Subgroups — #34182999

Order 20224.

664 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098850	C₂	1	1	yes	maximal, characteristic
2	#23766300	C₂	1	1	yes	maximal, characteristic
3	#23764349	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19098292	C₂	1	1	yes	maximal, characteristic
5	#23761283	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761240	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1956	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₃₁₆	C₂²	1	1	yes	characteristic
9	C₂×#14579123	—	2	1	no	—
10	C₂×C₄⋊C₄×D₇₉	—	2	1	no	—
11	#19098850	—	2	2	no	—
12	#19098850	C₄	1	4	yes	complemented
13	C₂×#14579092	—	2	1	no	—
14	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×#14579081	—	2	1	no	—
17	#19098459	—	2	1	no	—
18	#19098434	—	2	2	no	—
19	#19098420	—	2	1	no	—
20	C₄×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
21	#19098325	—	2	1	no	—
22	#19098325	—	2	1	no	—
23	#19098292	—	2	2	no	—
24	C₂×C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
25	C₂×#103×C₇₉	—	2	2	no	—
26	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
27	#384×C₇₉	C₂²	1	1	yes	characteristic
28	C₂²×D₃₁₆	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₇₉	—	2	1	no	—
30	C₂²×C₄×D₇₉	—	2	2	no	—
31	C₂²×C₇₉⋊C₈	—	2	1	no	—
32	C₂²×C₇₉⋊C₈	—	2	1	no	—
33	C₄×D₃₁₆	—	2	1	no	—
34	C₄×D₃₁₆	—	2	1	no	—
35	C₄×D₃₁₆	C₂×C₄	1	2	yes	—
36	C₄×D₃₁₆	D₄	1	2	yes	—
37	#14579123	—	4	2	no	—
38	#14579123	—	4	2	no	—
39	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
40	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
41	C₂×C₄⋊Dic₇₉	D₄	1	1	yes	characteristic
42	C₂×Dic₇₉⋊C₄	—	2	2	no	—
43	C₄⋊C₄×D₇₉	—	4	2	no	—
44	C₄⋊C₄×D₇₉	—	4	2	no	—
45	C₂×(C₂×D₇₉)⋊C₄	—	2	1	no	—
46	C₂×(C₂×D₇₉)⋊C₄	—	2	2	no	—
47	C₂×C₄×Dic₇₉	—	2	1	no	—
48	#14579092	—	2	4	no	—
49	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
50	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
51	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
52	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	complemented
53	#14579081	—	2	4	no	—
54	C₇₉⋊#95	—	2	2	no	—
55	C₇₉⋊#95	—	2	1	no	—
56	C₂²×Q₈×C₇₉	—	2	1	no	—
57	C₂²×C₈×C₇₉	—	2	1	no	—
58	C₄⋊Q₈×C₇₉	—	2	1	no	—
59	C₄⋊Q₈×C₇₉	—	2	1	no	—
60	C₄⋊Q₈×C₇₉	—	2	1	no	—
61	C₄⋊Q₈×C₇₉	C₂×C₄	1	2	yes	complemented
62	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
67	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
68	#103×C₇₉	—	4	4	no	—
69	C₄×C₈×C₇₉	—	2	1	no	—
70	C₄×C₈×C₇₉	—	2	1	no	—
71	C₂³×D₇₉	—	2	1	no	—
72	C₂×D₃₁₆	—	2	1	no	—
73	C₂×D₃₁₆	—	2	1	no	—
74	C₂×D₃₁₆	—	2	1	no	—
75	C₂×D₃₁₆	C₂²⋊C₄	1	2	yes	—
76	C₂×D₃₁₆	SD₁₆	1	2	yes	—
77	C₂×D₃₁₆	Q₁₆	1	2	yes	—
78	C₂²×Dic₇₉	—	2	1	no	—
79	C₂²×Dic₇₉	—	2	1	no	—
80	C₂²×Dic₇₉	—	2	1	no	—
