Subgroups — C₇₃×#25783 #32935187

Order 18688.

1774 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×SD₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#496×C₇₃	C₂	1	2	yes	maximal, complemented
3	C₂×#466×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#448×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#447×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2436	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2433	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2014	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2012	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1973	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1752	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₇₃	—	2	8	no	—
15	C₂²×SD₁₆×C₇₃	—	2	4	no	—
16	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
17	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
18	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	complemented
19	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
20	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
21	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×#127×C₇₃	C₂²	1	2	yes	—
23	C₂×#124×C₇₃	C₂²	1	2	yes	complemented
24	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#120×C₇₃	—	2	2	no	—
27	#496×C₇₃	—	2	8	no	—
28	#466×C₇₃	—	2	4	no	—
29	#448×C₇₃	—	2	4	no	—
30	#447×C₇₃	—	2	4	no	—
31	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×#103×C₇₃	C₂²	1	2	yes	complemented
33	C₂×#102×C₇₃	C₂²	1	2	yes	—
34	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
37	C₂×#97×C₇₃	C₂²	1	2	yes	complemented
38	#393×C₇₃	—	2	2	no	—
39	#392×C₇₃	—	2	2	no	—
40	#391×C₇₃	C₂²	1	2	yes	complemented
41	#390×C₇₃	C₂²	1	2	yes	—
42	#386×C₇₃	—	2	2	no	—
43	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
44	#336×C₇₃	C₂²	1	2	yes	complemented
45	C₂⁵×C₇₃	—	2	1	no	—
46	C₂²×Q₈×C₇₃	—	2	1	no	—
47	C₂²×Q₈×C₇₃	—	2	4	no	—
48	C₂²×Q₈×C₇₃	—	2	2	no	—
49	C₂²×Q₈×C₇₃	—	2	2	no	—
50	C₂²×Q₈×C₇₃	—	4	2	no	—
51	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
52	C₂²×D₄×C₇₃	—	2	4	no	—
53	C₂²×D₄×C₇₃	—	2	1	no	—
54	C₂²×D₄×C₇₃	—	2	1	no	—
55	C₂²×D₄×C₇₃	—	2	2	no	—
56	C₂²×D₄×C₇₃	—	2	2	no	—
57	C₂²×D₄×C₇₃	—	2	1	no	—
58	C₂²×D₄×C₇₃	—	2	4	no	—
59	C₂²×D₄×C₇₃	—	4	2	no	—
60	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₇₃	—	2	1	no	—
64	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
65	C₂×SD₁₆×C₇₃	—	2	32	no	—
66	C₂×SD₁₆×C₇₃	—	2	4	no	—
67	C₂×SD₁₆×C₇₃	—	2	4	no	—
68	C₂×SD₁₆×C₇₃	—	2	4	no	—
69	C₂×SD₁₆×C₇₃	—	2	4	no	—
70	C₂×SD₁₆×C₇₃	—	2	4	no	—
71	C₂×SD₁₆×C₇₃	—	2	4	no	—
72	C₂×SD₁₆×C₇₃	—	2	4	no	—
73	C₂×SD₁₆×C₇₃	—	4	2	no	—
74	C₂×SD₁₆×C₇₃	D₄	1	8	yes	complemented
