Subgroups — C₆₇×#60366 #30739617

Order 17152.

4782 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#585×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#575×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3449	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3013	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3012	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3011	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3010	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3009	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3008	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3002	C₂	1	8	yes	maximal, complemented
12	C₆₇×#2896	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#416×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#408×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	#585×C₆₇	—	2	8	no	—
16	#585×C₆₇	—	2	8	no	—
17	C₂×2₋¹⁺⁴×C₆₇	—	2	1	no	—
18	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	—
19	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	2	yes	complemented
20	C₂×H(5,𝔽₂)×C₆₇	—	2	2	no	—
21	C₂×H(5,𝔽₂)×C₆₇	—	2	1	no	—
22	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
23	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	complemented
24	C₂²×#41×C₆₇	—	2	2	no	—
25	C₂²×#41×C₆₇	—	2	2	no	—
26	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
27	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
28	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
29	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	C₂²×#41×C₆₇	C₂²	1	4	yes	complemented
31	#575×C₆₇	—	2	8	no	—
32	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
33	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
34	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
35	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
36	C₂×#135×C₆₇	—	2	8	no	—
37	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
38	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
39	C₂×#135×C₆₇	C₂²	1	4	yes	complemented
40	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
44	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#537×C₆₇	C₂²	1	4	yes	complemented
47	#536×C₆₇	—	2	1	no	—
48	#536×C₆₇	C₂²	1	2	yes	complemented
49	#535×C₆₇	—	2	1	no	—
50	#535×C₆₇	C₂²	1	2	yes	complemented
51	#534×C₆₇	—	2	2	no	—
52	#532×C₆₇	—	2	2	no	—
53	#525×C₆₇	—	2	2	no	—
54	#525×C₆₇	C₂²	1	4	yes	complemented
55	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	#452×C₆₇	C₂²	1	8	yes	complemented
57	#452×C₆₇	C₂²	1	8	yes	complemented
58	#451×C₆₇	C₂²	1	8	yes	complemented
59	#450×C₆₇	C₂²	1	8	yes	complemented
60	#449×C₆₇	C₂²	1	8	yes	complemented
61	#449×C₆₇	C₂²	1	8	yes	complemented
62	#448×C₆₇	C₂²	1	8	yes	complemented
63	#447×C₆₇	C₂²	1	8	yes	complemented
64	#419×C₆₇	C₂²	1	2	yes	complemented
65	#418×C₆₇	C₂²	1	2	yes	complemented
66	#417×C₆₇	C₂²	1	4	yes	complemented
67	#416×C₆₇	C₂²	1	2	yes	complemented
68	#416×C₆₇	C₂²	1	2	yes	complemented
69	#416×C₆₇	C₂²	1	4	yes	complemented
70	#416×C₆₇	C₂²	1	4	yes	complemented
71	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
72	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
73	#408×C₆₇	C₂²	1	2	yes	complemented
74	#408×C₆₇	C₂²	1	2	yes	complemented
75	#408×C₆₇	C₂²	1	4	yes	complemented
76	C₂×C₂²⋊C₈×C₆₇	C₂²	1	4	yes	complemented
77	2₋¹⁺⁴×C₆₇	—	2	16	no	—
78	2₋¹⁺⁴×C₆₇	—	2	8	no	—
79	2₋¹⁺⁴×C₆₇	—	2	8	no	—
80	2₋¹⁺⁴×C₆₇	—	2	8	no	—
81	2₋¹⁺⁴×C₆₇	—	2	8	no	—
82	H(5,𝔽₂)×C₆₇	—	2	16	no	—
83	H(5,𝔽₂)×C₆₇	—	2	32	no	—
84	H(5,𝔽₂)×C₆₇	—	2	8	no	—
85	H(5,𝔽₂)×C₆₇	—	2	8	no	—
86	H(5,𝔽₂)×C₆₇	—	2	8	no	—
87	H(5,𝔽₂)×C₆₇	—	2	8	no	—
88	C₂×#41×C₆₇	—	2	32	no	—
89	C₂×#41×C₆₇	—	2	32	no	—
90	C₂×#41×C₆₇	—	2	16	no	—
91	C₂×#41×C₆₇	—	2	16	no	—
92	C₂×#41×C₆₇	—	2	2	no	—
93	C₂×#41×C₆₇	—	2	2	no	—
94	C₂×#41×C₆₇	—	2	4	no	—
95	C₂×#41×C₆₇	—	2	2	no	—
96	C₂×#41×C₆₇	—	2	2	no	—
97	C₂×#41×C₆₇	—	2	4	no	—
98	C₂×#41×C₆₇	—	2	1	no	—
99	C₂×#41×C₆₇	—	2	1	no	—
100	C₂×#41×C₆₇	—	2	4	no	—
101	C₂×#41×C₆₇	—	2	1	no	—
102	C₂×#41×C₆₇	—	2	1	no	—
103	C₂×#41×C₆₇	—	2	4	no	—
104	C₂×#41×C₆₇	—	2	4	no	—
105	C₂×#41×C₆₇	—	2	4	no	—
106	C₂×#41×C₆₇	—	2	4	no	—
107	C₂×#41×C₆₇	—	2	4	no	—
108	C₂×#41×C₆₇	—	2	1	no	—
109	C₂×#41×C₆₇	—	2	1	no	—
110	C₂×#41×C₆₇	—	2	4	no	—
111	C₂×#41×C₆₇	—	2	4	no	—
112	C₂×#41×C₆₇	D₄	1	2	yes	—
113	C₂×#41×C₆₇	D₄	1	2	yes	—
114	C₂×#41×C₆₇	D₄	1	8	yes	complemented
115	C₂×#41×C₆₇	D₄	1	8	yes	complemented
116	C₂×#41×C₆₇	C₂³	1	4	yes	—
117	C₂×#41×C₆₇	C₂³	1	4	yes	—
118	C₂×#41×C₆₇	C₂³	1	2	yes	—
119	C₂×#41×C₆₇	C₂³	1	2	yes	—
120	C₂×#41×C₆₇	C₂³	1	2	yes	—
121	C₂×#41×C₆₇	C₂³	1	2	yes	—
122	C₂×#41×C₆₇	C₂³	1	2	yes	—
