Subgroups — C₂×#13123747 #16727233

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×#11719453	C₂	1	1	yes	maximal, characteristic
2	C₂×#11719450	C₂	1	2	yes	maximal, complemented
3	#13123747	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	C₂²×#88045	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#6127	C₂²	1	2	yes	—
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₁₃	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	#11719450	—	2	8	no	—
19	#11719450	C₂²	1	16	yes	complemented
20	C₂×#88161	—	2	4	no	—
21	C₂×M₁₆×D₁₃	—	2	4	no	—
22	C₂×#88158	C₂²	1	4	yes	—
23	C₂×#88155	C₂²	1	8	yes	complemented
24	C₄×C₁₃×M₁₆	C₂²	1	8	yes	complemented
25	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
26	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
27	#11718786	C₂²	1	8	yes	complemented
28	C₂×#88059	C₂²	1	4	yes	complemented
29	C₂×#88045	C₂²	1	4	yes	complemented
30	C₂×#88045	C₂²	1	4	yes	complemented
31	C₂×#88045	C₂²	1	16	yes	complemented
32	#11718378	C₂²	1	32	yes	complemented
33	#11718361	C₂²	1	32	yes	complemented
34	C₂³×C₄×C₁₃	—	2	1	no	—
35	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
36	C₂²×C₂²⋊D₁₃	—	2	2	no	—
37	C₂×#6127	—	2	2	no	—
38	C₂×#6127	—	2	4	no	—
39	C₂×#6127	—	2	2	no	—
40	C₂×#6127	—	2	4	no	—
41	C₂×#6127	C₂×C₄	1	4	yes	—
42	C₂×#6127	C₂×C₄	1	8	yes	—
43	C₂×#6127	C₂³	1	4	yes	—
44	C₂×#6127	C₂³	1	8	yes	—
45	C₂²×D₅₂	C₂×C₄	1	2	yes	—
46	C₂²×C₄×D₁₃	—	2	2	no	—
47	C₂²×Dic₂₆	C₂×C₄	1	2	yes	—
48	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
49	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
50	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
51	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
52	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
53	C₂×C₁₃×M₁₆	C₂³	1	4	yes	—
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
56	C₂×C₄²×C₁₃	—	2	1	no	—
57	C₂×C₄²×C₁₃	—	2	2	no	—
58	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
59	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
61	C₂×#6099	—	2	2	no	—
62	C₂×#6099	—	2	4	no	—
63	C₂×#6099	C₂³	1	4	yes	—
64	C₂×#6099	C₂³	1	8	yes	—
65	C₂²×#1055	—	2	2	no	—
66	#88163	C₂×C₄	1	32	yes	complemented
67	#88162	C₂×C₄	1	32	yes	complemented
68	#88161	—	2	32	no	—
69	M₁₆×D₁₃	—	2	32	no	—
70	C₂×Dic₅₂	C₂×C₄	1	4	yes	complemented
71	#88158	C₂×C₄	1	16	yes	complemented
72	#88158	C₂³	1	16	yes	—
73	C₂×D₁₀₄	C₂×C₄	1	4	yes	complemented
74	C₂×#6095	C₂×C₄	1	8	yes	complemented
75	#88155	—	2	16	no	—
76	#88155	C₂³	1	32	yes	complemented
77	C₂×#6094	—	2	8	no	—
78	C₂×C₈×D₁₃	—	2	8	no	—
79	C₁₃×#97	C₂³	1	8	yes	complemented
80	C₄×C₈×C₁₃	C₂³	1	8	yes	complemented
81	#88059	C₂³	1	16	yes	complemented
82	#88045	C₂³	1	16	yes	complemented
83	#88045	C₂³	1	16	yes	complemented
84	C₂×#2956	—	13	1	no	maximal, Sylow
85	C₂⁴×C₁₃	#41	1	1	yes	characteristic
86	C₂³×D₁₃	—	2	2	no	—
87	C₂²×C₄×C₁₃	—	2	1	no	—
