Subgroups — C₂×#13116573 #16015862

Order 3328.

1170 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88158	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718767	C₂	1	1	yes	maximal, characteristic, complemented
3	#13116573	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718110	C₂	1	4	yes	maximal, complemented
5	C₂²×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#6127	—	2	1	no	—
7	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×#88180	—	2	1	no	—
9	C₂²×Dic₅₂	C₄	1	1	yes	characteristic, complemented
10	C₂×#88158	—	2	1	no	—
11	C₂×#88158	—	2	2	no	—
12	C₂×#88158	—	2	1	no	—
13	C₂×#88158	—	2	2	no	—
14	C₂×#88158	C₄	1	2	yes	complemented
15	C₂×#88158	C₄	1	4	yes	complemented
16	C₂×#88158	C₂²	1	2	yes	—
17	C₂×#88158	C₂²	1	4	yes	—
18	C₂²×D₁₀₄	C₄	1	1	yes	characteristic, complemented
19	C₂²×#6095	—	2	1	no	—
20	C₂×C₁₃×M₃₂	—	2	1	no	—
21	C₂×C₁₃×M₃₂	—	2	2	no	—
22	C₂×C₁₃×M₃₂	C₂²	1	2	yes	complemented
23	C₂×C₁₃×M₃₂	C₂²	1	4	yes	complemented
24	C₂²×C₁₃×C₁₆	—	2	1	no	—
25	#11718767	—	2	2	no	—
26	#11718767	C₂²	1	4	yes	complemented
27	C₂×#88058	—	2	1	no	—
28	C₂×#88057	C₂²	1	2	yes	complemented
29	#11718110	C₂²	1	16	yes	complemented
30	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
31	C₂²×C₂²⋊D₁₃	—	4	1	no	—
32	C₂×#6127	—	2	2	no	—
33	C₂×#6127	—	2	4	no	—
34	C₂×#6127	—	2	2	no	—
35	C₂×#6127	—	2	4	no	—
36	C₂×#6127	—	4	1	no	—
37	C₂×#6127	—	4	2	no	—
38	C₂×#6127	—	4	1	no	—
39	C₂×#6127	—	4	2	no	—
40	C₂²×D₅₂	—	2	1	no	—
41	C₂²×C₄×D₁₃	—	4	1	no	—
42	C₂²×Dic₂₆	—	2	1	no	—
43	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
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×C₂²⋊Dic₁₃	—	4	1	no	—
54	#88180	—	2	4	no	—
55	#88180	—	4	2	no	—
56	C₂×C₄⋊Dic₁₃	—	2	2	no	—
57	C₂×C₄×Dic₁₃	—	4	1	no	—
58	C₂×Dic₅₂	—	2	2	no	—
59	C₂×Dic₅₂	—	2	1	no	—
60	C₂×Dic₅₂	C₂×C₄	1	2	yes	—
61	C₂×Dic₅₂	C₂×C₄	1	4	yes	complemented
62	#88158	—	2	4	no	—
63	#88158	—	2	4	no	—
64	#88158	—	2	4	no	—
65	#88158	—	2	2	no	—
66	#88158	—	2	4	no	—
67	#88158	—	2	2	no	—
68	#88158	—	2	4	no	—
69	#88158	C₂×C₄	1	4	yes	—
70	#88158	C₂×C₄	1	8	yes	complemented
71	#88158	C₂³	1	4	yes	—
72	C₂×D₁₀₄	—	2	2	no	—
73	C₂×D₁₀₄	—	2	1	no	—
74	C₂×D₁₀₄	C₂×C₄	1	2	yes	—
75	C₂×D₁₀₄	C₂×C₄	1	4	yes	complemented
76	C₂×#6095	—	2	4	no	—
77	C₂×#6095	—	2	2	no	—
78	C₂×#6095	—	2	2	no	—
79	C₂×#6095	—	2	4	no	—
80	C₁₃×M₃₂	—	2	4	no	—
81	C₁₃×M₃₂	—	2	2	no	—
82	C₁₃×M₃₂	C₂³	1	4	yes	complemented
83	C₂×C₁₃×C₁₆	—	2	2	no	—
84	C₂×C₁₃×C₁₆	—	2	4	no	—
85	#88058	—	2	4	no	—
86	#88057	—	2	2	no	—
87	#88057	C₂³	1	4	yes	complemented
