Subgroups — #34178503

Order 20224.

566 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	#23772032	C₂	1	1	yes	maximal, characteristic
2	#23772028	C₂	1	1	yes	maximal, characteristic
3	C₂×#19098585	C₂	1	1	yes	maximal, characteristic
4	#23761297	C₂	1	1	yes	maximal, characteristic, complemented
5	#23761296	C₂	1	1	yes	maximal, characteristic, complemented
6	#23761295	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₉×#1301	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#11929607	—	2	1	no	—
9	C₂×C₄²×D₇₉	C₂²	1	1	yes	characteristic
10	#19098619	—	2	1	no	—
11	#19098619	—	2	1	no	—
12	#19098619	C₄	1	2	yes	—
13	#19098617	C₄	1	2	yes	—
14	#19098616	C₂²	1	1	yes	characteristic
15	#19098615	—	2	1	no	—
16	#19098615	C₄	1	2	yes	—
17	#19098614	—	2	1	no	—
18	#19098587	C₂²	1	1	yes	characteristic
19	#19098585	—	2	1	no	—
20	#19098585	—	2	1	no	—
21	#19098585	—	2	1	no	—
22	#19098585	C₄	1	2	yes	—
23	#19098585	C₄	1	2	yes	—
24	C₂×C₄⋊(C₇₉⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×Dic₇₉⋊C₈	—	2	1	no	—
26	#19098526	—	2	1	no	—
27	#19098525	C₄	1	2	yes	—
28	M₁₆×Dic₇₉	—	2	1	no	—
29	C₄×#11929607	—	2	1	no	—
30	#431×C₇₉	C₂²	1	1	yes	characteristic
31	#423×C₇₉	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₇₉	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₇₉	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×D₇₉	D₄	1	1	yes	characteristic
35	C₂²×C₄×D₇₉	Q₈	1	1	yes	characteristic
36	C₂×#11929608	—	2	1	no	—
37	C₂×#11929607	—	2	2	no	—
38	C₂×#11929607	—	2	2	no	—
39	C₂×#11929607	—	2	2	no	—
40	C₂×#11929607	—	4	2	no	—
41	C₂×#11929607	—	4	2	no	—
42	C₂²×C₇₉⋊C₈	—	2	1	no	—
43	C₂×C₄×Dic₇₉	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×Dic₇₉	D₄	1	1	yes	characteristic
45	C₂×C₄×Dic₇₉	Q₈	1	1	yes	characteristic
46	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
47	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
48	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₇₉	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₇₉	D₄	1	1	yes	characteristic
51	C₄²×D₇₉	D₄	1	1	yes	characteristic
52	C₄²×D₇₉	D₄	1	1	yes	characteristic
53	C₄²×D₇₉	D₄	1	1	yes	characteristic
54	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
55	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
56	C₄⋊(C₇₉⋊C₈)	—	2	1	no	—
57	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
58	C₄⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
59	Dic₇₉⋊C₈	—	2	2	no	—
60	Dic₇₉⋊C₈	—	2	2	no	—
61	Dic₇₉⋊C₈	—	2	2	no	—
62	C₂²⋊(C₇₉⋊C₈)	C₂×C₄	1	2	yes	—
63	(C₂×D₇₉)⋊C₈	—	2	2	no	—
64	(C₂×D₇₉)⋊C₈	—	2	2	no	—
65	(C₂×D₇₉)⋊C₈	—	2	2	no	—
66	#14579071	—	2	2	no	—
67	#14579071	—	2	2	no	—
68	C₄×C₇₉⋊C₈	—	2	1	no	—
69	C₈×Dic₇₉	—	2	2	no	—
