Subgroups — C₇×#24985 #13202201

Order 1792.

646 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3067	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2080	C₂	1	2	yes	maximal, complemented
4	C₇×#2053	C₂	1	2	yes	maximal, complemented
5	C₇×#1976	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1945	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1906	C₂	1	2	yes	maximal, complemented
8	C₇×#1833	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1827	C₂	1	2	yes	maximal, complemented
10	C₇×#1812	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1764	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#575	C₂²	1	2	yes	—
13	C₂×C₇×#135	C₂²	1	1	yes	characteristic
14	C₂×C₇×#131	C₂²	1	1	yes	characteristic
15	C₄×C₇×#41	C₂²	1	2	yes	—
16	C₇×#473	—	2	1	no	—
17	C₇×#472	—	2	1	no	—
18	C₇×#471	—	2	2	no	—
19	C₄×C₇×Q₁₆	—	2	1	no	—
20	C₄×C₇×SD₁₆	—	2	2	no	—
21	C₄×C₇×D₈	—	2	1	no	—
22	C₂×C₇×#108	C₂²	1	1	yes	characteristic
23	C₇×#427	C₂²	1	1	yes	characteristic
24	C₇×#427	C₂²	1	1	yes	characteristic
25	C₇×#424	C₂²	1	2	yes	—
26	C₇×#421	C₂²	1	2	yes	—
27	C₂×C₇×#104	C₂²	1	1	yes	characteristic
28	C₇×#416	C₂²	1	2	yes	—
29	C₇×#416	C₂²	1	1	yes	characteristic
30	C₇×#413	C₂²	1	2	yes	—
31	C₇×#410	C₂²	1	2	yes	—
32	C₇×#410	C₂²	1	2	yes	—
33	C₇×#405	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic
35	C₇×#344	C₂²	1	2	yes	—
36	C₇×#341	C₂²	1	1	yes	characteristic
37	C₇×#339	C₂²	1	1	yes	characteristic
38	C₇×#339	C₂²	1	2	yes	—
39	C₇×H(3,ℤ/4)	C₂²	1	2	yes	—
40	C₇×H(3,ℤ/4)	C₂²	1	2	yes	—
41	#24985	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₇×#41	C₂³	1	2	yes	—
43	C₂×C₇×#41	C₂³	1	1	yes	characteristic
44	C₇×#137	—	2	2	no	—
45	C₇×#137	—	2	2	no	—
46	C₇×AGL(1,ℤ/8)	—	2	2	no	—
47	C₇×AGL(1,ℤ/8)	—	2	2	no	—
48	C₇×#135	—	2	1	no	—
49	C₇×#135	—	2	1	no	—
50	C₇×#135	—	2	1	no	—
51	C₇×#135	—	2	1	no	—
52	C₇×#135	—	4	2	no	—
53	C₂×C₇×Q₁₆	D₄	1	1	yes	characteristic
54	C₂×C₇×SD₁₆	D₄	1	2	yes	—
55	C₂×C₇×D₈	D₄	1	1	yes	characteristic
56	C₇×#131	—	2	1	no	—
57	C₇×#131	—	2	1	no	—
58	C₇×#131	—	2	1	no	—
59	C₇×#131	—	2	1	no	—
60	C₂×C₇×M₁₆	—	2	1	no	—
61	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
62	C₂×C₇×M₁₆	C₂³	1	2	yes	—
63	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
64	C₂²×C₇×C₈	—	2	1	no	—
65	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
66	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
67	C₄×C₇×Q₈	—	2	2	no	—
68	C₄×C₇×D₄	—	2	2	no	—
69	C₄×C₇×D₄	—	4	2	no	—
70	C₇×#117	—	2	2	no	—
71	C₇×#117	C₂³	1	1	yes	characteristic
72	C₇×#117	C₂³	1	2	yes	—
73	C₇×#117	C₂³	1	2	yes	—
74	C₂×C₄²×C₇	—	2	2	no	—
75	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
76	C₇×#108	—	2	1	no	—
77	C₇×#108	—	2	1	no	—
78	C₇×#107	—	2	1	no	—
