yes	—
138	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
142	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
143	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
144	C₁₃×C₄⋊C₄	—	2	4	no	—
145	C₁₃×C₂²⋊C₄	—	2	4	no	—
146	C₄²×C₁₃	—	2	2	no	—
147	C₄²×C₁₃	C₂⁴	1	4	yes	—
148	#6099	—	2	8	no	—
149	#6099	—	2	4	no	—
150	#6099	C₂⁴	1	8	yes	—
151	C₂×#1055	—	2	4	no	—
152	C₂×#1055	—	2	8	no	—
153	Dic₅₂	C₂²×C₄	1	16	yes	—
154	D₁₀₄	C₂²×C₄	1	16	yes	—
155	#6095	C₂²×C₄	1	32	yes	—
156	#6094	—	2	16	no	—
157	#6094	—	2	16	no	—
158	C₈×D₁₃	—	2	16	no	—
159	C₈×D₁₃	—	2	16	no	—
160	C₂×#575	—	13	1	no	—
161	C₂²×#131	—	13	2	no	—
162	#2955	—	13	16	no	—
163	C₂×#444	—	13	4	no	—
164	C₂×#443	—	13	4	no	—
165	C₂×#430	—	13	1	no	—
166	C₂×#421	—	13	2	no	—
167	C₂×#405	D₁₃	1	1	yes	characteristic, complemented
168	C₂³×C₁₃	—	4	2	no	—
169	C₂³×C₁₃	C₄×D₄	1	2	yes	—
170	C₂³×C₁₃	C₄×D₄	1	2	yes	—
171	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
172	C₂³×C₁₃	C₂×#41	1	2	yes	—
173	C₂²×D₁₃	—	2	8	no	—
174	C₂²×D₁₃	—	2	4	no	—
175	C₂²×D₁₃	—	4	8	no	—
176	C₂×C₄×C₁₃	—	2	4	no	—
177	C₂×C₄×C₁₃	—	4	4	no	—
178	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
179	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
180	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
181	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
185	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
187	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
190	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
191	C₂²⋊D₁₃	—	2	16	no	—
192	C₂²⋊D₁₃	—	2	8	no	—
193	C₂²⋊D₁₃	—	2	8	no	—
194	C₂×Dic₁₃	—	2	8	no	—
195	C₂×Dic₁₃	—	2	4	no	—
196	D₅₂	—	2	4	no	—
197	D₅₂	—	2	8	no	—
198	D₅₂	C₂³×C₄	1	8	yes	—
199	C₄×D₁₃	—	2	16	no	—
200	C₄×D₁₃	—	2	8	no	—
201	C₄×D₁₃	—	2	8	no	—
202	Dic₂₆	—	2	4	no	—
203	Dic₂₆	—	2	8	no	—
204	Dic₂₆	C₂³×C₄	1	8	yes	—
205	C₈×C₁₃	C₂³×C₄	1	8	yes	—
206	C₈×C₁₃	C₂²×D₄	1	2	yes	—
207	C₈×C₁₃	C₂²×D₄	1	4	yes	—
208	C₈×C₁₃	C₂²×D₄	1	2	yes	—
209	#1055	—	2	8	no	—
210	C₂²×#41	—	13	2	no	—
211	#575	—	13	8	no	—
212	#575	—	13	8	no	—
213	C₂×#137	—	13	4	no	—
214	C₂×AGL(1,ℤ/8)	—	13	4	no	—
215	C₂×#135	—	13	4	no	—
216	C₂×#131	—	13	4	no	—
217	C₂×#131	—	13	4	no	—
218	C₂×#131	—	13	16	no	—
219	C₂×#131	—	26	2	no	—
220	C₂×#131	—	26	8	no	—
221	C₂×#131	—	26	2	no	—
222	C₂²×M₁₆	—	13	2	no	—
223	C₂²×M₁₆	—	26	2	no	—
224	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
225	C₂³×C₈	—	26	2	no	—
226	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
227	C₂×#117	C₂×D₁₃	1	1	yes	characteristic
228	#444	—	13	32	no	—
229	#443	—	13	32	no	—
230	#430	—	13	8	no	—
231	C₂×#108	—	13	4	no	—
232	#421	—	13	16	no	—
233	C₂×#104	—	13	8	no	—
234	#405	C₂×D₁₃	1	8	yes	complemented
235	C₂×#97	C₂×D₁₃	1	2	yes	complemented
