Subgroups — C₄×#11718854 #16016235

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718854	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₁₀₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#13116710	C₂	1	2	yes	maximal, complemented
4	#13116698	C₂	1	2	yes	maximal, complemented
5	C₄×#88068	C₂	1	2	yes	maximal, complemented
6	C₄×#88066	C₂	1	2	yes	maximal, complemented
7	#13116625	C₂	1	1	yes	maximal, characteristic, complemented
8	#13116551	C₂	1	1	yes	maximal, characteristic, complemented
9	#13116548	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#88052	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₁₃×#135	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#135	C₂²	1	1	yes	characteristic
13	C₄×C₁₃×#41	—	2	1	no	—
14	C₂²×D₁₀₄	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₅₂	—	2	1	no	—
16	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
17	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic, complemented
18	C₄×C₁₃×SD₁₆	—	2	1	no	—
19	C₄×C₁₃×SD₁₆	—	2	1	no	—
20	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
21	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic, complemented
22	C₁₃×#427	C₂²	1	1	yes	characteristic
23	C₁₃×#416	—	2	1	no	—
24	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
25	#11718854	C₄	1	8	yes	direct product factor
26	C₂×#88068	C₂²	1	2	yes	—
27	C₂×#88066	C₂²	1	2	yes	—
28	C₂×#88061	—	2	1	no	—
29	C₂×#88058	C₂²	1	1	yes	characteristic
30	C₂×#88052	C₂²	1	1	yes	characteristic
31	C₂×#88052	C₂²	1	1	yes	characteristic
32	C₄×D₁₀₄	—	2	1	no	—
33	C₄×D₁₀₄	—	2	1	no	—
34	C₄×D₁₀₄	C₂²	1	2	yes	—
35	C₄×D₁₀₄	C₂²	1	2	yes	—
36	#11718156	C₂²	1	2	yes	complemented
37	#11718154	C₂²	1	2	yes	complemented
38	#11718083	C₂²	1	2	yes	—
39	#11718083	C₂²	1	2	yes	—
40	#11718082	C₂²	1	2	yes	complemented
41	#11718081	C₂²	1	2	yes	complemented
42	#11718053	C₂²	1	2	yes	complemented
43	C₄×#6090	C₂²	1	2	yes	complemented
44	C₂×C₁₃×#41	—	2	1	no	—
45	C₂²×D₅₂	—	2	1	no	—
46	C₂²×C₄×D₁₃	—	4	1	no	—
47	C₁₃×#135	—	2	2	no	—
48	C₁₃×#135	C₂×C₄	1	4	yes	complemented
49	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
50	C₂×C₁₃×SD₁₆	—	2	1	no	—
51	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₄×Q₈×C₁₃	—	2	1	no	—
55	C₄×Q₈×C₁₃	—	2	1	no	—
56	C₄×D₄×C₁₃	—	2	1	no	—
57	C₄×D₄×C₁₃	—	2	1	no	—
58	C₄×D₄×C₁₃	—	4	1	no	—
59	C₄×D₄×C₁₃	—	4	1	no	—
60	C₁₃×#117	—	2	1	no	—
61	C₁₃×#117	—	4	1	no	—
62	C₂×C₄²×C₁₃	—	4	1	no	—
63	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
64	C₂×#6103	—	4	1	no	—
65	C₂×C₄⋊Dic₁₃	—	2	1	no	—
66	C₂×D₁₀₄	—	2	1	no	—
67	C₂×D₁₀₄	—	2	2	no	—
68	C₂×D₁₀₄	C₂×C₄	1	4	yes	complemented
69	C₂×D₁₀₄	C₂³	1	2	yes	—
70	C₄×D₅₂	—	2	2	no	—
71	C₄×D₅₂	—	2	2	no	—
72	C₄×D₅₂	—	4	1	no	—
73	C₄×D₅₂	—	4	1	no	—
74	C₁₃×#107	C₂³	1	1	yes	characteristic
75	C₁₃×#107	C₂³	1	1	yes	characteristic
76	C₁₃×#106	—	2	1	no	—
