Subgroups — #35196984

Order 20224.

7330 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23777959	C₂	1	8	yes	maximal, complemented
2	#23777914	C₂	1	8	yes	maximal, complemented
3	#23777749	C₂	1	8	yes	maximal, complemented
4	#23777358	C₂	1	8	yes	maximal, complemented
5	#23777352	C₂	1	8	yes	maximal, complemented
6	#23777295	C₂	1	2	yes	maximal, complemented
7	#23777291	C₂	1	2	yes	maximal, complemented
8	#23777192	C₂	1	2	yes	maximal, complemented
9	#23777188	C₂	1	2	yes	maximal, complemented
10	#23777087	C₂	1	8	yes	maximal, complemented
11	#23777047	C₂	1	2	yes	maximal, complemented
12	#23777035	C₂	1	1	yes	maximal, characteristic, complemented
13	#23776692	C₂	1	2	yes	maximal, complemented
14	C₂²×#14579148	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₉×#3484	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14579208	C₂²	1	2	yes	complemented
17	C₂×#14579206	C₂²	1	1	yes	characteristic, complemented
18	C₂³×Dic₁₅₈	C₂²	1	1	yes	characteristic, complemented
19	#19099316	C₂²	1	8	yes	complemented
20	#19099308	C₂²	1	16	yes	complemented
21	#19099306	C₂²	1	8	yes	complemented
22	#19099299	C₂²	1	8	yes	complemented
23	#19099296	C₂²	1	8	yes	complemented
24	#19099283	C₂²	1	8	yes	complemented
25	#19099282	C₂²	1	8	yes	complemented
26	#19099277	C₂²	1	16	yes	complemented
27	#19099244	C₂²	1	16	yes	complemented
28	#19099244	C₂²	1	16	yes	complemented
29	#19099244	C₂²	1	8	yes	complemented
30	#19099241	C₂²	1	8	yes	complemented
31	#19099239	C₂²	1	16	yes	complemented
32	#19099239	C₂²	1	16	yes	complemented
33	D₄×Dic₁₅₈	C₂²	1	8	yes	complemented
34	#19099226	C₂²	1	8	yes	complemented
35	#19099222	C₂²	1	8	yes	complemented
36	#19099220	C₂²	1	8	yes	complemented
37	#19099219	C₂²	1	8	yes	complemented
38	#19099219	C₂²	1	8	yes	complemented
39	#19099210	C₂²	1	8	yes	complemented
40	#19099207	C₂²	1	8	yes	complemented
41	#19099207	C₂²	1	16	yes	complemented
42	#19099207	C₂²	1	16	yes	complemented
43	#19099207	C₂²	1	8	yes	complemented
44	#19099200	C₂²	1	16	yes	complemented
45	#19099200	C₂²	1	16	yes	complemented
46	D₄×C₂²⋊D₇₉	C₂²	1	8	yes	complemented
47	#19099189	C₂²	1	8	yes	complemented
48	#19099181	C₂²	1	16	yes	complemented
49	#19099180	C₂²	1	8	yes	complemented
50	#19099180	C₂²	1	16	yes	complemented
51	#19099178	C₂²	1	8	yes	complemented
52	#19099148	C₂²	1	16	yes	complemented
53	#19099148	C₂²	1	16	yes	complemented
54	#19099148	C₂²	1	16	yes	complemented
55	#19099145	C₂²	1	16	yes	complemented
56	#19099139	C₂²	1	2	yes	complemented
57	#19099135	C₂²	1	8	yes	complemented
58	#19099134	C₂²	1	2	yes	complemented
59	#19099134	C₂²	1	4	yes	complemented
60	#19099133	C₂²	1	4	yes	complemented
61	#19099130	C₂²	1	2	yes	—
62	#19099130	C₂²	1	4	yes	complemented
63	#19099126	C₂²	1	4	yes	complemented
64	#19099122	C₂²	1	4	yes	complemented
65	#19099122	C₂²	1	8	yes	complemented
66	#19099116	C₂²	1	2	yes	complemented
67	#19099115	C₂²	1	4	yes	complemented
68	#19099111	C₂²	1	4	yes	complemented
69	#19099109	C₂²	1	2	yes	complemented
70	#19099109	C₂²	1	4	yes	complemented
71	#19099108	C₂²	1	4	yes	complemented
72	#19099099	C₂²	1	4	yes	complemented
73	#19099095	C₂²	1	8	yes	complemented
74	#19099094	C₂²	1	4	yes	complemented
75	#19099094	C₂²	1	8	yes	complemented
76	#19099093	C₂²	1	8	yes	complemented
77	#19099090	C₂²	1	8	yes	complemented
78	C₂×#14579148	C₂²	1	2	yes	complemented
79	C₂×#14579148	C₂²	1	2	yes	complemented
80	C₂×#14579148	C₂²	1	8	yes	complemented
81	C₂×#14579148	C₂²	1	8	yes	complemented
82	C₂×#14579148	C₂²	1	4	yes	complemented
83	C₂×#14579148	C₂²	1	4	yes	complemented
84	#124×D₇₉	C₂²	1	4	yes	complemented
85	#19099074	C₂²	1	2	yes	complemented
86	#19099069	C₂²	1	8	yes	complemented
87	#19099069	C₂²	1	8	yes	complemented
88	C₂×#14579130	C₂²	1	4	yes	complemented
89	#19099040	C₂²	1	2	yes	complemented
90	#19099038	C₂²	1	1	yes	characteristic, complemented
91	#19099038	C₂²	1	8	yes	complemented
92	#19099036	C₂²	1	8	yes	complemented
93	#41×Dic₇₉	C₂²	1	2	yes	complemented
94	#19099031	C₂²	1	2	yes	complemented
95	C₄×#11929623	C₂²	1	8	yes	complemented
96	C₂²×C₂²⋊Dic₇₉	C₂²	1	4	yes	complemented
97	C₂²×C₄×Dic₇₉	C₂²	1	1	yes	characteristic, complemented
98	C₂×H(5,𝔽₂)×C₇₉	C₂²	1	1	yes	characteristic, complemented
99	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
100	#546×C₇₉	C₂²	1	8	yes	complemented
101	D₄²×C₇₉	C₂²	1	8	yes	complemented
102	#535×C₇₉	C₂²	1	2	yes	—
103	#534×C₇₉	C₂²	1	4	yes	complemented
104	#525×C₇₉	C₂²	1	2	yes	complemented
105	C₂×#120×C₇₉	C₂²	1	4	yes	complemented
106	#518×C₇₉	C₂²	1	1	yes	characteristic, complemented
107	#14579208	—	4	8	no	—
