Subgroups — #34183044

Order 20224.

660 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098763	C₂	1	1	yes	maximal, characteristic
2	#23764327	C₂	1	1	yes	maximal, characteristic
3	#23764205	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈⋊(C₇₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	#23761283	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761241	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₈×C₄⋊C₄×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#11929611	—	2	1	no	—
9	C₂×#14579158	C₂²	1	1	yes	characteristic
10	#19098763	—	2	2	no	—
11	#19098763	C₄	1	4	yes	complemented
12	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#14579081	—	2	1	no	—
15	C₂×#14579081	—	2	1	no	—
16	C₂×#14579081	—	2	1	no	—
17	C₂×#14579081	—	2	2	no	—
18	C₂×C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
19	Q₈⋊(C₇₉⋊C₈)	—	2	2	no	—
20	C₂×C₄×Q₈×C₇₉	—	2	1	no	—
21	C₂×C₄×Q₈×C₇₉	C₂²	1	1	yes	characteristic
22	#389×C₇₉	—	2	1	no	—
23	#389×C₇₉	—	2	2	no	—
24	#384×C₇₉	—	2	1	no	—
25	#384×C₇₉	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₇₉	—	2	1	no	—
27	C₄×C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
28	C₂²×D₃₁₆	—	2	1	no	—
29	C₂²×D₃₁₆	—	2	1	no	—
30	C₂²×D₃₁₆	—	2	1	no	—
31	C₂×#11929611	—	2	4	no	—
32	C₂×#11929611	—	4	2	no	—
33	C₂×#11929611	—	4	2	no	—
34	C₂²×C₇₉⋊C₈	—	2	1	no	—
35	C₂²×C₇₉⋊C₈	—	2	1	no	—
36	C₂²×C₇₉⋊C₈	—	2	1	no	—
37	#14579158	—	2	1	no	—
38	#14579158	—	2	1	no	—
39	#14579158	—	2	1	no	—
40	#14579158	C₂×C₄	1	2	yes	—
41	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
42	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
43	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
44	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
45	#14579081	—	2	4	no	—
46	#14579081	—	4	4	no	—
47	#14579081	—	4	2	no	—
48	#14579081	—	4	2	no	—
49	C₄×C₇₉⋊C₈	—	2	1	no	—
50	C₄×C₇₉⋊C₈	—	2	1	no	—
51	C₂²×Q₈×C₇₉	D₄	1	1	yes	characteristic
52	C₄×Q₈×C₇₉	—	2	1	no	—
53	C₄×Q₈×C₇₉	—	2	1	no	—
54	C₄×Q₈×C₇₉	—	4	2	no	—
55	C₄×Q₈×C₇₉	—	4	2	no	—
56	C₄×Q₈×C₇₉	C₂×C₄	1	2	yes	—
57	C₄×Q₈×C₇₉	D₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
61	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
62	C₂×C₄⋊C₄×C₇₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₇₉	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₇₉	D₄	1	2	yes	—
67	C₂×C₄²×C₇₉	—	2	1	no	—
68	C₂×C₄²×C₇₉	—	2	2	no	—
69	C₂×C₄²×C₇₉	—	2	1	no	—
70	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
71	#95×C₇₉	—	2	2	no	—
72	#95×C₇₉	—	2	1	no	—
73	C₂³×D₇₉	—	4	1	no	—
74	C₂×D₃₁₆	—	2	2	no	—
75	C₂×D₃₁₆	—	2	2	no	—
76	C₂×D₃₁₆	—	2	2	no	—
77	C₂×D₃₁₆	—	4	2	no	—
78	C₂×D₃₁₆	—	4	2	no	—
79	C₂×D₃₁₆	—	4	1	no	—
