Subgroups — C₂×#13126636 #16739145

Order 3328.

2766 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719457	C₂	1	2	yes	maximal, complemented
2	C₂×#11719474	C₂	1	2	yes	maximal, complemented
3	#13126636	C₂	1	16	yes	maximal, direct product factor
4	C₂×#11718356	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11718558	C₂	1	2	yes	maximal, complemented
6	C₂×#11718803	C₂	1	2	yes	maximal, complemented
7	C₂×#11718483	C₂	1	4	yes	maximal, complemented
8	C₂×#11718361	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#443	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#88256	C₂²	1	4	yes	complemented
11	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#131	C₂²	1	2	yes	complemented
13	C₂×#88203	C₂²	1	4	yes	complemented
14	#11719474	—	2	8	no	—
15	#11719474	C₂²	1	16	yes	complemented
16	C₂×#88173	—	2	2	no	—
17	C₂×#88168	—	2	4	no	—
18	C₂×D₈×D₁₃	—	2	2	no	—
19	#11719457	—	2	8	no	—
20	#11719457	C₂²	1	16	yes	complemented
21	C₂×#88162	—	2	4	no	—
22	C₂×#88162	C₂²	1	4	yes	complemented
23	C₂×#88158	—	2	2	no	—
24	C₂×#88158	C₂²	1	1	yes	characteristic
25	C₂²×D₁₀₄	—	2	2	no	—
26	C₂²×D₁₀₄	C₂²	1	2	yes	complemented
27	C₂²×D₁₀₄	C₂²	1	2	yes	complemented
28	C₂×#88155	C₂²	1	2	yes	complemented
29	C₂×#88128	C₂²	1	2	yes	complemented
30	C₁₃×#443	C₂²	1	8	yes	complemented
31	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₁₃×#104	C₂²	1	2	yes	complemented
33	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
34	#11718803	C₂²	1	16	yes	complemented
35	C₂×#88063	C₂²	1	4	yes	complemented
36	C₂×#88059	C₂²	1	1	yes	characteristic, complemented
37	C₂×#88045	C₂²	1	2	yes	complemented
38	#11718558	C₂²	1	16	yes	complemented
39	#11718483	C₂²	1	32	yes	complemented
40	#11718361	C₂²	1	8	yes	complemented
41	#11718356	C₂²	1	8	yes	complemented
42	C₂×C₁₃×#41	C₂³	1	2	yes	—
43	#88256	—	2	8	no	—
44	#88256	—	2	8	no	—
45	#88256	—	4	4	no	—
46	#88256	C₂³	1	16	yes	complemented
47	C₂×#6131	—	2	4	no	—
48	C₂×D₄×D₁₃	—	2	4	no	—
49	C₂×D₄×D₁₃	—	4	4	no	—
50	C₂×#6127	—	2	4	no	—
51	C₂×#6127	C₂³	1	2	yes	—
52	C₂²×D₅₂	—	2	4	no	—
53	C₂²×D₅₂	—	4	2	no	—
54	C₂²×D₅₂	C₂³	1	4	yes	—
55	C₁₃×#135	D₄	1	4	yes	complemented
56	C₁₃×#135	C₂³	1	4	yes	—
57	C₂×C₁₃×Q₁₆	D₄	1	1	yes	characteristic, complemented
58	C₂×C₁₃×SD₁₆	D₄	1	2	yes	complemented
59	C₂×C₁₃×D₈	D₄	1	1	yes	characteristic, complemented
60	C₁₃×#131	—	2	4	no	—
61	C₁₃×#131	C₂³	1	8	yes	complemented
62	C₂×C₁₃×M₁₆	—	2	2	no	—
63	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