108	#14579206	—	4	4	no	—
109	C₂×#11929624	C₂³	1	2	yes	—
110	C₂×#11929624	C₂³	1	4	yes	complemented
111	C₂×#11929623	C₂³	1	4	yes	—
112	C₂×#11929623	C₂³	1	8	yes	—
113	C₂×#11929623	C₂³	1	8	yes	—
114	C₂×#11929623	C₂³	1	4	yes	complemented
115	C₂²×Dic₁₅₈	—	4	4	no	—
116	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
117	C₂²×Dic₁₅₈	C₂³	1	8	yes	—
118	C₂²×Dic₁₅₈	C₂³	1	2	yes	—
119	C₂²×Dic₁₅₈	C₂³	1	4	yes	complemented
120	C₂×Q₈×D₇₉	C₂³	1	4	yes	complemented
121	C₂²×C₂²⋊D₇₉	C₂³	1	4	yes	—
122	C₂²×C₂²⋊D₇₉	C₂³	1	8	yes	—
123	C₂×D₄×D₇₉	C₂³	1	4	yes	—
124	C₂³×Dic₇₉	C₂³	1	2	yes	—
125	C₂³×Dic₇₉	C₂³	1	2	yes	—
126	#14579161	C₂³	1	4	yes	complemented
127	#14579160	C₂³	1	4	yes	complemented
128	#14579160	C₂³	1	16	yes	complemented
129	#14579159	C₂³	1	4	yes	complemented
130	#14579159	C₂³	1	2	yes	complemented
131	#14579157	C₂³	1	4	yes	—
132	#14579157	C₂³	1	2	yes	complemented
133	#14579156	C₂³	1	8	yes	complemented
134	#14579154	C₂³	1	16	yes	complemented
135	#14579154	C₂³	1	16	yes	complemented
136	#14579154	C₂³	1	8	yes	complemented
137	#14579154	C₂³	1	16	yes	complemented
138	#14579154	C₂³	1	16	yes	complemented
139	#14579152	C₂³	1	4	yes	complemented
140	#14579151	C₂³	1	8	yes	complemented
141	#14579150	C₂³	1	2	yes	complemented
142	#14579149	C₂³	1	4	yes	complemented
143	#14579148	C₂³	1	16	yes	—
144	#14579148	C₂³	1	4	yes	—
145	#14579148	C₂³	1	4	yes	—
146	#14579148	C₂³	1	4	yes	—
147	#14579148	C₂³	1	8	yes	—
148	#14579148	C₂³	1	8	yes	—
149	#14579148	C₂³	1	8	yes	—
150	#14579148	C₂³	1	8	yes	—
151	#14579148	C₂³	1	4	yes	—
152	#14579148	C₂³	1	4	yes	—
153	#14579148	C₂³	1	16	yes	complemented
154	#14579148	C₂³	1	16	yes	complemented
155	#14579148	C₂³	1	4	yes	complemented
156	#14579148	C₂³	1	2	yes	complemented
157	#14579147	C₂³	1	16	yes	complemented
158	#14579147	C₂³	1	16	yes	complemented
159	#14579147	C₂³	1	16	yes	complemented
160	#14579147	C₂³	1	8	yes	complemented
161	#14579145	C₂³	1	8	yes	—
162	#14579145	C₂³	1	8	yes	—
163	#14579144	C₂³	1	4	yes	—
164	#14579144	C₂³	1	16	yes	complemented
165	#14579143	C₂³	1	16	yes	complemented
166	#14579143	C₂³	1	16	yes	complemented
167	#14579142	C₂³	1	8	yes	—
168	#14579142	C₂³	1	8	yes	—
169	#14579142	C₂³	1	8	yes	—
170	#14579142	C₂³	1	16	yes	complemented
171	#14579142	C₂³	1	16	yes	complemented
172	#14579142	C₂³	1	16	yes	complemented
173	#14579141	C₂³	1	8	yes	complemented
174	#14579140	C₂³	1	4	yes	—
175	#14579140	C₂³	1	16	yes	complemented
176	#14579140	C₂³	1	8	yes	complemented
177	#14579140	C₂³	1	16	yes	complemented
178	#14579139	C₂³	1	16	yes	complemented
179	#14579138	C₂³	1	8	yes	—
180	#14579138	C₂³	1	16	yes	—
181	#14579138	C₂³	1	8	yes	—
182	#14579138	C₂³	1	16	yes	complemented
183	#14579138	C₂³	1	16	yes	complemented
184	#14579138	C₂³	1	16	yes	complemented
185	#14579135	C₂³	1	4	yes	—
186	#14579133	C₂³	1	8	yes	—
187	#14579133	C₂³	1	16	yes	—
188	#14579133	C₂³	1	16	yes	—
189	#14579133	C₂³	1	8	yes	—
190	#14579133	C₂³	1	16	yes	complemented
191	#14579133	C₂³	1	16	yes	complemented
192	#14579132	C₂³	1	8	yes	—
193	#14579132	C₂³	1	16	yes	complemented
194	#14579132	C₂³	1	16	yes	complemented
195	#14579130	C₂³	1	16	yes	—
196	#14579130	C₂³	1	8	yes	—
197	#14579130	C₂³	1	4	yes	—
198	#14579130	C₂³	1	16	yes	complemented
199	#14579129	C₂³	1	8	yes	—
200	#14579129	C₂³	1	16	yes	complemented
201	Q₈×Dic₇₉	C₂³	1	4	yes	complemented
202	C₄×Dic₁₅₈	C₂³	1	8	yes	complemented
203	C₄×Dic₁₅₈	C₂³	1	8	yes	complemented
204	#14579126	C₂³	1	8	yes	complemented
205	#14579126	C₂³	1	8	yes	complemented
206	#14579126	C₂³	1	4	yes	complemented
207	D₄×Dic₇₉	C₂³	1	8	yes	—
208	D₄×Dic₇₉	C₂³	1	16	yes	—
209	D₄×Dic₇₉	C₂³	1	8	yes	—
210	D₄×Dic₇₉	C₂³	1	8	yes	—
211	D₄×Dic₇₉	C₂³	1	16	yes	complemented
212	D₄×Dic₇₉	C₂³	1	16	yes	complemented
213	D₄×Dic₇₉	C₂³	1	4	yes	complemented
214	#14579123	C₂³	1	4	yes	complemented
215	C₄×C₂²⋊D₇₉	C₂³	1	8	yes	—
216	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
217	C₄×C₂²⋊D₇₉	C₂³	1	16	yes	complemented
218	C₄×C₂²⋊D₇₉	C₂³	1	8	yes	complemented
219	(C₂²⋊D₇₉)⋊C₄	C₂³	1	8	yes	—
220	(C₂²⋊D₇₉)⋊C₄	C₂³	1	16	yes	—
221	(C₂²⋊D₇₉)⋊C₄	C₂³	1	8	yes	—
222	(C₂²⋊D₇₉)⋊C₄	C₂³	1	8	yes	complemented
223	#14579120	C₂³	1	2	yes	—
224	#14579120	C₂³	1	4	yes	complemented
225	#14579120	C₂³	1	16	yes	complemented
226	#14579119	C₂³	1	8	yes	complemented
227	#14579118	C₂³	1	4	yes	complemented
228	#14579117	C₂³	1	8	yes	—
229	#14579117	C₂³	1	8	yes	—
230	#14579117	C₂³	1	16	yes	complemented
231	#14579117	C₂³	1	8	yes	complemented
232	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	—
233	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	—
