Subgroups — C₇₃×#29130 #32938534

Order 18688.

878 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#127×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2100	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2041	C₂	1	2	yes	maximal
5	C₇₃×#1936	C₂	1	4	yes	maximal, complemented
6	C₇₃×#1802	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1802	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
10	C₂×#125×C₇₃	—	2	1	no	—
11	C₂×C₄×D₄×C₇₃	—	2	1	no	—
12	C₂×C₄×D₄×C₇₃	—	2	1	no	—
13	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
14	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
15	C₂×#102×C₇₃	C₂²	1	4	yes	—
16	C₂×#102×C₇₃	C₂²	1	4	yes	—
17	C₂×#97×C₇₃	C₂²	1	2	yes	—
18	#390×C₇₃	—	2	1	no	—
19	#390×C₇₃	—	2	1	no	—
20	#390×C₇₃	C₂²	1	2	yes	—
21	#389×C₇₃	—	2	1	no	—
22	#389×C₇₃	—	2	1	no	—
23	#389×C₇₃	C₂²	1	2	yes	—
24	#389×C₇₃	C₂²	1	2	yes	—
25	#384×C₇₃	C₂²	1	1	yes	characteristic
26	#384×C₇₃	C₂²	1	1	yes	characteristic
27	#384×C₇₃	C₂²	1	1	yes	characteristic
28	#382×C₇₃	—	2	1	no	—
29	C₄³×C₇₃	C₂²	1	1	yes	characteristic
30	#340×C₇₃	C₂²	1	4	yes	—
31	#340×C₇₃	C₂²	1	4	yes	—
32	#336×C₇₃	C₂²	1	2	yes	—
33	C₂²×D₄×C₇₃	—	2	1	no	—
34	C₂²×D₄×C₇₃	—	2	1	no	—
35	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
36	C₂³×C₄×C₇₃	—	2	2	no	—
37	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
38	#127×C₇₃	—	2	4	no	—
39	#125×C₇₃	—	4	4	no	—
40	C₄×D₄×C₇₃	—	2	4	no	—
41	C₄×D₄×C₇₃	—	2	4	no	—
42	C₄×D₄×C₇₃	—	4	4	no	—
43	C₄×D₄×C₇₃	—	4	4	no	—
44	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
45	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
46	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
47	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
48	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
49	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
50	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
51	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
52	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
55	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
58	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
63	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
65	C₄⋊C₈×C₇₃	—	2	4	no	—
66	#102×C₇₃	—	2	8	no	—
67	#102×C₇₃	—	4	4	no	—
68	#97×C₇₃	—	4	2	no	—
69	#95×C₇₃	—	2	2	no	—
70	#95×C₇₃	—	2	2	no	—
71	C₂⁴×C₇₃	—	2	2	no	—
72	C₂×D₄×C₇₃	—	2	4	no	—
73	C₂×D₄×C₇₃	—	2	4	no	—
74	C₂×D₄×C₇₃	—	2	2	no	—
75	C₂×D₄×C₇₃	—	2	2	no	—
76	C₂×D₄×C₇₃	—	2	2	no	—
77	C₂×D₄×C₇₃	—	2	2	no	—
78	C₂×D₄×C₇₃	—	2	2	no	—
79	C₂×D₄×C₇₃	—	4	2	no	—
80	C₂×D₄×C₇₃	—	4	2	no	—
81	C₂×D₄×C₇₃	—	4	2	no	—
82	C₂×D₄×C₇₃	—	4	2	no	—
83	C₂×D₄×C₇₃	#41	1	4	yes	—
84	C₂²×C₄×C₇₃	—	2	2	no	—
85	C₂²×C₄×C₇₃	—	2	2	no	—
86	C₂²×C₄×C₇₃	—	2	2	no	—
87	C₂²×C₄×C₇₃	—	4	4	no	—