64	C₂²×C₈×C₁₃	—	2	2	no	—
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
68	#88203	—	2	8	no	—
69	#88203	C₂³	1	16	yes	complemented
70	C₂×#6106	—	2	4	no	—
71	C₂×#6104	—	2	4	no	—
72	C₂×#6099	C₂³	1	2	yes	—
73	#88173	—	2	16	no	—
74	#88168	—	2	32	no	—
75	D₈×D₁₃	—	2	16	no	—
76	#88162	—	2	8	no	—
77	#88162	—	2	32	no	—
78	#88162	C₂³	1	16	yes	complemented
79	C₂×Dic₅₂	D₄	1	1	yes	characteristic, complemented
80	#88158	—	2	16	no	—
81	#88158	D₄	1	4	yes	complemented
82	#88158	C₂³	1	4	yes	—
83	C₂×D₁₀₄	—	2	4	no	—
84	C₂×D₁₀₄	—	2	2	no	—
85	C₂×D₁₀₄	—	2	2	no	—
86	C₂×D₁₀₄	—	2	4	no	—
87	C₂×D₁₀₄	—	2	2	no	—
88	C₂×D₁₀₄	—	2	2	no	—
89	C₂×D₁₀₄	—	2	4	no	—
90	C₂×D₁₀₄	—	2	16	no	—
91	C₂×D₁₀₄	D₄	1	1	yes	characteristic, complemented
92	C₂×D₁₀₄	C₂³	1	8	yes	complemented
93	C₂×D₁₀₄	C₂³	1	8	yes	complemented
94	C₂×#6095	—	2	4	no	—
95	C₂×#6095	D₄	1	2	yes	complemented
96	#88155	—	2	4	no	—
97	#88155	C₂³	1	8	yes	complemented
98	C₂×#6094	—	2	2	no	—
99	C₂×C₈×D₁₃	—	2	2	no	—
100	#88128	—	4	2	no	—
101	#88128	C₂³	1	8	yes	complemented
102	C₁₃×#108	C₂³	1	4	yes	complemented
103	C₁₃×#104	C₂³	1	8	yes	complemented
104	C₄×C₈×C₁₃	C₂³	1	4	yes	complemented
105	#88063	C₂³	1	16	yes	complemented
106	#88059	C₂³	1	4	yes	complemented
107	#88045	C₂³	1	8	yes	complemented
108	C₂×#3292	—	13	1	no	maximal, Sylow
109	C₂³×D₁₃	—	2	4	no	—
110	C₂³×D₁₃	—	4	4	no	—
111	C₁₃×#41	—	2	2	no	—
112	C₁₃×#41	—	2	2	no	—
113	C₁₃×#41	C₂×D₄	1	4	yes	—
114	C₁₃×#41	C₂⁴	1	4	yes	—
115	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
116	C₂×D₄×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₂×C₂²⋊D₁₃	—	2	2	no	—
122	C₂×C₂²⋊D₁₃	—	4	4	no	—
123	#6131	—	2	16	no	—
124	#6131	—	4	8	no	—
125	D₄×D₁₃	—	2	16	no	—
126	D₄×D₁₃	—	4	8	no	—
127	D₄×D₁₃	—	4	16	no	—
128	D₄×D₁₃	—	4	16	no	—
129	#6127	—	2	2	no	—
130	#6127	—	2	2	no	—
131	#6127	—	2	16	no	—
132	#6127	—	4	8	no	—
133	#6127	C₂×D₄	1	4	yes	—
134	#6127	C₂⁴	1	4	yes	—
135	C₂×D₅₂	—	2	4	no	—
136	C₂×D₅₂	—	2	4	no	—
137	C₂×D₅₂	—	2	4	no	—
138	C₂×D₅₂	—	2	4	no	—
139	C₂×D₅₂	—	2	16	no	—
140	C₂×D₅₂	—	2	4	no	—
141	C₂×D₅₂	—	4	8	no	—
142	C₂×D₅₂	—	4	4	no	—
143	C₂×D₅₂	—	4	8	no	—
144	C₂×D₅₂	—	8	8	no	—
145	C₂×D₅₂	C₂×D₄	1	2	yes	—
146	C₂×D₅₂	C₂⁴	1	8	yes	—
147	C₂×C₄×D₁₃	—	2	2	no	—
148	C₂×C₄×D₁₃	—	4	4	no	—
149	C₂×Dic₂₆	C₂×D₄	1	2	yes	—
150	C₁₃×Q₁₆	C₂×D₄	1	4	yes	complemented
151	C₁₃×SD₁₆	C₂×D₄	1	8	yes	complemented
152	C₁₃×D₈	C₂×D₄	1	4	yes	complemented
153	C₁₃×M₁₆	—	2	2	no	—
154	C₁₃×M₁₆	—	2	8	no	—
155	C₁₃×M₁₆	C₂⁴	1	4	yes	—
156	C₂×C₈×C₁₃	—	2	2	no	—