234	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	—
235	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	—
236	C₂×C₂²⋊Dic₇₉	C₂³	1	16	yes	—
237	C₂×C₂²⋊Dic₇₉	C₂³	1	8	yes	—
238	C₂×C₂²⋊Dic₇₉	C₂³	1	4	yes	—
239	C₂×C₂²⋊Dic₇₉	C₂³	1	16	yes	complemented
240	C₂²⋊C₄×D₇₉	C₂³	1	16	yes	complemented
241	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
242	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
243	C₂×C₄×Dic₇₉	C₂³	1	2	yes	—
244	C₂×C₄×Dic₇₉	C₂³	1	4	yes	—
245	C₂×C₄×Dic₇₉	C₂³	1	4	yes	complemented
246	C₄²×D₇₉	C₂³	1	4	yes	complemented
247	C₂⁵×C₇₉	C₂³	1	2	yes	—
248	H(5,𝔽₂)×C₇₉	—	4	4	no	—
249	C₂×#41×C₇₉	C₂³	1	2	yes	—
250	C₂×#41×C₇₉	C₂³	1	4	yes	—
251	C₂²×D₄×C₇₉	—	4	4	no	—
252	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
253	C₂²×D₄×C₇₉	C₂³	1	1	yes	characteristic
254	C₂²×D₄×C₇₉	C₂³	1	8	yes	—
255	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
256	C₂²×D₄×C₇₉	C₂³	1	8	yes	—
257	C₂²×D₄×C₇₉	C₂³	1	4	yes	—
258	C₂²×D₄×C₇₉	C₂³	1	2	yes	—
259	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
260	#127×C₇₉	C₂³	1	4	yes	—
261	#124×C₇₉	C₂³	1	4	yes	—
262	#123×C₇₉	C₂³	1	8	yes	—
263	#123×C₇₉	C₂³	1	4	yes	—
264	C₂²⋊Q₈×C₇₉	C₂³	1	4	yes	—
265	#121×C₇₉	C₂³	1	16	yes	—
266	#121×C₇₉	C₂³	1	8	yes	—
267	#121×C₇₉	C₂³	1	4	yes	—
268	#120×C₇₉	C₂³	1	16	yes	—
269	#120×C₇₉	C₂³	1	8	yes	—
270	#120×C₇₉	C₂³	1	8	yes	—
271	#120×C₇₉	C₂³	1	4	yes	—
272	C₄×D₄×C₇₉	C₂³	1	8	yes	—
273	C₄×D₄×C₇₉	C₂³	1	8	yes	—
274	#117×C₇₉	C₂³	1	2	yes	—
275	C₂×C₂²⋊C₄×C₇₉	C₂³	1	8	yes	—
276	C₂×C₂²⋊C₄×C₇₉	C₂³	1	4	yes	—
277	C₂³×D₇₉	C₂⁴	1	4	yes	—
278	#11929624	—	2	8	no	—
279	#11929624	—	4	8	no	—
280	#11929623	—	4	16	no	—
281	#11929623	—	4	16	no	—
282	#11929623	—	4	8	no	—
283	#11929623	—	4	8	no	—
284	C₂×Dic₁₅₈	—	2	8	no	—
285	C₂×Dic₁₅₈	—	4	16	no	—
286	C₂×Dic₁₅₈	—	4	8	no	—
287	C₂×Dic₁₅₈	—	4	4	no	—
288	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
289	C₂×Dic₁₅₈	C₂⁴	1	4	yes	—
290	C₂×Dic₁₅₈	C₂⁴	1	2	yes	—
291	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
292	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
293	C₂×Dic₁₅₈	C₂⁴	1	8	yes	—
294	Q₈×D₇₉	—	4	8	no	—
295	C₂×D₃₁₆	C₂⁴	1	2	yes	—
296	C₂×C₂²⋊D₇₉	—	4	8	no	—
297	C₂×C₂²⋊D₇₉	—	4	16	no	—
298	C₂×C₂²⋊D₇₉	C₂⁴	1	4	yes	—
299	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
300	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
301	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
302	C₂×C₂²⋊D₇₉	C₂⁴	1	8	yes	—
303	C₂×C₂²⋊D₇₉	C₂⁴	1	16	yes	—
304	D₄×D₇₉	—	4	8	no	—
305	C₂²×Dic₇₉	—	4	4	no	—
306	C₂²×Dic₇₉	—	4	4	no	—
307	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
308	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
309	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
310	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
311	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
312	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
313	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
314	C₂²×Dic₇₉	C₂⁴	1	4	yes	—
315	C₂²×Dic₇₉	C₂⁴	1	2	yes	—
316	C₂²×Dic₇₉	C₂⁴	1	8	yes	—
317	C₂×C₄×D₇₉	C₂⁴	1	4	yes	—
318	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
319	C₂×C₄×D₇₉	C₂⁴	1	8	yes	—
320	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
321	C₄⋊Dic₇₉	C₂⁴	1	4	yes	—
322	C₄⋊Dic₇₉	C₂⁴	1	16	yes	—
323	C₄⋊Dic₇₉	C₂⁴	1	8	yes	—
324	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
325	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
326	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
327	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
328	Dic₇₉⋊C₄	C₂⁴	1	16	yes	—
329	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
330	Dic₇₉⋊C₄	C₂⁴	1	8	yes	—
331	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
332	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
333	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
334	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
335	C₂²⋊Dic₇₉	C₂⁴	1	4	yes	—
336	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
337	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
338	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
339	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
340	C₂²⋊Dic₇₉	C₂⁴	1	16	yes	—
341	C₂²⋊Dic₇₉	C₂⁴	1	8	yes	—
342	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
343	(C₂×D₇₉)⋊C₄	C₂⁴	1	16	yes	—
344	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
345	(C₂×D₇₉)⋊C₄	C₂⁴	1	8	yes	—
346	C₄×Dic₇₉	C₂⁴	1	2	yes	—
347	C₄×Dic₇₉	C₂⁴	1	8	yes	—
348	C₄×Dic₇₉	C₂⁴	1	2	yes	—
349	C₄×Dic₇₉	C₂⁴	1	2	yes	—
350	C₄×Dic₇₉	C₂⁴	1	4	yes	—
351	C₄×Dic₇₉	C₂⁴	1	4	yes	—
352	C₄×Dic₇₉	C₂⁴	1	2	yes	—
353	C₄×Dic₇₉	C₂⁴	1	8	yes	—