81	C₂×C₄×D₇₉	—	2	2	no	—
82	C₂×C₄×D₇₉	—	2	2	no	—
83	C₂×C₄×D₇₉	—	4	4	no	—
84	C₂×C₄×D₇₉	—	4	4	no	—
85	C₂×C₄×D₇₉	—	4	1	no	—
86	C₂×C₄×D₇₉	—	4	1	no	—
87	C₂×C₄×D₇₉	—	4	1	no	—
88	C₂×C₄×D₇₉	—	4	1	no	—
89	C₂×C₄×D₇₉	—	8	2	no	—
90	C₂×C₇₉⋊C₈	—	2	2	no	—
91	C₂×C₇₉⋊C₈	—	4	1	no	—
92	C₂×C₇₉⋊C₈	—	4	1	no	—
93	C₂×C₇₉⋊C₈	—	4	1	no	—
94	C₂×C₇₉⋊C₈	—	4	1	no	—
95	C₂×C₇₉⋊C₈	—	4	1	no	—
96	C₄⋊Dic₇₉	—	2	1	no	—
97	C₄⋊Dic₇₉	—	2	1	no	—
98	C₄⋊Dic₇₉	—	2	1	no	—
99	C₄⋊Dic₇₉	—	2	1	no	—
100	C₄⋊Dic₇₉	C₂²⋊C₄	1	2	yes	—
101	C₄⋊Dic₇₉	SD₁₆	1	2	yes	—
102	Dic₇₉⋊C₄	—	4	4	no	—
103	(C₂×D₇₉)⋊C₄	—	2	2	no	—
104	(C₂×D₇₉)⋊C₄	—	2	2	no	—
105	(C₂×D₇₉)⋊C₄	—	4	4	no	—
106	C₄×Dic₇₉	—	4	1	no	—
107	C₄×Dic₇₉	—	4	1	no	—
108	C₂×Q₈×C₇₉	—	2	2	no	—
109	C₂×Q₈×C₇₉	—	4	2	no	—
110	C₂×Q₈×C₇₉	—	4	2	no	—
111	C₂×Q₈×C₇₉	—	4	1	no	—
112	C₂²×C₄×C₇₉	—	2	2	no	—
113	C₂²×C₄×C₇₉	—	4	1	no	—
114	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₇₉	—	2	2	no	—
118	C₂×C₈×C₇₉	—	4	1	no	—
119	C₂×C₈×C₇₉	—	4	1	no	—
120	C₄⋊C₄×C₇₉	—	2	2	no	—
121	C₄⋊C₄×C₇₉	—	2	2	no	—
122	C₄⋊C₄×C₇₉	—	4	2	no	—
123	C₄⋊C₄×C₇₉	—	4	1	no	—
124	C₄⋊C₄×C₇₉	—	4	1	no	—
125	C₄⋊C₄×C₇₉	—	4	1	no	—
126	C₄⋊C₄×C₇₉	—	4	1	no	—
127	C₄⋊C₄×C₇₉	—	4	1	no	—
128	C₄⋊C₄×C₇₉	—	4	1	no	—
129	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₇₉	#41	1	1	yes	characteristic
132	C₄²×C₇₉	#41	1	1	yes	characteristic
133	C₂³×C₇₉	#120	1	1	yes	characteristic
134	C₂²×D₇₉	—	2	2	no	—
135	C₂²×D₇₉	—	2	2	no	—
136	C₂²×D₇₉	—	2	2	no	—
137	C₂²×D₇₉	—	4	1	no	—
138	C₂²×D₇₉	—	4	1	no	—
139	C₂²×D₇₉	—	4	1	no	—
140	C₂²×D₇₉	—	4	1	no	—
141	Q₈×C₇₉	—	4	4	no	—
142	Q₈×C₇₉	—	8	2	no	—
143	C₂×C₄×C₇₉	—	2	1	no	—
144	C₂×C₄×C₇₉	—	2	1	no	—
145	C₂×C₄×C₇₉	—	4	2	no	—
146	C₂×C₄×C₇₉	—	4	2	no	—
147	C₂×C₄×C₇₉	—	4	2	no	—
148	C₂×C₄×C₇₉	—	4	2	no	—
149	C₂×C₄×C₇₉	—	8	1	no	—
150	C₂×C₄×C₇₉	—	8	1	no	—
151	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
155	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
156	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
157	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
158	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
159	C₂×C₄×C₇₉	C₂×Q₁₆	1	1	yes	characteristic
160	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
161	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
164	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
165	C₂×Dic₇₉	—	2	2	no	—
166	C₂×Dic₇₉	—	2	2	no	—
167	C₂×Dic₇₉	—	4	1	no	—
168	C₂×Dic₇₉	—	4	1	no	—
169	C₂×Dic₇₉	—	4	1	no	—
170	C₂×Dic₇₉	—	4	1	no	—
171	C₂×Dic₇₉	—	4	1	no	—
172	C₂×Dic₇₉	—	4	1	no	—
173	C₂×Dic₇₉	—	4	1	no	—
174	D₃₁₆	—	2	2	no	—
175	D₃₁₆	—	2	2	no	—
176	D₃₁₆	—	2	2	no	—
177	D₃₁₆	#103	1	4	yes	complemented
178	C₄×D₇₉	—	4	2	no	—
179	C₄×D₇₉	—	4	2	no	—
180	C₄×D₇₉	—	4	2	no	—
181	C₄×D₇₉	—	4	2	no	—