157	C₂×C₈×C₁₃	—	2	8	no	—
158	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
161	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
164	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
165	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
166	C₄²×C₁₃	—	2	1	no	—
167	C₄²×C₁₃	C₂⁴	1	2	yes	—
168	#6106	—	2	16	no	—
169	#6104	—	2	16	no	—
170	#6099	—	2	2	no	—
171	#6099	C₂⁴	1	4	yes	—
172	C₂×#1055	—	2	2	no	—
173	Dic₅₂	C₂×D₄	1	4	yes	complemented
174	D₁₀₄	—	2	16	no	—
175	D₁₀₄	—	2	8	no	—
176	D₁₀₄	—	2	8	no	—
177	D₁₀₄	—	2	8	no	—
178	D₁₀₄	—	2	8	no	—
179	D₁₀₄	C₂×D₄	1	4	yes	complemented
180	#6095	—	2	16	no	—
181	#6095	C₂×D₄	1	8	yes	complemented
182	#6094	—	2	8	no	—
183	C₈×D₁₃	—	2	8	no	—
184	C₂×#576	—	13	2	no	—
185	C₂×#576	—	13	2	no	—
186	#3292	—	13	16	no	—
187	C₂×#493	—	13	1	no	—
188	C₂×#472	—	13	2	no	—
189	C₂×#472	—	13	2	no	—
190	C₂×#453	—	13	4	no	—
191	C₂×#443	—	13	1	no	—
192	C₂×#443	D₁₃	1	1	yes	characteristic, complemented
193	C₂³×C₁₃	—	2	2	no	—
194	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
195	C₂²×D₁₃	—	2	2	no	—
196	C₂²×D₁₃	—	2	8	no	—
197	C₂²×D₁₃	—	4	16	no	—
198	C₂²×D₁₃	—	4	4	no	—
199	C₂²×D₁₃	—	4	4	no	—
200	C₂²×D₁₃	—	8	8	no	—
201	C₂²×D₁₃	—	16	8	no	—
202	Q₈×C₁₃	—	2	2	no	—
203	Q₈×C₁₃	C₂²×D₄	1	4	yes	—
204	D₄×C₁₃	—	2	4	no	—
205	D₄×C₁₃	—	2	4	no	—
206	D₄×C₁₃	—	2	2	no	—
207	D₄×C₁₃	C₂²×D₄	1	4	yes	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
219	C₂²⋊D₁₃	—	2	4	no	—
220	C₂²⋊D₁₃	—	2	4	no	—
221	C₂²⋊D₁₃	—	4	16	no	—
222	C₂×Dic₁₃	—	2	2	no	—
223	D₅₂	—	2	2	no	—
224	D₅₂	—	2	8	no	—
225	D₅₂	—	2	8	no	—
226	D₅₂	—	4	16	no	—
227	D₅₂	—	4	4	no	—
228	D₅₂	—	4	4	no	—
229	D₅₂	—	8	16	no	—
230	D₅₂	C₂²×D₄	1	4	yes	—
231	C₄×D₁₃	—	2	4	no	—
232	C₄×D₁₃	—	2	4	no	—
233	C₄×D₁₃	—	4	16	no	—
234	Dic₂₆	—	2	2	no	—
235	Dic₂₆	C₂²×D₄	1	4	yes	—
236	C₈×C₁₃	—	2	4	no	—
237	C₈×C₁₃	C₂²×D₄	1	2	yes	—
238	C₈×C₁₃	C₂²×D₄	1	2	yes	—
239	C₈×C₁₃	C₂²×D₄	1	2	yes	—
240	C₈×C₁₃	C₂²×D₄	1	2	yes	—
241	#1055	—	2	4	no	—
242	C₂×H(5,𝔽₂)	—	13	4	no	—
243	#576	—	13	16	no	—
244	#576	—	13	16	no	—
245	#576	—	26	8	no	—
246	#576	—	26	8	no	—
247	C₂×AGL(1,ℤ/8)	—	13	4	no	—
248	C₂×AGL(1,ℤ/8)	—	13	4	no	—
249	C₂×AGL(1,ℤ/8)	—	26	4	no	—
250	C₂×AGL(1,ℤ/8)	—	26	4	no	—
251	C₂×#135	—	13	1	no	—
252	C₂×#135	—	26	2	no	—
253	C₂×#135	—	26	2	no	—
254	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
255	C₂²×D₈	—	13	2	no	—
256	C₂²×D₈	—	13	2	no	—
257	C₂²×D₈	—	26	2	no	—
258	C₂²×D₈	—	26	2	no	—
259	C₂×#131	—	13	2	no	—
260	C₂×#131	C₂×D₁₃	1	2	yes	complemented
