Subgroups — C₇₃×#25719 #32935123

Order 18688.

1598 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#532×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#494×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#492×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#452×C₇₃	C₂	1	4	yes	maximal, complemented
5	C₇₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2015	C₂	1	4	yes	maximal, complemented
7	C₇₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₂²⋊C₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₇₃	C₂²	1	2	yes	—
11	C₂²×Q₁₆×C₇₃	C₂²	1	4	yes	—
12	C₂²×SD₁₆×C₇₃	C₂²	1	4	yes	—
13	#532×C₇₃	—	2	4	no	—
14	#532×C₇₃	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×#124×C₇₃	C₂²	1	2	yes	—
19	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
20	C₂×#121×C₇₃	—	2	2	no	—
21	C₂×C₄×D₄×C₇₃	—	2	2	no	—
22	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
23	#494×C₇₃	—	2	4	no	—
24	#492×C₇₃	—	2	4	no	—
25	#452×C₇₃	—	2	16	no	—
26	C₂×#103×C₇₃	C₂²	1	4	yes	—
27	C₂×#102×C₇₃	C₂²	1	4	yes	—
28	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
31	#391×C₇₃	C₂²	1	2	yes	—
32	#389×C₇₃	—	2	2	no	—
33	#384×C₇₃	C₂²	1	1	yes	characteristic
34	#380×C₇₃	—	2	2	no	—
35	#336×C₇₃	C₂²	1	2	yes	—
36	C₂×#41×C₇₃	—	2	4	no	—
37	C₂×#41×C₇₃	—	2	4	no	—
38	C₂×#41×C₇₃	—	2	8	no	—
39	C₂×#41×C₇₃	—	4	4	no	—
40	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
41	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
42	C₂²×D₄×C₇₃	—	2	2	no	—
43	C₂²×D₄×C₇₃	—	2	2	no	—
44	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
45	C₂³×C₄×C₇₃	—	2	2	no	—
46	C₂³×C₄×C₇₃	D₄	1	2	yes	—
47	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
48	C₂×Q₁₆×C₇₃	—	2	8	no	—
49	C₂×Q₁₆×C₇₃	—	2	8	no	—
50	C₂×Q₁₆×C₇₃	—	4	4	no	—
51	C₂×SD₁₆×C₇₃	—	2	8	no	—
52	C₂×SD₁₆×C₇₃	—	2	8	no	—
53	C₂×SD₁₆×C₇₃	—	4	4	no	—
54	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
56	C₄⋊Q₈×C₇₃	—	2	2	no	—
57	C₄⋊Q₈×C₇₃	—	2	2	no	—
58	C₄⋊Q₈×C₇₃	—	2	2	no	—
59	C₄⋊Q₈×C₇₃	D₄	1	4	yes	—
60	#127×C₇₃	—	2	2	no	—
61	#127×C₇₃	D₄	1	4	yes	—
62	#124×C₇₃	—	2	4	no	—
63	#124×C₇₃	—	2	4	no	—
64	C₂²⋊Q₈×C₇₃	—	2	8	no	—
65	#121×C₇₃	—	2	16	no	—
66	C₄×D₄×C₇₃	—	2	16	no	—
67	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
68	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
69	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
70	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
71	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
72	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
74	C₂×C₄²×C₇₃	—	2	2	no	—
75	C₂×C₄²×C₇₃	—	2	2	no	—
76	C₂×C₄²×C₇₃	D₄	1	2	yes	—
77	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
79	#103×C₇₃	—	2	8	no	—
80	#102×C₇₃	—	2	8	no	—
