Subgroups — #34258254

Order 20224.

632 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773482	C₂	1	1	yes	maximal, characteristic
2	#23772375	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×Dic₁₅₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#23762280	C₂	1	2	yes	maximal, complemented
5	#23762273	C₂	1	2	yes	maximal, complemented
6	C₈×Dic₃₁₆	C₂	1	2	yes	maximal, complemented
7	C₈×#11929613	C₂	1	2	yes	maximal, complemented
8	#23762185	C₂	1	1	yes	maximal, characteristic, complemented
9	#23761848	C₂	1	1	yes	maximal, characteristic, complemented
10	#23761814	C₂	1	1	yes	maximal, characteristic
11	C₈×M₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#19099097	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₁₅₈	C₂²	1	1	yes	characteristic
14	#19098894	C₄	1	1	yes	characteristic
15	#19098877	C₄	1	1	yes	characteristic
16	#19098871	C₄	1	2	yes	—
17	#19098786	C₄	1	2	yes	—
18	#19098721	C₄	1	1	yes	characteristic
19	#19098704	C₄	1	1	yes	characteristic
20	#19098693	C₂²	1	1	yes	characteristic
21	C₈×Dic₁₅₈	—	2	1	no	—
22	C₈×Dic₁₅₈	—	2	1	no	—
23	C₈×Dic₁₅₈	C₂²	1	2	yes	—
24	C₈×Dic₁₅₈	C₂²	1	1	yes	characteristic
25	C₈×Dic₁₅₈	C₂²	1	2	yes	—
26	C₄×Dic₃₁₆	C₂²	1	2	yes	—
27	C₄×#11929613	C₂²	1	2	yes	—
28	#19098642	C₂²	1	1	yes	characteristic
29	#19098634	—	2	1	no	—
30	C₈×D₃₁₆	C₂²	1	1	yes	characteristic
31	C₈×C₂²⋊D₇₉	—	2	1	no	—
32	#19098622	—	2	1	no	—
33	#19098620	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
35	C₂×Dic₇₉⋊C₈	—	2	1	no	—
36	#19098517	—	2	1	no	—
37	C₂×C₈×Dic₇₉	—	2	1	no	—
38	#19098316	C₂²	1	2	yes	—
39	#19098314	C₂²	1	2	yes	—
40	#19098295	C₂²	1	2	yes	—
41	#19098295	C₂²	1	2	yes	—
42	#19098295	C₂²	1	2	yes	—
43	#19098292	C₂²	1	2	yes	—
44	#431×C₇₉	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₇₉	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
47	#322×C₇₉	C₂²	1	2	yes	—
48	C₈²×C₇₉	C₂²	1	2	yes	—
49	C₂²×Dic₁₅₈	C₂×C₄	1	1	yes	characteristic
50	C₂×Dic₃₁₆	C₂×C₄	1	2	yes	—
51	C₂×#11929613	C₂×C₄	1	2	yes	—
52	C₂×#11929607	—	2	1	no	—
53	C₂²×C₇₉⋊C₈	—	2	1	no	—
54	C₂×C₈×D₇₉	—	2	1	no	—
55	#14579155	—	2	1	no	—
56	#14579153	C₂×C₄	1	1	yes	characteristic
57	#14579149	C₂×C₄	1	1	yes	characteristic
58	#14579144	—	2	1	no	—
59	#14579140	C₂×C₄	1	1	yes	characteristic