261	C₂×#127	—	13	2	no	—
262	#493	—	13	8	no	—
263	#472	—	13	16	no	—
264	#472	—	13	16	no	—
265	#453	—	13	32	no	—
266	#443	—	13	8	no	—
267	#443	C₂×D₁₃	1	8	yes	complemented
268	C₂×#108	—	13	1	no	—
269	C₂×#108	C₂×D₁₃	1	1	yes	characteristic, complemented
270	C₂×#104	—	13	2	no	—
271	C₂×#104	C₂×D₁₃	1	2	yes	complemented
272	C₂×#100	—	13	4	no	—
273	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic, complemented
274	C₂²×C₁₃	—	2	2	no	—
275	C₂²×C₁₃	—	2	4	no	—
276	C₂²×C₁₃	—	4	4	no	—
277	C₂²×C₁₃	D₄²	1	1	yes	characteristic
278	C₂²×C₁₃	D₄²	1	1	yes	characteristic
279	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
280	C₂×D₁₃	—	2	4	no	—
281	C₂×D₁₃	—	4	4	no	—
282	C₂×D₁₃	—	4	8	no	—
283	C₂×D₁₃	—	8	8	no	—
284	C₂×D₁₃	—	8	8	no	—
285	C₂×D₁₃	—	16	16	no	—
286	C₂×D₁₃	—	16	4	no	—
287	C₄×C₁₃	—	2	4	no	—
288	C₄×C₁₃	—	2	4	no	—
289	C₄×C₁₃	D₄²	1	1	yes	characteristic
290	C₄×C₁₃	D₄²	1	1	yes	characteristic
291	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
292	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
293	Dic₁₃	—	2	4	no	—
294	H(5,𝔽₂)	—	13	16	no	—
295	H(5,𝔽₂)	—	26	8	no	—
296	H(5,𝔽₂)	—	26	8	no	—
297	H(5,𝔽₂)	—	52	4	no	—
298	C₂×#41	—	13	2	no	—
299	C₂×#41	—	26	4	no	—
300	C₂×#41	—	26	4	no	—
301	C₂×#41	C₂²×D₁₃	1	2	yes	—
302	C₂²×D₄	—	13	4	no	—
303	C₂²×D₄	—	26	4	no	—
304	C₂²×D₄	—	26	4	no	—
305	C₂²×D₄	—	52	2	no	—
306	C₂²×D₄	—	52	4	no	—
307	AGL(1,ℤ/8)	—	13	16	no	—
308	AGL(1,ℤ/8)	—	13	16	no	—
309	AGL(1,ℤ/8)	—	26	32	no	—
310	AGL(1,ℤ/8)	—	26	8	no	—
311	AGL(1,ℤ/8)	—	26	8	no	—
312	AGL(1,ℤ/8)	—	26	32	no	—
313	#135	—	13	4	no	—
314	#135	—	13	4	no	—
315	#135	—	26	16	no	—
316	#135	—	26	16	no	—
317	#135	D₅₂	1	4	yes	complemented
318	#135	C₂²×D₁₃	1	4	yes	—
319	C₂×Q₁₆	—	13	1	no	—
320	C₂×Q₁₆	D₅₂	1	1	yes	characteristic, complemented
321	C₂×SD₁₆	—	13	2	no	—
322	C₂×SD₁₆	—	26	4	no	—
323	C₂×SD₁₆	—	26	4	no	—
324	C₂×SD₁₆	D₅₂	1	2	yes	complemented
325	C₂×D₈	—	13	1	no	—
326	C₂×D₈	—	13	8	no	—
327	C₂×D₈	—	13	8	no	—
328	C₂×D₈	—	26	16	no	—
329	C₂×D₈	—	26	4	no	—
330	C₂×D₈	—	26	4	no	—
331	C₂×D₈	—	26	16	no	—
332	C₂×D₈	—	26	2	no	—
333	C₂×D₈	—	26	2	no	—
334	C₂×D₈	—	26	4	no	—
335	C₂×D₈	—	26	2	no	—
336	C₂×D₈	—	26	2	no	—
337	C₂×D₈	—	26	4	no	—
338	C₂×D₈	D₅₂	1	1	yes	characteristic, complemented
339	#131	—	2	4	no	—
340	#131	—	13	8	no	—
341	#131	—	26	4	no	—
342	#131	C₂²×D₁₃	1	8	yes	complemented
343	C₂×M₁₆	—	2	2	no	—
344	C₂×M₁₆	—	13	2	no	—
345	C₂×M₁₆	—	26	2	no	—
346	C₂×M₁₆	C₂²×D₁₃	1	2	yes	—
347	C₂²×C₈	—	2	2	no	—
348	C₂²×C₈	—	26	2	no	—