81	C₂²⋊C₈×C₇₃	D₄	1	8	yes	complemented
82	C₄×C₈×C₇₃	—	2	2	no	—
83	C₄×C₈×C₇₃	—	2	2	no	—
84	#95×C₇₃	—	2	4	no	—
85	C₂⁴×C₇₃	—	2	2	no	—
86	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
87	#41×C₇₃	—	4	16	no	—
88	#41×C₇₃	—	4	16	no	—
89	C₂×Q₈×C₇₃	—	2	2	no	—
90	C₂×Q₈×C₇₃	—	2	4	no	—
91	C₂×Q₈×C₇₃	—	2	4	no	—
92	C₂×Q₈×C₇₃	—	2	2	no	—
93	C₂×Q₈×C₇₃	—	2	2	no	—
94	C₂×Q₈×C₇₃	—	2	4	no	—
95	C₂×Q₈×C₇₃	—	2	4	no	—
96	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
97	C₂×D₄×C₇₃	—	2	8	no	—
98	C₂×D₄×C₇₃	—	2	8	no	—
99	C₂×D₄×C₇₃	—	2	4	no	—
100	C₂×D₄×C₇₃	—	2	2	no	—
101	C₂×D₄×C₇₃	—	2	4	no	—
102	C₂×D₄×C₇₃	—	4	4	no	—
103	C₂×D₄×C₇₃	—	4	4	no	—
104	C₂×D₄×C₇₃	—	4	4	no	—
105	C₂×D₄×C₇₃	—	4	4	no	—
106	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₇₃	—	2	1	no	—
108	C₂²×C₄×C₇₃	—	2	1	no	—
109	C₂²×C₄×C₇₃	—	2	2	no	—
110	C₂²×C₄×C₇₃	—	2	8	no	—
111	C₂²×C₄×C₇₃	—	2	2	no	—
112	C₂²×C₄×C₇₃	—	2	4	no	—
113	C₂²×C₄×C₇₃	—	2	4	no	—
114	C₂²×C₄×C₇₃	—	2	4	no	—
115	C₂²×C₄×C₇₃	—	2	2	no	—
116	C₂²×C₄×C₇₃	—	2	2	no	—
117	C₂²×C₄×C₇₃	—	4	4	no	—
118	C₂²×C₄×C₇₃	—	4	4	no	—
119	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
122	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
124	Q₁₆×C₇₃	—	4	16	no	—
125	SD₁₆×C₇₃	—	4	16	no	—
126	C₂×C₈×C₇₃	—	2	2	no	—
127	C₂×C₈×C₇₃	—	2	2	no	—
128	C₂×C₈×C₇₃	—	2	2	no	—
129	C₂×C₈×C₇₃	—	2	2	no	—
130	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
131	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
132	C₄⋊C₄×C₇₃	—	2	8	no	—
133	C₄⋊C₄×C₇₃	—	2	4	no	—
134	C₄⋊C₄×C₇₃	—	4	4	no	—
135	C₄⋊C₄×C₇₃	—	4	4	no	—
136	C₄⋊C₄×C₇₃	—	4	4	no	—
137	C₂²⋊C₄×C₇₃	—	2	16	no	—
138	C₂²⋊C₄×C₇₃	—	4	4	no	—
139	C₄²×C₇₃	—	2	4	no	—
140	C₄²×C₇₃	—	2	1	no	—
141	C₄²×C₇₃	—	2	1	no	—
142	C₄²×C₇₃	C₂×D₄	1	2	yes	—
143	C₄²×C₇₃	C₂×D₄	1	2	yes	—
144	C₂³×C₇₃	—	2	1	no	—
145	C₂³×C₇₃	—	2	1	no	—
146	C₂³×C₇₃	—	2	2	no	—
147	C₂³×C₇₃	—	2	2	no	—
148	C₂³×C₇₃	—	2	4	no	—
149	C₂³×C₇₃	—	4	2	no	—
150	C₂³×C₇₃	—	4	2	no	—
151	C₂³×C₇₃	—	4	4	no	—
152	C₂³×C₇₃	—	4	4	no	—
153	C₂³×C₇₃	#127	1	2	yes	—
154	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
155	Q₈×C₇₃	—	2	8	no	—
156	Q₈×C₇₃	—	4	4	no	—
157	Q₈×C₇₃	—	4	4	no	—
158	Q₈×C₇₃	—	4	4	no	—
159	D₄×C₇₃	—	2	8	no	—
160	D₄×C₇₃	—	4	16	no	—
161	D₄×C₇₃	—	4	4	no	—
162	D₄×C₇₃	—	4	16	no	—
163	C₂×C₄×C₇₃	—	2	1	no	—
164	C₂×C₄×C₇₃	—	2	1	no	—
165	C₂×C₄×C₇₃	—	2	4	no	—
166	C₂×C₄×C₇₃	—	2	4	no	—
167	C₂×C₄×C₇₃	—	2	2	no	—
168	C₂×C₄×C₇₃	—	2	4	no	—
169	C₂×C₄×C₇₃	—	2	2	no	—
170	C₂×C₄×C₇₃	—	2	2	no	—
171	C₂×C₄×C₇₃	—	4	16	no	—
172	C₂×C₄×C₇₃	—	4	2	no	—
173	C₂×C₄×C₇₃	—	4	2	no	—
174	C₂×C₄×C₇₃	—	4	8	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	—	4	4	no	—
180	C₂×C₄×C₇₃	#120	1	4	yes	—
181	C₂×C₄×C₇₃	#127	1	2	yes	—
182	C₂×C₄×C₇₃	#135	1	4	yes	—