123	C₂×#41×C₆₇	C₂³	1	2	yes	—
124	C₂×#41×C₆₇	C₂³	1	2	yes	—
125	C₂×#41×C₆₇	C₂³	1	2	yes	—
126	C₂²×Q₈×C₆₇	—	2	2	no	—
127	C₂²×Q₈×C₆₇	—	2	2	no	—
128	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
129	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
130	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
131	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
132	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
133	C₂²×D₄×C₆₇	—	2	1	no	—
134	C₂²×D₄×C₆₇	—	2	1	no	—
135	C₂²×D₄×C₆₇	—	2	4	no	—
136	C₂²×D₄×C₆₇	—	2	4	no	—
137	C₂²×D₄×C₆₇	—	2	2	no	—
138	C₂²×D₄×C₆₇	—	2	4	no	—
139	C₂²×D₄×C₆₇	—	2	2	no	—
140	C₂²×D₄×C₆₇	—	2	1	no	—
141	C₂²×D₄×C₆₇	D₄	1	2	yes	—
142	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
143	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
144	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
145	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
146	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₆₇	—	2	1	no	—
148	C₂³×C₄×C₆₇	—	2	1	no	—
149	C₂³×C₄×C₆₇	—	2	4	no	—
150	C₂³×C₄×C₆₇	—	2	1	no	—
151	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
152	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
153	#137×C₆₇	—	2	8	no	—
154	#137×C₆₇	—	2	8	no	—
155	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
156	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
157	#135×C₆₇	—	2	16	no	—
158	#135×C₆₇	—	2	16	no	—
159	#135×C₆₇	—	2	16	no	—
160	C₂×Q₁₆×C₆₇	—	2	4	no	—
161	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
162	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	—
163	C₂×SD₁₆×C₆₇	—	2	4	no	—
164	C₂×SD₁₆×C₆₇	—	2	4	no	—
165	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
166	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
167	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
168	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
169	C₂×D₈×C₆₇	—	2	4	no	—
170	C₂×D₈×C₆₇	C₂³	1	4	yes	—
171	C₂×D₈×C₆₇	C₂³	1	4	yes	—
172	C₂×M₁₆×C₆₇	—	2	4	no	—
173	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
174	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
175	C₂²×C₈×C₆₇	—	2	4	no	—
176	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
179	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
180	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
181	C₄⋊Q₈×C₆₇	—	2	2	no	—
182	#127×C₆₇	—	2	2	no	—
183	#124×C₆₇	—	2	2	no	—
184	#124×C₆₇	—	2	2	no	—
185	#123×C₆₇	—	2	4	no	—
186	#123×C₆₇	—	2	4	no	—
187	C₂²⋊Q₈×C₆₇	—	2	4	no	—
188	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	—
189	#121×C₆₇	—	2	4	no	—
190	#121×C₆₇	—	2	8	no	—
191	#121×C₆₇	C₂³	1	8	yes	—
192	#120×C₆₇	—	2	4	no	—
193	#120×C₆₇	—	2	4	no	—
194	C₄×D₄×C₆₇	—	2	8	no	—
195	#117×C₆₇	—	2	1	no	—
196	#117×C₆₇	—	2	1	no	—
197	#117×C₆₇	C₂³	1	2	yes	—
198	#117×C₆₇	C₂³	1	2	yes	—
199	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
201	C₂×C₄²×C₆₇	—	2	1	no	—
202	#103×C₆₇	C₂³	1	4	yes	—
203	#103×C₆₇	C₂³	1	8	yes	—
204	#103×C₆₇	C₂³	1	4	yes	—
205	#102×C₆₇	C₂³	1	4	yes	—
206	#102×C₆₇	C₂³	1	8	yes	—
207	#102×C₆₇	C₂³	1	4	yes	—
208	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
209	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	—
210	C₂⁴×C₆₇	—	2	4	no	—
211	C₂⁴×C₆₇	—	2	1	no	—
212	C₂⁴×C₆₇	—	2	1	no	—
213	C₂⁴×C₆₇	—	2	1	no	—
214	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
215	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
216	#41×C₆₇	—	2	32	no	—
217	#41×C₆₇	—	2	32	no	—
218	#41×C₆₇	—	2	32	no	—
219	#41×C₆₇	—	2	32	no	—
220	#41×C₆₇	—	2	16	no	—
221	#41×C₆₇	—	2	16	no	—
222	#41×C₆₇	—	2	16	no	—
223	#41×C₆₇	—	2	16	no	—
224	#41×C₆₇	—	2	8	no	—
225	#41×C₆₇	—	2	8	no	—
226	#41×C₆₇	—	2	8	no	—
227	#41×C₆₇	—	2	8	no	—
228	#41×C₆₇	—	2	8	no	—
229	#41×C₆₇	—	2	8	no	—
230	#41×C₆₇	—	2	8	no	—
231	#41×C₆₇	—	2	8	no	—
232	#41×C₆₇	—	2	8	no	—
233	#41×C₆₇	—	2	8	no	—
234	#41×C₆₇	—	2	4	no	—
235	#41×C₆₇	—	2	4	no	—
236	#41×C₆₇	—	2	4	no	—
237	#41×C₆₇	—	2	4	no	—
238	#41×C₆₇	—	2	4	no	—
239	#41×C₆₇	—	2	4	no	—
240	#41×C₆₇	—	2	4	no	—
241	#41×C₆₇	—	2	4	no	—
242	#41×C₆₇	—	2	4	no	—
243	#41×C₆₇	—	2	4	no	—
244	#41×C₆₇	—	2	4	no	—
245	#41×C₆₇	—	2	4	no	—
246	#41×C₆₇	—	4	4	no	—
247	#41×C₆₇	—	4	4	no	—
248	#41×C₆₇	C₂×D₄	1	8	yes	—
249	#41×C₆₇	C₂×D₄	1	8	yes	—
250	#41×C₆₇	C₂×D₄	1	8	yes	—
251	#41×C₆₇	C₂×D₄	1	8	yes	—
252	C₂×Q₈×C₆₇	—	2	16	no	—
253	C₂×Q₈×C₆₇	—	2	16	no	—
254	C₂×Q₈×C₆₇	—	2	8	no	—
255	C₂×Q₈×C₆₇	—	2	8	no	—
256	C₂×Q₈×C₆₇	—	2	4	no	—
257	C₂×Q₈×C₆₇	—	2	4	no	—
258	C₂×Q₈×C₆₇	—	2	1	no	—
259	C₂×Q₈×C₆₇	—	2	1	no	—
260	C₂×Q₈×C₆₇	—	2	2	no	—
261	C₂×Q₈×C₆₇	—	2	2	no	—
262	C₂×Q₈×C₆₇	—	2	1	no	—
263	C₂×Q₈×C₆₇	—	2	2	no	—
