Subgroups — C₇₃×#21897 #32931301

Order 18688.

1142 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#540×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#424×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2314	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#1989	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1982	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1895	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1893	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1804	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1802	C₂	1	2	yes	maximal, complemented
10	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
12	#540×C₇₃	—	2	4	no	—
13	#540×C₇₃	C₄	1	8	yes	complemented
14	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#123×C₇₃	—	2	2	no	—
17	C₂×#121×C₇₃	—	2	2	no	—
18	C₂×#121×C₇₃	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
20	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
21	#424×C₇₃	—	2	4	no	—
22	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
23	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
24	C₂×#102×C₇₃	C₂²	1	2	yes	—
25	C₂×#102×C₇₃	C₂²	1	2	yes	—
26	C₂×#102×C₇₃	C₂²	1	2	yes	—
27	C₂×#102×C₇₃	C₂²	1	2	yes	—
28	#388×C₇₃	—	2	2	no	—
29	#387×C₇₃	—	2	2	no	—
30	#384×C₇₃	C₂²	1	1	yes	characteristic
31	#382×C₇₃	C₂²	1	1	yes	characteristic
32	#380×C₇₃	C₂²	1	2	yes	—
33	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
34	#340×C₇₃	C₂²	1	2	yes	—
35	#340×C₇₃	C₂²	1	2	yes	—
36	#340×C₇₃	C₂²	1	2	yes	—
37	#340×C₇₃	C₂²	1	2	yes	—
38	C₂²×D₄×C₇₃	—	2	2	no	—
39	C₂²×D₄×C₇₃	—	2	2	no	—
40	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₇₃	—	2	2	no	—
42	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
43	C₂×M₁₆×C₇₃	—	2	2	no	—
44	C₂×M₁₆×C₇₃	—	4	1	no	—
45	C₂×M₁₆×C₇₃	—	4	1	no	—
46	C₂²×C₈×C₇₃	—	2	2	no	—
47	C₂²×C₈×C₇₃	—	4	1	no	—
48	C₂²×C₈×C₇₃	—	4	1	no	—
49	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
50	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
51	#127×C₇₃	—	2	2	no	—
52	#127×C₇₃	C₂×C₄	1	4	yes	—
53	#125×C₇₃	—	2	2	no	—
54	#125×C₇₃	C₂×C₄	1	4	yes	—
55	#123×C₇₃	—	2	16	no	—
56	#121×C₇₃	—	2	4	no	—
57	#121×C₇₃	—	2	16	no	—
58	#121×C₇₃	C₂×C₄	1	8	yes	—
59	C₄×D₄×C₇₃	—	2	4	no	—
60	C₄×D₄×C₇₃	C₂×C₄	1	8	yes	—
61	#117×C₇₃	C₂×C₄	1	4	yes	—
62	#117×C₇₃	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
65	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
73	C₂×C₄²×C₇₃	—	2	2	no	—
74	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
76	C₄⋊C₈×C₇₃	—	2	4	no	—
77	C₄⋊C₈×C₇₃	—	2	4	no	—
78	#102×C₇₃	—	4	2	no	—
79	#102×C₇₃	—	4	2	no	—
80	#102×C₇₃	—	4	2	no	—
81	#102×C₇₃	—	4	2	no	—
82	#95×C₇₃	—	2	2	no	—