354	C₄×Dic₇₉	C₂⁴	1	4	yes	—
355	C₄×Dic₇₉	C₂⁴	1	16	yes	—
356	C₂⁴×C₇₉	—	4	4	no	—
357	C₂⁴×C₇₉	—	4	8	no	—
358	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
359	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
360	C₂⁴×C₇₉	C₂⁴	1	8	yes	—
361	C₂⁴×C₇₉	C₂⁴	1	2	yes	—
362	C₂⁴×C₇₉	C₂⁴	1	4	yes	—
363	#41×C₇₉	—	2	8	no	—
364	#41×C₇₉	—	4	8	no	—
365	C₂×Q₈×C₇₉	C₂⁴	1	2	yes	—
366	C₂×D₄×C₇₉	—	2	4	no	—
367	C₂×D₄×C₇₉	—	2	4	no	—
368	C₂×D₄×C₇₉	—	4	16	no	—
369	C₂×D₄×C₇₉	—	4	8	no	—
370	C₂×D₄×C₇₉	—	4	4	no	—
371	C₂×D₄×C₇₉	—	4	16	no	—
372	C₂×D₄×C₇₉	—	4	8	no	—
373	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
374	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
375	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
376	C₂×D₄×C₇₉	C₂⁴	1	2	yes	—
377	C₂×D₄×C₇₉	C₂⁴	1	4	yes	—
378	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
379	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
380	C₂×D₄×C₇₉	C₂⁴	1	8	yes	—
381	C₂²×C₄×C₇₉	—	2	4	no	—
382	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
383	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
385	C₂²×C₄×C₇₉	C₂⁴	1	8	yes	—
386	C₂²×C₄×C₇₉	C₂⁴	1	4	yes	—
387	C₂²×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
388	C₄⋊C₄×C₇₉	C₂⁴	1	4	yes	—
389	C₄⋊C₄×C₇₉	C₂⁴	1	8	yes	—
390	C₂²⋊C₄×C₇₉	C₂⁴	1	4	yes	—
391	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
392	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
393	C₂²⋊C₄×C₇₉	C₂⁴	1	16	yes	—
394	C₂²⋊C₄×C₇₉	C₂⁴	1	8	yes	—
395	C₄²×C₇₉	C₂⁴	1	4	yes	—
396	C₂³×C₇₉	—	2	2	no	—
397	C₂³×C₇₉	—	2	4	no	—
398	C₂³×C₇₉	—	2	4	no	—
399	C₂³×C₇₉	—	2	4	no	—
400	C₂³×C₇₉	—	2	16	no	—
401	C₂³×C₇₉	—	4	8	no	—
402	C₂³×C₇₉	—	4	4	no	—
403	C₂³×C₇₉	—	4	8	no	—
404	C₂³×C₇₉	—	4	4	no	—
405	C₂³×C₇₉	—	4	4	no	—
406	C₂³×C₇₉	—	4	8	no	—
407	C₂³×C₇₉	—	8	16	no	—
408	C₂³×C₇₉	C₂⁵	1	4	yes	—
409	C₂³×C₇₉	C₂⁵	1	4	yes	—
410	C₂³×C₇₉	C₂⁵	1	4	yes	—
411	C₂³×C₇₉	C₂⁵	1	1	yes	characteristic
412	C₂³×C₇₉	C₂⁵	1	2	yes	—
413	C₂²×D₇₉	—	4	4	no	—
414	C₂²×D₇₉	—	4	8	no	—
415	C₂²×D₇₉	C₂⁵	1	4	yes	—
416	Q₈×C₇₉	—	2	4	no	—
417	D₄×C₇₉	—	2	8	no	—
418	D₄×C₇₉	—	2	16	no	—
419	D₄×C₇₉	—	2	8	no	—
420	D₄×C₇₉	—	2	4	no	—
421	D₄×C₇₉	—	2	8	no	—
422	D₄×C₇₉	—	4	8	no	—
423	D₄×C₇₉	—	4	8	no	—
424	D₄×C₇₉	—	4	16	no	—
425	C₂×C₄×C₇₉	—	2	2	no	—
426	C₂×C₄×C₇₉	—	2	8	no	—
427	C₂×C₄×C₇₉	—	2	8	no	—
428	C₂×C₄×C₇₉	—	4	8	no	—
429	C₂×C₄×C₇₉	—	4	4	no	—
430	C₂×C₄×C₇₉	H(5,𝔽₂)	1	4	yes	—
431	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
432	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
433	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
434	C₂×C₄×C₇₉	C₂⁵	1	2	yes	—
435	C₂²⋊D₇₉	—	2	8	no	—
436	C₂²⋊D₇₉	—	2	16	no	—
437	C₂²⋊D₇₉	—	4	8	no	—
438	C₂²⋊D₇₉	—	4	16	no	—
439	C₂²⋊D₇₉	—	4	8	no	—
440	C₂²⋊D₇₉	—	4	8	no	—
441	C₂×Dic₇₉	—	2	8	no	—
442	C₂×Dic₇₉	—	2	8	no	—
443	C₂×Dic₇₉	—	4	2	no	—
444	C₂×Dic₇₉	—	4	4	no	—
445	C₂×Dic₇₉	—	4	2	no	—
446	C₂×Dic₇₉	—	4	8	no	—
447	C₂×Dic₇₉	—	4	8	no	—
448	C₂×Dic₇₉	—	4	4	no	—
449	C₂×Dic₇₉	—	4	8	no	—
450	C₂×Dic₇₉	—	4	8	no	—
451	C₂×Dic₇₉	C₂⁵	1	4	yes	—
452	C₂×Dic₇₉	C₂⁵	1	4	yes	—
453	C₂×Dic₇₉	C₂⁵	1	8	yes	—
454	C₂×Dic₇₉	C₂⁵	1	8	yes	—
455	C₂×Dic₇₉	C₂⁵	1	4	yes	—
456	D₃₁₆	—	2	4	no	—
457	C₄×D₇₉	—	2	8	no	—
458	C₄×D₇₉	—	4	8	no	—
459	C₄×D₇₉	—	4	8	no	—
460	Dic₁₅₈	—	2	8	no	—
461	Dic₁₅₈	—	2	8	no	—
462	Dic₁₅₈	—	2	4	no	—
463	Dic₁₅₈	—	4	8	no	—
464	Dic₁₅₈	—	4	8	no	—
465	Dic₁₅₈	—	4	8	no	—
466	C₂²×C₇₉	—	2	8	no	—
467	C₂²×C₇₉	—	2	2	no	—
468	C₂²×C₇₉	—	2	2	no	—
469	C₂²×C₇₉	—	2	2	no	—
470	C₂²×C₇₉	—	2	4	no	—
471	C₂²×C₇₉	—	2	4	no	—
472	C₂²×C₇₉	—	2	4	no	—
473	C₂²×C₇₉	—	2	8	no	—
474	C₂²×C₇₉	—	2	8	no	—
475	C₂²×C₇₉	—	2	8	no	—
476	C₂²×C₇₉	—	8	4	no	—
477	C₂²×C₇₉	—	8	4	no	—
478	C₂²×C₇₉	—	8	16	no	—
479	C₂²×C₇₉	—	16	4	no	—
480	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	2	yes	—
481	C₂²×C₇₉	#585	1	4	yes	—
482	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
483	C₂×D₇₉	—	2	4	no	—
484	C₂×D₇₉	—	2	8	no	—
485	C₂×D₇₉	—	16	4	no	—
486	C₄×C₇₉	—	2	2	no	—
487	C₄×C₇₉	—	2	4	no	—
488	C₄×C₇₉	—	2	8	no	—
489	C₄×C₇₉	C₂×H(5,𝔽₂)	1	4	yes	—
490	Dic₇₉	—	2	4	no	—
491	Dic₇₉	—	2	8	no	—
492	Dic₇₉	—	2	8	no	—
493	Dic₇₉	—	2	4	no	—
494	Dic₇₉	—	2	4	no	—
495	#62824	—	79	1	no	maximal, Sylow
496	C₂×C₇₉	—	2	2	no	—
497	C₂×C₇₉	—	2	4	no	—
498	C₂×C₇₉	—	4	4	no	—
499	C₂×C₇₉	—	4	4	no	—
500	C₂×C₇₉	—	4	4	no	—
501	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
502	C₂×C₇₉	C₂×#585	1	2	yes	—
503	D₇₉	—	4	4	no	—
504	#3561	—	79	8	no	—
505	#3558	—	79	8	no	—
506	#3545	—	79	8	no	—
507	#3514	—	79	8	no	—
508	#3514	—	79	8	no	—
509	#3510	—	79	2	no	—
510	#3510	—	79	2	no	—
511	#3500	—	79	2	no	—
512	#3500	—	79	2	no	—
513	#3490	—	79	8	no	—