264	C₂×Q₈×C₆₇	—	2	2	no	—
265	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
266	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
267	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
268	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
269	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
270	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
271	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
272	C₂×D₄×C₆₇	—	2	32	no	—
273	C₂×D₄×C₆₇	—	2	32	no	—
274	C₂×D₄×C₆₇	—	2	32	no	—
275	C₂×D₄×C₆₇	—	2	16	no	—
276	C₂×D₄×C₆₇	—	2	16	no	—
277	C₂×D₄×C₆₇	—	2	8	no	—
278	C₂×D₄×C₆₇	—	2	8	no	—
279	C₂×D₄×C₆₇	—	2	8	no	—
280	C₂×D₄×C₆₇	—	2	4	no	—
281	C₂×D₄×C₆₇	—	2	4	no	—
282	C₂×D₄×C₆₇	—	2	2	no	—
283	C₂×D₄×C₆₇	—	2	2	no	—
284	C₂×D₄×C₆₇	—	2	2	no	—
285	C₂×D₄×C₆₇	—	2	2	no	—
286	C₂×D₄×C₆₇	—	2	8	no	—
287	C₂×D₄×C₆₇	—	2	8	no	—
288	C₂×D₄×C₆₇	—	2	2	no	—
289	C₂×D₄×C₆₇	—	2	2	no	—
290	C₂×D₄×C₆₇	—	2	8	no	—
291	C₂×D₄×C₆₇	—	2	4	no	—
292	C₂×D₄×C₆₇	—	2	4	no	—
293	C₂×D₄×C₆₇	—	2	1	no	—
294	C₂×D₄×C₆₇	—	2	1	no	—
295	C₂×D₄×C₆₇	—	2	2	no	—
296	C₂×D₄×C₆₇	—	2	2	no	—
297	C₂×D₄×C₆₇	—	2	2	no	—
298	C₂×D₄×C₆₇	—	2	2	no	—
299	C₂×D₄×C₆₇	—	2	1	no	—
300	C₂×D₄×C₆₇	—	4	4	no	—
301	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
302	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
303	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
304	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
305	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
306	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
307	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
308	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
309	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₆₇	—	2	32	no	—
311	C₂²×C₄×C₆₇	—	2	4	no	—
312	C₂²×C₄×C₆₇	—	2	1	no	—
313	C₂²×C₄×C₆₇	—	2	1	no	—
314	C₂²×C₄×C₆₇	—	2	8	no	—
315	C₂²×C₄×C₆₇	—	2	8	no	—
316	C₂²×C₄×C₆₇	—	2	4	no	—
317	C₂²×C₄×C₆₇	—	2	4	no	—
318	C₂²×C₄×C₆₇	—	2	2	no	—
319	C₂²×C₄×C₆₇	—	2	2	no	—
320	C₂²×C₄×C₆₇	—	2	4	no	—
321	C₂²×C₄×C₆₇	—	2	4	no	—
322	C₂²×C₄×C₆₇	—	2	2	no	—
323	C₂²×C₄×C₆₇	—	2	2	no	—
324	C₂²×C₄×C₆₇	—	2	1	no	—
325	C₂²×C₄×C₆₇	—	2	2	no	—
326	C₂²×C₄×C₆₇	—	2	2	no	—
327	C₂²×C₄×C₆₇	—	2	2	no	—
328	C₂²×C₄×C₆₇	—	4	4	no	—
329	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
330	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
331	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
335	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
336	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
337	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
340	Q₁₆×C₆₇	—	2	8	no	—
341	Q₁₆×C₆₇	—	2	8	no	—
342	SD₁₆×C₆₇	—	2	8	no	—
343	SD₁₆×C₆₇	—	2	8	no	—
344	SD₁₆×C₆₇	—	2	8	no	—
345	SD₁₆×C₆₇	—	2	8	no	—
346	D₈×C₆₇	—	2	8	no	—
347	D₈×C₆₇	—	2	8	no	—
348	M₁₆×C₆₇	—	2	4	no	—
349	M₁₆×C₆₇	—	2	4	no	—
350	C₂×C₈×C₆₇	—	2	2	no	—
351	C₂×C₈×C₆₇	—	2	2	no	—
352	C₂×C₈×C₆₇	—	2	4	no	—
353	C₂×C₈×C₆₇	—	2	4	no	—
354	C₂×C₈×C₆₇	—	2	4	no	—
355	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
356	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
357	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
358	C₄⋊C₄×C₆₇	—	2	2	no	—
359	C₄⋊C₄×C₆₇	—	2	8	no	—
360	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
361	C₂²⋊C₄×C₆₇	—	2	2	no	—
362	C₂²⋊C₄×C₆₇	—	2	2	no	—
363	C₂²⋊C₄×C₆₇	—	2	8	no	—
364	C₂²⋊C₄×C₆₇	—	2	8	no	—
365	C₄²×C₆₇	—	2	2	no	—
366	C₄²×C₆₇	—	2	2	no	—
367	C₂³×C₆₇	—	2	16	no	—
368	C₂³×C₆₇	—	2	2	no	—
369	C₂³×C₆₇	—	2	2	no	—
370	C₂³×C₆₇	—	2	4	no	—
371	C₂³×C₆₇	—	2	4	no	—
372	C₂³×C₆₇	—	2	4	no	—
373	C₂³×C₆₇	—	2	2	no	—
374	C₂³×C₆₇	—	4	2	no	—
375	C₂³×C₆₇	—	4	4	no	—
376	C₂³×C₆₇	—	4	2	no	—
377	C₂³×C₆₇	—	8	2	no	—
378	C₂³×C₆₇	—	8	2	no	—
379	C₂³×C₆₇	—	8	2	no	—
380	C₂³×C₆₇	—	8	8	no	—
381	C₂³×C₆₇	#120	1	4	yes	—
382	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
383	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
384	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
385	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
386	Q₈×C₆₇	—	2	16	no	—
387	Q₈×C₆₇	—	2	4	no	—
388	Q₈×C₆₇	—	2	4	no	—
389	Q₈×C₆₇	—	2	4	no	—
390	Q₈×C₆₇	—	2	4	no	—
391	Q₈×C₆₇	—	2	2	no	—
392	Q₈×C₆₇	—	2	2	no	—
393	Q₈×C₆₇	—	2	2	no	—
394	Q₈×C₆₇	—	2	2	no	—
395	Q₈×C₆₇	—	4	2	no	—
396	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
397	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
398	D₄×C₆₇	—	2	16	no	—
399	D₄×C₆₇	—	2	16	no	—
400	D₄×C₆₇	—	2	16	no	—
401	D₄×C₆₇	—	2	8	no	—
402	D₄×C₆₇	—	2	8	no	—
403	D₄×C₆₇	—	2	8	no	—
404	D₄×C₆₇	—	2	8	no	—
405	D₄×C₆₇	—	2	8	no	—
406	D₄×C₆₇	—	2	8	no	—
407	D₄×C₆₇	—	2	4	no	—
408	D₄×C₆₇	—	2	4	no	—
409	D₄×C₆₇	—	2	4	no	—