88	C₂×#2145	—	13	1	no	maximal, Sylow
89	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
90	C₂³×D₁₃	—	4	1	no	—
91	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
93	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	D₈	1	2	yes	—
96	C₂²×C₄×C₁₃	SD₁₆	1	1	yes	characteristic
97	C₂²×C₄×C₁₃	SD₁₆	1	1	yes	characteristic
98	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
99	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
101	C₂×C₂²⋊D₁₃	—	4	2	no	—
102	C₂×C₂²⋊D₁₃	—	4	4	no	—
103	C₂×C₂²⋊D₁₃	—	4	2	no	—
104	C₂×C₂²⋊D₁₃	—	4	4	no	—
105	C₂²×Dic₁₃	—	4	1	no	—
106	C₂²×Dic₁₃	—	4	2	no	—
107	#6127	—	2	4	no	—
108	#6127	—	2	8	no	—
109	#6127	—	2	4	no	—
110	#6127	—	4	4	no	—
111	#6127	—	4	4	no	—
112	#6127	—	4	4	no	—
113	#6127	—	4	4	no	—
114	#6127	—	4	2	no	—
115	#6127	—	4	2	no	—
116	#6127	—	4	4	no	—
117	C₂×D₅₂	—	2	2	no	—
118	C₂×D₅₂	—	2	4	no	—
119	C₂×D₅₂	—	4	2	no	—
120	C₂×D₅₂	—	4	1	no	—
121	C₂×C₄×D₁₃	—	4	4	no	—
122	C₂×C₄×D₁₃	—	4	2	no	—
123	C₂×C₄×D₁₃	—	4	2	no	—
124	C₂×C₄×D₁₃	—	4	4	no	—
125	C₂×Dic₂₆	—	2	2	no	—
126	C₂×Dic₂₆	—	2	4	no	—
127	C₂×Dic₂₆	—	4	2	no	—
128	C₂×Dic₂₆	—	4	1	no	—
129	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
130	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
131	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
133	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
134	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
135	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
136	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
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	1	yes	characteristic
143	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₂²⋊Dic₁₃	—	4	4	no	—
148	C₄⋊Dic₁₃	—	2	4	no	—
149	C₄⋊Dic₁₃	—	4	2	no	—
150	C₄×Dic₁₃	—	4	4	no	—
151	Dic₅₂	—	2	2	no	—
152	Dic₅₂	—	2	4	no	—
153	Dic₅₂	C₂²×C₄	1	4	yes	—
154	D₁₀₄	—	2	2	no	—
155	D₁₀₄	—	2	4	no	—
156	D₁₀₄	C₂²×C₄	1	4	yes	—
157	#6095	—	2	4	no	—
158	#6095	—	2	8	no	—
159	#6095	—	2	4	no	—
160	C₁₃×C₁₆	—	2	4	no	—
161	C₂²×#135	—	13	1	no	—
162	C₂²×M₃₂	D₁₃	1	1	yes	characteristic, complemented
163	C₂×#427	—	13	1	no	—
164	#2145	—	13	8	no	—
165	C₂×#360	—	13	4	no	—
166	C₂³×C₁₃	—	4	2	no	—
167	C₂³×C₁₃	#102	1	1	yes	characteristic
168	C₂³×C₁₃	#102	1	1	yes	characteristic
169	C₂³×C₁₃	#102	1	2	yes	—
170	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
171	C₂³×C₁₃	C₂×D₈	1	2	yes	—
172	C₂²×D₁₃	—	4	4	no	—
173	C₂²×D₁₃	—	4	2	no	—
174	C₂²×D₁₃	—	8	4	no	—
175	C₂×C₄×C₁₃	#102	1	2	yes	—
176	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
177	C₂×C₄×C₁₃	#102	1	2	yes	—