183	C₂×C₄×C₇₃	#137	1	4	yes	—
184	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
187	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
188	C₈×C₇₃	—	2	4	no	—
189	C₈×C₇₃	—	2	4	no	—
190	C₂²×C₇₃	—	2	2	no	—
191	C₂²×C₇₃	—	2	2	no	—
192	C₂²×C₇₃	—	2	2	no	—
193	C₂²×C₇₃	—	4	2	no	—
194	C₂²×C₇₃	—	4	2	no	—
195	C₂²×C₇₃	—	4	4	no	—
196	C₂²×C₇₃	—	4	8	no	—
197	C₂²×C₇₃	—	8	2	no	—
198	C₂²×C₇₃	—	8	2	no	—
199	C₂²×C₇₃	—	8	4	no	—
200	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
201	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
202	C₂²×C₇₃	#535	1	1	yes	characteristic
203	C₂²×C₇₃	C₂×#135	1	2	yes	—
204	C₂²×C₇₃	C₂×#137	1	2	yes	—
205	C₄×C₇₃	—	2	2	no	—
206	C₄×C₇₃	—	4	4	no	—
207	C₄×C₇₃	—	4	2	no	—
208	C₄×C₇₃	—	8	2	no	—
209	C₄×C₇₃	—	8	2	no	—
210	C₄×C₇₃	#452	1	8	yes	complemented
211	C₄×C₇₃	D₄²	1	2	yes	—
212	C₄×C₇₃	D₄²	1	2	yes	—
213	#25719	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂×C₇₃	—	4	2	no	—
215	C₂×C₇₃	—	8	4	no	—
216	C₂×C₇₃	#2433	1	1	yes	characteristic
217	C₂×C₇₃	C₂×#452	1	2	yes	—
218	C₂×C₇₃	#3147	1	1	yes	characteristic
219	C₂×C₇₃	#3152	1	1	yes	characteristic
220	C₂×C₇₃	#3210	1	2	yes	—
221	C₂×#532	C₂×C₇₃	1	1	yes	characteristic
222	C₂×#494	C₂×C₇₃	1	1	yes	characteristic, complemented
223	C₂×#492	C₂×C₇₃	1	1	yes	characteristic, complemented
224	C₂×#452	C₂×C₇₃	1	4	yes	complemented
225	#2857	C₂×C₇₃	1	1	yes	characteristic, complemented
226	#2015	C₂×C₇₃	1	4	yes	complemented
227	#1957	C₂×C₇₃	1	1	yes	characteristic, complemented
228	#1956	C₂×C₇₃	1	1	yes	characteristic, complemented
229	C₄×C₂²⋊C₈	C₂×C₇₃	1	1	yes	characteristic, complemented
230	C₇₃	#25719	1	1	yes	characteristic, direct product factor, Sylow
231	C₂²×#41	C₂²×C₇₃	1	2	yes	—
232	C₂²×Q₁₆	C₂²×C₇₃	1	4	yes	—
233	C₂²×SD₁₆	C₂²×C₇₃	1	4	yes	—
234	#532	—	2	4	no	—
235	#532	—	2	4	no	—
236	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
237	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
238	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
239	C₂×#124	C₂²×C₇₃	1	2	yes	—
240	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
241	C₂×#121	—	2	2	no	—
242	C₂×C₄×D₄	—	2	2	no	—
243	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
244	#494	—	2	4	no	—
245	#492	—	2	4	no	—
246	#452	—	2	16	no	—
247	C₂×#103	C₂²×C₇₃	1	4	yes	—
248	C₂×#102	C₂²×C₇₃	1	4	yes	—
249	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
250	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
251	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
252	#391	C₂²×C₇₃	1	2	yes	—
253	#389	—	2	2	no	—
254	#384	C₂²×C₇₃	1	1	yes	characteristic
255	#380	—	2	2	no	—
256	#336	C₂²×C₇₃	1	2	yes	—
257	C₂×#41	—	2	4	no	—
258	C₂×#41	—	2	4	no	—
259	C₂×#41	—	2	8	no	—
260	C₂×#41	—	4	4	no	—