410	D₄×C₆₇	—	2	4	no	—
411	D₄×C₆₇	—	2	2	no	—
412	D₄×C₆₇	—	2	2	no	—
413	D₄×C₆₇	—	2	2	no	—
414	D₄×C₆₇	—	2	2	no	—
415	D₄×C₆₇	—	4	4	no	—
416	D₄×C₆₇	—	4	4	no	—
417	D₄×C₆₇	—	4	2	no	—
418	D₄×C₆₇	—	8	8	no	—
419	D₄×C₆₇	C₂²×D₄	1	4	yes	—
420	D₄×C₆₇	C₂²×D₄	1	4	yes	—
421	C₂×C₄×C₆₇	—	2	16	no	—
422	C₂×C₄×C₆₇	—	2	16	no	—
423	C₂×C₄×C₆₇	—	2	16	no	—
424	C₂×C₄×C₆₇	—	2	4	no	—
425	C₂×C₄×C₆₇	—	2	4	no	—
426	C₂×C₄×C₆₇	—	2	4	no	—
427	C₂×C₄×C₆₇	—	2	2	no	—
428	C₂×C₄×C₆₇	—	2	2	no	—
429	C₂×C₄×C₆₇	—	2	8	no	—
430	C₂×C₄×C₆₇	—	2	8	no	—
431	C₂×C₄×C₆₇	—	2	8	no	—
432	C₂×C₄×C₆₇	—	2	8	no	—
433	C₂×C₄×C₆₇	—	2	8	no	—
434	C₂×C₄×C₆₇	—	2	4	no	—
435	C₂×C₄×C₆₇	—	2	4	no	—
436	C₂×C₄×C₆₇	—	2	4	no	—
437	C₂×C₄×C₆₇	—	2	2	no	—
438	C₂×C₄×C₆₇	—	4	2	no	—
439	C₂×C₄×C₆₇	—	4	4	no	—
440	C₂×C₄×C₆₇	—	4	4	no	—
441	C₂×C₄×C₆₇	—	8	2	no	—
442	C₂×C₄×C₆₇	#120	1	4	yes	—
443	C₂×C₄×C₆₇	#120	1	4	yes	—
444	C₂×C₄×C₆₇	#120	1	4	yes	—
445	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
446	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
449	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
450	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
451	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
452	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
453	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
454	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
456	C₈×C₆₇	—	2	2	no	—
457	C₈×C₆₇	—	2	2	no	—
458	C₈×C₆₇	—	2	4	no	—
459	C₂²×C₆₇	—	2	2	no	—
460	C₂²×C₆₇	—	2	2	no	—
461	C₂²×C₆₇	—	2	2	no	—
462	C₂²×C₆₇	—	2	8	no	—
463	C₂²×C₆₇	—	2	4	no	—
464	C₂²×C₆₇	—	2	4	no	—
465	C₂²×C₆₇	—	2	4	no	—
466	C₂²×C₆₇	—	4	4	no	—
467	C₂²×C₆₇	—	4	4	no	—
468	C₂²×C₆₇	—	4	4	no	—
469	C₂²×C₆₇	—	4	4	no	—
470	C₂²×C₆₇	—	4	2	no	—
471	C₂²×C₆₇	—	8	4	no	—
472	C₂²×C₆₇	—	8	4	no	—
473	C₂²×C₆₇	—	8	4	no	—
474	C₂²×C₆₇	—	8	4	no	—
475	C₂²×C₆₇	—	8	16	no	—
476	C₂²×C₆₇	C₂×#120	1	2	yes	—
477	C₂²×C₆₇	C₂×#120	1	2	yes	—
478	C₂²×C₆₇	C₂×#120	1	2	yes	—
479	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
480	C₄×C₆₇	—	2	4	no	—
481	C₄×C₆₇	—	2	4	no	—
482	C₄×C₆₇	—	2	4	no	—
483	C₄×C₆₇	—	4	4	no	—
484	C₄×C₆₇	—	4	2	no	—
485	C₄×C₆₇	C₂×#120	1	2	yes	—
486	C₄×C₆₇	C₂×#120	1	2	yes	—
487	C₄×C₆₇	C₂×#120	1	2	yes	—
488	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
489	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
490	#60366	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
491	C₂×C₆₇	—	2	2	no	—
492	C₂×C₆₇	—	2	2	no	—
493	C₂×C₆₇	—	2	2	no	—
494	C₂×C₆₇	—	4	4	no	—
495	C₂×C₆₇	—	4	4	no	—
496	C₂×C₆₇	—	4	4	no	—
497	C₂×C₆₇	—	8	2	no	—
498	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
499	C₂×C₆₇	#3584	1	2	yes	—
500	C₂×#585	C₂×C₆₇	1	1	yes	characteristic, complemented
501	C₂×#575	C₂×C₆₇	1	1	yes	characteristic, complemented
502	C₂²×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
503	#3449	C₂×C₆₇	1	1	yes	characteristic, complemented
504	#3013	C₂×C₆₇	1	4	yes	complemented
505	#3012	C₂×C₆₇	1	4	yes	complemented
506	#3011	C₂×C₆₇	1	2	yes	complemented
507	#3010	C₂×C₆₇	1	2	yes	complemented
508	#3009	C₂×C₆₇	1	2	yes	complemented
509	#3008	C₂×C₆₇	1	2	yes	complemented
510	#3002	C₂×C₆₇	1	8	yes	complemented
511	#2896	C₂×C₆₇	1	1	yes	characteristic, complemented
512	C₂×#416	C₂×C₆₇	1	1	yes	characteristic, complemented
513	C₂×#408	C₂×C₆₇	1	1	yes	characteristic, complemented
514	C₆₇	#60366	1	1	yes	characteristic, direct product factor, Sylow
515	#585	—	2	8	no	—
516	#585	—	2	8	no	—
517	C₂×2₋¹⁺⁴	—	2	1	no	—
518	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	—
519	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	2	yes	complemented
520	C₂×H(5,𝔽₂)	—	2	2	no	—
521	C₂×H(5,𝔽₂)	—	2	1	no	—
522	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
523	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	complemented
524	C₂²×#41	—	2	2	no	—
525	C₂²×#41	—	2	2	no	—
526	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
527	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
528	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
529	C₂²×#41	C₂²×C₆₇	1	4	yes	complemented
530	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
531	#575	—	2	8	no	—
532	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
533	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
534	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
535	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
536	C₂×#135	—	2	8	no	—
537	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
538	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
539	C₂×#135	C₂²×C₆₇	1	4	yes	complemented
540	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