80	C₂×D₃₁₆	—	4	1	no	—
81	C₂×D₃₁₆	—	4	1	no	—
82	C₂×D₃₁₆	—	4	1	no	—
83	C₂×D₃₁₆	—	4	1	no	—
84	C₂×D₃₁₆	—	4	1	no	—
85	C₂×D₃₁₆	—	4	1	no	—
86	C₂×D₃₁₆	—	4	1	no	—
87	C₂×D₃₁₆	—	4	1	no	—
88	C₂×D₃₁₆	—	4	1	no	—
89	C₂×D₃₁₆	—	4	1	no	—
90	#11929611	—	4	8	no	—
91	C₂×C₇₉⋊C₈	—	2	2	no	—
92	C₂×C₇₉⋊C₈	—	2	2	no	—
93	C₂×C₇₉⋊C₈	—	4	1	no	—
94	C₂×C₇₉⋊C₈	—	4	1	no	—
95	C₂×C₇₉⋊C₈	—	4	1	no	—
96	C₂×C₇₉⋊C₈	—	4	1	no	—
97	C₂×C₇₉⋊C₈	—	4	1	no	—
98	C₂×C₇₉⋊C₈	—	4	1	no	—
99	C₂×C₇₉⋊C₈	—	4	1	no	—
100	C₂×Q₈×C₇₉	—	2	1	no	—
101	C₂×Q₈×C₇₉	—	2	1	no	—
102	C₂×Q₈×C₇₉	—	2	1	no	—
103	C₂×Q₈×C₇₉	C₂²⋊C₄	1	2	yes	—
104	C₂×Q₈×C₇₉	D₈	1	2	yes	—
105	C₂×Q₈×C₇₉	SD₁₆	1	2	yes	—
106	C₂²×C₄×C₇₉	—	2	1	no	—
107	C₂²×C₄×C₇₉	—	2	1	no	—
108	C₂²×C₄×C₇₉	—	2	1	no	—
109	C₂²×C₄×C₇₉	—	2	1	no	—
110	C₂²×C₄×C₇₉	—	2	2	no	—
111	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
114	C₄⋊C₄×C₇₉	—	2	2	no	—
115	C₄⋊C₄×C₇₉	—	2	2	no	—
116	C₄⋊C₄×C₇₉	—	2	1	no	—
117	C₄⋊C₄×C₇₉	—	2	1	no	—
118	C₄⋊C₄×C₇₉	—	2	1	no	—
119	C₄⋊C₄×C₇₉	—	2	1	no	—
120	C₄⋊C₄×C₇₉	—	4	4	no	—
121	C₄⋊C₄×C₇₉	—	4	2	no	—
122	C₄⋊C₄×C₇₉	—	4	1	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	—	8	2	no	—
127	C₄⋊C₄×C₇₉	C₂²⋊C₄	1	2	yes	—
128	C₄⋊C₄×C₇₉	SD₁₆	1	2	yes	complemented
129	C₄²×C₇₉	—	2	2	no	—
130	C₄²×C₇₉	—	2	2	no	—
131	C₄²×C₇₉	—	4	4	no	—
132	C₄²×C₇₉	—	4	1	no	—
133	C₄²×C₇₉	—	4	1	no	—
134	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₇₉	#41	1	1	yes	characteristic
137	C₄²×C₇₉	#41	1	1	yes	characteristic
138	C₂³×C₇₉	#120	1	1	yes	characteristic
139	C₂²×D₇₉	—	4	2	no	—
140	C₂²×D₇₉	—	8	1	no	—
141	C₂²×D₇₉	—	8	1	no	—
142	C₂²×D₇₉	—	8	1	no	—
143	C₂²×D₇₉	—	8	1	no	—
144	C₂²×D₇₉	—	8	1	no	—
145	C₂²×D₇₉	—	8	1	no	—
146	Q₈×C₇₉	—	2	2	no	—
147	Q₈×C₇₉	—	2	2	no	—
148	Q₈×C₇₉	—	2	2	no	—
149	Q₈×C₇₉	#102	1	4	yes	complemented
150	C₂×C₄×C₇₉	—	2	2	no	—
151	C₂×C₄×C₇₉	—	2	2	no	—
152	C₂×C₄×C₇₉	—	2	2	no	—
153	C₂×C₄×C₇₉	—	2	1	no	—
154	C₂×C₄×C₇₉	—	2	1	no	—
155	C₂×C₄×C₇₉	—	2	2	no	—
156	C₂×C₄×C₇₉	—	2	2	no	—
157	C₂×C₄×C₇₉	—	4	1	no	—
158	C₂×C₄×C₇₉	—	4	1	no	—
159	C₂×C₄×C₇₉	—	4	1	no	—
160	C₂×C₄×C₇₉	—	4	1	no	—
161	C₂×C₄×C₇₉	—	4	2	no	—
162	C₂×C₄×C₇₉	—	4	1	no	—
163	C₂×C₄×C₇₉	—	4	1	no	—
164	C₂×C₄×C₇₉	—	4	2	no	—
165	C₂×C₄×C₇₉	—	4	2	no	—
166	C₂×C₄×C₇₉	—	4	1	no	—
167	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₇₉	#123	1	1	yes	characteristic
173	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
175	C₂×C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
176	C₂×C₄×C₇₉	#135	1	1	yes	characteristic
177	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
178	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
179	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
180	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