261	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
262	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
263	C₂²×D₄	—	2	2	no	—
264	C₂²×D₄	—	2	2	no	—
265	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
266	C₂³×C₄	—	2	2	no	—
267	C₂³×C₄	D₄×C₇₃	1	2	yes	—
268	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
269	C₂×Q₁₆	—	2	8	no	—
270	C₂×Q₁₆	—	2	8	no	—
271	C₂×Q₁₆	—	4	4	no	—
272	C₂×SD₁₆	—	2	8	no	—
273	C₂×SD₁₆	—	2	8	no	—
274	C₂×SD₁₆	—	4	4	no	—
275	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
276	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
277	C₄⋊Q₈	—	2	2	no	—
278	C₄⋊Q₈	—	2	2	no	—
279	C₄⋊Q₈	—	2	2	no	—
280	C₄⋊Q₈	D₄×C₇₃	1	4	yes	—
281	#127	—	2	2	no	—
282	#127	D₄×C₇₃	1	4	yes	—
283	#124	—	2	4	no	—
284	#124	—	2	4	no	—
285	C₂²⋊Q₈	—	2	8	no	—
286	#121	—	2	16	no	—
287	C₄×D₄	—	2	16	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
293	C₂×C₂²⋊C₄	—	2	4	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₄²	—	2	2	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	D₄×C₇₃	1	2	yes	—
298	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
299	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
300	#103	—	2	8	no	—
301	#102	—	2	8	no	—
302	C₂²⋊C₈	D₄×C₇₃	1	8	yes	complemented
303	C₄×C₈	—	2	2	no	—
304	C₄×C₈	—	2	2	no	—
305	#95	—	2	4	no	—
306	C₂⁴	—	2	2	no	—
307	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
308	#41	—	4	16	no	—
309	#41	—	4	16	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	2	4	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	4	no	—
316	C₂×Q₈	—	2	4	no	—
317	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
318	C₂×D₄	—	2	8	no	—
319	C₂×D₄	—	2	8	no	—
320	C₂×D₄	—	2	4	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	4	no	—
323	C₂×D₄	—	4	4	no	—
324	C₂×D₄	—	4	4	no	—
325	C₂×D₄	—	4	4	no	—
326	C₂×D₄	—	4	4	no	—
327	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	4	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	4	4	no	—
339	C₂²×C₄	—	4	4	no	—
340	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
343	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
344	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
345	Q₁₆	—	4	16	no	—
346	SD₁₆	—	4	16	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
352	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
353	C₄⋊C₄	—	2	8	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	4	4	no	—
356	C₄⋊C₄	—	4	4	no	—
357	C₄⋊C₄	—	4	4	no	—
358	C₂²⋊C₄	—	2	16	no	—
359	C₂²⋊C₄	—	4	4	no	—
360	C₄²	—	2	4	no	—
361	C₄²	—	2	1	no	—
362	C₄²	—	2	1	no	—
363	C₄²	C₂×D₄×C₇₃	1	2	yes	—
364	C₄²	C₂×D₄×C₇₃	1	2	yes	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	2	no	—
369	C₂³	—	2	4	no	—
370	C₂³	—	4	2	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	4	4	no	—
