Subgroups — C₇₃×#25632 #32935036

Order 18688.

1114 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#556×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#494×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#461×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#2568	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2015	C₂	1	4	yes	maximal
6	C₇₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1878	C₂	1	4	yes	maximal, complemented
9	C₄×#102×C₇₃	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₁₆×C₇₃	C₂²	1	4	yes	—
11	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
12	#556×C₇₃	—	2	4	no	—
13	#556×C₇₃	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×#126×C₇₃	—	2	2	no	—
17	C₂×#124×C₇₃	C₂²	1	2	yes	—
18	C₂×C₂²⋊Q₈×C₇₃	—	2	1	no	—
19	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×#117×C₇₃	—	2	1	no	—
23	#494×C₇₃	—	2	4	no	—
24	#461×C₇₃	—	2	4	no	—
25	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#103×C₇₃	C₂²	1	2	yes	—
27	C₂×#103×C₇₃	C₂²	1	4	yes	—
28	C₂×#102×C₇₃	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
30	#400×C₇₃	—	2	2	no	—
31	#391×C₇₃	—	2	1	no	—
32	#391×C₇₃	C₂²	1	4	yes	—
33	#382×C₇₃	—	2	1	no	—
34	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
35	#340×C₇₃	C₂²	1	2	yes	—
36	#336×C₇₃	C₂²	1	4	yes	—
37	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
38	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
39	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
40	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₇₃	—	2	1	no	—
42	C₂×Q₁₆×C₇₃	—	2	8	no	—
43	C₂×Q₁₆×C₇₃	—	2	8	no	—
44	C₂×Q₁₆×C₇₃	—	4	4	no	—
45	C₂×SD₁₆×C₇₃	—	2	4	no	—
46	C₂×SD₁₆×C₇₃	—	4	4	no	—
47	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
49	C₄⋊Q₈×C₇₃	—	2	2	no	—
50	C₄⋊Q₈×C₇₃	—	2	2	no	—
51	C₄⋊Q₈×C₇₃	—	2	2	no	—
52	C₄⋊Q₈×C₇₃	D₄	1	4	yes	—
53	#126×C₇₃	—	2	16	no	—
54	#124×C₇₃	—	2	4	no	—
55	#124×C₇₃	—	2	4	no	—
56	C₂²⋊Q₈×C₇₃	—	2	8	no	—
57	C₄×Q₈×C₇₃	—	2	4	no	—
58	C₄×Q₈×C₇₃	—	2	4	no	—
59	C₄×Q₈×C₇₃	—	2	2	no	—
60	C₄×Q₈×C₇₃	—	2	2	no	—
61	C₄×D₄×C₇₃	—	2	2	no	—
62	C₄×D₄×C₇₃	D₄	1	4	yes	—
63	#117×C₇₃	—	2	8	no	—
64	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
66	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
68	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
69	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
72	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
76	C₂×C₄²×C₇₃	—	2	2	no	—
77	C₂×C₄²×C₇₃	—	2	1	no	—
78	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
79	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₇₃	—	2	2	no	—
81	#103×C₇₃	—	2	4	no	—
82	#103×C₇₃	—	4	4	no	—
83	#102×C₇₃	—	2	4	no	—
84	C₄×C₈×C₇₃	—	2	2	no	—
85	#95×C₇₃	—	2	1	no	—
86	#95×C₇₃	—	2	4	no	—
87	#95×C₇₃	—	2	4	no	—
88	C₂⁴×C₇₃	—	2	1	no	—
89	C₂×Q₈×C₇₃	—	2	2	no	—
90	C₂×Q₈×C₇₃	—	2	2	no	—
91	C₂×Q₈×C₇₃	—	2	2	no	—
92	C₂×Q₈×C₇₃	—	2	2	no	—
93	C₂×Q₈×C₇₃	—	2	2	no	—
94	C₂×Q₈×C₇₃	—	2	2	no	—
95	C₂×Q₈×C₇₃	—	2	4	no	—
96	C₂×Q₈×C₇₃	—	2	4	no	—
97	C₂×Q₈×C₇₃	—	2	4	no	—