83	#95×C₇₃	—	2	2	no	—
84	#95×C₇₃	—	2	2	no	—
85	C₂⁴×C₇₃	—	2	2	no	—
86	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
87	C₂×D₄×C₇₃	—	2	8	no	—
88	C₂×D₄×C₇₃	—	2	8	no	—
89	C₂×D₄×C₇₃	—	2	2	no	—
90	C₂×D₄×C₇₃	—	2	2	no	—
91	C₂×D₄×C₇₃	—	2	2	no	—
92	C₂×D₄×C₇₃	—	2	2	no	—
93	C₂×D₄×C₇₃	—	2	2	no	—
94	C₂×D₄×C₇₃	—	8	2	no	—
95	C₂×D₄×C₇₃	—	8	2	no	—
96	C₂×D₄×C₇₃	—	8	2	no	—
97	C₂×D₄×C₇₃	—	8	2	no	—
98	C₂×D₄×C₇₃	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₇₃	—	2	1	no	—
100	C₂²×C₄×C₇₃	—	2	1	no	—
101	C₂²×C₄×C₇₃	—	2	1	no	—
102	C₂²×C₄×C₇₃	—	2	1	no	—
103	C₂²×C₄×C₇₃	—	2	2	no	—
104	C₂²×C₄×C₇₃	—	2	8	no	—
105	C₂²×C₄×C₇₃	—	2	2	no	—
106	C₂²×C₄×C₇₃	—	2	2	no	—
107	C₂²×C₄×C₇₃	—	8	2	no	—
108	C₂²×C₄×C₇₃	—	8	2	no	—
109	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
115	M₁₆×C₇₃	—	4	4	no	—
116	C₂×C₈×C₇₃	—	2	2	no	—
117	C₂×C₈×C₇₃	—	2	2	no	—
118	C₂×C₈×C₇₃	—	2	2	no	—
119	C₂×C₈×C₇₃	—	2	2	no	—
120	C₂×C₈×C₇₃	—	2	2	no	—
121	C₂×C₈×C₇₃	—	2	2	no	—
122	C₂×C₈×C₇₃	—	4	4	no	—
123	C₄⋊C₄×C₇₃	—	2	8	no	—
124	C₄⋊C₄×C₇₃	—	2	2	no	—
125	C₄⋊C₄×C₇₃	—	2	2	no	—
126	C₄⋊C₄×C₇₃	—	2	2	no	—
127	C₄⋊C₄×C₇₃	—	2	2	no	—
128	C₄⋊C₄×C₇₃	—	2	2	no	—
129	C₄⋊C₄×C₇₃	—	8	2	no	—
130	C₄⋊C₄×C₇₃	C₂²⋊C₄	1	8	yes	—
131	C₄⋊C₄×C₇₃	C₂²×C₄	1	4	yes	—
132	C₂²⋊C₄×C₇₃	—	2	8	no	—
133	C₂²⋊C₄×C₇₃	—	2	8	no	—
134	C₂²⋊C₄×C₇₃	—	8	2	no	—
135	C₂²⋊C₄×C₇₃	C₂²⋊C₄	1	8	yes	—
136	C₄²×C₇₃	—	8	2	no	—
137	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
138	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
139	C₄²×C₇₃	C₂×D₄	1	2	yes	—
140	C₄²×C₇₃	C₂×D₄	1	2	yes	—
141	C₂³×C₇₃	—	2	1	no	—
142	C₂³×C₇₃	—	2	1	no	—
143	C₂³×C₇₃	—	2	2	no	—
144	C₂³×C₇₃	—	2	2	no	—
145	C₂³×C₇₃	—	2	4	no	—
146	C₂³×C₇₃	—	4	2	no	—
147	C₂³×C₇₃	—	4	2	no	—
148	C₂³×C₇₃	—	4	2	no	—
149	C₂³×C₇₃	—	4	2	no	—
150	C₂³×C₇₃	—	4	2	no	—
151	C₂³×C₇₃	—	4	2	no	—
152	C₂³×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
153	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
154	D₄×C₇₃	—	2	4	no	—
155	D₄×C₇₃	—	2	4	no	—
156	D₄×C₇₃	—	4	2	no	—
157	D₄×C₇₃	—	4	2	no	—
158	D₄×C₇₃	—	8	8	no	—
159	D₄×C₇₃	—	8	8	no	—
160	C₂×C₄×C₇₃	—	2	1	no	—
161	C₂×C₄×C₇₃	—	2	1	no	—
162	C₂×C₄×C₇₃	—	2	2	no	—
163	C₂×C₄×C₇₃	—	2	2	no	—
164	C₂×C₄×C₇₃	—	2	2	no	—
165	C₂×C₄×C₇₃	—	2	2	no	—
166	C₂×C₄×C₇₃	—	2	2	no	—
167	C₂×C₄×C₇₃	—	2	2	no	—
168	C₂×C₄×C₇₃	—	2	2	no	—
169	C₂×C₄×C₇₃	—	2	2	no	—
170	C₂×C₄×C₇₃	—	2	4	no	—
171	C₂×C₄×C₇₃	—	4	2	no	—
172	C₂×C₄×C₇₃	—	4	2	no	—
173	C₂×C₄×C₇₃	—	4	2	no	—
174	C₂×C₄×C₇₃	—	4	2	no	—
175	C₂×C₄×C₇₃	—	4	2	no	—
176	C₂×C₄×C₇₃	—	4	2	no	—
177	C₂×C₄×C₇₃	—	4	2	no	—
178	C₂×C₄×C₇₃	—	4	2	no	—
179	C₂×C₄×C₇₃	—	8	8	no	—
180	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	4	yes	—
181	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	4	yes	—