60	#14579135	C₂×C₄	1	1	yes	characteristic
61	C₄×Dic₁₅₈	—	2	1	no	—
62	C₄×Dic₁₅₈	—	2	1	no	—
63	C₄×Dic₁₅₈	C₂×C₄	1	2	yes	—
64	C₄×Dic₁₅₈	C₂³	1	2	yes	—
65	C₄×Dic₁₅₈	C₂³	1	1	yes	characteristic
66	C₄×D₃₁₆	C₂³	1	1	yes	characteristic
67	C₄×C₂²⋊D₇₉	—	2	1	no	—
68	#14579118	—	2	1	no	—
69	C₂×C₄⋊Dic₇₉	C₂×C₄	1	1	yes	characteristic
70	C₂×Dic₇₉⋊C₄	—	2	1	no	—
71	C₂×C₄×Dic₇₉	—	2	1	no	—
72	#14579095	C₂×C₄	1	2	yes	—
73	#14579093	C₂×C₄	1	2	yes	—
74	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
75	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
76	C₄⋊(C₇₉⋊C₈)	C₂³	1	1	yes	characteristic
77	C₄⋊(C₇₉⋊C₈)	C₂³	1	2	yes	—
78	Dic₇₉⋊C₈	—	2	1	no	—
79	Dic₇₉⋊C₈	—	2	1	no	—
80	Dic₇₉⋊C₈	—	2	2	no	—
81	Dic₇₉⋊C₈	—	2	2	no	—
82	#14579086	C₂×C₄	1	2	yes	—
83	#14579086	C₂×C₄	1	2	yes	—
84	#14579086	C₂×C₄	1	2	yes	—
85	#14579083	C₂×C₄	1	2	yes	—
86	C₂²⋊(C₇₉⋊C₈)	—	2	1	no	—
87	(C₂×D₇₉)⋊C₈	—	2	1	no	—
88	(C₂×D₇₉)⋊C₈	—	2	1	no	—
89	#14579072	—	2	1	no	—
90	#14579071	—	2	1	no	—
91	C₈×Dic₇₉	—	2	1	no	—
92	C₈×Dic₇₉	—	2	2	no	—
93	C₈×Dic₇₉	—	2	2	no	—
94	C₂×M₁₆×C₇₉	—	2	1	no	—
95	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
96	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
99	C₂²⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
100	C₂²⋊C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
101	#97×C₇₉	—	2	1	no	—
102	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
103	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
104	C₄×C₈×C₇₉	C₂³	1	2	yes	—
105	C₄×C₈×C₇₉	C₂³	1	2	yes	—
106	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
108	C₂×Dic₁₅₈	—	2	4	no	—
109	C₂×Dic₁₅₈	—	2	1	no	—
110	C₂×Dic₁₅₈	C₂²×C₄	1	1	yes	characteristic
111	C₂×Dic₁₅₈	C₂²×C₄	1	2	yes	—
112	C₂×D₃₁₆	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₂²⋊D₇₉	—	2	1	no	—
114	C₂²×Dic₇₉	—	2	1	no	—
115	C₂²×Dic₇₉	—	2	1	no	—
116	C₂×C₄×D₇₉	—	2	1	no	—
117	Dic₃₁₆	—	2	4	no	—
118	#11929613	—	2	4	no	—
119	#11929607	—	4	2	no	—
120	C₂×C₇₉⋊C₈	—	2	2	no	—
121	C₂×C₇₉⋊C₈	—	2	1	no	—
122	C₂×C₇₉⋊C₈	—	2	1	no	—
123	C₂×C₇₉⋊C₈	—	4	2	no	—
124	C₈×D₇₉	—	4	2	no	—
125	C₄⋊Dic₇₉	—	2	1	no	—
126	C₄⋊Dic₇₉	C₂²×C₄	1	2	yes	—
127	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
128	C₄⋊Dic₇₉	C₂²×C₄	1	1	yes	characteristic
129	Dic₇₉⋊C₄	—	2	2	no	—