88	C₂²×C₄×C₇₃	—	4	4	no	—
89	C₂²×C₄×C₇₃	—	4	4	no	—
90	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
97	C₂×C₈×C₇₃	—	2	4	no	—
98	C₂×C₈×C₇₃	—	2	4	no	—
99	C₂×C₈×C₇₃	—	2	4	no	—
100	C₄⋊C₄×C₇₃	—	2	4	no	—
101	C₄⋊C₄×C₇₃	—	2	2	no	—
102	C₄⋊C₄×C₇₃	—	2	2	no	—
103	C₄⋊C₄×C₇₃	—	2	2	no	—
104	C₄⋊C₄×C₇₃	—	2	2	no	—
105	C₄⋊C₄×C₇₃	—	4	2	no	—
106	C₄⋊C₄×C₇₃	—	4	2	no	—
107	C₄⋊C₄×C₇₃	—	4	2	no	—
108	C₄⋊C₄×C₇₃	—	4	2	no	—
109	C₄⋊C₄×C₇₃	—	4	4	no	—
110	C₄⋊C₄×C₇₃	—	4	2	no	—
111	C₄⋊C₄×C₇₃	—	4	2	no	—
112	C₄⋊C₄×C₇₃	—	4	4	no	—
113	C₂²⋊C₄×C₇₃	—	4	4	no	—
114	C₂²⋊C₄×C₇₃	—	4	4	no	—
115	C₂²⋊C₄×C₇₃	—	4	4	no	—
116	C₄²×C₇₃	—	2	2	no	—
117	C₄²×C₇₃	—	2	2	no	—
118	C₄²×C₇₃	—	2	2	no	—
119	C₄²×C₇₃	—	2	2	no	—
120	C₄²×C₇₃	—	2	2	no	—
121	C₄²×C₇₃	—	2	1	no	—
122	C₄²×C₇₃	—	2	1	no	—
123	C₄²×C₇₃	#41	1	4	yes	—
124	C₂³×C₇₃	—	2	4	no	—
125	C₂³×C₇₃	—	4	2	no	—
126	C₂³×C₇₃	—	4	2	no	—
127	C₂³×C₇₃	—	4	2	no	—
128	C₂³×C₇₃	—	4	2	no	—
129	C₂³×C₇₃	—	4	2	no	—
130	C₂³×C₇₃	—	4	2	no	—
131	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
132	D₄×C₇₃	—	2	4	no	—
133	D₄×C₇₃	—	2	4	no	—
134	D₄×C₇₃	—	4	8	no	—
135	D₄×C₇₃	—	4	8	no	—
136	D₄×C₇₃	—	4	2	no	—
137	D₄×C₇₃	—	4	2	no	—
138	C₂×C₄×C₇₃	—	2	1	no	—
139	C₂×C₄×C₇₃	—	2	1	no	—
140	C₂×C₄×C₇₃	—	2	1	no	—
141	C₂×C₄×C₇₃	—	2	1	no	—
142	C₂×C₄×C₇₃	—	2	1	no	—
143	C₂×C₄×C₇₃	—	2	1	no	—
144	C₂×C₄×C₇₃	—	2	1	no	—
145	C₂×C₄×C₇₃	—	2	1	no	—
146	C₂×C₄×C₇₃	—	2	1	no	—
147	C₂×C₄×C₇₃	—	2	1	no	—
148	C₂×C₄×C₇₃	—	2	1	no	—
149	C₂×C₄×C₇₃	—	2	1	no	—
150	C₂×C₄×C₇₃	—	4	2	no	—
151	C₂×C₄×C₇₃	—	4	2	no	—
152	C₂×C₄×C₇₃	—	4	2	no	—
153	C₂×C₄×C₇₃	—	4	2	no	—
154	C₂×C₄×C₇₃	—	4	2	no	—
155	C₂×C₄×C₇₃	—	4	2	no	—
156	C₂×C₄×C₇₃	—	4	2	no	—
157	C₂×C₄×C₇₃	—	4	2	no	—
158	C₂×C₄×C₇₃	—	4	2	no	—
159	C₂×C₄×C₇₃	—	8	8	no	—
160	C₂×C₄×C₇₃	#124	1	2	yes	—
161	C₂×C₄×C₇₃	#124	1	2	yes	—
162	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
163	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
164	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
165	C₂×C₄×C₇₃	#137	1	2	yes	—
166	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
167	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
168	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
169	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
170	C₈×C₇₃	—	4	4	no	—
171	C₂²×C₇₃	—	4	4	no	—
172	C₂²×C₇₃	—	4	4	no	—
173	C₂²×C₇₃	—	4	4	no	—
174	C₂²×C₇₃	—	8	2	no	—
175	C₂²×C₇₃	—	8	2	no	—
176	C₂²×C₇₃	—	8	2	no	—
177	C₂²×C₇₃	—	8	2	no	—
178	C₂²×C₇₃	#525	1	1	yes	characteristic
179	C₂²×C₇₃	C₂×#124	1	1	yes	characteristic
180	C₂²×C₇₃	#537	1	1	yes	characteristic
181	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
185	C₄×C₇₃	—	2	2	no	—
186	C₄×C₇₃	—	2	2	no	—
187	C₄×C₇₃	—	2	2	no	—
188	C₄×C₇₃	—	4	1	no	—
189	C₄×C₇₃	—	4	1	no	—
190	C₄×C₇₃	—	8	2	no	—
191	C₄×C₇₃	—	8	2	no	—