181	D₃₁₆	—	4	4	no	—
182	D₃₁₆	—	4	2	no	—
183	D₃₁₆	—	4	2	no	—
184	D₃₁₆	—	4	2	no	—
185	D₃₁₆	—	4	2	no	—
186	D₃₁₆	—	8	2	no	—
187	D₃₁₆	—	8	1	no	—
188	D₃₁₆	—	8	1	no	—
189	D₃₁₆	—	8	1	no	—
190	D₃₁₆	—	8	1	no	—
191	C₇₉⋊C₈	—	4	2	no	—
192	C₇₉⋊C₈	—	4	2	no	—
193	C₇₉⋊C₈	—	8	1	no	—
194	C₂²×C₇₉	#386	1	1	yes	characteristic
195	C₂²×C₇₉	#447	1	1	yes	characteristic
196	C₂²×C₇₉	#448	1	1	yes	characteristic
197	C₂²×C₇₉	#448	1	1	yes	characteristic
198	C₂²×C₇₉	#449	1	1	yes	characteristic
199	C₂²×C₇₉	#453	1	1	yes	characteristic
200	C₂²×C₇₉	#454	1	1	yes	characteristic
201	C₂×D₇₉	—	8	2	no	—
202	C₂×D₇₉	—	8	2	no	—
203	C₂×D₇₉	—	8	2	no	—
204	C₂×D₇₉	—	16	1	no	—
205	C₂×D₇₉	—	16	1	no	—
206	C₂×D₇₉	—	16	1	no	—
207	C₂×D₇₉	—	16	1	no	—
208	C₄×C₇₉	—	2	4	no	—
209	C₄×C₇₉	—	2	1	no	—
210	C₄×C₇₉	—	2	1	no	—
211	C₄×C₇₉	—	4	2	no	—
212	C₄×C₇₉	—	4	2	no	—
213	C₄×C₇₉	—	8	1	no	—
214	C₄×C₇₉	—	8	2	no	—
215	C₄×C₇₉	C₂×#102	1	1	yes	characteristic
216	C₄×C₇₉	#417	1	1	yes	characteristic
217	C₄×C₇₉	C₄×SD₁₆	1	1	yes	characteristic
218	C₄×C₇₉	#440	1	1	yes	characteristic
219	C₄×C₇₉	#460	1	1	yes	characteristic
220	C₄×C₇₉	#464	1	1	yes	characteristic
221	C₄×C₇₉	#480	1	1	yes	characteristic
222	C₄×C₇₉	#481	1	1	yes	characteristic
223	#8979	—	79	1	no	maximal, Sylow
224	C₂×C₇₉	#1621	1	1	yes	characteristic
225	C₂×C₇₉	#1623	1	1	yes	characteristic
226	C₂×C₇₉	#1626	1	1	yes	characteristic
227	C₂×C₇₉	#1627	1	1	yes	characteristic
228	C₂×C₇₉	#1874	1	1	yes	characteristic
229	C₂×C₇₉	#1880	1	1	yes	characteristic
230	C₂×C₇₉	#1883	1	1	yes	characteristic
231	D₇₉	—	16	2	no	—
232	C₂×#460	—	79	1	no	—
233	Q₈×C₄⋊C₄	D₇₉	1	1	yes	characteristic, complemented
234	#1982	—	79	1	no	—
235	#1957	—	79	1	no	—
236	C₂×Q₈⋊C₈	—	79	1	no	—
237	#1296	—	79	1	no	—
238	#1279	—	79	1	no	—
239	C₇₉	#8979	1	1	yes	characteristic, complemented, Sylow
240	C₂²×SD₁₆	—	158	1	no	—
241	C₂×#127	—	79	1	no	—
242	C₂×C₄×Q₈	—	2	1	no	—
243	C₂×C₄×Q₈	C₂×D₇₉	1	1	yes	characteristic
244	#460	—	79	4	no	—
245	#460	—	158	2	no	—
246	C₂×C₄⋊C₈	—	79	1	no	—
247	C₂×C₄⋊C₈	—	79	1	no	—
248	C₂×#102	—	158	2	no	—
249	C₂×#102	—	158	1	no	—
250	C₂×#102	—	158	1	no	—
251	C₂×#102	—	158	1	no	—
252	C₂×C₄×C₈	—	79	1	no	—
253	#389	—	2	1	no	—
254	#389	—	2	2	no	—
255	#384	—	2	1	no	—
256	#384	C₂×D₇₉	1	1	yes	characteristic
257	C₄×C₄⋊C₄	—	2	1	no	—
258	C₄×C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
259	Q₈⋊C₈	—	158	2	no	—
260	C₂²×Q₈	C₂²⋊D₇₉	1	1	yes	characteristic
261	C₂²×D₄	—	158	1	no	—
262	C₂²×D₄	—	158	1	no	—
263	C₂²×D₄	—	158	1	no	—
264	C₂×SD₁₆	—	316	2	no	—
265	C₂×SD₁₆	—	316	2	no	—
266	C₂×SD₁₆	—	158	4	no	—
267	C₂²×C₈	—	158	1	no	—
268	C₂²×C₈	—	158	1	no	—
269	C₂²×C₈	—	158	1	no	—
270	#127	—	79	2	no	—