130	Dic₇₉⋊C₄	—	2	1	no	—
131	Dic₇₉⋊C₄	—	2	1	no	—
132	Dic₇₉⋊C₄	—	2	1	no	—
133	Dic₇₉⋊C₄	—	2	2	no	—
134	Dic₇₉⋊C₄	—	2	1	no	—
135	C₂²⋊Dic₇₉	—	2	1	no	—
136	(C₂×D₇₉)⋊C₄	—	2	1	no	—
137	(C₂×D₇₉)⋊C₄	—	2	1	no	—
138	(C₂×D₇₉)⋊C₄	—	2	1	no	—
139	(C₂×D₇₉)⋊C₄	—	2	1	no	—
140	C₄×Dic₇₉	—	2	2	no	—
141	C₄×Dic₇₉	—	2	2	no	—
142	C₄×Dic₇₉	—	2	1	no	—
143	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₉	#41	1	1	yes	characteristic
146	M₁₆×C₇₉	—	2	4	no	—
147	C₂×C₈×C₇₉	—	2	2	no	—
148	C₂×C₈×C₇₉	—	2	2	no	—
149	C₂×C₈×C₇₉	—	4	1	no	—
150	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₇₉	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₇₉	#41	1	1	yes	characteristic
159	C₄²×C₇₉	C₂⁴	1	1	yes	characteristic
160	C₂³×C₇₉	C₄×D₄	1	1	yes	characteristic
161	C₂²×D₇₉	—	2	1	no	—
162	C₂×C₄×C₇₉	—	2	2	no	—
163	C₂×C₄×C₇₉	—	2	2	no	—
164	C₂×C₄×C₇₉	—	2	1	no	—
165	C₂×C₄×C₇₉	—	2	1	no	—
166	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₇₉	C₂×#41	1	1	yes	characteristic
172	C₂²⋊D₇₉	—	4	2	no	—
173	C₂×Dic₇₉	—	2	4	no	—
174	C₂×Dic₇₉	—	2	2	no	—
175	C₂×Dic₇₉	—	2	2	no	—
176	C₂×Dic₇₉	—	2	1	no	—
177	C₂×Dic₇₉	—	2	1	no	—
178	C₂×Dic₇₉	—	2	1	no	—
179	C₂×Dic₇₉	—	4	2	no	—
180	D₃₁₆	—	2	2	no	—
181	C₄×D₇₉	—	4	1	no	—
182	C₄×D₇₉	—	4	1	no	—
183	Dic₁₅₈	—	2	4	no	—
184	Dic₁₅₈	—	2	2	no	—
185	Dic₁₅₈	—	2	2	no	—
186	Dic₁₅₈	#131	1	4	yes	—
187	C₈×C₇₉	—	2	4	no	—
188	C₈×C₇₉	—	2	2	no	—
189	C₈×C₇₉	—	2	2	no	—
190	C₈×C₇₉	—	2	1	no	—
191	C₈×C₇₉	—	2	1	no	—
192	C₈×C₇₉	—	2	1	no	—
193	C₈×C₇₉	#137	1	2	yes	—
194	C₇₉⋊C₈	—	4	1	no	—
195	C₇₉⋊C₈	—	4	2	no	—
196	C₇₉⋊C₈	—	4	1	no	—
197	C₂²×C₇₉	—	2	1	no	—
198	C₂²×C₇₉	—	2	1	no	—
199	C₂²×C₇₉	#443	1	2	yes	—
200	C₂²×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
201	C₂×D₇₉	—	4	1	no	—
202	C₂×D₇₉	—	4	1	no	—
203	C₂×D₇₉	—	4	1	no	—
204	C₄×C₇₉	—	2	1	no	—
205	C₄×C₇₉	—	2	1	no	—
206	C₄×C₇₉	—	2	1	no	—
207	C₄×C₇₉	—	2	1	no	—
208	C₄×C₇₉	C₂×#131	1	2	yes	—
209	C₄×C₇₉	C₂×#137	1	1	yes	characteristic
210	C₄×C₇₉	#575	1	1	yes	characteristic
211	Dic₇₉	—	2	4	no	—
212	Dic₇₉	—	4	1	no	—
213	Dic₇₉	—	4	1	no	—
214	Dic₇₉	—	4	1	no	—
215	Dic₇₉	—	4	2	no	—
216	#17911	—	79	1	no	maximal, Sylow
217	C₂×C₇₉	—	2	2	no	—
218	C₂×C₇₉	#2929	1	1	yes	characteristic
219	C₂×C₇₉	C₄×#137	1	1	yes	characteristic