192	C₄×C₇₃	—	8	2	no	—
193	C₄×C₇₃	#490	1	4	yes	—
194	C₄×C₇₃	#552	1	2	yes	—
195	C₄×C₇₃	#553	1	2	yes	—
196	#29130	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂×C₇₃	—	8	4	no	—
198	C₂×C₇₃	#2562	1	1	yes	characteristic
199	C₂×C₇₃	#3109	1	1	yes	characteristic
200	C₂×C₇₃	#3110	1	1	yes	characteristic
201	C₂×C₇₃	C₂×#490	1	1	yes	characteristic
202	C₂×C₇₃	#3141	1	1	yes	characteristic
203	C₂×C₇₃	#3253	1	1	yes	characteristic
204	C₂×C₇₃	#3254	1	1	yes	characteristic
205	#2859	C₂×C₇₃	1	1	yes	characteristic, complemented
206	C₄×#127	C₂×C₇₃	1	1	yes	characteristic
207	#2100	C₂×C₇₃	1	2	yes	complemented
208	#2041	C₂×C₇₃	1	2	yes	—
209	#1936	C₂×C₇₃	1	4	yes	complemented
210	#1802	C₂×C₇₃	1	2	yes	complemented
211	#1802	C₂×C₇₃	1	2	yes	complemented
212	#1767	C₂×C₇₃	1	1	yes	characteristic, complemented
213	C₇₃	#29130	1	1	yes	characteristic, direct product factor, Sylow
214	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
215	C₂×#125	—	2	1	no	—
216	C₂×C₄×D₄	—	2	1	no	—
217	C₂×C₄×D₄	—	2	1	no	—
218	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
219	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
220	C₂×#102	C₂²×C₇₃	1	4	yes	—
221	C₂×#102	C₂²×C₇₃	1	4	yes	—
222	C₂×#97	C₂²×C₇₃	1	2	yes	—
223	#390	—	2	1	no	—
224	#390	—	2	1	no	—
225	#390	C₂²×C₇₃	1	2	yes	—
226	#389	—	2	1	no	—
227	#389	—	2	1	no	—
228	#389	C₂²×C₇₃	1	2	yes	—
229	#389	C₂²×C₇₃	1	2	yes	—
230	#384	C₂²×C₇₃	1	1	yes	characteristic
231	#384	C₂²×C₇₃	1	1	yes	characteristic
232	#384	C₂²×C₇₃	1	1	yes	characteristic
233	#382	—	2	1	no	—
234	C₄³	C₂²×C₇₃	1	1	yes	characteristic
235	#340	C₂²×C₇₃	1	4	yes	—
236	#340	C₂²×C₇₃	1	4	yes	—
237	#336	C₂²×C₇₃	1	2	yes	—
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
241	C₂³×C₄	—	2	2	no	—
242	C₂²×C₈	C₂³×C₇₃	1	4	yes	—
243	#127	—	2	4	no	—
244	#125	—	4	4	no	—
245	C₄×D₄	—	2	4	no	—
246	C₄×D₄	—	2	4	no	—
247	C₄×D₄	—	4	4	no	—
248	C₄×D₄	—	4	4	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
259	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
264	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
265	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
266	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
268	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
270	C₄⋊C₈	—	2	4	no	—
271	#102	—	2	8	no	—
272	#102	—	4	4	no	—
273	#97	—	4	2	no	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	C₂⁴	—	2	2	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	#41×C₇₃	1	4	yes	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	4	4	no	—
293	C₂²×C₄	—	4	4	no	—
294	C₂²×C₄	—	4	4	no	—
295	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
296	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
301	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	2	4	no	—