514	#3486	—	79	2	no	—
515	#3484	—	79	1	no	—
516	#3484	D₇₉	1	1	yes	characteristic, complemented
517	#3444	—	79	2	no	—
518	C₂²×#124	—	79	1	no	—
519	C₇₉	#62824	1	1	yes	characteristic, complemented, Sylow
520	C₂×2₋¹⁺⁴	—	79	2	no	—
521	C₂×H(5,𝔽₂)	—	79	1	no	—
522	C₂×H(5,𝔽₂)	C₂×D₇₉	1	1	yes	characteristic, complemented
523	C₂³×Q₈	—	79	1	no	—
524	C₂³×D₄	C₂×D₇₉	1	1	yes	characteristic
525	#563	—	79	8	no	—
526	#562	—	79	16	no	—
527	H(3,𝔽₄)	—	79	8	no	—
528	#559	—	79	8	no	—
529	#559	—	79	8	no	—
530	#556	—	79	8	no	—
531	#556	—	79	8	no	—
532	#555	—	79	16	no	—
533	#551	—	79	8	no	—
534	#551	—	79	16	no	—
535	#551	—	79	16	no	—
536	#551	—	79	8	no	—
537	#551	—	79	16	no	—
538	#551	—	79	16	no	—
539	D₄×Q₈	—	79	8	no	—
540	D₄×Q₈	—	79	8	no	—
541	#548	—	79	8	no	—
542	#548	—	79	8	no	—
543	#548	—	79	8	no	—
544	#548	—	79	8	no	—
545	#546	—	79	8	no	—
546	#546	—	79	16	no	—
547	#546	—	79	16	no	—
548	#546	—	79	8	no	—
549	#546	—	79	8	no	—
550	#546	—	79	16	no	—
551	#546	—	79	16	no	—
552	#546	C₂×D₇₉	1	8	yes	complemented
553	D₄²	—	79	8	no	—
554	D₄²	C₂×D₇₉	1	8	yes	complemented
555	#543	—	79	8	no	—
556	#542	—	79	16	no	—
557	#542	—	79	8	no	—
558	#542	—	79	16	no	—
559	#542	—	79	8	no	—
560	#538	—	79	16	no	—
561	#538	—	79	16	no	—
562	#538	—	79	16	no	—
563	#538	—	79	16	no	—
564	#536	—	79	2	no	—
565	#536	—	79	4	no	—
566	#536	—	79	4	no	—
567	#536	—	79	8	no	—
568	#536	—	79	2	no	—
569	#535	—	79	2	no	—
570	#535	—	79	4	no	—
571	#535	—	79	4	no	—
572	#535	C₂×D₇₉	1	2	yes	—
573	#534	—	79	4	no	—
574	#534	—	79	8	no	—
575	#534	C₂×D₇₉	1	4	yes	complemented
576	#533	—	79	4	no	—
577	#533	—	79	2	no	—
578	#532	—	79	2	no	—
579	#532	—	79	4	no	—
580	#532	—	79	4	no	—
581	#532	—	79	4	no	—
582	#529	—	79	8	no	—
583	#529	—	79	4	no	—
584	#529	—	79	4	no	—
585	#529	—	79	8	no	—
586	#529	—	79	8	no	—
587	#529	—	79	8	no	—
588	C₂×#124	—	79	2	no	—
589	C₂×#124	—	79	2	no	—
590	C₂×#124	—	79	8	no	—
591	C₂×#124	—	79	4	no	—
592	C₂×#124	—	79	8	no	—
593	C₂×#124	—	79	4	no	—
594	C₂×#124	—	79	4	no	—
595	#525	—	79	2	no	—
596	#525	—	79	8	no	—
597	#525	—	79	8	no	—
598	#525	C₂×D₇₉	1	2	yes	complemented
599	C₂×#120	—	79	4	no	—
600	C₂×#120	C₂×D₇₉	1	4	yes	complemented
601	#519	—	79	2	no	—
602	#518	—	79	1	no	—
603	#518	—	79	8	no	—
604	#518	—	79	8	no	—
605	#518	C₂×D₇₉	1	1	yes	characteristic, complemented
606	C₄×#41	—	79	2	no	—
607	C₄×#41	—	79	8	no	—
608	C₄×#41	—	79	2	no	—
609	C₂²×C₂²⋊C₄	—	79	4	no	—
610	C₂²×C₄²	—	79	1	no	—
611	C₂⁵	C₂²×D₇₉	1	2	yes	—
612	2₋¹⁺⁴	—	316	8	no	—
613	H(5,𝔽₂)	—	4	4	no	—
614	H(5,𝔽₂)	—	316	4	no	—
615	C₂×#41	—	79	8	no	—
616	C₂×#41	—	79	8	no	—
617	C₂×#41	—	79	4	no	—
618	C₂×#41	—	79	4	no	—
619	C₂×#41	—	79	4	no	—
620	C₂×#41	—	79	2	no	—
621	C₂×#41	C₂²×D₇₉	1	2	yes	—
622	C₂×#41	C₂²×D₇₉	1	4	yes	—
623	C₂²×Q₈	—	316	4	no	—
624	C₂²×Q₈	—	79	4	no	—
625	C₂²×Q₈	—	79	2	no	—
626	C₂²×Q₈	—	79	8	no	—
627	C₂²×Q₈	—	79	4	no	—
628	C₂²×Q₈	—	79	2	no	—
629	C₂²×D₄	—	4	4	no	—
630	C₂²×D₄	—	79	8	no	—
631	C₂²×D₄	—	79	4	no	—
632	C₂²×D₄	—	79	4	no	—
633	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
634	C₂²×D₄	C₂²×D₇₉	1	1	yes	characteristic
635	C₂²×D₄	C₂²×D₇₉	1	8	yes	—
636	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
637	C₂²×D₄	C₂²×D₇₉	1	2	yes	—
638	C₂²×D₄	C₂²×D₇₉	1	8	yes	—
639	C₂²×D₄	C₂²×D₇₉	1	4	yes	—
640	C₂³×C₄	—	79	2	no	—
641	C₂³×C₄	—	79	2	no	—
642	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
643	C₄⋊Q₈	—	79	2	no	—
644	C₄⋊Q₈	—	79	4	no	—
645	C₄⋊Q₈	—	79	4	no	—
646	C₄⋊Q₈	—	79	16	no	—
647	C₄⋊Q₈	—	79	4	no	—
648	#127	—	79	2	no	—
649	#127	—	79	4	no	—
650	#127	C₂²×D₇₉	1	4	yes	—
651	#126	—	79	8	no	—
652	#126	—	79	8	no	—
653	#126	—	79	16	no	—
654	#126	—	79	16	no	—
655	#126	—	79	16	no	—
656	#126	—	79	16	no	—
657	#125	—	79	4	no	—
658	#125	—	79	8	no	—
659	#124	—	79	2	no	—
660	#124	—	79	4	no	—
661	#124	—	79	4	no	—
662	#124	—	79	4	no	—
663	#124	—	79	4	no	—
664	#124	—	79	16	no	—
665	#124	—	79	8	no	—
666	#124	—	79	8	no	—
667	#124	—	79	8	no	—
668	#124	—	79	8	no	—
669	#124	—	79	2	no	—
670	#124	—	79	4	no	—
671	#124	—	79	4	no	—
672	#124	—	79	16	no	—
673	#124	—	79	16	no	—
674	#124	—	79	16	no	—
675	#124	—	79	8	no	—
676	#124	—	79	16	no	—
677	#124	—	79	16	no	—
678	#124	—	79	4	no	—
679	#124	C₂²×D₇₉	1	4	yes	—
680	#123	—	79	8	no	—
681	#123	—	79	8	no	—
682	#123	—	79	16	no	—
683	#123	—	79	16	no	—
684	#123	—	79	8	no	—
685	#123	—	79	16	no	—
686	#123	—	79	4	no	—
687	#123	—	79	16	no	—
688	#123	—	79	8	no	—
689	#123	—	79	8	no	—
690	#123	—	79	16	no	—
691	#123	—	79	16	no	—
692	#123	C₂²×D₇₉	1	4	yes	—
693	#123	C₂²×D₇₉	1	8	yes	—
694	C₂²⋊Q₈	—	79	4	no	—
695	C₂²⋊Q₈	—	79	8	no	—
696	C₂²⋊Q₈	—	79	16	no	—
697	C₂²⋊Q₈	—	79	16	no	—