220	C₂×C₇₉	C₂×#443	1	1	yes	characteristic
221	D₇₉	—	8	1	no	—
222	#3108	—	79	1	no	—
223	#2966	—	79	1	no	—
224	C₂×C₈×Q₈	—	79	1	no	—
225	#1588	—	79	2	no	—
226	#1587	—	79	2	no	—
227	C₈×Q₁₆	—	79	2	no	—
228	C₈×SD₁₆	—	79	2	no	—
229	#1573	—	79	1	no	—
230	#1491	—	79	1	no	—
231	#1483	—	79	1	no	—
232	C₈×M₁₆	D₇₉	1	1	yes	characteristic, complemented
233	C₇₉	#17911	1	1	yes	characteristic, complemented, Sylow
234	#529	—	79	1	no	—
235	C₂×C₄×Q₈	—	79	1	no	—
236	#483	—	79	1	no	—
237	#480	—	79	1	no	—
238	#479	—	79	2	no	—
239	#464	—	79	2	no	—
240	#451	—	79	1	no	—
241	#448	—	79	1	no	—
242	#446	—	79	1	no	—
243	C₈×Q₈	—	79	2	no	—
244	C₈×Q₈	—	79	1	no	—
245	C₈×Q₈	—	79	2	no	—
246	C₈×Q₈	—	158	1	no	—
247	C₈×Q₈	—	158	1	no	—
248	C₄×Q₁₆	—	79	2	no	—
249	C₄×SD₁₆	—	79	2	no	—
250	#436	—	79	1	no	—
251	#435	—	158	1	no	—
252	C₈×D₄	—	79	1	no	—
253	C₈×D₄	—	158	1	no	—
254	#433	—	158	1	no	—
255	#432	—	79	1	no	—
256	#431	C₂×D₇₉	1	1	yes	characteristic
257	C₂×C₄⋊C₈	—	79	1	no	—
258	C₂×C₄⋊C₈	—	158	1	no	—
259	#405	—	158	1	no	—
260	C₄×M₁₆	C₂×D₇₉	1	1	yes	characteristic
261	C₂×C₄×C₈	—	158	1	no	—
262	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
263	#335	—	79	2	no	—
264	#334	—	79	2	no	—
265	Q₈⋊C₈	—	79	2	no	—
266	Q₈⋊C₈	—	79	2	no	—
267	Q₈⋊C₈	—	79	2	no	—
268	D₄⋊C₈	—	79	2	no	—
269	#322	C₂×D₇₉	1	2	yes	—
270	C₈²	C₂×D₇₉	1	2	yes	—
271	C₂²×Q₈	—	79	1	no	—
272	C₂×Q₁₆	—	79	2	no	—
273	C₂×SD₁₆	—	79	2	no	—
274	C₂×M₁₆	—	2	1	no	—
275	C₂×M₁₆	—	158	1	no	—
276	C₂²×C₈	—	158	1	no	—
277	C₂²×C₈	—	158	1	no	—
278	C₂²×C₈	D₃₁₆	1	1	yes	characteristic
279	C₂²×C₈	D₃₁₆	1	1	yes	characteristic
280	#126	—	158	1	no	—
281	#125	—	79	1	no	—
282	#124	—	79	1	no	—
283	#123	—	158	1	no	—
284	C₂²⋊Q₈	—	79	1	no	—
285	#121	—	79	1	no	—
286	C₄×Q₈	—	79	2	no	—
287	C₄×Q₈	—	79	2	no	—
288	C₄×Q₈	—	79	1	no	—
289	C₄×Q₈	—	158	1	no	—
290	C₄×Q₈	—	158	1	no	—
291	C₄×D₄	—	79	1	no	—
292	C₄×D₄	—	158	1	no	—
293	#117	—	158	1	no	—
294	C₂×C₄⋊C₄	—	79	1	no	—
295	C₂×C₄⋊C₄	—	158	1	no	—
296	C₂×C₄²	—	158	1	no	—
297	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
298	#107	—	79	2	no	—
299	#106	—	79	2	no	—
300	C₄⋊C₈	—	79	2	no	—
301	C₄⋊C₈	—	79	1	no	—
302	C₄⋊C₈	—	79	1	no	—
303	C₄⋊C₈	—	158	2	no	—
304	C₄⋊C₈	—	158	2	no	—
305	C₄⋊C₈	—	158	1	no	—
306	C₄⋊C₈	—	158	1	no	—
307	C₄⋊C₈	—	158	1	no	—