79	C₇×#107	—	2	1	no	—
80	C₇×#106	—	2	1	no	—
81	C₇×#106	—	2	1	no	—
82	C₇×C₄⋊C₈	—	4	2	no	—
83	C₇×#104	—	2	1	no	—
84	C₇×#104	—	2	1	no	—
85	C₇×#104	—	4	2	no	—
86	C₇×#103	—	2	2	no	—
87	C₇×#103	—	2	1	no	—
88	C₇×#102	—	2	2	no	—
89	C₇×#102	—	2	1	no	—
90	C₇×#101	—	2	2	no	—
91	C₇×#100	—	2	2	no	—
92	C₇×#99	—	4	2	no	—
93	C₇×#99	—	4	2	no	—
94	C₇×#97	—	2	1	no	—
95	C₄×C₇×C₈	—	2	1	no	—
96	C₄×C₇×C₈	—	2	1	no	—
97	C₄×C₇×C₈	—	2	1	no	—
98	#3067	C₂×C₇	1	1	yes	characteristic
99	C₄×#135	C₂×C₇	1	1	yes	characteristic, complemented
100	#2080	C₂×C₇	1	2	yes	complemented
101	#2053	C₂×C₇	1	2	yes	complemented
102	#1976	C₂×C₇	1	1	yes	characteristic, complemented
103	#1945	C₂×C₇	1	1	yes	characteristic, complemented
104	#1906	C₂×C₇	1	2	yes	complemented
105	#1833	C₂×C₇	1	1	yes	characteristic, complemented
106	#1827	C₂×C₇	1	2	yes	complemented
107	#1812	C₂×C₇	1	1	yes	characteristic, complemented
108	#1764	C₂×C₇	1	1	yes	characteristic, complemented
109	C₇×#41	—	2	1	no	—
110	C₇×#41	—	2	1	no	—
111	C₇×#41	—	2	1	no	—
112	C₇×#41	—	2	2	no	—
113	C₇×#41	—	2	2	no	—
114	C₇×#41	—	2	2	no	—
115	C₇×#41	—	2	2	no	—
116	C₇×#41	—	2	1	no	—
117	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
118	C₂×C₇×Q₈	#41	1	1	yes	characteristic
119	C₂×C₇×D₄	—	2	1	no	—
120	C₂×C₇×D₄	—	2	2	no	—
121	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
122	C₂×C₇×D₄	#41	1	1	yes	characteristic
123	C₂²×C₄×C₇	—	2	1	no	—
124	C₂²×C₄×C₇	—	2	2	no	—
125	C₂²×C₄×C₇	—	2	1	no	—
126	C₂²×C₄×C₇	—	4	2	no	—
127	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
128	C₇×Q₁₆	—	2	1	no	—
129	C₇×Q₁₆	—	2	1	no	—
130	C₇×Q₁₆	—	4	2	no	—
131	C₇×SD₁₆	—	2	2	no	—
132	C₇×SD₁₆	—	2	2	no	—
133	C₇×SD₁₆	—	4	2	no	—
134	C₇×SD₁₆	—	4	2	no	—
135	C₇×D₈	—	2	1	no	—
136	C₇×D₈	—	2	1	no	—
137	C₇×D₈	—	4	2	no	—
138	C₇×M₁₆	—	2	1	no	—
139	C₇×M₁₆	—	2	2	no	—
140	C₇×M₁₆	—	2	1	no	—
141	C₇×M₁₆	—	2	1	no	—
142	C₇×M₁₆	—	2	2	no	—
143	C₇×M₁₆	—	2	1	no	—
144	C₇×M₁₆	—	4	1	no	—
145	C₇×M₁₆	—	4	1	no	—
146	C₂×C₇×C₈	—	2	1	no	—
147	C₂×C₇×C₈	—	2	1	no	—
148	C₂×C₇×C₈	—	2	1	no	—
149	C₂×C₇×C₈	—	2	1	no	—
150	C₂×C₇×C₈	—	2	1	no	—
151	C₂×C₇×C₈	—	2	2	no	—
152	C₂×C₇×C₈	—	4	1	no	—
153	C₂×C₇×C₈	—	4	1	no	—
154	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
155	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
156	C₂×C₇×C₈	#41	1	1	yes	characteristic
157	C₂×C₇×C₈	#41	1	1	yes	characteristic
158	C₂×C₇×C₈	#41	1	1	yes	characteristic
159	C₂×C₇×C₈	#41	1	1	yes	characteristic
160	C₇×C₄⋊C₄	—	2	2	no	—
161	C₇×C₄⋊C₄	—	2	1	no	—
162	C₇×C₄⋊C₄	—	2	2	no	—
163	C₇×C₄⋊C₄	—	4	2	no	—
164	C₇×C₂²⋊C₄	—	2	2	no	—
165	C₇×C₂²⋊C₄	—	2	1	no	—
166	C₇×C₂²⋊C₄	—	2	2	no	—
167	C₇×C₂²⋊C₄	—	4	2	no	—
168	C₄²×C₇	—	2	1	no	—
169	C₄²×C₇	—	2	1	no	—
170	C₄²×C₇	—	2	2	no	—
171	C₄²×C₇	—	2	2	no	—