75	C₂×D₈×C₇₃	—	2	4	no	—
76	C₂×D₈×C₇₃	—	2	4	no	—
77	C₂×D₈×C₇₃	—	2	2	no	—
78	C₂×D₈×C₇₃	—	2	4	no	—
79	C₂×D₈×C₇₃	—	4	2	no	—
80	C₂²×C₈×C₇₃	—	2	4	no	—
81	C₂²×C₈×C₇₃	D₄	1	4	yes	complemented
82	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
83	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
85	#127×C₇₃	—	2	4	no	—
86	#127×C₇₃	—	4	2	no	—
87	#124×C₇₃	—	2	4	no	—
88	#124×C₇₃	—	4	2	no	—
89	#121×C₇₃	—	2	2	no	—
90	#121×C₇₃	—	2	2	no	—
91	#121×C₇₃	—	2	2	no	—
92	#121×C₇₃	—	2	2	no	—
93	#120×C₇₃	—	4	8	no	—
94	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
97	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
98	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
101	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
102	#107×C₇₃	—	2	2	no	—
103	#103×C₇₃	—	2	4	no	—
104	#102×C₇₃	—	2	4	no	—
105	#102×C₇₃	—	2	2	no	—
106	#102×C₇₃	—	2	2	no	—
107	C₂²⋊C₈×C₇₃	D₄	1	4	yes	complemented
108	#97×C₇₃	—	2	4	no	—
109	#95×C₇₃	—	2	4	no	—
110	#95×C₇₃	D₄	1	2	yes	—
111	C₂⁴×C₇₃	—	2	2	no	—
112	C₂⁴×C₇₃	—	2	1	no	—
113	C₂⁴×C₇₃	—	2	1	no	—
114	C₂⁴×C₇₃	—	4	4	no	—
115	C₂⁴×C₇₃	—	4	2	no	—
116	C₂⁴×C₇₃	—	4	4	no	—
117	C₂⁴×C₇₃	—	8	2	no	—
118	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
119	C₂×Q₈×C₇₃	—	2	2	no	—
120	C₂×Q₈×C₇₃	—	2	8	no	—
121	C₂×Q₈×C₇₃	—	2	2	no	—
122	C₂×Q₈×C₇₃	—	2	2	no	—
123	C₂×Q₈×C₇₃	—	2	2	no	—
124	C₂×Q₈×C₇₃	—	2	2	no	—
125	C₂×Q₈×C₇₃	—	4	4	no	—
126	C₂×Q₈×C₇₃	—	4	8	no	—
127	C₂×Q₈×C₇₃	—	4	4	no	—
128	C₂×Q₈×C₇₃	—	4	2	no	—
129	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
130	C₂×D₄×C₇₃	—	2	8	no	—
131	C₂×D₄×C₇₃	—	2	2	no	—
132	C₂×D₄×C₇₃	—	2	2	no	—
133	C₂×D₄×C₇₃	—	2	2	no	—
134	C₂×D₄×C₇₃	—	2	1	no	—
135	C₂×D₄×C₇₃	—	2	1	no	—
136	C₂×D₄×C₇₃	—	2	1	no	—
137	C₂×D₄×C₇₃	—	2	1	no	—
138	C₂×D₄×C₇₃	—	2	2	no	—
139	C₂×D₄×C₇₃	—	2	2	no	—
140	C₂×D₄×C₇₃	—	2	2	no	—
141	C₂×D₄×C₇₃	—	2	2	no	—
142	C₂×D₄×C₇₃	—	2	2	no	—
143	C₂×D₄×C₇₃	—	2	2	no	—
144	C₂×D₄×C₇₃	—	4	8	no	—
145	C₂×D₄×C₇₃	—	4	4	no	—
146	C₂×D₄×C₇₃	—	4	4	no	—
147	C₂×D₄×C₇₃	—	4	8	no	—
148	C₂×D₄×C₇₃	—	4	8	no	—
149	C₂×D₄×C₇₃	—	4	2	no	—
150	C₂×D₄×C₇₃	—	4	2	no	—
151	C₂×D₄×C₇₃	—	4	4	no	—
152	C₂×D₄×C₇₃	—	4	4	no	—
153	C₂×D₄×C₇₃	—	4	2	no	—
154	C₂×D₄×C₇₃	—	8	4	no	—
155	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
156	C₂²×C₄×C₇₃	—	2	2	no	—
157	C₂²×C₄×C₇₃	—	2	2	no	—
158	C₂²×C₄×C₇₃	—	2	2	no	—
159	C₂²×C₄×C₇₃	—	2	1	no	—
160	C₂²×C₄×C₇₃	—	2	1	no	—
161	C₂²×C₄×C₇₃	—	4	4	no	—
162	C₂²×C₄×C₇₃	—	4	2	no	—
163	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
164	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
168	SD₁₆×C₇₃	—	2	16	no	—
169	SD₁₆×C₇₃	—	2	16	no	—
170	SD₁₆×C₇₃	—	4	8	no	—
171	D₈×C₇₃	—	4	8	no	—
172	D₈×C₇₃	—	4	4	no	—