308	C₄⋊C₈	C₄×D₇₉	1	2	yes	—
309	#103	—	79	2	no	—
310	#103	—	79	2	no	—
311	#103	—	79	2	no	—
312	#102	—	79	2	no	—
313	C₂²⋊C₈	—	158	1	no	—
314	C₂²⋊C₈	—	158	1	no	—
315	C₂²⋊C₈	—	158	1	no	—
316	C₂²⋊C₈	C₄×D₇₉	1	1	yes	characteristic
317	C₂²⋊C₈	C₄×D₇₉	1	1	yes	characteristic
318	#97	—	2	1	no	—
319	#97	—	158	1	no	—
320	#97	—	158	1	no	—
321	C₄×C₈	—	158	2	no	—
322	C₄×C₈	—	158	2	no	—
323	C₄×C₈	—	158	1	no	—
324	C₄×C₈	D₃₁₆	1	1	yes	characteristic
325	C₄×C₈	D₃₁₆	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₇₉	1	2	yes	—
327	C₄×C₈	C₂²×D₇₉	1	2	yes	—
328	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
329	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
330	C₂×Q₈	—	79	2	no	—
331	C₂×Q₈	—	79	1	no	—
332	C₂×Q₈	—	158	4	no	—
333	C₂×Q₈	—	158	1	no	—
334	C₂×D₄	—	79	1	no	—
335	C₂×D₄	—	158	1	no	—
336	C₂²×C₄	—	158	1	no	—
337	C₂²×C₄	—	158	1	no	—
338	C₂²×C₄	—	158	1	no	—
339	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₃₁₆	1	1	yes	characteristic
341	C₂²×C₄	#11929624	1	1	yes	characteristic
342	Q₁₆	—	158	4	no	—
343	SD₁₆	—	158	4	no	—
344	M₁₆	—	2	4	no	—
345	M₁₆	—	316	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	316	2	no	—
350	C₂×C₈	—	316	2	no	—
351	C₂×C₈	—	158	2	no	—
352	C₂×C₈	—	158	1	no	—
353	C₂×C₈	—	158	1	no	—
354	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
355	C₂×C₈	C₂×C₄×D₇₉	1	2	yes	—
356	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
357	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
358	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
359	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
360	C₄⋊C₄	—	79	2	no	—
361	C₄⋊C₄	—	79	1	no	—
362	C₄⋊C₄	—	79	1	no	—
363	C₄⋊C₄	—	158	2	no	—
364	C₄⋊C₄	—	158	1	no	—
365	C₄⋊C₄	—	158	2	no	—
366	C₄⋊C₄	—	158	1	no	—
367	C₄⋊C₄	—	158	1	no	—
368	C₄⋊C₄	—	158	1	no	—
369	C₄⋊C₄	—	158	1	no	—
370	C₂²⋊C₄	—	158	1	no	—
371	C₂²⋊C₄	—	158	1	no	—
372	C₂²⋊C₄	—	158	1	no	—
373	C₂²⋊C₄	—	158	1	no	—
374	C₂²⋊C₄	—	158	1	no	—
375	C₄²	—	158	2	no	—
376	C₄²	—	158	2	no	—
377	C₄²	—	158	1	no	—
378	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
379	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
380	C₄²	#11929624	1	1	yes	characteristic
381	C₄²	C₂³×D₇₉	1	1	yes	characteristic
382	C₂³	—	158	1	no	—