541	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
542	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
543	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
544	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
545	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
546	#537	C₂²×C₆₇	1	4	yes	complemented
547	#536	—	2	1	no	—
548	#536	C₂²×C₆₇	1	2	yes	complemented
549	#535	—	2	1	no	—
550	#535	C₂²×C₆₇	1	2	yes	complemented
551	#534	—	2	2	no	—
552	#532	—	2	2	no	—
553	#525	—	2	2	no	—
554	#525	C₂²×C₆₇	1	4	yes	complemented
555	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic, complemented
556	#452	C₂²×C₆₇	1	8	yes	complemented
557	#452	C₂²×C₆₇	1	8	yes	complemented
558	#451	C₂²×C₆₇	1	8	yes	complemented
559	#450	C₂²×C₆₇	1	8	yes	complemented
560	#449	C₂²×C₆₇	1	8	yes	complemented
561	#449	C₂²×C₆₇	1	8	yes	complemented
562	#448	C₂²×C₆₇	1	8	yes	complemented
563	#447	C₂²×C₆₇	1	8	yes	complemented
564	#419	C₂²×C₆₇	1	2	yes	complemented
565	#418	C₂²×C₆₇	1	2	yes	complemented
566	#417	C₂²×C₆₇	1	4	yes	complemented
567	#416	C₂²×C₆₇	1	4	yes	complemented
568	#416	C₂²×C₆₇	1	2	yes	complemented
569	#416	C₂²×C₆₇	1	2	yes	complemented
570	#416	C₂²×C₆₇	1	4	yes	complemented
571	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
572	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
573	#408	C₂²×C₆₇	1	2	yes	complemented
574	#408	C₂²×C₆₇	1	2	yes	complemented
575	#408	C₂²×C₆₇	1	4	yes	complemented
576	C₂×C₂²⋊C₈	C₂²×C₆₇	1	4	yes	complemented
577	2₋¹⁺⁴	—	2	16	no	—
578	2₋¹⁺⁴	—	2	8	no	—
579	2₋¹⁺⁴	—	2	8	no	—
580	2₋¹⁺⁴	—	2	8	no	—
581	2₋¹⁺⁴	—	2	8	no	—
582	H(5,𝔽₂)	—	2	16	no	—
583	H(5,𝔽₂)	—	2	32	no	—
584	H(5,𝔽₂)	—	2	8	no	—
585	H(5,𝔽₂)	—	2	8	no	—
586	H(5,𝔽₂)	—	2	8	no	—
587	H(5,𝔽₂)	—	2	8	no	—
588	C₂×#41	—	2	32	no	—
589	C₂×#41	—	2	32	no	—
590	C₂×#41	—	2	16	no	—
591	C₂×#41	—	2	16	no	—
592	C₂×#41	—	2	2	no	—
593	C₂×#41	—	2	2	no	—
594	C₂×#41	—	2	4	no	—
595	C₂×#41	—	2	2	no	—
596	C₂×#41	—	2	2	no	—
597	C₂×#41	—	2	4	no	—
598	C₂×#41	—	2	1	no	—
599	C₂×#41	—	2	1	no	—
600	C₂×#41	—	2	4	no	—
601	C₂×#41	—	2	1	no	—
602	C₂×#41	—	2	1	no	—
603	C₂×#41	—	2	4	no	—
604	C₂×#41	—	2	4	no	—
605	C₂×#41	—	2	4	no	—
606	C₂×#41	—	2	4	no	—
607	C₂×#41	—	2	4	no	—
608	C₂×#41	—	2	1	no	—
609	C₂×#41	—	2	1	no	—
610	C₂×#41	—	2	4	no	—
611	C₂×#41	—	2	4	no	—
612	C₂×#41	D₄×C₆₇	1	2	yes	—
613	C₂×#41	D₄×C₆₇	1	2	yes	—
614	C₂×#41	D₄×C₆₇	1	8	yes	complemented
615	C₂×#41	D₄×C₆₇	1	8	yes	complemented
616	C₂×#41	C₂³×C₆₇	1	2	yes	—
617	C₂×#41	C₂³×C₆₇	1	2	yes	—
618	C₂×#41	C₂³×C₆₇	1	4	yes	—
619	C₂×#41	C₂³×C₆₇	1	4	yes	—
620	C₂×#41	C₂³×C₆₇	1	2	yes	—
621	C₂×#41	C₂³×C₆₇	1	2	yes	—
622	C₂×#41	C₂³×C₆₇	1	2	yes	—
623	C₂×#41	C₂³×C₆₇	1	2	yes	—
624	C₂×#41	C₂³×C₆₇	1	2	yes	—
625	C₂×#41	C₂³×C₆₇	1	2	yes	—
626	C₂²×Q₈	—	2	2	no	—
627	C₂²×Q₈	—	2	2	no	—
628	C₂²×Q₈	D₄×C₆₇	1	1	yes	characteristic
629	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
630	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
631	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
632	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
633	C₂²×D₄	—	2	1	no	—
634	C₂²×D₄	—	2	1	no	—
635	C₂²×D₄	—	2	4	no	—
636	C₂²×D₄	—	2	4	no	—
637	C₂²×D₄	—	2	2	no	—
638	C₂²×D₄	—	2	4	no	—
639	C₂²×D₄	—	2	2	no	—
640	C₂²×D₄	—	2	1	no	—
641	C₂²×D₄	D₄×C₆₇	1	2	yes	—
642	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
643	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
644	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
645	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
646	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
647	C₂³×C₄	—	2	1	no	—
648	C₂³×C₄	—	2	1	no	—
649	C₂³×C₄	—	2	4	no	—
650	C₂³×C₄	—	2	1	no	—
651	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
652	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
653	#137	—	2	8	no	—
654	#137	—	2	8	no	—
655	AGL(1,ℤ/8)	—	2	8	no	—
656	AGL(1,ℤ/8)	—	2	8	no	—
657	#135	—	2	16	no	—
658	#135	—	2	16	no	—
659	#135	—	2	16	no	—
660	C₂×Q₁₆	—	2	4	no	—
661	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
662	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	—
663	C₂×SD₁₆	—	2	4	no	—
664	C₂×SD₁₆	—	2	4	no	—
665	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
666	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
667	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
668	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
669	C₂×D₈	—	2	4	no	—
670	C₂×D₈	C₂³×C₆₇	1	4	yes	—
671	C₂×D₈	C₂³×C₆₇	1	4	yes	—
672	C₂×M₁₆	—	2	4	no	—
673	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
674	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
