Subgroups — C₇₃×#25779 #32935183

Order 18688.

2034 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#493×C₇₃	C₂	1	2	yes	maximal, complemented
3	C₂×#466×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#447×C₇₃	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2433	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2011	C₂	1	4	yes	maximal, complemented
7	C₇₃×#1970	C₂	1	2	yes	maximal, complemented
8	C₈×C₂²⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₇₃	C₂²	1	2	yes	—
10	C₂²×D₈×C₇₃	—	2	8	no	—
11	C₂²×D₈×C₇₃	—	2	4	no	—
12	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
13	C₂²×D₈×C₇₃	C₂²	1	2	yes	—
14	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
15	C₂²×D₈×C₇₃	C₂²	1	4	yes	complemented
16	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×#127×C₇₃	C₂²	1	4	yes	complemented
18	C₂×#121×C₇₃	C₂²	1	2	yes	—
19	C₂×#120×C₇₃	—	2	4	no	—
20	#493×C₇₃	—	2	8	no	—
21	#466×C₇₃	—	2	4	no	—
22	#447×C₇₃	—	2	8	no	—
23	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic, complemented
24	C₂×#102×C₇₃	C₂²	1	4	yes	complemented
25	C₂×#102×C₇₃	C₂²	1	2	yes	complemented
26	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₇₃	C₂²	1	2	yes	complemented
28	#392×C₇₃	—	2	4	no	—
29	#390×C₇₃	C₂²	1	4	yes	complemented
30	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
31	#336×C₇₃	C₂²	1	2	yes	complemented
32	C₂⁵×C₇₃	—	2	2	no	—
33	C₂²×D₄×C₇₃	—	2	8	no	—
34	C₂²×D₄×C₇₃	—	2	2	no	—
35	C₂²×D₄×C₇₃	—	2	4	no	—
36	C₂²×D₄×C₇₃	—	2	4	no	—
37	C₂²×D₄×C₇₃	—	2	2	no	—
38	C₂²×D₄×C₇₃	—	2	8	no	—
39	C₂²×D₄×C₇₃	—	4	4	no	—
40	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
41	C₂²×D₄×C₇₃	C₂³	1	4	yes	—
42	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
43	C₂×D₈×C₇₃	—	2	32	no	—
44	C₂×D₈×C₇₃	—	2	8	no	—
45	C₂×D₈×C₇₃	—	2	8	no	—
46	C₂×D₈×C₇₃	—	2	4	no	—
47	C₂×D₈×C₇₃	—	2	4	no	—
48	C₂×D₈×C₇₃	—	2	4	no	—
49	C₂×D₈×C₇₃	—	2	8	no	—
50	C₂×D₈×C₇₃	—	2	2	no	—
51	C₂×D₈×C₇₃	—	2	4	no	—
52	C₂×D₈×C₇₃	—	4	4	no	—
53	C₂×D₈×C₇₃	D₄	1	8	yes	complemented
54	C₂²×C₈×C₇₃	—	2	4	no	—
55	C₂²×C₈×C₇₃	D₄	1	4	yes	complemented
56	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
59	#127×C₇₃	—	2	8	no	—
60	#127×C₇₃	—	4	4	no	—
61	#121×C₇₃	—	2	4	no	—
62	#121×C₇₃	—	2	4	no	—
63	#120×C₇₃	—	4	16	no	—
64	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
66	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
68	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
69	#107×C₇₃	—	2	2	no	—
70	#102×C₇₃	—	2	8	no	—
71	#102×C₇₃	—	2	4	no	—
72	C₂²⋊C₈×C₇₃	D₄	1	4	yes	complemented
73	C₄×C₈×C₇₃	—	2	4	no	—
74	#95×C₇₃	D₄	1	2	yes	—
75	C₂⁴×C₇₃	—	2	4	no	—
76	C₂⁴×C₇₃	—	2	2	no	—
77	C₂⁴×C₇₃	—	4	8	no	—
78	C₂⁴×C₇₃	—	4	4	no	—
79	C₂⁴×C₇₃	—	4	8	no	—