383	C₂³	C₄×D₃₁₆	1	1	yes	characteristic
384	Q₈	—	79	4	no	—
385	Q₈	—	158	4	no	—
386	Q₈	—	158	2	no	—
387	Q₈	—	158	2	no	—
388	D₄	—	316	2	no	—
389	D₄	—	158	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	316	2	no	—
395	C₂×C₄	—	316	1	no	—
396	C₂×C₄	—	316	1	no	—
397	C₂×C₄	—	158	2	no	—
398	C₂×C₄	—	158	1	no	—
399	C₂×C₄	—	158	1	no	—
400	C₂×C₄	—	158	1	no	—
401	C₂×C₄	—	158	4	no	—
402	C₂×C₄	—	158	2	no	—
403	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
404	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
405	C₂×C₄	C₄×D₃₁₆	1	1	yes	characteristic
406	C₂×C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₃₁₆	1	1	yes	characteristic
408	C₂×C₄	C₂×#11929624	1	1	yes	characteristic
409	C₈	—	2	4	no	—
410	C₈	—	2	2	no	—
411	C₈	—	2	2	no	—
412	C₈	—	2	1	no	—
413	C₈	—	2	1	no	—
414	C₈	—	2	1	no	—
415	C₈	—	316	1	no	—
416	C₈	—	316	2	no	—
417	C₈	—	316	1	no	—
418	C₈	#14579194	1	2	yes	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	316	1	no	—
422	C₂²	—	316	1	no	—
423	C₂²	—	316	1	no	—
424	C₂²	#19098681	1	2	yes	—
425	C₂²	C₂×C₄×D₃₁₆	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	316	1	no	—
431	C₄	—	316	2	no	—
432	C₄	—	316	1	no	—
433	C₄	—	316	1	no	—
434	C₄	—	158	4	no	—
435	C₄	#131×D₇₉	1	2	yes	—
436	C₄	C₂×#14579194	1	1	yes	characteristic
437	C₄	#19099363	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	632	1	no	—
440	C₂	#23772096	1	1	yes	characteristic
441	C₂	C₄×#14579194	1	1	yes	characteristic
442	C₂	C₂×#19098681	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₃₁₆
commutator	C₂×C₄×C₇₉	C₂³×C₄
Frattini	C₄²	C₂³×D₇₉
Fitting	C₈×M₁₆×C₇₉	C₂
socle	C₂²×C₇₉	C₂×C₄×D₄
prime radical	#14579135	C₂×C₄
cosocle	C₄²×C₇₉	C₂⁴
hypercenter	C₈×M₁₆	D₇₉
hypocenter	C₇₉	#17911
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
3. C₂×C₈×Dic₁₅₈	C₂	semidirect
4. #23762280	C₂	semidirect
5. #23762273	C₂	semidirect
6. C₈×Dic₃₁₆	C₂	semidirect
7. C₈×#11929613	C₂	semidirect
8. #23762185	C₂	semidirect
9. #23761848	C₂	semidirect
11. C₈×M₁₆×C₇₉	C₂	semidirect
232. C₈×M₁₆	D₇₉	semidirect
233. C₇₉	#17911	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#23773482	2
#23772375	2
C₂×C₈×Dic₁₅₈	2
#23762280	2
#23762273	2
C₈×Dic₃₁₆	2
C₈×#11929613	2
#23762185	2
#23761848	2
#23761814	2
C₈×M₁₆×C₇₉	2
#17911	79