675	C₂²×C₈	—	2	4	no	—
676	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
677	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
678	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
679	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
680	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
681	C₄⋊Q₈	—	2	2	no	—
682	#127	—	2	2	no	—
683	#124	—	2	2	no	—
684	#124	—	2	2	no	—
685	#123	—	2	4	no	—
686	#123	—	2	4	no	—
687	C₂²⋊Q₈	—	2	4	no	—
688	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	—
689	#121	—	2	4	no	—
690	#121	—	2	8	no	—
691	#121	C₂³×C₆₇	1	8	yes	—
692	#120	—	2	4	no	—
693	#120	—	2	4	no	—
694	C₄×D₄	—	2	8	no	—
695	#117	—	2	1	no	—
696	#117	—	2	1	no	—
697	#117	C₂³×C₆₇	1	2	yes	—
698	#117	C₂³×C₆₇	1	2	yes	—
699	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
700	C₂×C₂²⋊C₄	—	2	1	no	—
701	C₂×C₄²	—	2	1	no	—
702	#103	C₂³×C₆₇	1	4	yes	—
703	#103	C₂³×C₆₇	1	4	yes	—
704	#103	C₂³×C₆₇	1	8	yes	—
705	#102	C₂³×C₆₇	1	4	yes	—
706	#102	C₂³×C₆₇	1	4	yes	—
707	#102	C₂³×C₆₇	1	8	yes	—
708	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
709	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	—
710	C₂⁴	—	2	4	no	—
711	C₂⁴	—	2	1	no	—
712	C₂⁴	—	2	1	no	—
713	C₂⁴	—	2	1	no	—
714	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
715	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
716	#41	—	2	32	no	—
717	#41	—	2	32	no	—
718	#41	—	2	32	no	—
719	#41	—	2	32	no	—
720	#41	—	2	16	no	—
721	#41	—	2	16	no	—
722	#41	—	2	16	no	—
723	#41	—	2	16	no	—
724	#41	—	2	8	no	—
725	#41	—	2	8	no	—
726	#41	—	2	8	no	—
727	#41	—	2	8	no	—
728	#41	—	2	8	no	—
729	#41	—	2	8	no	—
730	#41	—	2	8	no	—
731	#41	—	2	8	no	—
732	#41	—	2	8	no	—
733	#41	—	2	8	no	—
734	#41	—	2	4	no	—
735	#41	—	2	4	no	—
736	#41	—	2	4	no	—
737	#41	—	2	4	no	—
738	#41	—	2	4	no	—
739	#41	—	2	4	no	—
740	#41	—	2	4	no	—
741	#41	—	2	4	no	—
742	#41	—	2	4	no	—
743	#41	—	2	4	no	—
744	#41	—	2	4	no	—
745	#41	—	2	4	no	—
746	#41	—	4	4	no	—
747	#41	—	4	4	no	—
748	#41	C₂×D₄×C₆₇	1	8	yes	—
749	#41	C₂×D₄×C₆₇	1	8	yes	—
750	#41	C₂×D₄×C₆₇	1	8	yes	—
751	#41	C₂×D₄×C₆₇	1	8	yes	—
752	C₂×Q₈	—	2	16	no	—
753	C₂×Q₈	—	2	16	no	—
754	C₂×Q₈	—	2	8	no	—
755	C₂×Q₈	—	2	8	no	—
756	C₂×Q₈	—	2	4	no	—
757	C₂×Q₈	—	2	4	no	—
758	C₂×Q₈	—	2	1	no	—
759	C₂×Q₈	—	2	1	no	—
760	C₂×Q₈	—	2	2	no	—
761	C₂×Q₈	—	2	2	no	—
762	C₂×Q₈	—	2	1	no	—
763	C₂×Q₈	—	2	2	no	—
764	C₂×Q₈	—	2	2	no	—
765	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
766	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
767	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
768	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
769	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
770	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
771	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
772	C₂×D₄	—	2	32	no	—
773	C₂×D₄	—	2	32	no	—
774	C₂×D₄	—	2	32	no	—
775	C₂×D₄	—	2	16	no	—
776	C₂×D₄	—	2	16	no	—
777	C₂×D₄	—	2	8	no	—
778	C₂×D₄	—	2	8	no	—
779	C₂×D₄	—	2	8	no	—
780	C₂×D₄	—	2	4	no	—
781	C₂×D₄	—	2	4	no	—
782	C₂×D₄	—	2	2	no	—
783	C₂×D₄	—	2	2	no	—
784	C₂×D₄	—	2	2	no	—
785	C₂×D₄	—	2	2	no	—
786	C₂×D₄	—	2	8	no	—
787	C₂×D₄	—	2	8	no	—
788	C₂×D₄	—	2	2	no	—
789	C₂×D₄	—	2	2	no	—
790	C₂×D₄	—	2	8	no	—
791	C₂×D₄	—	2	4	no	—
792	C₂×D₄	—	2	4	no	—
793	C₂×D₄	—	2	1	no	—
794	C₂×D₄	—	2	1	no	—
795	C₂×D₄	—	2	2	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	2	2	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	4	4	no	—
801	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
802	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
803	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
804	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
805	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
806	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
807	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
808	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
809	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
810	C₂²×C₄	—	2	32	no	—
811	C₂²×C₄	—	2	4	no	—
812	C₂²×C₄	—	2	1	no	—
813	C₂²×C₄	—	2	1	no	—
814	C₂²×C₄	—	2	8	no	—
815	C₂²×C₄	—	2	8	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	—	2	2	no	—
818	C₂²×C₄	—	2	4	no	—
819	C₂²×C₄	—	2	4	no	—
820	C₂²×C₄	—	2	2	no	—
821	C₂²×C₄	—	2	2	no	—
822	C₂²×C₄	—	2	4	no	—
823	C₂²×C₄	—	2	4	no	—
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	2	no	—
826	C₂²×C₄	—	2	2	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	4	4	no	—
829	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
830	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