349	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
350	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
351	#127	—	13	8	no	—
352	#127	—	52	2	no	—
353	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
354	#108	—	13	4	no	—
355	#108	C₂²×D₁₃	1	4	yes	complemented
356	#104	—	13	8	no	—
357	#104	C₂²×D₁₃	1	8	yes	complemented
358	#100	—	13	16	no	—
359	C₄×C₈	C₂²×D₁₃	1	4	yes	complemented
360	C₂×C₁₃	—	2	1	no	—
361	C₂×C₁₃	—	2	1	no	—
362	C₂×C₁₃	—	4	4	no	—
363	C₂×C₁₃	#3292	1	2	yes	complemented
364	C₂×C₁₃	C₂×D₄²	1	1	yes	characteristic
365	D₁₃	—	4	4	no	—
366	D₁₃	—	8	8	no	—
367	C₂⁴	—	26	4	no	—
368	C₂⁴	—	52	4	no	—
369	#41	—	2	2	no	—
370	#41	—	2	2	no	—
371	#41	—	13	4	no	—
372	#41	—	13	4	no	—
373	#41	—	26	16	no	—
374	#41	—	26	2	no	—
375	#41	—	26	2	no	—
376	#41	—	26	16	no	—
377	#41	—	52	8	no	—
378	#41	—	52	8	no	—
379	#41	C₂×D₅₂	1	4	yes	—
380	#41	C₂³×D₁₃	1	4	yes	—
381	C₂×Q₈	—	13	2	no	—
382	C₂×Q₈	C₂×D₅₂	1	2	yes	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	13	2	no	—
385	C₂×D₄	—	13	8	no	—
386	C₂×D₄	—	26	16	no	—
387	C₂×D₄	—	26	2	no	—
388	C₂×D₄	—	26	16	no	—
389	C₂×D₄	—	26	4	no	—
390	C₂×D₄	—	26	4	no	—
391	C₂×D₄	—	26	4	no	—
392	C₂×D₄	—	26	4	no	—
393	C₂×D₄	—	26	4	no	—
394	C₂×D₄	—	52	8	no	—
395	C₂×D₄	—	52	4	no	—
396	C₂×D₄	—	52	8	no	—
397	C₂×D₄	—	52	8	no	—
398	C₂×D₄	—	52	4	no	—
399	C₂×D₄	—	52	16	no	—
400	C₂×D₄	—	52	16	no	—
401	C₂×D₄	—	104	8	no	—
402	C₂×D₄	C₂×D₅₂	1	2	yes	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	26	2	no	—
406	C₂²×C₄	—	52	4	no	—
407	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
408	Q₁₆	—	13	4	no	—
409	Q₁₆	C₂×D₅₂	1	4	yes	complemented
410	SD₁₆	—	13	8	no	—
411	SD₁₆	—	26	16	no	—
412	SD₁₆	—	26	16	no	—
413	SD₁₆	C₂×D₅₂	1	8	yes	complemented
414	D₈	—	13	4	no	—
415	D₈	—	26	16	no	—
416	D₈	—	26	16	no	—
417	D₈	—	26	8	no	—
418	D₈	—	26	8	no	—
419	D₈	—	26	8	no	—
420	D₈	—	26	8	no	—
421	D₈	C₂×D₅₂	1	4	yes	complemented
422	M₁₆	—	2	2	no	—
423	M₁₆	—	2	8	no	—
424	M₁₆	—	13	4	no	—
425	M₁₆	—	26	2	no	—
426	M₁₆	—	26	8	no	—
427	M₁₆	C₂³×D₁₃	1	4	yes	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	8	no	—
430	C₂×C₈	—	26	2	no	—
431	C₂×C₈	—	26	8	no	—
432	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
433	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
434	C₂×C₈	C₂×D₅₂	1	2	yes	—
435	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
436	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
437	C₂×C₈	D₄×D₁₃	1	2	yes	—
438	C₂×C₈	C₂³×D₁₃	1	2	yes	—
439	C₂×C₈	C₂³×D₁₃	1	2	yes	—
