Subgroups — C₂×#13123746 #16727232

Order 3328.

2674 conjugacy classes of subgroups.

The subgroup lattice has 434 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	#13123746	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	C₂×#11718786	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#88077	C₂	1	2	yes	maximal, complemented
7	C₂×M₁₆×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#575	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₁₃×#41	C₂²	1	2	yes	—
10	C₁₃×#575	C₄	1	8	yes	complemented
11	C₁₃×#575	C₂²	1	8	yes	—
12	C₂×C₁₃×#137	C₄	1	4	yes	complemented
13	C₂×C₁₃×AGL(1,ℤ/8)	C₄	1	4	yes	complemented
14	C₂×C₁₃×#135	C₂²	1	4	yes	—
15	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
16	#11719524	—	2	8	no	—
17	#11719524	C₂²	1	16	yes	complemented
18	C₂×#88202	—	2	4	no	—
19	C₂×#88202	C₂²	1	8	yes	complemented
20	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
21	C₂²×#6099	—	2	4	no	—
22	C₂²×#6099	C₂²	1	2	yes	—
23	C₂²×#6099	C₂²	1	1	yes	characteristic
24	C₂×#88077	C₂²	1	4	yes	complemented
25	C₂×#88077	C₂²	1	4	yes	complemented
26	C₂×#88077	C₂²	1	16	yes	complemented
27	#11718858	C₂²	1	32	yes	complemented
28	#11718857	C₂²	1	32	yes	complemented
29	#11718786	C₂²	1	8	yes	complemented
30	M₁₆×Dic₁₃	C₂²	1	8	yes	complemented
31	C₂×#88059	C₂²	1	4	yes	complemented
32	C₂×#88055	C₂²	1	2	yes	complemented
33	C₂×C₈×Dic₁₃	C₂²	1	2	yes	complemented
34	C₂×C₁₃×#41	—	2	2	no	—
35	C₂×C₁₃×#41	—	2	4	no	—
36	C₂×C₁₃×#41	—	2	2	no	—
37	C₂×C₁₃×#41	—	2	4	no	—
38	C₂×C₁₃×#41	C₂×C₄	1	4	yes	—
39	C₂×C₁₃×#41	C₂×C₄	1	8	yes	—
40	C₂×C₁₃×#41	C₂³	1	4	yes	—
41	C₂×C₁₃×#41	C₂³	1	8	yes	—
42	C₂²×Q₈×C₁₃	C₂×C₄	1	2	yes	—
43	C₂²×D₄×C₁₃	—	2	2	no	—
44	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
45	C₂³×C₄×C₁₃	—	2	2	no	—
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂³×Dic₁₃	—	2	1	no	—
48	C₁₃×#137	C₂×C₄	1	32	yes	complemented
49	C₁₃×AGL(1,ℤ/8)	C₂×C₄	1	32	yes	complemented
50	C₁₃×#135	C₂×C₄	1	16	yes	complemented
51	C₁₃×#135	C₂³	1	16	yes	—
52	C₂×C₁₃×Q₁₆	C₂×C₄	1	4	yes	complemented
53	C₂×C₁₃×SD₁₆	C₂×C₄	1	8	yes	complemented
54	C₂×C₁₃×D₈	C₂×C₄	1	4	yes	complemented
55	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
56	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
57	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
58	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
59	#88202	—	2	32	no	—
60	#88202	—	2	16	no	—
61	#88202	C₂³	1	32	yes	complemented
62	C₂×C₄×Dic₁₃	—	2	1	no	—
63	C₂×C₄×Dic₁₃	—	2	2	no	—
64	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
66	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