182	C₄×D₇₉	—	8	8	no	—
183	C₈×C₇₉	—	4	2	no	—
184	C₇₉⋊C₈	—	4	2	no	—
185	C₇₉⋊C₈	—	8	1	no	—
186	C₂²×C₇₉	#386	1	1	yes	characteristic
187	C₂²×C₇₉	#450	1	1	yes	characteristic
188	C₂²×C₇₉	#450	1	1	yes	characteristic
189	C₂²×C₇₉	#451	1	1	yes	characteristic
190	C₂²×C₇₉	#452	1	1	yes	characteristic
191	C₂²×C₇₉	#453	1	1	yes	characteristic
192	C₂²×C₇₉	#454	1	1	yes	characteristic
193	C₂×D₇₉	—	2	4	no	—
194	C₂×D₇₉	—	4	2	no	—
195	C₂×D₇₉	—	4	2	no	—
196	C₂×D₇₉	—	4	2	no	—
197	C₂×D₇₉	—	4	2	no	—
198	C₂×D₇₉	—	4	2	no	—
199	C₂×D₇₉	—	4	2	no	—
200	C₄×C₇₉	—	2	1	no	—
201	C₄×C₇₉	—	2	1	no	—
202	C₄×C₇₉	—	8	2	no	—
203	C₄×C₇₉	—	8	2	no	—
204	C₄×C₇₉	C₂×#103	1	1	yes	characteristic
205	C₄×C₇₉	#417	1	1	yes	characteristic
206	C₄×C₇₉	C₄×SD₁₆	1	1	yes	characteristic
207	C₄×C₇₉	#440	1	1	yes	characteristic
208	C₄×C₇₉	#461	1	1	yes	characteristic
209	C₄×C₇₉	#463	1	1	yes	characteristic
210	C₄×C₇₉	#483	1	1	yes	characteristic
211	C₄×C₇₉	#484	1	1	yes	characteristic
212	Dic₇₉	—	4	2	no	—
213	Dic₇₉	—	4	2	no	—
214	Dic₇₉	—	8	1	no	—
215	#8973	—	79	1	no	maximal, Sylow
216	C₂×C₇₉	#1629	1	1	yes	characteristic
217	C₂×C₇₉	#1632	1	1	yes	characteristic
218	C₂×C₇₉	#1635	1	1	yes	characteristic
219	C₂×C₇₉	#1637	1	1	yes	characteristic
220	C₂×C₇₉	#1872	1	1	yes	characteristic
221	C₂×C₇₉	#1877	1	1	yes	characteristic
222	C₂×C₇₉	#1883	1	1	yes	characteristic
223	D₇₉	—	4	4	no	—
224	C₂×#476	—	79	1	no	—
225	D₄×C₄⋊C₄	—	79	1	no	—
226	#1987	—	79	1	no	—
227	#1956	D₇₉	1	1	yes	characteristic, complemented
228	C₂×D₄⋊C₈	—	79	1	no	—
229	#1296	—	79	1	no	—
230	#1279	—	79	1	no	—
231	C₇₉	#8973	1	1	yes	characteristic, complemented, Sylow
232	C₂×C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
233	C₂×C₄×D₄	—	79	1	no	—
234	C₂×C₄×D₄	—	158	1	no	—
235	C₂²×C₄⋊C₄	—	158	1	no	—
236	#476	—	79	4	no	—
237	#476	—	158	2	no	—
238	C₂×#106	—	158	1	no	—
239	C₂×C₄⋊C₈	—	79	1	no	—
240	C₂×C₄⋊C₈	—	79	1	no	—
241	C₂×#103	—	2	2	no	—
242	C₂×#102	—	158	1	no	—
243	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
244	#389	—	158	1	no	—
245	#385	—	158	2	no	—
246	#384	C₂×D₇₉	1	1	yes	characteristic
247	#380	—	158	1	no	—
248	C₄×C₄⋊C₄	—	79	1	no	—
249	#340	—	158	1	no	—
250	#340	—	158	1	no	—
251	D₄⋊C₈	—	158	2	no	—
252	C₂²×Q₈	—	2	1	no	—
253	C₂²×D₄	—	79	1	no	—
254	C₂³×C₄	—	158	2	no	—
255	C₂³×C₄	—	158	1	no	—
256	C₂²×C₈	—	2	1	no	—
257	C₂²×C₈	—	158	1	no	—
258	C₂²×C₈	—	158	1	no	—
259	C₄⋊Q₈	—	2	1	no	—
260	C₄⋊Q₈	—	2	1	no	—
261	C₄⋊Q₈	—	2	1	no	—
262	C₄⋊Q₈	C₄×D₇₉	1	2	yes	complemented
263	C₄×D₄	—	316	2	no	—
264	C₄×D₄	—	316	2	no	—
265	C₄×D₄	—	79	2	no	—
266	C₄×D₄	—	79	2	no	—
267	C₄×D₄	—	158	1	no	—
268	C₄×D₄	—	158	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	316	2	no	—
274	C₂×C₄⋊C₄	—	316	2	no	—
275	C₂×C₄⋊C₄	—	79	1	no	—