182	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
183	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
184	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
188	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
189	C₈×C₇₃	—	4	2	no	—
190	C₈×C₇₃	—	4	2	no	—
191	C₂²×C₇₃	—	2	2	no	—
192	C₂²×C₇₃	—	2	4	no	—
193	C₂²×C₇₃	—	4	2	no	—
194	C₂²×C₇₃	—	4	1	no	—
195	C₂²×C₇₃	—	4	1	no	—
196	C₂²×C₇₃	—	4	4	no	—
197	C₂²×C₇₃	—	4	4	no	—
198	C₂²×C₇₃	—	4	4	no	—
199	C₂²×C₇₃	—	8	2	no	—
200	C₂²×C₇₃	—	8	2	no	—
201	C₂²×C₇₃	—	8	2	no	—
202	C₂²×C₇₃	—	8	2	no	—
203	C₂²×C₇₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
204	C₂²×C₇₃	#537	1	1	yes	characteristic
205	C₂²×C₇₃	#537	1	1	yes	characteristic
206	C₂²×C₇₃	#576	1	2	yes	—
207	C₂²×C₇₃	#577	1	2	yes	—
208	C₄×C₇₃	—	2	2	no	—
209	C₄×C₇₃	—	2	4	no	—
210	C₄×C₇₃	—	2	4	no	—
211	C₄×C₇₃	—	4	4	no	—
212	C₄×C₇₃	—	8	2	no	—
213	C₄×C₇₃	—	8	2	no	—
214	C₄×C₇₃	#520	1	1	yes	characteristic
215	C₄×C₇₃	#520	1	1	yes	characteristic
216	C₄×C₇₃	#535	1	1	yes	characteristic
217	C₄×C₇₃	#536	1	1	yes	characteristic
218	#21897	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂×C₇₃	—	4	2	no	—
220	C₂×C₇₃	—	8	4	no	—
221	C₂×C₇₃	#2311	1	1	yes	characteristic
222	C₂×C₇₃	#2897	1	2	yes	—
223	C₂×C₇₃	#3257	1	2	yes	—
224	C₂×C₇₃	#3259	1	1	yes	characteristic
225	C₂×C₇₃	#3260	1	1	yes	characteristic
226	C₂×#540	C₂×C₇₃	1	1	yes	characteristic
227	C₂×#424	C₂×C₇₃	1	1	yes	characteristic, complemented
228	#2314	C₂×C₇₃	1	1	yes	characteristic, complemented
229	#1989	C₂×C₇₃	1	2	yes	complemented
230	#1982	C₂×C₇₃	1	2	yes	complemented
231	#1895	C₂×C₇₃	1	2	yes	complemented
232	#1893	C₂×C₇₃	1	2	yes	complemented
233	#1804	C₂×C₇₃	1	2	yes	complemented
234	#1802	C₂×C₇₃	1	2	yes	complemented
235	C₇₃	#21897	1	1	yes	characteristic, direct product factor, Sylow
236	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
237	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
238	#540	—	2	4	no	—
239	#540	C₄×C₇₃	1	8	yes	complemented
240	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
241	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
242	C₂×#123	—	2	2	no	—
243	C₂×#121	—	2	2	no	—
244	C₂×#121	C₂²×C₇₃	1	2	yes	—
245	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
246	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
247	#424	—	2	4	no	—
248	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
249	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
250	C₂×#102	C₂²×C₇₃	1	2	yes	—
251	C₂×#102	C₂²×C₇₃	1	2	yes	—
252	C₂×#102	C₂²×C₇₃	1	2	yes	—
253	C₂×#102	C₂²×C₇₃	1	2	yes	—
254	#388	—	2	2	no	—
255	#387	—	2	2	no	—
256	#384	C₂²×C₇₃	1	1	yes	characteristic