698	C₂²⋊Q₈	—	79	8	no	—
699	C₂²⋊Q₈	—	79	16	no	—
700	C₂²⋊Q₈	—	79	8	no	—
701	C₂²⋊Q₈	—	79	8	no	—
702	C₂²⋊Q₈	—	79	16	no	—
703	C₂²⋊Q₈	—	79	16	no	—
704	C₂²⋊Q₈	—	79	16	no	—
705	C₂²⋊Q₈	—	79	16	no	—
706	C₂²⋊Q₈	C₂²×D₇₉	1	4	yes	—
707	#121	—	79	8	no	—
708	#121	—	79	8	no	—
709	#121	—	79	16	no	—
710	#121	—	79	8	no	—
711	#121	—	79	16	no	—
712	#121	—	79	16	no	—
713	#121	—	79	16	no	—
714	#121	—	79	16	no	—
715	#121	—	79	16	no	—
716	#121	—	79	4	no	—
717	#121	C₂²×D₇₉	1	4	yes	—
718	#121	C₂²×D₇₉	1	8	yes	—
719	#121	C₂²×D₇₉	1	16	yes	—
720	#120	—	79	4	no	—
721	#120	—	79	8	no	—
722	#120	—	79	16	no	—
723	#120	—	79	16	no	—
724	#120	—	79	16	no	—
725	#120	—	79	8	no	—
726	#120	C₂²×D₇₉	1	4	yes	—
727	#120	C₂²×D₇₉	1	8	yes	—
728	#120	C₂²×D₇₉	1	16	yes	—
729	#120	C₂²×D₇₉	1	8	yes	—
730	C₄×Q₈	—	79	4	no	—
731	C₄×Q₈	—	79	8	no	—
732	C₄×Q₈	—	79	4	no	—
733	C₄×Q₈	—	79	8	no	—
734	C₄×Q₈	—	79	8	no	—
735	C₄×Q₈	—	79	8	no	—
736	C₄×D₄	—	79	8	no	—
737	C₄×D₄	—	79	8	no	—
738	C₄×D₄	—	79	4	no	—
739	C₄×D₄	—	79	16	no	—
740	C₄×D₄	—	79	16	no	—
741	C₄×D₄	—	79	8	no	—
742	C₄×D₄	—	79	16	no	—
743	C₄×D₄	—	79	8	no	—
744	C₄×D₄	—	79	8	no	—
745	C₄×D₄	—	79	16	no	—
746	C₄×D₄	—	79	16	no	—
747	C₄×D₄	—	79	4	no	—
748	C₄×D₄	—	79	8	no	—
749	C₄×D₄	—	79	8	no	—
750	C₄×D₄	—	79	8	no	—
751	C₄×D₄	—	79	16	no	—
752	C₄×D₄	C₂²×D₇₉	1	8	yes	—
753	C₄×D₄	C₂²×D₇₉	1	8	yes	—
754	#117	—	79	2	no	—
755	#117	—	79	4	no	—
756	#117	—	79	16	no	—
757	#117	—	79	8	no	—
758	#117	—	79	8	no	—
759	#117	—	79	8	no	—
760	#117	—	79	16	no	—
761	#117	—	79	8	no	—
762	#117	—	79	4	no	—
763	#117	C₂²×D₇₉	1	2	yes	—
764	C₂×C₂²⋊C₄	—	79	8	no	—
765	C₂×C₂²⋊C₄	—	79	8	no	—
766	C₂×C₂²⋊C₄	—	79	8	no	—
767	C₂×C₂²⋊C₄	—	79	8	no	—
768	C₂×C₂²⋊C₄	—	79	16	no	—
769	C₂×C₂²⋊C₄	—	79	4	no	—
770	C₂×C₂²⋊C₄	—	79	8	no	—
771	C₂×C₂²⋊C₄	—	79	16	no	—
772	C₂×C₂²⋊C₄	—	79	16	no	—
773	C₂×C₂²⋊C₄	C₂²×D₇₉	1	8	yes	—
774	C₂×C₂²⋊C₄	C₂²×D₇₉	1	4	yes	—
775	C₂×C₄²	—	79	4	no	—
776	C₂×C₄²	—	79	4	no	—
777	C₂×C₄²	—	79	2	no	—
778	C₂×C₄²	—	79	2	no	—
779	C₂×C₄²	—	79	4	no	—
780	C₂×C₄²	—	79	4	no	—
781	C₂⁴	—	4	4	no	—
782	C₂⁴	—	4	8	no	—
783	C₂⁴	—	79	4	no	—
784	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
785	C₂⁴	C₂³×D₇₉	1	2	yes	—
786	C₂⁴	C₂³×D₇₉	1	8	yes	—
787	C₂⁴	C₂³×D₇₉	1	2	yes	—
788	C₂⁴	C₂³×D₇₉	1	4	yes	—
789	#41	—	2	8	no	—
790	#41	—	4	8	no	—
791	#41	—	316	8	no	—
792	#41	—	316	8	no	—
793	#41	—	316	8	no	—
794	#41	—	316	16	no	—
795	#41	—	316	16	no	—
796	#41	—	158	8	no	—
797	C₂×Q₈	—	316	16	no	—
798	C₂×Q₈	—	316	8	no	—
799	C₂×Q₈	—	316	4	no	—
800	C₂×Q₈	—	316	8	no	—
801	C₂×Q₈	—	79	8	no	—
802	C₂×Q₈	—	79	8	no	—
803	C₂×Q₈	—	79	8	no	—
804	C₂×Q₈	—	79	4	no	—
805	C₂×Q₈	—	79	4	no	—
806	C₂×Q₈	—	79	2	no	—
807	C₂×Q₈	—	158	8	no	—
808	C₂×Q₈	C₂³×D₇₉	1	2	yes	—
809	C₂×D₄	—	2	4	no	—
810	C₂×D₄	—	2	4	no	—
811	C₂×D₄	—	4	16	no	—
812	C₂×D₄	—	4	8	no	—
813	C₂×D₄	—	4	4	no	—
814	C₂×D₄	—	4	8	no	—
815	C₂×D₄	—	4	16	no	—
816	C₂×D₄	—	316	16	no	—
817	C₂×D₄	—	316	8	no	—
818	C₂×D₄	—	316	8	no	—
819	C₂×D₄	—	79	8	no	—
820	C₂×D₄	—	79	16	no	—
821	C₂×D₄	—	79	8	no	—
822	C₂×D₄	—	79	8	no	—
823	C₂×D₄	—	79	8	no	—
824	C₂×D₄	—	79	4	no	—
825	C₂×D₄	—	79	2	no	—
826	C₂×D₄	C₂³×D₇₉	1	8	yes	—
827	C₂×D₄	C₂³×D₇₉	1	4	yes	—
828	C₂×D₄	C₂³×D₇₉	1	4	yes	—
829	C₂×D₄	C₂³×D₇₉	1	2	yes	—
830	C₂×D₄	C₂³×D₇₉	1	4	yes	—
831	C₂×D₄	C₂³×D₇₉	1	16	yes	—
832	C₂×D₄	C₂³×D₇₉	1	8	yes	—
833	C₂×D₄	C₂³×D₇₉	1	8	yes	—
834	C₂²×C₄	—	2	4	no	—
835	C₂²×C₄	—	316	4	no	—
836	C₂²×C₄	—	316	4	no	—
837	C₂²×C₄	—	79	2	no	—
838	C₂²×C₄	—	79	4	no	—
839	C₂²×C₄	—	79	2	no	—
840	C₂²×C₄	—	79	8	no	—
841	C₂²×C₄	—	79	8	no	—
842	C₂²×C₄	—	79	8	no	—
843	C₂²×C₄	—	79	8	no	—
844	C₂²×C₄	—	79	4	no	—
845	C₂²×C₄	—	79	8	no	—
846	C₂²×C₄	—	79	8	no	—
847	C₂²×C₄	—	79	4	no	—
848	C₂²×C₄	—	79	4	no	—
849	C₂²×C₄	—	79	4	no	—
850	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
851	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
852	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
853	C₂²×C₄	C₂³×D₇₉	1	8	yes	—
854	C₂²×C₄	C₂³×D₇₉	1	4	yes	—
855	C₂²×C₄	C₂³×D₇₉	1	1	yes	characteristic
856	C₄⋊C₄	—	79	8	no	—
857	C₄⋊C₄	—	79	16	no	—
858	C₄⋊C₄	—	79	8	no	—
859	C₄⋊C₄	—	79	8	no	—
860	C₄⋊C₄	—	79	8	no	—
861	C₄⋊C₄	—	79	8	no	—
862	C₄⋊C₄	—	79	16	no	—
863	C₄⋊C₄	—	79	8	no	—
864	C₄⋊C₄	—	79	4	no	—
865	C₄⋊C₄	—	79	16	no	—
866	C₄⋊C₄	—	79	8	no	—
867	C₄⋊C₄	C₂³×D₇₉	1	8	yes	—
868	C₄⋊C₄	C₂³×D₇₉	1	4	yes	—
869	C₂²⋊C₄	—	79	16	no	—
870	C₂²⋊C₄	—	79	16	no	—
871	C₂²⋊C₄	—	79	16	no	—
872	C₂²⋊C₄	—	79	16	no	—
873	C₂²⋊C₄	—	79	4	no	—
874	C₂²⋊C₄	—	79	8	no	—
875	C₂²⋊C₄	—	79	8	no	—
876	C₂²⋊C₄	—	79	16	no	—
877	C₂²⋊C₄	—	79	8	no	—
878	C₂²⋊C₄	—	79	16	no	—
879	C₂²⋊C₄	—	79	8	no	—
880	C₂²⋊C₄	—	79	8	no	—
881	C₂²⋊C₄	—	79	16	no	—