67	C₂×#6099	—	2	2	no	—
68	C₂×#6099	—	2	4	no	—
69	C₂×#6099	—	2	32	no	—
70	C₂×#6099	—	2	8	no	—
71	C₂×#6099	D₄	1	4	yes	—
72	C₂×#6099	D₄	1	4	yes	—
73	C₂×#6099	C₂³	1	4	yes	—
74	C₂×#6099	C₂³	1	8	yes	—
75	C₂×#6099	C₂³	1	4	yes	—
76	C₂²×#1055	—	2	2	no	—
77	C₂²×#1055	—	2	8	no	—
78	C₂²×#1055	C₂³	1	2	yes	—
79	#88077	C₂³	1	16	yes	complemented
80	#88077	C₂³	1	16	yes	complemented
81	#88059	C₂³	1	16	yes	complemented
82	#88055	C₂³	1	8	yes	complemented
83	C₈×Dic₁₃	C₂³	1	8	yes	complemented
84	C₂×#2956	—	13	1	no	maximal, Sylow
85	C₂⁴×C₁₃	—	2	2	no	—
86	C₂⁴×C₁₃	#41	1	1	yes	characteristic
87	C₁₃×#41	—	2	8	no	—
88	C₁₃×#41	—	2	8	no	—
89	C₁₃×#41	—	2	8	no	—
90	C₁₃×#41	—	2	8	no	—
91	C₁₃×#41	—	2	4	no	—
92	C₁₃×#41	—	2	4	no	—
93	C₁₃×#41	—	2	8	no	—
94	C₁₃×#41	C₂²×C₄	1	8	yes	—
95	C₁₃×#41	C₂²×C₄	1	16	yes	—
96	C₁₃×#41	C₂⁴	1	8	yes	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	—	2	4	no	—
99	C₂×Q₈×C₁₃	C₂²×C₄	1	4	yes	—
100	C₂×Q₈×C₁₃	C₂²×C₄	1	8	yes	—
101	C₂×D₄×C₁₃	—	2	4	no	—
102	C₂×D₄×C₁₃	—	2	8	no	—
103	C₂×D₄×C₁₃	—	2	4	no	—
104	C₂×D₄×C₁₃	—	2	8	no	—
105	C₂×D₄×C₁₃	—	2	2	no	—
106	C₂×D₄×C₁₃	—	2	4	no	—
107	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
108	C₂×D₄×C₁₃	C₂²×C₄	1	8	yes	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	4	no	—
111	C₂²×C₄×C₁₃	—	2	8	no	—
112	C₂²×C₄×C₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₃	—	2	8	no	—
114	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	#41	1	2	yes	—
120	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
122	C₂²×Dic₁₃	—	2	1	no	—
123	C₂²×Dic₁₃	—	2	4	no	—
124	C₂²×Dic₁₃	—	2	1	no	—
125	C₂²×Dic₁₃	—	4	4	no	—
126	C₁₃×Q₁₆	C₂²×C₄	1	16	yes	complemented
127	C₁₃×SD₁₆	C₂²×C₄	1	32	yes	complemented
128	C₁₃×D₈	C₂²×C₄	1	16	yes	complemented
129	C₁₃×M₁₆	C₂²×C₄	1	16	yes	—
130	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
131	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
132	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
133	C₄×Dic₁₃	—	2	1	no	—
134	C₄×Dic₁₃	—	2	4	no	—
135	C₄×Dic₁₃	—	2	1	no	—
136	C₄×Dic₁₃	C₂⁴	1	2	yes	—
137	C₄×Dic₁₃	C₂⁴	1	2	yes	—
138	#6099	—	2	8	no	—
139	#6099	—	2	4	no	—
140	#6099	—	2	32	no	—
141	#6099	C₂×D₄	1	16	yes	—
142	#6099	C₂⁴	1	8	yes	—
143	C₂×#1055	—	2	4	no	—
144	C₂×#1055	—	2	8	no	—
145	C₂×#1055	—	2	32	no	—
146	C₂×#1055	C₂×D₄	1	4	yes	—
147	C₂×#1055	C₂×D₄	1	4	yes	—
148	C₂×#1055	C₂⁴	1	4	yes	—
149	C₂×#575	D₁₃	1	1	yes	characteristic
150	C₂×#568	—	13	2	no	—
151	#2956	—	13	16	no	—
152	C₂×#444	—	13	4	no	—
153	C₂×#443	—	13	4	no	—
154	C₂×#430	—	13	1	no	—
155	C₂²×#104	—	13	2	no	—
156	C₂×C₄×M₁₆	—	13	1	no	—