236	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	complemented
237	C₂²×C₁₃	—	2	2	no	—
238	C₂²×C₁₃	—	2	4	no	—
239	C₂²×C₁₃	—	4	2	no	—
240	C₂²×C₁₃	—	4	2	no	—
241	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
242	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
243	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
244	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
245	C₂×D₁₃	—	2	8	no	—
246	C₂×D₁₃	—	4	16	no	—
247	C₂×D₁₃	—	4	8	no	—
248	C₄×C₁₃	—	4	4	no	—
249	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
250	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
251	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
252	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
253	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
254	Dic₁₃	—	2	8	no	—
255	C₂×#41	—	13	4	no	—
256	C₂×#41	—	13	8	no	—
257	C₂×#41	—	13	4	no	—
258	C₂×#41	—	13	8	no	—
259	C₂×#41	—	26	2	no	—
260	C₂×#41	—	26	4	no	—
261	C₂×#41	—	26	2	no	—
262	C₂×#41	—	26	4	no	—
263	C₂²×Q₈	—	13	2	no	—
264	C₂²×D₄	—	13	2	no	—
265	C₂²×D₄	—	26	2	no	—
266	C₂³×C₄	—	26	2	no	—
267	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
268	#137	—	13	32	no	—
269	AGL(1,ℤ/8)	—	13	32	no	—
270	#135	—	13	16	no	—
271	#135	—	13	16	no	—
272	C₂×Q₁₆	—	13	4	no	—
273	C₂×SD₁₆	—	13	8	no	—
274	C₂×D₈	—	13	4	no	—
275	#131	—	13	16	no	—
276	#131	—	13	16	no	—
277	#131	—	26	16	no	—
278	#131	—	26	16	no	—
279	#131	—	26	8	no	—
280	#131	—	26	8	no	—
281	C₂×M₁₆	—	13	4	no	—
282	C₂×M₁₆	—	13	8	no	—
283	C₂×M₁₆	—	26	2	no	—
284	C₂×M₁₆	—	26	4	no	—
285	C₂×M₁₆	—	26	4	no	—
286	C₂×M₁₆	—	26	4	no	—
287	C₂×M₁₆	—	26	16	no	—
288	C₂×M₁₆	C₄×D₁₃	1	4	yes	—
289	C₂×M₁₆	C₄×D₁₃	1	4	yes	—
290	C₂×M₁₆	C₂²×D₁₃	1	4	yes	—
291	C₂²×C₈	—	26	2	no	—
292	C₂²×C₈	—	26	4	no	—
293	C₂²×C₈	—	26	16	no	—
294	C₂²×C₈	—	26	4	no	—
295	C₂²×C₈	D₅₂	1	2	yes	—
296	C₂²×C₈	D₅₂	1	4	yes	—
297	C₂²×C₈	D₅₂	1	2	yes	—
298	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
299	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
300	C₂²×C₈	C₂²×D₁₃	1	4	yes	—
301	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
302	#117	—	2	2	no	—
303	#117	C₂²×D₁₃	1	4	yes	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
307	#108	—	13	16	no	—
308	#104	—	13	32	no	—
309	#97	C₂²×D₁₃	1	8	yes	complemented
310	C₄×C₈	C₂²×D₁₃	1	8	yes	complemented
311	C₂×C₁₃	—	2	1	no	—
312	C₂×C₁₃	—	2	4	no	—
313	C₂×C₁₃	—	2	1	no	—
314	C₂×C₁₃	#2955	1	2	yes	complemented
315	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
316	D₁₃	—	4	8	no	—
317	C₂⁴	—	26	2	no	—
318	C₂⁴	#6127	1	1	yes	characteristic
319	#41	—	13	8	no	—
320	#41	—	13	16	no	—
321	#41	—	13	8	no	—
322	#41	—	26	8	no	—
323	#41	—	26	8	no	—
324	#41	—	26	8	no	—