80	C₂⁴×C₇₃	—	8	4	no	—
81	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
82	C₂×D₄×C₇₃	—	2	16	no	—
83	C₂×D₄×C₇₃	—	2	4	no	—
84	C₂×D₄×C₇₃	—	2	4	no	—
85	C₂×D₄×C₇₃	—	2	4	no	—
86	C₂×D₄×C₇₃	—	2	2	no	—
87	C₂×D₄×C₇₃	—	2	2	no	—
88	C₂×D₄×C₇₃	—	2	4	no	—
89	C₂×D₄×C₇₃	—	2	4	no	—
90	C₂×D₄×C₇₃	—	2	4	no	—
91	C₂×D₄×C₇₃	—	2	4	no	—
92	C₂×D₄×C₇₃	—	4	16	no	—
93	C₂×D₄×C₇₃	—	4	8	no	—
94	C₂×D₄×C₇₃	—	4	8	no	—
95	C₂×D₄×C₇₃	—	4	16	no	—
96	C₂×D₄×C₇₃	—	4	4	no	—
97	C₂×D₄×C₇₃	—	4	8	no	—
98	C₂×D₄×C₇₃	—	4	4	no	—
99	C₂×D₄×C₇₃	—	4	16	no	—
100	C₂×D₄×C₇₃	—	8	8	no	—
101	C₂×D₄×C₇₃	C₂×D₄	1	8	yes	—
102	C₂²×C₄×C₇₃	—	2	2	no	—
103	C₂²×C₄×C₇₃	—	2	2	no	—
104	C₂²×C₄×C₇₃	—	2	2	no	—
105	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
109	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
110	D₈×C₇₃	—	2	16	no	—
111	D₈×C₇₃	—	2	16	no	—
112	D₈×C₇₃	—	4	16	no	—
113	D₈×C₇₃	—	4	4	no	—
114	C₂×C₈×C₇₃	—	2	2	no	—
115	C₂×C₈×C₇₃	—	2	2	no	—
116	C₂×C₈×C₇₃	—	2	2	no	—
117	C₂×C₈×C₇₃	—	2	8	no	—
118	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
119	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
121	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
122	C₄⋊C₄×C₇₃	—	2	2	no	—
123	C₄⋊C₄×C₇₃	—	2	2	no	—
124	C₂²⋊C₄×C₇₃	—	4	4	no	—
125	C₂²⋊C₄×C₇₃	—	4	16	no	—
126	C₂²⋊C₄×C₇₃	D₈	1	8	yes	complemented
127	C₄²×C₇₃	—	2	2	no	—
128	C₄²×C₇₃	—	2	2	no	—
129	C₂³×C₇₃	—	2	2	no	—
130	C₂³×C₇₃	—	2	2	no	—
131	C₂³×C₇₃	—	2	8	no	—
132	C₂³×C₇₃	—	4	16	no	—
133	C₂³×C₇₃	—	4	4	no	—
134	C₂³×C₇₃	—	4	4	no	—
135	C₂³×C₇₃	—	4	8	no	—
136	C₂³×C₇₃	—	4	8	no	—
137	C₂³×C₇₃	—	4	2	no	—
138	C₂³×C₇₃	—	4	4	no	—
139	C₂³×C₇₃	—	4	4	no	—
140	C₂³×C₇₃	—	4	4	no	—
141	C₂³×C₇₃	—	8	32	no	—
142	C₂³×C₇₃	—	8	8	no	—
143	C₂³×C₇₃	—	8	8	no	—
144	C₂³×C₇₃	#127	1	2	yes	—
145	C₂³×C₇₃	C₂×D₈	1	4	yes	—
146	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
147	D₄×C₇₃	—	2	8	no	—
148	D₄×C₇₃	—	2	8	no	—
149	D₄×C₇₃	—	4	16	no	—
150	D₄×C₇₃	—	4	2	no	—
151	D₄×C₇₃	—	4	4	no	—
152	D₄×C₇₃	—	4	2	no	—
153	D₄×C₇₃	—	4	4	no	—
154	D₄×C₇₃	—	4	4	no	—
155	D₄×C₇₃	—	8	32	no	—
156	D₄×C₇₃	—	8	8	no	—
157	C₂×C₄×C₇₃	—	2	4	no	—
158	C₂×C₄×C₇₃	—	2	2	no	—
159	C₂×C₄×C₇₃	—	2	4	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	—	4	2	no	—
164	C₂×C₄×C₇₃	—	4	4	no	—
165	C₂×C₄×C₇₃	#127	1	2	yes	—
166	C₂×C₄×C₇₃	C₂×D₈	1	8	yes	complemented
167	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
169	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
171	C₈×C₇₃	—	2	2	no	—
172	C₈×C₇₃	—	2	4	no	—
173	C₈×C₇₃	#120	1	4	yes	complemented
174	C₂²×C₇₃	—	2	2	no	—
175	C₂²×C₇₃	—	2	2	no	—
176	C₂²×C₇₃	—	2	8	no	—
177	C₂²×C₇₃	—	4	8	no	—
178	C₂²×C₇₃	—	4	16	no	—
179	C₂²×C₇₃	—	8	32	no	—
180	C₂²×C₇₃	—	8	4	no	—
181	C₂²×C₇₃	—	8	4	no	—
182	C₂²×C₇₃	—	8	8	no	—