172	C₄²×C₇	—	4	2	no	—
173	C₄²×C₇	#41	1	1	yes	characteristic
174	C₄²×C₇	#41	1	1	yes	characteristic
175	#575	C₂²×C₇	1	2	yes	—
176	C₂×#135	C₂²×C₇	1	1	yes	characteristic
177	C₂×#131	C₂²×C₇	1	1	yes	characteristic
178	C₄×#41	C₂²×C₇	1	2	yes	—
179	#473	—	2	1	no	—
180	#472	—	2	1	no	—
181	#471	—	2	2	no	—
182	C₄×Q₁₆	—	2	1	no	—
183	C₄×SD₁₆	—	2	2	no	—
184	C₄×D₈	—	2	1	no	—
185	C₂×#108	C₂²×C₇	1	1	yes	characteristic
186	#427	C₂²×C₇	1	1	yes	characteristic
187	#427	C₂²×C₇	1	1	yes	characteristic
188	#424	C₂²×C₇	1	2	yes	—
189	#421	C₂²×C₇	1	2	yes	—
190	C₂×#104	C₂²×C₇	1	1	yes	characteristic
191	#416	C₂²×C₇	1	1	yes	characteristic
192	#416	C₂²×C₇	1	2	yes	—
193	#413	C₂²×C₇	1	2	yes	—
194	#410	C₂²×C₇	1	2	yes	—
195	#410	C₂²×C₇	1	2	yes	—
196	#405	C₂²×C₇	1	1	yes	characteristic
197	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic
198	#344	C₂²×C₇	1	2	yes	—
199	#341	C₂²×C₇	1	1	yes	characteristic
200	#339	C₂²×C₇	1	1	yes	characteristic
201	#339	C₂²×C₇	1	2	yes	—
202	H(3,ℤ/4)	C₂²×C₇	1	2	yes	—
203	H(3,ℤ/4)	C₂²×C₇	1	2	yes	—
204	C₂³×C₇	—	2	2	no	—
205	C₂³×C₇	—	2	1	no	—
206	C₂³×C₇	H(5,𝔽₂)	1	1	yes	characteristic
207	C₇×Q₈	—	2	2	no	—
208	C₇×Q₈	—	2	1	no	—
209	C₇×Q₈	—	2	1	no	—
210	C₇×Q₈	—	2	2	no	—
211	C₇×D₄	—	2	2	no	—
212	C₇×D₄	—	2	1	no	—
213	C₇×D₄	—	2	1	no	—
214	C₇×D₄	—	2	2	no	—
215	C₇×D₄	—	4	1	no	—
216	C₇×D₄	—	4	2	no	—
217	C₇×D₄	—	4	1	no	—
218	C₇×D₄	—	4	2	no	—
219	C₂×C₄×C₇	—	2	1	no	—
220	C₂×C₄×C₇	—	2	1	no	—
221	C₂×C₄×C₇	—	2	2	no	—
222	C₂×C₄×C₇	—	2	1	no	—
223	C₂×C₄×C₇	—	4	2	no	—
224	C₂×C₄×C₇	—	4	1	no	—
225	C₂×C₄×C₇	—	4	2	no	—
226	C₂×C₄×C₇	—	4	2	no	—
227	C₂×C₄×C₇	—	4	1	no	—
228	C₂×C₄×C₇	—	4	2	no	—
229	C₂×C₄×C₇	—	4	2	no	—
230	C₂×C₄×C₇	—	4	1	no	—
231	C₂×C₄×C₇	—	8	4	no	—
232	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
234	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
236	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
237	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
238	C₇×C₈	—	4	1	no	—
239	C₇×C₈	—	4	1	no	—
240	C₇×C₈	—	4	2	no	—
241	C₇×C₈	—	4	1	no	—
242	C₇×C₈	#123	1	1	yes	characteristic
243	C₇×C₈	#123	1	1	yes	characteristic
244	C₇×C₈	#123	1	1	yes	characteristic
245	C₇×C₈	#123	1	1	yes	characteristic
246	C₂×#41	C₂³×C₇	1	2	yes	—
247	C₂×#41	C₂³×C₇	1	1	yes	characteristic
248	#137	—	2	2	no	—
249	#137	—	2	2	no	—
250	AGL(1,ℤ/8)	—	2	2	no	—
251	AGL(1,ℤ/8)	—	2	2	no	—
252	#135	—	2	1	no	—
253	#135	—	2	1	no	—
254	#135	—	2	1	no	—
255	#135	—	2	1	no	—
256	#135	—	4	2	no	—
257	C₂×Q₁₆	C₇×D₄	1	1	yes	characteristic
258	C₂×SD₁₆	C₇×D₄	1	2	yes	—
259	C₂×D₈	C₇×D₄	1	1	yes	characteristic
260	#131	—	2	1	no	—
261	#131	—	2	1	no	—
262	#131	—	2	1	no	—
263	#131	—	2	1	no	—
264	C₂×M₁₆	—	2	1	no	—
265	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