440	C₄²	—	2	1	no	—
441	C₄²	C₂³×D₁₃	1	2	yes	—
442	C₁₃	C₂×#3292	1	1	yes	characteristic, complemented, Sylow
443	C₂³	—	2	2	no	—
444	C₂³	—	26	2	no	—
445	C₂³	—	26	8	no	—
446	C₂³	—	52	16	no	—
447	C₂³	—	52	4	no	—
448	C₂³	—	52	4	no	—
449	C₂³	—	104	8	no	—
450	C₂³	—	208	8	no	—
451	C₂³	#88256	1	1	yes	characteristic
452	Q₈	—	2	2	no	—
453	Q₈	—	13	4	no	—
454	Q₈	—	26	2	no	—
455	Q₈	C₂²×D₅₂	1	4	yes	—
456	D₄	—	2	4	no	—
457	D₄	—	2	4	no	—
458	D₄	—	2	2	no	—
459	D₄	—	13	4	no	—
460	D₄	—	26	4	no	—
461	D₄	—	26	4	no	—
462	D₄	—	26	2	no	—
463	D₄	—	26	8	no	—
464	D₄	—	26	8	no	—
465	D₄	—	52	16	no	—
466	D₄	—	52	16	no	—
467	D₄	—	52	4	no	—
468	D₄	—	52	4	no	—
469	D₄	—	104	16	no	—
470	D₄	C₂²×D₅₂	1	4	yes	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	26	2	no	—
477	C₂×C₄	—	26	4	no	—
478	C₂×C₄	—	26	4	no	—
479	C₂×C₄	—	52	16	no	—
480	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
481	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
482	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
483	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
484	C₂×C₄	#88256	1	1	yes	characteristic
485	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
486	C₈	—	2	4	no	—
487	C₈	—	26	4	no	—
488	C₈	C₂²×D₅₂	1	2	yes	—
489	C₈	C₂²×D₅₂	1	2	yes	—
490	C₈	C₂×D₄×D₁₃	1	2	yes	—
491	C₈	C₂×D₄×D₁₃	1	2	yes	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	4	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	26	4	no	—
496	C₂²	—	52	4	no	—
497	C₂²	—	52	8	no	—
498	C₂²	—	104	8	no	—
499	C₂²	—	104	8	no	—
500	C₂²	—	208	4	no	—
501	C₂²	—	208	16	no	—
502	C₂²	D₄×D₅₂	1	1	yes	characteristic
503	C₂²	D₄×D₅₂	1	1	yes	characteristic
504	C₂²	C₂×#88256	1	1	yes	characteristic
505	C₄	—	2	4	no	—
506	C₄	—	2	4	no	—
507	C₄	—	26	4	no	—
508	C₄	D₄×D₅₂	1	1	yes	characteristic
509	C₄	D₄×D₅₂	1	1	yes	characteristic
510	C₄	C₂³×D₅₂	1	1	yes	characteristic
511	C₄	C₂²×D₄×D₁₃	1	1	yes	characteristic
512	C₂	—	2	1	no	—
513	C₂	—	2	1	no	—
514	C₂	—	4	4	no	—
515	C₂	—	52	4	no	—
516	C₂	—	104	8	no	—
517	C₂	#13126636	1	2	yes	direct product factor
518	C₂	C₂×D₄×D₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₅₂
commutator, cosocle	C₂×C₄×C₁₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₁₃
Fitting	C₂×C₁₃×#443	C₂
socle	C₂²×C₁₃	D₄²
hypercenter	C₂×#443	D₁₃
hypocenter	C₁₃	C₂×#3292
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
1. C₂×#11719457	C₂	semidirect
2. C₂×#11719474	C₂	semidirect
3. #13126636	C₂	direct (N × H)
4. C₂×#11718356	C₂	semidirect