325	#41	—	26	8	no	—
326	#41	—	26	4	no	—
327	#41	—	26	4	no	—
328	#41	—	26	8	no	—
329	C₂×Q₈	—	13	4	no	—
330	C₂×Q₈	—	13	8	no	—
331	C₂×Q₈	—	26	2	no	—
332	C₂×Q₈	—	26	4	no	—
333	C₂×D₄	—	13	4	no	—
334	C₂×D₄	—	13	8	no	—
335	C₂×D₄	—	26	4	no	—
336	C₂×D₄	—	26	8	no	—
337	C₂×D₄	—	26	4	no	—
338	C₂×D₄	—	26	8	no	—
339	C₂×D₄	—	26	2	no	—
340	C₂×D₄	—	26	4	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	26	2	no	—
343	C₂²×C₄	—	26	4	no	—
344	C₂²×C₄	—	26	8	no	—
345	C₂²×C₄	—	26	4	no	—
346	C₂²×C₄	—	26	8	no	—
347	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
348	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
349	C₂²×C₄	C₂×D₅₂	1	2	yes	—
350	C₂²×C₄	C₂×D₅₂	1	2	yes	—
351	C₂²×C₄	#6127	1	1	yes	characteristic
352	C₂²×C₄	#6127	1	2	yes	—
353	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
355	Q₁₆	—	13	16	no	—
356	SD₁₆	—	13	32	no	—
357	D₈	—	13	16	no	—
358	M₁₆	—	13	8	no	—
359	M₁₆	—	26	8	no	—
360	M₁₆	—	26	4	no	—
361	M₁₆	—	26	16	no	—
362	M₁₆	—	26	16	no	—
363	M₁₆	C₂×C₄×D₁₃	1	16	yes	—
364	C₂×C₈	—	26	4	no	—
365	C₂×C₈	—	26	8	no	—
366	C₂×C₈	—	26	16	no	—
367	C₂×C₈	—	26	16	no	—
368	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
369	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
370	C₂×C₈	C₂×D₅₂	1	2	yes	—
371	C₂×C₈	C₂×D₅₂	1	8	yes	—
372	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
373	C₂×C₈	C₂×D₅₂	1	8	yes	—
374	C₂×C₈	C₂×D₅₂	1	2	yes	—
375	C₂×C₈	C₂×D₅₂	1	2	yes	—
376	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
377	C₂×C₈	C₂³×D₁₃	1	4	yes	—
378	C₂×C₈	C₂³×D₁₃	1	2	yes	—
379	C₂×C₈	C₂³×D₁₃	1	2	yes	—
380	C₄⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₄²	—	2	2	no	—
383	C₄²	C₂³×D₁₃	1	4	yes	—
384	C₁₃	C₂×#2955	1	1	yes	characteristic, complemented, Sylow
385	C₂³	—	4	2	no	—
386	C₂³	—	26	8	no	—
387	C₂³	—	26	4	no	—
388	C₂³	—	52	8	no	—
389	C₂³	C₄×D₅₂	1	2	yes	—
390	C₂³	C₄×D₅₂	1	2	yes	—
391	C₂³	C₂×#6127	1	1	yes	characteristic
392	C₂³	C₂×#6127	1	2	yes	—
393	Q₈	—	13	8	no	—
394	Q₈	—	26	8	no	—
395	Q₈	—	26	4	no	—
396	D₄	—	13	8	no	—
397	D₄	—	26	16	no	—
398	D₄	—	26	8	no	—
399	D₄	—	26	8	no	—
400	D₄	—	26	8	no	—
401	D₄	—	26	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	26	8	no	—
405	C₂×C₄	—	26	4	no	—
406	C₂×C₄	—	26	8	no	—
407	C₂×C₄	—	26	16	no	—
408	C₂×C₄	—	26	8	no	—
409	C₂×C₄	C₄×D₅₂	1	2	yes	—
410	C₂×C₄	C₄×D₅₂	1	4	yes	—
411	C₂×C₄	C₄×D₅₂	1	4	yes	—
412	C₂×C₄	C₄×D₅₂	1	2	yes	—
413	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
414	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₄×D₁₃	1	4	yes	—
416	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
417	C₂×C₄	C₂²×D₅₂	1	4	yes	—
418	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
419	C₂×C₄	C₂×#6127	1	1	yes	characteristic
420	C₂×C₄	C₂×#6127	1	2	yes	—