98	C₂×Q₈×C₇₃	—	2	4	no	—
99	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
100	C₂×D₄×C₇₃	—	2	1	no	—
101	C₂×D₄×C₇₃	—	2	2	no	—
102	C₂×D₄×C₇₃	—	2	2	no	—
103	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₇₃	—	2	1	no	—
105	C₂²×C₄×C₇₃	—	2	2	no	—
106	C₂²×C₄×C₇₃	—	2	4	no	—
107	C₂²×C₄×C₇₃	—	2	2	no	—
108	C₂²×C₄×C₇₃	—	2	2	no	—
109	C₂²×C₄×C₇₃	—	4	2	no	—
110	C₂²×C₄×C₇₃	—	4	2	no	—
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	1	yes	characteristic
114	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
116	Q₁₆×C₇₃	—	4	16	no	—
117	SD₁₆×C₇₃	—	4	8	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	4	no	—
122	C₂×C₈×C₇₃	#41	1	4	yes	—
123	C₄⋊C₄×C₇₃	—	2	8	no	—
124	C₄⋊C₄×C₇₃	—	2	4	no	—
125	C₄⋊C₄×C₇₃	—	2	4	no	—
126	C₄⋊C₄×C₇₃	—	2	2	no	—
127	C₄⋊C₄×C₇₃	—	2	4	no	—
128	C₄⋊C₄×C₇₃	—	2	1	no	—
129	C₄⋊C₄×C₇₃	—	2	2	no	—
130	C₄⋊C₄×C₇₃	—	2	2	no	—
131	C₄⋊C₄×C₇₃	—	4	2	no	—
132	C₄⋊C₄×C₇₃	—	4	2	no	—
133	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
134	C₂²⋊C₄×C₇₃	—	2	8	no	—
135	C₂²⋊C₄×C₇₃	—	2	8	no	—
136	C₂²⋊C₄×C₇₃	—	2	4	no	—
137	C₄²×C₇₃	—	2	8	no	—
138	C₄²×C₇₃	—	2	2	no	—
139	C₄²×C₇₃	—	2	2	no	—
140	C₄²×C₇₃	—	4	2	no	—
141	C₄²×C₇₃	C₂×D₄	1	2	yes	—
142	C₄²×C₇₃	C₂×D₄	1	2	yes	—
143	C₂³×C₇₃	—	2	2	no	—
144	C₂³×C₇₃	—	4	2	no	—
145	C₂³×C₇₃	—	4	1	no	—
146	C₂³×C₇₃	—	4	1	no	—
147	C₂³×C₇₃	—	4	2	no	—
148	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
149	Q₈×C₇₃	—	2	8	no	—
150	Q₈×C₇₃	—	4	2	no	—
151	Q₈×C₇₃	—	4	2	no	—
152	Q₈×C₇₃	—	4	4	no	—
153	Q₈×C₇₃	—	4	2	no	—
154	Q₈×C₇₃	—	4	2	no	—
155	Q₈×C₇₃	—	4	4	no	—
156	D₄×C₇₃	—	2	2	no	—
157	D₄×C₇₃	—	2	2	no	—
158	D₄×C₇₃	—	4	2	no	—
159	C₂×C₄×C₇₃	—	2	2	no	—
160	C₂×C₄×C₇₃	—	2	2	no	—
161	C₂×C₄×C₇₃	—	2	2	no	—
162	C₂×C₄×C₇₃	—	2	4	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	4	no	—
167	C₂×C₄×C₇₃	—	4	4	no	—
168	C₂×C₄×C₇₃	—	4	1	no	—
169	C₂×C₄×C₇₃	—	4	1	no	—
170	C₂×C₄×C₇₃	—	4	8	no	—
171	C₂×C₄×C₇₃	—	4	2	no	—
172	C₂×C₄×C₇₃	—	4	2	no	—
173	C₂×C₄×C₇₃	—	4	4	no	—
174	C₂×C₄×C₇₃	—	4	2	no	—
175	C₂×C₄×C₇₃	—	4	2	no	—
176	C₂×C₄×C₇₃	#120	1	2	yes	—
177	C₂×C₄×C₇₃	#120	1	2	yes	—
178	C₂×C₄×C₇₃	#135	1	2	yes	—
179	C₂×C₄×C₇₃	#137	1	2	yes	—
180	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
183	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
184	C₈×C₇₃	—	2	4	no	—
185	C₈×C₇₃	—	4	2	no	—
186	C₂²×C₇₃	—	4	2	no	—
187	C₂²×C₇₃	—	4	2	no	—
188	C₂²×C₇₃	—	4	2	no	—
189	C₂²×C₇₃	—	8	2	no	—
190	C₂²×C₇₃	—	8	2	no	—
191	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
192	C₂²×C₇₃	#550	1	2	yes	—
193	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
194	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
195	C₂²×C₇₃	#578	1	2	yes	—
196	C₄×C₇₃	—	2	2	no	—
197	C₄×C₇₃	—	4	4	no	—
198	C₄×C₇₃	—	4	2	no	—
199	C₄×C₇₃	—	4	2	no	—
200	C₄×C₇₃	—	4	2	no	—
201	C₄×C₇₃	—	8	2	no	—
202	C₄×C₇₃	—	8	2	no	—
203	C₄×C₇₃	#452	1	4	yes	—
204	C₄×C₇₃	#532	1	1	yes	characteristic
205	C₄×C₇₃	#535	1	1	yes	characteristic
206	C₄×C₇₃	#546	1	2	yes	—
207	#25632	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂×C₇₃	—	8	2	no	—