831	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
832	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
833	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
834	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
835	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
836	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
837	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
838	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
839	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
840	Q₁₆	—	2	8	no	—
841	Q₁₆	—	2	8	no	—
842	SD₁₆	—	2	8	no	—
843	SD₁₆	—	2	8	no	—
844	SD₁₆	—	2	8	no	—
845	SD₁₆	—	2	8	no	—
846	D₈	—	2	8	no	—
847	D₈	—	2	8	no	—
848	M₁₆	—	2	4	no	—
849	M₁₆	—	2	4	no	—
850	C₂×C₈	—	2	2	no	—
851	C₂×C₈	—	2	2	no	—
852	C₂×C₈	—	2	4	no	—
853	C₂×C₈	—	2	4	no	—
854	C₂×C₈	—	2	4	no	—
855	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
856	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
857	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	8	no	—
860	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
861	C₂²⋊C₄	—	2	2	no	—
862	C₂²⋊C₄	—	2	2	no	—
863	C₂²⋊C₄	—	2	8	no	—
864	C₂²⋊C₄	—	2	8	no	—
865	C₄²	—	2	2	no	—
866	C₄²	—	2	2	no	—
867	C₂³	—	2	16	no	—
868	C₂³	—	2	2	no	—
869	C₂³	—	2	2	no	—
870	C₂³	—	2	4	no	—
871	C₂³	—	2	4	no	—
872	C₂³	—	2	4	no	—
873	C₂³	—	2	2	no	—
874	C₂³	—	4	2	no	—
875	C₂³	—	4	4	no	—
876	C₂³	—	4	2	no	—
877	C₂³	—	8	2	no	—
878	C₂³	—	8	2	no	—
879	C₂³	—	8	2	no	—
880	C₂³	—	8	8	no	—
881	C₂³	#120×C₆₇	1	4	yes	—
882	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
883	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
884	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
885	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
886	Q₈	—	2	16	no	—
887	Q₈	—	2	4	no	—
888	Q₈	—	2	4	no	—
889	Q₈	—	2	4	no	—
890	Q₈	—	2	4	no	—
891	Q₈	—	2	2	no	—
892	Q₈	—	2	2	no	—
893	Q₈	—	2	2	no	—
894	Q₈	—	2	2	no	—
895	Q₈	—	4	2	no	—
896	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
897	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
898	D₄	—	2	16	no	—
899	D₄	—	2	16	no	—
900	D₄	—	2	16	no	—
901	D₄	—	2	8	no	—
902	D₄	—	2	8	no	—
903	D₄	—	2	8	no	—
904	D₄	—	2	8	no	—
905	D₄	—	2	8	no	—
906	D₄	—	2	8	no	—
907	D₄	—	2	4	no	—
908	D₄	—	2	4	no	—
909	D₄	—	2	4	no	—
910	D₄	—	2	4	no	—
911	D₄	—	2	2	no	—
912	D₄	—	2	2	no	—
913	D₄	—	2	2	no	—
914	D₄	—	2	2	no	—
915	D₄	—	4	4	no	—
916	D₄	—	4	4	no	—
917	D₄	—	4	2	no	—
918	D₄	—	8	8	no	—
919	D₄	C₂²×D₄×C₆₇	1	4	yes	—
920	D₄	C₂²×D₄×C₆₇	1	4	yes	—
921	C₂×C₄	—	2	16	no	—
922	C₂×C₄	—	2	16	no	—
923	C₂×C₄	—	2	16	no	—
924	C₂×C₄	—	2	4	no	—
925	C₂×C₄	—	2	4	no	—
926	C₂×C₄	—	2	4	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	8	no	—
930	C₂×C₄	—	2	8	no	—
931	C₂×C₄	—	2	8	no	—
932	C₂×C₄	—	2	8	no	—
933	C₂×C₄	—	2	8	no	—
934	C₂×C₄	—	2	4	no	—
935	C₂×C₄	—	2	4	no	—
936	C₂×C₄	—	2	4	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	4	2	no	—
939	C₂×C₄	—	4	4	no	—
940	C₂×C₄	—	4	4	no	—
941	C₂×C₄	—	8	2	no	—
942	C₂×C₄	#120×C₆₇	1	4	yes	—
943	C₂×C₄	#120×C₆₇	1	4	yes	—
944	C₂×C₄	#120×C₆₇	1	4	yes	—
945	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
946	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
947	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
948	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
949	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
950	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
951	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
952	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
953	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
954	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
955	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
956	C₈	—	2	2	no	—
957	C₈	—	2	2	no	—
958	C₈	—	2	4	no	—
959	C₂²	—	2	2	no	—
960	C₂²	—	2	2	no	—
961	C₂²	—	2	2	no	—
962	C₂²	—	2	8	no	—
963	C₂²	—	2	4	no	—
964	C₂²	—	2	4	no	—
965	C₂²	—	2	4	no	—
966	C₂²	—	4	4	no	—
967	C₂²	—	4	4	no	—
968	C₂²	—	4	4	no	—
969	C₂²	—	4	4	no	—
970	C₂²	—	4	2	no	—
971	C₂²	—	8	4	no	—
972	C₂²	—	8	4	no	—
973	C₂²	—	8	4	no	—
974	C₂²	—	8	4	no	—
975	C₂²	—	8	16	no	—
976	C₂²	C₂×#120×C₆₇	1	2	yes	—
977	C₂²	C₂×#120×C₆₇	1	2	yes	—
978	C₂²	C₂×#120×C₆₇	1	2	yes	—
979	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
980	C₄	—	2	4	no	—
981	C₄	—	2	4	no	—
982	C₄	—	2	4	no	—
983	C₄	—	4	4	no	—
984	C₄	—	4	2	no	—
985	C₄	C₂×#120×C₆₇	1	2	yes	—
986	C₄	C₂×#120×C₆₇	1	2	yes	—
987	C₄	C₂×#120×C₆₇	1	2	yes	—
988	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
989	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
990	C₂	—	2	2	no	—
991	C₂	—	2	2	no	—
992	C₂	—	2	2	no	—