70	C₂×M₁₆×C₇₉	—	2	1	no	—
71	C₂²×C₈×C₇₉	—	2	1	no	—
72	C₂×C₄²×C₇₉	C₂³	1	1	yes	characteristic
73	C₄⋊C₈×C₇₉	—	2	1	no	—
74	C₄⋊C₈×C₇₉	—	2	1	no	—
75	C₄⋊C₈×C₇₉	—	2	1	no	—
76	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
77	C₄⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
78	C₂²⋊C₈×C₇₉	C₂×C₄	1	2	yes	—
79	C₄×C₈×C₇₉	—	2	1	no	—
80	C₂³×D₇₉	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×D₇₉	—	2	1	no	—
85	C₂×C₄×D₇₉	—	2	1	no	—
86	C₂×C₄×D₇₉	—	2	1	no	—
87	C₂×C₄×D₇₉	—	2	1	no	—
88	C₂×C₄×D₇₉	—	4	2	no	—
89	C₂×C₄×D₇₉	—	4	2	no	—
90	C₂×C₄×D₇₉	C₄²	1	1	yes	characteristic
91	C₂×C₄×D₇₉	C₄²	1	1	yes	characteristic
92	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₇₉	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₇₉	C₄⋊C₄	1	1	yes	characteristic
102	#11929608	—	4	1	no	—
103	#11929608	—	4	1	no	—
104	#11929607	—	4	4	no	—
105	#11929607	—	4	4	no	—
106	#11929607	—	4	4	no	—
107	C₂×C₇₉⋊C₈	—	2	2	no	—
108	C₂×C₇₉⋊C₈	—	2	2	no	—
109	C₂×C₇₉⋊C₈	—	2	2	no	—
110	C₂×C₇₉⋊C₈	—	4	1	no	—
111	C₂×C₇₉⋊C₈	—	4	1	no	—
112	C₄×Dic₇₉	C₄²	1	1	yes	characteristic
113	C₄×Dic₇₉	C₄²	1	1	yes	characteristic
114	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
115	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
116	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
117	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
118	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
119	C₄×Dic₇₉	C₂²⋊C₄	1	1	yes	characteristic
120	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
121	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
122	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
123	C₄×Dic₇₉	C₄⋊C₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
127	M₁₆×C₇₉	—	4	1	no	—
128	M₁₆×C₇₉	—	4	1	no	—
129	C₂×C₈×C₇₉	—	2	2	no	—
130	C₂×C₈×C₇₉	—	2	2	no	—
131	C₂×C₈×C₇₉	—	2	2	no	—
132	C₂×C₈×C₇₉	—	4	1	no	—
133	C₂×C₈×C₇₉	—	4	1	no	—
134	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₇₉	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
138	C₂³×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂²×D₇₉	—	2	1	no	—
140	C₂²×D₇₉	—	2	1	no	—
141	C₂²×D₇₉	—	4	1	no	—
142	C₂²×D₇₉	—	4	1	no	—
143	C₂²×D₇₉	#95	1	1	yes	characteristic
144	C₂²×D₇₉	#95	1	1	yes	characteristic
145	C₂×C₄×C₇₉	—	2	2	no	—
146	C₂×C₄×C₇₉	—	4	1	no	—
147	C₂×C₄×C₇₉	C₂×C₄²	1	1	yes	characteristic
148	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₇₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
156	C₂×C₄×C₇₉	#137	1	1	yes	characteristic
157	C₂×Dic₇₉	—	2	1	no	—
158	C₂×Dic₇₉	—	2	1	no	—
159	C₂×Dic₇₉	—	2	2	no	—
160	C₂×Dic₇₉	—	4	1	no	—
161	C₂×Dic₇₉	#95	1	1	yes	characteristic
162	C₂×Dic₇₉	#95	1	1	yes	characteristic