276	C₂×C₄⋊C₄	—	79	1	no	—
277	C₂×C₄⋊C₄	—	79	1	no	—
278	C₂×C₄⋊C₄	—	158	2	no	—
279	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	2	yes	—
280	C₂×C₂²⋊C₄	—	158	2	no	—
281	C₂×C₂²⋊C₄	—	158	1	no	—
282	C₂×C₄²	—	158	1	no	—
283	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
284	#106	—	158	4	no	—
285	C₄⋊C₈	—	79	2	no	—
286	C₄⋊C₈	—	158	1	no	—
287	C₄⋊C₈	—	158	1	no	—
288	C₄⋊C₈	—	158	1	no	—
289	#103	—	4	4	no	—
290	#102	—	158	4	no	—
291	C₄×C₈	—	2	1	no	—
292	C₄×C₈	—	2	1	no	—
293	#95	—	158	2	no	—
294	#95	—	158	1	no	—
295	C₂⁴	—	158	1	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	4	2	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂×Q₈	—	4	1	no	—
300	C₂×D₄	—	79	2	no	—
301	C₂×D₄	—	79	2	no	—
302	C₂×D₄	—	79	2	no	—
303	C₂×D₄	—	158	1	no	—
304	C₂×D₄	—	158	1	no	—
305	C₂×D₄	—	158	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	316	4	no	—
309	C₂²×C₄	—	316	4	no	—
310	C₂²×C₄	—	316	1	no	—
311	C₂²×C₄	—	316	1	no	—
312	C₂²×C₄	—	316	1	no	—
313	C₂²×C₄	—	316	1	no	—
314	C₂²×C₄	—	632	2	no	—
315	C₂²×C₄	—	158	1	no	—
316	C₂²×C₄	—	158	1	no	—
317	C₂²×C₄	—	158	1	no	—
318	C₂²×C₄	—	158	2	no	—
319	C₂²×C₄	—	158	2	no	—
320	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
321	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	316	1	no	—
327	C₂×C₈	—	316	1	no	—
328	C₂×C₈	—	316	1	no	—
329	C₂×C₈	—	316	1	no	—
330	C₂×C₈	—	316	1	no	—
331	C₂×C₈	—	158	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	4	2	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₄⋊C₄	—	316	4	no	—
342	C₄⋊C₄	—	79	2	no	—
343	C₄⋊C₄	—	79	2	no	—
344	C₄⋊C₄	—	158	1	no	—
345	C₄⋊C₄	—	158	1	no	—
346	C₄⋊C₄	—	158	1	no	—
347	C₄⋊C₄	—	158	1	no	—
348	C₂²⋊C₄	—	316	4	no	—
349	C₂²⋊C₄	—	158	2	no	—
350	C₂²⋊C₄	—	158	2	no	—
351	C₄²	—	316	1	no	—
352	C₄²	—	316	1	no	—
353	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
354	C₄²	D₄×D₇₉	1	1	yes	characteristic
355	C₄²	#11929623	1	1	yes	characteristic
356	C₄²	#11929624	1	1	yes	characteristic
357	C₂³	—	316	1	no	—
358	C₂³	—	316	1	no	—
359	C₂³	—	316	1	no	—
360	C₂³	—	316	1	no	—
361	C₂³	—	158	2	no	—
362	C₂³	—	158	2	no	—
363	C₂³	—	158	2	no	—
364	C₂³	#14579129	1	1	yes	characteristic
365	Q₈	—	4	4	no	—
366	Q₈	—	8	2	no	—
367	D₄	—	79	4	no	—
368	D₄	—	158	2	no	—
369	D₄	—	158	2	no	—
370	D₄	—	158	2	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	8	1	no	—
378	C₂×C₄	—	8	1	no	—
379	C₂×C₄	—	316	1	no	—
380	C₂×C₄	—	316	1	no	—
381	C₂×C₄	—	316	1	no	—
382	C₂×C₄	—	316	1	no	—
383	C₂×C₄	—	316	2	no	—
384	C₂×C₄	—	316	2	no	—
385	C₂×C₄	—	316	2	no	—
386	C₂×C₄	—	316	2	no	—
387	C₂×C₄	—	316	1	no	—
388	C₂×C₄	—	316	1	no	—
389	C₂×C₄	—	316	1	no	—
390	C₂×C₄	—	632	8	no	—
391	C₂×C₄	—	158	2	no	—
392	C₂×C₄	—	158	2	no	—
393	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