257	#382	C₂²×C₇₃	1	1	yes	characteristic
258	#380	C₂²×C₇₃	1	2	yes	—
259	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
260	#340	C₂²×C₇₃	1	2	yes	—
261	#340	C₂²×C₇₃	1	2	yes	—
262	#340	C₂²×C₇₃	1	2	yes	—
263	#340	C₂²×C₇₃	1	2	yes	—
264	C₂²×D₄	—	2	2	no	—
265	C₂²×D₄	—	2	2	no	—
266	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
267	C₂³×C₄	—	2	2	no	—
268	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	—	4	1	no	—
271	C₂×M₁₆	—	4	1	no	—
272	C₂²×C₈	—	2	2	no	—
273	C₂²×C₈	—	4	1	no	—
274	C₂²×C₈	—	4	1	no	—
275	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
276	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
277	#127	—	2	2	no	—
278	#127	C₂×C₄×C₇₃	1	4	yes	—
279	#125	—	2	2	no	—
280	#125	C₂×C₄×C₇₃	1	4	yes	—
281	#123	—	2	16	no	—
282	#121	—	2	4	no	—
283	#121	—	2	16	no	—
284	#121	C₂×C₄×C₇₃	1	8	yes	—
285	C₄×D₄	—	2	4	no	—
286	C₄×D₄	C₂×C₄×C₇₃	1	8	yes	—
287	#117	C₂×C₄×C₇₃	1	4	yes	—
288	#117	D₄×C₇₃	1	4	yes	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
292	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
302	C₄⋊C₈	—	2	4	no	—
303	C₄⋊C₈	—	2	4	no	—
304	#102	—	4	2	no	—
305	#102	—	4	2	no	—
306	#102	—	4	2	no	—
307	#102	—	4	2	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	C₂⁴	—	2	2	no	—
312	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
313	C₂×D₄	—	2	8	no	—
314	C₂×D₄	—	2	8	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	8	2	no	—
321	C₂×D₄	—	8	2	no	—
322	C₂×D₄	—	8	2	no	—
323	C₂×D₄	—	8	2	no	—
324	C₂×D₄	C₂²×C₄×C₇₃	1	4	yes	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	8	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	8	2	no	—
334	C₂²×C₄	—	8	2	no	—
335	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
336	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
339	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
340	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
341	M₁₆	—	4	4	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	4	4	no	—
349	C₄⋊C₄	—	2	8	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	8	2	no	—
356	C₄⋊C₄	C₂²⋊C₄×C₇₃	1	8	yes	—
357	C₄⋊C₄	C₂²×C₄×C₇₃	1	4	yes	—
358	C₂²⋊C₄	—	2	8	no	—
359	C₂²⋊C₄	—	2	8	no	—
360	C₂²⋊C₄	—	8	2	no	—
361	C₂²⋊C₄	C₂²⋊C₄×C₇₃	1	8	yes	—
362	C₄²	—	8	2	no	—
363	C₄²	C₂²×C₄×C₇₃	1	2	yes	—
364	C₄²	C₂²×C₄×C₇₃	1	2	yes	—
365	C₄²	C₂×D₄×C₇₃	1	2	yes	—
366	C₄²	C₂×D₄×C₇₃	1	2	yes	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	4	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	2	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	4	2	no	—
378	C₂³	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
379	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
380	D₄	—	2	4	no	—