88	C₂²×C₄×C₁₃	—	2	4	no	—
89	C₂²×C₄×C₁₃	—	2	1	no	—
90	C₂²×C₄×C₁₃	—	4	4	no	—
91	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	#41	1	2	yes	—
97	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
99	C₂×C₂²⋊D₁₃	—	2	4	no	—
100	C₂×C₂²⋊D₁₃	—	2	8	no	—
101	C₂×C₂²⋊D₁₃	—	2	4	no	—
102	C₂×C₂²⋊D₁₃	—	2	8	no	—
103	C₂²×Dic₁₃	—	2	2	no	—
104	#6127	—	2	8	no	—
105	#6127	—	2	8	no	—
106	#6127	—	2	8	no	—
107	#6127	—	2	4	no	—
108	#6127	—	2	8	no	—
109	#6127	—	2	4	no	—
110	#6127	—	2	8	no	—
111	#6127	C₂²×C₄	1	8	yes	—
112	#6127	C₂²×C₄	1	16	yes	—
113	#6127	C₂⁴	1	8	yes	—
114	C₂×D₅₂	—	2	2	no	—
115	C₂×D₅₂	—	2	4	no	—
116	C₂×D₅₂	C₂²×C₄	1	4	yes	—
117	C₂×D₅₂	C₂²×C₄	1	8	yes	—
118	C₂×C₄×D₁₃	—	2	4	no	—
119	C₂×C₄×D₁₃	—	2	8	no	—
120	C₂×C₄×D₁₃	—	2	4	no	—
121	C₂×C₄×D₁₃	—	2	8	no	—
122	C₂×Dic₂₆	—	2	2	no	—
123	C₂×Dic₂₆	—	2	4	no	—
124	C₂×Dic₂₆	C₂²×C₄	1	4	yes	—
125	C₂×Dic₂₆	C₂²×C₄	1	8	yes	—
126	C₁₃×M₁₆	C₂²×C₄	1	16	yes	—
127	C₁₃×M₁₆	C₂×D₄	1	16	yes	—
128	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
129	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
130	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
131	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
132	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
133	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
134	C₄²×C₁₃	—	2	1	no	—
135	C₄²×C₁₃	—	2	4	no	—
136	C₄²×C₁₃	—	2	1	no	—
137	C₄²×C₁₃	C₂⁴	1	2	yes	—
138	C₄²×C₁₃	C₂⁴	1	2	yes	—
139	#6099	—	2	4	no	—
140	#6099	—	2	8	no	—
141	#6099	C₂⁴	1	8	yes	—
142	C₂×#1055	—	2	4	no	—
143	C₂×#1055	—	2	8	no	—
144	Dic₅₂	C₂²×C₄	1	16	yes	complemented
145	D₁₀₄	C₂²×C₄	1	16	yes	complemented
146	#6095	C₂²×C₄	1	32	yes	complemented
147	#6094	—	2	32	no	—
148	C₈×D₁₃	—	2	32	no	—
149	C₂×#575	—	13	1	no	—
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	D₁₃	1	1	yes	characteristic, complemented
157	C₂³×C₁₃	—	4	2	no	—
158	C₂³×C₁₃	C₄×D₄	1	2	yes	—
159	C₂³×C₁₃	C₄×D₄	1	2	yes	—
160	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
161	C₂³×C₁₃	C₂×#41	1	2	yes	—
162	C₂²×D₁₃	—	2	4	no	—
163	C₂²×D₁₃	—	2	8	no	—
164	C₂²×D₁₃	—	8	4	no	—
165	C₂×C₄×C₁₃	—	2	4	no	—
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	2	no	—
168	C₂×C₄×C₁₃	—	4	8	no	—
169	C₂×C₄×C₁₃	—	4	2	no	—
170	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
172	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
173	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂³×C₄	1	4	yes	—
177	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
178	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
182	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
183	C₂²⋊D₁₃	—	2	16	no	—
184	C₂²⋊D₁₃	—	2	8	no	—
185	C₂²⋊D₁₃	—	2	8	no	—
186	C₂×Dic₁₃	—	2	8	no	—
187	C₂×Dic₁₃	—	2	4	no	—
188	D₅₂	—	2	4	no	—
189	D₅₂	—	2	8	no	—
190	D₅₂	C₂³×C₄	1	8	yes	—
191	C₄×D₁₃	—	2	16	no	—
192	C₄×D₁₃	—	2	8	no	—
193	C₄×D₁₃	—	2	8	no	—
194	Dic₂₆	—	2	4	no	—