271	#127	—	158	1	no	—
272	#127	—	158	1	no	—
273	#127	—	158	1	no	—
274	C₄×Q₈	—	2	1	no	—
275	C₄×Q₈	—	2	1	no	—
276	C₄×Q₈	—	4	2	no	—
277	C₄×Q₈	—	4	2	no	—
278	C₄×Q₈	C₄×D₇₉	1	2	yes	—
279	C₄×Q₈	D₃₁₆	1	2	yes	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂²⋊D₇₉	1	2	yes	—
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	—	2	2	no	—
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
293	C₄⋊C₈	—	79	2	no	—
294	C₄⋊C₈	—	158	1	no	—
295	C₄⋊C₈	—	158	1	no	—
296	C₄⋊C₈	—	158	1	no	—
297	#102	—	316	2	no	—
298	#102	—	316	4	no	—
299	#102	—	316	2	no	—
300	#102	—	158	4	no	—
301	C₄×C₈	—	158	1	no	—
302	C₄×C₈	—	158	1	no	—
303	#95	—	2	2	no	—
304	#95	—	2	1	no	—
305	C₂⁴	—	316	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	(C₂×D₇₉)⋊C₄	1	2	yes	—
310	C₂×Q₈	#11929609	1	2	yes	—
311	C₂×Q₈	#11929611	1	2	yes	—
312	C₂×D₄	—	316	2	no	—
313	C₂×D₄	—	316	2	no	—
314	C₂×D₄	—	316	1	no	—
315	C₂×D₄	—	316	1	no	—
316	C₂×D₄	—	316	1	no	—
317	C₂×D₄	—	316	1	no	—
318	C₂×D₄	—	316	1	no	—
319	C₂×D₄	—	316	1	no	—
320	C₂×D₄	—	316	1	no	—
321	C₂×D₄	—	316	1	no	—
322	C₂×D₄	—	316	1	no	—
323	C₂×D₄	—	316	1	no	—
324	C₂×D₄	—	316	1	no	—
325	C₂×D₄	—	158	2	no	—
326	C₂×D₄	—	158	2	no	—
327	C₂×D₄	—	158	2	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
336	SD₁₆	—	316	8	no	—
337	C₂×C₈	—	316	1	no	—
338	C₂×C₈	—	316	1	no	—
339	C₂×C₈	—	316	1	no	—
340	C₂×C₈	—	316	1	no	—
341	C₂×C₈	—	316	1	no	—
342	C₂×C₈	—	316	1	no	—
343	C₂×C₈	—	316	1	no	—
344	C₂×C₈	—	158	2	no	—
345	C₂×C₈	—	158	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	4	2	no	—
353	C₄⋊C₄	—	4	4	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₄⋊C₄	—	8	2	no	—
359	C₄⋊C₄	(C₂×D₇₉)⋊C₄	1	2	yes	—
360	C₄⋊C₄	#11929611	1	2	yes	complemented
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	4	4	no	—
364	C₄²	—	4	1	no	—
365	C₄²	—	4	1	no	—
366	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
367	C₄²	C₂×D₃₁₆	1	1	yes	characteristic
368	C₄²	#11929624	1	1	yes	characteristic
369	C₄²	#11929624	1	1	yes	characteristic
370	C₂³	—	316	2	no	—
371	C₂³	—	632	1	no	—
372	C₂³	—	632	1	no	—
373	C₂³	—	632	1	no	—
374	C₂³	—	632	1	no	—
375	C₂³	—	632	1	no	—
376	C₂³	—	632	1	no	—
377	C₂³	#14579130	1	1	yes	characteristic
378	Q₈	—	2	2	no	—
379	Q₈	—	2	2	no	—
380	Q₈	—	2	2	no	—
381	Q₈	#14579081	1	4	yes	complemented
382	D₄	—	316	4	no	—
383	D₄	—	316	2	no	—
384	D₄	—	316	2	no	—
385	D₄	—	316	2	no	—
386	D₄	—	316	2	no	—
387	D₄	—	632	2	no	—
388	D₄	—	632	1	no	—
389	D₄	—	632	1	no	—
390	D₄	—	632	1	no	—
391	D₄	—	632	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	C₂×(C₂×D₇₉)⋊C₄	1	1	yes	characteristic
410	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