993	C₂	—	4	4	no	—
994	C₂	—	4	4	no	—
995	C₂	—	4	4	no	—
996	C₂	—	8	2	no	—
997	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic
998	C₂	C₆₇×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
socle	C₂²×C₆₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ C₂²×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#585×C₆₇	C₂	semidirect
2. C₂×#575×C₆₇	C₂	semidirect
3. C₂²×#135×C₆₇	C₂	semidirect
4. C₆₇×#3449	C₂	semidirect
5. C₆₇×#3013	C₂	semidirect
6. C₆₇×#3012	C₂	semidirect
7. C₆₇×#3011	C₂	semidirect
8. C₆₇×#3010	C₂	semidirect
9. C₆₇×#3009	C₂	semidirect
10. C₆₇×#3008	C₂	semidirect
11. C₆₇×#3002	C₂	semidirect
12. C₆₇×#2896	C₂	semidirect
13. C₂×#416×C₆₇	C₂	semidirect
14. C₂×#408×C₆₇	C₂	semidirect
19. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
23. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
29. C₂²×#41×C₆₇	C₂²	semidirect
30. C₂²×#41×C₆₇	C₂²	semidirect
32. C₂×#137×C₆₇	C₂²	semidirect
33. C₂×#137×C₆₇	C₂²	semidirect
34. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
35. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
37. C₂×#135×C₆₇	C₂²	semidirect
38. C₂×#135×C₆₇	C₂²	semidirect
39. C₂×#135×C₆₇	C₂²	semidirect
40. C₂²×Q₁₆×C₆₇	C₂²	semidirect
41. C₂²×SD₁₆×C₆₇	C₂²	semidirect
42. C₂²×SD₁₆×C₆₇	C₂²	semidirect
43. C₂²×D₈×C₆₇	C₂²	semidirect
44. C₂²×M₁₆×C₆₇	C₂²	semidirect
45. C₂³×C₈×C₆₇	C₂²	semidirect
46. #537×C₆₇	C₂²	semidirect
48. #536×C₆₇	C₂²	semidirect
50. #535×C₆₇	C₂²	semidirect
54. #525×C₆₇	C₂²	semidirect
55. C₂×#117×C₆₇	C₂²	semidirect
56. #452×C₆₇	C₂²	semidirect
57. #452×C₆₇	C₂²	semidirect
58. #451×C₆₇	C₂²	semidirect
59. #450×C₆₇	C₂²	semidirect
60. #449×C₆₇	C₂²	semidirect
61. #449×C₆₇	C₂²	semidirect
62. #448×C₆₇	C₂²	semidirect
63. #447×C₆₇	C₂²	semidirect
64. #419×C₆₇	C₂²	semidirect
65. #418×C₆₇	C₂²	semidirect
66. #417×C₆₇	C₂²	semidirect
67. #416×C₆₇	C₂²	semidirect
68. #416×C₆₇	C₂²	semidirect
69. #416×C₆₇	C₂²	semidirect
70. #416×C₆₇	C₂²	semidirect
71. C₂×#103×C₆₇	C₂²	semidirect
72. C₂×#102×C₆₇	C₂²	semidirect
73. #408×C₆₇	C₂²	semidirect
74. #408×C₆₇	C₂²	semidirect
75. #408×C₆₇	C₂²	semidirect
76. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
114. C₂×#41×C₆₇	D₄	semidirect
115. C₂×#41×C₆₇	D₄	semidirect
490. #60366	C₆₇	direct (N × H)
500. C₂×#585	C₂×C₆₇	semidirect
501. C₂×#575	C₂×C₆₇	semidirect
502. C₂²×#135	C₂×C₆₇	semidirect
503. #3449	C₂×C₆₇	semidirect
504. #3013	C₂×C₆₇	semidirect
505. #3012	C₂×C₆₇	semidirect
506. #3011	C₂×C₆₇	semidirect
507. #3010	C₂×C₆₇	semidirect
508. #3009	C₂×C₆₇	semidirect
509. #3008	C₂×C₆₇	semidirect
510. #3002	C₂×C₆₇	semidirect
511. #2896	C₂×C₆₇	semidirect
512. C₂×#416	C₂×C₆₇	semidirect
513. C₂×#408	C₂×C₆₇	semidirect
514. C₆₇	#60366	direct (N × H)
519. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
523. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
529. C₂²×#41	C₂²×C₆₇	semidirect
530. C₂²×#41	C₂²×C₆₇	semidirect
532. C₂×#137	C₂²×C₆₇	semidirect
533. C₂×#137	C₂²×C₆₇	semidirect
534. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
535. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
537. C₂×#135	C₂²×C₆₇	semidirect
538. C₂×#135	C₂²×C₆₇	semidirect
539. C₂×#135	C₂²×C₆₇	semidirect
540. C₂²×Q₁₆	C₂²×C₆₇	semidirect
541. C₂²×SD₁₆	C₂²×C₆₇	semidirect
542. C₂²×SD₁₆	C₂²×C₆₇	semidirect
543. C₂²×D₈	C₂²×C₆₇	semidirect
544. C₂²×M₁₆	C₂²×C₆₇	semidirect
545. C₂³×C₈	C₂²×C₆₇	semidirect
546. #537	C₂²×C₆₇	semidirect
548. #536	C₂²×C₆₇	semidirect
550. #535	C₂²×C₆₇	semidirect
554. #525	C₂²×C₆₇	semidirect
555. C₂×#117	C₂²×C₆₇	semidirect
556. #452	C₂²×C₆₇	semidirect
557. #452	C₂²×C₆₇	semidirect
558. #451	C₂²×C₆₇	semidirect
559. #450	C₂²×C₆₇	semidirect
560. #449	C₂²×C₆₇	semidirect
561. #449	C₂²×C₆₇	semidirect
562. #448	C₂²×C₆₇	semidirect
563. #447	C₂²×C₆₇	semidirect
564. #419	C₂²×C₆₇	semidirect
565. #418	C₂²×C₆₇	semidirect
566. #417	C₂²×C₆₇	semidirect
567. #416	C₂²×C₆₇	semidirect
568. #416	C₂²×C₆₇	semidirect
569. #416	C₂²×C₆₇	semidirect
570. #416	C₂²×C₆₇	semidirect
571. C₂×#103	C₂²×C₆₇	semidirect
572. C₂×#102	C₂²×C₆₇	semidirect
573. #408	C₂²×C₆₇	semidirect
574. #408	C₂²×C₆₇	semidirect
575. #408	C₂²×C₆₇	semidirect
576. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
614. C₂×#41	D₄×C₆₇	semidirect
615. C₂×#41	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#585×C₆₇	2
C₂×#575×C₆₇	2
C₂²×#135×C₆₇	2
C₆₇×#3449	2
C₆₇×#3013	2
C₆₇×#3012	2
C₆₇×#3011	2
C₆₇×#3010	2
C₆₇×#3009	2
C₆₇×#3008	2
C₆₇×#3002	2
C₆₇×#2896	2
C₂×#416×C₆₇	2
C₂×#408×C₆₇	2
#60366	67

Subgroups — C67×#60366 #30739617

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60366 #30739617