195	Dic₂₆	—	2	8	no	—
196	Dic₂₆	C₂³×C₄	1	8	yes	—
197	C₈×C₁₃	C₂³×C₄	1	8	yes	—
198	C₈×C₁₃	C₂²×D₄	1	8	yes	—
199	#1055	—	2	8	no	—
200	C₂²×#41	—	13	2	no	—
201	#575	—	13	8	no	—
202	#575	—	13	8	no	—
203	C₂×#137	—	13	4	no	—
204	C₂×AGL(1,ℤ/8)	—	13	4	no	—
205	C₂×#135	—	13	4	no	—
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	2	no	—
211	C₂²×M₁₆	—	26	4	no	—
212	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
213	C₂²×M₁₆	C₂×D₁₃	1	1	yes	characteristic
214	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
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	C₂×D₁₃	1	8	yes	complemented
223	C₂×#97	C₂×D₁₃	1	2	yes	complemented
224	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	complemented
225	C₂²×C₁₃	—	2	2	no	—
226	C₂²×C₁₃	—	2	4	no	—
227	C₂²×C₁₃	—	4	2	no	—
228	C₂²×C₁₃	—	4	2	no	—
229	C₂²×C₁₃	C₂×C₄×D₄	1	4	yes	—
230	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
231	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
232	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
233	C₂×D₁₃	—	2	8	no	—
234	C₂×D₁₃	—	4	8	no	—
235	C₂×D₁₃	—	8	8	no	—
236	C₄×C₁₃	—	2	4	no	—
237	C₄×C₁₃	—	4	2	no	—
238	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
239	C₄×C₁₃	C₂×C₄×D₄	1	4	yes	—
240	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
241	C₄×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
242	C₄×C₁₃	C₂³×D₄	1	1	yes	characteristic
243	Dic₁₃	—	2	8	no	—
244	C₂×#41	—	13	4	no	—
245	C₂×#41	—	13	8	no	—
246	C₂×#41	—	13	4	no	—
247	C₂×#41	—	13	8	no	—
248	C₂×#41	—	26	2	no	—
249	C₂×#41	—	26	4	no	—
250	C₂×#41	—	26	2	no	—
251	C₂×#41	—	26	4	no	—
252	C₂²×Q₈	—	13	2	no	—
253	C₂²×D₄	—	13	2	no	—
254	C₂²×D₄	—	26	2	no	—
255	C₂³×C₄	—	2	1	no	—
256	C₂³×C₄	—	26	2	no	—
257	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
258	#137	—	13	32	no	—
259	AGL(1,ℤ/8)	—	13	32	no	—
260	#135	—	13	16	no	—
261	#135	—	13	16	no	—
262	C₂×Q₁₆	—	13	4	no	—
263	C₂×SD₁₆	—	13	8	no	—
264	C₂×D₈	—	13	4	no	—
265	#131	—	13	32	no	—
266	#131	—	26	32	no	—
267	#131	—	26	16	no	—
268	C₂×M₁₆	—	13	4	no	—
269	C₂×M₁₆	—	13	8	no	—
270	C₂×M₁₆	—	26	2	no	—
271	C₂×M₁₆	—	26	4	no	—
272	C₂×M₁₆	—	26	32	no	—
273	C₂×M₁₆	—	26	8	no	—
274	C₂×M₁₆	C₄×D₁₃	1	4	yes	—
275	C₂×M₁₆	C₄×D₁₃	1	4	yes	—
276	C₂×M₁₆	D₅₂	1	4	yes	—
277	C₂×M₁₆	D₅₂	1	4	yes	—
278	C₂×M₁₆	C₂²×D₁₃	1	4	yes	—
279	C₂×M₁₆	C₂²×D₁₃	1	4	yes	—
280	C₂²×C₈	—	26	2	no	—
281	C₂²×C₈	—	26	8	no	—
282	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
283	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	—	2	2	no	—
286	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
287	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
288	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
289	#108	—	13	16	no	—
290	#104	—	13	16	no	—
291	#104	—	13	16	no	—
292	#97	C₂²×D₁₃	1	8	yes	complemented
293	C₄×C₈	C₂²×D₁₃	1	8	yes	complemented
294	C₂×C₁₃	—	2	1	no	—