178	C₂×C₄×C₁₃	#102	1	2	yes	—
179	C₂×C₄×C₁₃	#102	1	2	yes	—
180	C₂×C₄×C₁₃	#102	1	2	yes	—
181	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
183	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
186	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
187	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
188	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
189	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
192	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
193	C₂²⋊D₁₃	—	4	4	no	—
194	C₂²⋊D₁₃	—	4	4	no	—
195	C₂²⋊D₁₃	—	4	8	no	—
196	C₂×Dic₁₃	—	4	4	no	—
197	C₂×Dic₁₃	—	4	2	no	—
198	C₂×Dic₁₃	—	4	4	no	—
199	C₂×Dic₁₃	—	8	4	no	—
200	D₅₂	—	2	4	no	—
201	D₅₂	—	4	2	no	—
202	D₅₂	—	4	4	no	—
203	C₄×D₁₃	—	4	4	no	—
204	C₄×D₁₃	—	4	4	no	—
205	C₄×D₁₃	—	4	8	no	—
206	Dic₂₆	—	2	4	no	—
207	Dic₂₆	—	4	2	no	—
208	Dic₂₆	—	4	4	no	—
209	C₈×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
211	C₈×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
212	C₈×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
213	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
214	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
215	C₂²×#41	—	26	1	no	—
216	C₂×#135	—	13	2	no	—
217	C₂×#135	—	13	4	no	—
218	C₂×#135	—	13	2	no	—
219	C₂×#135	—	13	4	no	—
220	C₂×#135	—	26	1	no	—
221	C₂×#135	—	26	2	no	—
222	C₂×#135	—	26	1	no	—
223	C₂×#135	—	26	2	no	—
224	C₂²×Q₁₆	—	13	1	no	—
225	C₂²×SD₁₆	—	26	1	no	—
226	C₂²×D₈	—	13	1	no	—
227	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
228	C₂×#117	—	26	1	no	—
229	C₂×M₃₂	—	2	1	no	—
230	C₂×M₃₂	—	2	2	no	—
231	C₂×M₃₂	C₂×D₁₃	1	2	yes	complemented
232	C₂×M₃₂	C₂×D₁₃	1	4	yes	complemented
233	C₂²×C₁₆	—	2	1	no	—
234	#427	—	13	4	no	—
235	#427	—	26	2	no	—
236	C₂×#107	—	26	1	no	—
237	C₂×#106	—	13	2	no	—
238	#360	—	13	16	no	—
239	C₂²×C₁₃	—	2	2	no	—
240	C₂²×C₁₃	—	2	2	no	—
241	C₂²×C₁₃	—	2	2	no	—
242	C₂²×C₁₃	—	4	2	no	—
243	C₂²×C₁₃	—	4	2	no	—
244	C₂²×C₁₃	C₂×#102	1	2	yes	—
245	C₂²×C₁₃	C₂×#102	1	2	yes	—
246	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
247	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
248	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
249	C₂×D₁₃	—	4	4	no	—
250	C₂×D₁₃	—	8	8	no	—
251	C₂×D₁₃	—	8	4	no	—
252	C₄×C₁₃	C₂×#102	1	2	yes	—
253	C₄×C₁₃	C₂×#102	1	1	yes	characteristic
254	C₄×C₁₃	C₂×#102	1	1	yes	characteristic
255	C₄×C₁₃	C₂×#102	1	2	yes	—
256	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
257	C₄×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
258	Dic₁₃	—	4	4	no	—
259	Dic₁₃	—	8	4	no	—