163	C₂×Dic₇₉	#95	1	1	yes	characteristic
164	C₂×Dic₇₉	#95	1	1	yes	characteristic
165	C₂×Dic₇₉	#95	1	1	yes	characteristic
166	C₂×Dic₇₉	#95	1	1	yes	characteristic
167	C₄×D₇₉	—	2	1	no	—
168	C₄×D₇₉	—	2	1	no	—
169	C₄×D₇₉	—	2	1	no	—
170	C₄×D₇₉	—	2	1	no	—
171	C₄×D₇₉	—	2	1	no	—
172	C₄×D₇₉	—	2	1	no	—
173	C₄×D₇₉	—	2	1	no	—
174	C₄×D₇₉	—	2	1	no	—
175	C₄×D₇₉	—	2	2	no	—
176	C₄×D₇₉	—	2	2	no	—
177	C₄×D₇₉	—	2	2	no	—
178	C₄×D₇₉	—	2	2	no	—
179	C₄×D₇₉	—	4	1	no	—
180	C₄×D₇₉	—	4	1	no	—
181	C₄×D₇₉	—	4	1	no	—
182	C₄×D₇₉	—	4	1	no	—
183	C₈×C₇₉	—	4	2	no	—
184	C₈×C₇₉	—	4	2	no	—
185	C₈×C₇₉	—	4	2	no	—
186	C₇₉⋊C₈	—	4	2	no	—
187	C₇₉⋊C₈	—	4	2	no	—
188	C₇₉⋊C₈	—	4	2	no	—
189	C₂²×C₇₉	—	2	1	no	—
190	C₂²×C₇₉	—	2	1	no	—
191	C₂²×C₇₉	C₂×#95	1	1	yes	characteristic
192	C₂²×C₇₉	#428	1	1	yes	characteristic
193	C₂²×C₇₉	#428	1	1	yes	characteristic
194	C₂×D₇₉	—	2	1	no	—
195	C₂×D₇₉	—	2	1	no	—
196	C₂×D₇₉	—	2	1	no	—
197	C₂×D₇₉	—	2	1	no	—
198	C₂×D₇₉	—	2	1	no	—
199	C₂×D₇₉	—	2	1	no	—
200	C₂×D₇₉	—	4	2	no	—
201	C₂×D₇₉	—	4	2	no	—
202	C₄×C₇₉	—	2	1	no	—
203	C₄×C₇₉	—	2	1	no	—
204	C₄×C₇₉	—	2	1	no	—
205	C₄×C₇₉	#417	1	1	yes	characteristic
206	C₄×C₇₉	#417	1	1	yes	characteristic
207	C₄×C₇₉	#418	1	1	yes	characteristic
208	C₄×C₇₉	#419	1	1	yes	characteristic
209	C₄×C₇₉	#430	1	2	yes	—
210	Dic₇₉	—	2	1	no	—
211	Dic₇₉	—	2	1	no	—
212	Dic₇₉	—	2	1	no	—
213	Dic₇₉	—	2	1	no	—
214	Dic₇₉	—	2	1	no	—
215	Dic₇₉	#344	1	2	yes	—
216	#8078	—	79	1	no	maximal, Sylow
217	C₂×C₇₉	—	2	1	no	—
218	C₂×C₇₉	—	2	1	no	—
219	C₂×C₇₉	#1736	1	1	yes	characteristic
220	C₂×C₇₉	#1738	1	1	yes	characteristic
221	C₂×C₇₉	C₂×#344	1	1	yes	characteristic
222	D₇₉	—	4	1	no	—
223	D₇₉	—	4	1	no	—
224	#2920	—	79	1	no	—
225	#2920	—	79	1	no	—
226	C₂×#423	—	79	1	no	—
227	#1301	—	79	1	no	—
228	#1301	—	79	1	no	—
229	#1301	—	79	1	no	—
230	#1301	D₇₉	1	1	yes	characteristic, complemented
231	C₇₉	#8078	1	1	yes	characteristic, complemented, Sylow
232	C₂²×M₁₆	—	158	1	no	—
233	C₂²×C₄²	—	79	1	no	—
234	#432	—	79	2	no	—
235	#432	—	79	2	no	—
236	#432	—	158	1	no	—
237	#432	—	158	1	no	—
238	#431	—	79	1	no	—
239	#431	—	79	2	no	—
240	#431	—	158	1	no	—
241	#431	—	158	1	no	—
242	#431	C₂×D₇₉	1	1	yes	characteristic
243	#423	—	79	1	no	—
244	#423	—	79	2	no	—
245	#423	—	79	2	no	—
246	#423	—	158	1	no	—
247	#423	—	158	1	no	—
248	#423	—	158	1	no	—
249	#423	C₂×D₇₉	1	1	yes	characteristic
250	C₂×C₄⋊C₈	—	79	1	no	—
251	C₂×C₄⋊C₈	—	158	1	no	—
252	C₂×C₄⋊C₈	C₂×D₇₉	1	1	yes	characteristic
253	#407	—	79	2	no	—
254	#407	—	158	1	no	—
255	C₄×M₁₆	—	158	1	no	—
256	C₄×M₁₆	—	158	1	no	—
257	C₂³×C₄	—	79	1	no	—
258	C₂³×C₄	—	79	1	no	—
259	C₂³×C₄	—	79	1	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	316	2	no	—
262	C₂×M₁₆	—	316	2	no	—
263	C₂×M₁₆	—	158	2	no	—