373	C₂³	—	4	4	no	—
374	C₂³	#127×C₇₃	1	2	yes	—
375	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
376	Q₈	—	2	8	no	—
377	Q₈	—	4	4	no	—
378	Q₈	—	4	4	no	—
379	Q₈	—	4	4	no	—
380	D₄	—	2	8	no	—
381	D₄	—	4	16	no	—
382	D₄	—	4	16	no	—
383	D₄	—	4	4	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	16	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	8	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	#120×C₇₃	1	4	yes	—
402	C₂×C₄	#127×C₇₃	1	2	yes	—
403	C₂×C₄	#135×C₇₃	1	4	yes	—
404	C₂×C₄	#137×C₇₃	1	4	yes	—
405	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
406	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
407	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
408	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
409	C₈	—	2	4	no	—
410	C₈	—	2	4	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	8	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	8	4	no	—
419	C₂²	—	8	2	no	—
420	C₂²	—	8	2	no	—
421	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
422	C₂²	C₂×#127×C₇₃	1	1	yes	characteristic
423	C₂²	#535×C₇₃	1	1	yes	characteristic
424	C₂²	C₂×#135×C₇₃	1	2	yes	—
425	C₂²	C₂×#137×C₇₃	1	2	yes	—
426	C₄	—	2	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	4	no	—
429	C₄	—	8	2	no	—
430	C₄	—	8	2	no	—
431	C₄	#452×C₇₃	1	8	yes	complemented
432	C₄	D₄²×C₇₃	1	2	yes	—
433	C₄	D₄²×C₇₃	1	2	yes	—
434	C₂	—	4	2	no	—
435	C₂	—	8	4	no	—
436	C₂	C₇₃×#2433	1	1	yes	characteristic
437	C₂	C₂×#452×C₇₃	1	2	yes	—
438	C₂	C₇₃×#3147	1	1	yes	characteristic
439	C₂	C₇₃×#3152	1	1	yes	characteristic
440	C₂	C₇₃×#3210	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#532×C₇₃	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂²×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#494×C₇₃	C₂	semidirect
3. C₂×#492×C₇₃	C₂	semidirect
4. C₂×#452×C₇₃	C₂	semidirect
5. C₇₃×#2857	C₂	semidirect
6. C₇₃×#2015	C₂	semidirect
7. C₇₃×#1957	C₂	semidirect
8. C₇₃×#1956	C₂	semidirect
9. C₄×C₂²⋊C₈×C₇₃	C₂	semidirect
81. C₂²⋊C₈×C₇₃	D₄	semidirect
210. C₄×C₇₃	#452	semidirect
213. #25719	C₇₃	direct (N × H)
222. C₂×#494	C₂×C₇₃	semidirect
223. C₂×#492	C₂×C₇₃	semidirect
224. C₂×#452	C₂×C₇₃	semidirect
225. #2857	C₂×C₇₃	semidirect
226. #2015	C₂×C₇₃	semidirect
227. #1957	C₂×C₇₃	semidirect
228. #1956	C₂×C₇₃	semidirect
229. C₄×C₂²⋊C₈	C₂×C₇₃	semidirect
230. C₇₃	#25719	direct (N × H)
302. C₂²⋊C₈	D₄×C₇₃	semidirect
431. C₄	#452×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#532×C₇₃	2
C₂×#494×C₇₃	2
C₂×#492×C₇₃	2
C₂×#452×C₇₃	2
C₇₃×#2857	2
C₇₃×#2015	2
C₇₃×#1957	2
C₇₃×#1956	2
C₄×C₂²⋊C₈×C₇₃	2
#25719	73

Subgroups — C73×#25719 #32935123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25719 #32935123