173	C₂×C₈×C₇₃	—	2	2	no	—
174	C₂×C₈×C₇₃	—	2	2	no	—
175	C₂×C₈×C₇₃	—	2	2	no	—
176	C₂×C₈×C₇₃	—	2	8	no	—
177	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
178	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
179	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
180	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
181	C₄⋊C₄×C₇₃	—	2	1	no	—
182	C₄⋊C₄×C₇₃	—	2	1	no	—
183	C₄⋊C₄×C₇₃	—	2	1	no	—
184	C₄⋊C₄×C₇₃	—	2	1	no	—
185	C₂²⋊C₄×C₇₃	—	2	4	no	—
186	C₂²⋊C₄×C₇₃	—	4	8	no	—
187	C₂²⋊C₄×C₇₃	—	4	8	no	—
188	C₂²⋊C₄×C₇₃	—	4	2	no	—
189	C₂²⋊C₄×C₇₃	—	4	2	no	—
190	C₄²×C₇₃	—	2	2	no	—
191	C₄²×C₇₃	—	2	2	no	—
192	C₂³×C₇₃	—	2	2	no	—
193	C₂³×C₇₃	—	2	2	no	—
194	C₂³×C₇₃	—	2	4	no	—
195	C₂³×C₇₃	—	4	8	no	—
196	C₂³×C₇₃	—	4	2	no	—
197	C₂³×C₇₃	—	4	2	no	—
198	C₂³×C₇₃	—	4	4	no	—
199	C₂³×C₇₃	—	4	4	no	—
200	C₂³×C₇₃	—	4	1	no	—
201	C₂³×C₇₃	—	4	1	no	—
202	C₂³×C₇₃	—	4	2	no	—
203	C₂³×C₇₃	—	4	2	no	—
204	C₂³×C₇₃	—	4	2	no	—
205	C₂³×C₇₃	—	4	2	no	—
206	C₂³×C₇₃	—	4	2	no	—
207	C₂³×C₇₃	—	4	2	no	—
208	C₂³×C₇₃	—	8	16	no	—
209	C₂³×C₇₃	—	8	4	no	—
210	C₂³×C₇₃	—	8	4	no	—
211	C₂³×C₇₃	#127	1	2	yes	—
212	C₂³×C₇₃	AGL(1,ℤ/8)	1	4	yes	—
213	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
214	Q₈×C₇₃	—	2	4	no	—
215	Q₈×C₇₃	—	2	4	no	—
216	Q₈×C₇₃	—	4	8	no	—
217	Q₈×C₇₃	—	4	2	no	—
218	Q₈×C₇₃	—	4	2	no	—
219	D₄×C₇₃	—	2	4	no	—
220	D₄×C₇₃	—	2	4	no	—
221	D₄×C₇₃	—	4	8	no	—
222	D₄×C₇₃	—	4	1	no	—
223	D₄×C₇₃	—	4	1	no	—
224	D₄×C₇₃	—	4	2	no	—
225	D₄×C₇₃	—	4	1	no	—
226	D₄×C₇₃	—	4	1	no	—
227	D₄×C₇₃	—	4	2	no	—
228	D₄×C₇₃	—	4	2	no	—
229	D₄×C₇₃	—	4	2	no	—
230	D₄×C₇₃	—	8	16	no	—
231	D₄×C₇₃	—	8	4	no	—
232	D₄×C₇₃	—	8	4	no	—
233	C₂×C₄×C₇₃	—	2	2	no	—
234	C₂×C₄×C₇₃	—	2	2	no	—
235	C₂×C₄×C₇₃	—	2	2	no	—
236	C₂×C₄×C₇₃	—	2	4	no	—
237	C₂×C₄×C₇₃	—	2	4	no	—
238	C₂×C₄×C₇₃	—	2	4	no	—
239	C₂×C₄×C₇₃	—	2	4	no	—
240	C₂×C₄×C₇₃	—	2	4	no	—
241	C₂×C₄×C₇₃	—	4	8	no	—
242	C₂×C₄×C₇₃	—	4	2	no	—
243	C₂×C₄×C₇₃	—	4	2	no	—
244	C₂×C₄×C₇₃	—	4	1	no	—
245	C₂×C₄×C₇₃	—	4	1	no	—
246	C₂×C₄×C₇₃	—	4	2	no	—
247	C₂×C₄×C₇₃	—	4	2	no	—
248	C₂×C₄×C₇₃	#127	1	2	yes	—
249	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
251	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
253	C₈×C₇₃	—	2	2	no	—
254	C₈×C₇₃	—	2	4	no	—
255	C₈×C₇₃	#120	1	4	yes	complemented
256	C₂²×C₇₃	—	2	2	no	—
257	C₂²×C₇₃	—	2	2	no	—
258	C₂²×C₇₃	—	2	8	no	—
259	C₂²×C₇₃	—	4	4	no	—
260	C₂²×C₇₃	—	4	8	no	—
261	C₂²×C₇₃	—	8	16	no	—
262	C₂²×C₇₃	—	8	2	no	—
263	C₂²×C₇₃	—	8	2	no	—
264	C₂²×C₇₃	—	8	4	no	—
265	C₂²×C₇₃	—	8	1	no	—
266	C₂²×C₇₃	—	8	1	no	—
267	C₂²×C₇₃	—	8	1	no	—
268	C₂²×C₇₃	—	8	1	no	—
269	C₂²×C₇₃	—	8	1	no	—
270	C₂²×C₇₃	—	8	1	no	—
271	C₂²×C₇₃	—	8	4	no	—
272	C₂²×C₇₃	—	8	4	no	—