295	C₂×C₁₃	—	2	4	no	—
296	C₂×C₁₃	—	2	1	no	—
297	C₂×C₁₃	#2956	1	2	yes	complemented
298	C₂×C₁₃	C₂²×C₄×D₄	1	1	yes	characteristic
299	D₁₃	—	4	8	no	—
300	C₂⁴	—	26	2	no	—
301	C₂⁴	#6127	1	1	yes	characteristic
302	#41	—	13	8	no	—
303	#41	—	13	16	no	—
304	#41	—	13	8	no	—
305	#41	—	26	8	no	—
306	#41	—	26	8	no	—
307	#41	—	26	8	no	—
308	#41	—	26	8	no	—
309	#41	—	26	4	no	—
310	#41	—	26	4	no	—
311	#41	—	26	8	no	—
312	C₂×Q₈	—	13	4	no	—
313	C₂×Q₈	—	13	8	no	—
314	C₂×Q₈	—	26	2	no	—
315	C₂×Q₈	—	26	4	no	—
316	C₂×D₄	—	13	4	no	—
317	C₂×D₄	—	13	8	no	—
318	C₂×D₄	—	26	4	no	—
319	C₂×D₄	—	26	8	no	—
320	C₂×D₄	—	26	4	no	—
321	C₂×D₄	—	26	8	no	—
322	C₂×D₄	—	26	2	no	—
323	C₂×D₄	—	26	4	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	4	4	no	—
328	C₂²×C₄	—	26	2	no	—
329	C₂²×C₄	—	26	4	no	—
330	C₂²×C₄	—	26	8	no	—
331	C₂²×C₄	—	26	8	no	—
332	C₂²×C₄	—	26	4	no	—
333	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
334	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
335	C₂²×C₄	C₂×D₅₂	1	2	yes	—
336	C₂²×C₄	C₂×D₅₂	1	2	yes	—
337	C₂²×C₄	#6127	1	1	yes	characteristic
338	C₂²×C₄	#6127	1	2	yes	—
339	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
340	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
341	Q₁₆	—	13	16	no	—
342	SD₁₆	—	13	32	no	—
343	D₈	—	13	16	no	—
344	M₁₆	—	13	8	no	—
345	M₁₆	—	26	8	no	—
346	M₁₆	—	26	4	no	—
347	M₁₆	—	26	32	no	—
348	M₁₆	C₂×C₄×D₁₃	1	16	yes	—
349	M₁₆	C₂×D₅₂	1	16	yes	—
350	C₂×C₈	—	26	8	no	—
351	C₂×C₈	—	26	4	no	—
352	C₂×C₈	—	26	32	no	—
353	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
354	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
355	C₂×C₈	C₂×D₅₂	1	4	yes	—
356	C₂×C₈	C₂×D₅₂	1	4	yes	—
357	C₂×C₈	C₂³×D₁₃	1	4	yes	—
358	C₂×C₈	C₂³×D₁₃	1	4	yes	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	4	no	—
361	C₄²	—	2	1	no	—
362	C₄²	C₂³×D₁₃	1	2	yes	—
363	C₄²	C₂³×D₁₃	1	2	yes	—
364	C₁₃	C₂×#2956	1	1	yes	characteristic, complemented, Sylow
365	C₂³	—	4	2	no	—
366	C₂³	—	26	4	no	—
367	C₂³	—	26	8	no	—
368	C₂³	—	104	4	no	—
369	C₂³	C₄×D₅₂	1	2	yes	—
370	C₂³	C₄×D₅₂	1	2	yes	—
371	C₂³	C₂×#6127	1	1	yes	characteristic
372	C₂³	C₂×#6127	1	2	yes	—
373	Q₈	—	13	8	no	—
374	Q₈	—	26	8	no	—
375	Q₈	—	26	4	no	—
376	D₄	—	13	8	no	—
377	D₄	—	26	16	no	—
378	D₄	—	26	8	no	—
379	D₄	—	26	8	no	—
380	D₄	—	26	8	no	—
381	D₄	—	26	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	8	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	26	8	no	—
388	C₂×C₄	—	26	4	no	—
389	C₂×C₄	—	26	8	no	—
390	C₂×C₄	—	26	16	no	—
391	C₂×C₄	—	26	8	no	—
392	C₂×C₄	C₄×D₅₂	1	2	yes	—
393	C₂×C₄	C₄×D₅₂	1	4	yes	—
394	C₂×C₄	C₄×D₅₂	1	4	yes	—
395	C₂×C₄	C₄×D₅₂	1	2	yes	—
396	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
397	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
398	C₂×C₄	C₂²×C₄×D₁₃	1	4	yes	—
399	C₂×C₄	C₂²×D₅₂	1	4	yes	—
400	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