266	C₂×M₁₆	C₂³×C₇	1	2	yes	—
267	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
271	C₄×Q₈	—	2	2	no	—
272	C₄×D₄	—	2	2	no	—
273	C₄×D₄	—	4	2	no	—
274	#117	—	2	2	no	—
275	#117	C₂³×C₇	1	2	yes	—
276	#117	C₂³×C₇	1	1	yes	characteristic
277	#117	C₂³×C₇	1	2	yes	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
280	#108	—	2	1	no	—
281	#108	—	2	1	no	—
282	#107	—	2	1	no	—
283	#107	—	2	1	no	—
284	#106	—	2	1	no	—
285	#106	—	2	1	no	—
286	C₄⋊C₈	—	4	2	no	—
287	#104	—	2	1	no	—
288	#104	—	2	1	no	—
289	#104	—	4	2	no	—
290	#103	—	2	2	no	—
291	#103	—	2	1	no	—
292	#102	—	2	2	no	—
293	#102	—	2	1	no	—
294	#101	—	2	2	no	—
295	#100	—	2	2	no	—
296	#99	—	4	2	no	—
297	#99	—	4	2	no	—
298	#97	—	2	1	no	—
299	C₄×C₈	—	2	1	no	—
300	C₄×C₈	—	2	1	no	—
301	C₄×C₈	—	2	1	no	—
302	C₂²×C₇	—	4	1	no	—
303	C₂²×C₇	—	4	1	no	—
304	C₂²×C₇	—	4	2	no	—
305	C₂²×C₇	—	8	2	no	—
306	C₂²×C₇	—	8	1	no	—
307	C₂²×C₇	#540	1	1	yes	characteristic
308	C₂²×C₇	#546	1	1	yes	characteristic
309	C₂²×C₇	#553	1	1	yes	characteristic
310	C₄×C₇	—	2	2	no	—
311	C₄×C₇	—	4	1	no	—
312	C₄×C₇	—	4	2	no	—
313	C₄×C₇	—	4	1	no	—
314	C₄×C₇	—	8	2	no	—
315	C₄×C₇	—	8	1	no	—
316	C₄×C₇	—	8	2	no	—
317	C₄×C₇	C₂×#123	1	1	yes	characteristic
318	C₄×C₇	#529	1	1	yes	characteristic
319	C₄×C₇	#546	1	1	yes	characteristic
320	C₄×C₇	#555	1	1	yes	characteristic
321	#41	—	2	1	no	—
322	#41	—	2	1	no	—
323	#41	—	2	1	no	—
324	#41	—	2	2	no	—
325	#41	—	2	2	no	—
326	#41	—	2	2	no	—
327	#41	—	2	2	no	—
328	#41	—	2	1	no	—
329	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
330	C₂×Q₈	C₇×#41	1	1	yes	characteristic
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
334	C₂×D₄	C₇×#41	1	1	yes	characteristic
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
340	Q₁₆	—	2	1	no	—
341	Q₁₆	—	2	1	no	—
342	Q₁₆	—	4	2	no	—
343	SD₁₆	—	2	2	no	—
344	SD₁₆	—	2	2	no	—
345	SD₁₆	—	4	2	no	—
346	SD₁₆	—	4	2	no	—
347	D₈	—	2	1	no	—
348	D₈	—	2	1	no	—
349	D₈	—	4	2	no	—
350	M₁₆	—	2	1	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	1	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	2	1	no	—
356	M₁₆	—	4	1	no	—
357	M₁₆	—	4	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
367	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
368	C₂×C₈	C₇×#41	1	1	yes	characteristic
369	C₂×C₈	C₇×#41	1	1	yes	characteristic
370	C₂×C₈	C₇×#41	1	1	yes	characteristic
371	C₂×C₈	C₇×#41	1	1	yes	characteristic
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	—	2	2	no	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	2	2	no	—
384	C₄²	—	4	2	no	—
385	C₄²	C₇×#41	1	1	yes	characteristic
386	C₄²	C₇×#41	1	1	yes	characteristic
387	C₂×C₇	—	2	1	no	—
388	C₂×C₇	—	2	1	no	—
389	C₂×C₇	—	2	1	no	—
390	C₂×C₇	—	8	2	no	—
391	C₂×C₇	—	8	1	no	—