209	C₂×C₇₃	#2431	1	1	yes	characteristic
210	C₂×C₇₃	C₂×#452	1	1	yes	characteristic
211	C₂×C₇₃	#3011	1	1	yes	characteristic
212	C₂×C₇₃	#3393	1	2	yes	—
213	C₂×C₇₃	#3398	1	2	yes	—
214	C₂×#556	C₂×C₇₃	1	1	yes	characteristic
215	C₂×#494	C₂×C₇₃	1	1	yes	characteristic, complemented
216	C₂×#461	C₂×C₇₃	1	1	yes	characteristic
217	#2568	C₂×C₇₃	1	1	yes	characteristic, complemented
218	#2015	C₂×C₇₃	1	4	yes	—
219	#1984	C₂×C₇₃	1	1	yes	characteristic, complemented
220	#1981	C₂×C₇₃	1	1	yes	characteristic, complemented
221	#1878	C₂×C₇₃	1	4	yes	complemented
222	C₄×#102	C₂×C₇₃	1	1	yes	characteristic
223	C₇₃	#25632	1	1	yes	characteristic, direct product factor, Sylow
224	C₂²×Q₁₆	C₂²×C₇₃	1	4	yes	—
225	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
226	#556	—	2	4	no	—
227	#556	—	2	4	no	—
228	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
229	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
230	C₂×#126	—	2	2	no	—
231	C₂×#124	C₂²×C₇₃	1	2	yes	—
232	C₂×C₂²⋊Q₈	—	2	1	no	—
233	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
234	C₂×C₄×Q₈	C₂²×C₇₃	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂²×C₇₃	1	1	yes	characteristic
236	C₂×#117	—	2	1	no	—
237	#494	—	2	4	no	—
238	#461	—	2	4	no	—
239	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
240	C₂×#103	C₂²×C₇₃	1	2	yes	—
241	C₂×#103	C₂²×C₇₃	1	4	yes	—
242	C₂×#102	C₂²×C₇₃	1	2	yes	—
243	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
244	#400	—	2	2	no	—
245	#391	—	2	1	no	—
246	#391	C₂²×C₇₃	1	4	yes	—
247	#382	—	2	1	no	—
248	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
249	#340	C₂²×C₇₃	1	2	yes	—
250	#336	C₂²×C₇₃	1	4	yes	—
251	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
252	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
253	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
254	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
255	C₂³×C₄	—	2	1	no	—
256	C₂×Q₁₆	—	2	8	no	—
257	C₂×Q₁₆	—	2	8	no	—
258	C₂×Q₁₆	—	4	4	no	—
259	C₂×SD₁₆	—	2	4	no	—
260	C₂×SD₁₆	—	4	4	no	—
261	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
262	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
263	C₄⋊Q₈	—	2	2	no	—
264	C₄⋊Q₈	—	2	2	no	—
265	C₄⋊Q₈	—	2	2	no	—
266	C₄⋊Q₈	D₄×C₇₃	1	4	yes	—
267	#126	—	2	16	no	—
268	#124	—	2	4	no	—
269	#124	—	2	4	no	—
270	C₂²⋊Q₈	—	2	8	no	—
271	C₄×Q₈	—	2	4	no	—
272	C₄×Q₈	—	2	4	no	—
273	C₄×Q₈	—	2	2	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	D₄×C₇₃	1	4	yes	—
277	#117	—	2	8	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
284	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	1	no	—
289	C₂×C₂²⋊C₄	—	2	2	no	—
290	C₂×C₄²	—	2	2	no	—
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
293	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
294	C₄⋊C₈	—	2	2	no	—
295	#103	—	2	4	no	—
296	#103	—	4	4	no	—
297	#102	—	2	4	no	—
298	C₄×C₈	—	2	2	no	—
299	#95	—	2	1	no	—
300	#95	—	2	4	no	—
301	#95	—	2	4	no	—
302	C₂⁴	—	2	1	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	4	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	2	4	no	—