157	C₂³×C₁₃	—	2	4	no	—
158	C₂³×C₁₃	—	2	8	no	—
159	C₂³×C₁₃	—	4	2	no	—
160	C₂³×C₁₃	—	8	4	no	—
161	C₂³×C₁₃	C₄×D₄	1	2	yes	—
162	C₂³×C₁₃	C₄×D₄	1	2	yes	—
163	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
164	C₂³×C₁₃	C₂×#41	1	2	yes	—
165	Q₈×C₁₃	—	2	8	no	—
166	Q₈×C₁₃	—	2	4	no	—
167	Q₈×C₁₃	C₂³×C₄	1	8	yes	—
168	D₄×C₁₃	—	2	16	no	—
169	D₄×C₁₃	—	2	8	no	—
170	D₄×C₁₃	—	2	8	no	—
171	D₄×C₁₃	—	2	8	no	—
172	D₄×C₁₃	—	2	4	no	—
173	D₄×C₁₃	C₂³×C₄	1	8	yes	—
174	C₂×C₄×C₁₃	—	2	8	no	—
175	C₂×C₄×C₁₃	—	2	4	no	—
176	C₂×C₄×C₁₃	—	2	8	no	—
177	C₂×C₄×C₁₃	—	2	16	no	—
178	C₂×C₄×C₁₃	—	2	8	no	—
179	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
180	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
181	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
182	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
183	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
186	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
187	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
191	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
192	C₂×Dic₁₃	—	2	4	no	—
193	C₂×Dic₁₃	—	2	2	no	—
194	C₂×Dic₁₃	—	2	2	no	—
195	C₂×Dic₁₃	—	4	8	no	—
196	C₂×Dic₁₃	—	4	2	no	—
197	C₈×C₁₃	C₂³×C₄	1	8	yes	—
198	#1055	—	2	8	no	—
199	#1055	C₂²×D₄	1	8	yes	—
200	C₂²×#41	C₂×D₁₃	1	2	yes	—
201	#575	Dic₁₃	1	8	yes	complemented
202	#575	C₂×D₁₃	1	8	yes	—
203	C₂×#137	Dic₁₃	1	4	yes	complemented
204	C₂×AGL(1,ℤ/8)	Dic₁₃	1	4	yes	complemented
205	C₂×#135	C₂×D₁₃	1	4	yes	—
206	#568	—	13	16	no	—
207	#568	—	26	8	no	—
208	C₂×#131	—	13	8	no	—
209	C₂×#131	—	26	4	no	—
210	C₂²×M₁₆	—	13	1	no	—
211	C₂²×M₁₆	—	13	2	no	—
212	C₂²×M₁₆	—	26	4	no	—
213	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
214	C₂²×C₄²	—	13	1	no	—
215	#444	—	13	32	no	—
216	#443	—	13	32	no	—
217	#430	—	13	8	no	—
218	C₂×#108	—	13	4	no	—
219	C₂×#104	—	13	4	no	—
220	C₂×#104	—	13	4	no	—
221	C₂×#104	—	13	16	no	—
222	C₄×M₁₆	—	13	8	no	—
223	C₂×#97	—	13	2	no	—
224	C₂×C₄×C₈	—	13	2	no	—
225	C₂²×C₁₃	—	2	2	no	—
226	C₂²×C₁₃	—	2	4	no	—
227	C₂²×C₁₃	—	2	8	no	—
228	C₂²×C₁₃	—	4	2	no	—
229	C₂²×C₁₃	—	4	2	no	—
230	C₂²×C₁₃	—	4	8	no	—
231	C₂²×C₁₃	—	8	8	no	—
232	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
233	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
234	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
235	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
236	C₄×C₁₃	—	2	8	no	—
237	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
238	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
239	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