183	C₂²×C₇₃	—	8	2	no	—
184	C₂²×C₇₃	—	8	2	no	—
185	C₂²×C₇₃	—	8	2	no	—
186	C₂²×C₇₃	—	8	8	no	—
187	C₂²×C₇₃	#493	1	4	yes	complemented
188	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
189	C₂²×C₇₃	D₄²	1	2	yes	—
190	C₂²×C₇₃	C₂²×D₈	1	2	yes	—
191	C₂²×C₇₃	#576	1	2	yes	—
192	C₄×C₇₃	—	2	2	no	—
193	C₄×C₇₃	—	2	8	no	—
194	C₄×C₇₃	—	8	2	no	—
195	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
196	C₄×C₇₃	#535	1	1	yes	characteristic
197	C₄×C₇₃	D₄²	1	2	yes	—
198	#25779	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂×C₇₃	—	2	4	no	—
200	C₂×C₇₃	—	8	8	no	—
201	C₂×C₇₃	—	16	2	no	—
202	C₂×C₇₃	#2433	1	1	yes	characteristic
203	C₂×C₇₃	C₂×#493	1	1	yes	characteristic
204	C₂×C₇₃	#3155	1	1	yes	characteristic
205	C₂×C₇₃	D₄×D₈	1	4	yes	—
206	C₂³×D₈	C₂×C₇₃	1	1	yes	characteristic, complemented
207	C₂×#493	C₂×C₇₃	1	2	yes	complemented
208	C₂×#466	C₂×C₇₃	1	1	yes	characteristic, complemented
209	C₂×#447	C₂×C₇₃	1	2	yes	complemented
210	#2433	C₂×C₇₃	1	2	yes	complemented
211	#2011	C₂×C₇₃	1	4	yes	complemented
212	#1970	C₂×C₇₃	1	2	yes	complemented
213	C₈×C₂²⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
214	C₇₃	#25779	1	1	yes	characteristic, direct product factor, Sylow
215	C₂³×D₄	C₂²×C₇₃	1	2	yes	—
216	C₂²×D₈	—	2	8	no	—
217	C₂²×D₈	—	2	4	no	—
218	C₂²×D₈	C₂²×C₇₃	1	2	yes	—
219	C₂²×D₈	C₂²×C₇₃	1	2	yes	—
220	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
221	C₂²×D₈	C₂²×C₇₃	1	4	yes	complemented
222	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
223	C₂×#127	C₂²×C₇₃	1	4	yes	complemented
224	C₂×#121	C₂²×C₇₃	1	2	yes	—
225	C₂×#120	—	2	4	no	—
226	#493	—	2	8	no	—
227	#466	—	2	4	no	—
228	#447	—	2	8	no	—
229	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic, complemented
230	C₂×#102	C₂²×C₇₃	1	4	yes	complemented
231	C₂×#102	C₂²×C₇₃	1	2	yes	complemented
232	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
233	C₂×C₄×C₈	C₂²×C₇₃	1	2	yes	complemented
234	#392	—	2	4	no	—
235	#390	C₂²×C₇₃	1	4	yes	complemented
236	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
237	#336	C₂²×C₇₃	1	2	yes	complemented
238	C₂⁵	—	2	2	no	—
239	C₂²×D₄	—	2	8	no	—
240	C₂²×D₄	—	2	2	no	—
241	C₂²×D₄	—	2	4	no	—
242	C₂²×D₄	—	2	4	no	—
243	C₂²×D₄	—	2	2	no	—
244	C₂²×D₄	—	2	8	no	—
245	C₂²×D₄	—	4	4	no	—
246	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
247	C₂²×D₄	C₂³×C₇₃	1	4	yes	—
248	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
249	C₂×D₈	—	2	32	no	—
250	C₂×D₈	—	2	8	no	—
251	C₂×D₈	—	2	8	no	—
252	C₂×D₈	—	2	4	no	—
253	C₂×D₈	—	2	4	no	—
254	C₂×D₈	—	2	4	no	—
255	C₂×D₈	—	2	8	no	—
256	C₂×D₈	—	2	2	no	—
257	C₂×D₈	—	2	4	no	—
258	C₂×D₈	—	4	4	no	—
259	C₂×D₈	D₄×C₇₃	1	8	yes	complemented
260	C₂²×C₈	—	2	4	no	—