77	C₁₃×#103	—	2	1	no	—
78	C₁₃×#103	—	2	1	no	—
79	C₁₃×#102	—	2	1	no	—
80	C₁₃×#102	—	2	1	no	—
81	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
82	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
83	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	#88068	C₂×C₄	1	8	yes	complemented
86	#88066	C₂×C₄	1	8	yes	complemented
87	#88061	—	2	2	no	—
88	#88061	—	2	2	no	—
89	#88058	—	2	1	no	—
90	#88058	C₂³	1	2	yes	—
91	#88052	—	2	2	no	—
92	#88052	C₂×C₄	1	4	yes	complemented
93	C₂×#6090	C₂³	1	2	yes	—
94	C₂×#6090	C₂³	1	2	yes	—
95	C₄×#509	—	13	1	no	maximal, Sylow
96	C₂³×D₁₃	—	4	1	no	—
97	C₁₃×#41	—	2	4	no	—
98	C₁₃×#41	—	4	2	no	—
99	C₂×Q₈×C₁₃	—	2	1	no	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	4	1	no	—
102	C₂²×C₄×C₁₃	—	4	1	no	—
103	C₂²×C₄×C₁₃	—	4	1	no	—
104	C₂²×C₄×C₁₃	—	4	1	no	—
105	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×Dic₁₃	—	4	1	no	—
109	C₂×D₅₂	—	2	4	no	—
110	C₂×D₅₂	—	2	2	no	—
111	C₂×D₅₂	—	4	1	no	—
112	C₂×D₅₂	—	4	2	no	—
113	C₂×C₄×D₁₃	—	4	2	no	—
114	C₂×C₄×D₁₃	—	4	2	no	—
115	C₂×C₄×D₁₃	—	8	4	no	—
116	C₁₃×Q₁₆	—	2	1	no	—
117	C₁₃×Q₁₆	C₂²×C₄	1	2	yes	complemented
118	C₁₃×SD₁₆	—	2	4	no	—
119	C₁₃×D₈	—	2	1	no	—
120	C₁₃×D₈	C₂²×C₄	1	2	yes	complemented
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₁₃	#41	1	2	yes	—
127	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	4	1	no	—
131	C₁₃×C₄⋊C₄	—	4	1	no	—
132	C₁₃×C₂²⋊C₄	—	4	1	no	—
133	C₁₃×C₂²⋊C₄	—	4	1	no	—
134	C₁₃×C₂²⋊C₄	—	4	1	no	—
135	C₄²×C₁₃	—	4	1	no	—
136	C₄²×C₁₃	—	4	1	no	—
137	C₄²×C₁₃	—	4	1	no	—
138	C₄²×C₁₃	D₈	1	1	yes	characteristic
139	C₄²×C₁₃	D₈	1	1	yes	characteristic
140	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
142	#6103	—	4	2	no	—
143	#6103	—	4	2	no	—
144	C₄⋊Dic₁₃	—	2	2	no	—
145	C₄⋊Dic₁₃	—	4	1	no	—
146	D₁₀₄	—	2	4	no	—
147	D₁₀₄	—	2	2	no	—
148	D₁₀₄	C₂²×C₄	1	4	yes	—
149	#6090	—	2	2	no	—
150	#6090	C₂²×C₄	1	4	yes	complemented
151	C₂×#509	—	13	1	no	—
152	C₄×#135	D₁₃	1	1	yes	characteristic, complemented
153	C₂×C₄×D₈	—	13	1	no	—
154	#2177	—	13	2	no	—
155	#2175	—	13	2	no	—
156	C₄×SD₃₂	—	13	2	no	—
157	C₄×D₁₆	—	13	2	no	—
158	#2159	—	13	1	no	—
159	#2140	—	13	1	no	—
160	#2139	—	13	1	no	—
161	C₄×M₃₂	—	13	1	no	—
162	C₂³×C₁₃	—	4	1	no	—
163	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
164	C₂²×D₁₃	—	4	2	no	—
165	C₂²×D₁₃	—	4	4	no	—
166	C₂²×D₁₃	—	8	2	no	—
167	C₂²×D₁₃	—	8	2	no	—
168	Q₈×C₁₃	—	2	2	no	—
169	Q₈×C₁₃	—	4	1	no	—
170	D₄×C₁₃	—	2	2	no	—
171	D₄×C₁₃	—	4	4	no	—
172	D₄×C₁₃	—	4	1	no	—
173	C₂×C₄×C₁₃	—	2	2	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	4	4	no	—
177	C₂×C₄×C₁₃	—	4	1	no	—
178	C₂×C₄×C₁₃	—	4	1	no	—
179	C₂×C₄×C₁₃	—	8	2	no	—
180	C₂×C₄×C₁₃	—	8	2	no	—
181	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
187	C₂×C₄×C₁₃	#135	1	2	yes	—
188	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×Dic₁₃	—	4	2	no	—
190	C₂×Dic₁₃	—	8	2	no	—