240	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
241	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
242	Dic₁₃	—	2	4	no	—
243	Dic₁₃	—	4	2	no	—
244	C₂×#41	—	2	2	no	—
245	C₂×#41	—	2	4	no	—
246	C₂×#41	—	2	2	no	—
247	C₂×#41	—	2	4	no	—
248	C₂×#41	C₂×Dic₁₃	1	4	yes	—
249	C₂×#41	C₂×Dic₁₃	1	8	yes	—
250	C₂×#41	C₂²×D₁₃	1	4	yes	—
251	C₂×#41	C₂²×D₁₃	1	8	yes	—
252	C₂²×Q₈	C₂×Dic₁₃	1	2	yes	—
253	C₂²×D₄	—	2	2	no	—
254	C₂²×D₄	C₂×Dic₁₃	1	2	yes	—
255	C₂³×C₄	—	2	2	no	—
256	C₂³×C₄	—	26	1	no	—
257	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
258	#137	C₂×Dic₁₃	1	32	yes	complemented
259	AGL(1,ℤ/8)	C₂×Dic₁₃	1	32	yes	complemented
260	#135	C₂×Dic₁₃	1	16	yes	complemented
261	#135	C₂²×D₁₃	1	16	yes	—
262	C₂×Q₁₆	C₂×Dic₁₃	1	4	yes	complemented
263	C₂×SD₁₆	C₂×Dic₁₃	1	8	yes	complemented
264	C₂×D₈	C₂×Dic₁₃	1	4	yes	complemented
265	#131	—	13	32	no	—
266	#131	—	26	16	no	—
267	#131	—	26	32	no	—
268	C₂×M₁₆	—	13	4	no	—
269	C₂×M₁₆	—	13	4	no	—
270	C₂×M₁₆	—	13	4	no	—
271	C₂×M₁₆	—	13	4	no	—
272	C₂×M₁₆	—	13	8	no	—
273	C₂×M₁₆	—	26	8	no	—
274	C₂×M₁₆	—	26	32	no	—
275	C₂×M₁₆	—	26	2	no	—
276	C₂×M₁₆	—	26	4	no	—
277	C₂×M₁₆	C₂×Dic₁₃	1	4	yes	—
278	C₂×M₁₆	C₂×Dic₁₃	1	4	yes	—
279	C₂×M₁₆	C₂²×D₁₃	1	4	yes	—
280	C₂²×C₈	—	13	2	no	—
281	C₂²×C₈	—	26	8	no	—
282	C₂²×C₈	—	26	2	no	—
283	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
284	C₂×C₄²	—	13	1	no	—
285	C₂×C₄²	—	13	1	no	—
286	C₂×C₄²	—	13	4	no	—
287	C₂×C₄²	—	26	1	no	—
288	C₂×C₄²	—	26	2	no	—
289	#108	—	13	16	no	—
290	#104	—	13	16	no	—
291	#104	—	13	16	no	—
292	#97	—	13	8	no	—
293	C₄×C₈	—	13	8	no	—
294	C₂×C₁₃	—	2	1	no	—
295	C₂×C₁₃	—	2	4	no	—
296	C₂×C₁₃	—	2	1	no	—
297	C₂×C₁₃	—	4	8	no	—
298	C₂×C₁₃	#2956	1	2	yes	complemented
299	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
300	C₂⁴	—	2	2	no	—
301	C₂⁴	#6129	1	1	yes	characteristic
302	#41	—	2	8	no	—
303	#41	—	2	8	no	—
304	#41	—	2	8	no	—
305	#41	—	2	4	no	—
306	#41	—	2	8	no	—
307	#41	—	2	4	no	—
308	#41	—	2	8	no	—
309	#41	C₂²×Dic₁₃	1	8	yes	—
310	#41	C₂²×Dic₁₃	1	16	yes	—
311	#41	C₂³×D₁₃	1	8	yes	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	—	2	4	no	—
314	C₂×Q₈	C₂²×Dic₁₃	1	4	yes	—
315	C₂×Q₈	C₂²×Dic₁₃	1	8	yes	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	2	8	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	8	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	C₂²×Dic₁₃	1	4	yes	—
323	C₂×D₄	C₂²×Dic₁₃	1	8	yes	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	8	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	26	1	no	—
330	C₂²×C₄	—	26	4	no	—
331	C₂²×C₄	—	26	1	no	—
332	C₂²×C₄	—	52	4	no	—
333	C₂²×C₄	D₄×D₁₃	1	2	yes	—