261	C₂²×C₈	D₄×C₇₃	1	4	yes	complemented
262	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
264	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
265	#127	—	2	8	no	—
266	#127	—	4	4	no	—
267	#121	—	2	4	no	—
268	#121	—	2	4	no	—
269	#120	—	4	16	no	—
270	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
271	C₂×C₂²⋊C₄	—	2	8	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
274	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
275	#107	—	2	2	no	—
276	#102	—	2	8	no	—
277	#102	—	2	4	no	—
278	C₂²⋊C₈	D₄×C₇₃	1	4	yes	complemented
279	C₄×C₈	—	2	4	no	—
280	#95	D₄×C₇₃	1	2	yes	—
281	C₂⁴	—	2	4	no	—
282	C₂⁴	—	2	2	no	—
283	C₂⁴	—	4	8	no	—
284	C₂⁴	—	4	4	no	—
285	C₂⁴	—	4	8	no	—
286	C₂⁴	—	8	4	no	—
287	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
288	C₂×D₄	—	2	16	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	4	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	4	16	no	—
299	C₂×D₄	—	4	8	no	—
300	C₂×D₄	—	4	8	no	—
301	C₂×D₄	—	4	16	no	—
302	C₂×D₄	—	4	4	no	—
303	C₂×D₄	—	4	8	no	—
304	C₂×D₄	—	4	4	no	—
305	C₂×D₄	—	4	16	no	—
306	C₂×D₄	—	8	8	no	—
307	C₂×D₄	C₂×D₄×C₇₃	1	8	yes	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
315	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
316	D₈	—	2	16	no	—
317	D₈	—	2	16	no	—
318	D₈	—	4	16	no	—
319	D₈	—	4	4	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	8	no	—
324	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
325	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
326	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
327	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	4	4	no	—
331	C₂²⋊C₄	—	4	16	no	—
332	C₂²⋊C₄	D₈×C₇₃	1	8	yes	complemented
333	C₄²	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	8	no	—
338	C₂³	—	4	16	no	—
339	C₂³	—	4	4	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	8	no	—
342	C₂³	—	4	8	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	4	no	—
345	C₂³	—	4	4	no	—
346	C₂³	—	4	4	no	—
347	C₂³	—	8	32	no	—
348	C₂³	—	8	8	no	—
349	C₂³	—	8	8	no	—
350	C₂³	#127×C₇₃	1	2	yes	—
351	C₂³	C₂×D₈×C₇₃	1	4	yes	—
352	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
353	D₄	—	2	8	no	—
354	D₄	—	2	8	no	—
355	D₄	—	4	16	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	4	no	—
358	D₄	—	4	2	no	—
359	D₄	—	4	4	no	—
360	D₄	—	4	4	no	—
361	D₄	—	8	32	no	—
362	D₄	—	8	8	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	#127×C₇₃	1	2	yes	—
372	C₂×C₄	C₂×D₈×C₇₃	1	8	yes	complemented
373	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
374	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
375	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
376	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
377	C₈	—	2	2	no	—