313	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	—	4	2	no	—
325	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
327	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
329	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
330	Q₁₆	—	4	16	no	—
331	SD₁₆	—	4	8	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	4	no	—
336	C₂×C₈	#41×C₇₃	1	4	yes	—
337	C₄⋊C₄	—	2	8	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
348	C₂²⋊C₄	—	2	8	no	—
349	C₂²⋊C₄	—	2	8	no	—
350	C₂²⋊C₄	—	2	4	no	—
351	C₄²	—	2	8	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	—	4	2	no	—
355	C₄²	C₂×D₄×C₇₃	1	2	yes	—
356	C₄²	C₂×D₄×C₇₃	1	2	yes	—
357	C₂³	—	2	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	4	1	no	—
361	C₂³	—	4	2	no	—
362	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
363	Q₈	—	2	8	no	—
364	Q₈	—	4	4	no	—
365	Q₈	—	4	2	no	—
366	Q₈	—	4	2	no	—
367	Q₈	—	4	2	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	4	no	—
370	D₄	—	2	2	no	—
371	D₄	—	2	2	no	—
372	D₄	—	4	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	4	4	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	8	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	#120×C₇₃	1	2	yes	—
391	C₂×C₄	#120×C₇₃	1	2	yes	—
392	C₂×C₄	#135×C₇₃	1	2	yes	—
393	C₂×C₄	#137×C₇₃	1	2	yes	—
394	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
396	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
397	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
398	C₈	—	2	4	no	—
399	C₈	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
406	C₂²	#550×C₇₃	1	2	yes	—
407	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
408	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
409	C₂²	#578×C₇₃	1	2	yes	—
410	C₄	—	2	2	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	4	no	—
415	C₄	—	8	2	no	—
416	C₄	—	8	2	no	—
417	C₄	#452×C₇₃	1	4	yes	—
418	C₄	#532×C₇₃	1	1	yes	characteristic
419	C₄	#535×C₇₃	1	1	yes	characteristic
420	C₄	#546×C₇₃	1	2	yes	—
421	C₂	—	8	2	no	—
422	C₂	C₇₃×#2431	1	1	yes	characteristic
423	C₂	C₂×#452×C₇₃	1	1	yes	characteristic
424	C₂	C₇₃×#3011	1	1	yes	characteristic
425	C₂	C₇₃×#3393	1	2	yes	—
426	C₂	C₇₃×#3398	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂²×D₄×C₇₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄×Q₈×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#494×C₇₃	C₂	semidirect
4. C₇₃×#2568	C₂	semidirect
6. C₇₃×#1984	C₂	semidirect
7. C₇₃×#1981	C₂	semidirect
8. C₇₃×#1878	C₂	semidirect
207. #25632	C₇₃	direct (N × H)
215. C₂×#494	C₂×C₇₃	semidirect
217. #2568	C₂×C₇₃	semidirect
219. #1984	C₂×C₇₃	semidirect
220. #1981	C₂×C₇₃	semidirect
221. #1878	C₂×C₇₃	semidirect
223. C₇₃	#25632	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#556×C₇₃	2
C₂×#494×C₇₃	2
C₂×#461×C₇₃	2
C₇₃×#2568	2
C₇₃×#2015	2
C₇₃×#1984	2
C₇₃×#1981	2
C₇₃×#1878	2
C₄×#102×C₇₃	2
#25632	73

Subgroups — C73×#25632 #32935036

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25632 #32935036