260	C₂×#41	—	26	4	no	—
261	C₂×#41	—	26	2	no	—
262	C₂×#41	—	26	2	no	—
263	C₂×#41	—	26	4	no	—
264	C₂×#41	—	52	1	no	—
265	C₂×#41	—	52	2	no	—
266	C₂×#41	—	52	2	no	—
267	C₂×#41	—	52	1	no	—
268	C₂²×Q₈	—	26	1	no	—
269	C₂²×D₄	—	26	1	no	—
270	C₂²×D₄	—	52	1	no	—
271	C₂³×C₄	—	52	1	no	—
272	C₂³×C₄	D₅₂	1	1	yes	characteristic
273	#135	—	13	4	no	—
274	#135	—	13	8	no	—
275	#135	—	13	4	no	—
276	#135	—	26	4	no	—
277	#135	—	26	4	no	—
278	#135	—	26	4	no	—
279	#135	—	26	2	no	—
280	#135	—	26	4	no	—
281	#135	—	26	4	no	—
282	#135	—	26	2	no	—
283	C₂×Q₁₆	—	13	2	no	—
284	C₂×Q₁₆	—	13	4	no	—
285	C₂×Q₁₆	—	26	1	no	—
286	C₂×Q₁₆	—	26	2	no	—
287	C₂×SD₁₆	—	26	2	no	—
288	C₂×SD₁₆	—	26	4	no	—
289	C₂×SD₁₆	—	26	2	no	—
290	C₂×SD₁₆	—	26	4	no	—
291	C₂×D₈	—	13	2	no	—
292	C₂×D₈	—	13	4	no	—
293	C₂×D₈	—	26	1	no	—
294	C₂×D₈	—	26	2	no	—
295	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
296	C₂²×C₈	C₄×D₁₃	1	2	yes	—
297	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
298	C₂²×C₈	D₅₂	1	1	yes	characteristic
299	C₂²×C₈	D₅₂	1	2	yes	—
300	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
301	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
302	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
303	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
304	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
305	#117	—	26	4	no	—
306	#117	—	52	2	no	—
307	C₂×C₄⋊C₄	—	26	2	no	—
308	C₂×C₂²⋊C₄	—	52	1	no	—
309	C₂×C₄²	—	52	1	no	—
310	M₃₂	—	2	4	no	—
311	M₃₂	—	2	2	no	—
312	M₃₂	C₂²×D₁₃	1	4	yes	complemented
313	C₂×C₁₆	—	2	2	no	—
314	C₂×C₁₆	—	2	4	no	—
315	#107	—	26	4	no	—
316	#106	—	13	4	no	—
317	#106	—	26	2	no	—
318	C₂×C₁₃	—	2	1	no	—
319	C₂×C₁₃	—	2	2	no	—
320	C₂×C₁₃	—	2	1	no	—
321	C₂×C₁₃	—	2	2	no	—
322	C₂×C₁₃	#2145	1	2	yes	complemented
323	C₂×C₁₃	C₂²×#102	1	1	yes	characteristic
324	D₁₃	—	8	4	no	—
325	C₂⁴	—	52	1	no	—
326	C₂⁴	D₁₀₄	1	1	yes	characteristic
327	#41	—	26	4	no	—
328	#41	—	26	8	no	—
329	#41	—	26	4	no	—
330	#41	—	52	2	no	—
331	#41	—	52	4	no	—
332	#41	—	52	4	no	—
333	#41	—	52	2	no	—
334	#41	—	52	4	no	—
335	#41	—	52	4	no	—
336	#41	—	52	4	no	—
337	C₂×Q₈	—	26	2	no	—
338	C₂×Q₈	—	26	4	no	—
339	C₂×Q₈	—	52	2	no	—
340	C₂×Q₈	—	52	1	no	—
341	C₂×D₄	—	26	2	no	—
342	C₂×D₄	—	26	4	no	—
343	C₂×D₄	—	52	2	no	—
344	C₂×D₄	—	52	4	no	—
345	C₂×D₄	—	52	2	no	—
346	C₂×D₄	—	52	4	no	—
347	C₂×D₄	—	52	2	no	—
348	C₂×D₄	—	52	1	no	—
349	C₂²×C₄	—	52	1	no	—
350	C₂²×C₄	—	52	4	no	—
351	C₂²×C₄	—	52	2	no	—
352	C₂²×C₄	—	52	4	no	—
353	C₂²×C₄	—	52	2	no	—
354	C₂²×C₄	—	52	2	no	—
355	C₂²×C₄	#6095	1	1	yes	characteristic