394	C₂×C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
395	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
396	C₂×C₄	#14579132	1	1	yes	characteristic
397	C₂×C₄	#14579134	1	1	yes	characteristic
398	C₂×C₄	#14579143	1	1	yes	characteristic
399	C₂×C₄	SD₁₆×D₇₉	1	1	yes	characteristic
400	C₂×C₄	SD₁₆×D₇₉	1	1	yes	characteristic
401	C₂×C₄	Q₁₆×D₇₉	1	1	yes	characteristic
402	C₂×C₄	#14579184	1	1	yes	characteristic
403	C₂×C₄	#14579188	1	1	yes	characteristic
404	C₂×C₄	#14579188	1	1	yes	characteristic
405	C₂×C₄	#14579193	1	1	yes	characteristic
406	C₂×C₄	#14579193	1	1	yes	characteristic
407	C₈	—	4	2	no	—
408	C₈	—	316	2	no	—
409	C₈	—	632	1	no	—
410	C₂²	—	316	2	no	—
411	C₂²	—	316	2	no	—
412	C₂²	—	316	2	no	—
413	C₂²	—	316	2	no	—
414	C₂²	—	316	2	no	—
415	C₂²	—	316	2	no	—
416	C₂²	—	158	4	no	—
417	C₂²	#19098439	1	1	yes	characteristic
418	C₂²	#19098712	1	1	yes	characteristic
419	C₂²	#19098712	1	1	yes	characteristic
420	C₂²	#19098717	1	1	yes	characteristic
421	C₂²	#19098724	1	1	yes	characteristic
422	C₂²	#19098730	1	1	yes	characteristic
423	C₂²	#19098735	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	8	2	no	—
427	C₄	—	8	2	no	—
428	C₄	—	316	2	no	—
429	C₄	—	316	2	no	—
430	C₄	—	632	1	no	—
431	C₄	#103×D₇₉	1	1	yes	characteristic
432	C₄	#19098563	1	1	yes	characteristic
433	C₄	#19098648	1	1	yes	characteristic
434	C₄	#19098666	1	1	yes	characteristic
435	C₄	#19098767	1	1	yes	characteristic
436	C₄	#19098781	1	1	yes	characteristic
437	C₄	#19098892	1	1	yes	characteristic
438	C₄	#19098897	1	1	yes	characteristic
439	C₂	—	316	4	no	—
440	C₂	#23762514	1	1	yes	characteristic
441	C₂	#23762531	1	1	yes	characteristic
442	C₂	#23762548	1	1	yes	characteristic
443	C₂	#23762562	1	1	yes	characteristic
444	C₂	#23763704	1	1	yes	characteristic
445	C₂	#23763731	1	1	yes	characteristic
446	C₂	#23763779	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14579129
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1956	C₂
socle	C₂³×C₇₉	#120
prime radical	C₂²×D₃₁₆	D₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1956	D₇₉
hypocenter	C₇₉	#8973
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1956

Complements

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

N	H ≅ G/N	type
3. #23764349	C₂	semidirect
5. #23761283	C₂	semidirect
6. #23761240	C₂	semidirect
7. C₇₉×#1956	C₂	semidirect
12. #19098850	C₄	semidirect
52. C₄⋊(C₇₉⋊C₈)	C₂×C₄	semidirect
61. C₄⋊Q₈×C₇₉	C₂×C₄	semidirect
177. D₃₁₆	#103	semidirect
227. #1956	D₇₉	semidirect
231. C₇₉	#8973	semidirect
262. C₄⋊Q₈	C₄×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098850	2
#23766300	2
#23764349	2
C₂×#19098292	2
#23761283	2
#23761240	2
C₇₉×#1956	2
#8973	79