264	C₂×M₁₆	—	158	2	no	—
265	C₂×M₁₆	—	158	2	no	—
266	C₂×M₁₆	—	158	1	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	158	1	no	—
269	C₂×C₄²	—	79	1	no	—
270	C₂×C₄²	—	79	1	no	—
271	C₂×C₄²	—	79	1	no	—
272	C₂×C₄²	—	79	1	no	—
273	C₂×C₄²	—	79	1	no	—
274	C₂×C₄²	—	79	1	no	—
275	C₂×C₄²	—	79	1	no	—
276	C₂×C₄²	—	79	1	no	—
277	C₂×C₄²	—	79	1	no	—
278	C₂×C₄²	—	79	1	no	—
279	C₂×C₄²	—	79	1	no	—
280	C₂×C₄²	C₂²×D₇₉	1	1	yes	characteristic
281	C₄⋊C₈	—	2	1	no	—
282	C₄⋊C₈	—	2	1	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	79	2	no	—
285	C₄⋊C₈	—	79	2	no	—
286	C₄⋊C₈	—	158	2	no	—
287	C₄⋊C₈	—	158	2	no	—
288	C₄⋊C₈	—	158	2	no	—
289	C₄⋊C₈	—	158	1	no	—
290	C₄⋊C₈	—	158	1	no	—
291	C₄⋊C₈	—	158	1	no	—
292	C₄⋊C₈	C₄×D₇₉	1	2	yes	—
293	C₄⋊C₈	C₄×D₇₉	1	2	yes	—
294	C₂²⋊C₈	—	79	2	no	—
295	C₂²⋊C₈	—	158	2	no	—
296	C₂²⋊C₈	—	158	2	no	—
297	C₂²⋊C₈	—	158	2	no	—
298	C₂²⋊C₈	C₄×D₇₉	1	2	yes	—
299	#97	—	158	2	no	—
300	#97	—	158	2	no	—
301	C₄×C₈	—	2	1	no	—
302	C₄×C₈	—	158	2	no	—
303	C₄×C₈	—	158	1	no	—
304	C₂⁴	—	79	1	no	—
305	C₂²×C₄	—	316	2	no	—
306	C₂²×C₄	—	316	2	no	—
307	C₂²×C₄	—	79	1	no	—
308	C₂²×C₄	—	79	1	no	—
309	C₂²×C₄	—	79	1	no	—
310	C₂²×C₄	—	79	1	no	—
311	C₂²×C₄	—	79	1	no	—
312	C₂²×C₄	—	79	1	no	—
313	C₂²×C₄	—	79	1	no	—
314	C₂²×C₄	—	79	1	no	—
315	C₂²×C₄	—	79	1	no	—
316	C₂²×C₄	—	79	1	no	—
317	C₂²×C₄	—	79	1	no	—
318	C₂²×C₄	—	79	1	no	—
319	C₂²×C₄	—	79	1	no	—
320	C₂²×C₄	—	79	1	no	—
321	C₂²×C₄	—	79	1	no	—
322	C₂²×C₄	—	158	1	no	—
323	C₂²×C₄	—	158	1	no	—
324	C₂²×C₄	—	158	1	no	—
325	C₂²×C₄	—	158	1	no	—
326	C₂²×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
327	C₂²×C₄	D₄×D₇₉	1	1	yes	characteristic
328	C₂²×C₄	Q₈×D₇₉	1	1	yes	characteristic
329	M₁₆	—	4	1	no	—
330	M₁₆	—	4	1	no	—
331	M₁₆	—	316	4	no	—
332	M₁₆	—	316	4	no	—
333	M₁₆	—	316	4	no	—
334	M₁₆	—	316	1	no	—
335	M₁₆	—	316	1	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	316	1	no	—
342	C₂×C₈	—	316	1	no	—
343	C₂×C₈	—	158	2	no	—
344	C₂×C₈	—	158	2	no	—
345	C₂×C₈	—	158	2	no	—
346	C₄²	—	79	1	no	—
347	C₄²	—	79	1	no	—
348	C₄²	—	79	1	no	—
349	C₄²	—	79	1	no	—
350	C₄²	—	79	1	no	—
351	C₄²	—	79	1	no	—
352	C₄²	—	79	1	no	—
353	C₄²	—	79	1	no	—
354	C₄²	—	79	1	no	—
355	C₄²	—	79	1	no	—
356	C₄²	—	79	1	no	—
357	C₄²	—	79	1	no	—
358	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
359	C₄²	C₂×C₄×D₇₉	1	1	yes	characteristic
360	C₄²	D₄×D₇₉	1	1	yes	characteristic
361	C₄²	D₄×D₇₉	1	1	yes	characteristic
362	C₂³	—	316	1	no	—
363	C₂³	—	316	1	no	—
364	C₂³	—	79	1	no	—
365	C₂³	—	79	1	no	—
366	C₂³	—	158	1	no	—
367	C₂³	—	158	1	no	—
368	C₂³	C₄⋊C₄×D₇₉	1	1	yes	characteristic
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	316	1	no	—
372	C₂×C₄	—	316	1	no	—
373	C₂×C₄	—	316	1	no	—