411	C₂×C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
412	C₂×C₄	#14579135	1	1	yes	characteristic
413	C₂×C₄	#14579135	1	1	yes	characteristic
414	C₂×C₄	#14579144	1	1	yes	characteristic
415	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
416	C₂×C₄	C₂×#11929611	1	1	yes	characteristic
417	C₂×C₄	C₂×#11929611	1	1	yes	characteristic
418	C₂×C₄	#14579181	1	1	yes	characteristic
419	C₂×C₄	#14579186	1	1	yes	characteristic
420	C₂×C₄	#14579187	1	1	yes	characteristic
421	C₂×C₄	#14579192	1	1	yes	characteristic
422	C₂×C₄	#14579192	1	1	yes	characteristic
423	C₈	—	316	2	no	—
424	C₈	—	316	2	no	—
425	C₈	—	632	1	no	—
426	C₂²	—	632	2	no	—
427	C₂²	—	632	2	no	—
428	C₂²	—	632	2	no	—
429	C₂²	—	1264	1	no	—
430	C₂²	—	1264	1	no	—
431	C₂²	—	1264	1	no	—
432	C₂²	—	1264	1	no	—
433	C₂²	#19098442	1	1	yes	characteristic
434	C₂²	#19098697	1	1	yes	characteristic
435	C₂²	#19098702	1	1	yes	characteristic
436	C₂²	#19098702	1	1	yes	characteristic
437	C₂²	#19098708	1	1	yes	characteristic
438	C₂²	#19098731	1	1	yes	characteristic
439	C₂²	#19098736	1	1	yes	characteristic
440	C₄	—	2	4	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	2	no	—
445	C₄	—	8	1	no	—
446	C₄	—	8	2	no	—
447	C₄	C₂×#14579081	1	1	yes	characteristic
448	C₄	#19098562	1	1	yes	characteristic
449	C₄	C₄×#11929611	1	1	yes	characteristic
450	C₄	#19098661	1	1	yes	characteristic
451	C₄	#19098763	1	1	yes	characteristic
452	C₄	#19098785	1	1	yes	characteristic
453	C₄	#19098876	1	1	yes	characteristic
454	C₄	#19098881	1	1	yes	characteristic
455	C₂	—	1264	2	no	—
456	C₂	#23762465	1	1	yes	characteristic
457	C₂	#23762478	1	1	yes	characteristic
458	C₂	#23762496	1	1	yes	characteristic
459	C₂	#23762503	1	1	yes	characteristic
460	C₂	#23763717	1	1	yes	characteristic
461	C₂	#23763755	1	1	yes	characteristic
462	C₂	#23763776	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14579130
commutator	C₄²×C₇₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	Q₈×C₄⋊C₄×C₇₉	C₂
socle	C₂³×C₇₉	#120
prime radical	C₂×#14579158	C₂²
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	Q₈×C₄⋊C₄	D₇₉
hypocenter	C₇₉	#8979
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ Q₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. C₂×Q₈⋊(C₇₉⋊C₈)	C₂	semidirect
5. #23761283	C₂	semidirect
6. #23761241	C₂	semidirect
7. Q₈×C₄⋊C₄×C₇₉	C₂	semidirect
11. #19098763	C₄	semidirect
128. C₄⋊C₄×C₇₉	SD₁₆	semidirect
149. Q₈×C₇₉	#102	semidirect
233. Q₈×C₄⋊C₄	D₇₉	semidirect
239. C₇₉	#8979	semidirect
360. C₄⋊C₄	#11929611	semidirect
381. Q₈	#14579081	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19098763	2
#23764327	2
#23764205	2
C₂×Q₈⋊(C₇₉⋊C₈)	2
#23761283	2
#23761241	2
Q₈×C₄⋊C₄×C₇₉	2
#8979	79