5. C₂×#11718558	C₂	semidirect
6. C₂×#11718803	C₂	semidirect
7. C₂×#11718483	C₂	semidirect
8. C₂×#11718361	C₂	semidirect
9. C₂×C₁₃×#443	C₂	semidirect
10. C₂×#88256	C₂²	semidirect
12. C₂×C₁₃×#131	C₂²	semidirect
13. C₂×#88203	C₂²	semidirect
15. #11719474	C₂²	semidirect
20. #11719457	C₂²	semidirect
22. C₂×#88162	C₂²	semidirect
26. C₂²×D₁₀₄	C₂²	semidirect
27. C₂²×D₁₀₄	C₂²	semidirect
28. C₂×#88155	C₂²	semidirect
29. C₂×#88128	C₂²	semidirect
30. C₁₃×#443	C₂²	semidirect
31. C₂×C₁₃×#108	C₂²	semidirect
32. C₂×C₁₃×#104	C₂²	semidirect
33. C₂×C₄×C₈×C₁₃	C₂²	semidirect
34. #11718803	C₂²	semidirect
35. C₂×#88063	C₂²	semidirect
36. C₂×#88059	C₂²	semidirect
37. C₂×#88045	C₂²	semidirect
38. #11718558	C₂²	semidirect
39. #11718483	C₂²	semidirect
40. #11718361	C₂²	semidirect
41. #11718356	C₂²	semidirect
46. #88256	C₂³	semidirect
55. C₁₃×#135	D₄	semidirect
57. C₂×C₁₃×Q₁₆	D₄	semidirect
58. C₂×C₁₃×SD₁₆	D₄	semidirect
59. C₂×C₁₃×D₈	D₄	semidirect
61. C₁₃×#131	C₂³	semidirect
69. #88203	C₂³	semidirect
78. #88162	C₂³	semidirect
79. C₂×Dic₅₂	D₄	semidirect
81. #88158	D₄	semidirect
91. C₂×D₁₀₄	D₄	semidirect
92. C₂×D₁₀₄	C₂³	semidirect
93. C₂×D₁₀₄	C₂³	semidirect
95. C₂×#6095	D₄	semidirect
97. #88155	C₂³	semidirect
101. #88128	C₂³	semidirect
102. C₁₃×#108	C₂³	semidirect
103. C₁₃×#104	C₂³	semidirect
104. C₄×C₈×C₁₃	C₂³	semidirect
105. #88063	C₂³	semidirect
106. #88059	C₂³	semidirect
107. #88045	C₂³	semidirect
150. C₁₃×Q₁₆	C₂×D₄	semidirect
151. C₁₃×SD₁₆	C₂×D₄	semidirect
152. C₁₃×D₈	C₂×D₄	semidirect
173. Dic₅₂	C₂×D₄	semidirect
179. D₁₀₄	C₂×D₄	semidirect
181. #6095	C₂×D₄	semidirect
192. C₂×#443	D₁₃	semidirect
260. C₂×#131	C₂×D₁₃	semidirect
267. #443	C₂×D₁₃	semidirect
269. C₂×#108	C₂×D₁₃	semidirect
271. C₂×#104	C₂×D₁₃	semidirect
273. C₂×C₄×C₈	C₂×D₁₃	semidirect
317. #135	D₅₂	semidirect
320. C₂×Q₁₆	D₅₂	semidirect
324. C₂×SD₁₆	D₅₂	semidirect
338. C₂×D₈	D₅₂	semidirect
342. #131	C₂²×D₁₃	semidirect
355. #108	C₂²×D₁₃	semidirect
357. #104	C₂²×D₁₃	semidirect
359. C₄×C₈	C₂²×D₁₃	semidirect
363. C₂×C₁₃	#3292	semidirect
409. Q₁₆	C₂×D₅₂	semidirect
413. SD₁₆	C₂×D₅₂	semidirect
421. D₈	C₂×D₅₂	semidirect
442. C₁₃	C₂×#3292	semidirect
517. C₂	#13126636	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×#11719457	2
C₂×#11719474	2
#13126636	2
C₂×#11718356	2
C₂×#11718558	2
C₂×#11718803	2
C₂×#11718483	2
C₂×#11718361	2
C₂×C₁₃×#443	2
C₂×#3292	13

Subgroups — C2×#13126636 #16739145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13126636 #16739145