356	C₂²×C₄	#6095	1	2	yes	—
357	C₂²×C₄	#6095	1	1	yes	characteristic
358	C₂²×C₄	D₁₀₄	1	2	yes	—
359	C₂²×C₄	D₁₀₄	1	1	yes	characteristic
360	C₂²×C₄	#6103	1	1	yes	characteristic
361	C₂²×C₄	#6103	1	2	yes	—
362	C₂²×C₄	#6103	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
364	C₂²×C₄	C₂×D₅₂	1	2	yes	—
365	Q₁₆	—	13	4	no	—
366	Q₁₆	—	26	2	no	—
367	Q₁₆	—	26	4	no	—
368	SD₁₆	—	26	4	no	—
369	SD₁₆	—	26	8	no	—
370	SD₁₆	—	26	4	no	—
371	D₈	—	13	4	no	—
372	D₈	—	26	2	no	—
373	D₈	—	26	4	no	—
374	C₂×C₈	#6103	1	1	yes	characteristic
375	C₂×C₈	#6103	1	2	yes	—
376	C₂×C₈	#6103	1	1	yes	characteristic
377	C₂×C₈	#6103	1	2	yes	—
378	C₂×C₈	#6103	1	2	yes	—
379	C₂×C₈	#6103	1	2	yes	—
380	C₂×C₈	#6103	1	2	yes	—
381	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
382	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
383	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
384	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
385	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
386	C₂×C₈	C₂×D₅₂	1	2	yes	—
387	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
388	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
389	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
390	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
391	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
392	C₄⋊C₄	—	26	4	no	—
393	C₄⋊C₄	—	52	2	no	—
394	C₂²⋊C₄	—	52	4	no	—
395	C₄²	—	52	4	no	—
396	C₁₆	—	2	4	no	—
397	C₁₃	C₂×#2145	1	1	yes	characteristic, complemented, Sylow
398	C₂³	—	4	2	no	—
399	C₂³	—	52	4	no	—
400	C₂³	—	52	2	no	—
401	C₂³	—	104	4	no	—
402	C₂³	#88061	1	1	yes	characteristic
403	C₂³	#88061	1	1	yes	characteristic
404	C₂³	#88061	1	2	yes	—
405	C₂³	C₂×D₁₀₄	1	1	yes	characteristic
406	C₂³	C₂×D₁₀₄	1	2	yes	—
407	Q₈	—	26	4	no	—
408	Q₈	—	52	4	no	—
409	Q₈	—	52	2	no	—
410	D₄	—	26	4	no	—
411	D₄	—	52	4	no	—
412	D₄	—	52	4	no	—
413	D₄	—	52	8	no	—
414	D₄	—	52	4	no	—
415	D₄	—	52	2	no	—
416	C₂×C₄	—	52	4	no	—
417	C₂×C₄	—	52	2	no	—
418	C₂×C₄	—	52	4	no	—
419	C₂×C₄	—	52	4	no	—
420	C₂×C₄	—	52	8	no	—
421	C₂×C₄	—	52	4	no	—
422	C₂×C₄	—	104	4	no	—
423	C₂×C₄	#88061	1	2	yes	—
424	C₂×C₄	#88061	1	2	yes	—
425	C₂×C₄	#88061	1	1	yes	characteristic
426	C₂×C₄	#88061	1	2	yes	—
427	C₂×C₄	#88061	1	2	yes	—
428	C₂×C₄	#88061	1	2	yes	—
429	C₂×C₄	#88061	1	1	yes	characteristic
430	C₂×C₄	C₂×#6095	1	1	yes	characteristic
431	C₂×C₄	C₂×#6095	1	2	yes	—
432	C₂×C₄	C₂×#6095	1	1	yes	characteristic
433	C₂×C₄	C₂×#6095	1	2	yes	—
434	C₂×C₄	C₂×D₁₀₄	1	2	yes	—
435	C₂×C₄	C₂×D₁₀₄	1	1	yes	characteristic
436	C₂×C₄	C₂×#6103	1	2	yes	—