191	D₅₂	—	2	4	no	—
192	D₅₂	—	4	2	no	—
193	D₅₂	—	4	4	no	—
194	C₄×D₁₃	—	8	4	no	—
195	C₄×D₁₃	—	8	4	no	—
196	C₈×C₁₃	—	2	1	no	—
197	C₈×C₁₃	—	2	1	no	—
198	C₈×C₁₃	C₄×D₄	1	2	yes	—
199	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
200	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
201	C₂×#135	C₂×D₁₃	1	1	yes	characteristic
202	C₂²×D₈	—	13	1	no	—
203	C₄×#41	—	2	1	no	—
204	C₂×C₄×D₄	—	26	1	no	—
205	#509	—	13	8	no	—
206	C₂×SD₃₂	—	13	2	no	—
207	C₂×D₁₆	—	13	2	no	—
208	C₂×M₃₂	—	13	1	no	—
209	C₂×M₃₂	—	13	1	no	—
210	C₄×Q₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
211	C₄×Q₁₆	C₂×D₁₃	1	1	yes	characteristic, complemented
212	C₄×SD₁₆	—	2	1	no	—
213	C₄×SD₁₆	—	2	1	no	—
214	C₄×D₈	—	13	2	no	—
215	C₄×D₈	—	13	2	no	—
216	C₄×D₈	—	26	1	no	—
217	C₄×D₈	—	26	1	no	—
218	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic, complemented
219	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic, complemented
220	#427	C₂×D₁₃	1	1	yes	characteristic
221	C₂×#107	—	13	1	no	—
222	#416	—	2	1	no	—
223	C₂×#102	—	26	1	no	—
224	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
225	#367	—	13	2	no	—
226	#366	—	13	2	no	—
227	#358	—	13	2	no	—
228	#357	—	13	2	no	—
229	#357	—	13	2	no	—
230	#357	—	13	2	no	—
231	#346	—	13	2	no	—
232	C₄×C₁₆	—	13	2	no	—
233	C₂²×C₁₃	—	2	1	no	—
234	C₂²×C₁₃	—	2	1	no	—
235	C₂²×C₁₃	—	4	2	no	—
236	C₂²×C₁₃	—	8	1	no	—
237	C₂²×C₁₃	—	8	1	no	—
238	C₂²×C₁₃	C₄×D₈	1	2	yes	—
239	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
240	C₂×D₁₃	—	4	4	no	—
241	C₂×D₁₃	—	8	8	no	—
242	C₂×D₁₃	—	8	2	no	—
243	C₂×D₁₃	—	8	2	no	—
244	C₄×C₁₃	—	2	1	no	—
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	—	4	2	no	—
248	C₄×C₁₃	—	8	1	no	—
249	C₄×C₁₃	—	8	1	no	—
250	C₄×C₁₃	C₄×D₈	1	2	yes	—
251	C₄×C₁₃	#509	1	2	yes	complemented
252	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
253	C₄×C₁₃	C₂×#135	1	1	yes	characteristic
254	Dic₁₃	—	8	2	no	—
255	C₂×#41	—	2	1	no	—
256	C₂²×D₄	—	26	1	no	—
257	C₂³×C₄	—	52	1	no	—
258	#135	—	2	2	no	—
259	#135	C₄×D₁₃	1	4	yes	complemented
260	C₂×Q₁₆	C₂²×D₁₃	1	1	yes	characteristic
261	C₂×SD₁₆	—	2	1	no	—
262	C₂×D₈	—	13	4	no	—
263	C₂×D₈	—	13	2	no	—
264	C₂×D₈	—	26	2	no	—
265	C₂×D₈	—	26	1	no	—
266	C₂×D₈	C₂²×D₁₃	1	1	yes	characteristic
267	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
268	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
269	C₄×Q₈	—	2	1	no	—
270	C₄×Q₈	—	2	1	no	—
271	C₄×D₄	—	2	1	no	—
272	C₄×D₄	—	2	1	no	—
273	C₄×D₄	—	4	1	no	—
274	C₄×D₄	—	4	1	no	—
275	C₄×D₄	—	26	2	no	—
276	C₄×D₄	—	26	2	no	—
277	C₄×D₄	—	52	1	no	—
278	C₄×D₄	—	52	1	no	—
279	#117	—	2	1	no	—
280	#117	—	4	1	no	—
281	C₂×C₄⋊C₄	—	26	1	no	—
282	C₂×C₂²⋊C₄	—	52	1	no	—
283	C₂×C₄²	—	4	1	no	—
284	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
285	SD₃₂	—	13	8	no	—
286	D₁₆	—	13	8	no	—
287	M₃₂	—	13	4	no	—
288	M₃₂	—	26	2	no	—