334	C₂²×C₄	D₄×D₁₃	1	2	yes	—
335	C₂²×C₄	#6129	1	1	yes	characteristic
336	C₂²×C₄	#6129	1	2	yes	—
337	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
338	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
339	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
340	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
341	Q₁₆	C₂²×Dic₁₃	1	16	yes	complemented
342	SD₁₆	C₂²×Dic₁₃	1	32	yes	complemented
343	D₈	C₂²×Dic₁₃	1	16	yes	complemented
344	M₁₆	—	13	16	no	—
345	M₁₆	—	13	8	no	—
346	M₁₆	—	26	32	no	—
347	M₁₆	—	26	8	no	—
348	M₁₆	—	26	4	no	—
349	M₁₆	C₂²×Dic₁₃	1	16	yes	—
350	C₂×C₈	—	13	4	no	—
351	C₂×C₈	—	13	4	no	—
352	C₂×C₈	—	13	4	no	—
353	C₂×C₈	—	26	32	no	—
354	C₂×C₈	—	26	8	no	—
355	C₂×C₈	—	26	4	no	—
356	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
357	C₂×C₈	C₂²×Dic₁₃	1	4	yes	—
358	C₂×C₈	C₂³×D₁₃	1	4	yes	—
359	C₄²	—	13	2	no	—
360	C₄²	—	13	2	no	—
361	C₄²	—	26	1	no	—
362	C₄²	—	26	4	no	—
363	C₄²	—	26	1	no	—
364	C₁₃	C₂×#2956	1	1	yes	characteristic, complemented, Sylow
365	C₂³	—	2	4	no	—
366	C₂³	—	2	8	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	8	4	no	—
369	C₂³	D₄×Dic₁₃	1	2	yes	—
370	C₂³	D₄×Dic₁₃	1	2	yes	—
371	C₂³	C₂×#6129	1	1	yes	characteristic
372	C₂³	C₂×#6129	1	2	yes	—
373	Q₈	—	2	8	no	—
374	Q₈	—	2	4	no	—
375	Q₈	C₂³×Dic₁₃	1	8	yes	—
376	D₄	—	2	16	no	—
377	D₄	—	2	8	no	—
378	D₄	—	2	8	no	—
379	D₄	—	2	8	no	—
380	D₄	—	2	4	no	—
381	D₄	C₂³×Dic₁₃	1	8	yes	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	2	16	no	—
386	C₂×C₄	—	2	8	no	—
387	C₂×C₄	—	26	4	no	—
388	C₂×C₄	—	26	2	no	—
389	C₂×C₄	—	26	2	no	—
390	C₂×C₄	—	52	8	no	—
391	C₂×C₄	—	52	2	no	—
392	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
393	C₂×C₄	D₄×Dic₁₃	1	4	yes	—
394	C₂×C₄	D₄×Dic₁₃	1	4	yes	—
395	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
396	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
397	C₂×C₄	C₂×D₄×D₁₃	1	4	yes	—
398	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
399	C₂×C₄	C₂×#6129	1	1	yes	characteristic
400	C₂×C₄	C₂×#6129	1	2	yes	—
401	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
402	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
403	C₂×C₄	C₂³×Dic₁₃	1	4	yes	—
404	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
405	C₈	—	13	8	no	—
406	C₈	—	26	8	no	—
407	C₈	C₂³×Dic₁₃	1	8	yes	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	2	8	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	8	no	—
414	C₂²	—	8	8	no	—
415	C₂²	C₂×D₄×Dic₁₃	1	4	yes	—
416	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
417	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