273	C₂²×C₇₃	#496	1	4	yes	complemented
274	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
275	C₂²×C₇₃	D₄²	1	2	yes	—
276	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
277	C₂²×C₇₃	#577	1	2	yes	—
278	C₄×C₇₃	—	2	2	no	—
279	C₄×C₇₃	—	4	4	no	—
280	C₄×C₇₃	—	4	4	no	—
281	C₄×C₇₃	—	8	1	no	—
282	C₄×C₇₃	—	8	1	no	—
283	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
284	C₄×C₇₃	#535	1	1	yes	characteristic
285	C₄×C₇₃	D₄²	1	2	yes	—
286	#25783	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂×C₇₃	—	2	4	no	—
288	C₂×C₇₃	—	8	4	no	—
289	C₂×C₇₃	—	16	1	no	—
290	C₂×C₇₃	—	16	1	no	—
291	C₂×C₇₃	#2433	1	1	yes	characteristic
292	C₂×C₇₃	C₂×#496	1	1	yes	characteristic
293	C₂×C₇₃	#3154	1	1	yes	characteristic
294	C₂×C₇₃	#3265	1	4	yes	—
295	C₂³×SD₁₆	C₂×C₇₃	1	1	yes	characteristic, complemented
296	C₂×#496	C₂×C₇₃	1	2	yes	complemented
297	C₂×#466	C₂×C₇₃	1	1	yes	characteristic, complemented
298	C₂×#448	C₂×C₇₃	1	1	yes	characteristic, complemented
299	C₂×#447	C₂×C₇₃	1	1	yes	characteristic, complemented
300	#2436	C₂×C₇₃	1	1	yes	characteristic, complemented
301	#2433	C₂×C₇₃	1	1	yes	characteristic, complemented
302	#2014	C₂×C₇₃	1	2	yes	complemented
303	#2012	C₂×C₇₃	1	2	yes	complemented
304	#1973	C₂×C₇₃	1	2	yes	complemented
305	#1752	C₂×C₇₃	1	1	yes	characteristic, complemented
306	C₇₃	#25783	1	1	yes	characteristic, direct product factor, Sylow
307	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
308	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
309	C₂²×SD₁₆	—	2	8	no	—
310	C₂²×SD₁₆	—	2	4	no	—
311	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
312	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
313	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	complemented
314	C₂²×D₈	C₂²×C₇₃	1	2	yes	—
315	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
316	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
317	C₂×#127	C₂²×C₇₃	1	2	yes	—
318	C₂×#124	C₂²×C₇₃	1	2	yes	complemented
319	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
320	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
321	C₂×#120	—	2	2	no	—
322	#496	—	2	8	no	—
323	#466	—	2	4	no	—
324	#448	—	2	4	no	—
325	#447	—	2	4	no	—
326	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic, complemented
327	C₂×#103	C₂²×C₇₃	1	2	yes	complemented
328	C₂×#102	C₂²×C₇₃	1	2	yes	—
329	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic, complemented
330	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic, complemented
331	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
332	C₂×#97	C₂²×C₇₃	1	2	yes	complemented
333	#393	—	2	2	no	—
334	#392	—	2	2	no	—
335	#391	C₂²×C₇₃	1	2	yes	complemented