421	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
422	C₈	—	26	8	no	—
423	C₈	C₂²×C₄×D₁₃	1	8	yes	—
424	C₈	C₂²×D₅₂	1	2	yes	—
425	C₈	C₂²×D₅₂	1	4	yes	—
426	C₈	C₂²×D₅₂	1	2	yes	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	26	8	no	—
432	C₂²	—	52	16	no	—
433	C₂²	—	52	8	no	—
434	C₂²	C₂×C₄×D₅₂	1	4	yes	—
435	C₂²	C₂×C₄×D₅₂	1	1	yes	characteristic
436	C₂²	C₂×C₄×D₅₂	1	1	yes	characteristic
437	C₂²	C₂²×#6127	1	1	yes	characteristic
438	C₄	—	4	4	no	—
439	C₄	—	26	8	no	—
440	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
441	C₄	C₂×C₄×D₅₂	1	4	yes	—
442	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
443	C₄	C₂³×C₄×D₁₃	1	1	yes	characteristic
444	C₄	C₂³×D₅₂	1	1	yes	characteristic
445	C₂	—	2	1	no	—
446	C₂	—	2	4	no	—
447	C₂	—	2	1	no	—
448	C₂	—	52	8	no	—
449	C₂	#13123740	1	2	yes	direct product factor
450	C₂	C₂²×C₄×D₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₅₂
commutator	C₄×C₁₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₂×C₁₃×#405	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×#11719453	C₂
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₂×#405	D₁₃
hypocenter	C₁₃	C₂×#2955
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂³×C₈ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
2. C₂²×#88155	C₂	semidirect
3. #13123740	C₂	direct (N × H)
4. C₂×#11718378	C₂	semidirect
5. C₂×#11718361	C₂	semidirect
6. C₂×#11718786	C₂	semidirect
7. C₂×#11718666	C₂	semidirect
8. C₂×C₁₃×#405	C₂	semidirect
14. #11719453	C₄	semidirect
16. C₂×#88163	C₄	semidirect
17. C₂×#88162	C₄	semidirect
22. C₂×#88155	C₂²	semidirect
23. C₂×#88155	C₂²	semidirect
24. C₂×#88155	C₂²	semidirect
27. C₁₃×#405	C₂²	semidirect
28. C₂×C₁₃×#97	C₂²	semidirect
29. C₂×C₄×C₈×C₁₃	C₂²	semidirect
30. #11718786	C₂²	semidirect
31. C₂×#88059	C₂²	semidirect
32. #11718666	C₂²	semidirect
33. C₂×#88045	C₂²	semidirect
34. #11718378	C₂²	semidirect
35. #11718361	C₂²	semidirect
69. #88163	C₂×C₄	semidirect
70. #88162	C₂×C₄	semidirect
80. #88155	C₂³	semidirect
81. #88155	C₂³	semidirect
88. C₁₃×#97	C₂³	semidirect
89. C₄×C₈×C₁₃	C₂³	semidirect
90. #88059	C₂³	semidirect
91. #88045	C₂³	semidirect
167. C₂×#405	D₁₃	semidirect
234. #405	C₂×D₁₃	semidirect
235. C₂×#97	C₂×D₁₃	semidirect
236. C₂×C₄×C₈	C₂×D₁₃	semidirect
309. #97	C₂²×D₁₃	semidirect
310. C₄×C₈	C₂²×D₁₃	semidirect
314. C₂×C₁₃	#2955	semidirect
384. C₁₃	C₂×#2955	semidirect
449. C₂	#13123740	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×#11719453	2
C₂²×#88155	2
#13123740	2
C₂×#11718378	2
C₂×#11718361	2
C₂×#11718786	2
C₂×#11718666	2
C₂×C₁₃×#405	2
C₂×#2955	13

Subgroups — C2×#13123740 #16727225

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13123740 #16727225