289	C₂×C₁₆	—	13	2	no	—
290	C₂×C₁₆	—	13	2	no	—
291	#107	—	13	2	no	—
292	#107	—	26	1	no	—
293	#107	C₂²×D₁₃	1	1	yes	characteristic
294	#107	C₂²×D₁₃	1	1	yes	characteristic
295	#106	—	2	1	no	—
296	#103	—	2	1	no	—
297	#103	—	2	1	no	—
298	#102	—	2	1	no	—
299	#102	—	2	1	no	—
300	#102	—	26	2	no	—
301	#102	—	26	2	no	—
302	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
303	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
304	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
305	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
306	C₂×C₁₃	—	2	2	no	—
307	C₂×C₁₃	—	8	2	no	—
308	C₂×C₁₃	C₂×C₄×D₈	1	1	yes	characteristic
309	C₂×C₁₃	C₂×#509	1	1	yes	characteristic
310	C₂×C₁₃	#3414	1	1	yes	characteristic
311	D₁₃	—	8	4	no	—
312	C₂⁴	—	52	1	no	—
313	#41	—	2	4	no	—
314	#41	—	4	2	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	4	1	no	—
318	C₂×D₄	—	26	4	no	—
319	C₂×D₄	—	26	2	no	—
320	C₂×D₄	—	52	1	no	—
321	C₂×D₄	—	52	2	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	52	1	no	—
326	C₂²×C₄	—	52	2	no	—
327	C₂²×C₄	—	52	2	no	—
328	C₂²×C₄	—	104	4	no	—
329	C₂²×C₄	#6104	1	1	yes	characteristic
330	C₂²×C₄	#6104	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
332	Q₁₆	—	2	1	no	—
333	Q₁₆	C₂×C₄×D₁₃	1	2	yes	complemented
334	SD₁₆	—	2	4	no	—
335	D₈	—	2	1	no	—
336	D₈	—	13	4	no	—
337	D₈	—	26	4	no	—
338	D₈	—	26	2	no	—
339	D₈	C₂×C₄×D₁₃	1	2	yes	complemented
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
342	C₂×C₈	#6127	1	2	yes	—
343	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
344	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
345	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
346	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₄⋊C₄	—	26	2	no	—
352	C₄⋊C₄	—	52	1	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₂²⋊C₄	—	4	1	no	—
355	C₂²⋊C₄	—	4	1	no	—
356	C₂²⋊C₄	—	52	2	no	—
357	C₂²⋊C₄	—	52	2	no	—
358	C₄²	—	4	1	no	—
359	C₄²	—	4	1	no	—
360	C₄²	—	4	1	no	—
361	C₄²	#6104	1	1	yes	characteristic
362	C₄²	#6104	1	1	yes	characteristic
363	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
364	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
365	C₁₆	—	13	4	no	—
366	C₁₆	—	26	2	no	—
367	C₁₃	C₄×#509	1	1	yes	characteristic, complemented, Sylow
368	C₂³	—	4	1	no	—
369	C₂³	—	52	4	no	—
370	C₂³	—	52	2	no	—
371	C₂³	—	104	2	no	—
372	C₂³	—	104	2	no	—
373	C₂³	C₂×#6104	1	1	yes	characteristic
374	Q₈	—	2	2	no	—
375	Q₈	—	4	1	no	—
376	D₄	—	2	2	no	—
377	D₄	—	4	4	no	—
378	D₄	—	4	1	no	—
379	D₄	—	26	4	no	—
380	D₄	—	52	4	no	—
381	D₄	—	52	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	8	2	no	—
389	C₂×C₄	—	8	2	no	—
390	C₂×C₄	—	52	2	no	—
391	C₂×C₄	—	104	4	no	—
392	C₂×C₄	—	104	2	no	—
393	C₂×C₄	—	104	4	no	—
394	C₂×C₄	C₄×C₂²⋊D₁₃	1	2	yes	—
395	C₂×C₄	C₂×#6104	1	1	yes	characteristic
396	C₂×C₄	C₂×#6104	1	1	yes	characteristic