336	#390	C₂²×C₇₃	1	2	yes	—
337	#386	—	2	2	no	—
338	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
339	#336	C₂²×C₇₃	1	2	yes	complemented
340	C₂⁵	—	2	1	no	—
341	C₂²×Q₈	—	2	1	no	—
342	C₂²×Q₈	—	2	4	no	—
343	C₂²×Q₈	—	2	2	no	—
344	C₂²×Q₈	—	2	2	no	—
345	C₂²×Q₈	—	4	2	no	—
346	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
347	C₂²×D₄	—	2	4	no	—
348	C₂²×D₄	—	2	1	no	—
349	C₂²×D₄	—	2	1	no	—
350	C₂²×D₄	—	2	2	no	—
351	C₂²×D₄	—	2	2	no	—
352	C₂²×D₄	—	2	1	no	—
353	C₂²×D₄	—	2	4	no	—
354	C₂²×D₄	—	4	2	no	—
355	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
356	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
357	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
358	C₂³×C₄	—	2	1	no	—
359	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
360	C₂×SD₁₆	—	2	32	no	—
361	C₂×SD₁₆	—	2	4	no	—
362	C₂×SD₁₆	—	2	4	no	—
363	C₂×SD₁₆	—	2	4	no	—
364	C₂×SD₁₆	—	2	4	no	—
365	C₂×SD₁₆	—	2	4	no	—
366	C₂×SD₁₆	—	2	4	no	—
367	C₂×SD₁₆	—	2	4	no	—
368	C₂×SD₁₆	—	4	2	no	—
369	C₂×SD₁₆	D₄×C₇₃	1	8	yes	complemented
370	C₂×D₈	—	2	4	no	—
371	C₂×D₈	—	2	4	no	—
372	C₂×D₈	—	2	2	no	—
373	C₂×D₈	—	2	4	no	—
374	C₂×D₈	—	4	2	no	—
375	C₂²×C₈	—	2	4	no	—
376	C₂²×C₈	D₄×C₇₃	1	4	yes	complemented
377	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
378	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
379	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
380	#127	—	2	4	no	—
381	#127	—	4	2	no	—
382	#124	—	2	4	no	—
383	#124	—	4	2	no	—
384	#121	—	2	2	no	—
385	#121	—	2	2	no	—
386	#121	—	2	2	no	—
387	#121	—	2	2	no	—
388	#120	—	4	8	no	—
389	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
391	C₂×C₂²⋊C₄	—	2	4	no	—
392	C₂×C₂²⋊C₄	—	2	1	no	—
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₂²⋊C₄	—	2	4	no	—
395	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
396	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
397	#107	—	2	2	no	—
398	#103	—	2	4	no	—
399	#102	—	2	4	no	—
400	#102	—	2	2	no	—
401	#102	—	2	2	no	—
402	C₂²⋊C₈	D₄×C₇₃	1	4	yes	complemented
403	#97	—	2	4	no	—
404	#95	—	2	4	no	—
405	#95	D₄×C₇₃	1	2	yes	—
406	C₂⁴	—	2	2	no	—
407	C₂⁴	—	2	1	no	—
408	C₂⁴	—	2	1	no	—
409	C₂⁴	—	4	4	no	—
410	C₂⁴	—	4	2	no	—
411	C₂⁴	—	4	4	no	—
412	C₂⁴	—	8	2	no	—
413	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	2	8	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	2	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	4	4	no	—
421	C₂×Q₈	—	4	8	no	—
422	C₂×Q₈	—	4	4	no	—
423	C₂×Q₈	—	4	2	no	—
424	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
425	C₂×D₄	—	2	8	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	4	8	no	—
440	C₂×D₄	—	4	4	no	—
441	C₂×D₄	—	4	4	no	—
442	C₂×D₄	—	4	8	no	—