418	C₂²	C₂²×#6129	1	1	yes	characteristic
419	C₄	—	2	8	no	—
420	C₄	—	26	4	no	—
421	C₄	—	52	2	no	—
422	C₄	C₂×D₄×Dic₁₃	1	1	yes	characteristic
423	C₄	C₂×D₄×Dic₁₃	1	4	yes	—
424	C₄	C₂×D₄×Dic₁₃	1	1	yes	characteristic
425	C₄	C₂²×D₄×D₁₃	1	1	yes	characteristic
426	C₄	C₂⁴×Dic₁₃	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	4	no	—
429	C₂	—	2	1	no	—
430	C₂	—	4	8	no	—
431	C₂	#13123746	1	2	yes	direct product factor
432	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	C₂×C₁₃×#575	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₂×#575	D₁₃
hypocenter	C₁₃	C₂×#2956
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#575

Complements

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

N	H ≅ G/N	type
1. C₂×#11719524	C₂	semidirect
2. #13123746	C₂	direct (N × H)
3. C₂×#11718858	C₂	semidirect
4. C₂×#11718857	C₂	semidirect
5. C₂×#11718786	C₂	semidirect
6. C₂²×#88077	C₂	semidirect
7. C₂×M₁₆×Dic₁₃	C₂	semidirect
10. C₁₃×#575	C₄	semidirect
12. C₂×C₁₃×#137	C₄	semidirect
13. C₂×C₁₃×AGL(1,ℤ/8)	C₄	semidirect
17. #11719524	C₂²	semidirect
19. C₂×#88202	C₂²	semidirect
24. C₂×#88077	C₂²	semidirect
25. C₂×#88077	C₂²	semidirect
26. C₂×#88077	C₂²	semidirect
27. #11718858	C₂²	semidirect
28. #11718857	C₂²	semidirect
29. #11718786	C₂²	semidirect
30. M₁₆×Dic₁₃	C₂²	semidirect
31. C₂×#88059	C₂²	semidirect
32. C₂×#88055	C₂²	semidirect
33. C₂×C₈×Dic₁₃	C₂²	semidirect
48. C₁₃×#137	C₂×C₄	semidirect
49. C₁₃×AGL(1,ℤ/8)	C₂×C₄	semidirect
50. C₁₃×#135	C₂×C₄	semidirect
52. C₂×C₁₃×Q₁₆	C₂×C₄	semidirect
53. C₂×C₁₃×SD₁₆	C₂×C₄	semidirect
54. C₂×C₁₃×D₈	C₂×C₄	semidirect
61. #88202	C₂³	semidirect
79. #88077	C₂³	semidirect
80. #88077	C₂³	semidirect
81. #88059	C₂³	semidirect
82. #88055	C₂³	semidirect
83. C₈×Dic₁₃	C₂³	semidirect
126. C₁₃×Q₁₆	C₂²×C₄	semidirect
127. C₁₃×SD₁₆	C₂²×C₄	semidirect
128. C₁₃×D₈	C₂²×C₄	semidirect
201. #575	Dic₁₃	semidirect
203. C₂×#137	Dic₁₃	semidirect
204. C₂×AGL(1,ℤ/8)	Dic₁₃	semidirect
258. #137	C₂×Dic₁₃	semidirect
259. AGL(1,ℤ/8)	C₂×Dic₁₃	semidirect
260. #135	C₂×Dic₁₃	semidirect
262. C₂×Q₁₆	C₂×Dic₁₃	semidirect
263. C₂×SD₁₆	C₂×Dic₁₃	semidirect
264. C₂×D₈	C₂×Dic₁₃	semidirect
298. C₂×C₁₃	#2956	semidirect
341. Q₁₆	C₂²×Dic₁₃	semidirect
342. SD₁₆	C₂²×Dic₁₃	semidirect
343. D₈	C₂²×Dic₁₃	semidirect
364. C₁₃	C₂×#2956	semidirect
431. C₂	#13123746	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
#13123746	2
C₂×#11718858	2
C₂×#11718857	2
C₂×#11718786	2
C₂²×#88077	2
C₂×M₁₆×Dic₁₃	2
C₂×C₁₃×#575	2
C₂×#2956	13

Subgroups — C2×#13123746 #16727232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13123746 #16727232