392	C₂×C₇	#2420	1	1	yes	characteristic
393	C₂³	—	2	2	no	—
394	C₂³	—	2	1	no	—
395	C₂³	C₇×H(5,𝔽₂)	1	1	yes	characteristic
396	Q₈	—	2	2	no	—
397	Q₈	—	2	1	no	—
398	Q₈	—	2	1	no	—
399	Q₈	—	2	2	no	—
400	D₄	—	2	2	no	—
401	D₄	—	2	1	no	—
402	D₄	—	2	1	no	—
403	D₄	—	2	2	no	—
404	D₄	—	4	1	no	—
405	D₄	—	4	2	no	—
406	D₄	—	4	1	no	—
407	D₄	—	4	2	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	8	4	no	—
421	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
422	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
423	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
424	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
425	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
426	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
427	C₈	—	4	1	no	—
428	C₈	—	4	1	no	—
429	C₈	—	4	2	no	—
430	C₈	—	4	1	no	—
431	C₈	C₇×#123	1	1	yes	characteristic
432	C₈	C₇×#123	1	1	yes	characteristic
433	C₈	C₇×#123	1	1	yes	characteristic
434	C₈	C₇×#123	1	1	yes	characteristic
435	C₇	#24985	1	1	yes	characteristic, direct product factor, Sylow
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	8	1	no	—
441	C₂²	C₇×#540	1	1	yes	characteristic
442	C₂²	C₇×#546	1	1	yes	characteristic
443	C₂²	C₇×#553	1	1	yes	characteristic
444	C₄	—	2	2	no	—
445	C₄	—	4	1	no	—
446	C₄	—	4	2	no	—
447	C₄	—	4	1	no	—
448	C₄	—	8	2	no	—
449	C₄	—	8	2	no	—
450	C₄	—	8	1	no	—
451	C₄	C₂×C₇×#123	1	1	yes	characteristic
452	C₄	C₇×#529	1	1	yes	characteristic
453	C₄	C₇×#546	1	1	yes	characteristic
454	C₄	C₇×#555	1	1	yes	characteristic
455	C₂	—	2	1	no	—
456	C₂	—	2	1	no	—
457	C₂	—	2	1	no	—
458	C₂	—	8	2	no	—
459	C₂	—	8	1	no	—
460	C₂	C₇×#2420	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₇	#555
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂×C₇	#2420
prime radical	C₇×#3067	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₇×#135	C₂	semidirect
3. C₇×#2080	C₂	semidirect
4. C₇×#2053	C₂	semidirect
5. C₇×#1976	C₂	semidirect
6. C₇×#1945	C₂	semidirect
7. C₇×#1906	C₂	semidirect
8. C₇×#1833	C₂	semidirect
9. C₇×#1827	C₂	semidirect
10. C₇×#1812	C₂	semidirect
11. C₇×#1764	C₂	semidirect
41. #24985	C₇	direct (N × H)
99. C₄×#135	C₂×C₇	semidirect
100. #2080	C₂×C₇	semidirect
101. #2053	C₂×C₇	semidirect
102. #1976	C₂×C₇	semidirect
103. #1945	C₂×C₇	semidirect
104. #1906	C₂×C₇	semidirect
105. #1833	C₂×C₇	semidirect
106. #1827	C₂×C₇	semidirect
107. #1812	C₂×C₇	semidirect
108. #1764	C₂×C₇	semidirect
435. C₇	#24985	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3067	2
C₄×C₇×#135	2
C₇×#2080	2
C₇×#2053	2
C₇×#1976	2
C₇×#1945	2
C₇×#1906	2
C₇×#1833	2
C₇×#1827	2
C₇×#1812	2
C₇×#1764	2
#24985	7

Subgroups — C7×#24985 #13202201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#24985 #13202201