443	C₂×D₄	—	4	8	no	—
444	C₂×D₄	—	4	2	no	—
445	C₂×D₄	—	4	2	no	—
446	C₂×D₄	—	4	4	no	—
447	C₂×D₄	—	4	4	no	—
448	C₂×D₄	—	4	2	no	—
449	C₂×D₄	—	8	4	no	—
450	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	4	4	no	—
457	C₂²×C₄	—	4	2	no	—
458	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
459	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
461	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
462	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
463	SD₁₆	—	2	16	no	—
464	SD₁₆	—	2	16	no	—
465	SD₁₆	—	4	8	no	—
466	D₈	—	4	8	no	—
467	D₈	—	4	4	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	8	no	—
472	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
473	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
474	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
475	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	4	8	no	—
482	C₂²⋊C₄	—	4	8	no	—
483	C₂²⋊C₄	—	4	2	no	—
484	C₂²⋊C₄	—	4	2	no	—
485	C₄²	—	2	2	no	—
486	C₄²	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	4	8	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	4	4	no	—
494	C₂³	—	4	4	no	—
495	C₂³	—	4	1	no	—
496	C₂³	—	4	1	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	2	no	—
499	C₂³	—	4	2	no	—
500	C₂³	—	4	2	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	8	16	no	—
504	C₂³	—	8	4	no	—
505	C₂³	—	8	4	no	—
506	C₂³	#127×C₇₃	1	2	yes	—
507	C₂³	AGL(1,ℤ/8)×C₇₃	1	4	yes	—
508	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
509	Q₈	—	2	4	no	—
510	Q₈	—	2	4	no	—
511	Q₈	—	4	8	no	—
512	Q₈	—	4	2	no	—
513	Q₈	—	4	2	no	—
514	D₄	—	2	4	no	—
515	D₄	—	2	4	no	—
516	D₄	—	4	8	no	—
517	D₄	—	4	1	no	—
518	D₄	—	4	1	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	2	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	2	no	—
525	D₄	—	8	16	no	—
526	D₄	—	8	4	no	—
527	D₄	—	8	4	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	4	8	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	#127×C₇₃	1	2	yes	—
544	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
545	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
546	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
547	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
548	C₈	—	2	2	no	—
549	C₈	—	2	4	no	—
550	C₈	#120×C₇₃	1	4	yes	complemented
551	C₂²	—	2	8	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	4	8	no	—
555	C₂²	—	4	4	no	—
556	C₂²	—	8	16	no	—
557	C₂²	—	8	4	no	—
558	C₂²	—	8	2	no	—
559	C₂²	—	8	2	no	—
560	C₂²	—	8	4	no	—
561	C₂²	—	8	4	no	—
562	C₂²	—	8	1	no	—
563	C₂²	—	8	1	no	—
564	C₂²	—	8	1	no	—
565	C₂²	—	8	1	no	—
566	C₂²	—	8	1	no	—
567	C₂²	—	8	1	no	—
568	C₂²	#496×C₇₃	1	4	yes	complemented