378	C₈	—	2	4	no	—
379	C₈	#120×C₇₃	1	4	yes	complemented
380	C₂²	—	2	8	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	4	16	no	—
384	C₂²	—	4	8	no	—
385	C₂²	—	8	32	no	—
386	C₂²	—	8	8	no	—
387	C₂²	—	8	4	no	—
388	C₂²	—	8	4	no	—
389	C₂²	—	8	8	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	#493×C₇₃	1	4	yes	complemented
394	C₂²	C₂×#127×C₇₃	1	1	yes	characteristic
395	C₂²	D₄²×C₇₃	1	2	yes	—
396	C₂²	C₂²×D₈×C₇₃	1	2	yes	—
397	C₂²	#576×C₇₃	1	2	yes	—
398	C₄	—	2	8	no	—
399	C₄	—	2	2	no	—
400	C₄	—	8	2	no	—
401	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
402	C₄	#535×C₇₃	1	1	yes	characteristic
403	C₄	D₄²×C₇₃	1	2	yes	—
404	C₂	—	2	4	no	—
405	C₂	—	8	8	no	—
406	C₂	—	16	2	no	—
407	C₂	C₇₃×#2433	1	1	yes	characteristic
408	C₂	C₂×#493×C₇₃	1	1	yes	characteristic
409	C₂	C₇₃×#3155	1	1	yes	characteristic
410	C₂	D₄×D₈×C₇₃	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×D₈×C₇₃	C₂	semidirect
2. C₂×#493×C₇₃	C₂	semidirect
3. C₂×#466×C₇₃	C₂	semidirect
4. C₂×#447×C₇₃	C₂	semidirect
5. C₇₃×#2433	C₂	semidirect
6. C₇₃×#2011	C₂	semidirect
7. C₇₃×#1970	C₂	semidirect
8. C₈×C₂²⋊C₄×C₇₃	C₂	semidirect
14. C₂²×D₈×C₇₃	C₂²	semidirect
15. C₂²×D₈×C₇₃	C₂²	semidirect
17. C₂×#127×C₇₃	C₂²	semidirect
23. C₂×#107×C₇₃	C₂²	semidirect
24. C₂×#102×C₇₃	C₂²	semidirect
25. C₂×#102×C₇₃	C₂²	semidirect
27. C₂×C₄×C₈×C₇₃	C₂²	semidirect
29. #390×C₇₃	C₂²	semidirect
31. #336×C₇₃	C₂²	semidirect
53. C₂×D₈×C₇₃	D₄	semidirect
55. C₂²×C₈×C₇₃	D₄	semidirect
72. C₂²⋊C₈×C₇₃	D₄	semidirect
126. C₂²⋊C₄×C₇₃	D₈	semidirect
166. C₂×C₄×C₇₃	C₂×D₈	semidirect
173. C₈×C₇₃	#120	semidirect
187. C₂²×C₇₃	#493	semidirect
198. #25779	C₇₃	direct (N × H)
206. C₂³×D₈	C₂×C₇₃	semidirect
207. C₂×#493	C₂×C₇₃	semidirect
208. C₂×#466	C₂×C₇₃	semidirect
209. C₂×#447	C₂×C₇₃	semidirect
210. #2433	C₂×C₇₃	semidirect
211. #2011	C₂×C₇₃	semidirect
212. #1970	C₂×C₇₃	semidirect
213. C₈×C₂²⋊C₄	C₂×C₇₃	semidirect
214. C₇₃	#25779	direct (N × H)
220. C₂²×D₈	C₂²×C₇₃	semidirect
221. C₂²×D₈	C₂²×C₇₃	semidirect
223. C₂×#127	C₂²×C₇₃	semidirect
229. C₂×#107	C₂²×C₇₃	semidirect
230. C₂×#102	C₂²×C₇₃	semidirect
231. C₂×#102	C₂²×C₇₃	semidirect
233. C₂×C₄×C₈	C₂²×C₇₃	semidirect
235. #390	C₂²×C₇₃	semidirect
237. #336	C₂²×C₇₃	semidirect
259. C₂×D₈	D₄×C₇₃	semidirect
261. C₂²×C₈	D₄×C₇₃	semidirect
278. C₂²⋊C₈	D₄×C₇₃	semidirect
332. C₂²⋊C₄	D₈×C₇₃	semidirect
372. C₂×C₄	C₂×D₈×C₇₃	semidirect
379. C₈	#120×C₇₃	semidirect
393. C₂²	#493×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂³×D₈×C₇₃	2
C₂×#493×C₇₃	2
C₂×#466×C₇₃	2
C₂×#447×C₇₃	2
C₇₃×#2433	2
C₇₃×#2011	2
C₇₃×#1970	2
C₈×C₂²⋊C₄×C₇₃	2
#25779	73

Subgroups — C73×#25779 #32935183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25779 #32935183