401	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
402	C₂×C₄	C₂×#6127	1	1	yes	characteristic
403	C₂×C₄	C₂×#6127	1	2	yes	—
404	C₂×C₄	C₂⁴×D₁₃	1	1	yes	characteristic
405	C₈	—	26	8	no	—
406	C₈	C₂²×C₄×D₁₃	1	8	yes	—
407	C₈	C₂²×D₅₂	1	8	yes	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	26	8	no	—
413	C₂²	—	52	8	no	—
414	C₂²	—	104	8	no	—
415	C₂²	C₂×C₄×D₅₂	1	4	yes	—
416	C₂²	C₂×C₄×D₅₂	1	1	yes	characteristic
417	C₂²	C₂×C₄×D₅₂	1	1	yes	characteristic
418	C₂²	C₂²×#6127	1	1	yes	characteristic
419	C₄	—	2	4	no	—
420	C₄	—	4	2	no	—
421	C₄	—	26	8	no	—
422	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
423	C₄	C₂×C₄×D₅₂	1	4	yes	—
424	C₄	C₂×C₄×D₅₂	1	1	yes	characteristic
425	C₄	C₂³×C₄×D₁₃	1	1	yes	characteristic
426	C₄	C₂³×D₅₂	1	1	yes	characteristic
427	C₂	—	2	1	no	—
428	C₂	—	2	4	no	—
429	C₂	—	2	1	no	—
430	C₂	—	52	8	no	—
431	C₂	#13123747	1	2	yes	direct product factor
432	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×C₄×C₁₃×M₁₆	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	C₂×#11719453	C₂
cosocle	C₂×C₄×C₁₃	C₂⁵
hypercenter	C₂×C₄×M₁₆	D₁₃
hypocenter	C₁₃	C₂×#2956
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×M₁₆ ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×#11719450	C₂	semidirect
3. #13123747	C₂	direct (N × H)
4. C₂×#11718378	C₂	semidirect
5. C₂×#11718361	C₂	semidirect
6. C₂×#11718786	C₂	semidirect
7. C₂²×#88045	C₂	semidirect
8. C₂×C₄×C₁₃×M₁₆	C₂	semidirect
14. #11719453	C₄	semidirect
16. C₂×#88163	C₄	semidirect
17. C₂×#88162	C₄	semidirect
19. #11719450	C₂²	semidirect
23. C₂×#88155	C₂²	semidirect
24. C₄×C₁₃×M₁₆	C₂²	semidirect
25. C₂×C₁₃×#97	C₂²	semidirect
26. C₂×C₄×C₈×C₁₃	C₂²	semidirect
27. #11718786	C₂²	semidirect
28. C₂×#88059	C₂²	semidirect
29. C₂×#88045	C₂²	semidirect
30. C₂×#88045	C₂²	semidirect
31. C₂×#88045	C₂²	semidirect
32. #11718378	C₂²	semidirect
33. #11718361	C₂²	semidirect
66. #88163	C₂×C₄	semidirect
67. #88162	C₂×C₄	semidirect
70. C₂×Dic₅₂	C₂×C₄	semidirect
71. #88158	C₂×C₄	semidirect
73. C₂×D₁₀₄	C₂×C₄	semidirect
74. C₂×#6095	C₂×C₄	semidirect
76. #88155	C₂³	semidirect
79. C₁₃×#97	C₂³	semidirect
80. C₄×C₈×C₁₃	C₂³	semidirect
81. #88059	C₂³	semidirect
82. #88045	C₂³	semidirect
83. #88045	C₂³	semidirect
144. Dic₅₂	C₂²×C₄	semidirect
145. D₁₀₄	C₂²×C₄	semidirect
146. #6095	C₂²×C₄	semidirect
156. C₂×C₄×M₁₆	D₁₃	semidirect
222. C₄×M₁₆	C₂×D₁₃	semidirect
223. C₂×#97	C₂×D₁₃	semidirect
224. C₂×C₄×C₈	C₂×D₁₃	semidirect
292. #97	C₂²×D₁₃	semidirect
293. C₄×C₈	C₂²×D₁₃	semidirect
297. C₂×C₁₃	#2956	semidirect
364. C₁₃	C₂×#2956	semidirect
431. C₂	#13123747	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
C₂×#11719450	2
#13123747	2
C₂×#11718378	2
C₂×#11718361	2
C₂×#11718786	2
C₂²×#88045	2
C₂×C₄×C₁₃×M₁₆	2
C₂×#2956	13

Subgroups — C2×#13123747 #16727233

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13123747 #16727233