304	C₂×C₈	—	2	4	no	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	2	no	—
313	C₄⋊C₄	—	4	2	no	—
314	C₄⋊C₄	—	4	4	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	4	no	—
318	C₂²⋊C₄	—	4	4	no	—
319	C₂²⋊C₄	—	4	4	no	—
320	C₂²⋊C₄	—	4	4	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	2	1	no	—
328	C₄²	#41×C₇₃	1	4	yes	—
329	C₂³	—	2	4	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
337	D₄	—	2	4	no	—
338	D₄	—	2	4	no	—
339	D₄	—	4	8	no	—
340	D₄	—	4	8	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	8	8	no	—
365	C₂×C₄	#124×C₇₃	1	2	yes	—
366	C₂×C₄	#124×C₇₃	1	2	yes	—
367	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
368	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
369	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
370	C₂×C₄	#137×C₇₃	1	2	yes	—
371	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
372	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
373	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
374	C₂×C₄	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
375	C₈	—	4	4	no	—
376	C₂²	—	4	4	no	—
377	C₂²	—	4	4	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	8	2	no	—
383	C₂²	#525×C₇₃	1	1	yes	characteristic
384	C₂²	C₂×#124×C₇₃	1	1	yes	characteristic
385	C₂²	#537×C₇₃	1	1	yes	characteristic
386	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
387	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
388	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
389	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	8	2	no	—
396	C₄	—	8	2	no	—
397	C₄	—	8	2	no	—
398	C₄	#490×C₇₃	1	4	yes	—
399	C₄	#552×C₇₃	1	2	yes	—
400	C₄	#553×C₇₃	1	2	yes	—
401	C₂	—	8	4	no	—
402	C₂	C₇₃×#2562	1	1	yes	characteristic
403	C₂	C₇₃×#3109	1	1	yes	characteristic
404	C₂	C₇₃×#3110	1	1	yes	characteristic
405	C₂	C₂×#490×C₇₃	1	1	yes	characteristic
406	C₂	C₇₃×#3141	1	1	yes	characteristic
407	C₂	C₇₃×#3253	1	1	yes	characteristic
408	C₂	C₇₃×#3254	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#127×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₄³×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#2859	C₂	semidirect
3. C₇₃×#2100	C₂	semidirect
5. C₇₃×#1936	C₂	semidirect
6. C₇₃×#1802	C₂	semidirect
7. C₇₃×#1802	C₂	semidirect
8. C₇₃×#1767	C₂	semidirect
196. #29130	C₇₃	direct (N × H)
205. #2859	C₂×C₇₃	semidirect
207. #2100	C₂×C₇₃	semidirect
209. #1936	C₂×C₇₃	semidirect
210. #1802	C₂×C₇₃	semidirect
211. #1802	C₂×C₇₃	semidirect
212. #1767	C₂×C₇₃	semidirect
213. C₇₃	#29130	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₃×#2859	2
C₄×#127×C₇₃	2
C₇₃×#2100	2
C₇₃×#2041	2
C₇₃×#1936	2
C₇₃×#1802	2
C₇₃×#1767	2
#29130	73

Subgroups — C73×#29130 #32938534

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#29130 #32938534