437	C₂×C₄	C₂×#6103	1	1	yes	characteristic
438	C₂×C₄	C₂×#6103	1	1	yes	characteristic
439	C₂×C₄	C₂×#6103	1	2	yes	—
440	C₂×C₄	C₂²×D₅₂	1	1	yes	characteristic
441	C₈	C₂×#6103	1	1	yes	characteristic
442	C₈	C₂×#6103	1	2	yes	—
443	C₈	C₂×#6103	1	1	yes	characteristic
444	C₈	C₂×#6103	1	2	yes	—
445	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
446	C₈	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	2	2	no	—
450	C₂²	—	4	2	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	52	4	no	—
453	C₂²	—	104	8	no	—
454	C₂²	—	104	4	no	—
455	C₂²	C₂×#88061	1	2	yes	—
456	C₂²	C₂×#88061	1	1	yes	characteristic
457	C₂²	C₂×#88061	1	2	yes	—
458	C₂²	C₂×#88061	1	1	yes	characteristic
459	C₂²	C₂²×D₁₀₄	1	1	yes	characteristic
460	C₄	—	52	4	no	—
461	C₄	—	104	4	no	—
462	C₄	C₂×#88061	1	1	yes	characteristic
463	C₄	C₂×#88061	1	2	yes	—
464	C₄	C₂×#88061	1	2	yes	—
465	C₄	C₂×#88061	1	1	yes	characteristic
466	C₄	C₂²×#6095	1	1	yes	characteristic
467	C₄	C₂²×#6103	1	1	yes	characteristic
468	C₂	—	2	1	no	—
469	C₂	—	2	2	no	—
470	C₂	—	2	1	no	—
471	C₂	—	2	2	no	—
472	C₂	—	104	4	no	—
473	C₂	#13116573	1	2	yes	direct product factor
474	C₂	C₂²×#88061	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#88061
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂²×C₁₃×M₃₂	C₂
socle	C₂²×C₁₃	C₂×#102
prime radical	C₂²×#88158	C₂
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂²×M₃₂	D₁₃
hypocenter	C₁₃	C₂×#2145
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂²×M₃₂

Complements

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

N	H ≅ G/N	type
2. C₂×#11718767	C₂	semidirect
3. #13116573	C₂	direct (N × H)
4. C₂×#11718110	C₂	semidirect
5. C₂²×C₁₃×M₃₂	C₂	semidirect
9. C₂²×Dic₅₂	C₄	semidirect
14. C₂×#88158	C₄	semidirect
15. C₂×#88158	C₄	semidirect
18. C₂²×D₁₀₄	C₄	semidirect
22. C₂×C₁₃×M₃₂	C₂²	semidirect
23. C₂×C₁₃×M₃₂	C₂²	semidirect
26. #11718767	C₂²	semidirect
28. C₂×#88057	C₂²	semidirect
29. #11718110	C₂²	semidirect
61. C₂×Dic₅₂	C₂×C₄	semidirect
70. #88158	C₂×C₄	semidirect
75. C₂×D₁₀₄	C₂×C₄	semidirect
82. C₁₃×M₃₂	C₂³	semidirect
87. #88057	C₂³	semidirect
162. C₂²×M₃₂	D₁₃	semidirect
231. C₂×M₃₂	C₂×D₁₃	semidirect
232. C₂×M₃₂	C₂×D₁₃	semidirect
312. M₃₂	C₂²×D₁₃	semidirect
322. C₂×C₁₃	#2145	semidirect
397. C₁₃	C₂×#2145	semidirect
473. C₂	#13116573	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×#88158	2
C₂×#11718767	2
#13116573	2
C₂×#11718110	2
C₂²×C₁₃×M₃₂	2
C₂×#2145	13

Subgroups — C2×#13116573 #16015862

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13116573 #16015862