381	D₄	—	2	4	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	2	no	—
384	D₄	—	8	8	no	—
385	D₄	—	8	8	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	8	8	no	—
406	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	4	yes	—
407	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	4	yes	—
408	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
409	C₂×C₄	C₂³×C₄×C₇₃	1	1	yes	characteristic
410	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
411	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
412	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
413	C₂×C₄	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
414	C₂×C₄	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
415	C₈	—	4	2	no	—
416	C₈	—	4	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	4	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	4	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	8	2	no	—
426	C₂²	—	8	2	no	—
427	C₂²	—	8	2	no	—
428	C₂²	—	8	2	no	—
429	C₂²	C₂²×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
430	C₂²	#537×C₇₃	1	1	yes	characteristic
431	C₂²	#537×C₇₃	1	1	yes	characteristic
432	C₂²	#576×C₇₃	1	2	yes	—
433	C₂²	#577×C₇₃	1	2	yes	—
434	C₄	—	2	2	no	—
435	C₄	—	2	4	no	—
436	C₄	—	2	4	no	—
437	C₄	—	4	4	no	—
438	C₄	—	8	2	no	—
439	C₄	—	8	2	no	—
440	C₄	#520×C₇₃	1	1	yes	characteristic
441	C₄	#520×C₇₃	1	1	yes	characteristic
442	C₄	#535×C₇₃	1	1	yes	characteristic
443	C₄	#536×C₇₃	1	1	yes	characteristic
444	C₂	—	4	2	no	—
445	C₂	—	8	4	no	—
446	C₂	C₇₃×#2311	1	1	yes	characteristic
447	C₂	C₇₃×#2897	1	2	yes	—
448	C₂	C₇₃×#3257	1	2	yes	—
449	C₂	C₇₃×#3259	1	1	yes	characteristic
450	C₂	C₇₃×#3260	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#540×C₇₃	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×#117×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#424×C₇₃	C₂	semidirect
3. C₇₃×#2314	C₂	semidirect
4. C₇₃×#1989	C₂	semidirect
5. C₇₃×#1982	C₂	semidirect
6. C₇₃×#1895	C₂	semidirect
7. C₇₃×#1893	C₂	semidirect
8. C₇₃×#1804	C₂	semidirect
9. C₇₃×#1802	C₂	semidirect
13. #540×C₇₃	C₄	semidirect
218. #21897	C₇₃	direct (N × H)
227. C₂×#424	C₂×C₇₃	semidirect
228. #2314	C₂×C₇₃	semidirect
229. #1989	C₂×C₇₃	semidirect
230. #1982	C₂×C₇₃	semidirect
231. #1895	C₂×C₇₃	semidirect
232. #1893	C₂×C₇₃	semidirect
233. #1804	C₂×C₇₃	semidirect
234. #1802	C₂×C₇₃	semidirect
235. C₇₃	#21897	direct (N × H)
239. #540	C₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#540×C₇₃	2
C₂×#424×C₇₃	2
C₇₃×#2314	2
C₇₃×#1989	2
C₇₃×#1982	2
C₇₃×#1895	2
C₇₃×#1893	2
C₇₃×#1804	2
C₇₃×#1802	2
#21897	73

Subgroups — C73×#21897 #32931301

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#21897 #32931301