569	C₂²	C₂×#127×C₇₃	1	1	yes	characteristic
570	C₂²	D₄²×C₇₃	1	2	yes	—
571	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	2	yes	—
572	C₂²	#577×C₇₃	1	2	yes	—
573	C₄	—	2	2	no	—
574	C₄	—	4	4	no	—
575	C₄	—	4	4	no	—
576	C₄	—	8	1	no	—
577	C₄	—	8	1	no	—
578	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
579	C₄	#535×C₇₃	1	1	yes	characteristic
580	C₄	D₄²×C₇₃	1	2	yes	—
581	C₂	—	2	4	no	—
582	C₂	—	8	4	no	—
583	C₂	—	16	1	no	—
584	C₂	—	16	1	no	—
585	C₂	C₇₃×#2433	1	1	yes	characteristic
586	C₂	C₂×#496×C₇₃	1	1	yes	characteristic
587	C₂	C₇₃×#3154	1	1	yes	characteristic
588	C₂	C₇₃×#3265	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₄×C₂²⋊C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×SD₁₆×C₇₃	C₂	semidirect
2. C₂×#496×C₇₃	C₂	semidirect
3. C₂×#466×C₇₃	C₂	semidirect
4. C₂×#448×C₇₃	C₂	semidirect
5. C₂×#447×C₇₃	C₂	semidirect
6. C₇₃×#2436	C₂	semidirect
7. C₇₃×#2433	C₂	semidirect
8. C₇₃×#2014	C₂	semidirect
9. C₇₃×#2012	C₂	semidirect
10. C₇₃×#1973	C₂	semidirect
11. C₇₃×#1752	C₂	semidirect
18. C₂²×SD₁₆×C₇₃	C₂²	semidirect
20. C₂²×D₈×C₇₃	C₂²	semidirect
23. C₂×#124×C₇₃	C₂²	semidirect
31. C₂×#107×C₇₃	C₂²	semidirect
32. C₂×#103×C₇₃	C₂²	semidirect
34. C₂×#102×C₇₃	C₂²	semidirect
35. C₂×#102×C₇₃	C₂²	semidirect
37. C₂×#97×C₇₃	C₂²	semidirect
40. #391×C₇₃	C₂²	semidirect
44. #336×C₇₃	C₂²	semidirect
74. C₂×SD₁₆×C₇₃	D₄	semidirect
81. C₂²×C₈×C₇₃	D₄	semidirect
107. C₂²⋊C₈×C₇₃	D₄	semidirect
255. C₈×C₇₃	#120	semidirect
273. C₂²×C₇₃	#496	semidirect
286. #25783	C₇₃	direct (N × H)
295. C₂³×SD₁₆	C₂×C₇₃	semidirect
296. C₂×#496	C₂×C₇₃	semidirect
297. C₂×#466	C₂×C₇₃	semidirect
298. C₂×#448	C₂×C₇₃	semidirect
299. C₂×#447	C₂×C₇₃	semidirect
300. #2436	C₂×C₇₃	semidirect
301. #2433	C₂×C₇₃	semidirect
302. #2014	C₂×C₇₃	semidirect
303. #2012	C₂×C₇₃	semidirect
304. #1973	C₂×C₇₃	semidirect
305. #1752	C₂×C₇₃	semidirect
306. C₇₃	#25783	direct (N × H)
313. C₂²×SD₁₆	C₂²×C₇₃	semidirect
315. C₂²×D₈	C₂²×C₇₃	semidirect
318. C₂×#124	C₂²×C₇₃	semidirect
326. C₂×#107	C₂²×C₇₃	semidirect
327. C₂×#103	C₂²×C₇₃	semidirect
329. C₂×#102	C₂²×C₇₃	semidirect
330. C₂×#102	C₂²×C₇₃	semidirect
332. C₂×#97	C₂²×C₇₃	semidirect
335. #391	C₂²×C₇₃	semidirect
339. #336	C₂²×C₇₃	semidirect
369. C₂×SD₁₆	D₄×C₇₃	semidirect
376. C₂²×C₈	D₄×C₇₃	semidirect
402. C₂²⋊C₈	D₄×C₇₃	semidirect
550. C₈	#120×C₇₃	semidirect
568. C₂²	#496×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂³×SD₁₆×C₇₃	2
C₂×#496×C₇₃	2
C₂×#466×C₇₃	2
C₂×#448×C₇₃	2
C₂×#447×C₇₃	2
C₇₃×#2436	2
C₇₃×#2433	2
C₇₃×#2014	2
C₇₃×#2012	2
C₇₃×#1973	2
C₇₃×#1752	2
#25783	73

Subgroups — C73×#25783 #32935187

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25783 #32935187