882	C₂²⋊C₄	—	79	8	no	—
883	C₂²⋊C₄	—	79	8	no	—
884	C₂²⋊C₄	C₂³×D₇₉	1	16	yes	—
885	C₂²⋊C₄	C₂³×D₇₉	1	4	yes	—
886	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
887	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
888	C₂²⋊C₄	C₂³×D₇₉	1	8	yes	—
889	C₄²	—	79	2	no	—
890	C₄²	—	79	2	no	—
891	C₄²	—	79	2	no	—
892	C₄²	—	79	4	no	—
893	C₄²	—	79	4	no	—
894	C₄²	—	79	2	no	—
895	C₄²	—	79	8	no	—
896	C₄²	—	79	8	no	—
897	C₄²	—	79	4	no	—
898	C₄²	—	79	16	no	—
899	C₄²	C₂³×D₇₉	1	4	yes	—
900	C₂³	—	2	2	no	—
901	C₂³	—	2	4	no	—
902	C₂³	—	2	4	no	—
903	C₂³	—	2	4	no	—
904	C₂³	—	2	16	no	—
905	C₂³	—	4	8	no	—
906	C₂³	—	4	4	no	—
907	C₂³	—	4	8	no	—
908	C₂³	—	4	4	no	—
909	C₂³	—	4	4	no	—
910	C₂³	—	4	8	no	—
911	C₂³	—	8	16	no	—
912	C₂³	—	316	4	no	—
913	C₂³	—	316	8	no	—
914	C₂³	—	79	4	no	—
915	C₂³	C₂⁴×D₇₉	1	4	yes	—
916	C₂³	C₂⁴×D₇₉	1	4	yes	—
917	C₂³	C₂⁴×D₇₉	1	4	yes	—
918	C₂³	C₂⁴×D₇₉	1	1	yes	characteristic
919	C₂³	C₂⁴×D₇₉	1	2	yes	—
920	Q₈	—	2	4	no	—
921	Q₈	—	316	8	no	—
922	Q₈	—	316	8	no	—
923	Q₈	—	316	8	no	—
924	Q₈	—	158	8	no	—
925	Q₈	—	158	8	no	—
926	Q₈	—	158	4	no	—
927	D₄	—	2	8	no	—
928	D₄	—	2	16	no	—
929	D₄	—	2	8	no	—
930	D₄	—	2	8	no	—
931	D₄	—	2	4	no	—
932	D₄	—	4	8	no	—
933	D₄	—	4	8	no	—
934	D₄	—	4	16	no	—
935	D₄	—	316	8	no	—
936	D₄	—	316	16	no	—
937	D₄	—	316	8	no	—
938	D₄	—	316	8	no	—
939	D₄	—	158	8	no	—
940	D₄	—	158	16	no	—
941	D₄	—	158	4	no	—
942	C₂×C₄	—	2	2	no	—
943	C₂×C₄	—	2	8	no	—
944	C₂×C₄	—	2	8	no	—
945	C₂×C₄	—	4	8	no	—
946	C₂×C₄	—	4	4	no	—
947	C₂×C₄	—	316	8	no	—
948	C₂×C₄	—	316	8	no	—
949	C₂×C₄	—	316	8	no	—
950	C₂×C₄	—	316	2	no	—
951	C₂×C₄	—	316	4	no	—
952	C₂×C₄	—	316	2	no	—
953	C₂×C₄	—	316	4	no	—
954	C₂×C₄	—	316	8	no	—
955	C₂×C₄	—	316	8	no	—
956	C₂×C₄	—	316	8	no	—
957	C₂×C₄	—	79	4	no	—
958	C₂×C₄	—	79	4	no	—
959	C₂×C₄	—	79	8	no	—
960	C₂×C₄	—	79	8	no	—
961	C₂×C₄	—	79	4	no	—
962	C₂×C₄	—	158	8	no	—
963	C₂×C₄	—	158	8	no	—
964	C₂×C₄	—	158	8	no	—
965	C₂×C₄	#14579206	1	4	yes	—
966	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
967	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
968	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
969	C₂×C₄	C₂⁴×D₇₉	1	2	yes	—
970	C₂²	—	2	8	no	—
971	C₂²	—	2	2	no	—
972	C₂²	—	2	2	no	—
973	C₂²	—	2	2	no	—
974	C₂²	—	2	4	no	—
975	C₂²	—	2	4	no	—
976	C₂²	—	2	4	no	—
977	C₂²	—	2	8	no	—
978	C₂²	—	2	8	no	—
979	C₂²	—	2	8	no	—
980	C₂²	—	8	4	no	—
981	C₂²	—	8	4	no	—
982	C₂²	—	8	16	no	—
983	C₂²	—	16	4	no	—
984	C₂²	—	158	4	no	—
985	C₂²	—	158	8	no	—
986	C₂²	—	1264	4	no	—
987	C₂²	C₂×#14579206	1	2	yes	—
988	C₂²	#19099398	1	4	yes	—
989	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
990	C₄	—	2	2	no	—
991	C₄	—	2	4	no	—
992	C₄	—	2	8	no	—
993	C₄	—	158	4	no	—
994	C₄	—	158	8	no	—
995	C₄	—	158	4	no	—
996	C₄	—	158	8	no	—
997	C₄	—	158	4	no	—
998	C₄	C₂×#14579206	1	4	yes	—
999	C₂	—	2	2	no	—
1000	C₂	—	2	4	no	—
1001	C₂	—	4	4	no	—
1002	C₂	—	4	4	no	—
1003	C₂	—	4	4	no	—
1004	C₂	—	316	4	no	—
1005	C₂	C₂²×#14579206	1	1	yes	characteristic
1006	C₂	C₂×#19099398	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₇₉
commutator, socle, cosocle	C₂²×C₇₉	C₂⁶
Fitting	C₇₉×#3484	C₂
hypercenter	#3484	D₇₉
hypocenter	C₇₉	#62824
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ #3484

Complements

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

N	H ≅ G/N	type
1. #23777959	C₂	semidirect
2. #23777914	C₂	semidirect
3. #23777749	C₂	semidirect
4. #23777358	C₂	semidirect
5. #23777352	C₂	semidirect
6. #23777295	C₂	semidirect
7. #23777291	C₂	semidirect
8. #23777192	C₂	semidirect
9. #23777188	C₂	semidirect
10. #23777087	C₂	semidirect
11. #23777047	C₂	semidirect
12. #23777035	C₂	semidirect
13. #23776692	C₂	semidirect
14. C₂²×#14579148	C₂	semidirect
15. C₇₉×#3484	C₂	semidirect
16. C₂×#14579208	C₂²	semidirect
17. C₂×#14579206	C₂²	semidirect
18. C₂³×Dic₁₅₈	C₂²	semidirect
19. #19099316	C₂²	semidirect
20. #19099308	C₂²	semidirect
21. #19099306	C₂²	semidirect
22. #19099299	C₂²	semidirect
23. #19099296	C₂²	semidirect
24. #19099283	C₂²	semidirect
25. #19099282	C₂²	semidirect
26. #19099277	C₂²	semidirect
27. #19099244	C₂²	semidirect
28. #19099244	C₂²	semidirect
29. #19099244	C₂²	semidirect
30. #19099241	C₂²	semidirect
31. #19099239	C₂²	semidirect
32. #19099239	C₂²	semidirect
33. D₄×Dic₁₅₈	C₂²	semidirect
34. #19099226	C₂²	semidirect
35. #19099222	C₂²	semidirect
36. #19099220	C₂²	semidirect
37. #19099219	C₂²	semidirect
38. #19099219	C₂²	semidirect
39. #19099210	C₂²	semidirect
40. #19099207	C₂²	semidirect
41. #19099207	C₂²	semidirect
42. #19099207	C₂²	semidirect
43. #19099207	C₂²	semidirect
44. #19099200	C₂²	semidirect