374	C₂×C₄	—	316	1	no	—
375	C₂×C₄	—	316	1	no	—
376	C₂×C₄	—	79	1	no	—
377	C₂×C₄	—	79	1	no	—
378	C₂×C₄	—	79	1	no	—
379	C₂×C₄	—	79	1	no	—
380	C₂×C₄	—	79	1	no	—
381	C₂×C₄	—	79	1	no	—
382	C₂×C₄	—	158	2	no	—
383	C₂×C₄	—	158	2	no	—
384	C₂×C₄	—	158	2	no	—
385	C₂×C₄	—	158	1	no	—
386	C₂×C₄	—	158	1	no	—
387	C₂×C₄	—	158	1	no	—
388	C₂×C₄	—	158	1	no	—
389	C₂×C₄	—	158	1	no	—
390	C₂×C₄	—	158	1	no	—
391	C₂×C₄	—	158	1	no	—
392	C₂×C₄	—	158	1	no	—
393	C₂×C₄	—	158	1	no	—
394	C₂×C₄	—	158	1	no	—
395	C₂×C₄	—	158	2	no	—
396	C₂×C₄	—	158	2	no	—
397	C₂×C₄	C₄²×D₇₉	1	1	yes	characteristic
398	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
399	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
400	C₂×C₄	C₂²⋊C₄×D₇₉	1	1	yes	characteristic
401	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
402	C₂×C₄	C₄⋊C₄×D₇₉	1	1	yes	characteristic
403	C₂×C₄	#14579185	1	1	yes	characteristic
404	C₂×C₄	#14579188	1	1	yes	characteristic
405	C₂×C₄	#14579190	1	1	yes	characteristic
406	C₂×C₄	#14579193	1	1	yes	characteristic
407	C₈	—	4	2	no	—
408	C₈	—	4	2	no	—
409	C₈	—	4	2	no	—
410	C₈	—	316	2	no	—
411	C₈	—	316	2	no	—
412	C₈	—	316	2	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	316	2	no	—
416	C₂²	—	316	2	no	—
417	C₂²	—	158	1	no	—
418	C₂²	—	158	1	no	—
419	C₂²	—	158	1	no	—
420	C₂²	—	158	1	no	—
421	C₂²	—	158	1	no	—
422	C₂²	—	158	1	no	—
423	C₂²	#95×D₇₉	1	1	yes	characteristic
424	C₂²	#19098602	1	1	yes	characteristic
425	C₂²	#19098604	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	79	2	no	—
430	C₄	—	158	1	no	—
431	C₄	—	158	1	no	—
432	C₄	—	158	1	no	—
433	C₄	—	158	1	no	—
434	C₄	—	158	1	no	—
435	C₄	#19098561	1	1	yes	characteristic
436	C₄	#19098563	1	1	yes	characteristic
437	C₄	#19098566	1	1	yes	characteristic
438	C₄	#19098570	1	1	yes	characteristic
439	C₄	#19098610	1	2	yes	—
440	C₂	—	2	1	no	—
441	C₂	—	2	1	no	—
442	C₂	—	316	1	no	—
443	C₂	—	316	1	no	—
444	C₂	#23763118	1	1	yes	characteristic
445	C₂	#23763125	1	1	yes	characteristic
446	C₂	#344×D₇₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₇₉
Fitting	C₇₉×#1301	C₂
socle	C₂²×C₇₉	C₂×#95
prime radical	C₂³×D₇₉	C₄⋊C₄
cosocle	C₂×C₄²×C₇₉	C₂³
hypercenter	#1301	D₇₉
hypocenter	C₇₉	#8078
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1301

Complements

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

N	H ≅ G/N	type
4. #23761297	C₂	semidirect
5. #23761296	C₂	semidirect
6. #23761295	C₂	semidirect
7. C₇₉×#1301	C₂	semidirect
230. #1301	D₇₉	semidirect
231. C₇₉	#8078	semidirect

Maximal subgroups

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

subgroup	index
#23772032	2
#23772028	2
C₂×#19098585	2
#23761297	2
#23761296	2
#23761295	2
C₇₉×#1301	2
#8078	79