397	C₂×C₄	C₂×#6104	1	1	yes	characteristic
398	C₂×C₄	C₂×#6104	1	1	yes	characteristic
399	C₂×C₄	C₂×#6104	1	1	yes	characteristic
400	C₂×C₄	#88204	1	2	yes	—
401	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	C₄×C₂²⋊D₁₃	1	2	yes	—
405	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
406	C₈	C₂×#6127	1	1	yes	characteristic
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	8	1	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	52	4	no	—
413	C₂²	—	104	8	no	—
414	C₂²	—	104	2	no	—
415	C₂²	—	104	2	no	—
416	C₂²	C₄×#6104	1	2	yes	—
417	C₂²	C₂²×#6104	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	4	2	no	—
422	C₄	—	8	1	no	—
423	C₄	—	8	1	no	—
424	C₄	—	104	2	no	—
425	C₄	C₄×#6104	1	2	yes	—
426	C₄	#11718854	1	2	yes	direct product factor
427	C₄	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
428	C₄	C₂×#88204	1	1	yes	characteristic
429	C₂	—	2	2	no	—
430	C₂	—	8	2	no	—
431	C₂	—	104	4	no	—
432	C₂	C₂×C₄×#6104	1	1	yes	characteristic
433	C₂	C₂×#11718854	1	1	yes	characteristic
434	C₂	#13127970	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#6104
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₄×C₁₃×#135	C₂
socle	C₂²×C₁₃	C₂²×D₈
prime radical	C₂×#11718854	C₂
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₄×#135	D₁₃
hypocenter	C₁₃	C₄×#509
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₁₀₄	C₂	semidirect
3. #13116710	C₂	semidirect
4. #13116698	C₂	semidirect
5. C₄×#88068	C₂	semidirect
6. C₄×#88066	C₂	semidirect
7. #13116625	C₂	semidirect
8. #13116551	C₂	semidirect
9. #13116548	C₂	semidirect
10. C₄×#88052	C₂	semidirect
11. C₄×C₁₃×#135	C₂	semidirect
16. C₄×C₁₃×Q₁₆	C₂²	semidirect
17. C₄×C₁₃×Q₁₆	C₂²	semidirect
20. C₄×C₁₃×D₈	C₂²	semidirect
21. C₄×C₁₃×D₈	C₂²	semidirect
25. #11718854	C₄	direct (N × H)
36. #11718156	C₂²	semidirect
37. #11718154	C₂²	semidirect
40. #11718082	C₂²	semidirect
41. #11718081	C₂²	semidirect
42. #11718053	C₂²	semidirect
43. C₄×#6090	C₂²	semidirect
48. C₁₃×#135	C₂×C₄	semidirect
68. C₂×D₁₀₄	C₂×C₄	semidirect
85. #88068	C₂×C₄	semidirect
86. #88066	C₂×C₄	semidirect
92. #88052	C₂×C₄	semidirect
117. C₁₃×Q₁₆	C₂²×C₄	semidirect
120. C₁₃×D₈	C₂²×C₄	semidirect
150. #6090	C₂²×C₄	semidirect
152. C₄×#135	D₁₃	semidirect
210. C₄×Q₁₆	C₂×D₁₃	semidirect
211. C₄×Q₁₆	C₂×D₁₃	semidirect
218. C₄×D₈	C₂×D₁₃	semidirect
219. C₄×D₈	C₂×D₁₃	semidirect
251. C₄×C₁₃	#509	semidirect
259. #135	C₄×D₁₃	semidirect
333. Q₁₆	C₂×C₄×D₁₃	semidirect
339. D₈	C₂×C₄×D₁₃	semidirect
367. C₁₃	C₄×#509	semidirect
426. C₄	#11718854	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×#11718854	2
C₂×C₄×D₁₀₄	2
#13116710	2
#13116698	2
C₄×#88068	2
C₄×#88066	2
#13116625	2
#13116551	2
#13116548	2
C₄×#88052	2
C₄×C₁₃×#135	2
C₄×#509	13

Subgroups — C4×#11718854 #16016235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718854 #16016235