45. #19099200	C₂²	semidirect
46. D₄×C₂²⋊D₇₉	C₂²	semidirect
47. #19099189	C₂²	semidirect
48. #19099181	C₂²	semidirect
49. #19099180	C₂²	semidirect
50. #19099180	C₂²	semidirect
51. #19099178	C₂²	semidirect
52. #19099148	C₂²	semidirect
53. #19099148	C₂²	semidirect
54. #19099148	C₂²	semidirect
55. #19099145	C₂²	semidirect
56. #19099139	C₂²	semidirect
57. #19099135	C₂²	semidirect
58. #19099134	C₂²	semidirect
59. #19099134	C₂²	semidirect
60. #19099133	C₂²	semidirect
62. #19099130	C₂²	semidirect
63. #19099126	C₂²	semidirect
64. #19099122	C₂²	semidirect
65. #19099122	C₂²	semidirect
66. #19099116	C₂²	semidirect
67. #19099115	C₂²	semidirect
68. #19099111	C₂²	semidirect
69. #19099109	C₂²	semidirect
70. #19099109	C₂²	semidirect
71. #19099108	C₂²	semidirect
72. #19099099	C₂²	semidirect
73. #19099095	C₂²	semidirect
74. #19099094	C₂²	semidirect
75. #19099094	C₂²	semidirect
76. #19099093	C₂²	semidirect
77. #19099090	C₂²	semidirect
78. C₂×#14579148	C₂²	semidirect
79. C₂×#14579148	C₂²	semidirect
80. C₂×#14579148	C₂²	semidirect
81. C₂×#14579148	C₂²	semidirect
82. C₂×#14579148	C₂²	semidirect
83. C₂×#14579148	C₂²	semidirect
84. #124×D₇₉	C₂²	semidirect
85. #19099074	C₂²	semidirect
86. #19099069	C₂²	semidirect
87. #19099069	C₂²	semidirect
88. C₂×#14579130	C₂²	semidirect
89. #19099040	C₂²	semidirect
90. #19099038	C₂²	semidirect
91. #19099038	C₂²	semidirect
92. #19099036	C₂²	semidirect
93. #41×Dic₇₉	C₂²	semidirect
94. #19099031	C₂²	semidirect
95. C₄×#11929623	C₂²	semidirect
96. C₂²×C₂²⋊Dic₇₉	C₂²	semidirect
97. C₂²×C₄×Dic₇₉	C₂²	semidirect
98. C₂×H(5,𝔽₂)×C₇₉	C₂²	semidirect
100. #546×C₇₉	C₂²	semidirect
101. D₄²×C₇₉	C₂²	semidirect
103. #534×C₇₉	C₂²	semidirect
104. #525×C₇₉	C₂²	semidirect
105. C₂×#120×C₇₉	C₂²	semidirect
106. #518×C₇₉	C₂²	semidirect
110. C₂×#11929624	C₂³	semidirect
114. C₂×#11929623	C₂³	semidirect
119. C₂²×Dic₁₅₈	C₂³	semidirect
120. C₂×Q₈×D₇₉	C₂³	semidirect
126. #14579161	C₂³	semidirect
127. #14579160	C₂³	semidirect
128. #14579160	C₂³	semidirect
129. #14579159	C₂³	semidirect
130. #14579159	C₂³	semidirect
132. #14579157	C₂³	semidirect
133. #14579156	C₂³	semidirect
134. #14579154	C₂³	semidirect
135. #14579154	C₂³	semidirect
136. #14579154	C₂³	semidirect
137. #14579154	C₂³	semidirect
138. #14579154	C₂³	semidirect
139. #14579152	C₂³	semidirect
140. #14579151	C₂³	semidirect
141. #14579150	C₂³	semidirect
142. #14579149	C₂³	semidirect
153. #14579148	C₂³	semidirect
154. #14579148	C₂³	semidirect
155. #14579148	C₂³	semidirect
156. #14579148	C₂³	semidirect
157. #14579147	C₂³	semidirect
158. #14579147	C₂³	semidirect
159. #14579147	C₂³	semidirect
160. #14579147	C₂³	semidirect
164. #14579144	C₂³	semidirect
165. #14579143	C₂³	semidirect
166. #14579143	C₂³	semidirect
170. #14579142	C₂³	semidirect
171. #14579142	C₂³	semidirect
172. #14579142	C₂³	semidirect
173. #14579141	C₂³	semidirect
175. #14579140	C₂³	semidirect
176. #14579140	C₂³	semidirect
177. #14579140	C₂³	semidirect
178. #14579139	C₂³	semidirect
182. #14579138	C₂³	semidirect
183. #14579138	C₂³	semidirect
184. #14579138	C₂³	semidirect
190. #14579133	C₂³	semidirect
191. #14579133	C₂³	semidirect
193. #14579132	C₂³	semidirect
194. #14579132	C₂³	semidirect
198. #14579130	C₂³	semidirect
200. #14579129	C₂³	semidirect
201. Q₈×Dic₇₉	C₂³	semidirect
202. C₄×Dic₁₅₈	C₂³	semidirect
203. C₄×Dic₁₅₈	C₂³	semidirect
204. #14579126	C₂³	semidirect
205. #14579126	C₂³	semidirect
206. #14579126	C₂³	semidirect
211. D₄×Dic₇₉	C₂³	semidirect
212. D₄×Dic₇₉	C₂³	semidirect
213. D₄×Dic₇₉	C₂³	semidirect
214. #14579123	C₂³	semidirect
216. C₄×C₂²⋊D₇₉	C₂³	semidirect
217. C₄×C₂²⋊D₇₉	C₂³	semidirect
218. C₄×C₂²⋊D₇₉	C₂³	semidirect
222. (C₂²⋊D₇₉)⋊C₄	C₂³	semidirect
224. #14579120	C₂³	semidirect
225. #14579120	C₂³	semidirect
226. #14579119	C₂³	semidirect
227. #14579118	C₂³	semidirect
230. #14579117	C₂³	semidirect
231. #14579117	C₂³	semidirect
239. C₂×C₂²⋊Dic₇₉	C₂³	semidirect
240. C₂²⋊C₄×D₇₉	C₂³	semidirect
245. C₂×C₄×Dic₇₉	C₂³	semidirect
246. C₄²×D₇₉	C₂³	semidirect
516. #3484	D₇₉	semidirect
519. C₇₉	#62824	semidirect
522. C₂×H(5,𝔽₂)	C₂×D₇₉	semidirect
552. #546	C₂×D₇₉	semidirect
554. D₄²	C₂×D₇₉	semidirect
575. #534	C₂×D₇₉	semidirect
598. #525	C₂×D₇₉	semidirect
600. C₂×#120	C₂×D₇₉	semidirect
605. #518	C₂×D₇₉	semidirect

Maximal subgroups

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

subgroup	index
#23777959	2
#23777914	2
#23777749	2
#23777358	2
#23777352	2
#23777295	2
#23777291	2
#23777192	2
#23777188	2
#23777087	2
#23777047	2
#23777035	2
#23776692	2
C₂²×#14579148	2
C₇₉×#3484	2
#62824	79